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# Question: How To Manually Compute Square Root?
## How do you figure the square root of a number?
Divide the number by your guess. Now you have two numbers that multiply to get your original number. Take the average of these two numbers. This becomes your second guess for the square root.
## What is the shortcut key for square root?
The Alt code for the symbol for the Square root is Alt +251 or 221A, then Alt+X. Follow these three simple steps to attach the symbol using the Alt code: – Position the pointer in the place where you want the square root symbol inserted. – Press and hold down the Alt key and type 251 from the numeric keypad.
## What is the square of 15?
List of Perfect Squares
NUMBER SQUARE SQUARE ROOT
14 196 3.742
15 225 3.873
16 256 4.000
17 289 4.123
## Is 24 a perfect square?
Perfect Square. A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system. 24 is NOT a perfect square. 24 is a natural number, but since there is no other natural number that can be squared to result in the number 24, 24 is NOT a perfect square
## What is the perfect square formula?
When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b).
You might be interested: How To Find The Square Root Of A Binomial?
## What is the root square of 169?
The square root of 169 is 13. | crawl-data/CC-MAIN-2021-39/segments/1631780058467.95/warc/CC-MAIN-20210927181724-20210927211724-00556.warc.gz | null |
# 6.02 Applications of exponential functions
Lesson
## Exponential growth and decay
An exponential function is the appropriate model to use when a quantity is increasing or decreasing at a rate that depends on the quantity present.
For example, in the final rounds of a sports competition, the number of competing teams is halved at every stage. Thus, if $16$16 teams reached the first semifinal, there would be $8$8 in the second semifinal, and so on. The number of teams playing drops from $16$16 to $8$8 and then to $4$4 and finally, $2$2 and we see that the reduction in the number of teams playing at each stage depends on the number in the previous round.
This is an example of exponential decay. The rate of decrease gets progressively smaller. Many processes show the opposite pattern and exhibit exponential growth. In this, the rate of increase increases progressively.
Remember!
If we are looking at an exponential function of the form $y=ab^x$y=abx, then
• $b$b is tells us whether the function is growing (increasing) or decaying (decreasing)
• If $b>1$b>1, it is growth
### Outcomes
#### A.CED.A.2^
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. ^Equations using all available types of expressions, including simple root functions
#### F.IF.B.4'''
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. '''Include rational, square root and cube root; emphasize selection of appropriate models.
#### F.IF.C.8'''
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. '''Include rational and radical; Focus on using key features to guide selection of appropriate type of model function | crawl-data/CC-MAIN-2022-05/segments/1642320304760.30/warc/CC-MAIN-20220125035839-20220125065839-00505.warc.gz | null |
By: Aaron McCall, Audrey Roberge, Brett Moffit
Bartonella henselae is the bacterial species that causes Bartonellosis, Cat Scratch Disease (CSD), or Cat Scratch Fever in humans. This species of Bartonella is a facultative intracellular Gram-negative bacteria that commonly infects cats and less commonly dogs. As it’s common name suggests, Cat Scratch Disease is contracted through the scratch or bite of an infected cat (Figure 1).
The reservoir host for Bartonella henselae are cats which are therefore asymptomatic carriers. Cats contract B. henselae upon being infested with the common cat flea, Ctenocephalides felis where they reside in the gut and are expelled onto the cat’s skin via flea droppings. The cat becomes infected upon grooming itself which causes the bacteria contaminated flea feces to spread to its mouth and claws. Hence, transmission to humans results from the bite or scratch of an infected cat resulting in the inoculation of the flea feces and consequently the bacteria, into the open wound. Other potential vectors include additional blood sucking insects and arthropods such as ticks, lice and biting flies, namely the sand fly.
B. henselae causes disease primarily given the fact that it is able to evade the immune system by establishing an intracellular infection, as it is a facultative intracellular pathogen. Infection begins once the bacteria get inoculated through a bite or scratch wound and initially infect macrophages, the white blood cells that protect the body by “eating” pathogens. This allows the bacteria to subsequently infect the cells of the blood vessel lining, the endothelium. During this stage of infection, generally no symptoms are observed in immunocompetent individuals; however, bacillary angiomatosis is seen in immunocompromised patients. In this case, the bacteria trigger the endothelium lining cells to divide continuously, as well as block apoptosis, the ability for cells to self destruct. Therefore, resulting in the massive proliferation of the endothelium cells causing tumor-like structures that outgrow giving the appearance of papule lesions on the skin of the individual. Following infection of the endothelium, B. henselae can then infect red blood cells– also called erythrocytes– allowing them to establish a chronic infection as they are able to go undetected since red blood cells do not express MHC 1, an immune system activating signal protein that indicates that a cell has an intracellular pathogen. With the absence of MHC 1 the cytotoxic pathway of the adaptive immune system is not activated and therefore cannot effectively kill the intracellular pathogen. Infection in the blood also provides the bacteria with a highway by which it can travel to infect various organs. A common site of infection are the lymph nodes resulting in lymphadenopathy, which is severe regional inflammation of the lymph nodes. This is caused by the ongoing activation of the adaptive immune response as macrophages continually present B. henselae antigens to naive T cells,T cells who have not yet differentiated into a specific immunological role, either Killer T cells or Helper T cells. The continual presentation of B. henselae antigens to naive T cells triggers them to differentiate in order for the appropriate adaptive immune response to take place. However, since B. henselae establishes a proliferant intracellular infection of macrophages, this results in overwhelming the naive T cells to differentiate at a rate of which the lymphoid tissue can not keep up, resulting in hyperplasia of the lymph nodes, increasing the size of the tissue to compensate for the high demand of naive T cell differentiation. It has also been suggested that bartonella effector proteins (BEPs) also play a role in the presentation of this symptom, which will be discussed in greater detail in the virulence section. Another possible organ where infection takes place are the cells of the heart. This results in endocarditis and myocarditis– an inflammation of the heart– causing malfunctioning of the heart as it becomes more strenuous to pump blood throughout the body. This inflammation is clinically distinguished by the presence of heart murmurs.
The most common species of Bartonella found in infected cats is B. henselae. Within B. henselae, there are two different genotypes known to infect cats: Houston-1 (type 1), and Marseille (type 2). Type 1 B. henselae are more prevalent in Asia, while type 2 are found more commonly in western United States, western continental Europe, the United Kingdom, and Australia. Worldwide, infections of B. henselae are found more often in warm humid areas than in colder climates. However, regardless of the genotype that is most prevalent within a given country, the strains isolated from infected humans is most often type 1. The age and lifestyle of the cat also affects the probability of infection; young cats under the age of 1 year old and stray or feral cats are more likely bacteremic. This means that young, stray, or feral cats have a high probability of carrying or having this species of bacteria in their blood. Conversely, as cats get older, their probability of being seropositive for B. henselae increases. This is because as the young bacteremic cats age, their immune systems fight the infection and develop specialized antibodies designed to destroy the B. henselae cells present in the blood. After the cat recovers from the infection, the antibodies produced will persist in the blood and cause seropositivity. Antibody persistence is a part of acquired immunity and will help the cat fight off any subsequent infections of B. henselae more quickly and more efficiently.
B. henselae employs specialized systems, called virulence factors, that help it colonize a host, infect the host’s cells, spread, and cause damage. The bacteria will infect the primary niches, which are the cells that help it migrate to the blood (macrophages and endothelial cells). The mechanism of this step is unclear, but the bacteria become competent after a priming period inside the primary niche, during which it stimulates inflammation but inhibits programmed cell death. It will then adhere to erythrocytes and force the erythrocyte to deform (with a protein called deformin) and internalize it, despite the erythrocyte’s usual lack of endocytic activity (internalizing something from outside the cell). Once in the erythrocyte, B. henselae can protect itself within a vacuole in the cell. This is also a potent virulence factor because it allows the bacteria to hide from the host’s immune defences. They also can evade the host’s immune system by hiding or modifying pathogen-associated molecular patterns which are patterns that the host would recognize as foreign bacteria. Once it has established itself in the blood, B. henselae will activate other virulence factors that are mostly involved in migrating from erythrocytes into other tissues. These mechanisms are poorly studied, although the bacteria express the same proteins that other types of bacteria employ, so these proteins likely are involved. When in other host cells, B. henselae use a type IV secretion system (T4SS) which delivers toxins directly to the host’s cells to release specific proteins called bartonella effector proteins (BEPs) that will cause the human host to produce a pathologic amount of erythrocytes so that the bacteria has more cells to colonize, as well as damaging the structure of many host cells to make them easier to invade. Other virulence factors cause hyperactivation of the adaptive immune system in lymph nodes (Figure 2), causing an intense immune response that will damage the host and direct tissue damage, especially to the heart, which is likely mediated by BEPs.
Generally, Bartonellosis subsides on its own with no medical intervention needed. A two-week treatment of Azithromycin, an antibiotic, is sometimes used to treat and diminish the time of lymphadenopathy presentation. A much lengthier treatment is required for more severe cases, especially in immunocompromised individuals, with an antibiotic treatment that can last up to six weeks. In this case, antibiotics of choice maybe be doxycycline, erythromycin and rifampin or any combination of the three medications. In cases where a patient has reached endocarditis, heart failure medications are also administered to manage the cardiac symptoms and valve replacement may be recommended.
Alexandre Harms, C. D. (2012). Intruders Below the Radar: Molecular Pathogenesis of Barontella spp. American Society for microbiology. Retrieved from: https://cmr.asm.org/content/25/1/42
Angelakis, E., & Raoult, D. (2014). Pathogenicity and treatment of Bartonella infections. International Journal of Antimicrobial Agents, 44(1), 16–25. doi: 10.1016/j.ijantimicag.2014.04.006
CDC. (n.d.). Bartonella Infection (Cat Scratch Disease, Trench Fever and Carrion’s Fever). Centers for Disease Control and Prevention. Retrieved from: https://www.cdc.gov/bartonella/index.html
Oskouizadeh, K., Zahraei-Salehi, T., & Aledavood, S. (2010). Detection of Bartonella henselae in domestic cats’ saliva. Iranian journal of microbiology, 2(2), 80–84. Sykes, J. E. (2014). Bartonellosis. In C. a. Diseases, Jane E Sykes (pp. 498-511). St Louis: Elsevier. | <urn:uuid:4496c3c0-ec1a-402c-b12e-8c72c4bbcdd1> | {
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The Equal Rights Initiative
The ultimate goal of the Equal Rights Initiative is to reach a future where people of all genders - male, female, or non-binary - have equal rights under federal law. To achieve this, we believe that the Equal Rights Amendment (ERA) must be added to the Constitution of the United States of America once and for all.
What is the ERA?
The amendment simply states:
“Equality of rights under the law shall not be denied or abridged by the United States or by any state on account of sex.”
If it were to pass all genders would be legally entitled to equal rights, nobody could be discriminated against based on sex, and fair and equal pay would be the law of the land.
Did you know...
A recent poll by the ERA Coalition shows that 94% of Americans support the principles of the amendment (regardless of gender, age, or political affiliation). Meanwhile 80% think it already exists in the Constitution. The truth is that in 2018, all genders do NOT have equal rights under federal law.
Women’s movements of today, such as #MeToo and Time’s Up, are full of powerful momentum, but we cannot allow ourselves to become complacent. It is time to act now. We have been fighting for the Equal Rights Amendment for nearly 100 years. Only by raising awareness and gathering support will we have a chance of passing it.
The ERA was first proposed by Alice Paul, founder of the National Women’s Party, in 1923 after the passing of the 19th Amendment, which gave women the right to vote in 1920. Through the decades, it was met with significant opposition from those who believed that it would threaten existing power structures and what at that time represented traditional family values.
It did not move forward until the Women’s Liberation movement of the 60s and 70s brought it back into public attention. Motivated by the momentum of the civil rights movement, women came together to demand their own equal rights. Finally, in 1972, the ERA was passed in the House and the Senate with two-thirds majority and was sent to the states for ratification.
But the fight was far from over. By the 1982 deadline, only 35 of the required 38 states had ratified the amendment. On top of that, five states rescinded their ratification almost immediately, though the legal status of these motions is still unclear.
The Equal Rights Amendment has been brought to congress every year since 1982 ...
Finally, in 2017, Nevada ratified the ERA, 35 years after the deadline, arguing that the imposed time limit is irrelevant.
This paved the way for Illinois to follow suit in May of 2018.
Many experts agree that this puts us only one state away from potentially adding the Equal Rights Amendment to the United States Constitution. | <urn:uuid:8ddaaa71-a24d-4d7c-b798-8f5e5984ffec> | {
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Exocoetidae, commonly called Flying Fish, is a family of fishes aptly named for their ability to emerge out of the water and glide for long distances with their outstretched pectoral fins. Their streamlined torpedo shape helps them gather enough underwater speed to break the surface, and their large, wing-like fins get them airborne. Once in the air, these fishes can glide over considerable distances. Their flights are typically around 50 meters, but some fishes have been recorded to fly up to 200 meters or more. Some species of flying fish have enlarged pelvic fins as well as enlarged pectoral fins, which allows them to fly further than two winged gliders (up to 400 meters), and have far greater maneuverability. These fishes are known as four-winged flying fish.
To glide upward out of the water, a flying fish moves its tail up to 70 times per second. It then spreads its pectoral fins and tilts them slightly upward to provide lift. At the end of a glide, it folds its pectoral fins to reenter the sea, or drops its tail into the water to push against the water to lift itself for another glide, possibly changing direction. The curved profile of the "wing" is comparable to the aerodynamic shape of a bird wing. The fish is known to take advantage of updrafts created by air currents to increase its time of flight.
Flying fish are thought to have evolved this remarkable gliding ability to escape predators, of which they have many. Their pursuers include mackerel, tuna, swordfish, marlin, and other larger fish. Unfortunately, this evasive maneuver is not enough to escape the biggest predator on earth – humans.
Flying fish is commercially fished in Asian countries such as Japan, Vietnam and China, including the Caribbean where it’s a coveted delicacy. In Japanese cuisine, the fish is used to make some types of sushi. It is also a staple in the diet of the Tao people of Taiwan. In Barbados, flying fish were threatened by pollution and overfishing, changing the occurrences of flying fish in the waters off of Barbados. This sparked a fishing controversy between Barbados, and Trinidad and Tobago. | <urn:uuid:a8b11360-2283-4f28-ad4f-053562509b8a> | {
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# Demonstrate that equation sinx + 2(cos(x/2))^2=1 have roots. find the roots
Posted on
You need to use the following half angle identity, such that:
`cos^2(x/2) = (1 + cos x)/2`
Replacing `(1 + cos x)/2` for the term of equation `cos^2(x/2)` , yields:
`sin x + 2*(1 + cos x)/2 = 1`
Reducing duplicate factors, yields:
`sin x + 1 + cos x = 1`
`sin x + cos x + 1 - 1 = 0 `
`sin x + cos x = 0`
You may divide by `cos x` both sides, such that:
`sin x/cos x + 1 = 0`
Using the trigonometric identity `sin x/cos x = tan x` , yields:
`tan x + 1 = 0`
`tan x = -1 => x = tan^(-1) (-1) + k*pi`
`x = -pi/4 + k*pi`
Hence, checking if the given equation has solutions, the answer is affirmative and the general solution to the equation is `x = -pi/4 + k*pi.`
Sources: | crawl-data/CC-MAIN-2016-18/segments/1461860111809.10/warc/CC-MAIN-20160428161511-00033-ip-10-239-7-51.ec2.internal.warc.gz | null |
# How does the collision of vehicles in car accidents related to momentum?
When a collision occurs in an isolated system, the total momentum of the system of objects is conserved. Provided that there are no net external forces acting upon the objects, the momentum of all objects before the collision equals the momentum of all objects after the collision.
## What is collision in physics example?
collision, also called impact, in physics, the sudden, forceful coming together in direct contact of two bodies, such as, for example, two billiard balls, a golf club and a ball, a hammer and a nail head, two railroad cars when being coupled together, or a falling object and a floor.
## What are 3 examples of collisions?
Motor vehicle crash involves three types of collisions: vehicle collision, human collision, and internal collision.
## What happens when two cars collide physics?
If there are only two objects involved in the collision, then the momentum change of the individual objects are equal in magnitude and opposite in direction. Certain collisions are referred to as elastic collisions. Elastic collisions are collisions in which both momentum and kinetic energy are conserved.
## What is the formula for collision?
From the conservation of momentum, the equation for the collision between two objects is given by: m1v1 + m2v2 = m1v’1 + m2v’2. From this expression, the initial and final velocities can be derived.
## What happens when a moving car hits a stationary car?
When a moving car hits a parked car and causes the parked car to move, it means that the parked car gains velocity after being hit by a moving car. As said earlier, a moving object possesses kinetic energy, so the parked car has gained some kinetic energy from the moving car.
## How many types of collisions are there give example?
There are two types of collisions between two bodies – 1) Head-on collisions or one-dimensional collisions – where the velocity of each body just before impact is along the line of impact, and 2) Non-head-on collisions, oblique collisions or two-dimensional collisions – where the velocity of each body just before …
## How do you calculate momentum collision?
Multiply the second object’s mass by its velocity. For example, if it weighs1,000 and has a velocity of -30 meters per second, then its momentum will be 30,000 kg meters per second. Add the two velocities together to determine which way the objects will move after collision.
## How many collisions occur when a vehicle hits a solid object?
When a vehicle hits a solid object 3 collisions occur… The vehicle hits the object and stops. The occupant/s either hit inside of the vehicle or their restraint devices. Occupants may suffer internal collisions as their organs impact inside their bodies.
## How can three collisions occur in one crash between a car and a wall?
Describe the how three collisions can occur during a single crash between a truck and a wall. The first collision is between the truck and the wall. The second is between the driver and the truck’s interior. And the third is between the driver’s internal organs and the inside walls of his or her body cavities.
## How many collisions occur in a vehicle crash?
There Are Three Collisions There are actually three collisions in every crash: the vehicle collision; the human collision; and the internal collision (inside your body).
## What is the physics of A car collision?
The physics of a car collision will never, no matter how energetic, emit a completely new car. The car would experience exactly the same force in both cases. The only force that acts on the car is the sudden deceleration from v to 0 velocity in a brief period of time, due to the collision with another object.
## What happens if two cars crash at the same speed?
“Although the two-car crash doubles the speed, the energy the crash is transferred to twice the mass resulting in a crash that looks like just one car hitting a wall at 50 mph.” Here is the graphic that went with that.
## What type of collision is A car crash physics?
Momentum is conserved, because the total momentum of both objects before and after the collision is the same. However, kinetic energy is not conserved. Some of the kinetic energy is converted into sound, heat, and deformation of the objects. A high speed car collision is an inelastic collision.
## What is the total momentum before and after collision of colliding cars?
The total momentum of two objects before a collision is the same as their total momentum after the collision – provided there are no external forces.
## How do you find the momentum of two objects before a collision?
An object’s momentum before collision is given by P = mv. In the absence of external force, its motion and momentum do not vary before the collision.
## What forces are involved in a car collision?
• Gravitational force –pulls objects towards the centre of the earth. This causes the car to roll down the ramp.
• Frictional force – resistance caused by the wheels of the car rubbing against the cardboard and the air against the car.
• Applied force – the block applies a force on the car to stop the car.
## When two cars crash what happens to the kinetic energy?
3.2Collision energy conversion Most of the kinetic energy in the collision process is converted into the internal energy of the car, because the metal plastic deformation after the collision increases the internal energy a lot. Other kinetic energy is converted into heat energy, sound energy, etc.
## How do you calculate the speed of a car after a collision?
How Do I Calculate Speed and Distance in a Car Accident Case? The formula for speed and distance is the same for a car as any other object: distance ÷ time. So if you want to calculate the speed of a car at sixty miles an hour, the math is (60 x 5280) ÷ (60 x 60) = 88 feet per second.
## When a moving object collides with an object at rest?
When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater collision force. When a moving object collides with a stationary object of identical mass, the stationary object encounters the greater momentum change.
## What happens in terms of energy when a moving car hits a parked car?
What happens in terms of energy when a moving car hits a parked car, causing the parked car to move? The moving car transfers kinetic energy to the parked car.
## When a heavy truck and a light car collide with each other which of the two vehicles exerts more force?
When a truck and a car collide, the impact of the crash will be considerably greater in the car, because the mass of the truck is so much larger, and therefore will take much longer to stop. This means that the G force in the car will be much higher as it goes from moving to a full stop in a shorter period of time.
## Which is an example of an elastic collision?
Elastic Collision Examples When a ball at a billiard table hits another ball, it is an example of elastic collision. When you throw a ball on the ground and it bounces back to your hand, there is no net change in the kinetic energy, and hence, it is an elastic collision. | crawl-data/CC-MAIN-2024-10/segments/1707947475311.93/warc/CC-MAIN-20240301125520-20240301155520-00096.warc.gz | null |
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# Combinatorics: More than One Scenario - Calculate Separately and Add (OR relations)
A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing next to each other, how many different photographs can the photographer take?
Correct [[snippet]] Let's start with the photographs with girls and boys standing in the order G-B-G-B-G. Since there's no repetition, the number of options for each successive child from the same gender decreases. For example, if there are 4 choices for the first girl, then there are only 3 choices for the next girl (third place), and 2 choices for last girl (fifth place). The same goes for boys (second and fourth places). >$$\mathop{\fbox{{4}}}\limits^{{}{}\hspace{0.33em}{\text{G}}} \hspace{0.33em}\times\mathop{\fbox{{4}}}\limits^{{}{}\hspace{0.33em} {\text{B}}}\hspace{0.33em}\times \mathop{\fbox{{3}}}\limits^{{}{}\hspace{0.33em}{\text{G}}} \hspace{0.33em}\times\mathop{\fbox{{3}}}\limits^{{}{}\hspace{0.33em}{\text{B}}}\hspace{0.33em} \times\mathop{\fbox{{2}}}\limits^{{}{}\hspace{0.33em}{\text{G}}}={288}$$ Now, do the same for photographs with girls and boys standing in the order B-G-B-G-B. Note that intuitively, this scenario should have the same number of permutations, as we have an identical 4 boys and 4 girls to choose from. >$$\mathop{\fbox{{4}}}\limits^{{}{}\hspace{0.33em}{\text{B}}} \hspace{0.33em}\times\mathop{\fbox{{4}}}\limits^{{}{}\hspace{0.33em} {\text{G}}}\hspace{0.33em}\times \mathop{\fbox{{3}}}\limits^{{}{}\hspace{0.33em}{\text{B}}} \hspace{0.33em}\times\mathop{\fbox{{3}}}\limits^{{}{}\hspace{0.33em}{\text{G}}}\hspace{0.33em} \times\mathop{\fbox{{2}}}\limits^{{}{}\hspace{0.33em}{\text{B}}}={288}$$ Since there is an "or" relationship here between either of the two types of photographs that can be taken, add the combinations. >$$\text{Arrangements} = 288 + 288 = 576$$
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]]
$$80$$
$$288$$
$$4^4$$
$$576$$
$$288^2$$ | crawl-data/CC-MAIN-2020-45/segments/1603107869785.9/warc/CC-MAIN-20201020021700-20201020051700-00325.warc.gz | null |
This image, taken with the Hubble Space Telescope in 1995, shows evaporating gaseous globules (EGGs) emerging from pillars of molecular hydrogen gas and dust. The giant pillars are light years in length and are so dense that interior gas contracts gravitationally to form stars. At each pillars' end, the intense radiation of bright young stars causes low density material to boil away, leaving stellar nurseries of dense EGGs exposed. The Eagle Nebula, associated with the open star cluster M16, lies about 7000 light years away.
NASA Web Site Statements, Warnings, and Disclaimers
NASA Official: Jay Norris. Specific rights apply.
A service of: LHEA at NASA / GSFC
& Michigan Tech. U.
Based on Astronomy Picture Of the Day
Publications with keywords: star formation
Publications with words: star formation | <urn:uuid:0a8f4d5b-f8ef-4695-8dcc-62685065289e> | {
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"I got chills the first time I held these," Jean Beagle Ristaino says. She gingerly spreads the shriveled leaves of five potato plants on a worktable. They look as if they’ve been moldering away under a refrigerator somewhere. But Ristaino, a plant pathologist at North Carolina State University in Raleigh, has been using them as Exhibit A in a demonstration of molecular detective work so deft one learned journal recently dubbed her "the Sherlock of Spuds."
Scientists have long assumed they knew what caused the potato blight that starved a million Irish in the mid-19th century: the 1b strain of the funguslike water mold called Phytophthora infestans, a disease that is believed to have originated in Mexico. Ristaino did not doubt that some strain of P. infestans was the cause, but she was not so sure about 1b. So she and her colleagues studied DNA from infected potato leaves collected in Ireland, Britain and France during the mid-1840s.
DNA, or deoxyribonucleic acid, is the double strand of molecules that carries a cell’s unique genetic code. Within the past decade or so, DNA analysis of criminal evidence has overturned the convictions of more than 100 inmates in U.S. prisons, including 12 on death row. Ristaino’s project marked the first time the technique had been used to investigate a historic plant disease, and last year she asserted that it proved 1b was not the culprit after all. "This was a fantastic application of a novel technique that told us we were on the wrong path," says Greg Forbes of the International Potato Center, a research facility in Lima, Peru.
But if 1b wasn’t responsible for the Irish famine, which strain was? Did it originate in Mexico or somewhere else? If we knew how the disease evolved, could modern outbreaks be prevented? Today, Ristaino is wrestling with these vexing questions.
The study of plant diseases is not for everyone. Those who do this specialized work—the American Phytopathological Society (APS), based in St. Paul, Minnesota, lists nearly 5,000 members—tend to be driven perfectionists. Typically a researcher inoculates healthy plants with fungi, a virus or bacteria to learn how a disease works. Breakthroughs like Ristaino’s are rare, but when they do occur they can change history.
In 1977 Eugene Nester of the University of Washington in Seattle discovered that a bacterium that produces plant tumors actually incorporates its own DNA into the DNA of a host plant’s cells. In time, that insight led scientists to be able to replace that bacterium’s "bad" genes with "good" ones, and use the technique to engineer disease- and herbicide-resistant cotton and soybeans. In 1993, Gregory Martin of the Boyce Thompson Institute for Plant Research in Ithaca, New York, became the first pathologist to clone a disease resistance gene. More than two dozen such genes have since been cloned, enabling breeders to grow hardier strains of tobacco, tomato, rice and flax.
Ristaino’s revelation that 1b did not cause the Irish potato famine is controversial—some researchers question her methodology—but her further suggestion that P. infestans could have originated in South America undercuts conventional wisdom. "There’s a big debate about this," cautions Stephen Goodwin, a U.S. Department of Agriculture (USDA) plant pathologist at Purdue University, whose own genetics studies a decade ago shored up the theory of a Mexican origin. "More work needs to be done." Meanwhile, fungicide-resistant new strains of the old disease are devastating potato fields all over the world.
A sixth-generation native of Washington, D.C., Ristaino entered the University of Maryland as a history major, then switched to biology. As a student at the USDA’s sprawling research center in Beltsville, Maryland, she worked part-time washing petri dishes and hauling sacks of alfalfa. One day she stumbled upon an enormous fungus collection squirreled away in the basement. "That’s where I discovered plant pathology," she says, her blue eyes glittering. "Lots of old specimens, things like rotten potatoes in bottles that were collected by famous pathologists."
While at Maryland, she married Andre Ristaino, and they soon headed west for the University of California at Davis, where she earned her doctorate in 1987. A few months later, she started her work in Raleigh. In the mid-1990s, Ristaino read about scientists who were analyzing DNA from such ancient materials as dinosaur bones and prehistoric insects preserved in amber. "I thought, 'Why not DNA from a plant pathogen?'" Her interest in the potato blight was underscored at a 1995 conference she attended in Ireland on the 150th anniversary of the Great Hunger. Two years later, she took a sabbatical. Poring through herbarium sheets containing infected potato plants, she collected the leaves from which she extracted the tiny bits of P. infestans DNA. She also came upon a trove of fascinating letters written by scientists during and after the famine. In the course of her study, Ristaino learned that when P. infestans began its fateful journey to Ireland, male laborers there typically consumed 12 to 14 pounds of potatoes a day. "People didn’t understand that pathogens cause disease," she says. "The Irish blamed bad weather, or the spirits, or acts of God." Today, in addition to figuring out how the blight mutates in infected modern potatoes to "outwit" fungicide, she continues a historic investigation into the disease’s true origins. "Gene genealogy," she calls it. Eventually it should lead to improved methods of diagnosing the disease, tracking its spread and controlling it in the field.
As for the resistance to her findings, the 45-year-old mother of two is undaunted. "I knew I was challenging major dogma," she says. "That’s part of the scientific process." And a small price to pay, she feels, for the knowledge that results. "This pathogen precipitated a major movement of people around the world and devastated an entire country," she adds. "What could be more exciting than trying to figure it out?" | <urn:uuid:fca8d05a-6e75-48d7-94e6-ffa8fb63c3e8> | {
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# Solving second-order nonlinear autonomous differential equations
For some physical purposes, I am now interested in differential equations of the form $$y''=f(y)$$ Now, this resource gives a general solution to this equation (sans constant solutions) as $$\int dy\left(C_1+2\int dy \,f(y)\right)^{-1/2}=C_2\pm x$$
but I have no idea how this formula was derived, and I can't find any resources on it other than the above; is this formula correct, and if so, how is it derived?
Hint: $$y''=f(y)$$ Multiply by $$2y′$$ both sides: $$2y'y''=2f(y)y'$$ Integrate to reduce the order. $$y'^2=2\int f(y) dy +C_1$$ It's separable.
Starting from
$$y'' = f(y), \tag 1$$
we multiply through by $$y'$$:
$$y''y' = f(y)y'; \tag 2$$
we observe that
$$\dfrac{1}{2}((y')^2)' = \dfrac{1}{2} (2y'y'') = y'y'', \tag 3$$
whence (2) may be written
$$\dfrac{1}{2}((y')^2)' = f(y)y', \tag 4$$
or
$$((y')^2)' = 2f(y)y'; \tag 5$$
we integrate with respect to $$x$$:
$$(y')^2 = \displaystyle \int ((y')^2)' \; dx + C_1$$ $$= 2 \displaystyle \int f(y)y' \; dx + C_1 = 2 \int f(y) \; dy + C_1; \tag 6$$
we isolate $$y'$$:
$$\dfrac{dy}{dx} = y' = \pm \left (2 \displaystyle \int f(y) \; dy + C_1 \right)^{1/2}, \tag 7$$
whence
$$\dfrac{dx}{dy} = \pm \left (2 \displaystyle \int f(y) \; dy + C_1 \right )^{-1/2}; \tag 8$$
we may now integrate again over $$y$$:
$$x + C_2 = \displaystyle \int \dfrac{dx}{dy} \; dy = \pm \int \left (2 \int f(y) \; dy + C_1\right )^{-1/2} \; dy, \tag 9$$
or
$$\pm(x + C_2) = \displaystyle \int \dfrac{dx}{dy} \; dy = \int \left (2 \int f(y) \; dy + C_1\right )^{-1/2} \; dy; \tag{10}$$
we may absorb the $$\pm$$ sign into $$C_2$$ since it is an arbitrary constant, and write
$$\pm x + C_2 = \displaystyle \int \dfrac{dx}{dy} \; dy = \int \left (2 \int f(y) \; dy + C_1\right )^{-1/2} \; dy, \tag{11}$$
which is essentially identical to the formula given by our OP John Dumancic in the body of the question itself.
There is another way to do it.
Switch variables and write the equation as $$-\frac{x''}{(x')^3}=f(y)$$ Now, reduction of order $$p=x'$$ to give $$-\frac{p'}{p^3}=f(y)\implies \frac{1}{2p^2}=\int f(y)\,dy=F(y)+C\implies p=\frac{\pm1}{\sqrt{C_1+2 F(y)}}$$ $$x=\pm \int \frac{dy}{\sqrt{C_1+2 F(y)}}+C_2$$ | crawl-data/CC-MAIN-2024-38/segments/1725700651995.50/warc/CC-MAIN-20240919061514-20240919091514-00807.warc.gz | null |
Hugh Pickens writes "The Telegraph reports that huge plant-eating dinosaurs called sauropods may have produced enough greenhouse gas by breaking wind to alter the Earth's climate. Scientists believe that, just as in cows, methane-producing bacteria aided the digestion of sauropods by fermenting their plant food. 'A simple mathematical model suggests that the microbes living in sauropod dinosaurs may have produced enough methane to have an important effect on the Mesozoic climate,' says study leader Dr Dave Wilkinson. 'Indeed, our calculations suggest that these dinosaurs could have produced more methane than all modern sources — both natural and man-made — put together.' The key factor is the total mass of the animals which included some of the largest animals to walk the Earth, such as Diplodocus, which measured 150 feet and weighed up to 45 tons. Medium-sized sauropods weighed about 20 tons and lived in herds of up to a few tens of individuals per square kilometer so global methane emissions from the animals would have amounted to around 472 million tons per year, the scientists calculated. Sauropods alone may have been responsible for an atmospheric methane concentration of one to two parts per million (ppm), say the scientists and studies have suggested that the Earth was up to 10C (18F) warmer in the Mesozoic Era. ''The Mesozoic trend to sauropod gigantism led to the evolution of immense microbial vats unequaled in modern land animals. Methane was probably important in Mesozoic greenhouse warming. Our simple proof-of-concept model suggests greenhouse warming by sauropod megaherbivores could have been significant in sustaining warm climates.'"
cylonlover writes "The hashtag or "#" symbol has taken on a lot more use in recent years, especially with the rise of social media tools like Twitter, where it's used to highlight popular topics. So in a way, it's a fitting model for an apartment building designed to act as a self-contained neighborhood, which is exactly the idea behind the Cross # Towers planned for South Korea. Dutch architectural firm, Bjarke Ingels Group (BIG), is modeling the look of the proposed building after the familiar symbol, by placing two interlocking bridges between two skyscrapers, which will also support outdoor park areas to mimic the sort of spaces you'd normally find on the ground."
Hentes writes "The internet has made many things easier, but unfortunately this also includes crime: it seems that nowadays not even people wanting to know their future are safe from fraud. Two fortune tellers are being investigated, after the Romanian police uncovered that they have utilized some extraordinary help in their clairvoyant acts. The pair used information collected from internet search and social networks to gain the trust of their customers, claiming that they could see their personal data through their crystal ball. In some cases, they also used high-tech surveillance techniques such as hidden cameras and phone tapping. But they didn't stop at merely spying on their victims: their most bizarre case involved a scuba diver dressed as a monster." Nice to know that internet-based fraud isn't limited to motivational speakers with real-estate seminars and other get-rich-quick flim-flam.
First time accepted submitter ElectronicHouseGrant writes "Freshman Derek Low rigged up his Berkeley dorm room with something he calls B.R.A.D., which is short for 'Berkeley Ridiculously Automated Dorm.' The room includes automated lighting, drapes, music, motion detection, and more. He can control everything through voice recognition, but a wireless remote, his iPhone and his iPad are also in on the control party. Derek started the install on February 4 and finished just a few days ago."
Freshly Exhumed writes in with a Wired story about a nerd/super-villian dream come true. "Marine biologist-cum-TV personality Luke Tipple attached a 50-milliwatt green laser to a lemon shark off the coast of the Bahamas in late April. The escapade was sponsored by Wicked Lasers, a consumer-focused laser manufacturer based in Hong Kong that produces some of the most brilliant — and potentially dangerous — handheld lasers in the world. 'This was definitely a world first,' Tipple told Wired. 'Initially, I told them no. I thought it was a frivolous stunt. But then I considered that it would give us an opportunity to test our clips and attachments, and whatever is attached to that clip, I really don't care. It was a low-powered laser that couldn't be dangerous to anyone, and there's actually useful applications in having a laser attached to the animal.'"
mikejuk writes, quoting I Programmer: "If you are looking for an exciting hardware project, KegDroid deserves a look. It is a sophisticated system that involves Android, Arduino, NFC, plumbing and — beer. Perhaps the final stroke of genius is to package the whole thing in a Droid body. Some how the little green fella looks at home on the bar. You have heard of desktop and laptop apps now we have bartop apps to add to the list" Details are fuzzy currently, but from all appearances this is a repackaged KegBot in a very fancy shell. (Video for those without Flash.)
mikejuk writes "John Graham-Cumming is the leading light behind a project to actually build the analytical engine dreamed of by Charles Babbage. There is a tendency to think that everything that Babbage thought up was little more than a calculating machine, but as the video makes 100% clear the analytical engine was a real computer that could run programs. From the article: 'Of course Ada Lovelace was the first programmer, but more importantly her work with Babbage took the analytical engine from the realms of mathematical table construction into the wider world of non-mathematical programming. Her notes indicate that had the machine been built there is no question that it would have been exploited just as we use silicon-based machines today. To see the machine built and running programs would be the final proof that Babbage really did invent the general purpose computer in the age of the steam engine.'"
First time accepted submitter a90Tj2P7 writes "Apple is building a 21,468 square foot private restaurant in Cupertino so employees can talk shop over lunch without being overheard. Apple's director of real estate facilities, Dan Wisenhunt, stated that: 'We like to provide a level of security so that people and employees can feel comfortable talking about their business, their research and whatever project they're engineering without fear of competition sort of overhearing their conversations.'"
Barence writes "Microsoft challenged the editor of PC Pro to return to Hotmail after six years of using Gmail, to prove that its webmail service had vastly improved — but the challenge backfired when he had his Hotmail account hacked. PC Pro's editor say he was quietly impressed with a number of new Hotmail features, including SkyDrive integration and mailbox clean-up features. He'd even imported his Gmail and contacts into Microsoft's service. But the two-week experiment came to an abrupt end when Hotmail sent a message containing a malicious link to all of his contacts. 'What's even more worrying is that it's not only my webmail that's been compromised, but my Xbox login (which holds my credit card details) and now my PC login too. Because Windows 8 practically forces you to login with your Windows Live/Hotmail details to access features such as the Metro Store, synchronization and SkyDrive,' he writes."
mikejuk writes with this excerpt from I Programmer: "A movie that features science and technology is always welcome, but is it not often we have one that focuses on computer science. Travelling Salesman is just such a rare movie. As you can guess from its name, it is about the Travelling Salesman problem, more precisely about the P=NP question. Written and directed by Timothy Lanzone, and produced by Fretboard Pictures, it should premiere on June 16. As the blurb to the movie trailer says: 'Travelling Salesman is an intellectual thriller about four of the world's smartest mathematicians hired by the U.S. government to solve the most elusive problem in computer science history — P vs. NP. The four have jointly created a "system" which could be the next major advancement for humanity or the downfall of society.'"
redletterdave writes with an amusing tale of missent email. From the article: "On Friday, more than 1,300 employees of London-based Aviva Investors walked into their offices, strolled over to their desks, booted up their computers and checked their emails, only to learn the shocking news: They would be leaving the company. The email ordered them to hand over company property and security passes before leaving the building, and left the staff with one final line: 'I would like to take this opportunity to thank you and wish you all the best for the future. 'This email was sent to Aviva's worldwide staff of 1,300 people, with bases in the U.S., UK, France, Spain, Sweden, Canada, Italy, Ireland, Germany, Norway, Poland, Switzerland, Belgium, Austria, Finland and the Netherlands. And it was all one giant mistake: The email was intended for only one individual."
Jake Elliott and Jon (not Elwood) Cates are the ones who describe Glitch Art people as 'weirdos within the weirdos' in the context of Notacon 9, which was recently held in Cleveland. It's 'an annual event that focuses on people who like to build, make, break and hack stuff,' and even in the Notacon context the Glitch Artwork crowd stands out. Sit down with Jake and Jon and share their joy in working with "feral glitches... before they are domesticated," and see some of the output from artist Dave Musgrave's circuit-bent consoles.
First time accepted submitter v3rgEz writes "Six months ago, the toilets of the General Services Administration started exploding, injuring two employees and beginning the agency's spiral down the drain of bad press (this is the same GSA now under fire for pricey Vegas conference flings). E-mails just released under FOIA now show the culprit: Compressed air + ancient plumbing + leaving it all unattended."
linuxwrangler writes "It started with a dream of building a full-sized jet flight simulator. Now, 20 years, $150,000 and one divorce later, James Price can walk to his garage and fly the 737 simulator he built built from the nose of a surplus 737. From the article: 'James Price had one must-have when looking for a new home -- the garage had to be able to hold the nose of a Boeing 737 jetliner. "Once I realized I could get it in here, I was OK with the house," Price said. In his spacious three-car garage Price has a well-traveled jetliner cockpit tucked in next to the family car. Aviation experts say Price, 52, is one of only a handful of people in the world who have built their own flight simulator cockpit in an actual jet nose."
Fluffeh writes "Teller, the silent half of the well-known magic duo Penn and Teller, has sued a rival magician for copying one of his most famous illusions. The case promises to test the boundaries of copyright law as it applies to magic tricks. A Dutch magician with the stage name Gerard Bakardy (real name: Gerard Dogge) saw Teller perform the trick in Las Vegas and developed his own version — then started selling a kit — including a fake rose, instructions, and a DVD — for about $3,000. Teller had Bakardy's video removed with a DMCA takedown notice, then called Bakardy to demand that the magician stop using his routine. Teller offered to buy Bakardy out, but they were unable to agree on a price. So Teller sued Bakardy last week in a Nevada federal court." | <urn:uuid:c48ed77d-d36a-4d6c-b2b6-c7b0345b3865> | {
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Burning oil from BP spill produced carbon plumes
Chalk up another environmental impact from last summer's Deepwater Horizon oil spill: Nine weeks of burning off oil slicks from the surface of the Gulf of Mexico following the BP spill released an estimated 1 million pounds of soot into the atmosphere, according to a study released by the National Oceanic and Atmospheric Administration.
The burns were conducted to reduce the size of the slicks and to minimize the amount of oil reaching the gulf’s coast and wetlands systems. But the study, which was co-written by researchers at the Cooperative Institute for Research in Environmental Sciences in Boulder, Colo., found the plumes of smoke from the burns produced an amount of carbon equal to the total black carbon emissions normally released by all ships that travel the Gulf of Mexico during a nine-week period.
Black carbon, whose primary component is often called soot, is among the most light-absorbing particles in the atmosphere. The new study, published online in Geophysical Research Letters, provides some of the most detailed observations made of black carbon sent airborne by burning surface oil.
The study found that the soot plumes reached much higher into the atmosphere than ship emissions normally rise, and that the average size of the soot particles was larger than normally emitted from other sources in the gulf region. Researchers also found that the soot particles were almost all black carbon, unlike forest fires, for example, which produce other particles along with black carbon.
-- Julie Cart
Photo: A controlled burn on June 19, 2010, attempting to remove oil floating near the leaking BP well in the Gulf of Mexico. Credit: Carolyn Cole / Los Angeles Times | <urn:uuid:37682dc0-a949-4be3-a19a-6adedf8a4c95> | {
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- Размер: 622 Кб
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Описание презентации LECTURE 2. PHONEMES AND THEIR VARIANTS (ALLOPHONES) Points по слайдам
LECTURE 2. PHONEMES AND THEIR VARIANTS (ALLOPHONES) Points for Discussion: • The Notion of the Phoneme • The Relationship between the Phoneme and Its Allophones • The Aspects of the Phoneme • The Functions of the Phoneme
The human speaking apparatus is capable of articulating a great number of various sounds. Some of the differences exist as physical facts and are not always linguistic facts. Cf. : p eak – s p eak aspiration – no aspiration
The only important things for language are those which can be associated with meaning and be used for the purposes of communication. We can differentiate and distinguish, recognize the shapes of words only when opposing one sound shape to another or even to many of them.
The opposition of different sound shapes is the basis of understanding. E. g. bead [bi d] ː bed [bed] bid [b d] ɪ bad [bæd] board [b d] ɔː bard [b d]ɑː bird [b d] ɜː bud [b d]ʌ Opposing the vowels [i ], [e], [æ], [ ], ː ɪ ɔː ɑː ɜː [ ] ʌ we can see that they are used as independent units for the purposes of word differentiation. The consonants [n] – [f], [t] – [d], [p] – [t] are opposed in the following pairs of words line – life, try – dry, pen – ten.
There exist speech sounds which are the basis for the differentiation of the sound shapes of words and grammatical forms of one and the same word. We call such sounds phonemes.
According to professor V. O. Vasyliev (V. A. Vassilyev), the segmental phoneme is the smallest (i. e. further indivisible into smaller consecutive segments) language unit (sound type) that exists in the speech of all the members of a given community as such speech sounds which are capable of distinguishing one word from another word of the same language or one grammatical form of a word from another grammatical form of the same word [2, p. 131].
M. O. Sokolova et al. give a more concise definition: The phoneme is a minimal abstract linguistic unit realized in speech in the form of speech sounds opposable to other phonemes of the same language to distinguish the meaning of morphemes and words [3, p. 40].
Ivan Oleksandrovych (Jan Niecisław) Baudouin de Courtenay used the term ‘phoneme’ and developed it into the phoneme theory. During the first stage of the development of his phoneme theory he views the phoneme as a component of the morpheme and tries to analyze phonemes according to their function in the morphemes.
In 1890 s the psychological approach in linguistics began to prevail, and the scientist abandoned his morphological conception and tried to find a unit which would not be bound by the limits of the morpheme. He began to consider the phoneme as a general idea of a sound which arises in a person’s mind before s/he utters a sound.
Lev Volodymyrovych Scherba was the first to suggest the idea of the sense-differentiating function of the phoneme. Moreover, he attached considerable importance to phonemic variants , or allophones , and stressed that one of the main reasons why variants are important is that they represent phonemes in actual speech.
Any phoneme only exists in the form of actually pronounced speech sounds which are its variants. In the course of research work it was discovered that the representatives of any linguistic community utter much more sounds in comparison with the number of phonemes.
[leɪ t ] [ t en] [ t raɪ] [ˈbæ tə l] [ t uː]
Each word contains the sound [t]. Each of these [t]-sounds has its neighboring sounds and positions in the word. Due to these factors each of them has its own peculiarities of articulation.
In the word [le t] ɪ the sound [t] is in the final position and undergoes the least possible influence from the neighboring phonemes. Thus, it is the nearest to the cardinal phoneme [t]. In [ten] the sound [t] is in the initial position before the front vowel [e], so it is slightly palatalized under its influence.
In the word [tra ] ɪ the sound [t] stands before the postalveolar forelingual phoneme [r] and under its influence it becomes postalveolar as well. In the word [ bæt ˈə l] plosive [t] becomes lateral under the influence of the lateral sonorant [l]. In the word [tu ] ː the phoneme becomes labialized under the influence of the labial [u ]. ː
From the acoustic point of view each of these [t]-sounds has its peculiarities and slightly differs from others. Each of them is articulate in its own way but from the point of view of p hon ology we perceive all these [t]-sounds as one and the same [t]-phoneme because they do not change the meaning of words to the degree of quite new ones.
According to L. V. Borysova , allophones [from the Greek: λλος, állos, «other» and φωνή, phōnē, ἄ «voice, sound“] (or variants) of a certain phoneme are speech sounds which are realizations of one and the same phoneme and which, therefore, cannot distinguish words. Allophones of a phoneme which never occur in identical positions are said to be in complementary distribution [1, pp. 28 -29].
When a person wishes to pronounce a phoneme in isolation s/he usually pronounces the so-called principal/typical allophone. Besides the principal allophone which preserves typical articulatory features of the phoneme there are subsidiary allophones which are subdivided into combinatory and positional.
Combinatory allophones are those which due to the influence of neighboring sounds are the products of assimilation, adaptation or accommodation. Positional allophones are those which are used in definite positions traditionally, i. e. according to the orthoepic norms of the language rather than because of the influence of the neighboring sounds.
Lev Volodymyrovych Scherba wrote: » In actual speech we utter a much greater variety of sounds that we are in aware of; in every language these sounds are united in an comparatively small number of sound types which are capable of distinguishing the meaning and the form of words, i. e. they serve the purpose of communication. It is these sound types that we have in mind when discussing sounds. Such sound types will be called phonemes“.
The variant sounds that we actually utter and which are the individual representing the universal may be called phonemic variants. All phonemic variants differ from each other in some respects but at the same time they share certain common properties which in phonetics are called distinctive features.
MODERN TREATMENT OF THE PHONEME One of theories worked by Prof. V. O. Vasyliev (V. A. Vassilyev) presents the phoneme as a dialectical unity of three aspects : 1. material, real, and objective; 2. abstractional or generalized; 3. functional.
1. THE PHONEME IS MATERIAL, REAL AND OBJECTIVE. The materiality of the phoneme is confirmed by its real existence in language. The phoneme is a concrete speech sound which possesses certain acoustic and articulatory properties. The objectivity of the phoneme consists in the fact that it exists irrespective of the will of the individual.
2. THE PHONEME IS ABSTRACTIONAL AND GENERALIZED. The relationship between the phoneme and its variants is a vivid instance of the many-sided relation between what is abstract and general , on the one hand, and what is concrete and specific , on the other.
3. FUNCTIONAL ASPECT OF THE PHONEME. It performs three principal functions in speech: Constitutive – phonemes form the sound-shape of morphemes and words. Recognitive / Identificatory – phonemes help identify words. Distinctive – phonemes help differentiate the meaning of words and grammatical forms.
According to V. Yu. Paraschuk, the distinctive function is subdivided into: The morpheme-distinctive function E. g. dream er — dream y The word-distinctive E. g. p en – t en – B en – m en – d en – h en The sentence distinctive E. g. It was g old. – It was c old. – It was s old. It depends on which hierarchically higher language units are differentiated [2, p. 136].
REFERENCES 1. Борисова Л. В. , Метлюк А. А. Теоретическая фонетика английского языка : [ Учеб. пособие для ин-тов и факультетов иностр. яз. ] / Борисова Л. В. , Метлюк А. А. – Мн. : Выш. школа, 1980. – C. 28 -30. 2. Паращук В. Ю. Тео ретич на фонетика англійської мови: Навчальний посібник для студентів факультетів іноземних мов / Паращук В. Ю. — Вінниця, НОВА КНИГА, 2005. – C. 130 -136. 3. Теоретическая фонетика английского языка: Учеб. для студ. выш. учеб. заведений / М. А. Соколова, К. П. Гинтовт, И. С. Тихонова, Р. М. Тихонова. – 3 -е изд. , стереотип. – М. : Гуманит. изд. центр ВЛАДОС, 2003. – C. 39 -51. | <urn:uuid:0e9ee4ac-9460-4c19-b6e0-b0e430b1553e> | {
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Race bikes along a track. Try to pick a winner before the races start. Add the numbers on a pair of dice to determine which bike moves. Explore how many rolls are needed to complete a race. Work out the least and greatest number of rolls possible for two track lengths. Look at larger samples of race results. Compare the shape of theoretical data distributions with experimental results. This learning object is one in a series of 11 objects.
Key learning objectives
- Students collect and handle data about random events to test conjectures about statistical variation.
- Students interpret frequency graphs to compare experimental results with theoretical probabilities.
- Students compare the shape of theoretical and experimentally derived data distributions in situations where there is bias.
- Students relate the shape of data distributions to statements about sample variation and sample size.
- Students distinguish between even and uneven data distributions.
- Provides scenarios for students to use dice as a means to explore relationships between sample size, random variation, and statistical distributions.
- Demonstrates that conclusions based on small sample sizes can be incorrect due to random variation.
- Introduces mathematical ideas underpinning uneven distributions via an on-screen tutorial.
- Includes scenarios involving uneven distributions.
- Automatically collates experimental results and displays them as frequency graphs. | <urn:uuid:3d9351f8-19de-467f-a4a8-76dd1a967d30> | {
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Hadley Vinson July 24, 2020 Anatomy
Scientific names for the parts and structures of the human body are usually in Latin; for example, the name musculus biceps brachii denotes the biceps muscle of the upper arm. Some such names were bequeathed to Europe by ancient Greek and Roman writers, and many more were coined by European anatomists from the 16th century on. Expanding medical knowledge meant the discovery of many bodily structures and tissues, but there was no uniformity of nomenclature, and thousands of new names were added as medical writers followed their own fancies, usually expressing them in a Latin form.
In contrast, micro- means “small,” and microscopic anatomy is the study of structures that can be observed only with the use of a microscope or other magnification devices (Figure 1b). Microscopic anatomy includes cytology, the study of cells and histology, the study of tissues. As the technology of microscopes has advanced, anatomists have been able to observe smaller and smaller structures of the body, from slices of large structures like the heart, to the three-dimensional structures of large molecules in the body.
And out of these 79 organs, five are crucial for survival, and any damage to these five organs might result in termination of life. These five crucial human body parts are the brain, heart, liver, lungs and kidneys. Read on to explore more about these body parts and their functions in detail:The process of digestion starts with mastication (chewing food). Then, the saliva mixes with food and forms a bolus, a small rounded mass that can be easily swallowed. Once swallowed, the food travels down the oesophagus and into the stomach. The stomach secretes strong acids and powerful enzymes that break the food down into a paste.
The use of the microscope in discovering minute, previously unknown features was pursued on a more systematic basis in the 18th century, but progress tended to be slow until technical improvements in the compound microscope itself, beginning in the 1830s with the gradual development of achromatic lenses, greatly increased that instrument’s resolving power. These technical advances enabled Matthias Jakob Schleiden and Theodor Schwann to recognize in 1838–39 that the cell is the fundamental unit of organization in all living things.
Even to this day, scientists are newly discovering organs that were previously overlooked or have been mistakenly identified as other existing tissues. In 2018, scientists had discovered a new, body-wide organ called the Interstitium that exists right under the skin.
This ancient discipline reached its culmination between 1500 and 1850, by which time its subject matter was firmly established. None of the world’s oldest civilizations dissected a human body, which most people regarded with superstitious awe and associated with the spirit of the departed soul. Beliefs in life after death and a disquieting uncertainty concerning the possibility of bodily resurrection further inhibited systematic study. Nevertheless, knowledge of the body was acquired by treating wounds, aiding in childbirth, and setting broken limbs. The field remained speculative rather than descriptive, though, until the achievements of the Alexandrian medical school and its foremost figure, Herophilus (flourished 300 bce), who dissected human cadavers and thus gave anatomy a considerable factual basis for the first time. Herophilus made many important discoveries and was followed by his younger contemporary Erasistratus, who is sometimes regarded as the founder of physiology.
Tag Clouddiagram of ovaries in human body comparative anatomy and physiology biodigital 3d human tarsal bone anatomy structure of human eye male reproductive pain in shoulder blade hurts to breathe frog male and female reproductive system anatomy and physiology 2 endocrine system about our body anatomy and physiology of neurological system arm vein anatomy cardiology anatomy and physiology female reproductive system of goat continuous neck and shoulder pain stiff shoulder muscles muscles of the body diagram left arm jumping best shoulder and tricep workout left rhomboid pain | <urn:uuid:58ee6b85-5425-45a6-b33b-2d627387b115> | {
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Take a bird's eye view of the rainforest and you can't see the wood for the trees. According to a large survey in the Amazon, satellites can't accurately measure the carbon stored in trees.
That's a problem, because satellite measurements are key to monitoring a global initiative known as Reducing Emissions from Deforestation and Forest Degradation (REDD). Under a future global climate deal on limiting carbon emissions, REDD would allow big emitters to offset carbon emissions by paying for conservation schemes that prevent deforestation.
Edward Mitchard at the University of Edinburgh, UK, and his colleagues used data gathered from the forest floor to calculate the biomass of millions of trees in more than 400 plots across the Amazon basin, taken from a long-standing project called Rainfor, the Amazon Forest Inventory Network.
They then compared this data with estimates made by widely used satellite maps of forest biomass.
They found a huge mismatch. "I was expecting some differences, but not as dramatic as what occurred," says Mitchard.
Missed a bit
Satellite estimates of carbon stored in large areas of forests were frequently out by more than 25 per cent, far greater than the uncertainties of 5 per cent or less claimed in the remote sensing studies
Most strikingly, said Mitchard, "the satellite-based maps have missed a massive gradient from the south-west to the north-east of the [Amazon] basin". That's because satellites measure the height of the canopy, and can't tell that some trees are less dense and so contain less carbon.
"None of the space-borne technologies used in the satellite [carbon] maps actually measure biomass," said Shaun Quegan, who studies terrestrial carbon dynamics at the University of Sheffield, UK. He agrees with Mitchard's conclusion. "Clearly, the remote sensing maps are not as accurate as they would have you believe," he says.
Addicted to tech
The findings suggest that only ground-based assessments can accurately monitor REDD schemes.
The work has set off a row between forest researchers. Critics of the paper argue that the Rainfor field data is flawed. Daniel Nepstad at the Earth Innovation Institute in San Francisco says the studied plots may not be representative of overall forest biomass.
But Simon Lewis from University College London, a co-author of the paper, says the study highlights flaws in how such data is collected. "We are enthralled by expensive technology like satellites, but less willing to fund unglamorous work like ground-truthing their data," he says.
Journal reference: Global Ecology and Biogeography, 10.1111/geb.12168
If you would like to reuse any content from New Scientist, either in print or online, please contact the syndication department first for permission. New Scientist does not own rights to photos, but there are a variety of licensing options available for use of articles and graphics we own the copyright to. | <urn:uuid:99924097-2e8d-46f0-b43f-b4a6a2e00349> | {
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Scientists investigating rocks in Oman have found new windows into the creation of mountains and continents.
Dr Ian Alsop, of the University of St Andrews, has just returned from a trip to the mountains of Oman where he investigated ancient rock folds up to 70 million years old. Such folds give insights into how the plates that make up the Earth’s crust form and move.
Along with colleagues from Oxford University, Dr Alsop found examples of rock folds which were larger and more clearly exposed than any found before, allowing for greater insights to be gained.
“As rocks deep underground are pressed and heated, they melt and begin to flow. This forms folds, like a rucked-up carpet”, explained Dr Alsop, an international expert on folds.
The folds in Oman show that the rocks moved many tens of kilometres while deep within the Earth. They also show what Dr Alsop calls “huge amounts of shearing,¿ which refers to the stresses that deform the rock.
“The folds that we have been analysing in Oman formed about 70 million years ago and are unique in that they display some of the largest, best exposed curved geometries exposed anywhere on Earth,” says Dr Alsop, who works in the School of Geography and Geosciences at St Andrews.
Oman has rugged mountains split by steep wadis, or dry riverbeds, which expose many of these folds in great detail. Such folds may be pushed as deep as 100 kilometres underground before returning to the Earth’s surface in a dramatic mountain range like this one. Also visible now are portions of crust which were once under the ocean.
Dr Alsop and his colleagues will return to Oman for more fieldwork later in the year, as part of an ongoing project funded by the Royal Society.
He said, “It is likely that similar formations occur in mountain ranges elsewhere in the world but are less well exposed and more difficult to identify than in Oman.”
NOTE TO EDITORS:
DR ALSOP IS AVAILABLE FOR INTERVIEW: TEL 01334 463937, email [email protected]
NOTE TO PICTURE EDITORS:
IMAGES ARE AVAILABLE FROM THE PRESS OFFICE – CONTACTS BELOW.
Issued by Press Office, University of St Andrews
Contact Gayle Cook, Press Officer on 01334 467227 / 462529, mobile 07900 050 103, or email gec3@st- andrews.ac.uk
Ref: Oman rocks 120207.doc
View the latest University press releases at http://www.st- andrews.ac.ukResearch | <urn:uuid:f706810c-9fa3-4a64-bbcf-020559096620> | {
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Introduction to Counter/Timer Hardware
Sun, 2007-12-02 04:56 - webmaster
Counter units (aka, timer units) are crucial components of most embedded systems and included in many microcontrollers. Here's a primer on the hardware.
In some cases, a timer measures elapsed time (counting processor cycles or clock ticks). In others, we want to count external events. The names counter and timer can be used interchangeably when talking about the hardware. The difference in terminology has more to do with how the hardware is used in a given application.
Figure 1 shows a simple timer similiar to those often included on-chip within a microcontroller. You could build something similar from a couple of 74HC161 counters or a programmable logic device. The timer shown consists of a loadable 8-bit count register, an input clock signal, and an output signal. Software loads the count register with an initial value between 0x00 and 0xFF. Each subsequent transition of the input clock signal increments that value.
When the 8-bit count overflows, the output signal is asserted. The output signal may thereby trigger an interrupt at the processor or set a bit that the processor can read. To restart the timer, software reloads the count register with the same or a different initial value.
If a counter is an up counter, it counts up from the initial value toward 0xFF. A down counter counts down, toward 0x00.
A typical counter will have some means to start the counter running once it is loaded, usually by setting a bit in a control register. This is not shown in the figure. A real counter would generally also provide a way for the processor to read the current value of the count register at any time, over the data bus.
A timer with automatic reload capability will have a latch register to hold the count written by the processor. When the processor writes to the latch, the count register is written as well. When the timer later overflows, it first generates an output signal. Then, it automatically reloads the contents of the latch into the count register. Since the latch still holds the value written by the processor, the counter will begin counting again from the same initial value.
Such a timer will produce a regular output with the same accuracy as the input clock. This output could be used to generate a periodic interrupt like a real-time operating system (RTOS) timer tick, provide a baud rate clock to a UART, or drive any device that requires a regular pulse.
A variation of this feature found in some timers uses the value written by the processor as the endpoint rather than the initial count. In this case, the processor writes into a terminal count register that is constantly compared with the value in the count register. The count register is always reset to zero and counts up. When it equals the value in the terminal count register, the output signal is asserted. Then the count register is reset to zero and the process repeats. The terminal count remains the same. The overall effect is the same as an overflow counter. A periodic signal of a pre-determined length will then be produced.
If a timer supports automatic reloading, it will often make this a software-selectable feature. To distinguish between a count that will not repeat automatically and one that will, the hardware is said to be in one of two modes: one-shot or periodic. The mode is generally controlled by a field in the timer's control register.
Input capture timers
An input capture timer, like the one shown in Figure 2, has a latch connected to the timer's count register. The timer is run at a constant clock rate (usually a derivative of the processor clock), so that the count register is constantly incrementing (or decrementing, for a down counter). An external signal latches the value of the free-running timer into the processor-visible register and generates an output signal (typically an interrupt).
One use for an input capture timer is to measure the time between the leading edge of two pulses. By reading the value currently in the latch and comparing it with a previous reading, the software can determine how many clock cycles elapsed between the two pulses. In some cases, the timer's count register might be automatically reset just after its value is latched. If so, the software can directly interpret the value it reads as the number of clock ticks elapsed. An input capture pin can usually be programmed to capture on either the rising or falling edge of the input signal.
Many timers provide a means to prescale the input clock signal. For example, the 8-bit timer in Atmel's AT90S8515 microcontroller can be incremented with every processor clock cycle, every 8th, every 64th, every 256th, or every 1,024th. Selecting a less frequent update cycle is called prescaling the input clock. Similarly, each increment could occur on either the rising or falling edge of some other signal entirely. In the Atmel part, these features are software-selectable.
Some timers can directly control a general-purpose I/O pin. When an overflow occurs, the pin can be automatically set to 1, reset to 0, or toggled. This can be useful in, for example, generating a PWM signal. Using two different initial or terminal count values and a one-shot timer that toggles the I/O pin on overflow, the pin could be set to 1 for a desired amount of time, then 0 for a different amount of time, then 1 again, and so on. The period of the PWM signal would be a function of the sum of the two timer lengths. The duty cycle would then be the length of time that the pin is set to 1 as a percentage of the period.
Although the examples here have focused on 8-bit timers, the concepts apply to larger timers as well.
This article was published in the September 2002 issue of Embedded Systems Programming. If you wish to cite the article in your own work, you may find the following MLA-style information helpful:
Ball, Stuart and Michael Barr. "Introduction to Counter/Timer Hardware," Embedded Systems Programming, September 2002, pp. 55-56. | <urn:uuid:c38674be-ea57-46bd-a82c-afd838f95cf8> | {
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You are reading an older version of this FlexBook® textbook: CK-12 Geometry Concepts Go to the latest version.
# Chapter 5: Relationships with Triangles
Difficulty Level: At Grade Created by: CK-12
## Introduction
This chapter introduces different segments within triangles and how they relate to each other. We will explore the properties of midsegments, perpendicular bisectors, angle bisectors, medians, and altitudes. Next, we will look at the relationship of the sides of a triangle, how they relate to each other and how the sides of one triangle can compare to another.
## Summary
This chapter begins with an introduction to the Midsegment Theorem. The definition of a perpendicular bisector is presented and the Perpendicular Bisector Theorem and its converse are explored. Now that the bisectors of segments have been discussed, the definition of an angle bisector is next and the Angle Bisector Theorem and its converse are presented. The properties of medians and altitudes of triangles are discussed in detail. The entire chapter builds to a discovery of the relationships between the angles and sides in triangles as a foundation for the Triangle Inequality Theorem. The chapter ends with a presentation of indirect proofs.
### Chapter Keywords
• Midsegment
• Midsegment Theorem
• Perpendicular Bisector Theorem
• Perpendicular Bisector Theorem Converse
• Point of Concurrency
• Circumcenter
• Concurrency of Perpendicular Bisectors Theorem
• Angle Bisector Theorem
• Angle Bisector Theorem Converse
• Incenter
• Concurrency of Angle Bisectors Theorem
• Median
• Centroid
• Concurrency of Medians Theorem
• Altitude
• Orthocenter
• Triangle Inequality Theorem
• SAS Inequality Theorem
• SSS Inequality Theorem
• Indirect Proof
### Chapter Review
If $C$ and $E$ are the midpoints of the sides they lie on, find:
1. The perpendicular bisector of $\overline{FD}$.
2. The median of $\overline{FD}$.
3. The angle bisector of $\angle FAD$.
4. A midsegment.
5. An altitude.
6. Trace $\triangle FAD$ onto a piece of paper with the perpendicular bisector. Construct another perpendicular bisector. What is the point of concurrency called? Use this information to draw the appropriate circle.
7. Trace $\triangle FAD$ onto a piece of paper with the angle bisector. Construct another angle bisector. What is the point of concurrency called? Use this information to draw the appropriate circle.
8. Trace $\triangle FAD$ onto a piece of paper with the median. Construct another median. What is the point of concurrency called? What are its properties?
9. Trace $\triangle FAD$ onto a piece of paper with the altitude. Construct another altitude. What is the point of concurrency called? Which points of concurrency can lie outside a triangle?
10. A triangle has sides with length $x + 6$ and $2x - 1$. Find the range of the third side.
### Texas Instruments Resources
In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9690.
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Often metaphorically characterized as a camera, Flashbulb memory is very much like a photograph that arbitrarily seizes and preserves a scene (Swar & Kihlstrom, 2002). It is a scene that is defined by a particular kind of “memory, which forms only for highly surprising and highly consequential events (Swar & Kihlstrom, 2002).” These events vary from such instances like the explosion of the Space Shuttle Challenger on January 28, 1986 to the John F. Kennedy Assassination in November 22, 1963. These events are noted to be fixed in the mind for a long period of time so deep that it is perceived to be ultimately permanent. Flashbulb memories often result in one’s recollection in detail as to where they were, when the event happened, who told them, who was with them, what their emotional reaction, and so on. Brown and Kulik (1977) redefined the way many view the phenomenon of flashbulb memories. In their classic study, they asked participants, 40 black and 40 white Americans, whether they recalled vivid memories of hearing about various assassinations or attempted killings of national or international figures that had occurred within a decade. Such assassinations or attempts would include John F. Kennedy, Malcolm “X,” Martin Luther King, Gerald Ford, and Ted Kennedy. Brown and Kulik suggested that each individual has a physiological mechanism referred to as the now print that is elicited for events that are highly consequential and emotional to an individual. In short, they tested their hypothesis by comparing non-consequential events against consequential events. As a result, the John F. Kennedy assassination ranked the highest amongst White and Black Americans in consequentiality because it ultimately affected all families across the country regardless of race. In recent event, there has been much debate over Brown and Kulik’s theory of Flashbulb Memories. Criticisms arise from their claim that “these memories do not decay like memories for other events: they are always there, and unchanging (Wright, Gaskell, & O’Muircheartaigh 1998).” Substantial recall could also reflect the considerable amount of publicity through mass media that was reported at that time. These memories, in other words, can be encoded by means of rehearsal, repetition. Also, the quality of the responses and ability to vividly recall such crucial events give reasons for psychologists to dispute the accuracy and reliability behind this theory. Regardless, their research has enhanced the way we view the physiological makeup underlying memory recall. The increasing popularity of this subject allows researchers to learn more about this fascinating psychological process that is most likely to occur in any major event. Gender differences are widely studied in many research experiments; thus, we thought it might be interesting to see if there is any relation between gender and flashbulb memories. We often discuss visuospatial and episodic memories in relation to gender differences. In recent studies, there has been a clear gender distinction in episodic memory tasks between males and females (Herlitz & Yonker, 2002). Women tend to dominate in episodic memories as opposed to men who out perform women in accessing visuospatial memories (Herlitz & Yonker, 2002). In this study, we focus our attention to episodic memories primarily because it pertains to the recall and recognition of events. The presence of gender differences in episodic memories reflects in differences between men and women on other cognitive tasks (Herlitz & Yonker, 2002). Sehulster (1988) found that females were more likely to have a memory ability that was high on autobiographical memory as opposed to males (Goddard, Dritschel, & Burton, 1998). Sehulster suggested that females elicit a greater amount of access to emotional and autobiographical material by means of rehearsed and organized conversations. Males, on the other hand, often access factual information by means of conversation and in return results in the greater rehearsal and organization of verbal and factual material rather than autobiographical memories (Goddard, Dritschel, & Burton, 1998). This present study attempts to focus on gender differences in Flashbulb Memories regarding the recent event of September 11, 2001. It was a consequential event where hijacked jetliners hit the World Trade Center in New York and the Pentagon outside of Washington killing innocent people and turning the United States into turmoil. September 11th sparked the beginning of change and unity in the United Stages and is a day in which most Americans could never forget. Thus, factors such as age, interest, race, gender, and so on all have relevance to this study. We direct our attention to gender solely because of the availability of time and subjects at Loyola University. Females and males often differ in perceptions, interpretations, and tendencies to recall such incidents (Morse & Woodward, 1993). Although both genders clearly remember instances from this event, we hypothesize that females are likely to recall more specific events from September 11th than males simply because they have a greater access to episodic memories.
Participants A total of fifty-seven undergraduate students, freshmen through seniors, from Loyola University New Orleans volunteered to participate in the study. The age range was from 17 years of age to 37 years of age (mean age=19.91), twenty-five being males and thirty-one were females. Participants were recruited strictly by means of volunteer basis. Sampling strategies included posting up sign up sheets documenting information about the study and available times, convenience sampling, the Loyola University psychology department human participants’ pool, and by word of mouth where professors introduced studies being conducted in their various psychology classes. Materials Participants were asked to sign and date two consent forms, one for their records and the other one for the researchers’ records. The informed consent included the researchers’ names, email addresses, and phone numbers along with the sponsors’ contact information regarding any questions or concerns the participants may have. The form gave an overview of the experiments and outlined the participants’ rights and safety regarding the study. A questionnaire was the primary apparatus used for this study. There was a brief description of the study at the beginning. The questionnaire was divided into four sections. Part I asked for demographic information specifically asking participants their gender, age (in years), class status, and hometown (city, state, country). The second section was a free-recall portion where the participants were asked to write a narrative overview of their experiences and to describe in detail the vivid images that were portrayed from September 11, 2001. Such images would include location, initial reaction, emotions, thoughts and concerns, and so on. Hence, we asked participants to write down anything that came to mind; specifically, any details that they were willing to share. The statements read “Please specifically describe the details primarily surrounding you when you first learned that the United States had been attacked on September 11, 2001. Vividly depict as many features as possible from your recollection such as your specific location, your specific initial reaction, your means of notification, etcetera.” Part III was a simple multiple choice section containing four questions asking participants questions such as “How important did you feel these events were to you in your personal life,” “ How emotionally unprepared did you feel for these events,” and “How vivid do you consider your memories of the events to be.” For the previous questions participants were asked to circle one of the following choices: extremely, very, somewhat, not very, or not at all. The final section simply asked for approximate amount of hours of televised media coverage watched within one day during that period.Brown and Kulik’s (1977) method of coding was used for this study. Their “canonical” form included six categories of Flashbulb memories. Brown and Kulik suggested that an informant was most likely to report their “place” in which they learned of the event, the “ongoing event” that interrupted the event at that time, the “informant” who brought the news to their attention, the “affect of others” around them, their “own affect,” and the immediate “aftermath” of the event after learning about it. We also incorporated two other categories including the “time” in which the informant learned about the event, and “other specific people present” during the event. Design and Procedure
This study was a non-experimental, correlational design. Gender and amount of flashbulb memories from September 11, 2001 were the two variables being tested. As previously stated in the introduction, we hypothesize that females are more likely to recall more flashbulb memories than males are because of their episodic memory advantages. Although there was more than one way to code such flashbulb memories from the free-recall portion of the survey, we chose to use Brown and Kulik’s scale as a benchmark along with two other factors; time and others present. The multiple-choice questions provided information about the accuracy of the individual’s account of September 11, 2001. The questionnaire simply made an attempt to relate gender to flashbulb memories trusting that the participants were as honest as possible when answering them. Investigators placed sign up sheets on the Loyola Psychology Department bulletin board setting up different times and dates available for participants to sign up within a one-week period. The sign up sheets also included a description of the study and an approximate time frame of fifteen minutes necessary for study to be completed. When participants arrived at the scheduled classroom, they were greeted and then asked sit in any desk. Once seated, participants were each given a packet which including six pages of information; two being the informed consent forms and the other four composed of the questionnaire. After receiving the packet, participants were asked to briefly read through the consent forms allowing them the opportunity to ask any questions or concerns they might have. Once signed, the participants were allotted as much time as needed to complete the questionnaire. When completed, participants were asked to step outside the door while the others were still finishing up their questionnaires. While outside, participants were debriefed about the actual purpose of the study as well as counseling services that are available to them at any time if they were saddened or depressed from the questionnaire. Finally, there was a last call for questions and then the participants were allowed to leave. Other participants were randomly selected from Loyola University’s campus grounds. Investigators approached students sitting on campus benches and asked if they could spare fifteen minutes. Those participants who responded with a “yes” were given a packet that contained all the forms necessary for the study including the two informed consents and the questionnaire. Participants were asked to read through and sign the consent forms first before the questionnaire was administered. When completed, the participants were debriefed with appropriate information concerning the study and counseling services.
Results There were 56 total participants, 31 females and 25 males. We calculated the mean number of details that all female participants could recall and the mean number of details that male participants recalled. The independent groups t-test was used to compare the means of males (M=4.32, SD=1.57) and females’ (M=3.97, SD=1.47) ability to recall events from September 11, 2001. The overall results (t(54)=-.863, n.s.) indicated that there are no significant differences in flashbulb memories between males and females which ultimately indicated that our hypothesis was not supported. There were four multiple-choice questions on the questionnaire. The first question showed no significant difference between males and females asking how important the events were in relation to the participant’s personal life for females (M=2.26, SD=0.89) and males (M=2.12, SD=0.93). The second question referred to the emotional preparation of the individual for females (M=2.29, SD=.97) and males (M=2.72, SD=1.21). The third question referred to how vivid the individual felt his or her recollections of the events were for females (M=1.97, SD=.84) and males (M=1.80, SD=.71). The final question asked the individual to rate his or her emotional intensity of the event for females (M=2.32, SD=.75) and males (M=2.32, SD=1.22). We hypothesized that because females would recall more than males, females would also have a higher ratings on specific questions relating to emotional significance and vividness of the event. As a result, all four multiple choices showed that there is no significant difference in responses between males and females (Table 1).
The results did not support the hypothesis that stated females would have more recollection and flashbulb memories from September 11, 2001 than would males. According to the results, there was no significant difference between the male and female participants in this study. In addition, a significant difference did not appear between the recall of males and females in answers for the four multiple-choice questions in the questionnaire. Brown and Kulik (1977) coined a biological explanation that claims the brain elicits a “now print” mechanism. Due to this “now print” mechanism, an individual is able to remember personal jolts or memories of crucial events when they were initially learned or heard about. Brown and Kulik ultimately revolutionized the way many perceive flashbulb memories and has sparked a greater interest among others psychologist in this theory. Regardless, Brown and Kulik (1977) did not specifically focus on gender differences but rather focused on proving that flashbulb memories do ultimately exist. Other researchers such as Morse, Woodward, and Zweigenhaft (1993) attempted to show that gender differences in flashbulb memories might actually exist but only for particular consequential events that affect or target one gender more than the other. Their study was based on the Clarence Thomas Hearings in 1991, which dealt with Thomas’s sexual harassment of Anita Hill. This case sparked national attention because it was one of the first harassment cases against women recognized. In this study, females did report more autobiographical facts from the case than men did. This is apparent because sexual harassment and abuse occurs far more often towards women than men. Hence, this may be the reason why women recalled more information from the event than men did. The present study measured as many variables as possible including hometown and age along with the individual’s gender. There are many problems that may have occurred while the research study was conducted. On one hand, the study may have been carried out for a longer than necessary period of time. Sessions ran at Loyola University for a week and a half. Within that period, students who have taken the questionnaire may have revealed the purpose of the study within their classes to other participants prior to the study. On the other hand, some students might have taken the surveys more seriously than others did. The small sample size may have also influenced the results. Although the number of males and females who participated in the study was similarly equal, a larger sample size may be able to shift the results one way or the other. A large problem factor might also be present in the validity of the individual responses. The free response question was left open-ended allowing participants to write as much information as possible. There is no concrete method of verifying each individual’s recollection. Thus, the information written down was seen as reliable “recollections” and was recorded as data. If this research were conducted as well as Neisser and Harsh’s (1992) study on Flashbulb Memories and the Challenger Explosion, validity would have been easily established. Neisser and Harsch (1992) attempted to test the accuracy of flashbulb memories by performing two tests, one right after a consequential event (Challenger explosion) and the other 32-34 months after the event. One hundred and six participants were surveyed twenty-four hours right after the event occurred. Under three years later, forty-four subjects were asked to recall this information once again. As a result, they found discrepancies between the two sets of recollections especially from those who felt confident in their answers. Specifically, 25% of the subjects were wrong about every recollection and only three were perfectly correct. The free recall section was specifically coded to fit the investigators’ interpretation of what actually defined a flashbulb memory. For instance, most participants remembered a location in which they learned about the event. Thus, in our opinion, the plain answer school did not constitute as a flashbulb memory unless the participant specified a class such as English or Biology, an office location such as the principal’s or counselor’s office, the bathroom, and so on. The canonical category of time was included and surprisingly enough there were some participants who remembered the specific time they had heard of the news. Some participants failed to respond to what the question really asked. Some misconstrued flashbulb memories to be the memory of the central newsworthy portion, which pertained to hijackers taking over the planes that hit the twin towers rather than discussing the memory for the circumstances in which they first heard or learned about the event. Unfortunately, these problems may have influenced our data results. Questionnaires with central newsworthy information were obviously irrelevant. In addition, there is no indication that shows that the participants either did not specifically remember the detailed account such as location and time or just failed to mention it. For further research purposes, there are many ways this study can be improved. First, there should be a larger amount of participants. I would estimate a range from one hundred to one hundred fifty participants would give great results if not more. Second, I would suggest testing gender differences and flashbulb memories for another consequential event rather than September 11, 2001. I would choose an event that sparked national attention for a long time but not as big as September 11, 2001. September 11th was an event too powerful that no one regardless of gender could ever forget. Lastly, I would suggest that this study be conducted at a large university where psychology classes are large and there are many unfamiliar faces in the participants’ pool. That would alleviate leaks about the purpose of the study. Obviously, both males and females clearly remember instances from September 11th. These instances differ from individual to individual. It is information that only he or she could remember. In our results, some did remember more than others. It would be hasty to underestimate males’ ability to recall such vivid memories since such an occurrence affected almost everyone individually. Although there were no significant results in this study, it was really interesting to experiment with flashbulb memories and learn about its outcome among college men and women. It increases one’s awareness about the human mind and its ability to encode such memories during a traumatic event. As far as contribution to science, this research study proposes a challenge to dig deeper and understand that there are differences among men and women that may not be apparent in our study but are clearly obvious in other types of studies. Genetic factors or even environmental factors might influence us as human beings today. In essence men and women are somewhat engineered differently to face different types of situations. Thus, an event that is more crucial to one gender over the other will create reactions, thinking, and memories that will ultimately be different. In context, one gender will remember more from that event than the other will. The theoretical implications behind flashbulb memories and the “now print” mechanism may never prove to be true, but it allows one to apply this information to the real world. Our study primarily focused on college students and their recollections during September 11, 2001. How would these recollections differ among students in high school or even those in grammar school? Would age play a large factor in how much we recall from an event such as this? Our study wanted to enhance people’s knowledge about flashbulb memories and prove that they do in fact affect our everyday lives. Although there were many that were indirectly affected by this event, there are those number of families who were directly targeted emotionally by this event. Those families who were victims of September 11th have no choice but to remember the day that their son, daughter, cousin, father, mother, and so on fell prey to terrorist attacks. This was a national tragedy that sparked attention world wide, and it is a day that most can never forget, only remember.
REFERENCES Brown, R., & Kulik, J. (1977). Flashbulb memories. Cognition, 5, 73-99.Goddard, L., Dritschel, B., & Burton, A. (1998). Gender differences in the dual-task effects on autobiographical memory retrieval during social problem solving. British Journal of Psychology, 89, 611-628.Herlitz, A., & Yonker, J. (2002). Sex differences in episodic memory: The influence ofintelligence. Journal of Clinical and Experimental Neuropsychology, 24, 107-114.Morse, C., & Woodward, E. (1993). Gender differences in flashbulb memories elicited by the Clarence Thomas Hearings. Journal of Social Psychology, 133, 453- 459.Neisser, U., & Harsch, N. (1992). Phantom flashbulbs: False recollections of hearing the news about Challenger. In E. Winograd & U. Neisser (Eds.), Affect and accuracy in recall: Studies of “flashbulb memories” (pp.9-31). Cambridge, England: Cambridge University Press.Swar, M., & Kihlstrom, J. (2002). Flashbulb Memories: Historical and personal memories and flashbulb quality. Retrieved October 20, 2003.Wright, D., Gaskell, G., & O’Muircheartaigh, C. (1997). The reliability of the subjective reports of memories. European Journal of Cognitive Psychology, 9, 313-323.
Description: The purpose of this study is to research the ability to recall flashbulb memories of the terrorist attacks on September 11, 2001.
Part I: Demographic Information
1. Please circle your sex:
2. Age (In Years)_________________
3. Please circle your class status:
Freshman Sophomore Junior Senior
4. Hometown (city, state, country)___________________________
Please specifically describe the details primarily surrounding you when you first learned that the United States had been attacked on September 11, 2001. Vividly depict as many features as possible from your recollection such as your specific location, your specific initial reaction, your means of notification, etcetera.
Part III: Please circle one of the following choices.
1. How important did you feel these events were to you in your personal life?
A. Extremely Important
B. Very Important
C. Somewhat important
D. Not very important
E. Not important at all
2. How emotionally unprepared did you feel for the events of September 11, 2001?
A. Extremely emotionally unprepared
B. Very emotionally unprepared
C. Somewhat emotionally unprepared
D. Not very emotionally unprepared
E. Not emotionally unprepared at all
3. How vivid do you consider your memories of the events to be?
A. Extremely Vivid
B. Very Vivid
C. Somewhat Vivid
D. Not very vivid
E. Not vivid at all
4. Please rate the emotional intensity of the event for you personally?
A. Extremely emotional
B. Very emotional
C. Somewhat emotional
D. Not very emotional
E. Not emotional at all
1. Approximately how many hours of televised media coverage did you watch within one day during that period?
______________ (in hours)
TablesMean Scores on Survey Questions (Responses on a Scale of 1-5, 5 being the highest) Mean (Male) Mean (Female) Standard Deviation (Male) Standard Deviation (Female) tQuestion 1 2.12 2.26 .93 .89 .563, n.s.Question 2 2.72 2.29 1.21 .97 -1.475, n.s.Question 3 1.80 1.97 .71 .84 .799, n.s.Question 4 2.32 2.32 1.22 .75 .010, n.s. | <urn:uuid:d0c2387c-bf62-43f2-ab06-6d9b9531e479> | {
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Given this sort of disagreement in 1787, it’s no surprise that as the House has debated impeaching President Trump — culminating in Wednesday’s vote — the discussions have produced reams of commentary and analysis. As we plumb the historical record to understand what misdeeds impeachment was intended to address, we also should consider why and how we know it. The texts that describe impeachment, essential to our debate, are accessible because of a collective commitment to accountable and transparent government — and the work of archivists, librarians, documentary editors and historians, to preserve its records. Like impeachment itself, the preservation of and access to historical records is a key check on power.
One source is obvious: The Constitution of the United States lays out the responsibilities and role of each branch of the federal government in a presidential impeachment. In Article 1, Section 2, the House of Representatives “shall have the sole Power of Impeachment.” In Article 1, Section 3, the Senate “shall have the sole Power to try all Impeachments.” In Article 2, Section 2, the president “shall have Power to grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment.” In Article 2, Section 4, “The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.” The Constitution is housed at the National Archives, which not only preserves the document and makes it available for visitors but also hosts transcription and images for download online.
Lawyers, journalists and historians working to contextualize and interpret the Constitution’s brief depictions often turn to the later writings of convention delegates, including the Federalist Papers, written in 1787 and 1788 during the effort to gain ratification of the new constitution, the text of which the Library of Congress hosts online through Congress.gov. In these essays, Alexander Hamilton and James Madison offered thoughts on the president’s powers, including how that power would be checked. In Federalist 69, for example, Hamilton argued that impeachment was what separated a presidency from a monarchy. These essays can help us to understand how the thinking of men like Madison and Hamilton evolved, and even how they differed on issues including impeachment.
Another key resource is the contemporary records of debate at the constitutional Convention of 1787, when delegates considered, defined and refined impeachment. Over 16 weeks, between May and September of 1787, delegates hashed out the structure and function of the federal government. Through Madison’s views, Pinckney’s views and those of others, we can discern how impeachment, as articulated in Articles 1 and 2, came to be defined.
The delegates debated the very complex, weighty issues that we’re still debating today: whether a process could be fair and effective enough to overturn the results of an election; whether the transgressions to trigger such a process should be precisely defined or left to the circumstances; whether the Senate or another body should convene the trial (they all agreed the House should be the locus for impeachment itself). Into September 1787, for example, they were still debating whether the Senate was the right venue to try an impeachment, rather than the Supreme Court, with the delegates arguing about which institution would be more beholden to the president and thus less likely to manage the case with integrity.
While commentators are raising these points daily, you don’t have to take their — or my — word for it. People can read for themselves how the delegates debated and voted on every clause pertaining to impeachment. Thanks to much labor and determination, contemporary manuscript sources, written in iron gall ink on 18th-century paper, are now available in more widely accessible and understandable forms like bound volumes and digital platforms.
The records of the Constitutional Convention include the original Journals of the proceedings, kept by Secretary William Jackson and the notes of various delegates, most crucially Madison. The Journals are at the National Archives, along with other records including official credentials of the delegates. Images of these can be viewed online via Fold3.com, an Ancestry.com company focused on military records.
Jackson took care with recording procedural motions and vote tallies, while Madison aimed to represent a fuller sense of the arguments and positions advanced by the delegates — quite possibly to keep his friend Thomas Jefferson, then abroad as the ambassador to France, informed. Madison’s detailed notes are at the Library of Congress where high-resolution images are available online. Only a few other delegates kept notes during the convention that have survived, in theory because the proceedings were meant to be confidential. James McHenry’s notes for August and early September provide the only other information about the final debates.
In 1911, historian Max Farrand brought together all of these materials in a three-volume set, which remains an indispensable resource, allowing us to see for any individual day what the journal records, and what Madison and any of the other note takers recorded. This helps track the development of issues such as impeachment over time. Sept. 8, 1787, for example, was a busy day. Jackson recorded in the “journal” that on presidential impeachment, delegates voted 7 to 4 to insert the words “or other high crimes and misdemeanors against the State” after the word “bribery.” But “to strike out the words ‘by the Senate’ ” failed on a vote of 9 to 2. Madison’s notes record a vigorous renewal of the debate about whether the Senate was the right venue for an impeachment trial. He was a vocal opponent and one of the “no” votes.
Madison reiterated that he “would prefer the supreme Court for the trial of impeachments, or rather a tribunal of which that should form a part.” Gouverneur Morris, however, argued that the Supreme Court was inappropriate, as they were “too few in number and might be warped or corrupted.”
Farrand’s original three volumes are available in multiple online locations, including the Library of Congress’s American Memory project and on archive.org, where they can be downloaded in various formats. Their importance is hard to overstate; in 2012, the George Washington Law Review devoted a special issue to commemorating their centennial, with an introduction and a Q & A about textualism co-authored by Supreme Court Justice Antonin Scalia, and an invaluable essay about the structure and intent of the various convention records by historian Mary Sarah Bilder.
But scholars have not stopped trying to glean a better understanding of the debates at the Constitutional Convention. In 1987, for the bicentennial of the Constitution, the head of the manuscript division at the Library of Congress, James H. Hutson, added a key “Supplement to Max Farrand’s Records” with newly available material. Many of those documents can also now be read and downloaded at Founders Online, a resource that makes freely available and fully searchable more than 180,000 items from the edited and annotated papers of six founders.
Tellingly, the final decision of the Constitutional Convention was the disposition of its records. After the delegates had voted to adopt the Constitution and to initiate the ratification process, George Washington raised the question of “what the Convention meant should be done with the Journals & c.” The last vote William Jackson recorded, on the final convention day, Sept. 17, 1787, was “To deliver over the Journals and papers to the President.” The State Department became the first repository for the records of the federal government.
That we know about the intense debate about impeachment at the founding is the result of the long-standing commitment to keeping, preserving and making accessible America’s government and key historical records. It is the work of professional archivists, librarians, documentary editors, historians, Web developers and more. It is funded by a combination of private foundations and public investment, crucially by such institutions as the National Archives, the National Endowment for the Humanities and the Library of Congress.
That we can read and study the Constitution and the convention debates reminds us that accountability and transparency are critical democratic values and critical democratic practices. As the country takes up one of the most consequential actions imagined by the framers of the Constitution, let us also understand this key feature of democracy: Access to reliable information requires consistent caretaking. It is not only journalists, politicians or historians — all of whom are vocal in their need for access to these materials — but also every American whose investment is repaid by access to our history. We should not only advocate for funding for these projects but also recognize that making records as readily available as possible is essential because they are, and will continue to be, crucial to the very form of governance they document. | <urn:uuid:dd6ee050-3ee4-4693-96ea-e01a8b2b2f08> | {
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Buy that special someone an AP Physics prep book, now with 180 five-minute quizzes aligned with the exam: 5 Steps to a 5 AP Physics 1
Visit Burrito Girl's handmade ceramics shop, The Muddy Rabbit: Yarn bowls, tea sets, dinner ware...
## 29 August 2011
### Equilibrium: quantitative demonstrations (or, how I teach vector math without teaching vector math)
That's a 2 N weight hanging by two strings. The left-hand rope passes over a pulley to a 1 N weight; the diagonal rope is attached to a digital scale at the top of the picture.
In Honors or AP Physics, I begin the year with equilibrium, not with motion. In a few days, the class gets comfortable with free body diagrams, forces, and two-dimensional vector analysis.
Next comes motion in one dimension (graphs first, then algebra), followed by projectile motion. Finally, we cover Newton's second law. Since we did equlilibrium already, students are comfortable with free body diagrams and writing a vector sum of forces; since we did motion already, they already have some idea of what acceleration is. Rather than a tough *new* topic, the second law becomes a way to review and solidify the first two topics.
The picture shows my third or fourth demonstration of the school year. We begin by equating horizontal tensions in ropes pulling on a stationary block. Next, I hang a 200 g mass vertically to find the tension in the supporting rope. Easy stuff, so far.
And then, I attach a horizontal rope over a pulley attached to a 1 N weight. (In the picture, the hanging weight on the left is below the table, and out of the frame.) When we make the free body diagram, everyone's comfortable with the weight of the 2 N weight acting down, and the horizontal rope pulling leftwards. We draw the arrow representing the diagornal rope's force at an angle, of course. Then what?
The class has already been taught that in equilibrium, up forces = down forces and left forces = right forces. I ask, which is this diagonal rope, an up force or a left force? Someone always comes up with a reasonable answer: "both." I redraw the free body diagram, with the tension in the diagonal rope replaced by two arrows, one up, and one to the side.
The class is totally comfortable with the upward component being equal to the mass's weight of 2 N; and with the leftward component being equal to the weight hanging over the pully of 1 N. (They're also totally comfortable with me using the term "component" without preamble.) It only takes a suggestive diagram to get someone to suggest that the resultant tension in the rope itself will be not 2 N + 1 N, but the pythagorean sum of 2.2 N.
The clincher comes when I call a student to the front to read the digital scale attached to the rope. It reads... 2.2 N. Physics works. I can even predict (and then measure) the angle made by the diagonal rope.
The key to this whole process is that I'm *not* just telling the class how to solve abstract vector addition problems. I'm not telling them anything at all, really; I'm drawing diagrams and asking questions, getting someone in the class to suggest the next step wherever possible. I model the correct problem solving method for equilibrium problems on the board, of course, but everything I do flows naturally from the fundamental principles of equilibrium: up = down, left = right. I don't use any words like "vector" or "reference frame" or "coordinate system." The only technical term I'm introducing is "component," which was introduced organically.
The final demonstration with this setup involves adding a "mystery weight" to the stuff hanging over the pulley. I measure the new angle that the diagonal rope makes, so I have a chance to suggest how to use sines and cosines to "break an angled force into components." We predict the reading in the spring scale, and the amount of mystery weight that I added. Once again, physics works. | crawl-data/CC-MAIN-2019-43/segments/1570986684854.67/warc/CC-MAIN-20191018204336-20191018231836-00059.warc.gz | null |
# If 2 Tables and 3 Chairs Cost Rs. 3500 and 3 Tables and 2 Chairs Cost Rs. 4000, then How Much does a Table Cost?
### Computer MCQs Series for PPSC, FPSC – Most Repeated MCQs | Set 6
What are you looking for? Let’s dig in quickly
## Explanation
• If 2 tables and 3 chairs cost Rs. 3500.
• 3 tables and 2 chairs cost Rs. 4000
Then price of a table can be calculate as;
Let suppose “t” shows price of a table and “c” price of a chair. Now 2t + 3c will be equal to Rs. 3500;
2t + 3c = 3500 ________ (i)
In the same way; 3 tables and 2 chairs will be equal to Rs. 4000;
3t + 2c = 4000 ________ (ii)
Now; we have two equation and by solving them simultaneously we can easily figure out the price of a table.
## To Find
Price of a table = ?
## Solution
Let suppose
Price of a chair = c
Price of t table = t
Now;
2t + 3c = 3500 ________ (i)
3t + 2c = 4000 ________ (ii)
Multiplying both sides of equation (i) with 2 and equation (ii) with 3.
4t + 6c = 7000 ________ (iii)
9t + 6c = 12000 ________ (iv)
Subtracting equation (iv) from (iii)
5t = 5000
## Conclusion
If 2 tables and 3 chairs cost Rs. 3500 and 3 tables and 2 chairs cost Rs. 4000, then price of a table would be Rs. 1000. | crawl-data/CC-MAIN-2023-50/segments/1700679100452.79/warc/CC-MAIN-20231202203800-20231202233800-00154.warc.gz | null |
Although the amount of time that a whale can hold its breath varies by species, the beaked whale can hold its breath for up to 2 hours. The sperm whale can hold its breath for up to 90 minutes.
The secret to the whale's capability for holding its breath lies in its specially developed breathing system that allows it to absorb up to 90 percent of the oxygen breathed in. By contrast, humans only absorb around 15 percent.
According to the University of California, Santa Barbara ScienceLine, whales breathe in through blowholes on the tops of their heads. Because the whale only breathes at the surface, it has evolved with the ability to choose when to breathe and cannot breathe underwater. | <urn:uuid:e9ec1b1d-fb32-4727-9bec-eb6251312a4b> | {
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cerebral cavernous malformation
Cerebral cavernous malformations are collections of small blood vessels (capillaries) in the brain that are enlarged and irregular in structure. These capillaries have abnormally thin walls, and they lack other support tissues, such as elastic fibers, which normally make them stretchy. As a result, the blood vessels are prone to leakage, which can cause the health problems related to this condition. Cavernous malformations can occur anywhere in the body, but usually produce serious signs and symptoms only when they occur in the brain and spinal cord (which are described as cerebral).
Approximately 25 percent of individuals with cerebral cavernous malformations never experience any related health problems. Other people with this condition may experience serious signs and symptoms such as headaches, seizures, paralysis, hearing or vision loss, and bleeding in the brain (cerebral hemorrhage). Severe brain hemorrhages can result in death. The location and number of cerebral cavernous malformations determine the severity of this disorder. These malformations can change in size and number over time.
There are two forms of the condition: familial and sporadic. The familial form is passed from parent to child, and affected individuals typically have multiple cerebral cavernous malformations. The sporadic form occurs in people with no family history of the disorder. These individuals typically have only one malformation.
Cerebral cavernous malformations affect about 0.5 percent of the population worldwide.
The precise functions of these genes are not fully understood. Studies show that the proteins produced from these genes are found in the junctions connecting neighboring blood vessel cells. The proteins interact with each other as part of a complex that strengthens the interactions between cells and limits leakage from the blood vessels. Mutations in any of the three genes impair the function of the protein complex, resulting in weakened cell-to-cell junctions and increased leakage from vessels as seen in cerebral cavernous malformations.
Mutations in these three genes account for 85 to 95 percent of all cases of familial cerebral cavernous malformations. The remaining 5 to 15 percent of cases may be due to mutations in unidentified genes or to other unknown causes. Mutations in the KRIT1, CCM2, and PDCD10 genes are not involved in sporadic cerebral cavernous malformations. The cause of this form of the condition is unknown.
This condition has an autosomal dominant pattern of inheritance, which means one copy of the altered gene in each cell is sufficient to cause the disorder. In the familial form, an affected person inherits the mutation from one affected parent.
Most people with cerebral cavernous malformations have the sporadic form of the disorder. These cases occur in people with no history of the disorder in their family.
These resources address the diagnosis or management of cerebral cavernous malformation:
These resources from MedlinePlus offer information about the diagnosis and management of various health conditions:
- central nervous system cavernous hemangioma
- cerebral cavernous hemangioma
- familial cavernous hemangioma
- familial cavernous malformation
- familial cerebral cavernous angioma
- familial cerebral cavernous malformation
- intracerebral cavernous hemangioma
- Boston Children's Hospital: Cavernous Malformations
- Disease InfoSearch: Cerebral Cavernous Malformation
- Johns Hopkins Medicine
- MalaCards: cerebral cavernous malformation, familial
- Massachusetts General Hospital Neurovascular Center
- Orphanet: Cerebral cavernous malformations
- University of Toronto Brain Vascular Malformation Study Group | <urn:uuid:376504b9-4f54-4d4e-acbd-31b2aa9609a6> | {
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Last October geographer Luis Andueza clambered into a battered, motorized dugout canoe in Nueva Unión, a village on Peru’s Chambira River. The boatman yanked a starter cord, and the rusty outboard sputtered to life. “Watch out for snakes,” called a villager in Spanish from a dock. “Are there many?” Andueza yelled back.
Andueza was heading out for a slog through a swamp where pit vipers patrol the undergrowth and carnivorous caimans, hidden in dark pools, eye passersby. Andueza, a researcher at the University of St. Andrews in Scotland, studies how the Urarina people, a tribe of several thousand individuals, use the wetlands here. Scientists have discovered that this Kentucky-size territory contains an enormous underground cache of carbon, in the form of peat—partially decomposed plant matter. Katherine Roucoux, principle investigator of Andueza’s research, says keeping that carbon in the ground “is a very important thing.” If the peat dries, it will decompose—or catch fire—releasing huge amounts of carbon dioxide into the atmosphere.
And Andueza’s work shows that the peatlands’ fate might rest on whether the Urarina continue their traditional harvesting of the trees for food, fiber, and fuel, or leave that life behind as young adults are tempted to move out and join Peru’s encroaching modernism.
Don’t Drain the Swamp
An event two decades ago on the other side of the globe alerted scientists to just how greatly peatlands can exhale carbon when they are developed. In 1997—and again in 2015—huge tracts of peat in Indonesia went up in flames. Palm oil farms had drained the perpetually soggy, carbon-rich soil, and dry peat burns easily. A carelessly quenched campfire can ignite a raging wildfire. According to calculations published after the fires, the 1997 conflagration gave off between three billion and almost 10 billion metric tons of carbon dioxide, measurably increasing the concentration of the climate-warming gas in the atmosphere. Climate scientists began issuing warnings that the world’s other two big tropical peat deposits—in the Congo and Amazon basins—could suffer the same catastrophic fate.
Researchers have determined that the Peruvian region known as the Pastaza-Marañón Foreland basin contains the largest peat swamp in the Amazon, stabilizing about three billion metric tons of captured carbon. That amount is twice as much as what the U.S. releases each year by burning oil, gas and coal.
No one had previously tried to gauge the chance that the basin’s lands could suffer the same fate as those in Indonesia. “They’re not ideal candidates” for industrial agriculture, says Roucoux, a paleoecologist at St. Andrews. “It doesn’t seem like a very likely thing to happen now.” The wetlands are remote and distributed in patches between higher dry ground. But, she warns, new highways on the drawing board for the region could make them accessible, and future demand for arable land might make them desirable. “It can happen,” Roucoux says. “If it’s economically viable, people can do it.”
The key question is: Would the region’s indigenous residents—the Urarina that Andueza studies, along with the Kichwa, Achuar, and Kandoshi and other indigenous groups—allow development? Manuel Martín, director of the Research of Amazonian Societies program at the Research Institute of the Peruvian Amazon and one of Andueza’s collaborators, says that although the Urarina find swamps unpleasant, they need the land for hunting and for obtaining culturally important plants. Urarina women weave intricate sleeping mats and death shrouds with fiber from the leaves of the aguaje, a palm tree harvested mostly in peat swamps. Learning this craft is a rite of passage when girls reach puberty. As long as their traditions remain intact, Martín says, they “won’t let anyone in who will damage” their soggy jungles.
A Bountiful Tree
An hour upstream of Nueva Unión, Andueza’s boatman, José Inuma Macusi, shut his engine, grabbed his machete and leaped onto a dirt bank, slinging a single-barrel shotgun over his shoulder. Andueza, trailing behind, could have passed for Indiana Jones if he shaved his beard and picked up a whip; he wore a chocolate-brown safari shirt and a wide-brimmed waxed hat. The two sloshed through thickets of short, wrist-thick trees, along muddy trails that Inuma said had been worn down by tapirs (somewhat akin to wild boars). He had brought the gun, he said, hoping he might spot one.
At intervals, the walkers came across aguaje trees as straight and stout as telephone poles and twice as tall. In season, they hang heavy with clusters of a sweet, plum-size fruit that the Urarina eat and sell to traders. Inuma spied an aguaje with a spear-shaped bud enclosing the palm’s immature leaves. Urarina women boil the juvenile fronds to extract the filaments they twist into balls of weaving twine. With a few powerful machete whacks, Inuma felled the tree and carried off an armload of prizes.
Andueza says that indigenous uses of peatlands—harvesting fruit, fiber, medicinal plants and edible grubs, as well as hunting tapirs and monkeys—generate powerful incentives for the Urarina to protect their waterlogged territory. They are also tied to the land through their belief that stern spirits, known in Spanish as dueños (owners) or madres (mothers), exist there.
But Andueza is seeing indications that the Urarina are becoming unmoored from their traditional ways—after centuries of holding out against modernism brought in by successive waves of Jesuit priests, evangelist missionaries, rubber barons and the Peruvian state. Most young people now appear to reject drinking a hallucinogenic potion called ayahuasca, a practice Andueza calls “an important part of what being Urarina is.” Now “they don’t know anything. They don’t know our life,” laments Medardo Arahuata Manisari, one of Nueva Unión oldest inhabitants. Andueza’s collaborator Martín says the Urarina risk losing their identity, which has global consequences. “If they lose their knowledge, the peat is in danger,” he adds.
Apart from the local activity of the Urarina, other indigenous groups and some nonindigenous people, the Pastaza-Marañón peatlands remain in nearly pristine condition. National and regional parks already protect 24 percent of the basin’s peatlands. No companies appear poised to drain the land for industrial plantations, as had occurred in Indonesia. But Roucoux worries that someday oil palm harvesters or other farmers will target the area for development. The healthy indigenous communities and their attachment to the land could determine whether its carbon will stay safely stored in the ground.
Roucoux adds that climate change could also potentially dry the peat and release the cache of carbon. Some of her colleagues are building computer models to study that possibility.
Ripe for Change
In late 2018 the entire population of Nueva Unión, including 50 families, relocated from a more isolated site on a small tributary of the Chambira, several hours upstream. Andueza says the community’s younger residents favored the move, which the elders opposed. The new generation wanted easier access to nonindigenous trading towns downstream, such as Ollanta and Nauta. And South American oil company Pluspetrol, whose pipeline crosses Urarina territory, offered them incentives to move. The old town had highlands that remained dry year-round, where the Urarina farmed staples such as yucca and plantains. The new location floods completely for months every year, so such crops cannot grow there. Now the community buys these necessities from traders, accelerating what Andueza calls a “commodification of their existence.”
Beyond collecting rent for the pipeline’s right-of-way and payments for keeping that corridor clear of brush, Nueva Unión’s residents have few sources of money. But their needs for cash, for buying everything from outboard motors to music downloads for flip phones, is increasing. In the future, what might they trade for goods?
The cruel irony, Martín says, is that the Urarina have been “more resistant” to pressure to abandon their customs and language than any of the other indigenous peoples occupying the peat swamps. If they cannot withstand the gravitational pull of modern Peruvian society, it is hard to imagine that any local group can, Andueza says. “It’s all in flux right now.”
Andueza says that maybe the Urarina will find a way to support themselves without abandoning or degrading their swamps. One entrepreneur in Iquitos, a city on the edge of the Pastaza-Marañón region, is promoting the market for aguaje fruit, which, he predicts, could be the next superfruit. He says that increased aguaje harvesting could both preserve the peatlands and support the people who live by them. Andueza has his doubts about that assertion, though. Indigenous people have rarely come out on top in more than 100 years of rubber and timber booms. “Who’s likely to end up using this environment for their advantage?” he says. “I don’t think it is likely to be the indigenous people.” | <urn:uuid:1a9cf64a-4357-47d9-b961-800fac9304b7> | {
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The Blaine Amendment was proposed in 1875 by James G. Blaine, a Republican Congressman from Maine and future presidential candidate. It was an amendment to the federal Constitution that would forbid the public funding of private, denominational schools. The proposal was never voted upon and did not become part of federal law, although several states did put similar provisions in their state constitutions.
The Blaine Amendment read:
- No State shall make any law respecting an establishment of religion or prohibiting the free exercise thereof; and no money raised by taxation in any State for the support of public schools, or derived from any public fund therefore, nor any public lands devoted thereto, shall ever be under the control of any religious sect, nor shall any money so raised or lands so devoted be divided between religious sects or denominations.
The Constitutional amendment passed the House by a vote of 180 yeas and only 7 nays, but failed by 4 votes in the Senate to obtain the required 2/3 margin for a Constitutional amendment and never became federal law. The Blaine amendment became pivotal in state debates on the role of religion in public education, religious establishment, and religious expression for the next thirty-five years, and is a live issue in the 21st century.
Read (2004) examines the role of the GOP in creating a series of state public school systems in the North and West that were strongly shaped by Protestantism. To achieve this goal, Republicans supported amendments, legislation, and regulation in both national and state governments. In the South Bourbon Democrats drafted and ratified constitutions which restricted public funding of denominational schools to keep blacks and poor whites from access to education and the polling place. By 1911, about 30 states had a Blaine-like amendment in their state constitutions.
The majority of new immigrants 1880-1910 were Roman Catholics German Lutherans or Jews who represented non-pietistic religious values. As pietistic Protestants found their political power challenged by these newcomers, they sought to prevent the emergence of an unamerican (or un-republican) presence. In 1890, however, the GOP suffered heavy losses in part because of the issue of parochial schools. In 1896 William McKinley supported pluralism, promising all ethnic and religious groups would prosper and none would be the target of hostile federal action.
The issue came alive in the 21st century as evangelical and Catholic churches operating their own parochial schools wanted a voucher system so that parents could get state tuition money to attend these schools. A large majority of states already provide some limited kinds of aid to religiously-affiliated private schools, but vouchers are highly controversial, primarily because they are opposed by teacher unions.
- Deforrest, Mark Edward. "An Overview and Evaluation of State Blaine Amendments: Origins, Scope, and First Amendment Concerns." Harvard Journal of Law & Public Policy. Volume: 26#2 2003. pp 551+. online version
- Green, Steven K. "The Blaine Amendment Reconsidered," The American Journal of Legal History, Vol. 36, No. 1 (Jan., 1992), pp. 38-69 in JSTOR
- Read, Margery. "The Blaine Amendment and the Legislation It Engendered: Nativism and Civil Religion in the Late Nineteenth Century." PhD dissertation U. of Maine 2004. 248 pp. DAI 2005 66(1): 314-A. DA3159835
- Viteritti, Joseph P. "Blaine's Wake: School Choice, the First Amendment, and State Constitutional Law," Harvard Journal of Law & Public Policy, Vol. 27, 2003. | <urn:uuid:b42117d3-738c-4ba3-9649-11e366b9df02> | {
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# Assignment 2: Completing the Parabolic Square
## Motivation
In high school mathematics, one common task is graphing a parabola, commonly given in the form
y = x^2 + Bx + C
Searching Google on graphing parabolas found about 167,000 results, including Clayton State, and Regents Prep, and Sparknotes, and many many more. Quickly glancing through the results, the top few suggest making a data table, and then connecting points with a smooth curve. While this accomplishes the task, it doesn't give us any feel for shape. Graphing Calculator can easily plot parabolas for us. This Graphing Calculator file produced the following window. It's tough to see similarities when the equations are in this form, and we have to work to find the vertex.
There's a much better way to show the vertex, but to do so we need a different representation. We can complete the square! Unlike the name of this reference website, the math may not be fun, but it is very useful. To complete the square in the equation above:
y = x^2 + Bx + C = x^2 - 2 ~ \left( - \frac{B}{2} \right) ~ x + C
y = \left[ x^2 - 2 ~ \left( - \frac{B}{2} \right) ~ x + \frac{B^2}{4} \right] + C - \frac{B^2}{4}
y = \left[ x - \frac{B}{2} \right]^2 + \left(C - \frac{B^2}{4} \right)
We have two numbers to manipulate, one inside the square and one outside. It's a little awkward, because inside the square we have a minus and outside we have a plus, but mathematical equations aren't always beautiful and neat. To make things easier, let's call the value inside H and the value outside V. This makes our equation
y = \left[ x - H \right]^2 + V
## Graphs for H and V
Let's start by examining one graph in Graphing Calculator, y = \left[ x - 2 \right]^2 + 1.5 . The red dot indicates the vertex, which lies at x = 2 and y = 1.5, right on H and V.
You might be suspicious that I specifically chose 2 and 1.5, so let's look at other values of H and V. In all five cases shown, the vertex lies at the point (H, V).
If you like, you can experiment with various values of H and V through a GeoGebra Java applet. Click through to the handv.html page. Once the applet loads, you can click on the play button towards the bottom to watch an animation, which then becomes a pause button to stop. Alternatively, you can click on the H and V buttons on the bottom to drag them around the space.
## Mathematics of the Vertex
Now that we've seen the relationship graphically, we can find the vertex mathematically. The value of Y sums the constant V and the value of \left[ x - H \right]^2 . We're working with real numbers, so the value of the square is never negative, and will be minimized when \left[ x - H \right] = 0 . This minimum occurs at x = H. At this point, we solve for the minimum value of Y:
y = \left[ H - H \right]^2 + V = 0 + V = V
Thus, our minimum value, the vertex, is at (H, V), as we've seen. If we need the original formula, we can solve B = -2 H and then substitute into V = C - \frac{B^2}{4} to find C = V + H^2 . Looking at both parabolic forms,
y = \left[ x - H \right]^2 + V = x^2 + (- 2 H) x + (V + H^2) | crawl-data/CC-MAIN-2018-47/segments/1542039744513.64/warc/CC-MAIN-20181118155835-20181118181835-00477.warc.gz | null |
# GMAT Tip of the Week: Brought to You by the Letter C
In a Valentine’s Day surprise yesterday, the standard Thursday Veritas Prep staff meeting was crashed by a lovable intruder. Cookie Monster – yes, the one-track-minded carnivore from Sesame Street – barreled into the meeting with a singing telegram for our Director of Admissions Consulting and Worldwide GMAT Instructor of the Year, Travis Morgan. Bearing a message of love and his standard message of “me want cookie”, he also reminded the GMAT staff of why Cookie Monster would fail miserably at the GMAT:
On the GMAT, you cannot have a one-track mind.
If you grew up watching Sesame Street you know all about Cookie Monster’s one-track mind – in his zeal to eat as many cookies as humanly possible (a pretty realistic goal for the toddlers who adore him) he’ll eat absolutely anything: chairs, tables, flowers, whatever you put in front of him. And in a way this caricature of a food-crazed lunatic looks a lot like many GMAT test-takers, who in their zeal to solve quantitative problems will calculate anything that’s put in front of them.
But just as Cookie Monster is designed to be absurd, so is the idea that you must get the right answer to every problem no matter how many calculations similarly absurd. The GMAT will punish that one-track-mindedness the same way that stomach pains will someday punish Cookie Monster’s.
GMAT problems are designed in many cases to waste your time, or rather to waste the time of those not astute enough to see that trap. Some questions are structured so that there’s an easy out for those who recognize it, like:
What is the square root of 5929?
(A) 67
(B) 72
(C) 75
(D) 77
(E) 83
Here you *could* try to square each answer choice, but that math could be pretty time consuming. This type of question is designed to reward you for recognizing that B and C cannot produce a number ending in 9 when squared, and that A is too small (70^2 would be 4900 so 67^2 will be far less than 5929) and E is too big (80^2 would be 6400, so 83^2 will be far too big), leading you to answer choice D.
Other questions may waste your time simply because you fail to see the “missing link”. This happens quite often in geometry – if you don’t see that there’s a direct relationship between supplemental angles or you fail to notice that the radii of a circle must be equal leading to an isosceles triangle in the figure, for example, you could work for several minutes to no avail. But that one-track-mindedness of “I’ll solve this problem or run out of time trying” has befallen many a would-be high-scorer. Years ago the holder of a PhD in engineering from MIT called the Veritas Prep offices in near tears, having well underperformed his expected quantitative score. The reason? He spent close to eight minutes on a problem early in the quant section and knew for certain that he had answered it correctly…but was good enough at math to realize that with an average of 2 minutes per question he had put himself in trouble by spending 4 times that amount on just one question, and he panicked from there.
Similarly, one of the chief architects of the GMAT at GMAC headquarters recounted to us recently that he – a PhD in statistics – encountered the same situation while taking the GMAT for R&D purposes last year. Seeking a perfect score to brag around the office, he encountered a geometry problem that took him several minutes to solve, and at a certain point he had to laugh that “for a living I tell people not to fall into this bottomless pit of time, yet here I am”. When he dub into the administrator account to view his test item-by-item he found this: while he did ultimately get that question right in several more minutes than he’d advise anyone to take on it, it turned out to be an unscored, experimental question that didn’t even count toward his score.
So here’s today’s GMAT lesson, brought to you by the letter C: don’t have a one-track mind on GMAT quant questions. If the calculations look to be too time-consuming or labor-intensive:
1) Try to find a more efficient way, often by considering the answer choices to see if an estimate or a number property can help you avoid the work altogether
2) Know when it’s time to make an educated guess and move on. Pacing is personal – some students can afford 3-4 minutes on one question because they’re so efficient on others, but must cannot. Take practice tests and get a feel for your own pacing and your own barometer for when it’s time to guess and move on. The GMAT is a war, and it’s easy to lose a war when your goal is to win every single battle. Nearly all of us need to retreat on a question here or there to regroup for the ones we can win. Don’t have that one-track “me want correct answer” Cookie Monster mindset – a more flexible frame of mind is your best path to be on your way to where the air is sweet, be it Cambridge, Palo Alto, or whatever campus you want to get to.
Plan on taking the GMAT soon? We have online GMAT prep courses starting all the time! And, be sure to find us on Facebook and Google+, and follow us on Twitter! | crawl-data/CC-MAIN-2018-26/segments/1529267865098.25/warc/CC-MAIN-20180623152108-20180623172108-00376.warc.gz | null |
# in a mountain climbing expeditions 5 men and 7 women are to walk
in a mountain climbing expeditions 5 men and 7 women are to walk single file so that no 2 men are adjacent. How many ways are possible?
• This is combinatorics not statistics, consider revising your tag – HBeel Jan 11 '15 at 12:23
• @Henry, I have changed the tag. – FundThmCalculus Jan 11 '15 at 12:35
• I thought that walking in a single file no two people are ever adjacent. – Marc van Leeuwen Jan 11 '15 at 12:42
• I think OP means next to each other in the line – HBeel Jan 11 '15 at 12:47
• @Henry: I think you meant behind each other. How English is difficult! – Marc van Leeuwen Jan 11 '15 at 12:50
Arrange the women in a line, in $7!$ ways. The $5$ men now each have to choose one of the eight possible positions: between, in front, or behind the women, this in $A_8^5$ ways. We get
$$7! \cdot \frac{8!}{3!}= 33,868,800$$
ways.
Compare this with the number of all the orderings $$12! = 479,001,600$$
The ratio of these numbers is $\frac{7}{99}=0.07070707\ldots$,
There are $7!$ permutations of the women and $5!$ permutations of the men, so for every valid placement we get $7!5!=604800$ different solutions; I will count placements, and multiply by that factor if that is intended.
After lining up, the $7$ women delimit $8$ spaces (among which two at the ends). The $5$ men must occupy a subset of those spaces, for $\binom85=56$ possibilities.
It is not fully clear from the problem if the sequences are unique or not, so I'll explain both:
1) All sequences are unique. In this case we need to account for every MF sequence (12! total). First, we fix the positions of F: 7!, since all women are different. We have 8 gaps in the sequence, every 'gap' can be filled by anything between 0 and 5 men. A better way of looking at it is by considering 5 'slots' (mean), and each slot takes any value between 1 and 8 (since we can put a man in any gap), so there are $8^5$ of allocating men, but we do not want 2 men in 1 gap, so clearly there are $\frac{8!}{3!}$ ways for this. Putting it all together, there are $\frac{7!8!}{3!}$ unique sequences.
2)All sequences are the same. In this case we have only 1 sequence for women (or $\frac{7!}{7!}$ if you want) and the number of allocations for men is differnt only in the selected gaps, so we need to divide $\frac{8!}{3!}$ through $5!$, hence the solution is $\binom{8}{3}$.
• It is not clear what you mean by sequences being unique or the sqme. Certainly all sequences are not the same. – Marc van Leeuwen Jan 12 '15 at 11:22
• are sequences $M_1 F_1 M_2$ the same as $M_2 F_1 M_1$? – Alex Jan 12 '15 at 12:18 | crawl-data/CC-MAIN-2019-35/segments/1566027319082.81/warc/CC-MAIN-20190823214536-20190824000536-00557.warc.gz | null |
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Teacherbot 02 Sep, 13:14:17
1. Fraction Sorting: Provide a variety of objects such as blocks, toys, or pictures and ask the child to sort them into groups based on whether they are whole or divided into parts. This helps them understand the concept of fractions as parts of a whole.
2. Fraction Puzzles: Create simple puzzles where the child has to match different shapes or pictures that are divided into equal parts. This helps them recognize and understand different fractions.
3. Fraction Pizza: Use a paper plate or a circular cutout to represent a pizza. Divide it into different slices and ask the child to color a certain fraction of the pizza. For example, “Color 1/4 of the pizza.” This helps them visualize fractions in a real-life context.
4. Fraction Snack: Give the child a snack such as crackers or fruit slices and ask them to divide it into equal parts. For example, “Divide the apple slice into halves.” This helps them understand fractions as equal parts of a whole.
5. Fraction Bingo: Create a bingo game where the child has to match different fraction cards to the corresponding fractions on their bingo board. This helps them practice recognizing and identifying fractions.
6. Fraction Book: Create a simple book with pictures or drawings of different objects divided into equal parts. Ask the child to color a certain fraction of each object. For example, “Color 1/3 of the cake.” This helps them practice identifying and coloring fractions.
7. Fraction Memory Game: Create a memory game where the child has to match fraction cards with their corresponding numerical representation. For example, matching a card with “1/2” to a card with “0.5”. This helps them practice associating fractions with their numerical values.
8. Fraction Playdough: Provide the child with playdough and ask them to divide it into equal parts. For example, “Divide the playdough into four equal pieces.” This helps them understand fractions as equal parts of a whole.
9. Fraction Board Game: Create a board game where the child has to move their game piece based on the fraction they roll on a dice. For example, if they roll a 1/3, they move their piece one-third of the way around the board. This helps them practice recognizing and using fractions in a game setting.
10. Fraction Art: Provide the child with different colored paper or craft materials and ask them to create a picture using different fractions. For example, they can create a flower using petals that are divided into halves or quarters. This helps them express their creativity while understanding fractions.
You 02 Sep, 13:14:54
Now I want to create 3 different versions of this. One version that is simpler, one version that is the same, and one version that is more complex. Format the output in 3 nice sections.
Teacherbot 02 Sep, 13:14:54
Simpler Version: 1. Fraction Sorting: Provide a variety of objects such as blocks, toys, or pictures and ask the child to sort them into two groups - whole objects and objects divided into parts. This activity helps them understand the basic concept of fractions as parts of a whole.
1. Fraction Puzzles: Create simple puzzles where the child has to match different shapes or pictures that are divided into two equal parts. This helps them recognize and understand the concept of halves.
2. Fraction Snack: Give the child a snack such as crackers or fruit slices and ask them to divide it into two equal parts. For example, “Divide the apple slice into halves.” This hands-on activity helps them understand fractions as equal parts of a whole.
Same Version: 1. Fraction Sorting: Provide a variety of objects such as blocks, toys, or pictures and ask the child to sort them into groups based on whether they are whole, divided into halves, or divided into quarters. This activity helps them understand fractions as parts of a whole and introduces the concept of quarters.
1. Fraction Puzzles: Create puzzles where the child has to match different shapes or pictures that are divided into halves or quarters. This helps them practice recognizing and understanding different fractions.
2. Fraction Pizza: Use a paper plate or a circular cutout to represent a pizza. Divide it into halves and quarters and ask the child to color a certain fraction of the pizza. For example, “Color 1/4 of the pizza.” This activity helps them visualize and practice fractions in a real-life context.
More Complex Version: 1. Fraction Sorting: Provide a variety of objects such as blocks, toys, or pictures and ask the child to sort them into groups based on whether they are whole, divided into halves, quarters, or thirds. This activity helps them understand fractions as parts of a whole and introduces the concept of thirds.
1. Fraction Puzzles: Create puzzles where the child has to match different shapes or pictures that are divided into halves, quarters, or thirds. This helps them practice recognizing and understanding different fractions.
2. Fraction Board Game: Create a board game where the child has to move their game piece based on the fraction they roll on a dice. The fractions can include halves, quarters, and thirds. This activity helps them practice recognizing and using fractions in a game setting and reinforces their understanding of different fractions. | crawl-data/CC-MAIN-2024-38/segments/1725700650826.4/warc/CC-MAIN-20240907095856-20240907125856-00132.warc.gz | null |
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# Algorithms (1st Edition)Solutions for Chapter 5
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Chapter: Problem:
100% (8 ratings)
Consider the following graph.
(a) What is the cost of its minimum spanning tree?
(b) How many minimum spanning trees does it have?
(c) Suppose Kruskal’s algorithm is run on this graph. In what order are the edges added to the MST? For each edge in this sequence, give a cut that justifies its addition.
SAMPLE SOLUTION
Chapter: Problem:
100% (8 ratings)
• Step 1 of 4
Minimum spanning tree:
The minimum spanning tree is an edge-weighted graph whose weight is not more than the weight of any other spanning tree.
a) Cost of minimum spanning tree:
Determine the number of edges for minimum spanning tree is given below:
…… (1)
Substitute the value for “number of vertices = 8” in Equation (1).
Steps to determine the minimum spanning tree:
• The vertex “A” contains two edges with weight of 6 from A to B vertices and 1 from A to E vertices.
• Here, the minimum weight is 1 from A to E vertices and is shown below:
Next, starts with vertex “B”.
• The vertex “B” contains four edges with weight of 6 from B to A vertices, 5 from B to C vertices, 2 from B to E vertices, and 2 from B to F vertices.
• Here, the minimum weights are 2 from B to E vertices and 2 from B to F vertices. Consider the first minimum weight value.
o So, the minimum weight 2 from B to E vertices and is shown below:
Next, starts with vertex “C”.
• The vertex “C” contains four edges with weight of 5 from C to B vertices, 6 from C to D vertices, 5 from C to F vertices, and 4 from C to G vertices.
• Here, the minimum weight is 4 from C to G vertices and is shown below:
Next, starts with vertex “D”.
• The vertex “D” contains three edges with weight of 6 from D to C vertices, 5 from D to G vertices, and 7 from D to H vertices.
• Here, the minimum weight is 5 from D to G vertices and is shown below:
Next, starts with vertex “E”.
• The vertex “E” contains three edges with weight of 1 from E to A vertices, 2 from E to B vertices, and 1 from E to F vertices.
• The weight 1 and 2 are already drawn.
o Here, the minimum weight is 1 from E to F vertices and is shown below:
Next, starts with vertex “F”.
• The vertex “F” contains four edges with weight of 1 from F to E vertices, 2 from F to B vertices, 5 from F and C vertices, and 3 from F to G vertices.
• The weight 1 and 2 are already drawn.
o Here, the minimum weight is 3 from F to G vertices and is shown below:
• Step 2 of 4
Next, starts with vertex “G”.
• The vertex “G” contains four edges with weight of 3 from G to F vertices, 4 from G to C vertices, 5 from G and D vertices, and 3 from G to H vertices.
• The weight 3 and 4 are already drawn.
o Here, the minimum weight is 3 from G to H vertices and is shown below:
Finally, the minimum spanning tree is shown below:
The cost of the minimum spanning tree is the sum of all the weighted edges.
Therefore, the cost of the minimum spanning tree is.
• Step 3 of 4
b) Number of minimum spanning tree in this graph:
In the given graph, there are two possibilities of the minimum spanning tree. That is, we can take the weight 2 from B to E or weight 2 from E to F.
One possible minimum spanning tree with weight 2 from B to E and is given below:
Another possible minimum spanning tree with weight 2 from E to F and is given below:
Therefore, the number of minimum spanning tree in this graph is.
• Step 4 of 4
c) Run the MST using Kruskal’s algorithm:
The minimum spanning tree using the Kruskal’s algorithm is given below:
In this MST,
• There are 7 edges are included into the minimum spanning tree such as,
o AE, EF, BE, FG, GH, CG, and GD.
• For AE edge, the cuts are {A, B, C, D} and {E, F, G, H}.
• For EF edge, the cuts are {A, B, C, D, E} and {F, G, H}.
• For BE edge, the cuts are {A, E, F, G, H} and {B, C, D}.
• For FG edge, the cuts are {A, B, E} and {C, D, F, G, H}.
• For GH edge, the cuts are {A, B, E, F, G} and {C, D, H}.
• For CG edge, the cuts are {A, B, E, F, G, H} and {C, D}.
• For GD edge, the cuts are {A, B, C, E, F, G, H} and {D}.
Corresponding Textbook
Algorithms | 1st Edition
9780077388492ISBN-13: 0077388496ISBN:
This is an alternate ISBN. View the primary ISBN for: Algorithms 1st Edition Textbook Solutions | crawl-data/CC-MAIN-2016-36/segments/1471982290634.12/warc/CC-MAIN-20160823195810-00015-ip-10-153-172-175.ec2.internal.warc.gz | null |
Carbon paper is an inexpensive reprographic device used to make a single copy concurrently with the original, as in credit card transaction receipts, legal documents, manuscripts, letters, and other simple forms.
Even up to the twentieth century, copying documents for business purposes was a difficult, labor-intensive process. Copy clerks, like the scribes of churches and government offices before them, were common in the business offices of the nineteenth century.
The first attempt at copying important business correspondence is attributed to the Scottish engineer James Watt, who improved the steam engine. Watt disliked trusting scribes to copy business letters, so he invented a method of pressing a tissue paper that had been moistened with special liquids onto an original, which had been written using special ink. By 1779, he was ready to market the process, but it didn't catch on.
In 1806 Ralph Wedgwood invented the Stylographic Manifold Writer. A paper saturated with printer's ink was placed between a piece of tissue paper and a piece of regular paper. A metal stylus then scratched an impression onto the tissue paper, creating a copy that read correctly and another that was a mirror image, though easily read through the thin tissue paper. It was necessary to prepare copies in this manner because the pens of the time (quills) couldn't press hard enough, and pencils could be erased. Around 1820 it became possible to use paper that had been inked on one side only and an indelible pencil to produce the original. This early carbon paper was not a huge success, apparently because business owners, fearing forgery, preferred items written in ink.
In 1823 Cyrus P. Dakin began making carbons, papers coated with oil and carbon black. In the 1860s Lebbeus H. Rogers attempted to sell these carbons to businesses, but it wasn't until the invention of the type-writer in 1867 that carbon paper came to be accepted (typewriters produced a cleaner copy as well as a quality original). Rogers originally made carbon paper by placing paper on a stone table and slathering it with a mixture containing carbon black (soot), oil, and naphtha (a liquid hydrocarbon). Later he developed a machine that applied hot wax to the carbon paper, doing away with the manual brushing.
The production of carbon paper has stayed basically the same since Rogers's technological advances. In a quaint manufacturing tradebook put out around the turn of this century, carbon paper is described as consisting of various pigments, including carbon black, and wax or oils brushed onto thin, strong paper. While modern carbon paper is made using essentially the same formula, manufacturers have concentrated on increasing the cleanliness of the process and improving the quality of the reproduction by using more refined materials.
A typical piece of carbon paper consists of a sheet of paper that has been impregnated with carbon and sandwiched between two sheets of regular paper. All components are standard, except for the coated sheet that performs the reprography. Its coating is made up of several materials, the most important of which is carbon black. Carbon black is a very
Some carbon paper can be reused. This comes in handy for use in sales books, for example, because only one sheet of carbon paper is needed to write out receipts for several sales. Reusable oil-soluble pencil carbon produces indelible copy. It is commonly coated with a mixture of talc (39%), carnauba wax (23%), lard oil (16%), oleic acid (15%), and victoria blue base (7%). Reusable pigment pencil carbon paper produces erasable copy. It is coated with a mixture that commonly consists of milori blue (25%), carnauba wax (20%), mineral oil (16%), amber petrolatum (11%), petrolatum (11%), toning iron blue (10%), and paraffin wax (7%). Typewriter carbon is also reusable, and because of the heavy striking force of the typewriter key, it uses higher quality carbon black and finer ingredients than one-time or pencil carbon paper. It is commonly coated with an ink that consists of carnauba wax (32%), mineral oil (26%), carbon black (12%), amber petrolatum (6%), beeswax (5%), ouricury wax (5%), ozokerite wax (5%), oleic acid (3%), pigmented purple toner (3%), crystal violet dye (2%), and victoria blue base (1%). For further protection, it also has a backing wax composed of carnauba wax (40%), ouricury wax (40%), and microcrystalline wax (20%).
Carbon paper's most important ingredient, carbon black, has changed in recent years. Before 1940, 90 percent of the carbon black produced in the United States was made from channel or impingement carbon, where tiny jets of gas flame impinged (struck) onto a cool metallic surface, such as an iron channel (or groove). The resultant soot from the partial combustion was then scraped off, producing carbon particles of approximately 10 -8 meters in diameter This superb method of creating fine carbon black was abandoned in 1976, however, because of a large increase in the price of natural gas. The current method of producing carbon black uses the furnace process, described below. The finished carbon black is then coated onto paper using a series of offset rollers.
Typewriter carbon paper differs from one-time carbon paper in that it usually has an ink coating and backing wax, as well as printed material on the back. In this production method, a Flexographic set-up comprising a dope roll, metering roll, print roll, and impression roll provides the means to print on the back of paper that has been supplied from a mill roll. After printing, the paper passes over a dope roll to receive a carbon ink coating that is smoothed with an equalizer rod as in the Mayer method. Next, the paper travels to a wax dope roll, which coats it with backing wax. As in the other methods, a chill roll then solidifies the wax. A felt buffing roll is sometimes used to improve the product's appearance before it is rolled onto a rewind roll.
The principle behind carbon paper is simple, yet producing it is difficult. A modern manufacturer of carbon paper tests all incoming raw materials for quality. A large number of tests can be applied to carbon black, including those for pigments and sulfur content. The carbon black selected should also be of fine particle size, which is determined by measuring the average diameter of a carbon black particle with an electron microscope. In addition, it should have low oil absorption, and the absorbency and pH of the carbon black are tested prior to use. The inks are tested for fineness of grain, which affects the final smoothness of the coating. The wax binder should penetrate only slightly into the paper and have the proper viscosity. To ensure proper lettering, the amount of wax released under pressure is tested. The paper itself should be smooth, nonporous, and free of surface defects. Although it must be a thin tissue, it should also be strong and dense. The finished carbon paper must be free of defects: no offset, flaking, wrinkles, or curl. It must work properly; the resultant copy must be clean and legible. The coating should be hard enough to meet its intended use; for example, one-time carbon doesn't require as hard a coating as typewriter carbon, which must also have a compounded coating of good color so it can be reused.
Other tests exist for finished carbon paper. To determine the amount of ink that was deposited, a specimen of carbon paper is selected and weighed. Its deposit of ink is then chemically removed before it is reweighed. The difference in weight indicates the amount of ink deposited. Curl is a frequent complaint about carbon paper, even though carbon paper is frequently coated on both sides (one side with the carbon, the other with backing wax) to combat the problem. To test for curl under different conditions, a piece of carbon paper is placed on a flat surface and, under controlled temperature, subjected to different humidities. The durability of reusable typewriter carbon paper is checked by repeatedly typing on one space until the carbon wears out. The cleanliness of both the copy and the carbon paper itself is important. To test the first, a document is typed and the copy is examined to see if it is clean. To test the second, the carbon side is rubbed with a clean, crumpled sheet of paper, which is then examined to see how much carbon has rubbed off. The color and thickness of the carbon must be inspected visually to see if they meet quality standards.
In 1991, over 62,000 metric tons of carbon paper were produced in the United States. However, during the same period, over 600,000 metric tons of carbonless transfer paper were manufactured. Ideal for handwritten records, carbonless paper utilizes chemically coated sheets that react under pressure, producing a colored image. Although carbonless paper weighs significantly more than carbon paper and is less suitable for typewritten and computerized records, its demand is increasing at the expense of carbon paper. (This demand for "regular" paper can also be attributed to the increasing availability of photocopiers.) It is likely that, as electronic communication becomes more prevalent, carbon paper will become obsolete. Presently, though, there is enough demand from businesses that utilize carbon paper for credit card receipts and computerized records to insure the survival of this simple, inexpensive product for some time to come.
Casey, James P. Chemistry and Chemical Technology, Vol. IV, Pulp and Paper. John Wiley and Sons, 1983.
Mantell, Charles L. Carbon and Graphite Handbook. John Wiley and Sons, 1968.
The Manufacture of Pulp & Paper: Science & Engineering Concepts. Technical Association of the Pulp & Paper Industry, 1988.
Mosher, Robert H. and Dale S. Davis. Industrial and Specialty Papers, Vol. III: Applications. Chemical Publishing, 1969.
Proudfoot, W. B. The Origin of Stencil Duplicating. Hutchinson and Company, 1972.
— Rose Secrest | <urn:uuid:3b7ffa9c-a56c-4035-9e94-544385c32a05> | {
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# The table below shows the daily expenditure on food of 25 household in a locality
Question:
The table below shows the daily expenditure on food of 25 household in a locality
Find the mean daily expenditure on food by a suitable method.
Solution:
Let the assumed mean a = 225 and h = 50
Now,
$\sum f_{i}=25$
$\sum f_{i} u_{i}=-7$
Mean, $\bar{x}=a+\left(\frac{\sum f_{i} u_{i}}{\sum f_{i}}\right) \times h$
$=225+\left(\frac{-7}{25}\right) \times(50)$
$=225-14$
$=211$
Therefore, mean daily expenditure on food is Rs 211.
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# ASSIGNMENT WORKSHEETS FOR CLASS 6
DOON PUBLIC SCHOOL, PASCHIM VIHAR, NEW DELHI Summer Vacation Worksheet Subject: Science Q1 Group the objects in the box on the basis of the given prop...
ASSIGNMENT WORKSHEETS FOR CLASS 6
NOTE: Solve the following worksheets separately on different pages.
DOON PUBLIC SCHOOL, PASCHIM VIHAR FRENCH WORKSHEET
DOON PUBLIC SCHOOL, PASCHIM VIHAR MATHEMATICS HOLIDAY HOMEWORK WORKSHEET
Q1. Fill in the blanks: a) The set of natural number with Zero is called a ____________ number. b) Every natural number is a ____________ number but vice versa is not true. c) The largest whole number is ____________. d) The smallest whole number is ____________. e) The whole number that does not have a predecessor is _____________. f) Commutative property of addition and multiplication holds good for ___________ whole numbers. g) The property used for addition and multiplication for three or more numbers is ______________. h) ____________ is the additive identity and _____________ is the multiplicative identity. i) All the properties of whole numbers are closed or satisfied for _____________ and ______________. j) A number that divides the given no. completely or exactly is its ___________. k) Factors of a number are always _____________. l) ____________ is a factor of every number. m) Every no. is a ___________ or _____________ of itself. n) __________ is the only even prime number. o) Two numbers are _____________ if their common factor is only 1. p) The sum of two even numbers is always ____________. q) The seventh multiple of 18 is _____________. Q2. Use number line to find: a) 3 + 2 b) 6 – 3
c) 2 X 4 Q3. If a = 156, b = 93, verify a – b is not equal to b – a. Q4. Verify the associative property of addition and multiplication for the given numbers: a) 5, 4, 2
b) 8, 7, 5
c) 0, 8, 6
Q5. Verify the distributive property of multiplication for the following: a = 38, b = 20, c = 12 a = 5, b = 6, c = 3 Q6. If a = 112, b = 56 and c = 98, show that a x ( b + c ) = ab + ac. Q7. Divide and check using Dividend = divisor x quotient + remainder for 2256 ÷ 15 Q8. Find the factors of 169, 264 and 525. Q9. Find the first five multiples of 18, 19 and 26. Q10. Which of the following are co-prime numbers? a) 14 and 18
b) 24 and 108
Q11. Verify if 298 is a perfect number. Q12. Check the divisibility of 3178964 for all the numbers from 2 to 12.
DOON PUBLIC SCHOOL, PASCHIM VIHAR, NEW DELHI Summer Vacation Worksheet Subject: Science Q1 Group the objects in the box on the basis of the given properties. (One object can have more than one property)
Steel knife, glass window pane, ceramic tea cup, iron nail, rubber tyres, cardboard case, black board, marble statue
Property
Lustrous
Rough
Hard
Transparent
Objects
Q2.
Answer the following a) b) c) d) e) f) g) h) i) j) k) l)
Name any two translucent objects. Why mustard oil does not mix with water? Name any immiscible liquids. How can we make paper translucent? Name the theory given by John Dalton. Name two gases soluble in water. A property that resist deformity. A property that decides the floating and sinking of an object. Smallest particle of a molecule. Which has greater density? Ice or water? Two gases insoluble in water. Name the smallest particle of element.
Q3. Water and milk flow easily but honey and honey flow slowly. Why? Q4. Why frosted glass is used in bathroom? Q5. What is rusting? Q6. Can solubility help aquatic plants and animals to survive in their habitat? How? Q7. Find out the formula of the following compounds. a) b) c) d) e) f) g) h)
Water Salt Sugar Carbon dioxide Carbon monoxide Vinegar Washing soda Baking soda
Doon Public School, PaschimVihar GEOGRAPHY CHAPTER 2: LATITUDES AND LONGITUDES
Q1. Define the following Globe, equator, axis, parallel of latitudes, meridian of longitudes, standard time, Indian standard time. Q2.How are the lines of longitudes and latitudes useful? Q3.Name 5 important parallels of latitudes? Q4.What is the longitudinal degree of Greenwich? Q5.What is the standard meridian of India? Q6.Which hemisphere is ahead of Greenwich? Q7.what is the difference between Greenwich and Indian standard time? Q8.Fill in the blanks:A) Line which divides earth in two equal parts is called__________. B) Part of earth which is toward north of equator______. C) Part of earth which is towards south of equator_______. D) Network of parallels and meridians is called_______. E) Meridian which passes through greenwhich_______. F) Sun takes_____minutes to cross one degree of longItude.
Q9.. Draw a diagram of the earth and label the following. Torrid zone, Frigid zone, Temperate zone, Equator, Tropic of Cancer, Tropic of Capricorn, Arctic Circle, Antarctic Circle, North Pole, South Pole Q10. Name whether Latitude or Longitude:
STATEMENT 1.
They are parallel to each other.
2.
They are drawn at intervals of 1 degree.
3.
Vertical lines that join at the poles.
4. They are also called Meridians. 5. The distance between 2 lines is 111 km. 6. The equator is a 7. There are 181 of them. 8.
They help us to determine time.
They divide the earth into 9. Eastern and Western Hemispheres. They divide the earth into 10. Northern and Southern Hemisphere.
LATITUDE OR LONGITUDE
DOON PUBLIC SCHOOL, PASCHIM VIHAR Subject: English Name: _____________
Roll No: _____________
B. Choose the word that best complete the sentences.
1. I talked to Bob two weeks ago. I thought he wanted to know about my cat, but I misunderstood him. He asked me where _______, not my cat.
A. is my hat B) my hat was C) my hat is D) was my hat
2. "The people in the apartment upstairs must have a lot of children." "I don't know how many _______," but it sounds as if they have a dozen." A. children do they have B. do they have children C. children they have D. they have children
3. "There is too much noise in this room. I can't understand what _______" "Neither can I." A) is the professor saying B) is saying the professor C) that the professor is saying D) the professor is saying 4."Sorry, I can't. The boss has an urgent report for me to write. She demanded that it _______ on her desk by 5 p.m. Today."
A) was
B) will be
C) is
D) be
5. "Did you tell Carol where _______ us this evening?" "Yes, I did. I can't understand why she is late." A) should she meet
B) she to meet
C) she meets
D) to meet
6. "Bill Frazer seems like a good person for the job, but we don't know why he left his last job." "I know why. He told me _______ a serious policy disagreement with his boss last January."
7. ……… prompt is important to our boss.
A) A person is
B) Is a person
C) if a person
D) Whether or not a person is
8. A scientific observer of wildlife must note every detail of how _______ in their environment: their eating and sleeping habits, their social relationship, and their methods of self-protection.
A) do animals live
B) live animals
C) do live animals
D) animals live
9. The mysterious movie was clever and suspenseful. The audience couldn't predict _______ rescued the wounded penguin until the ending.
A) who we
C) that who
D) that
10. "Nothing ………… want is much too expensive."
A) That I
B) What I
C) That what I
D) What do I
DOON PUBLIC SCHOOL, PASCHIM VIHAR Subject: English Name: _____________
Roll No: _____________
A.Complete the exercise with correct forms of the given nouns. Use each noun only one time.
attorney
beach
box
cliff
discovery
laboratory
man
match
medium
ox
piano
tooth
1. The age at which the first tooth appears differs greatly from child to child. Very occasionally, children are born with one or more . 2. I need some
to light the fire.
3. Studies are showing that women.
process information differently from
4. Maria needed some legal advice for her businesses, so she contacted two .
5. New scientific world.
6. The farmer loaded his cart with to market. His cart was pulled by two
throughout the
of fresh vegetables to take .
7. The north side of the island has no There are only steep rock.
for people to walk on.
. No one can climb theses steep walls of
8. The music building at the university has 27 on.
for students to play
9. People get most of their news about the world through the mass , that is, through radio, television, the internet, newspapers, and magazines
DOON PUBLIC SCHOOL, PASCHIM VIHAR COMPUTER WORKSHEET Lesson -9 I. Fill in the blanks. 1) A __________can be evaluated to either true or_________in a program. 2) _________are special symbols or words that perform some action on constants/variables and return an output. 3) A_________is a quantity whose value does not change during the execution of the program. 4) ____________are special keywords that instruct the computer to perform a specific task. 5) The___________statement is used for testing multiple conditions in a program. 6) You can run a QBasic program by pressing _______key. 7) The _______statement is used to assign values to variables in a program. 8) ______________operator helps to perform comparisons in a program. II. Answer in True/False. 1) The select case statement is used to test a single condition in a program. 2) The constant is a quantity whose value can change during the execution of a program. 3) CLS command is used for assigning values to a variable. 4) QBasic is developed by Microsoft. 5) String constants are letters, numbers or a combination of both. 6) Numeric constants cannot hold numeric values. 7) Print commands prints a value of a variable.
8) Condition is a relational expression that evaluates to either “True or False” III.MCQs 1) Which of these is not a type of variable? a) Select b) String c) Numerical 2) Which of these can test multiple conditions? a) Select case b) For c) IF 3) Which is a mathematical operator? a) + b) > c) == 4) Which is used to separate multiple values with input statement? a) Comma (,) b) Semi colon (;) c) colon (:) 5) How many ELSEIF statements can be included between the if and else keyword a) Unlimited b) four c) two IV. Answer the following questions a) What is if….then…else statement? Ans:
b) What is a variable? Ans:
c) What is IF…THEN statement? Ans:
d) What is the difference between Mathematical and Relational operators? Ans : | crawl-data/CC-MAIN-2020-24/segments/1590347392057.6/warc/CC-MAIN-20200527013445-20200527043445-00086.warc.gz | null |
## College Algebra (11th Edition)
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\dfrac{2}{x+2}+\dfrac{1}{x+4}=\dfrac{4}{x^2+6x+8} ,$ factor all expressions that can be factored. Then multiply both sides by the $LCD$ and isolate the variable. Finally, do checking and ensure that any denominator does not become $0.$ $\bf{\text{Solution Details:}}$ Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the factored form of the equation above is \begin{array}{l}\require{cancel} \dfrac{2}{x+2}+\dfrac{1}{x+4}=\dfrac{4}{(x+2)(x+4)} .\end{array} The $LCD$ of the denominators, $x+2,x+4,$ and $(x+2)(x+4)$ is $(x+2)(x+4)$ since it is the lowest expression which can be divided exactly by all the given denominators. Multiplying both sides by the $LCD= (x+2)(x+4) ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} (x+2)(x+4)\left( \dfrac{2}{x+2}+\dfrac{1}{x+4} \right)=\left( \dfrac{4}{(x+2)(x+4)} \right) (x+2)(x+4) \\\\ (x+4)(2)+(x+2)(1)=1(4) \\\\ 2x+8+x+2=4 \\\\ 2x+x=4-8-2 \\\\ 3x=-6 \\\\ x=-\dfrac{6}{3} \\\\ x=-2 .\end{array} If $x=-2,$ the part of the given equation, $\dfrac{2}{x+2} ,$ becomes $\dfrac{2}{0} ,$ which is undefined. Hence, there is $\text{ no solution .}$ | crawl-data/CC-MAIN-2019-04/segments/1547583897417.81/warc/CC-MAIN-20190123044447-20190123070447-00598.warc.gz | null |
Geosat [US Navy]
The Geosat (GEOdetic SATellite) was a dedicated US Navy military oceanographic satellite consisting of a radar altimeter designed to obtain closely spaced, precise mapping of the earth's geoid over the ocean. On 8 November 1986, the satellite was moved into an Exact Repeat Mission (ERM) orbit with a repeat cycle of 17.05 days. The Geosat mission was originally managed by the Office of Naval Research (ONR). During the development phase, the program responsibility was transferred to the Naval Electronics Systems Command, now called the Space and Naval Warfare Systems Command (SPAWAR) in Washington, D.C. The Applied Physics Laboratory (APL) was the prime contractor for the spacecraft and radar altimeter and performed spacecraft command and control operations and collected the satellite data. The data was distributed to the Naval Surface Weapons Center (NSWC), the Naval Ocean Research and Development Activity (NORDA), and NOAA. An arrangement was made with the National Ocean Service of NOAA to obtain the classified Geosat geophysical data records (GDR) providing wind, wave and sea-level products and made available to the user community. NASA obtained Geosat data for extensive waveform modeling and ice sheet research.
The basic structure of the Geosat is similar to the GEOS-3 satellite: The design consists of a conical structure below the core for the structural attachment of the velocity control system. The Geosat attitude control subsystem was designed to point the radar altimeter to within 1 degree of nadir 98 percent of the time. The system components were a 20-foot scissors boom with 100-pound end mass, redundant momentum wheels for roll and yaw stiffness, and pitch and roll attitude control thrusters. Attitude sensing was provided through the use of three digital sun-attitude detectors and a three-axis vector magnetometer. Spacecraft command was accomplished via a VHF uplink from the APL ground station. The telemetry subsystem consisted of two S-band transmitters, two tape recorders, and two encryption units. The Geosat was equipped with two Odetics dual-track high-density tape recorders that independently recorded the 10.205 kbps telemetry stream and played it back at 833 kbps for transmission to the ground. The Geosat also included redundant Doppler beacons for continuous tracking by a network of ground stations within the Defense Mapping Agency (DMA) and for a source of accurate timing to the radar altimeter and the telemetry subsystem. A C-band transponder was also included on Geosat.
Geosat operated until January 1990. The mission was continued by the GFO satellite, which was launched in 1998.
|Type / Application:||Altimetry|
|Contractors:||Johns Hopkins University Applied Physics Laboratory (APL)|
|Power:||8 deployable fixed solar arrays, batteries|
|Lifetime:||3 years (design); 5 years (reached)|
|Orbit:||757 km × 814 km, 108.1°|
|Geosat||1985-021A||13.03.1985||Va SLC-3W||Atlas-E OIS| | <urn:uuid:c770fc77-f0d6-499b-b9c6-7603a3ced49c> | {
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# Engaging students: Dividing fractions
In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission again comes from my former student Chelsea Hancock. Her topic, from Pre-Algebra: dividing fractions.
Applications (A1)
Students can encounter the division of fractions in a variety of places outside of the classroom. Some of these instances could even happen in your own home! When using fractions, the most common examples include slicing pizza or pie into equal slices. Here is one of those problems:
1. Assume you have seven-eighths of a whole pizza left. Three of your friends walk into the kitchen and ask for one-fourth of the whole pizza each. If you wanted to share with your friends, will you have enough pizza for each friend to get the amount they want? (Divide 7/8 by 1/4 and see if it’s bigger than three).
$\displaystyle \frac{7/8}{1/4} = \displaystyle \frac{7 \times 4}{8 \times 1} = \displaystyle \frac{28}{8} = 3 \frac{1}{2}$
It is bigger than three, therefore there is, in fact, enough pizza left for all three of your friends to get the amount they wanted.
Other problems might involve finding a fraction of a fraction of a whole. Here is an example of this:
1. I have a giant cookie jar with 36 cookies in it. My family comes over and eats some of the cookies. If 1/3 of the cookies are eaten and 3/4 of the eaten cookies had frosting, how many of the eaten cookies had frosting? (Multiply 36 by 1/3 to get 12. Then multiply 12 by 3/4).
$\displaystyle 36 \times \frac{1}{3} = \displaystyle \frac{36}{3} =12$
$\displaystyle 12 \times \frac{3}{4} = \displaystyle \frac{12 \times 3}{4} = \frac{36}{4} = 9$.
Curriculum (B2)
In previous mathematics classes, students have obtained a wide variety of skills which can be used when dividing fractions. These skills include the multiplication of whole numbers, the division of whole numbers, and how to reduce fractions to their simplest form. Dividing fractions is an extension of these skills. It can also be said that students already understand what a fraction is. On a separate note, we will discuss how many students relate to fractions and how they think of fractions when confronted with them.
Many students find fractions difficult and intimidating, often freezing when they see a fraction. Involve more than one fraction in a problem and students will get easily frustrated and give up. This can be caused by the way a student perceives fractions. Many students are taught that a fraction is simply part of a bigger whole number. While this is true, many students lose focus on the big picture and get caught up on the fact that a fraction is less than 1 whole unit. In order to help avoid this, teachers could instead try explaining fractions in a slightly different way: a fraction is just a number written like a division problem. The video found at http://www.youtube.com/watch?v=3xwDryouw6o can help to provide a more in-depth explanation about this new perspective on fractions.
By thinking of a fraction as simply a division problem, students automatically incorporate their previous knowledge on dividing whole numbers. When students work through a problem with dividing fractions, they will go through the steps of “keep, change, and flip.” Once they have changed the division symbol to a multiplication symbol and flipped the second fraction, the students will be ready to use their previous knowledge on multiplying whole numbers. After the numerators and denominators are multiplied respectively and the new fraction is obtained, the students must recall previous knowledge on the reduction of fractions to their simplest form.
Technology (E1)
A video can be used to engage students and give them a foundation for dividing fractions. The video I chose, which can be found at http://www.youtube.com/watch?v=uMz4Hause-o, is an excellent example of an acceptable engagement tool. In the video Flocabulary uses music and repetition to describe how to perform the task of dividing fractions. This will help the students be able to recall the information about dividing fractions later on when they need to. Flocabulary explains the process step-by-step and then demonstrates the method in action, using two different fractions to help students understand how it works. Then the video goes on to explain why we flip the second fraction in a division problem, which is vital for ensuring that actual learning is taking place and not simple memorization. Students need to know why they perform certain steps and why the trick works. While the cartoon animations are meant to target a younger audience, this clip is easy to follow and the repetitious nature of the music puts an interesting spin on learning mathematics.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | crawl-data/CC-MAIN-2023-06/segments/1674764500017.27/warc/CC-MAIN-20230202101933-20230202131933-00008.warc.gz | null |
## Adding Two And Three Digit Numbers
Here are the steps to adding two digit numbers:
Example: 25 + 34 = 59
• Always begin by adding the numbers in the ones column first: 5 + 4 = 9.
• Next add the numbers in the tens column: 2 + 3 = 5. Remember that the 2, 3 and 5 in the tens column actually stand for 20 + 30 = 50.
• The final answer or sum is 59.
Place Value
Tens
Ones
## 9
The next example is trickier.
Example: 59 + 37 = 96
• Add the numbers in the ones column: 9 + 7 = 16. Notice that only the 6 is written in the ones column. This is because the 1 belongs in the tens column as it is in the tens place in the number 16. The one is "carried over" to the tens column.
• Add the numbers in the tens column: 1 + 5 + 3 = 9. Remember those numbers actually represent 10, 50, 30 and 90.
• The final answer or sum is 96.
Example: Adding Two Digit Numbers with Carrying
Place Value
Tens
Ones
Carried number
## 6
The same process takes place with bigger numbers - follow the steps:
Example: 589 + 373 = 962
• First add the numbers in the ones column: 9 + 3 = (1)2. Notice there is a 1 that must be carried to the tens column. This represents the number 10.
• Next add the numbers in the tens column: 1 + 8 + 7 = (1)6. This represents the numbers 10 + 80 + 70 = 150 Now there is a 1 that must be carried to the hundreds column. This represents the number 100.
• Finally add the numbers in the hundreds column: 1 + 5 + 3 = 9. This represents the numbers 100 + 500 + 300 = 900
• The final answer or sum is 962..
.
.
.
Place Value
Hundreds
Tens
Ones
Carried number
(1)
(1)
## 2
.
Addition - Subtraction - Multiplication - Division - Place Value - Rounding
.
. | crawl-data/CC-MAIN-2024-18/segments/1712296818464.67/warc/CC-MAIN-20240423033153-20240423063153-00598.warc.gz | null |
How to Multiply Numbers
To multiply numbers, you need to know how to work with the different times signs as well as parentheses. If you multiply large numbers, you also need to know how to stack them in columns, so that you can work with them.
Multiplication is often described as a sort of shorthand for repeated addition. For example, when you multiply 4 by 3, you are adding 4 to itself 3 times: 4 + 4 + 4 = 12.
9 6 means add 9 to itself 6 times: 9 + 9 + 9 + 9 + 9 + 9 = 54
100 2 means add 100 to itself 2 times: 100 + 100 = 200
Although multiplication isn’t as warm and fuzzy as addition, it’s a great timesaver. For example, suppose you coach a Little League baseball team and you’ve just won a game against the toughest team in the league. As a reward, you promised to buy three hot dogs for each of the nine players on the team. To find out how many hot dogs you need, you could add 3 together 9 times. Or you can save time by multiplying 3 times 9, which gives you 27. Therefore, you need 27 hot dogs (plus a whole lot of mustard and sauerkraut).
When you multiply two numbers, the two numbers that you’re multiplying are called factors, and the result is the product.
In multiplication, the first number is also called the multiplicand and the second number is the multiplier. But almost nobody ever remembers these words.
Use signs and parentheses in multiplication
When you’re first introduced to multiplication, you use the times sign (). However, algebra uses the letter x a lot, which looks similar to the times sign, so people often choose to use other multiplication symbols for clarity.
Keep in mind that in math beyond arithmetic, the symbol · replaces .
That’s all there is to it. Just use the symbol anywhere you would’ve used the standard times sign ().
Remember that in math beyond arithmetic, using parentheses without another operator stands for multiplication. The parentheses can enclose the first number, the second number, or both numbers. For example,
However, notice that when you place another operator between a number and a parenthesis, that operator takes over. For example,
Note: In the third example, you don’t really need the , but it isn’t doing any harm, either.
Multiply larger numbers
The main reason to know the multiplication table is so you can more easily multiply larger numbers. For example, suppose you want to multiply 53 7. Start by stacking these numbers one on top of another with a line underneath, and then multiply 3 by 7. Because 3 7 = 21, write down the 1 and carry the 2:
Next, multiply 7 by 5. This time, 5 7 is 35. But you also need to add the 2 that you carried over, which makes the result 37. Because 5 and 7 are the last numbers to multiply, you don’t have to carry, so write down the 37 — you find that 53 7 = 371:
When multiplying larger numbers, the idea is similar. For example, suppose you want to multiply 53 by 47. (The first few steps — multiplying by the 7 in 47 — are the same, so you pick up with the next step.) Now you’re ready to multiply by the 4 in 47. But remember that this 4 is in the tens column, so it really means 40. So to begin, put a 0 directly under the 1 in 371:
This 0 acts as a placeholder so that this row is arranged properly.
When multiplying by larger numbers with two digits or more, use one placeholding zero when multiplying by the tens digit, two placeholding zeros when multiplying the hundreds digit, three zeros when multiplying by the thousands digit, and so forth.
Now you multiply 3 4 to get 12, so write down the 2 and carry the 1:
Continuing, multiply 5 4 to get 20 and then add the 1 that you carried over, giving a result of 21:
To finish up, add the two products (the multiplication results):
So 53 47 = 2,491. | <urn:uuid:9e389531-4bd2-409e-a57c-ac7899b95180> | {
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Rain Water Harvesting :-
Rainwater harvesting is the process of collecting rainwater from roof tops and directing it to an appropriate location where it is stored for ground water recharge. On an average, one spell of rain for two hours is enough to recharge 8000 liters of water.
Hydroelectricity is the term referring to electricity generated by hydro power : The production of electrical power through the use of the gravitational force of falling or flowing water.
Wind Energy :-
Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to make electricity, windmills for mechanical power, wind pumps for water pumping or drainage, or sails to propel ships.
Solar Energy :-
Solar Power is the conversion of sunlight into electricity, either directly using photo voltaics (PV), or indirectly using concentrated solar power (CSP). CSP systems use lenses or mirrors and tracking systems to focus a large area of sunlight into a small beam. PV converts light into electric current using the photoelectric effect.
Deforestation is the removal of a forest or stand of trees where the land thereafter converted to a non-forest use. Examples of deforestation include conversion of forest land to farms, ranches or urban use. | <urn:uuid:137a3757-56f3-45bf-ae33-4a8250d3f563> | {
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# Trigonometry
Trigonometry is a branch of mathematics that focuses on the relationships between the angles and sides of triangles. It’s a fundamental field of mathematics that has applications in various scientific, engineering, and practical contexts, including physics, engineering, astronomy, and more. Trigonometry is particularly useful for solving problems involving angles, distances, and the relationships between different parts of a triangle.
Some of the basic concepts in trigonometry are:
1. Basic Trigonometric Functions: Trigonometry involves six primary trigonometric functions:
• Sine (sin): The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse (the longest side).
• Cosine (cos): The cosine of an angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
• Tangent (tan): The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
• Cosecant (csc), Secant (sec), and Cotangent (cot): These are the reciprocals of sine, cosine, and tangent, respectively.
2. Unit Circle: The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate plane. It’s used to define the trigonometric functions for any angle, not just those within a right triangle. The coordinates of points on the unit circle correspond to the values of sine and cosine for various angles.
3. Trigonometric Identities: Trigonometric identities are equations involving trigonometric functions that hold true for all angles. These identities are used to simplify expressions, solve equations, and establish relationships between different trigonometric functions.
4. Trigonometric Equations: Trigonometric equations involve trigonometric functions and angles. Solving these equations often requires applying trigonometric identities and algebraic techniques.
5. Inverse Trigonometric Functions: Inverse trigonometric functions (e.g., arcsin, arccos, arctan) provide a way to find an angle given the ratio of sides. They essentially “undo” the effects of trigonometric functions (sin-1x, cos-1x, cot-1 x, tan-1 x, cosec-1 x, and sec-1 x).
6. Applications: Trigonometry is widely used in various fields. For instance, it’s used in geometry to calculate distances and angles in triangles and polygons. In physics, it’s applied to describe oscillations, waves, and rotational motion. Engineers use trigonometry for designing structures, analyzing circuits, and more.
The roots of trigonometry can be traced back to ancient civilizations, where the need to measure angles and distances played a crucial role.
1. Ancient Mesopotamia: The earliest known trigonometric tables, dating back to around 1900 BC, were found in Mesopotamia. These tables contained values of trigonometric ratios for specific angles and were used for practical purposes like surveying.
2. Ancient Greece: Greek mathematicians, such as Hipparchus and Ptolemy, made significant contributions to trigonometry. Hipparchus, known as the “father of trigonometry,” created a table of chords, a precursor to modern trigonometric functions.
3. Indian Mathematics: Indian mathematicians, particularly Aryabhata and Brahmagupta, developed their own trigonometric methods. They introduced concepts like sine and cosine and used them to solve problems in astronomy and mathematics.
4. Islamic Golden Age: During the Islamic Golden Age, scholars like Al-Khwarizmi and Al-Battani made substantial advancements in trigonometry, developing the concept of sine as it is known today.
Trigonometry has also been essential for navigation throughout history. Sailors and explorers used trigonometric principles to determine their positions at sea, contributing to the Age of Exploration. It is at the heart of music theory as well. The properties of sine and cosine waves are crucial for understanding musical tones and harmonics. And there is of course the space exploration. It helps calculate spacecraft trajectories, angles of satellite dishes, and even the positions of celestial objects.
It bridges the gap between theory and practice and it is a subject worth exploring to gain clear understanding how profound its impact is on every day life. | crawl-data/CC-MAIN-2023-50/segments/1700679102637.84/warc/CC-MAIN-20231210190744-20231210220744-00707.warc.gz | null |
# 3TH / VWO §9.1/§9.4 Calculating with fractions
3T havo §9.1 Calculating with fractions
3T vwo §9.4 the same (almost)!
1 / 21
Slide 1: Tekstslide
WiskundeMiddelbare schoolhavoLeerjaar 3
In deze les zitten 21 slides, met interactieve quizzen en tekstslides.
Lesduur is: 50 min
## Onderdelen in deze les
3T havo §9.1 Calculating with fractions
3T vwo §9.4 the same (almost)!
#### Slide 1 -Tekstslide
A short recap:
When adding or subtracting fractions, the denominators (noemers) have to be the same. If they're not, let's make them the same! As follows:
53+76=3521+3530=3551
#### Slide 2 -Tekstslide
+ Now with variables too!
+ Many times we just multiply the denominators to find the new one.
+ Like here: 5 x 8 = 40
#### Slide 3 -Tekstslide
+ another one comes up
+ watch: the 2nd fraction is not changed by us!
+ 5x is a fine denominator
#### Slide 4 -Tekstslide
+ One more.
+ The final result has a sum as numerator.
+ That's because 4 and 3x are not like terms!
#### Slide 6 -Tekstslide
Take a scrap paper (or your Notebook) and work out:
Write as one fraction and key in your answer in the next slide:
#### Slide 9 -Tekstslide
Do you remember that doing 'times' is much simpler than doing
'plus or minus', with fractions?
Reason: denominators may be unequal. Who cares?
x = =
65
83
4815
165
#### Slide 10 -Tekstslide
I remember something about making denominators equal. So here I go about the job:
x = x =
However now I am completely stranded..... So let's look once more at the right way to do it!
65
83
4815
165
4818
4840
.....75
........
#### Slide 11 -Tekstslide
Do you remember that doing 'times' is much simpler than doing
'plus or minus', with fractions?
Reason: denominators may be unequal. Who cares?
x = =
65
83
4815
165
#### Slide 12 -Tekstslide
When multiplying we just multiply numerators and
denominators. Period!
#### Slide 13 -Tekstslide
Simplification is the reverse of multiplication.
Now we divide numerator and denominator by the same number!
#### Slide 14 -Tekstslide
2 more examples of simplifications:
The book (where I took this from)
like to write the numbers as
products of letters and prime numbers
(priemgetallen). This may seem
unnecessary, but it makes clear
what is really happening when
simplifying!
#### Slide 15 -Tekstslide
Simplify yourself now and key in your answer in the next slide:
#### Slide 17 -Woordweb
The 2nd step
you may leave out.
#### Slide 19 -Tekstslide
There's one more new thing in §9.1....
That's about splitting up a fraction
in 2 new ones.
In exercises 8, 9 and 10 (havo)
and 32, 33 (vwo)
you'll discover
this for yourself!
Homework time | crawl-data/CC-MAIN-2024-30/segments/1720763515300.51/warc/CC-MAIN-20240720144323-20240720174323-00344.warc.gz | null |
Iron oxide materials yield pigments that are nontoxic, nonbleeding, weather resistant, and lightfast. Natural iron oxides include a combination of one or more ferrous or ferric oxides, and impurities, such as manganese, clay, or organics. Synthetic iron oxides can be produced in various ways, including thermal decomposition of iron salts, such as ferrous sulfate, to produce reds; precipitation to produce yellows, reds, browns, and blacks (e.g., the Penniman-Zoph process); and reduction of organic compounds by iron (e.g., nitrobenzene reduced to aniline in the presence of particular chemicals) to produce yellows and blacks. Reds can be produced by calcining either yellow or blacks.
If you are interested in receiving an email notice when a publication is added to this page, please refer to Minerals Information List Services.
- Iron Oxide Pigments
| 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |
| 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |
| 1932-1993 |
- Historical Statistics for Mineral and Material Commodities in the United States
Data Series 140
- USGS Mineral Commodity Specialist
Arnold O. Tanner | <urn:uuid:15b54e0c-a9d5-448e-a0f9-2103ddf5f4f5> | {
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Hydropower is usually touted as clean energy, but a new study has found man-made reservoirs are producing far more greenhouse gases than previously believed, with most of those emissions in the form of methane, a potent climate-warming gas.
Researchers found that reservoirs are producing 1.3 per cent of all greenhouse gases produced by humans, or, to put the figure in context, more than all greenhouse gases produced in Canada annually.
“We weren’t super-surprised at the magnitude of the emissions, but one thing we were surprised to see is the per area rate of methane emissions. They are 25 per cent higher than previously thought,” Washington State University researcher Bridget Deemer, lead author of the study, published Wednesday in the journal BioScience, told DeSmog Canada.
“(Methane emissions) contribute about 80 per cent of the total global warming impact of the gases from reservoirs.” The remaining emissions are carbon dioxide and nitrous oxide.
Methane is 34 times more potent than carbon dioxide and emissions have previously been difficult to measure, but new research is using tools such as bubble-tracking sonar to measure methane bubbles.
Researchers from the Washington State University along with colleagues from around the world looked at the results of more than 100 studies of emissions from 250 reservoirs around the world.
The startling results are leading to calls for reservoir emissions to be included in calculations made by countries and organizations such as the Intergovernmental Panel on Climate Change when gauging greenhouse gas emissions.
The emissions from reservoir water surfaces are comparable to those from rice paddies or biomass burning, both of which are incorporated in carbon budgeting, the study says.
The new information also points to the need for countries to look carefully at where they build dams.
The emissions, including carbon dioxide and nitrous oxide, come from decomposing plant material under the water and methane is produced by microbes devouring rotting material, such as algae, in sediment that builds up behind dams. The emissions are then boosted by nutrients that come from human activities such as agriculture or septic systems.
Natural lakes produce less greenhouse gases as there is not so much rotting material beneath the water and because reservoirs have more fluctuations in water levels than natural lakes — something which enhances methane production.
Ideally, to reduce emissions, dams should be built in areas with minimal vegetation and human activity as biologically productive reservoirs, with more algae and nutrient-rich systems, produce more methane, Deemer said.
More than one-million dams exist around the world and thousands of hydroelectric dams are in the planning or building stages, including the controversial Site C dam in B.C.’s Peace River Valley, which will create an 83-kilometre long reservoir in an agriculturally rich region of the province.
Deemer said Site C was not part of the study and she could not immediately estimate the emissions from a reservoir of that size.
The study did not look at how emissions from reservoirs compared to power generated by natural gas or coal, but a 2013 study by Edgar G. Hertwich of the Norwegian University of Science and Technology found that carbon dioxide emissions from hydropower, per unit of electricity delivered, were 10 per cent higher than emissions from natural gas-fired plants.
One of the B.C. government’s major arguments in favour of construction of the $9-billion Site C dam is that it would provide clean energy to British Columbians for more than a century, but this latest study brings into question whether hydropower from reservoirs can be described as green.
The project will flood 5,500 hectares of prime agricultural land and, as former farmland and forests disappear beneath the water, the reservoir will meet all criteria, pinpointed in the research paper for producing large quantities of methane and other greenhouse gases.
Site C critic Ken Boon, who is being forced off his third-generation family farm by BC Hydro to allow for highway re-alignment away from the Site C flood zone, said the study provides some interesting revelations.
“Going through the environmental assessment process, BC Hydro really diminished the greenhouse gases that would result from Site C, so it really wasn’t a big issue going through the review hearings,” he said. A June 2016 report released by the University of British Columbia found the greenhouse gas impacts of the Site C dam eliminate any possibility of the project’s advantage over alternative forms of power production like wind and solar.
“Now, again, the landscape changes and it’s one more strike against building large hydroelectric dams,” he said.
Boon hopes that Premier Christy Clark will take notice of the new information, but he is not optimistic.
“She seems to have a whole hypocritical, twisted view of climate change,” Boon said.
Helen Knott, a member of the Prophet River First Nation and active Site C opponent, pointed out that the provincial government’s reason in 2010 for exempting Site C from a B.C. Utilities Commission review was that it was a green project.
“Actually it is not a green project and this is just one more reason why it should not be built,” said Knott, pointing to myriad other problems with Site C such as questionable economics, opposition by First Nations and loss of agricultural land and food security.
“And now there is this. It’s just a project that doesn’t make sense,” Knott said.
BC Hydro and Environment Ministry spokespeople did not respond to questions about the study by time of publication.
And since you’re here, we have a favour to ask. Our independent, ad-free journalism is made possible because the people who value our work also support it (did we mention our stories are free for all to read, not just those who can afford to pay?).
As a non-profit, reader-funded news organization, our goal isn’t to sell advertising or to please corporate bigwigs — it’s to bring evidence-based news and analysis to the surface for all Canadians. And at a time when most news organizations have been laying off reporters, we’ve hired eight journalists over the past year.
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A contingency table presents the joint density of one or more categorical variables. Each entry in a contingency table is a count of the number of times a particular set of factors levels occurs in the dataset. For example, consider a list of plant species where each species is assigned a relative seed size (small, medium, or large) and a growth form (tree, shrub, or herb).
seed.sizes <- c("small", "medium", "large") growth.forms <- c("tree", "shrub", "herb") species.traits <- data.frame( seed.size = seed.sizes[c(1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3)], growth.form = growth.forms[c(3, 3, 2, 2, 1, 2, 2, 3, 1, 1, 1, 1)] )
A contingency table will tell us how many times each combination of seeds.sizes and growth.forms occur.
tbl <- table(species.traits)
The output contingency table are of class
table. The behaviour of
these objects is not quite like a data frame. In fact, trying to
convert them to a data frame gives a non-intuitive result.
Coercion of the table into a data frame puts each factor of the
contingency table into its own column along with the frequency,
rather than keeping the same structure as original
If we wanted to turn the table into a data frame keeping the
original structure we use
as.data.frame.matrix. This function is
not well-documented in R, and this is probably the only situation in
which it would be used. But, it works. | <urn:uuid:ff87a7bf-16a5-47ad-b745-ea65221855e3> | {
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By measuring elusive antimatter particles formed within the Earth's mantle, physicists can determine how much heat forms inside the Earth.
By Tia Ghose
Scientists have tentatively identified several particles lurking deep inside the Earth's mantle that could reveal how much heat the planet produces and confirm that the Earth formed from materials from the sun.
The wacky particles are called geoneutrinos, or the antimatter partners of neutrinos (exotic fundamental particles that can pass right through Earth), that form deep within the Earth's mantle. Every matter particle has an antimatter partner particle that has an opposite charge, and when the two meet they annihilate each other. The findings were detailed described Monday in the preprint journal arXiv.org.
Geoneutrinos aren't the only particles scientists are hoping to find inside Earth. An experiment using the Earth as a source of electrons recently narrowed down the search for a new force-bearing particle, possibly the so-called unparticle, placing tighter limits on the force it carries.
When Earth formed, the radioactive elements thorium and uranium were distributed in Earth's interior at different concentrations within the crust (the planet's outer layer) and mantle. As these elements within the mantle radioactively decay, they give off heat and also form subatomic particles known as geoneutrinos, said study co-author Aldo Ianni, a physicist at the Gran Sasso National Laboratory in Italy.
The heat formed from this decay is the engine that drives the motion of the viscous, oozing material that forms the Earth's mantle. That, in turn can shift the tectonic plates, causing earthquakes. Whereas researchers have models to predict how much heat is generated inside the Earth, measuring it has proved tricky. [50 Amazing Facts About Planet Earth]
That's partly because mantle lies miles beneath the Earth's surface, so "if you want to understand how much heat is produced by these radioactive elements, the only way today to understand how much is this so-called radiogenic heat is through the geoneutrinos," Ianni said.
To do so, researchers at the Gran Sasso underground laboratory, which is nearly a mile below a mountain in Italy, looked for signals in a vast pool of oil-based liquid that scintillates, or produces flashes of light when particles such as protons pass through it. When geoneutrinos pass through the scintillating liquid they bump into protons and emit a positron and then a neutron, creating a distinctive signal, Ianni told LiveScience.
Many of the particles they initially identified actually came from nuclear reactors from power plants. But by measuring the energy levels of the neutrinos, they could isolate the 30 percent that came from the Earth's mantle, Ianni said.
The geoneutrinos are created from the decay of radioactive thorium and uranium in a reaction that gives off a known amount of heat. As a result, how frequently the researchers find the particles can reveal the quantity of the radioactive elements lurking in Earth's mantle, and in turn how much heat they generate. That can help scientists refine their knowledge of plate tectonics, Ianni said.
But it may also confirm the theory that the Earth formed from the sun, Ianni said. Meteorites that come from the solar system's early history contain distinctive ratios of uranium and thorium that very closely mirror the composition of the sun's surface. By comparing that ratio with the amount found inside the Earth, they can confirm the Earth's solar origins.
- Wacky Physics: The Coolest Little Particles in Nature
- What's That? Your Physics Questions Answered
- Image Gallery: One-of-a-Kind Places on Earth
Copyright 2013 LiveScience, a TechMediaNetwork company. All rights reserved. This material may not be published, broadcast, rewritten or redistributed. | <urn:uuid:87461880-b019-45f0-a70d-4997fa09ec8c> | {
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Associated Topics || Dr. Math Home || Search Dr. Math
### What Is N Factorial Used For?
```
Date: 08/29/2001 at 18:02:22
From: Stuart Reed
Subject: What is n factorial used for?
Can you please tell me what n! or n factorial is used for. I know what
it is (5! is 120, because 1*2*3*4*5 = 120), but not what it is used
for. I have heard that it is used in probability, but what for, and
how? How does it work, and what are its uses?
```
```
Date: 08/30/2001 at 10:49:46
From: Doctor Ian
Subject: Re: What is n factorial used for?
Hi Stuart,
The factorial function is useful in computing the number of
combinations or permutations that can be constructed from a set of
Permutations and Combinations
http://mathforum.org/dr.math/faq/faq.comb.perm.html
Very briefly, here is the kind of problem that would give rise to the
factorial function.
Suppose you have three people (Alan, Bob, Cindy), and you want to know
how many ways they can stand in line. For a small number like 3, the
answer is easy to construct by trial and error:
Alan, Bob, Cindy
Alan, Cindy, Bob
Bob, Alan, Cindy
Bob, Cindy, Alan
Cindy, Alan, Bob
Cindy, Bob, Alan
But for larger numbers of people, it becomes very difficult to avoid
duplicating some sequences, or skipping some by accident.
With a little thought, we can see that if we have N people, then there
are N choices for who might go into the first position:
1. Alan
2. Bob
3. Cindy
4. Diane
Having made that first choice, there are N-1 choices for who might go
in the second position, for _each_ of the original choices:
1. Alan 1. Bob
2. Cindy
3. Diane
2. Bob 1. Alan
2. Cindy
3. Diane
3. Cindy 1. Alan
2. Bob
3. Diane
4. Diane 1. Alan
2. Bob
3. Cindy
And there are N-2 choices for who might go into the third position,
again for _each_ of the previous sets of choices:
1. Alan 1. Bob 1. Cindy
2. Diane
2. Cindy 1. Bob
2. Diane
3. Diane 1. Bob
2. Cindy
2. Bob 1. Alan etc.
2. Cindy
3. Diane
3. Cindy 1. Alan
2. Bob
3. Diane
4. Diane 1. Alan
2. Bob
3. Cindy
I'll leave the rest of the chart for you to fill in, if you wish.
Note that the final number of possible orderings of N objects will be
ways to
make the
next choice
|
v
N * (N-1) * (N-2) * ... * 1
^ ^
| |
ways to ways to
make the make the
first choice final choice
which is exactly the factorial function.
When dealing with combinations and permutations (and, by extension,
when dealing with probabilities), this kind of reasoning comes up over
and over again, which is why the factorial function is so important.
Does this help?
- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Permutations and Combinations
High School Probability
Middle School Factorials
Middle School Probability
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# A triangle has sides with lengths of 3, 7, and 6. What is the radius of the triangles inscribed circle?
Jan 19, 2016
$r = \frac{\sqrt{5}}{2}$
#### Explanation:
To find the radius, we use the fact that the triangle contains three internal triangles whose height is the radius $r$. The sum of the areas of these triangles equals the area of the triangle ABC, which is calculated using Heron's formula
$A = \sqrt{p \left(p - a\right) \left(p - b\right) \left(p - c\right)}$ where $p = \frac{a + b + c}{2}$
$p = \frac{3 + 7 + 6}{2} = 8$
$\therefore A = \sqrt{8 \cdot 5 \cdot 1 \cdot 2} = \sqrt{80} = \sqrt{16 \cdot 5} = 4 \sqrt{5}$
The three internal triangles have areas
${a}_{1} = \frac{1}{2} \cdot 3 \cdot r = \frac{3 r}{2}$
${a}_{2} = \frac{1}{2} \cdot 7 \cdot r = \frac{7 r}{2}$
${a}_{3} = \frac{1}{2} \cdot 6 \cdot r = 3 r$
${a}_{1} + {a}_{2} + {a}_{3} = A$
$r \left(\frac{3}{2} + \frac{7}{2} + 3\right) = 4 \sqrt{5}$
$\therefore r = 4 \frac{\sqrt{5}}{8} = \frac{\sqrt{5}}{2}$ | crawl-data/CC-MAIN-2019-51/segments/1575540579703.26/warc/CC-MAIN-20191214014220-20191214042220-00106.warc.gz | null |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are reading an older version of this FlexBook® textbook: Algebra II Go to the latest version.
# 12.1: Modeling Data with Functions
Difficulty Level: At Grade Created by: CK-12
Name: __________________
Direct Variation
1. Suppose I make $\6/\mathrm{hour}$. Let $t$ represent the number of hours I work, and $m$ represent the money I make.
a. Make a table showing different $t$ values and their corresponding $m$ values. ($m$ is not how much money I make in that particular hour—it’s how much total money I have made, after working that many hours.)
time $(t)$ money $(m)$
b. Which is the dependent variable, and which is the independent variable?
c. Write the function.
d. Sketch a quick graph of what the function looks like.
e. In general: if I double the number of hours, what happens to the amount of money?
2. I am stacking bricks to make a wall. Each brick is $4$" high. Let $b$ represent the number of bricks, and $h$ represent the height of the wall.
a. Make a table showing different $b$ values and their corresponding $h\;\mathrm{values}$.
bricks $(b)$ height $(h)$
b. Which is the dependent variable, and which is the independent variable?
c. Write the function.
d. Sketch a quick graph of what the function looks like.
e. In general: if $I$ triple the number of bricks, what happens to the height?
3. The above two scenarios are examples of direct variation. If a variable $y$ “varies directly” with $x$, then it can be written as a function $y=kx$, where $k$ is called the constant of variation. (We also sometimes say that “$y$ is proportional to $x$,” where $k$ is called the constant of proportionality. Why do we say it two different ways? Because, as you’ve always suspected, we enjoy making your life difficult. Not “students in general,” but just you personally.) So, if $y$ varies directly with $x \ldots$
a. What happens to $y$ if $x$ doubles? (Hint: You can find and prove the answer from the equation $y=kx$.)
b. What happens to $y$ if $x$ is cut in half?
c. What does the graph $y(x)$ look like? What does $k$ represent in this graph?
4. Make up a word problem like numbers $(1)$ and $(2)$ above, on the subject of fast food. Your problem should not involve getting paid or stacking bricks. It should involve two variables that vary directly with each other. Make up the scenario, define the variables, and then do problems a-e exactly like my two problems.
Name: __________________
Homework Inverse Variation
1. An astronaut in space is performing an experiment with three balloons. The balloons are all different sizes, but they have the same amount of air in them. As you might expect, the balloons that are very small experience a great deal of air pressure (the air inside pushing out on the balloon); the balloons that are very large, experience very little air pressure. He measures the volumes and pressures and comes up with the following chart.
Volume $(V)$ Pressure $(P)$
$5$ $270$
$10$ $135$
$15$ $90$
$20$ $67\frac{1}{2}$
a. Which is the dependent variable, and which is the independent variable?
b. When the volume doubles, what happens to the pressure?
c. When the volume triples, what happens to the pressure?
d. Based on your answers to parts (a) - (c), what would you expect the pressure to be for a balloon with a volume of $30$?
e. On the right of the table add a third column that represents the quantity $\mathrm{PV}$: pressure times volume. Fill in all four values for this quantity. What do you notice about them?
f. Plot all four points on the graph paper, and fill in a sketch of what the graph looks like.
g. Write the function $P(V)$. Make sure that it accurately gets you from the first column to the second in all four instances! (Part (e) is a clue to this.)
h. Graph your function $P(V)$ on your calculator, and copy the graph onto the graph paper. Does it match your graph in part $(f)$?
2. The three little pigs have built three houses—made from straw, Lincoln Logs$^\circledR$, and bricks, respectively. Each house is $20'\mathrm{high}$. The pieces of straw are $\frac{1}{10}"$ thick; the Lincoln Logs$^\circledR$ are $1"$ thick; the bricks are $4"$ thick. Let $t$ be the thickness of the building blocks, and let $n$ be the number of such blocks required to build a house $20'\mathrm{high}$. (Note: There are $12"$ in $1'$. But you probably knew that ...)
a. Make a table showing different $t$ values and their corresponding $n\;\mathrm{values}$.
Building Blocks thickness $(t)$ number $(n)$
Straw
Lincoln Logs$^\circledR$
Bricks
b. Which is the dependent variable, and which is the independent variable?
c. When the thickness of the building blocks doubles, what happens to the number required?
(*Not sure? Pretend that the pig’s cousin used $8"$ logs, and his uncle used $16"$ logs. See what happens to the number required as you go up in this sequence...)
d. When the thickness of the building blocks is halved, what happens to the number required?
e. On the right of the table add a fourth column, that represents the quantity $tn$: thickness times number. Fill in all three values for this quantity. What do you notice about them? What do they actually represent, in our problem?
f. Plot all three points on the graph paper, and fill in a sketch of what the graph looks like.
g. Write the function $n(t)$.
h. Graph your function $n(t)$ on your calculator, and copy the graph onto the graph paper. Does it match your graph in part (f)?
3. The above two scenarios are examples of inverse variation. If a variable $y$, “varies inversely” with $x$, then it can be written as a function $y=\frac{k}{x}$, where $k$ is called the constant of variation. So, if $y$ varies inversely with $x$...
a. What happens to $y$ if $x$ doubles? (Hint: You can find and prove the answer from the equation $y=\frac{k}{x}$ )
b. What happens to $y$ if $x$ is cut in half?
c. What does the graph $y(x)$ look like? What happens to this graph when $k$ increases? (* You may want to try a few different ones on your calculator to see the effect $k$ has.)
4. Make up a word problem like numbers $(1)$ and $(2)$ above. Your problem should not involve pressure and volume, or building a house. It should involve two variables that vary inversely with each other. Make up the scenario, define the variables, and then do problems a-h exactly like my two with each other. Make up the scenario, define the variables, and then do problems a-h exactly like my two problems.
Name: __________________
Homework Direct and Inverse Variation
For questions $1-3$, Please note that these numbers are meant to simulate real world data—that is to say, they are not necessarily exact! If it is “darn close to” direct or inverse variation, that’s good enough.
1. For the following set of data...
$x$ $y$
$3$ $5$
$6$ $11$
$21$ $34$
a. Does it represent direct variation, inverse variation, or neither?
b. If it is direct or inverse, what is the constant of variation?
c. If $x=30$, what would $y$ be?
d. Sketch a quick graph of this relationship.
2. For the following set of data...
$x$ $y$
$3$ $18$
$4$ $32$
$10$ $200$
a. Does it represent direct variation, inverse variation, or neither?
b. If it is direct or inverse, what is the constant of variation
c. If $x=30$, what would $y$ be?
d. Sketch a quick graph of this relationship.
3. For the following set of data$\ldots$
$x$ $y$
$3$ $20$
$6$ $10$
$21$ $3$
a. Does it represent direct variation, inverse variation, or neither?
b. If it is direct or inverse, what is the constant of variation?
c. If $x=30$, what would $y$ be?
d. Sketch a quick graph of this relationship.
4. In number $2$ above, as you (hopefully) saw, the relationship is neither direct nor inverse. However, the relationship can be expressed this way: $y$ is directly proportional to $x^2$. Write the function that indicates this relationship. What is $k$? one table is miss
5. In June, 2007, Poland argued for a change to the voting system in the European Union Council of Ministers. The Polish suggestion: each member’s voting strength should be directly proportional to the square root of his country’s population. This idea, traditionally known as Pensore’s Rule, is “almost sacred” among “people versed in the game theory of voting” according to one economist.
I swear I am not making this up.
Also in the category of “things I am not making up,” the following table of European Populations comes from Wikipedia.
$&\text {Germany} && 83,251,851\\& \text{Italy} && 59,715,625\\&\text{Poland} && 38,625,478\\&\text{Luxemberg} && 48,569$
a. Write an equation that represents Pensore’s Rule. Be sure to clearly label your variables.
b. Suppose that Pensore’s Rule was followed, and suppose that Poland voting strength was exactly $100$ (which I did actually make up, but of course it doesn’t matter). What would the voting strength of Germany, Italy, and Luxembourg be?
6. Write a “real world” word problem involving an inverse relationship, on the topic of movies. Identify the constant of variation. Write the function that shows how the dependent variable depends inversely upon the independent variable. Create a specific numerical question, and use your function to answer that question.
7. Joint Variation: The term “Joint Variation” is used to indicate that one variable varies directly as two different variables. This is illustrated in the following example.
Al is working as a waiter. When a group of people sit down at a table, he calculates his expected tip $(T)$ as follows: multiply the number of people $(N)$, times the average meal cost $(C)$, times $0.15$ (for a $15\%$ tip).
a. If the number of people at the table doubles, does Al’s expected tip double?
b. If the average cost per meal doubles, does Al’s expected tip double?
c. Write the function that expresses the dependent variable, $T$, as a function of the two independent variables, $N$ and $C$.
d. Write the general function that states “$z$ varies jointly as both $x$ and $y$.” Your function will have an unknown $k$ in it, a constant of variation.
8. Light Intensity: Stacy visits a tanning booth, where she spends several hours with lamps shining on her skin, thus giving her a beautiful copper-colored tan and a sharply increased risk of skin cancer. For reasons known only to herself, she considers this a good trade-off. Anyway, Stacy has a lot of time to just lie there and think, and she starts to consider the question: which bulb is shining on her skin with the most intensity? The answer is that the intensity I of a bulb varies directly with the strength $S$ of the bulb, and varies inversely with the square of the distance $d$ of the bulb from her skin.
a. Bulbs $A$ and $B$ are the same distance away, but bulb $B$ is twice as strong as bulb $A$. If bulb $A$ shines with an intensity of $5$, what is the intensity of bulb $B$?
b. Bulbs $A$ and $C$ are the same strength as each other, but bulb $A$ is twice as far away from Stacy as bulb $C$. If bulb $A$ shines with an intensity of $5$, what is the intensity of bulb $B$?
c. Write a function to represent the statement “the intensity I of a bulb varies directly with the strength $S$ of the bulb, and varies inversely with the square of the distance d of the bulb from Stacy’s skin.” Your function will have an unknown $k$ in it, a constant of variation.
Name: _________________
Homework: Calculator Regression
1. Canadian Voters: The following table shows the percentage of Canadian voters who voted in the 1996 federal election.
$&\text{Age} && 20 && 30 && 40 && 50 && 60\\&\% \text{voted} && 59 && 86 && 87 && 91 && 94$
a. Enter these points on your calculator lists.
b. Set the Window on your calculator so that the $x-$values go from $0$ to $60$, and the $y-$values go from $0$ to $100$. Then view a graph of the points on your calculator. Do they increase steadily (like a line), or increase slower and slower (like a log), or increase more and more quickly (like a parabola or an exponent)?
c. Use the [STAT] function on your calculator to find an appropriate function to model this data. Write that function below.
d. Graph the function on your calculator. Does it match the points well? Are any of the points “outlyers?”
2. Height and Weight: A group of students record their height (in inches) and weight (in pounds). The results are on the table below.
$&\text{Height} && 68 && 74 && 66 && 68 && 72 && 69 && 65 && 71 && 69 && 72 && 71 && 64 && 65\\&\text{weight} && 180 && 185 && 150 && 150 && 200 && 160 && 125 && 220 && 220 && 180 && 190 &&120 && 110$
a. Enter these points on your calculator lists.
b. Set the Window on your calculator appropriately, and then view a graph of the points on your calculator. Do they increase steadily (like a line), or increase slower and slower (like a log), or increase more and more quickly (like a parabola or an exponent)?
c. Use the [STAT] function on your calculator to find an appropriate function to model this data. Write that function below.
d. Graph the function on your calculator. Does it match the points well? Are any of the points “outlyers?”
3. Gas Mileage: The table below shows the weight (in hundreds of pounds) and gas mileage (in miles per gallon) for a sample of domestic new cars.
$&\text{Weight} && 29 && 35 && 28 && 44 && 25 && 34 && 30 && 33 && 28 && 24\\&\text{mileage} && 31 && 27 && 29 && 25 && 31 && 29 && 28 && 28 && 28 && 33$
a. Enter these points on your calculator lists.
b. Set the Window on your calculator appropriately, and then view a graph of the points on your calculator. Do they decrease steadily (like a line), or decrease slower and slower (like a log), or decrease more and more quickly (like a parabola or an exponent)?
c. Use the [STAT] function on your calculator to find an appropriate function to model this data. Write that function below.
d. Graph the function on your calculator. Does it match the points well? Are any of the points “outlyers?”
4. TV and GPA: A graduate student named Angela Hershberger at Indiana University-South Bend did a study to find the relationship between TV watching and Grade Point Average among high school students. Angela interviewed $50$ high school students, turning each one into a data point, where the independent $(x)$ value was the number of hours of television watched per week, and the dependent $(y)$ value was the high school grade point average. (She also checked the types of television watched—eg news or sitcoms—and found that it made very little difference. Quantity, not quality, mattered.)
In a study that you can read all about at www.iusb.edu/~journal/2002/hershberger/hershberger.html, Angela found that her data could best be modeled by the linear function $y=–0.0288 x + 3.4397$. Assuming that this line is a good fit for the data
a. What does the number $3.4397$ tell you? (Don’t tell me about lines and points: tell me about students, TV, and grades.)
b. What does the number $–0.0288$ tell you? (Same note.)
Name: _________________
Sample Test: Modeling Data with Functions
1. Three cars and an airplane are traveling to New York City. But they all go at different speeds, so they all take different amounts of time to make the $500-$mile trip. Fill in the following chart.
Speed(s) - miles per hour Time(t) - hours
$50$
$75$
$100$
$500$
a. Is this an example of direct variation, inverse variation, or neither of the above?
b. Write the function $s(t)$.
c. If this is one of our two types, what is the constant of variation?
2. There are a bunch of squares on the board, of different sizes.
s - length of teh side of a square A - area of the square
$1$
$2$
$3$
$4$
a. Is this an example of direct variation, inverse variation, or neither of the above?
b. Write the function $A(s)$.
c. If this is one of our two types, what is the constant of variation?
3. Anna is planning a party. Of course, as at any good party, there will be a lot of on hand! $50$ Coke cans fit into one recycling bin. So, based on the amount of Coke she buys, Anna needs to make sure there are enough recycling bins.
c-Coke cans Anna buys b - recycling bins she will need
$50$
$100$
$200$
$400$
a. Is this an example of direct variation, inverse variation, or neither of the above?
b. Write the function $b(c)$.
c. If this is one of our two types, what is the constant of variation?
4. Make up a word problem involving inverse variation, on the topic of skateboarding.
a. Write the scenario.
b. Label and identify the independent and dependent variables.
c. Show the function that relates the dependent to the independent variable. This function should (of course) be an inverse relationship, and it should be obvious from your scenario!
5. I found a Web site (this is true, really) that contains the following sentence:
[This process] introduces an additional truncation error [directly] proportional to the original error and inversely proportional to the gain $(g)$ and the truncation parameter $(q)$.
I don’t know what most of that stuff means any more than you do. But if we use $T$ for the “additional truncation error” and E for the “original error,” write an equation that expresses this relationship.
6. Which of the following correctly expresses, in words, the relationship of the area of a circle to the radius?
A. The area is directly proportional to the radius
B. The area is directly proportional to the square of the radius
C. The area is inversely proportional to the radius
D. The area is inversely proportional to the square of the radius
7. Now, suppose we were to write the inverse of that function: that is, express the radius as a function of the area. Then we would write:
The radius of a circle is ___________ proportional to _____________________ the area.
8. Death by Cholera: In 1852, William Farr reported a strong association between low elevation and deaths from cholera. Some of his data are reported below.
$&\text{E:Elevation(ft)} && 10 && 30 && 50 && 70 && 90 && 100 && 350\\&\text{C:Cholera morality}(\text{per} 10,000) && 102 && 65 && 34 && 27 && 22 && 17 && 8$
a. Use your calculator to create the following models, and write the appropriate functions $C(E)$ in the blanks.
Linear: $C=$
Quadratic: $C=$
Lograthamic: $C=$
exponential: $C=$
b. Which model do you think is the best? Why?
c. Based on his very strong correlation, Farr concluded that bad air had settled into low-lying areas, causing outbreaks of cholera. We now know that air quality has nothing to do with causing cholera: the water-borne bacterial Vibrio cholera causes the disease. What might explain Farr’s results without justifying his conclusion?
Feb 23, 2012
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What you will study
The study material for this module is organised into 8 learning guides, which include audio-visual material and online and print-based readings:
Learning Guide 1: Young lives – begins to examine the range of factors that influence the divergent lives and complex experiences of children and young people today. Issues that students will explore include whether this is a good time to be young, and the impact of discrimination, poverty and inequality. They will also begin to consider the many issues for people working in children’s services today .
Learning Guide 2: Society and community – encourages students to use a range of data and research in order to critically examine how community and society are experienced and related to the wellbeing and life chances of children and young people. Students will examine the concept of time within individual everyday experience and wider social change, such as demographic changes, changes in the law and changes in relationships. They will also critically reflect on the extent to which society is a meritocracy and apply theories of social capital and cultural capital to explain social mobility and inequalities.
Learning Guide 3: Working together – focuses on practice and explores how practitioners work together to support children, young people, parents and families. Students will consider the opportunities, as well as the potential challenges, presented by multi-agency and inter-professional working, and they will look at ways in which values, ethics and legal frameworks inform practice in this area. They will also examine some of the ethical dilemmas that practitioners may encounter, and the ways in which they might deal with ethical dilemmas in their practice with children, young people, parents and families.
Learning Guide 4: Children and childhood – focuses on children (particularly those aged 0–12 years) and examines several of the key issues embedded in modern childhood such as inclusion, gender, rights and child protection. It uses a range of material to enable students to acquire a deeper and more nuanced understanding of children and childhood and of the skills and values of effective and equitable work with children.
Learning Guide 5: Youth and young people – looks at social and cultural aspects of being young and the concept of ‘youth’. Students critically explore changing understandings of young people’s lives and examine how different professionals engage with young people. Young people’s involvement in crime and policing, music and popular culture are featured, alongside questions of gender, race and class.
Learning Guide 6: Parents and parenting – focuses on parents and parenting, and relationships between practitioners and parents. Students are asked to consider a range of perspectives on parenting, including what it means to be a ‘good parent’, and to look at case studies and research related to the intersection of parenting and society. Issues examined include the role and function of parenting support and education, for example, parenting classes, programmes targeted for ‘troubled families’, and the role of informal support and online communities. Children and young people’s perspectives on parenting will also be explored.
Learning Guide 7: Families matter – examines the family and family structures historically and in relation to contemporary social change. It considers ways in which social and economic change impact on families and the role of service providers in addressing the disadvantages arising from these. It looks at the experience of children and young people living outside of their ‘birth families’, and their experience of the care system. It also reflects on some of the problems that families might encounter, asking how professionals can intervene in ways that enhance social capital and encourage empowerment.
Learning Guide 8: Reviewing your learning – focuses on supporting students in reviewing their learning over the course of the module and preparing for the end-of-module assessment (which is an EMA).
This module will be relevant if you are currently working with children, young people, parents and families, or if you have an interest in moving into this area of work. It will also be relevant if you have a general interest in issues related to children, young people, parenting and families. | <urn:uuid:a2c24c1c-a516-45be-8db8-6b395fbb2472> | {
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Etc., e.g., esp., Eng., and Inc. are examples of some common abbreviations. EnglishLeap.com, InfoPlease.com, FactMoster.com and AResearchGuide.com are websites that provide lists of many abbreviations, as of 2015. The sites do not require users to register to view their contents.Continue Reading
Abbreviations are the short form of words or phrases. They are easy to remember, concise and convenient. The more familiar and successful an abbreviation is, the less the need for the full form. Abbreviations are letter-based, syllable-based and hybrid. Abbreviations help in note-taking, making of inventories, file making and cataloging, according to Encyclopedia.com. Acronyms are a form of abbreviation.
There are various methods employed when writing abbreviations. The first method involves the use of capital letters and points. For example, U.S. for the United States. The second method is the use of capital letters without points: CNN for Cable News Network. The third way is the use of lowercase letters with points, for example, i.e. for that is.
Another method involves the use of mixed capitals and lowercase without points. For example, mRNA for messenger ribonucleic acid. Another technique for creating abbreviations is the use of internal capitals, such as DigiPulse for Digital Pulse. Hybrid forms of abbreviations also exist, for example, B.com to represent Bachelor of Commerce.Learn more about Writing | <urn:uuid:89dd6a1c-925f-4b35-b703-26df11c4786c> | {
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# Inverse Function Rule in Differentiation
How to solve the inverse function rule in differentiation problems: formula, examples, and their solutions.
## Formula
The reciprocal of dy/dx is dx/dy.
So it's obvious that dy/dx = 1 / (dx/dy).
So, to find dy/dx:
First find dx/dy.
Then find dy/dx
by getting the reciprocal of dx/dy.
## Example 1
Differentiate the given equation
with respect to y.
Then dx/dy = 3y2 - 1.
Derivative of polynomials
So dy/dx = 1 / (3y2 - 1).
## Example 2
Differentiate the given equation
with respect to x.
Then dy/dx = 3y2.
Derivative of polynomials
So dx/dy = 1 / 3x2.
It says find dx/dy at y = 3.
But dx/dy = 1 / 3x2 has x, not y.
So find the x value when y = 3
by putting y = 3 into the given equation: y = x3 + 2.
Then x = 1.
Then [dx/dy]x = 1 = 1/3. | crawl-data/CC-MAIN-2019-43/segments/1570986692126.27/warc/CC-MAIN-20191019063516-20191019091016-00386.warc.gz | null |
A Website Dedicated to Improving Student’s Writing through Writer’s Workshop
In general, mini-lessons should last approximately 10-15 minutes. “Maxi-Lessons”, such as lessons that introduce a new skill or multiple techniques, may require more time. However, during a longer lesson, there should be significant time for students to practice with the skill, not just listen to the teacher.
A typical mini-lesson will include:
1. A direct statement about the concept or skill to be taught. Examples from literature and student writing are helpful during this time.
2. The teacher models the concept using his/her piece of writing as the basis for modeling. A discussion takes place a this time. Students are encouraged to explain how the writing is effective as a result of the technique used.
3. The class tries out the technique, either using their piece of writing as the content base or using a teacher determined example to begin.
4. The teacher determines when it is time for students to apply the lesson to their own writing. This should occur directly after the concept/skill introduction and practice.
5. The teacher should evaluate the progress students are making by circulating the room, to check on progress. Additionally, it is recommended that some students share their attempts at using the strategy. This will serve as added examples, particularly for struggling writers.
6. Individual and small group conferences may take place in order to assist students with more tailored teacher support with their writing.
7. Revisiting the concept and additional modeling will take place as needed. The same skill may be modeled several times during the year. For example, when teaching students how to elaborate on their writing, the teacher may decide to complete a lesson on this skill for every piece of writing throughout the year.
What are mini-lessons?
Opening with a Hook
Just Say More
Closing with a Punch
Bury the Word/Overused Words
Author as Source
Parts of Speech
Snapshots in Time
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Absolute pitch (AP), widely referred to as perfect pitch, is the ability of a person to identify or re-create a given musical note without the benefit of an external reference.
Absolute pitch (AP), or perfect pitch, is the ability to name or reproduce a tone without reference to an external standard.
The naming/labeling of notes need not be verbal. AP can also be demonstrated by other codes such as auditory imagery or sensorimotor responses, for example, reproducing a tone on an instrument. Therefore a musician from an aural tradition, with no musical notation, can still exhibit AP when asked to reproduce a sounded note.
Possessors of absolute pitch exhibit the ability in varying degrees. Generally, absolute pitch implies some or all of the following abilities when done without reference to an external standard:
- Identify by name individual pitches (e.g. A, B, C♯) played on various instruments
- Name the key of a given piece of tonal music just by listening (without reference to an external tone)
- Identify and name all the tones of a given chord or other tonal mass
- Accurately sing a given pitch without an external reference
- Name the pitches of common everyday noises such as car horns
- Identify the numerical value in hertz of a given note.
Individuals may possess both absolute pitch and relative pitch ability in varying degrees. Both relative and absolute pitch work together in actual musical listening and practice, although individuals exhibit preferred strategies in using each skill.
History of study and terminologies
Scientific study of absolute pitch appears to have commenced in the 19th century, focusing on the phenomenon of musical pitch and methods of measuring it. While the term absolute pitch, or absolute ear, was in use by the late 19th century by both English and German researchers, its application was not universal; other terms such as musical ear, absolute tone consciousness, or positive pitch were also used to refer to the ability. The skill is not exclusively musical, or limited to human perception; absolute pitch has been demonstrated in animals such as bats, wolves, gerbils, and birds, for whom specific pitches facilitate identification of mates or meals.
Difference in cognition, not elementary sensation
Physically and functionally, the auditory system of an absolute listener does not appear to be measurably different from a non-absolute listener. Rather, "AP perception is not dependent on a special kind of ear; it reflects a particular ability to analyze frequency information, presumably involving high-level cortical processing." Absolute pitch is an act of cognition, needing memory of the frequency, a label for the frequency (such as "B-flat"), and exposure to the range of sound encompassed by that categorical label. Absolute pitch may be directly analogous to recognizing colors, phonemes (speech sounds) or other categorical perception of sensory stimuli. Just as most people have learned to recognize and name the color blue by the frequencies of the electromagnetic radiation that is perceived as light, it is possible that those who have been exposed to musical notes together with their names early in life will be more likely to identify, for example, the note C. Absolute pitch may also be related to certain genes, possibly an autosomal dominant genetic trait, though it "might be nothing more than a general human capacity whose expression is strongly biased by the level and type of exposure to music that people experience in a given culture."
Influence by music experience
Absolute pitch sense appears to be influenced by cultural exposure to music, especially in the familiarization of the equal-tempered C-major scale. Most of the absolute listeners that were tested in this respect identified the C-major tones more reliably and, except for B, more quickly than the five "black key" tones, which corresponds to the higher prevalence of these tones in ordinary musical experience. One study of Dutch non-musicians also demonstrated a bias toward using C-major tones in ordinary speech, especially on syllables related to emphasis.
Absolute pitch is more common among speakers of tonal languages such as most dialects of Chinese or Vietnamese, which depend heavily on pitch variation across single words for lexical meaning (ex. Mandarin with four possible pitch variations, Cantonese with six or seven, Minnan with seven or eight (depending on dialect), and Vietnamese with six.) Speakers of Sino-Tibetan languages have been reported to speak a word in the same absolute pitch (within a quarter-tone) on different days; it has therefore been suggested that absolute pitch may be acquired by infants when they learn to speak in a tonal language (and possibly also by infants when they learn to speak in a pitch stress language). However, the brains of tonal-language speakers do not naturally process musical sound as language; perhaps such individuals may be more likely to acquire absolute pitch for musical tones when they later receive musical training. Also many native speakers of a tone language, even those with little musical training, are observed to sing the same piece in the same key consistently. Among music students of East Asian ethnic heritage, those who speak a tone language very fluently have a much higher prevalence of absolute pitch than those who speak only nontone language.
It is possible that level-tone languages which are found in Africa—such as Yoruba, with three pitch levels, and Mambila, with four—may be better suited to study the role of absolute pitch in speech than the pitch and contour tone languages of East Asia.
Further, speakers of European languages have been found to make use of an absolute, though subconscious, pitch memory when speaking.
Absolute pitch is the ability to perceive chroma and to mentally categorize sounds according to perceived chroma. Chroma is a tonal quality which recurs among tones which share the relationship of an octave. While the boundaries of musical pitch categories vary among human cultures, the recognition of octave relationships is a natural characteristic of the mammalian auditory system. Accordingly, absolute pitch is not the ability to estimate a pitch value from the dimension of pitch evoking frequency (30–5000 Hz), but to identify a chroma category within the dimension of pitch class (e.g., C-C♯-D ... B-C).
An absolute listener's sense of hearing is typically no keener than that of a non-absolute ("normal") listener. Absolute pitch does not depend upon a refined ability to perceive and discriminate gradations of sound frequencies; furthermore, the tasks of identification (recognizing and naming a pitch) and discrimination (detecting changes or differences in rate of vibration) are accomplished with different brain mechanisms.
Genetics and absolute pitch
The prevalence of absolute pitch is considerably higher among individuals with early childhood in East Asia. While this difference might seem to be genetic in origin; individuals of East Asian ancestry who are born or reared in the United States or Canada are significantly less likely to develop absolute pitch than those raised in East Asia. This presents the likelihood that the difference is explained by cultural experience rather than genetic heritage. Language may be an important factor; many East Asians speak tonal languages such as Mandarin and Cantonese, while others (such as those in Japan and certain provinces of Korea) speak pitch accent languages, and the prevalence of absolute pitch may be partly explained by exposure to pitches together with meaningful musical labels very early in life.
Nature vs. nurture
Many people have believed that musical ability itself is an inborn talent. Some scientists currently believe absolute pitch may have an underlying genetic basis and are trying to locate genetic correlates; while evidence suggesting a genetic locus has recently arisen, most believe that the acquisition of absolute pitch requires early training during a critical period of development, regardless of whether a genetic predisposition toward development exists. The "unlearning theory", first proposed by Otto Abraham, has recently been revived by developmental psychologists who argue that every person possesses absolute pitch (as a mode of perceptual processing) as an infant, but that a shift in cognitive processing styles (from local, absolute processing to global, relational processing) causes most people to unlearn it; or, at least, causes children with musical training to discard absolute pitch as they learn to identify musical intervals. Additionally, any nascent absolute pitch may be lost simply by the lack of reinforcement or lack of clear advantages in most activities in which the developing child is involved. An unequivocal resolution to the ongoing debate would require controlled experiments that are both impractical and unethical.
Researchers have been trying to teach absolute pitch ability for more than a century, and various commercial absolute-pitch training courses have been offered to the public since the early 1900s. No adult has ever been documented to have acquired the ability, as all adults who have undergone AP training have failed, when formally tested, to show "an unqualified level of accuracy... comparable to that of AP possessors".
For children aged 2–4, observations have suggested a certain method of music education may be successful in training absolute pitch, but the same method has also been shown to fail with students 5 years and older.
While very few people have the ability to name a pitch with no external reference, pitch memory can be activated by repeated exposure. People who are not skilled singers will often sing popular songs in the correct key, and can usually recognize when TV themes have been shifted into the wrong key. Members of the Venda culture in South Africa also sing familiar children's songs in the key in which the songs were learned.
This phenomenon is apparently unrelated to musical training. The skill may be associated more closely with vocal production. Violin students learning the Suzuki method are required to memorize each composition in a fixed key and play it from memory on their instrument, but they are not required to sing. When tested, these students did not succeed in singing the memorized Suzuki songs in the correct key.
People who have absolute pitch may feel irritated when a piece is transposed to a different key or played at a nonstandard pitch. Musicians with absolute pitch may fail to develop relative pitch skills when following standard curricula, conceptualizing music as a sequence of absolute tones instead; it thus becomes difficult for them to transpose or play a transposing instrument. They may also not be able to continue playing or singing with a group when the pitch drops, or with an orchestra that is not tuned to standard concert pitch A4 = 440 Hz (variable); this may be due to a perception of pitch which is categorical rather than freely adjustable.
The prevalence of absolute pitch is higher among those who are blind from birth as a result of optic nerve hypoplasia, and it has been claimed that it is higher among those with Williams Syndrome and those with an autism spectrum disorder.
Correlation with musical talent
Absolute pitch is not a prerequisite for developing a high level of talent as a musician or composer, and musicians may disagree about the overall value and relevance of absolute pitch ability to musical experience. Owing to uncertainty in the historical record, and, until recently, lack of objective tests, it is often impossible to determine whether notable composers and musicians had absolute pitch or not. Since absolute pitch is rare in European musical culture, claims that any particular musician possessed it are to be doubted, unless there is clear contemporary evidence. Among composers of the Baroque and Classical eras, such evidence is available only for Mozart's perfect pitch. He famously attained it at the age of 3. Experts have only surmised that Beethoven had it, merely due to his remarkable ability to compose undetrimented music long after becoming completely deaf. For 19th-century musicians such as Camille Saint-Saëns and John Philip Sousa, it became more common for the presence of absolute pitch to be recorded. Nicolas Slonimsky was discovered to have perfect pitch as a child of six, which led to him being given music lessons by his aunt Isabelle Vengerova, and a life as a musician. He even titled his 1988 autobiography Perfect Pitch: A Life Story (ISBN 0-19-315155-3). The same was the case with jazz pianist Keith Jarrett, starting with his parents discovering his ability to reproduce musical lines on the piano at the age of three.
Main article: Relative pitch
Many musicians have quite good relative pitch, a skill which can be learned. With practice, it is possible to listen to a single known pitch once (from a pitch pipe or a tuning fork) and then have stable, reliable pitch identification by comparing the notes heard to the stored memory of the tonic pitch. Unlike absolute pitch, this skill is dependent on a recently perceived tonal center.
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- ^ Cetas, J.S., Price, R.O., Crowe, J.J., Velenovsky, D.S., McMullen, N.T. (2003). "Dendritic orientation and laminar architecture in the rabbit auditory thalamus". J. Comp. Neurol. 458 (3): 307–317. doi:10.1002/cne.10595. PMID 12619083.
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- ^ Braun, M., Chaloupka, V. (2005). "Carbamazepine induced pitch shift and octave space representation". Hear. Res. 210 (1-2): 85–92. doi:10.1016/j.heares.2005.05.015. PMID 16181754.
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- ^ Tervaniemi, M., Alho, K., Paavilainen, P., Sams, M., and Näätänen, R. (1993). "Absolute pitch and event-related brain potentials". Music Perception 10: 305–316.
- ^ P. K. Gregersen, E. Kowalsky, N. Kohn, and E. Marvin (2000). "Early childhood music education and predisposition to absolute pitch". Am. J. Med. Gen. 98: 280–282. doi:10.1002/1096-8628(20010122)98:3<280::AID-AJMG1083>3.0.CO;2-6.
- ^ a b D. Deutsch, T. Henthorn, E. W. Marvin, and H.-S. Xu (2006.). "Absolute pitch among American and Chinese conservatory students: Prevalence differences, and evidence for a speech-related critical period (L)a)". J. Acoust. Soc. Am. 119 (2): 719–722. doi:10.1121/1.2151799. PMID 16521731. Full Text
- ^ a b c Deutsch, D; Deutsch, D (2006). "The enigma of absolute pitch". Acoustics Today 2 (1): 11–19. doi:10.1002/ajmg.a.31596. PMID 17163519. Full Text
- ^ a b c Henthorn, T. & Deutsch, D. (2007). "Ethnicity versus Early Environment: Comment on 'Early childhood music education and predisposition to absolute pitch: Teasing apart genes and environment' by Peter K. Gregersen, Elena Kowalsky, Nina Kohn, and Elizabeth West Marvin (2000).". American Journal of Medical Genetics 143A (1): 102–103. doi:10.1002/ajmg.a.31596. PMID 17163519. Full Text
- ^ Zatorre, R.. Absolute Pitch: A model for understanding the influence of genes and development on neural and cognitive function. Full Text
- ^ Deutsch, D., Henthorn, T., and Dolson, M. (2004). "Absolute pitch, speech, and tone language: Some experiments and a proposed framework". Music Perception 21: 339–356. doi:10.1525/mp.2004.21.3.339. Full text
- ^ Drayna, D., Manichaikul, A., DeLange, M., Snieder, H., and Spector, T. (2001). "Genetic correlates of musical pitch recognition in humans". Science 291 (5510): 1969–1972. doi:10.1126/science.291.5510.1969. PMID 11239158.
- ^ Theusch, E., Basu, A., and Gitschier, J. (2009). "Genome-wide Study of Families with Absolute Pitch Reveals Linkage to 8q24.21 and Locus Heterogeneity". American Journal of Human Genetics 85 (1): 112–119. doi:10.1016/j.ajhg.2009.06.010. PMID 19576568.
- ^ Chin, C. (2003). "The development of absolute pitch". Psychology of Music 31: 155–171.
- ^ Abraham, O. (1901). "Das absolute tonbewußtsein". Sammelbände der Internationalen Musikgesellschaft 3: 1–86. Full text Full text (English)
- ^ Saffran, J. R. & Griepentrog, G. J. (2001). "Absolute pitch in infant auditory learning: Evidence for developmental reorganization". Developmental Psychology 37 (1): 74–85. doi:10.1037/0012-16188.8.131.52. PMID 11206435. Full text
- ^ Meyer, M. (1899). "Is the memory of absolute pitch capable of development by training?". Psychological Review 6: 514–516. doi:10.1037/h0069034. Full text
- ^ Maryon, E. (1924). The Science of Tone-Color. Boston: C. C. Birchard & Co.. Full text
- ^ Levitin, D. J. & Rogers, S. E. (2005). "Absolute pitch: Perception, coding, and controversies". Trends in Cognitive Sciences 9 (1): 29. doi:10.1016/j.tics.2004.11.007. PMID 15639438. Full text
- ^ Takeuchi, A. H. & Hulse, S. H. (1993). "Absolute pitch". Psychological Bulletin 113: 358. doi:10.1037/0033-2909.113.2.345.
- ^ Oura, Y. & Eguchi, K. (1982). "Absolute pitch training program for children". Music Education Research 32: 162–171.
- ^ Sakakibara, A. (1999). "A longitudinal study of a process for acquiring absolute pitch". Japanese Journal of Educational Psychology 47.
- ^ Sakakibara, A. (2004). "Why are people able to acquire absolute pitch only during early childhood?: Training age and acquisition of absolute pitch". Japanese Journal of Educational Psychology 52: 485–496.
- ^ Levitin, D. (1994). "Absolute memory for musical pitch: evidence from production of learned melodies.". Perception and Psychophysics 56 (4): 414–423. PMID 7984397. Full text
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- ^ Blacking, John (1995). "Music and Historical Process in Vendaland". in Reginald Byron (Ed.). Music Culture and Experience. Chicago: University of Chicago Press. pp. 136. ISBN 0-226-08829-4.
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- ^ Although it is not unknown—Ludwig Wittgenstein had perfect pitch and played the clarinet.
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- ^ Lenhoff, H. M., Perales, O., & Hickok, G. (2001). "Absolute pitch in Williams syndrome.". Music Perception 18: 491–503. doi:10.1525/mp.2001.18.4.491.
- ^ Heaton, P., Hermelin, B., & Pring, L. (1998). "Autism and pitch processing: A precursor for savant musical ability". Music Perception 15: 291–305.
- ^ Sacks, O. (2007). Musicophilia: Tales of Music and the Brain. New York: Knopf. ISBN 1-4000-4081-7.
- ^ D. Deutsch (2006), "The Enigma of Absolute Pitch", Acoustics Today.
- ^ Fresh Air with Terry Gross, September 11, 2000, interview with Keith Jarrett.
- ^ Brady, P. T. (1970). "Fixed-scale mechanism of absolute pitch". Journal of the Acoustical Society of America 48 (4): 883–887. doi:10.1121/1.1912227. PMID 5480385. | <urn:uuid:75287771-fa3d-4086-b94a-bbcfec44cc13> | {
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# NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.4
NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.4 (Optional) Coordinate Geometry निर्देशांक ज्यामिति PDF in Hindi Medium as well as in English Medium or View in Video Format free to DOWNLOAD or use ONLINE without downloading. All NCERT Solutions and CBSE Apps are updated on the basis of Latest CBSE Syllabus 2019-20.
Class 10: Maths – गणित Chapter 7: Coordinate Geometry (Exercise 7.4)
## NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.4
### Class 10 Maths Chapter 7 Exercise 7.4 Solutions in English
Class 10 Maths Chapter 7 Exercise 7.4 (Optional) Coordinate Geometry in English Medium free to use ONLINE or DOWNLOAD as PDF to use offline or View in Video Format. Click here to move Class 10 Maths Chapter 7 for other exercises to download or online study. CLICK HERE for Hindi Medium Solutions.
### Class 10 Maths Chapter 7 Exercise 7.4 के हल हिंदी में
Class 10 Maths Chapter 7 Exercise 7.4 (Optional) निर्देशांक ज्यामिति solutions in Hindi Medium or View in Video Format. प्रश्नावली ७.४ के प्रश्न शेष प्रश्नावलियों के तुलना में कुछ अलग हैं। प्रत्येक प्रश्न आपने आप में विविधता लिए हुए है, जो इसको अन्य प्रश्नावलियों से अलग करता है। Click here to move Class 10 Maths Chapter 7 for all exercises of chapter 7 online study. Go back to English Medium Solutions.
### 10 Maths Chapter 7 Exercise 7.4 Sols in Video
NCERT Solutions for class 10 Maths Exercise 7.4 in video format with complete description.
#### Important Terms on Coordinate Geometry
• Let XOX’ and YOY’ are two mutually perpendicular lines. These lines are called co-ordinate axis. XOX’ is called x-axis and YOY’ is called y-axis.
• Point of intersection of x-axis and y-axis i.e. O is called the origin whose coordinates are (0,0).
• x-coordinate of a point is called abscissa & y-coordinate is called the ordinate.
• Four Quadrants: A plane is divided by the axis in four quadrants given as follows:
1. In first quadrant, both x and y coordinates of a point are + ve. For example (2, 3) lies in first Quadrant.
2. In second quadrant, x-coordinate is – ve and y-coordinates is + ve. For example (-2, 3) lies in Second Quadrant.
3. In third quadrant, both x and y coordinates of a point are negative. For example (-2, -3) lies in Third Quadrant.
4. In fourth quadrant, x-coordinate is + ve and y-coordinate is – ve. For example (2, -3) lies in Fourth Quadrant. | crawl-data/CC-MAIN-2020-05/segments/1579251694071.63/warc/CC-MAIN-20200126230255-20200127020255-00333.warc.gz | null |
A group of issues associated with inadequate nutrient intake is known as short bowel syndrome. People who have had at least half of their small intestine removed, as well as occasionally all or part of their large intestine, or who have substantial small intestine damage or poor intestinal motility, are more likely to develop short bowel syndrome. Depending on how well the small intestine is functioning, short bowel syndrome can range from mild to serious. People who have short bowel syndrome do not properly receive nutrients from their food, including water, vitamins, minerals, protein, fat, and calories.
The short bowel syndrome market is expanding at a CAGR of 14.7 % from 2023 to 2030 (forecast period).
Diarrhea is the main sign, and it can lead to starvation, dehydration, and weight loss. Bloating, heartburn, fatigue, lactose intolerance, and bad-smelling stool are some additional signs that may occur. Kidney stones and dehydration are examples of complications. particular diet, medicines, or surgery may be used as treatments. The diet may include short, frequent meals, vitamin and mineral supplements, slightly sweet and salty liquids, and an avoidance of foods rich in fat. Parenteral nutrition, or the administration of nourishment through an intravenous line, may occasionally be necessary. Antibiotics, antacids, loperamide, teduglutide, and growth hormone are just a few of the drugs that might be used. Some individuals may benefit from various surgical procedures, including intestinal transplants.
Short Bowel Syndrome Market to Recover Amid COVID-19 Pandemic
Numerous studies have demonstrated that the effects of the coronavirus on the digestive system can result in a variety of gastrointestinal problems. Angiotensin-converting enzyme 2 (ACE-2) in the intestine is where the SARS-CoV-2 virus attaches, impacting the digestive system. According to information provided by UpToDate, Inc., one-third of COVID-19 patients who were severely ill in 2021 were thought to have experienced gastrointestinal problems. Along with several other gastrointestinal diseases, the SARS-CoV-2 infection led to a number of complications, including inflammatory bowel disease and other gastrointestinal tract infections. Additionally, COVID-19 impacted people who had severe inflammatory bowel disease, which led to a rise in Crohn’s disease cases because of weakened immune systems. Due to lengthy hospital stays and other problems related to parenteral nutrition therapy, it was not widely used during the pandemic. Due to this, there is now a greater market desire for medications based on GLP-2. These elements collectively contributed to the market’s expansion.
Increasing Prevalence of GI disorders to Boost Short Bowel Syndrome Market
The major factors attributing to the growth of the SBS market are the increased prevalence of GI disorders such as volvulus, Inflammatory bowel disease (IBD), Crohn’s disease (CD), and mesenteric ischemia, rising awareness by non-profit organizations, and rising initiatives from the key players in the launch of key products, among others.
According to a study that was published in Surgery Today in January 2021, SBS is predicted to affect 24.5 out of every 100,000 live births, and before selecting from the various nutritional, pharmaceutical, and surgical treatment options, a thorough evaluation is required. As a result of the widespread use of therapies to treat the condition, the high prevalence of SBS is anticipated to spur market expansion. Over the course of the forecast period, market growth is anticipated to be fueled by the growing efforts taken by market participants in the development of therapies for SBS. For instance, the clinical-stage company 9 Meters Biopharma published encouraging topline findings from the phase II study of VurolenatIde for SBS in June 2022. As a result, the market participants’ increased research efforts will result in the creation of new SBS therapies, which will boost adoption and fuel market growth.
Therefore, it is anticipated that growing launches of therapies for SBS and rising prevalence of GI disorders will propel market development.
North America to Spearhead the Short Bowel Syndrome Market
North America is the fastest-growing segment in the short bowel syndrome market due to several factors, including:
- Rising prevalence of SBS: Increasing incidences of short bowel syndrome in North America is fueling the market for short bowel syndrome in this region. In the United States, there are approximately 120 home parenteral nutrition cases per million people each year, with SBS accounting for about 25% of cases, according to a study released in UpToDate in November 2021. Due to the increased use of SBS treatments in the country, the market is anticipated to expand as a result of the high prevalence of SBS there.
- Increasing Investment in Healthcare: Governments and private organizations in North America are investing heavily in healthcare infrastructure and research and development. This investment is driving innovation and the development of new therapies for a range of diseases.
- Increased sedentary life: The increase in sedentary lifestyles has made it harder to prioritize eating wholesome foods, leading to an increase in the consumption of unhealthy and junk food and the ensuing intestinal diseases, which is a major factor driving market growth in the region.
- Rising funding for research: Increase in grants from government bodies is responsible for the large share of the North American short bowel syndrome market. For instance, a researcher at Saint Louis University School of Medicine (SBS) received financing of USD 1.9 million in October 2021 to study SBS.
Companies operating in the short bowel syndrome market have adopted several growth strategies to expand their market share and increase their revenue. Some of the key players in the short bowel syndrome market are Takeda Pharmaceutical Company Limited, Merck KGaA, Zealand Pharma A/S, OxThera, VectivBio AG, 9 Meters Biopharma, Inc., Nutrinia Ltd., Hanmi Pharm.Co., Ltd., Pharmascience, Inc., Johnsons & Johnsons Services Inc , Boehringer Ingelheim International GmbH, Sun Pharmaceutical Industries Ltd., Sanofi , GSK Plc., Novartis AG, Pfizer Inc., Amneal Pharmaceuticals LLC. , Alvogen , and Hikma Pharmaceuticals PLC
- Partnerships and Collaborations: Companies are forming partnerships and collaborations to share expertise and resources to accelerate the development of new short bowel syndrome drugs. These partnerships enable companies to leverage their strengths and develop new therapies more efficiently.
- Product Development and Launches: Companies are investing in research and development to develop new short bowel syndrome drugs and improve existing products. These companies are launching new products in the market to expand their product portfolios and gain a competitive advantage.
- Geographical Expansion: Companies are expanding their geographical presence by entering new markets and establishing a presence in regions with high growth potential. This enables companies to tap into new customer bases and increase their revenue. Nestlé Health Science invested USD 50.0 million in July 2020 to the construction of a manufacturing facility in the United States that produces infant formula and medical nutrition goods like peptamen. The distribution of the goods in Canada, Brazil, Mexico, Australia, and Taiwan is another goal of this venture.
- Acquisitions and Mergers: Companies are acquiring or merging with other companies to gain access to new technologies, expertise, and product pipelines. These acquisitions and mergers enable companies to expand their capabilities and product offerings and increase their market share. By changing its name from Innovate Biopharmaceuticals, Inc. to 9 Meters Biopharma, Inc. on April 30, 2020, 9 Meters Biopharma, Inc. completed its merger with privately owned RDD Pharma, Ltd., an Israeli company (“RDD”). By completing the acquisition of Shire plc in January 2019, Takeda Pharmaceutical Company Limited transformed into a leading biopharmaceutical company with a worldwide focus on values-based R&D
- Marketing and Promotional Activities: Companies are investing in marketing and promotional activities to increase awareness and educate healthcare professionals and patients about the benefits of short bowel syndrome drugs. This enables companies to increase demand for their products and drive sales.
Overall, these growth strategies enable companies to expand their market presence, develop new products, and increase their revenue in the short bowel syndrome market | <urn:uuid:b5191c92-7021-4ffe-aeaa-ad3ac347f227> | {
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# What is 1/421 as a decimal?
## Solution and how to convert 1 / 421 into a decimal
1 / 421 = 0.002
Fraction conversions explained:
• 1 divided by 421
• Numerator: 1
• Denominator: 421
• Decimal: 0.002
• Percentage: 0.002%
1/421 or 0.002 can be represented in multiple ways (even as a percentage). The key is knowing when we should use each representation and how to easily transition between a fraction, decimal, or percentage. Decimals and Fractions represent parts of numbers, giving us the ability to represent smaller numbers than the whole. The difference between using a fraction or a decimal depends on the situation. Fractions can be used to represent parts of an object like 1/8 of a pizza while decimals represent a comparison of a whole number like \$0.25 USD. So let’s dive into how and why you can convert 1/421 into a decimal.
1 / 421 as a percentage 1 / 421 as a fraction 1 / 421 as a decimal
0.002% - Convert percentages 1 / 421 1 / 421 = 0.002
## 1/421 is 1 divided by 421
The first step of teaching our students how to convert to and from decimals and fractions is understanding what the fraction is telling is. 1 is being divided into 421. Think of this as our directions and now we just need to be able to assemble the project! Fractions have two parts: Numerators on the top and Denominators on the bottom with a division symbol between or 1 divided by 421. To solve the equation, we must divide the numerator (1) by the denominator (421). Here's how our equation is set up:
### Numerator: 1
• Numerators are the portion of total parts, showed at the top of the fraction. Comparatively, 1 is a small number meaning you will have less parts to your equation. The bad news is that it's an odd number which makes it harder to covert in your head. Smaller numerators doesn't mean easier conversions. Time to evaluate 421 at the bottom of our fraction.
### Denominator: 421
• Denominators represent the total parts, located at the bottom of the fraction. 421 is a large number which means you should probably use a calculator. But the bad news is that odd numbers are tougher to simplify. Unfortunately and odd denominator is difficult to simplify unless it's divisible by 3, 5 or 7. Ultimately, don't be afraid of double-digit denominators. So without a calculator, let's convert 1/421 from a fraction to a decimal.
## How to convert 1/421 to 0.002
### Step 1: Set your long division bracket: denominator / numerator
$$\require{enclose} 421 \enclose{longdiv}{ 1 }$$
Use long division to solve step one. This is the same method we all learned in school when dividing any number against itself and we will use the same process for number conversion as well.
### Step 2: Extend your division problem
$$\require{enclose} 00. \\ 421 \enclose{longdiv}{ 1.0 }$$
Uh oh. 421 cannot be divided into 1. So we will have to extend our division problem. Add a decimal point to 1, your numerator, and add an additional zero. This doesn't add any issues to our denominator but now we can divide 421 into 10.
### Step 3: Solve for how many whole groups you can divide 421 into 10
$$\require{enclose} 00.0 \\ 421 \enclose{longdiv}{ 1.0 }$$
How many whole groups of 421 can you pull from 10? 0 Multiply this number by 421, the denominator to get the first part of your answer!
### Step 4: Subtract the remainder
$$\require{enclose} 00.0 \\ 421 \enclose{longdiv}{ 1.0 } \\ \underline{ 0 \phantom{00} } \\ 10 \phantom{0}$$
If there is no remainder, you’re done! If you have a remainder over 421, go back. Your solution will need a bit of adjustment. If you have a number less than 421, continue!
### Step 5: Repeat step 4 until you have no remainder or reach a decimal point you feel comfortable stopping. Then round to the nearest digit.
In some cases, you'll never reach a remainder of zero. Looking at you pi! And that's okay. Find a place to stop and round to the nearest value.
### Why should you convert between fractions, decimals, and percentages?
Converting fractions into decimals are used in everyday life, though we don't always notice. Remember, fractions and decimals are both representations of whole numbers to determine more specific parts of a number. And the same is true for percentages. It’s common for students to hate learning about decimals and fractions because it is tedious. But each represent values in everyday life! Here are examples of when we should use each.
### When you should convert 1/421 into a decimal
Dining - We don't give a tip of 1/421 of the bill (technically we do, but that sounds weird doesn't it?). We give a 0% tip or 0.002 of the entire bill.
### When to convert 0.002 to 1/421 as a fraction
Distance - Any type of travel, running, walking will leverage fractions. Distance is usually measured by the quarter mile and car travel is usually spoken the same.
### Practice Decimal Conversion with your Classroom
• If 1/421 = 0.002 what would it be as a percentage?
• What is 1 + 1/421 in decimal form?
• What is 1 - 1/421 in decimal form?
• If we switched the numerator and denominator, what would be our new fraction?
• What is 0.002 + 1/2?
### Convert more fractions to decimals
From 1 Numerator From 421 Denominator What is 1/422 as a decimal? What is 2/421 as a decimal? What is 1/423 as a decimal? What is 3/421 as a decimal? What is 1/424 as a decimal? What is 4/421 as a decimal? What is 1/425 as a decimal? What is 5/421 as a decimal? What is 1/426 as a decimal? What is 6/421 as a decimal? What is 1/427 as a decimal? What is 7/421 as a decimal? What is 1/428 as a decimal? What is 8/421 as a decimal? What is 1/429 as a decimal? What is 9/421 as a decimal? What is 1/430 as a decimal? What is 10/421 as a decimal? What is 1/431 as a decimal? What is 11/421 as a decimal? What is 1/432 as a decimal? What is 12/421 as a decimal? What is 1/433 as a decimal? What is 13/421 as a decimal? What is 1/434 as a decimal? What is 14/421 as a decimal? What is 1/435 as a decimal? What is 15/421 as a decimal? What is 1/436 as a decimal? What is 16/421 as a decimal? What is 1/437 as a decimal? What is 17/421 as a decimal? What is 1/438 as a decimal? What is 18/421 as a decimal? What is 1/439 as a decimal? What is 19/421 as a decimal? What is 1/440 as a decimal? What is 20/421 as a decimal? What is 1/441 as a decimal? What is 21/421 as a decimal?
### Convert similar fractions to percentages
From 1 Numerator From 421 Denominator 2/421 as a percentage 1/422 as a percentage 3/421 as a percentage 1/423 as a percentage 4/421 as a percentage 1/424 as a percentage 5/421 as a percentage 1/425 as a percentage 6/421 as a percentage 1/426 as a percentage 7/421 as a percentage 1/427 as a percentage 8/421 as a percentage 1/428 as a percentage 9/421 as a percentage 1/429 as a percentage 10/421 as a percentage 1/430 as a percentage 11/421 as a percentage 1/431 as a percentage | crawl-data/CC-MAIN-2024-26/segments/1718198861773.80/warc/CC-MAIN-20240618171806-20240618201806-00844.warc.gz | null |
## The Coordinate Of Origin Is
The Coordinate Of Origin Is. Web the x coordinate is the number of units to the right of the origin. Origin of coordinates synonyms, origin of coordinates pronunciation,. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0). Web you can use a circle with any radius, as long as the center is at the origin. It has been unequivocally been answered as (0,0).………… i give you an example, the refractive index of glass is quoted as 1.5 this value is. Web the meaning of origin of coordinates is the point of intersection of coordinate axes.
Then o (x,y) = o (0,0) the coordinates are (0, 0) hmmm. The graph below shows the origin. Web origin is at points (0, 0) in coordinate geometry. Web the two axes (plural for axis) intersect at a point called the origin. The axes intersect when both x and y are zero. A set of values that show an exact position are known as the coordinates. The origin divides each of these axes into two halves, a.
## The origin divides each of these axes into two halves, a.
On graphs it is usually a pair of numbers: The first number shows the. In a cartesian coordinate system, the origin is the point where the axes of the system intersect. (if it is to the left of the origin the x coordinate is negative.) the y coordinate is the number of units. Web you can use a circle with any radius, as long as the center is at the origin. The axes intersect when both x and y are zero. The coordinate system is with respect to the system origin as the figure below. A point is named by its ordered pair.
### Web The X Coordinate Is The Number Of Units To The Right Of The Origin.
The coordinates of the origin are (0, 0). Web the meaning of origin of coordinates is the point of intersection of coordinate axes. Web answer (1 of 5): Any point in the coordinate plane can be named by coordinates. Web the coordinate of origin is (0,0) to find : (if it is to the left of the origin the x coordinate is negative.) the y coordinate is the number of units. The coordinate system is with respect to the system origin as the figure below. The first number shows the.
## Web The Coordinates Of The Origin Are Always All Zero, For Example (0,0) In Two Dimensions And (0,0,0) In Three.
Web the coordinates of the origin are (0, 0). Web origin is at points (0, 0) in coordinate geometry. (if it is to the left of the origin the x coordinate is negative.) the y coordinate is the number of units. If you are shifting/translating the origin, you have to add the respective x and y coordinates of the new origin with. The first number shows the. The graph below shows the origin. Write down the point for which coordinates to find. The origin divides each of these axes into two halves, a.
## Conclusion of The Coordinate Of Origin Is.
. The coordinate system is with respect to the system origin as the figure below. Normalized means x, y, z of gaze vector is in the 0~1,.
Source | crawl-data/CC-MAIN-2023-06/segments/1674764499826.71/warc/CC-MAIN-20230130165437-20230130195437-00636.warc.gz | null |
# Multiplication Flash Cards 3rd Grade
Understanding multiplication soon after counting, addition, as well as subtraction is good. Youngsters understand arithmetic using a organic progression. This advancement of learning arithmetic is often the adhering to: counting, addition, subtraction, multiplication, and ultimately department. This assertion brings about the question why discover arithmetic within this pattern? More importantly, why discover multiplication soon after counting, addition, and subtraction before section?
## The subsequent information answer these concerns:
1. Youngsters learn counting initial by associating aesthetic things because of their hands. A concrete instance: How many apples exist inside the basket? Much more abstract example is just how aged are you currently?
2. From counting amounts, the subsequent plausible phase is addition followed by subtraction. Addition and subtraction tables can be extremely helpful training tools for kids since they are aesthetic tools generating the changeover from counting simpler.
3. Which ought to be discovered after that, multiplication or department? Multiplication is shorthand for addition. At this moment, kids use a business knowledge of addition. As a result, multiplication is the next plausible form of arithmetic to find out.
## Review fundamentals of multiplication. Also, evaluate the fundamentals how to use a multiplication table.
Let us assessment a multiplication case in point. Employing a Multiplication Table, flourish several times 3 and obtain a response twelve: 4 x 3 = 12. The intersection of row three and column a number of of a Multiplication Table is a dozen; 12 may be the response. For children starting to learn multiplication, this really is simple. They can use addition to solve the situation as a result affirming that multiplication is shorthand for addition. Instance: 4 by 3 = 4 4 4 = 12. It is an superb introduction to the Multiplication Table. A further gain, the Multiplication Table is visible and demonstrates to discovering addition.
## Where will we commence learning multiplication utilizing the Multiplication Table?
1. Initially, get familiar with the table.
2. Get started with multiplying by 1. Start at row # 1. Proceed to line number 1. The intersection of row a single and line one is the best solution: one.
3. Repeat these steps for multiplying by a single. Increase row one particular by posts 1 by means of 12. The responses are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 respectively.
4. Recurring these actions for multiplying by two. Grow row two by columns a single by way of five. The solutions are 2, 4, 6, 8, and 10 correspondingly.
5. We will hop forward. Recurring these methods for multiplying by 5. Increase row 5 various by posts one by way of 12. The responses are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60 correspondingly.
6. Now we will raise the quantity of issues. Perform repeatedly these techniques for multiplying by a few. Flourish row a few by posts 1 by way of a dozen. The solutions are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, and 36 correspondingly.
7. Should you be comfortable with multiplication up to now, use a test. Resolve the next multiplication troubles in your mind after which examine your answers on the Multiplication Table: increase 6 and 2, flourish 9 and about three, grow one and 11, grow four and 4, and flourish seven and two. The trouble replies are 12, 27, 11, 16, and 14 respectively.
If you got 4 from several problems proper, make your personal multiplication tests. Calculate the answers in your head, and look them using the Multiplication Table. | crawl-data/CC-MAIN-2024-18/segments/1712296816863.40/warc/CC-MAIN-20240414002233-20240414032233-00772.warc.gz | null |
Figure. No caption available.
Smell is the sense that drives behavior. Over the course of millions of years, whether foraging, mating, bonding, or recognizing predators, the nose has been a powerful source of information—far beyond answering the question, “What's for dinner?” The areas of the brain that process smell are also involved in emotion and memory, which is why a whiff of cinnamon can conjure up childhood memories of mom's apple pie.
In the 1970s, researchers learned that smell is compromised in neurodegenerative conditions like Alzheimer's disease, Parkinson's disease, Huntington's disease, and multiple sclerosis (MS). Now, they are discovering that loss of smell can be a hallmark symptom in the earliest stages of many diseases.
“Recent studies of brains from Alzheimer's and Parkinson's disease patients reveal structural and biochemical alterations in regions associated with the sense of smell,” says Richard Doty, Ph.D., professor and director of the Smell & Taste Center at the University of Pennsylvania. Loss of smell occurs 90 percent of the time in Parkinson's disease. This is greater than the prevalence of tremor, a cardinal sign of the disorder.
Yet in one study of Parkinson's patients, 72 percent were unaware they had a smell disorder before undergoing standardized testing. Only two out of 34 Alzheimer's disease patients reported suffering from smell and/or taste problems—even though 90 percent of the patients scored lower on standardized smell tests than healthy subjects.
Odors enter the nasal cavity and travel a set of cells at the roof of the nose called the olfactory receptor. When an aroma reaches the receptor, it sends a signal to the brain that says, “Oh, that's vanilla,” or “Bacon!” If the receptors are blocked or dead due to aging or certain medical conditions, the smell won't be perceived.
How do you know if your system is functioning appropriately? Ask your doctor for a sniff test. Most neurologists don't test olfactory function or ask patients about their sense of smell, says Dr. Doty.
The University of Pennsylvania Smell Identification Test consists of four booklets, each containing 10 odorants. A multiple-choice question with four possible answers for each item is located above the “scratch and sniff” odorized strips, and the subject must choose one of the four alternatives.
“On the 40-item test, Alzheimer's and Parkinson's patients average a score of 20—even at the earliest stages of the disease—while healthy subjects typically score 34 and above,” Dr. Doty says. The higher the score, the more accurate your sense of smell. And there is no association between the type of drug therapy and the degree of olfactory dysfunction, which means the drugs aren't causing the loss of smell—it's the disorders.
“When people lose their sense of smell, it can be devastating,” says Ronald Devere, M.D., director of the Alzheimer's Disease and Memory Disorders Center in Austin, TX. “It severely diminishes a person's quality of life and safety.”
People with smell loss are almost twice as likely as people with normal olfactory function to have cooking-related accidents, be exposed to an undetected fire or gas leak, or eat spoiled foods or toxic substances. There are no medical treatments to restore your sense of smell, but making a few simple changes can keep you safe:
▸ Cook foods on the grill or use an oven with automatic shut-off features.
▸ Label foods with dates as soon as you return from grocery shopping.
▸ Install smoke alarms and sensing devices for gas.
▸ Don't stop trying to use your nose.
“Animal studies suggest that exposure to odorants may enhance some regeneration at the periphery [olfactory cells in the nose] and stimulate the formation of additional synaptic connections in central brain structures, including the olfactory bulb,” says Dr. Doty. One unpublished study found that people with compromised smell improved their function by sniffing a number of odorants twice upon awakening and twice before going to bed.
Experts claim that 80 percent of food appreciation comes from the olfactory system, which is why foods seem tasteless when the nose is blocked by a cold. When you chew your food, odors go to the back of the mouth where the olfactory system translates them into flavor.
Even if your sense of smell is compromised, the basics of taste often remain intact: sweet, salty, sour, bitter, and umami, which is a Japanese word meaning “savory” or “meaty.” You'll also be able to appreciate temperature and texture. It's the more subtle nuances of flavor that are lost, such as the complexity of dark chocolate or the deep tannins of a robust merlot. For some people, this is hard to bear.
“Patients are idiosyncratic in terms of how smell loss affects them,” says Dr. Doty. “Some people eat colorful foods with a lot of texture and aren't fazed at all; others are suicidal over it. They don't find food satisfying and start to waste away.”
One common solution is to drown food in salt, which is still recognized by taste buds that can't detect other flavors. Unfortunately, adding salt can raise blood pressure and increase one's risk for stroke. Instead enhance flavors by chewing thoroughly and alternating bites of different foods in one meal. Both tactics stimulate taste and smell receptors and prevent your taste buds from getting so accustomed to one flavor that the food tastes flat. “Play with texture and temperatures to create sensations in your mouth,” suggests Dr. Devere. “Add spices to food, marinate chicken in fruit juices, and experiment with flavors you used to like.”
▸ Place a smoke detector in every room that might have a fire or where people sleep.
▸ Opt for an electric stove over gas, but if you must go the gas route, make sure it is equipped with an automatic pilot light.
▸ Purchase propane detectors, natural gas detectors, and gasoline detectors (available through the gas company, recreational vehicle dealers, or marine electronics stores).
▸ Take care when preparing food, particularly leftovers, since spoiled food can wreak havoc on your intestinal tract.
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Beginning in 1915, some six million black African Americans from the South joined an exodus to the northern cities – Chicago, Detroit, Philadelphia, New York and many others. This was the Great Migration. It was the result both of the conditions in which African Americans found themselves in the South and the labour needs of Northern employers.
After post-Civil War Reconstruction, white supremacy had largely been restored across the South, enforced though the Jim Crow laws. It was a segregated world, in which blacks were denied they most basic of rights from votes to education, a world of oppression, terror and unremitting poverty. Meanwhile, the First World War had created a shortage of labour in Northern cities as European immigration came to an end. Labour shortage was made more acute by war production. So Northern employers looked to the South for labour. By 1920, the black population of Detroit had increased by 611 per cent, that of Philadelphia by 500 per cent. It was a migration that was to transform America.
No artist has better depicted the Great Migration, and its existential impact, than Jacob Lawrence, one of America’s great twentieth century painters, though one who has rarely received great public recognition. Born in 1917 in the North – in Atlantic City, New Jersey – Lawrence was nevertheless in many ways a product of the Great Migration. The Great Migration transformed not just America’s demography but its political and cultural consciousness too, from the reconfiguration of blues and jazz – it was out of that exodus that Chicago blues and bebop emerged – to the remaking of American literature, through the works of Langston Hughes, Zora Neale Hurston, Nella Larsen, Jean Toomer, Richard Wright, Ralph Ellison, and countless others. Central to all this was the Harlem Renaissance, the literary, artistic, and intellectual movement of the 1920s and 30s that helped kindle a new black cultural identity. It was, as the critic and writer, and central figure of the Harlem Renaissance, Alan Locke, put it, the ‘spiritual coming of age’ of the black community.
Lawrence, who lived in Harlem from the age of 23, and attended the Harlem Art Workshop, was deeply shaped by these changes. Lawrence’s significance was to take the forms of European modernism – his debt to Picasso and to Matisse is particularly evident – and to reshape them to speak to the experiences both of America as a nation and of African Americans specifically. In his American Visions: The Epic History of American Art, the art critic Robert Hughes, notes perceptively of Lawrence:
Younger than the artists and writers who took part in the Harlem Renaissance of the 1920s, Lawrence was also at an angle to them: he was not interested in the kind of idealized, fake-primitive images of blacks – the Noble Negroes in Art Deco guise – that tended to be produced as an antidote to the toxic racist stereotypes with which white popular culture had flooded America since Reconstruction. Nevertheless, he gained self-confidence from the Harlem cultural milieu – in particular, from the art critic Alain Locke, a Harvard-trained esthete (and America’s first black Rhodes scholar) who believed strongly in the possibility of an art created by blacks which could speak explicitly to African-Americans and still embody the values, and self-critical powers, of modernism. Or, in Locke’s own words, ‘There is in truly great art no essential conflict between racial or national traits and universal human values.’ This would not sit well with today’s American cultural separatists who trumpet about the incompatibility of American experiences – ‘It’s a black thing, you wouldn’t understand’- but it was vital to Lawrence’s own growth as an artist.
Or, as Lawrence himself put it, ‘I do not look upon the story of the Blacks in America as a separate experience to the American culture but as a part of the American heritage and experience as a whole.’
Lawrence’s most famous work was a sequence of 60 panels depicting the Great Migration. It was commissioned in 1940 by the Rosenwald Foundation and completed over the following two years. It is, in its own way, as much a work of historical memory as of art. Lawrence spent months ensconced in the Schomburg Collection of the New York Public Library, New York’s principal archive on African-American life and history. The paintings are, however, more than simply an act of remembrance. ‘I don’t think in terms of history about that series’, Lawrence observed. ‘I think in terms of contemporary life. It was such a part of me that I didn’t think of something outside. It was like I was doing a portrait of something. If it was a portrait, it was a portrait of myself, a portrait of my family, a portrait of my peers.’
Again, Robert Hughes is perceptive about Lawrence’s method:
The series is notable for the language it does not use. Lawrence was not a propagandist. He eschewed the caricatural apparatus of Popular Front Social Realism, then at its high tide in America. Considering the violence and pathos of so much of his subject matter – prisons, deserted villages, city slums, race riots, labor camps – his images are restrained, and all the more piercing for their lack of bombast. When he painted a lynching, for instance, he left out the dangling body and the jeering crowd: there is only bare earth, a branch, an empty noose, and the huddled lump of a grieving woman. He set aside the influence of Rivera and the Mexican muralists, which lay so heavily on other artists; he wasn’t painting murals, but images closer in size to single pages, no more than eighteen inches by twelve. Nevertheless, he imagined the paintings as integrally connected – a single work of art, no less unified than a mural, but portable. Migration is a visual ballad, each image a stanza, compressed, like the blues, to the minimum needs of narration. Number 10, ‘They were very poor’, pares the elements of a black sharecropper’s life down to the least common denominator: a man and a woman staring at empty bowls on a bare brown plane, an empty basket hung on the wall by an enormous nail – the sort of nail you imagine in a crucifixion. There isn’t a trace of the sentimentality that coats Picasso’s Blue Period, or the work of most American Social Realists.
The 60 panels of the Great Migration series were eventually divided between the Phillips Collection in Washington and New York’s Museum of Modern Art (bizarrely, perhaps, Phillips took the odd-numbered paintings, MoMA the even-numbered ones). Next year, on the centenary of the start of the Great Migration, all 60 panels will be reunited, first in an exhibition at MoMA and then in the Phillips Collection in 2016. And over the next few weeks, I will publish on Pandaemonium the complete sequence of 60 panels, ten at a time, together with Lawrence’s original captions, that are as much part of the series as are the paintings themselves.
During the World War there was a great migration North
by Southern Negroes
The World War had caused a great shortage
in Northern industry and also citizens of foreign countries
were returning home.
In every town Negroes were leaving by the hundreds
to go North and enter into Northern industry.
The Negro was the largest source of labor to be found
after all others had been exhausted.
The Negroes were given free passage on the railroads
which was paid back by Northern industry.
It was an agreement that the people brought North
on these railroads were to pay back their passage
after they had received jobs.
The trains were packed continually with migrants.
The Negro, who had been part of the soil for many years,
was now going into and living a new life
in the urban centers.
They did not always leave
because they were promised work in the North.
Many of them left because of Southern conditions,
one of them being great floods that ruined the crops,
and therefore they were unable
to make a living where they were.
Another great ravager of the crops was the boll weevil. | <urn:uuid:7f7392e3-46ff-4e03-9430-35f075d9b238> | {
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Lath and plaster
||This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (November 2011)|
Lath and plaster is a building process used to finish mainly interior walls and ceilings in Canada and the United States until the late 1950s. After the 1950s, drywall began to replace the lath and plaster process in the United States.
In the United Kingdom, lath and plaster was often used for interior partition walls and the construction of ceilings, before the introduction of plasterboard in the 1930s. In the U.K., riven or split hardwood laths were often used of random lengths and sizes. Splitting the timber, as opposed to sawing in straight lines, followed the grain of the timber which greatly improved strength and durability. Also, reed mat was used as a lath.
|This section does not cite any references or sources. (March 2012)|
The wall or ceiling finishing process begins with wood laths. These are narrow strips of wood, or split boards, are nailed horizontally across the wall studs or ceiling joists. Each wall frame is covered in lath, tacked at the studs. The lath is typically about one inch wide by four feet long by 1⁄4 inch (6.4 mm) thick. Each horizontal course of lath is spaced about 3⁄8 inch (9.5 mm) away from its neighboring courses.
Temporary lath guides are then placed vertically to the wall, usually at the studs. Plaster is then applied, typically using a wooden board as the application tool. The applier drags the board upward over the wall, forcing the plaster into the gaps between the lath and leaving a layer on the front the depth of the temporary guides, typically about 1⁄4 inch (6.4 mm). A helper feeds new plaster onto the board, as the plaster is applied in quantity. When the wall is fully covered, the vertical lath "guides" are removed, and their "slots" are filled in, leaving a fairly uniform undercoat.
In three coat plastering it is standard to apply a second layer in the same fashion, leaving about a half inch of rough, sandy plaster (called a brown coat). A smooth, white finish coat goes on last. After the plaster is completely dry, the walls are ready to be painted. In this article's photo ("lath seen from the back...") the curls of plaster are called keys and are necessary to keep the plaster on the lath. Traditional lime based mortar/plaster often incorporates horsehair which reinforces the plasterwork, thereby helping to prevent the keys from breaking away.
Eventually the wood laths became less common, and were replaced with rock lath (also known as "button board"), which is a type of gypsum wall board with holes spaced regularly across it, usually in sheets sized 2 feet (24 in) by 4 feet (48 in). The purpose of the four-foot length is so that the sheet of lath reaches exactly across four wall studs, which are spaced 16 inches (410 mm) apart on center (United States building code standard measurements). The holes serve the same purpose as the spaces between the wood lath strips, allowing plaster to ooze through the board when the plaster is applied, making the keys to hold the plaster to the wall board.
In addition to rock lath, there were various types of metal lath which is categorized according to weight, type of ribbing, and whether the lath is galvanized or not. Metal lathing was spaced across a 13.5 inch center, attached by tie wires using lathers' nippers. Sometimes, the mesh was dimpled to be self-furring.
An advantage of using lath is for ornamental or unusual shapes. For instance, building a rounded wall would be difficult if drywall were used exclusively, as drywall is not flexible enough to allow tight radii.
Traditional lath and plaster has superior sound-proofing qualities when used with lime plaster (which is denser than modern gypsum board).
In many historic buildings lath and plaster ceilings have a major role for the prevention of fire spread. "They are critical to the protection of horizontal elements such as timber joisted floors, including the flooring on top, which in terms of fire performance is often in a poor condition due to the presence of gaps."
- Jeff Howell, On the level: is the old plaster best?, The Telegraph (London), May 10, 2006. Retrieved 2012-03-30.
- "Fire Resistance of Historic Fabric" by Peter Jackman - http://www.buildingconservation.com/articles/fireresist/fire_resistance.htm
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# Plot a scatter graph and describe correlation
Plot a scatter graph and describe correlation
Quiz:
# Intro quiz - Recap from previous lesson
Before we start this lesson, let’s see what you can remember from this topic. Here’s a quick quiz!
## Question 3
Q1.Calculate the mean mark from the grouped frequency table.
1/3
Q2.Calculate the mean weight from the grouped frequency table, to 1 decimal place.
2/3
Q3.Calculate the mean age from the grouped frequency table, to 1 decimal place.
3/3
Quiz:
# Intro quiz - Recap from previous lesson
Before we start this lesson, let’s see what you can remember from this topic. Here’s a quick quiz!
## Question 3
Q1.Calculate the mean mark from the grouped frequency table.
1/3
Q2.Calculate the mean weight from the grouped frequency table, to 1 decimal place.
2/3
Q3.Calculate the mean age from the grouped frequency table, to 1 decimal place.
3/3
# Video
Click on the play button to start the video. If your teacher asks you to pause the video and look at the worksheet you should:
• Click "Close Video"
• Click "Next" to view the activity
Your video will re-appear on the next page, and will stay paused in the right place.
# Worksheet
These slides will take you through some tasks for the lesson. If you need to re-play the video, click the ‘Resume Video’ icon. If you are asked to add answers to the slides, first download or print out the worksheet. Once you have finished all the tasks, click ‘Next’ below.
Quiz:
# Plot a scatter graph and describe correlation
Don’t worry if you get a question wrong! Forgetting is an important step in learning. We will recap next lesson.
Q1.
1/3
Q2.
2/3
Q3.
3/3
Quiz:
# Plot a scatter graph and describe correlation
Don’t worry if you get a question wrong! Forgetting is an important step in learning. We will recap next lesson.
Q1.
1/3
Q2.
2/3
Q3.
3/3
# Lesson summary: Plot a scatter graph and describe correlation
## Time to move!
Did you know that exercise helps your concentration and ability to learn?
For 5 mins...
Move around:
Jog
On the spot:
Chair yoga | crawl-data/CC-MAIN-2021-25/segments/1623487617599.15/warc/CC-MAIN-20210615053457-20210615083457-00633.warc.gz | null |
## I CAN MEASURE!
Comment 0
We have been learning about measurement in our Math class. We we were able to practice two ways of measuring. One is Non-Standard Measurement which is using everyday materials such as cubes, pens, markers, etc. Another is Standard Measurement wherein we used real measuring tools such as rulers, weighing scales, etc.
Measuring size is the first thing we learned. We learned new words such as “puny”, “just right” and “enormous” to compare the sizes of objects.
We used clay to represent our knowledge of “small, medium, and large”.
We also learned about length. Length is usually measured in a sleeping line. We learned the terms long and short.
What we enjoyed the most was a game we played in pairs called “longest line”. We used toys from the math and building center and we made sure that they were lined up from end to end to make our “longest line” count.
We also built long roads and short roads which we tested out using different types of land vehicles.
We also learned how to measure using rulers. Rulers tell you the exact measurement of an object. It has lines and numbers that will help us find out how long an object is.
Our teacher gave us ribbons of different sizes. Our task was to measure the length of the ribbons using unifix cubes as well. Some of us wanted to know the exact measurement of our ribbons so we used rulers in stead. Rulers are better to use since it can show you the exact length of an object.
One of the more challenging activities is arranging straws of different sizes from longest to shortest. We made sure that the straws were first all aligned on a straight line, then we checked which should go first, second, etc before we stuck it with white glue. We also wanted to find out the length of the cubby holes outside our classroom. For this activity, we used markers and crayons to measure.
We also wanted to find out the length of the different items we have at our classroom using unifix cubes. We were able to do this activity on our own. We made sure that we measured the objects from end to end so that we can arrive at the exact measurement.
We were also able to match given number measurements to paper strips that were provided to us.
Our class also discussed Height. Height is usually measured in a standing line. It is measuring how tall or short and object or person is.
We used unifix cubes to measure the height of our dolls.
We even got the chance to measure our own height using beanbags and boxes. We learned that if our heights don’t reach all the way to the end of the box or beanbag, we can record our measurements using, halves, quarters, and three quarters.
We were also able to measure our own height with the help of the nurse at the clinic. Who is the tallest kid in our class? How about the shortest?
Weight is measuring how heavy or light an object is.
Our teacher gave us different material that we can use to make our improvised balancing scale. We found it quite confusing at first but we were able to figure it out when we worked in pairs. We then tested it out by weighing unifix cubes.
We really enjoyed exploring the use of a balancing scale. We learned that, if the balancing scale goes down, it means that the object/s in it is heavier, while the object on the scale that goes up is lighter.
It was quite amusing to realized that not all objects that are bigger are always heavier. There are lots of things that we need to consider such as the type of material, if the object is hallow or filled, and if the objects have something in it.
We were also able to learn how to use the weighing scale at the clinic. We then recorded our answers on a poster. We wonder if our weight will change if grow much taller at the end of the school year.
Capacity is probably one of the trickier concepts that we learned. It is measuring how much a container can hold, both liquids and solids.
We had so much fun measuring how much containers can hold. We filled up cups with water then poured them in our balancing scale. We got a little messy but we managed to clean up after ourselves. We were also able to measure the capacity of containers using unifix cubes. Can you believe we were able to count till 127?
Oh what fun it is to measure! | crawl-data/CC-MAIN-2019-22/segments/1558232256764.75/warc/CC-MAIN-20190522063112-20190522085112-00114.warc.gz | null |
What is the largest and smallest bone of human body?
Largest and smallest bones in the human body
- The largest bone in the human body is the femur (or thigh bone).
- The smallest bones in the human body are the ossicles.
- The ossicles (or auditory ossicles) are three bones of the middle ear: malleus, incus, and stapes.
Which bone is the strongest in the human body?
Which is the largest bones in human body?
Femur, or thighbone, is the biggest bone in the body. The head of femur fits into the hip socket and the bottom end connects to your knee. The two bones beneath the knee that make up your shin are tibia and fibula.
Which is the weakest bone in your body?
The lacrimal bone is perhaps the most fragile bone of the face and one of the smallest bones in the body. Spanning between the middle of each eye socket, each lacrimal is thin and scalelike and serves as support for the eye. The pair of lacrimal bones are two of the fourteen facial bones.
What is the heaviest bone in your body?
What are the 4 smallest bones in the human body?
What’s the smallest bone in the human body? Conveniently, that would be the stapes. It is one of three tiny bones in the middle ear that convey sound from the outer ear to the inner ear. Collectively called the ossicles, these bones are individually known as the malleus, incus, and stapes.
What are the hardest bones to break?
The hardest bone to break is the femur. The femur is the strongest bone in the human body. It extends from the hip to the knee. It can resist a force of up to 1,800 to 2,500 pounds.
What is the weakest bone in your body?
The femur is the longest and strongest bone in the body. It is located in your thigh. The weakest bone in your body would be the spine or spinal cord. or your nose. You probably mean weakest because of its sheer smallness.
Are teeth stronger than bones?
Enamel – the hard, outer layer of your teeth – is made of minerals like calcium phosphate. Enamel is harder than your bones. In fact, it’s the hardest substance in your whole body. However, unlike your bones, your enamel doesn’t contain any living tissues.
What is the weakest bone in your leg?
Femur – the bone in the thigh. Patella – the knee cap. Tibia – the shin bone, the larger of the two leg bones located below the knee cap. Fibula – the smaller of the two leg bones located below the knee cap.
What is the hardest bone in your body?
The femur is the strongest bone in the human body. It extends from the hip to the knee. It can resist a force of up to 1,800 to 2,500 pounds. Only events of a large amount of force can cause it to break, such as by a car accident or a fall from an extreme height, taking months to heal.
What’s the strongest muscle in your body?
So here are the top five strongest muscles in the body based on these different ways to measure strength:
- Heart. The heart, which consists of cardiac muscle, is said to be the hardest working muscle in the body.
- Gluteus Maximus.
What is the easiest bone to break in the body?
As it turns out, the clavicle, also known as the collar bone, located between your shoulder and the front of the neck, is the bone which is most likely to get broken in the human body. The clavicles can be easily fractured by impacts to the shoulder, from the force of falling on outstretched arms, and by a direct hit.
Which is the softest bone in human body?
The smallest and lightest is the stapes of the middle ear. I don’t know what the softest would be, but it wouldn’t be any of the middle-ear bones. Those three bones are more heavily calcified and less organic than other bones in the body.
Do sprains hurt worse than breaks?
With a severe sprain, ligaments tear completely or separate from the bone. Although the intensity varies, all sprains commonly cause pain, swelling, bruising, and inflammation. The ankle is the most commonly sprained joint. And a sprained ankle is more likely if you’ve had a previous sprain there.
What’s the heaviest body part?
The largest internal organ is the liver. It is also the heaviest organ, with an average of 1.6 kilograms (3.5 pounds). The largest external organ, which is also the largest organ in general, is the skin.
What is the lightest bone in the human body?
Is the jaw bone the strongest bone in the body?
The mandible, lower jaw or jawbone is the largest, strongest and lowest bone in the human face. It forms the lower jaw and holds the lower teeth in place. The mandible sits beneath the maxilla. It is the only movable bone of the skull (discounting the ossicles of the middle ear).
What is the longest thing in your body?
The Longest & Largest Things In The Human Body
- The longest bone in the human body is the femur.
- The largest artery is the aorta and the largest vein is the inferior vena cava.
- The largest internal organ is the liver.
- The longest muscle is the sartorius muscle in the thigh.
- The longest single nerve is the sciatic nerve in the thigh, counting its branches and axons.
Are bones alive?
Bones in our body are living tissue. They have their own blood vessels and are made of living cells, which help them to grow and to repair themselves. As well, proteins, minerals and vitamins make up the bone.
What is the fattiest organ in the human body?
What is the heaviest muscle in the body?
The gluteus maximus is the largest muscle in the human body. It is large and powerful because it has the job of keeping the trunk of the body in an erect posture. It is the chief antigravity muscle that aids in walking up stairs. The hardest working muscle is the heart.
Which has more bones hands or feet?
More than half of the bones in your body are found in your hands and feet. There are 27 in each hand and 26 in each foot, and the way that they are arranged is remarkably similar.
Is your tongue one of the strongest muscles in your body?
By that measure, the hardest working muscle in your body is the one that’s pump-pump-pumping 24/7 to keep your blood flowing round and round, including to all the other muscles: your heart. The tongue may not be as strong as the glutes, jaw or heart but strengthening it may still be useful.
What is the strongest part of the tooth?
Tooth enamel is a protective barrier that surrounds the visible part of the tooth. It is composed of strong minerals, including calcium phosphate. Tooth enamel is the hardest substance in the human body, and healthy enamel is resistant to cavity-causing bacteria.
What is the strongest tooth?
Tooth enamel is the hardest substance in the body. The shiny, white enamel that covers your teeth is even stronger than bone. This resilient surface is 96 percent mineral, the highest percentage of any tissue in your body – making it durable and damage-resistant.
Can teeth heal like bones?
Getting a cavity is an unpleasant experience — and a painful reminder that teeth, unlike bones, can’t heal themselves once they’re damaged. And when the tooth erodes, there aren’t any living cells around to swoop in and heal the tooth.
Photo in the article by “DeviantArt” | <urn:uuid:3e6349d3-0387-4be1-8c07-9cbfa727106a> | {
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Anxiety is the fearful anticipation of further danger or problems accompanied by an intense unpleasant feeling (dysphoria) or physical symptoms. Anxiety is not uncommon in children and adolescents. Anxiety in children may present as:
- Separation Anxiety Disorder: Excessive anxiety concerning separation from home or from those to whom the child is attached. The youngster may develop excessive worrying to the point of being reluctant or refusing to go to school, being alone, or sleeping alone. Repeated nightmares and complaints of physical symptoms (such as headaches, stomach aches, nausea, or vomiting) may occur.
- Generalized Anxiety Disorder: Excessive anxiety and worry about events or activities such as school. The child or adolescent has difficulty controlling worries. There may also be restlessness, fatigue, difficulty concentrating, irritability, muscle tension, and sleep difficulties.
- Panic Disorder: The presence of recurrent, unexpected panic attacks and persistent worries about having attacks. Panic Attack refers to the sudden onset of intense apprehension, fearfulness, or terror, often associated with feelings of impending doom. There may also be shortness of breath, palpitations, chest pain or discomfort, choking or smothering sensations, and fear of "going crazy" or losing control.
- Phobias: Persistent, irrational fears of a specific object, activity, or situation (such as flying, heights, animals, receiving an injection, seeing blood). These intense fears cause the child or adolescent to avoid the object, activity, or situation.
For additional information see:
Anxiety Disorders Resource Center
Facts for Families: #47 - The Anxious Child | <urn:uuid:8361974c-5cd3-43d9-baf7-d1f279b9ef7b> | {
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Giant Hogweed Spreads!
There have been reported sightings of giant hogweed in residential areas. Hogweed is an invasive species of plant that can cause major harm to those who come in contact with it. If you get some of it’s clear liquid on your skin, it will cause a chemical reaction when exposed to UV light and cause your skin to blister and burn. The central fisheries board have also said that not only is this giant hogweed a threat to human health, but it is also a concern to streams and rivers.
This giant hogweed thrives along rivers and streams. Giant hogweed has a big canopy that blocks light from surrounding plants thus killing off the plants that hold the riverbanks together. Without these plants the banks of streams and rivers could erode away. The reason why giant hogweed spreads so quickly and in vast numbers is because when it comes time to produce seeds, all of the seeds from the plant just fall into the river or stream and are carried down great distances until they are washed ashore and more giant hogweed grows. Giant hogweed plants produce about 5000 seeds per plant so you can imagine the amount of hogweed plants are produced each year. Winter floods will brake apart the weak riverbanks and wash dirt into rivers and it has been shown (Gargan & Caffrey, 1991; Caf- frey, 1992) (E.I.F.A.C., 1974; Reiser & White, 1988) that this dirt will affect the spawning of fish in the area. This dirt build up in slow flowing parts of the river will create a perfect habitat for water plants to grow (Caffrey, 1990) and could potentially slow down the river or stream and may even block it completely, destroying many animal’s habitats.
Even though there is a lot of hogweed found along rivers and streams, there is also an abundance of hogweed along roadsides. This could pose a danger for people because you don’t feel pain when you first come into contact with hogweed, you just get a clear liquid on you and within ten minutes the chemical reaction will occur with the UV light and cause blistering. The fluid from hogweed can cause temporary and even permanent blindness if you get this fluid in your eyes. Small children are in danger because this plant is about as tall as a child and if, for example, they are playing in vacant lot, a stream, or a river, even under parental supervision they can come into contact with giant hogweed and get this clear liquid on them.
Scientists are studying giant hogweed very closely and trying to figure out how to stop it from spreading and eventually get rid of the invasive plant. They have decided to try and cut the plant down to the ground at different times of the year. Tiley & Philp found that when the giant hogweed is cut down in the end of June, they produce less seeds and therefore less new giant hogweed plants are produced. Other methods of controlling this giant invasive species have been tried, but are very expensive compared to just cutting down the giant hogweed. These other methods include various types of pesticides but the problem with these pesticides do not just kill the giant hogweed, the surrounding native plants are also killed. You can target big clusters of giant hogweed, but you can not get rid of all of it without killing other plants with these methods.
Authorities are asking residents to purchase a hogweed removal tool to cut down some of the giant hogweed in their local area. This tool is a blade on the end of a long pole so that the user can cut down the giant hogweed without getting any of the dangerous liquid on them. With the help of the community and the research done by these scientists we can eradicate this invasive giant hogweed.
Hydrobiologia 415: 223–228, 1999. J. M. Caffrey, P. R. F. Barrett, M. T. Ferreira, I.S. Moreira, K. J. Murphy & P. M. Wade (eds), Biology, Ecology and Management of Aquatic Plants. © 1999 Kluwer Academic Publishers. Printed in the Netherlands. | <urn:uuid:5907fc0a-8ece-472b-9a02-cf322924eefd> | {
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Today's Image of Mars shows a segment of Olympica Fossae, as taken by HiRISE.
Olympica Fossae is a 420km long set of troughs, or fossae, in the Tharsis Quadrangle on Mars. Fossae are created when the crust stretches and fractures along two parallel faults. When this happens the area between the two faults sinks down and forms a trough.
Scientists speculate that at one point in the Martian past the troughs of Olympica Fossae served as outflow channels, redirecting floods of water, while at another point they served as channels for lava. This is possible because Mars has experienced many different climates over the past few billion years.
Because HiRISE has yet to caption this image, clicking on it will take you to a map of Tharsis Quadrangle showcased by Mars Travel. | <urn:uuid:b36b33c1-7618-479b-8164-8f74d38180f8> | {
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# Congruence of Sum of Digits to Base Less 1
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## Theorem
Let $x \in \Z$, and $b \in \N, b > 1$.
Let $x$ be written in base $b$:
$x = \sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0}_b$
Then:
$\ds \map {s_b} x = \sum_{j \mathop = 0}^m r_j \equiv x \pmod {b - 1}$
where $\map {s_b} x$ is the digit sum of $x$ in base $b$ notation.
That is, the digit sum of any integer $x$ in base $b$ notation is congruent to $x$ modulo $b - 1$.
## Proof
Let $x \in \Z, x > 0$, and $b \in \N, b > 1$.
Then from the Basis Representation Theorem, $x$ can be expressed uniquely as:
$\ds x = \sum_{j \mathop = 0}^m r_j b^j, r_0, r_1, \ldots, r_m \in \set {0, 1, \ldots, b - 1}$
Proof by induction:
For all $n \in \N_{>0}$, let $\map P n$ be the proposition $\ds \sum_{j \mathop = 0}^n r_j \equiv x \pmod {b - 1}$.
### Basis for the Induction
$\map P 1$ is trivially true:
$\forall x: 0 \le x \le b: x \equiv x \pmod {b - 1}$
This is our basis for the induction.
### Induction Hypothesis
Now we need to show that, if $\map P k$ is true, where $k \ge 2$, then it logically follows that $\map P {k + 1}$ is true.
So this is our induction hypothesis:
$\ds \sum_{j \mathop = 0}^k r_j \equiv \sum_{j \mathop = 0}^k r_j b^j \pmod {b - 1}$
Then we need to show:
$\ds \sum_{j \mathop = 0}^{k \mathop + 1} r_j \equiv \sum_{j \mathop = 0}^{k \mathop + 1} r_j b^j \pmod {b - 1}$
### Induction Step
This is our induction step:
Let $y$ be expressed as:
$\ds y = \sum_{j \mathop = 0}^{k \mathop + 1} {r_j b^j}, r_0, r_1, \ldots, r_{k + 1} \in \set {0, 1, \ldots, b}$
Then:
$\ds y = \sum_{j \mathop = 0}^k r_j b^j + r_{k + 1} b^{k + 1}$
Now from Congruence of Powers:
$b \equiv 1 \pmod {b - 1} \leadsto b^n \equiv 1^n \pmod {b - 1} \leadsto b^n \equiv 1 \pmod {b - 1}$
So by modulo multiplication:
$r_{k + 1} b^{k + 1} \equiv r_{k + 1} \pmod {b - 1}$
From the induction hypothesis:
$\ds \sum_{j \mathop = 0}^{k \mathop + 1} r_j \equiv y \pmod {b - 1}$
Thus by modulo addition:
$\ds \sum_{j \mathop = 0}^{k \mathop + 1} r_j \equiv \sum_{j \mathop = 0}^k r_j + r_{k + 1} \pmod {b - 1}$
Hence $\map P k \implies \map P {k + 1}$ and the result follows by the Principle of Mathematical Induction:
$\ds \sum_{j \mathop = 0}^n r_j \equiv \sum_{j \mathop = 0}^n r_j b^j \pmod {b - 1}$
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A Brief History
On December 11, 1941, dictators Adolf Hitler of Germany and Benito Mussolini of Italy made an enormous blunder, perhaps one that cost them the World War II, when they declared war on the United States.
(Summary and translation of the above video: Hitler speaks to the Reichstag and, in the presence of the Italian and Japanese ambassadors, declares war on the U.S., calling American President Franklin D. Roosevelt (FDR) a war agitator and a hypocrite.)
The declaration came just 3 days after the U.S. had declared war on Japan the day after having been attacked at Pearl Harbor. (Of course, Japan had declared war on the U.S. immediately after the attack.) Although Germany and Italy had a mutual defense pact with each other and with Japan, in which they vowed to defend each other if they were attacked by another country, since Japan had attacked the U.S. and thus initiated hostilities, Germany and Italy were not obligated to also declare war on the U.S.
Apparently, at that point in World War II, the Axis powers (Germany, Italy and now Japan) must have thought things were going well enough to risk inviting the direct involvement of the United States, an industrial power house whose population was greater that that of Germany and Italy combined. In their deliberations, the Axis warlords also seemed to have neglected the fact that at that time, the American industrial plants could not directly be attacked by ground, sea or even air due to technology not yet being advanced enough to easily reach them without interception.
With Great Britain still not conquered and with the Soviet Union just revving up its engines to go, prudence should have dictated a bit more caution on the part of Hitler and Mussolini, but this, of course, that was not their forte.
As it turned out, the U.S. supplied a peak military strength of about 10 million men to the Allied effort, as well as a stunning amount of weapons and supplies. Not to be discounted was also the contribution of American ingenuity to the mix, especially in the race to create the first atom bombs. Had Germany not been defeated early in 1945, the Germans may well have suffered the indignity of being the first nation nuked.
The lessons to be learned here are to “not count your chickens before they are hatched,” and to never think an enemy is defeated before they actually are. These realizations should still have been apparent from World War I, when the contributions of the United States pushed the balance firmly in the Allies’ favor. Perhaps another lesson to be learned is to not allow megalomaniac dictators to run your country!
Question for students (and subscribers): Why do we still have dictators even in the twenty-first century? Please let us know in the comments section below this article.
Your readership is much appreciated!
For more information, please see…
Corvaja, Santi and Robert Miller. Hitler & Mussolini: The Secret Meetings. Enigma Books, 2008. | <urn:uuid:47eb9224-822f-4f0c-8f77-c1943d289d65> | {
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A Brief History of Helena, AR During the Civil War
Phillips County’s rich soil, ideal for growing cotton, drew hundreds of settlers to the Arkansas frontier in the 1830s and 1840s. Plantations were hewn from the wilderness. By the late 1850s Phillips County was the wealthiest county in Arkansas. Helena, the county seat, was a lively port town on the Mississippi, the busiest river in the country.
On the eve of the Civil War, thirty-two people owned ninety-four per cent of the land in Phillips County. Nine thousand slaves worked that land to produce an abundance of cotton, that made a very few very wealthy and benefitted the slaves not at all.
The uneasy peace in a nation that could not compromise over the issue of slavery ended with the election of Abraham Lincoln in 1860. The nation broke apart. South Carolina seceded and others followed. In May 1861, Arkansas became the ninth state to join the newly organized Confederate States of America.
By late spring, most of the men in Phillips County had enlisted in the Confederate army, a few in the Union army. Seven men from Phillips County became high ranking Confederate officers: Charles Adams, Archibald Dobbins, Daniel C. Govan, Thomas C. Hindman, Lucius Polk and James C. Tappan. Patrick Cleburne, a shy Irish immigrant, earned the most lasting fame as one of the Confederacy’s most able commanders.
The women left behind ran plantations, farms and businesses, and faced hardships unimaginable before the war. Many who could afford to leave did. Wealthy Confederate sympathizers sent family members and slaves to less vulnerable areas. Those who remained in Helena saw the unthinkable happen on July 12, 1862. Union General Samuel Curtis and his Army of the Southwest marched into the city unopposed. They seized homes for hospitals, headquarters and depots, and took crops, livestock, forage and fodder. Residents of Helena lived under martial law, their civil liberties curtailed. Travel in and out of the city required a pass signed by the Union commander. Union authorities controlled trade. Civilians could not take goods out of the city, and those in the county who refused to sign the Oath of Allegiance to the U.S. government could not come into the city to buy food and other necessities.
Two thousand slaves who had fled farms and plantations in hope of protection and freedom followed the federal army into Helena. The freedom seekers, whom the army called Contraband, found themselves wards of an army that had no idea how to feed, clothe and house destitute civilians. Contraband lived in stables and churches, and in tents and rough shacks grouped into camps. Men worked for the army as teamsters, officer’s servants and laborers, women as cooks and laundresses.
Within months, charitable organizations began to send food, supplies and help. They acted as advocates for the freedom seekers, provided health care and established schools. The Indiana Yearly Meeting of Friends operated an orphan asylum and school that evolved into Southland College, a teachers’ college for African Americans, after the war.
When Curtis marched into Helena he was not sure if he would remain, but the city’s location made it a valuable strategic resource. Contraband, often given little choice, built Fort Curtis and four batteries, A, B, C and D, on Crowley’s Ridge—defenses to protect Helena from an attack by the Confederates based in Little Rock.
The second year of the Union occupation brought a number of changes for Helena’s Contraband population. On January 1, 1863, the Emancipation Proclamation freed slaves in states in rebellion against the United States, including Arkansas.
That spring, the Union army began recruiting Freedmen into the newly formed United States Colored Troops. Hundreds of men in Helena joined the army, eventually forming several regiments. About the same time, the army began confiscating plantations abandoned by Confederate sympathizers. Union authorities leased the land to individuals, some of them African American, who in turn hired Freedmen to grow cotton. It was the first time many of the Freedmen had been paid for their labor.
On July 4, 1863, the second day of the Battle of Gettysburg and the day that Vicksburg finally surrendered to General Ulysses S. Grant, nearly 8,000 Confederate soldiers under the command of General Theophilus H. Holmes attempted to retake Helena.
The Confederates hit Batteries A and D at first light. After hours of bloody fighting, the attack ground to a halt. At sunrise, when the other attacks were stalling, the assault on Battery C began. After three frontal attacks Battery C fell. Orders came for a detachment of Confederate soldiers on Battery C to take Fort Curtis, which stood below the battery. The attack failed in the face of Union heavy artillery and small arms fire.
The Confederates retreated, the pursuing Union infantry capturing hundreds of men. By one o’clock the battle was over. The Confederates withdrew. They pulled back to the Allen Polk plantation, which became a hospital and graveyard. The defeated Confederate army never threatened Helena again.
Helena was a Union stronghold in Confederate-controlled Arkansas. Supplies and troops flowed in and out of the city, aiding operations in Mississippi, Louisiana and Arkansas. Thousands of troops from Helena participated in the Vicksburg Campaign, including the Yazoo Pass Expedition in 1863. Troops from Helena also took part in the White River Expedition, the Little Rock Campaign, the Camden Campaign and countless smaller operations.
Thousands of men passing through the city, overcrowded camps, hot weather, mosquitoes and poor sanitation led to epidemics of yellow fever, typhoid, diarrhea, and other illnesses. The death rate was staggering and Helena soon became known as “Hell-in-Arkansas” to many Union soldiers. Northern benevolent organizations sent men and women and supplies to help in the hospitals and to give aid to the Union soldiers, but there was often little they could do other than make the men comfortable.
Scouts and patrols left Helena every few days, foraging for food and fodder and keeping an eye on Confederate activity. On July 26, 1864, some 400 U.S. Colored Infantry and Artillery encountered about 1,000 dismounted Confederate cavalry at Big Creek in Phillips County. Colonel Archibald Dobbins, who before the war was a very wealthy Phillips County planter, commanded the Confederates.
The outnumbered Union troops held their ground for several hours, Union artillery driving back the charging Confederates. Finally, a column of the 15th Illinois Cavalry arrived and the battered Union column retreated safely to Helena.
After four long years and the deaths of over 600,000 men, the Civil War ended. Confederate General Robert E. Lee surrendered to Union General Ulysses S. Grant at Appomattox Court House, Virginia, on April 9, 1865, ending the war in the Eastern Theater. The war in the Trans-Mississippi continued until May 26, when Confederate General Edmund Kirby Smith surrendered the last major Confederate force at Galveston, Texas.
The Union army remained in Helena for a number of months after the war ended. For the most part, regiments of United States Colored Troops garrisoned the city. They assisted the Bureau of Refugees, Freedmen and Abandoned Lands, better known as the Freedmen’s Bureau, in its task to help Freedmen transition from slavery to citizenship. They also enforced the policies of Abraham Lincoln’s, and later Andrew Johnson’s, Reconstruction policies, which were intended to reintegrate the former Confederate states back into the United States. A number of black regiments mustered out in Helena before the Union army finally left the city in 1867. | <urn:uuid:55c76d7c-02c5-4e3a-a102-69c6ece1d885> | {
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The history of Waterton Lakes National Park is as deep and rich as its natural beauty. Its story begins more than 10,000 years ago when alpine glaciers melted out of the main valleys, making way for the first signs of human habitation.
For thousands of years nomadic tribes camped, hunted and gathered plants along the Waterton Lakes and river in relative harmony. The introduction of horses and guns in the 1700's changed their relationship to the land and to each other.
European expeditions in western Canada led to an altogether new perspective on this area. In 1858 Lt. Thomas Blakiston, originally a member of the Palliser Expedition, embarked on an expedition of his own looking for a railway pass through the mountains. On his journey, he encountered members of the Kutenai tribe who told him of the South Kootenay Pass. Taking their advice, Blakiston re-crossed the divide, traveling along what would later be called Blakiston (Pass) Creek and out to a chain of three large lakes.
On September 6, 1858, he wrote:
"After two hours traveling on level ground along Red-stone creek (Red-Rock) we emerged on the Saskatchewan plains, just six geographical miles north of the 49th parallel and camped at the lakes...
The scenery here is grand and picturesque...."
Blakiston named the lakes "Waterton", after British naturalist Charles Waterton, although the locals continued to call them Kootenay Lakes for many years after.
Other trailblazers exploring the area at that time were British and American surveying parties sent to mark the International Boundary established by the Oregon Treaty in 1846. In 1874, they reached Waterton, but found working in the mountains so difficult that they managed to erect only two markers in the area. Today, these markers represent the longest undefended border in the world. Visitors to Upper Waterton Lake still marvel at the line, a 20 foot cleared swath through the forests and across the mountains.
An Order in Council in 1895 to protect Waterton as a unique forest park set in motion a series of events that would eventually lead to its National Park status in 1930. John George 'Kootenai' Brown, Waterton's first park official, and American ranger Henry 'Death on the Trail' Reynolds (of Goat Haunt Montana) were the first to propose the idea of creating an International Peace Park with Glacier Park in Montana. As the parks shared the same geology, climate, wildlife and ecology, both Brown and Reynolds felt strongly that the lake and valley could not and should not be divided.
Reynolds wrote "the Geology recognizes no boundaries, and as the lake lay ... no man-made boundary could cleve the waters apart." Kootenai Brown agreed, saying, "it seems advisable to greatly enlarge this park ... it might be well to have a preserve and breeding grounds in conjunction with the United States Glacier Park."
The seeds for an International Peace Park were thus planted and taken a step further by the Cardston Rotary Club, who initiated a meeting of several regional clubs from Alberta and Montana. This first "annual goodwill meeting" convened in 1931 at the Prince of Wales Hotel, where the idea of establishing an International Peace Park in the Waterton/Glacier area was unanimously endorsed.
In 1932, Waterton Lakes National Park in Canada and the United States Glacier National Park united to form the world's first International Peace Park. On June 18, 1932, this partnership was dedicated to world peace by Sir Charles Arthur Mander on behalf of Rotary International. Today, this park continues to symbolize the bonds of peace and friendship between the people of the United States and Canada.
Several different ecological regions meet in Waterton - with prairie plants of the Great Plains, Rocky Mountain plants from northern areas, and coastal plants from the Pacific Northwest all overlapping. This means Waterton has an unusually rich and varied number of plants for its size; many of them are rare or threatened. More than half of Alberta's plant species can be found in Waterton. For this reason, Waterton Lakes National Park was designated a biosphere reserve as part of UNESCO's Man and the Biosphere Programme in 1979. Waterton was the first Canadian national park to receive this designation, the core zone covering the entire national park area.
On December 6, 1995, Waterton-Glacier International Peace Park was officially designated a UNESCO World Heritage Site, recognising its significance in ecological diversity and its model of cooperation and good will, not as two separate parks, but as one.
Waterton is a global treasure that enjoys a unique, triple distinction:
- International Peace Park
- UNESCO World Heritage Site
- UNESCO Biosphere Reserve
Today Waterton remains a spectacular natural wonder - a blend of unusual geology, mild climate, rare wild flowers and an abundance of wildlife. Waterton offers an "all natural" experience like no other place in the world.
This is due in large part to the people who live here that have worked to preserve and maintain its magnificence. We are passionate about our community, our wildlife and the glorious mountains and vegetation that surround us. We think you will share that passion from the moment you arrive. | <urn:uuid:39c5bad3-c3c5-4952-97ca-39aa3a57f517> | {
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Today’s image for Day 252 of the VM_365 project is an illustrations produced by Dave Perkins to explain how crop and soil marks, indicating the presence of buried archaeological deposits, form in the growing plants in Thanet’s agricultural fields. These cropmarks are usually identified by aerial photography.
Pits or ditches that have been cut into the bedrock retain moisture in dry spells and crops planted above them grow taller and darker (A) and (a). The intensity of the cropmark vary, shallow features give only faint marks (B) and deeply buried remains can produce nothing at all (C). Buried masonry, where there is less moisture and soil for the crop to grow, produces a negative mark, where the crop is shorter than the surrounding area (D).
Soil marks result when ploughing brings different coloured material from ancient deposits to the surface of a field (E).
Crop and soil marks have been a valuable resource for plotting archaeological sites over very large areas of agricultural landscape, particularly in the central agricultural areas of Thanet outside the main towns. The presence of mapped cropmarks has helped to predict what archaeological features may be found before excavations have taken place. However although they have been a good indication of the scale of buried sites, excavation has often revealed considerably more detail and complexity which was not present in the cropmarks. | <urn:uuid:0ebb4cbf-f82b-4a97-bc39-70ec991244bb> | {
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Debate over repealing the ivory trade ban dominates conferences of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES). Resolving this controversy requires accurate estimates of elephant population trends and rates of illegal killing. Most African savannah elephant populations are well known; however, the status of forest elephants, perhaps a distinct species, in the vast Congo Basin is unclear. We assessed population status and incidence of poaching from line-transect and reconnaissance surveys conducted on foot in sites throughout the Congo Basin. Results indicate that the abundance and range of forest elephants are threatened from poaching that is most intense close to roads. The probability of elephant presence increased with distance to roads, whereas that of human signs declined. At all distances from roads, the probability of elephant occurrence was always higher inside, compared to outside, protected areas, whereas that of humans was always lower. Inside protected areas, forest elephant density was correlated with the size of remote forest core, but not with size of protected area. Forest elephants must be prioritised in elephant management planning at the continental scale.
Forest elephants, perhaps a distinct species of African elephant, occur in the forests of West and Central Africa. Compared to the more familiar savannah elephant of Eastern and Southern Africa, forest elephant biology and their conservation status are poorly known. To provide robust scientific data on the status and distribution of forest elephants to inform and guide conservation efforts, we conducted surveys on foot of forest elephant abundance and of illegal killing of elephants in important conservation sites throughout Central Africa. We covered a combined distance of over 8,000 km on reconnaissance walks, and we systematically surveyed a total area of some 60,000 km2 under the auspices of the Monitoring of the Illegal Killing of Elephants (MIKE) programme. Our results indicate that forest elephant numbers and range are severely threatened by hunting for ivory. Elephant abundance increased with increasing distance from the nearest road, and poaching pressure was most concentrated near roads. We found that protected areas have a positive impact on elephant abundance, probably because management interventions reduced poaching rates inside protected areas compared to non-protected forest. Law enforcement to bring the illegal ivory trade under control, and effective management and protection of large and remote national parks will be critical if forest elephants are to be successfully conserved.
Citation: Blake S, Strindberg S, Boudjan P, Makombo C, Bila-Isia I, Ilambu O, et al. (2007) Forest Elephant Crisis in the Congo Basin. PLoS Biol 5(4): e111. doi:10.1371/journal.pbio.0050111
Academic Editor: Georgina M. Mace, Imperial College London, United Kingdom
Received: July 5, 2006; Accepted: February 21, 2007; Published: April 3, 2007
Copyright: © 2007 Blake et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The MIKE surveys were financed by the United States Fish and Wildlife Service, the European Union, the Wildlife Conservation Society, and the World Wildlife Fund. The Canadian Centre for International Studies and Cooperation provided in-kind support. The European Union, the Wildlife Conservation Society, and the Central African World Heritage Forest Initiative funded the survey of Odzala-Koukoua National Park. The Megatransect was funded by the National Geographic Society and the Wildlife Conservation Society, with in-kind support from the Ecosystèmes Forestiers d'Afrique Centrale (ECOFAC) Programme, and the World Wildlife Fund.
Competing interests: The authors have declared that no competing interests exist.
Abbreviations: MIKE, Monitoring of the Illegal Killing of Elephants; NP, national park
Between 1970 and 1989, half of Africa's elephants (Loxodonta africana), perhaps 700,000 individuals, were killed, mostly to supply the international ivory trade . This catastrophic decline prompted the Conference of the Parties (CoP) to the Convention on the International Trade in Endangered Species of Wild Flora and Fauna (CITES) to list African elephants on Appendix I of the convention, banning the international ivory trade. Today, opinions on the management of African elephants, including their international trade status, are polarized among range states, economists, and wildlife managers . Southern African nations and wildlife managers argue that their ability to control poaching and manage elephants should be rewarded through the harvest and sale of their ivory stocks, thereby generating revenue for conservation programmes. A strong lobby headed by Kenya, the Central and West African nations, and conservationists in these regions maintain that re-opening the trade will increase the demand for ivory and stimulate the resumption of uncontrollable illegal killing of elephants throughout the continent. Among economists, conclusions are equivocal on whether resumption of the trade will have a positive or negative impact on elephant populations [3,4].
Central to an informed resolution of this debate is a clear understanding of the size and trends in elephant populations and rates of illegal killing for ivory across Africa. The status of savannah elephant (L. africana africana) populations in Eastern, Western, and Southern Africa are relatively well known, and most appear to be stable or increasing with generally low poaching rates , though in Angola, Mozambique, and Zimbabwe, poaching for ivory may be on the increase . The status of forest elephants (L. africana cyclotis) in the vast equatorial forest of Africa remains poorly known because methodological problems and severe logistical constraints have inhibited reliable population surveys and estimates of illegal killing . In African savannahs, both elephant populations and illegal killing can be monitored through aerial surveys , whereas an elephant massacre can remain undetected in the depths of the forest.
The forest of Central Africa is of critical importance for elephants, comprising over 23% of the total continental elephant range, and the largest contiguous elephant habitat left on the continent . In 1989, following reconnaissance surveys on foot, the forest elephant population of the Congo Basin was estimated at 172,400 individuals, nearly one third of Africa's elephants at that time . Poaching was rampant in some areas, notably the Democratic Republic of Congo (then Zaire), whereas Gabon's elephants were relatively unaffected . Human activity, particularly road infrastructure, was found to be the major factor influencing the distribution of forest elephants [9,12,13]. Since 1989, no further region-wide surveys have been conducted, despite dramatic increases in logging, road infrastructure development, growing human populations, and conflict [14–16], accompanied by considerable development of the protected areas network and conservation funding .
Today, forest elephant population estimates are based on guesswork , and inventory and monitoring must be improved for five main reasons: (1) forest elephants may still comprise a significant proportion of Africa's total elephant population ; (2) forest elephants are distinctive on morphological, ecological, behavioural, and genetic criteria, constituting at least a subspecies and possibly a distinct species of African elephant ; (3) Central Africa's forests are the source of much of the world's illicitly traded ivory ; (4) the trade status of ivory from Southern African elephants may have a serious impact on poaching levels in Central Africa due to changes in the dynamics of the international legal and illegal ivory trade ; and (5) logging and road development in the Congo Basin are increasing dramatically, which is opening up accessibility both to remaining elephant strongholds and to markets.
During 2003–2005, under the auspices of the Monitoring of the Illegal Killing of Elephants (MIKE) programme and the Projet Espèces Phares of the European Union, we collected data on the distribution, abundance, and illegal killing of forest elephants by means of systematic foot surveys on line transects and reconnaissance walks (see Materials and Methods) at six sites (Figure 1). These MIKE survey sites were centred on protected areas thought to contain nationally important forest elephant populations. We also collected complementary data in 1999 and 2000 on a single, continuous survey of over 2,000 km dubbed the “Megatransect” , which ran through some of the most remote forest blocks in Africa (Figure 1). Our goals were to evaluate the conservation status of forest elephants, including population size, distribution, and levels of illegal killing in relation to human activity, isolation from roads, and the impact of protected areas.
Forest Elephant Abundance by MIKE Site
Our results indicate that a combination of illegal killing and other human disturbance has had a profound impact on forest elephant abundance and distribution, including inside national parks (NPs). The density of elephants in NPs surveyed varied over two orders of magnitude. In the Salonga NP, a remote United Nations Educational, Scientific, and Cultural Organization (UNESCO) World Heritage site, as few as 1,900 forest elephants remain at a mean density of 0.05 elephant km−2. Salonga is the largest forested NP in Africa and the second largest on earth. In Nouabalé-Ndoki and Dzanga-Sangha NPs and their buffer zones (Ndoki-Dzanga MIKE site), 3,900 elephants were estimated within a survey area of 10,375 km2 (0.4 elephant km−2). Mean estimated forest elephant densities in the three NP sectors at this site were 0.66, 0.65, and 0.56 individuals km−2 for Nouabalé-Ndoki NP, Dzanga NP, and Ndoki NP respectively, compared with densities of 0.14 and 0.1 individuals km−2 in the peripheral zones of these NPs. In the 2,382-km2 Boumba Bek NP in southeast Cameroon, an estimated 318 elephants occurred (0.1 elephant km−2). In the Bangassou Forest, one of only two regions in the Central African Republic (CAR) that still contain forest elephants, a formal estimate of elephant abundance was not made, but systematic observations along reconnaissance walks suggest that in the 12,000-km2 survey area, fewer than 1,000 forest elephants remain. In only two protected areas, Minkébé NP, northeast Gabon, and Odzala-Koukoua NP, northern Congo, did the mean estimated elephant density exceed 1.0 individual km−2. Estimated population size was 22,000 individuals in the 7,592-km2 Minkébé NP (2.9 elephants km−2) and 14,000 in the 13,545-km2 Odzala-Koukoua NP (1.0 elephant km−2).
Elephant Poaching in MIKE Sites
Poached elephant carcasses were found in all MIKE sites, even large, well-established NPs (Table 1). We found 53 confirmed elephant poaching camps and 41 elephant carcasses from 4,477 km of reconnaissance walks; we confirmed 27 carcasses as having been poached. Poached carcass encounter rate was highest in the Minkébé site, at 13.7 carcasses 1,000 km−1, followed by Ndoki-Dzanga with 7.1 carcasses 1,000 km−1. The tusks had been removed from all poached carcasses, though due to the level of decay, it was not possible to determine whether they had been poached primarily for ivory or for meat.
Elephant Poaching Camps and Carcasses Found during Reconnaissance Walks, Line Transects, and Fieldwork-Related MIKE Surveysa
Forest Elephants, Human Activity, and Roads in MIKE Sites
Logistic regression using the pooled elephant dung-count data from the Ndoki-Dzanga, Boumba Bek, Salonga, and Odzala-Koukoua surveys indicated a significant positive relationship between the probability of presence of elephants and increasing distance from the nearest major road (Figure 2A). The data for Minkébé were omitted from this analysis because, unique to this site, forest elephant dung was recorded on all transects regardless of the distance from a road, and therefore the data were not informative for logistic regression. Model results were improved by including site as a factor covariate. The exceptions were Ndoki-Dzanga and Odzala that not only had the same slope, but also the same intercept term. Odzala-Koukoua and Ndoki-Dzanga consistently had the highest probability of elephant occurrence at all distances from the nearest road, with intermediate probability for Boumba Bek. Salonga, where elephant dung was recorded on just 22 out of 130 line transects, had the lowest probability of elephant occurrence (see Figure 2A). Performing separate logistic regression analyses on each site's data confirmed the relationship between the probability of elephant occurrence and the distance from the nearest road, except for the Salonga site (see Figure 3), in which distance from the nearest road had no effect on the probability of elephant dung occurrence.
Distance to road (in kilometres) and site were used as explanatory variables. (A) shows the elephant data, and (B) shows the human data. The observations and regression lines are colour-coded by site and the dashed line shows the regression line without the inclusion of site as a covariate. The covariates distance to road and site are significant for both elephant and human probability of occurrence. The dissimilarity between sites is more pronounced when modelling the probability of elephant occurrence.
Distance to road (in kilometres) was used as the explanatory variable (except for probability of elephant occurrence for Minkébé where modelling is not required due to an effective probability of 1). Elephant data are shown to the left, and human data to the right. The observations and regression lines are colour-coded by site, and the 95% confidence interval is indicated by the dotted lines. The probability of elephant occurrence is significantly related to distance to road for all sites except Minkébé and Salonga. Due to the imprecision in the data and other influences not captured by distance to road, the probability of human presence is only significantly related to distance to road for the Ndoki-Dzanga site for the separate site analyses.
Using the human-sign data pooled across the same MIKE survey sites, but this time including Minkébé, we found that the probability of human presence decreased with increasing distance from the nearest road, in contrast to the probability of elephant occurrence (Figure 2B). However, the probability of human presence was not as dissimilar between the five sites as was the probability of elephant occurrence. In this case, Ndoki-Dzanga and Odzala were the most dissimilar, having the highest and lowest probability of human presence at all distances from the nearest road, respectively. Minkébé, Salonga, and Boumba Bek occupied the middle ground in terms of the probability of human presence and were not significantly dissimilar from one another. Like human sign, the encounter rate of poached elephant carcasses decreased with distance from the nearest road (Spearman correlation coefficient ρ = −0.663, n = 13, p = 0.014), and no poached carcasses were found beyond 45 km of a road.
Generalized Additive Models provide a flexible, non-parametric technique for modelling the extreme variation in the elephant dung counts. Conditioning on elephant presence, the results indicate a significant positive relationship between elephant density and distance from roads. However, including the site covariate in addition dramatically increased the deviance explained from 22.5% to 95.4% and reduced the Generalized Cross Validation (GCV) score (which is equivalent to Akaike's Information Criterion), from 14.734 to 6.742. Figure 4 illustrates the estimated conditional dependence of elephant dung-pile numbers on distance from road. The significant difference between the MIKE sites highlighted by the site covariate indicates that there are site-specific ecological influences or additional local human pressures not captured by distance to the nearest major road.
Estimates (solid line) and confidence intervals (dashed lines), with a rug plot indicating observation density along the bottom of the plot, are shown. To avoid over-fitting, the degrees of freedom were restricted to two for the distance-to-road covariate.
The scale of the Megatransect transcended site-level surveys and thus provided a useful extensive comparison to the more intensive, but localised, MIKE surveys. The Megatransect also traversed six protected areas, which allowed the effect of protected area status on forest elephants and human presence to be examined. Applying logistic regression to the Megatransect data indicated a significant relationship between the probability of presence of elephants and the distance from the nearest road (Figure 5A), consistent with the analysis of the MIKE dataset. Model results were not improved by including distance to the nearest protected area boundary as a covariate, but they were significantly improved by including a binary factor covariate describing whether or not the count data were collected within or outside of a protected area. Although the pattern of response of the probability of elephant occurrence to increasing distance from road is similar for within and outside of protected areas, protected areas consistently had the highest probability of elephant occurrence at all distances from the nearest road (Figure 5A).
Distance to road (in kilometres) and location within or outside the protected areas were used as explanatory variables. (A) shows the elephant data, and (B) shows the human data. The observations and regression lines are colour-coded to correspond to within or outside the protected areas and the dashed line shows the regression line with only the distance to road covariate. The covariates distance to road and location within or outside the protected areas are significant for both elephant and human probability of occurrence.
Consistent with MIKE survey data, the probability of human presence on the Megatransect decreased significantly with increasing distance from the nearest road in contrast to the probability of elephant occurrence, and was consistently lower inside protected areas compared to outside for all distances from the nearest road (Figure 5B).
Generalized Additive Models were applied to the elephant dung counts from the Megatransect while conditioning on elephant presence. The results indicate a significant relationship between elephant dung counts and both distance from roads and distance to protected areas. However, in contrast to the model fit to the MIKE data, this model is only able to explain 19.7% of the deviance. Figure 6 illustrates the estimated conditional dependence of elephant dung-pile numbers on distance from road (Figure 6A) and distance to protected areas (Figure 6B) that shows a positive relationship with increasing distance from roads and a negative relationship for increasing distance from protected areas.
(A) shows the effect of distance from the road, and (B) shows the effect of distance to the nearest boundary of the protected area. Negative distances indicate locations inside protected areas. Estimates (solid lines) and confidence intervals (dashed lines), with a rug plot indicating observation density along the bottom of the plot, are shown. To avoid over-fitting, the degrees of freedom for this model were restricted to 3 for both covariates.
Our surveys confirmed the observations of conservationists that numbers and range of forest elephant populations are in decline and that they continue to be poached for ivory, and probably meat, including inside NPs. In common with previous work in the Congo Basin , distance from the nearest road was a strong predictor of forest elephant abundance, human presence, and levels of poaching.
Within the consistent pattern of increasing elephant abundance and decreasing human-sign frequency with increasing distance from roads, site-level differences were variable and informative. Minkébé was the only site in which elephant dung was recorded on all transects. For other sites, the probability of occurrence decreased in the order Odzala-Koukoua, Ndoki-Dzanga, Boumba Bek, and finally Salonga. Elephant density by NP decreased in the same order, which is consistent with the remoteness of sites from the nearest road (Figure 7). Total NP area was not correlated with elephant density; however, there was a significant positive correlation between the area of parks that was over 40 km from a road and mean elephant density (ρ = 0.9, n = 5, p = 0.037). Thus, although Salonga NP is close to three times bigger than any other park surveyed, it comprises two separate sectors with some 46% of the total surface area within 10 km of a road, and nowhere in the park is beyond 40 km from a road. By contrast, just 0.7% of the Minkébé NP is within 10 km of a road, and a full 59% is more than 40 km from a road. Only in Minkébé and Odzala-Koukoua NPs do areas exist that are more than 60 km from the nearest road.
It is noteworthy that the road system of Salonga NP, which was well developed during colonial and immediately post-colonial times, has gradually fallen into disrepair, and today, the roads are used primarily as footpaths. In all other MIKE sites surveyed, the closest roads to the site are open to regular vehicular traffic, and many have been opened within only the last 10–20 y. Salonga has, therefore, a longer history of penetration by roads than other sites, which may be reflected, not only in the dearth of elephants, but the distribution of human signs, which were more likely to occur further from roads rather than closer to them. The long-term accessibility to the forest and heavy hunting in Salonga, including hunting for elephants , appears to have extirpated wildlife close to roads, forcing hunters to become more active in the most-remote areas of the park. Several navigable rivers also run through Salonga NP, which provide access and may confound an effect of roads as a proxy for isolation.
The trends observed in the other MIKE sites (Figure 3) indicate that they have not yet reached such an advanced state of degradation as Salonga because strong relationships still exist between elephant abundance, human-sign frequency, and distance from the nearest road. Elephants still occur in moderate to high densities in remote areas, and at an exceptional density in Minkébé. However, it is clear that elephants are being concentrated into the most-remote sectors of all sites in a near-perfect juxtaposition with the distribution of human activity as exemplified by the simple interpolations of human-sign and elephant dung frequency from Ndoki-Dzanga (Figure 8). This startling image is reminiscent of Parker and Graham's description of savannah elephant distribution as the “negative” of human density , which was identified as a major factor in the decline of the elephant in Eastern Africa. Without effective management intervention to reduce fragmentation of remote forests , the human–elephant interface will move deeper into the forest, and elephants will continue to retreat into an increasingly less-remote core in the face of an advancing “human front.”
Increasing colour intensity signifies increasing dung and human-sign frequency.
It is important to remember that the MIKE sites likely represent the “best-case” conservation status scenario because they were deliberately chosen from among the longest-established protected areas in some of the most-remote locations in Central Africa. Landscape-level conservation plans, which include conservation measures to reduce hunting and trafficking of bushmeat along roads, have been underway in Minkébé, Ndoki-Dzanga, Odzala-Koukoua, and Boumba Bek for at least a decade, and even Salonga has benefited from some conservation effort. Most of the remainder of the Congo Basin does not receive any tangible wildlife management, and the conservation status of forest elephants is probably considerably worse. A simple analysis of the degree of fragmentation caused by roads across the range of the forest elephant is revealing (Figure 7). In the 1,893,000 km2 of potentially available forest elephant habitat in the Congo Basin, some 1,229,173 km2 (64.9%) is within 10 km of a road. Just 21,845 km2 is over 50 km from the nearest road in just three countries, Congo, Gabon, and the Democratic Republic of Congo. Only Congo has potential elephant habitat beyond 70 km from a road, in the vast Likouala swamps to the northeast of the country. The road shapefile (Environmental Systems Research Institute [ESRI]) used is also restricted to major roads and thoroughfares, since most logging roads are either not geo-referenced or not mapped. Therefore the true degree of fragmentation of Central Africa's forest is considerably worse than is depicted on this map.
Figure 7 indicates that the current NP system in the Congo Basin does a reasonable job of capturing the most remote tracts of forest that remain (with the exception of the Likouala swamps). Despite considerable budgetary increases in recent years, funding for NPs and conservation landscapes remains below that necessary for even minimal management [27,28], and an appropriate question to ask is whether or not protected areas actually protect forest elephants. The Megatransect data suggest strongly that NPs and protected areas are making a positive contribution to conservation because at any given distance from the nearest road, protected areas have (1) lower incidence of human sign, and (2) higher incidence of forest elephant sign than non-protected forest, at least in Congo and Gabon.
The situation in the rest of the protected areas system and the forest at large is likely to be considerably worse, particularly in areas of armed conflict, civil disorder, and deteriorating socio-economic conditions . In the Ituri Forest of eastern Democratic Republic of Congo, for example, where some of the bloodiest fighting seen in recent decades has occurred, an estimated 17,000 kg of ivory was evacuated from a 25,000 km2 forest block in a 6 mo period during 2003 . Given a mean estimated weight of ivory from African elephants of 6.8 kg , this could represent some 2,500 elephants. There is no doubt that forest elephants are under threat from illegal killing across Central Africa's forests, and soon, the only elephants left to poach will be those that remain in the interior of a few remote, well-funded, and well-managed NPs in politically stable countries.
In this paper, we have shown that even with a near-universal ban of the trade in ivory in place, forest elephant range and numbers are in serious decline. This is in contrast to much of the recent literature on “the African elephant” that indicates generally stable or increasing populations in Eastern and Southern Africa , and in some cases, dramatic population growth and a “return of the giants” . The decline of the ecologically, socially, morphologically, and genetically distinct forest elephant, (perhaps a separate species or, at the very least, an “evolutionary significant unit” worthy of high conservation status) has profound implications for the diversity and resilience of the African elephant. Given their vulnerability compared to savannah elephants, the wellbeing of forest elephants must be given priority when making decisions about elephant management on the continental scale. Key issues that fall into this category include the future of the ivory trade and resource allocation for international support programmes, such as MIKE.
Forest elephants will continue to decline unless four immediate actions are successfully implemented. First, a national- and regional-scale approach to road development planning and construction is necessary in which reduction of fragmentation of Africa's last forest elephant strongholds is a central component. Second, law enforcement, including aggressive anti-poaching, of remaining priority elephant populations in NPs must gain the financial and political commitment required to ensure management success. Third, the illegal trade in ivory must be brought under control in elephant-range states, transit countries, and destination nations. Forth, effective partnerships must be developed with private logging and mining companies to reduce their negative impacts in the peripheries of protected areas and stop encroachment into NPs.
Materials and Methods
Density estimates of forest elephants in MIKE survey sites were obtained from dung counts conducted on systematic line-transect distance sampling surveys designed and analysed using the Distance 4.1 software package . Distance sampling is a standard survey method for abundance estimation in both terrestrial and marine environments but, as far as we are aware, has never been used for ground-based surveys on foot on a scale approaching that of the present study, which comprised a total area of 60,895 km2 in some of the most remote and difficult terrain in forested Africa. Site boundaries were defined following discussions with the MIKE directorate, national wildlife directors, and site-based personnel, and were ultimately constrained by the total operating budget. Rivers, flooded forest, and swamps were excluded from site definitions because elephant dung piles cannot be surveyed in these habitats.
An attempt was made to design site boundaries that captured the gradient of human impacts on elephants, balanced against the need for a reasonable level of precision within each survey stratum. “Reasonable” precision was defined as a 25% coefficient of variation (CV) for estimates of elephant dung density for each survey stratum. To improve precision, each MIKE site was stratified according to expected elephant dung-pile encounter rate (n0/L0) based on either data from short pilot studies or from expert opinion in the case of the vast Salonga site, where a pilot study was prohibitively expensive. The effort in terms of total length of transect line required to attain the required precision was estimated according to the equation on page 242 of using a value of three for the dispersion parameter b as recommended by Buckland et al. : where CVt( D^) denotes the target CV for the density estimate.
Survey designs were completed using the “systematic segmented trackline sampling” option of Distance 4.1, as systematic designs with a random start are more robust to variations in the distribution of the population being sampled in terms of estimator precision . This is a survey design class that superimposes a systematic set of parallel tracklines onto the survey region with a random start, along which line-transect segments are evenly spaced, again with a random start, at intervals and lengths determined by the user. Spacing and length of line transects varied by stratum and site according to the required sampling intensity. To potentially improve precision, line transects were oriented at 90° to major river drainages to run parallel to possible gradients in elephant density.
The start and end point of each line transect was uploaded to a Garmin 12XL GPS (global positioning system; http://www.garmin.com) to assist field navigation. If in the field, a line transect began in a swamp or river, it was displaced to the nearest location that could be found on terra firma. Similarly, when line transects traversed inundated areas, that portion of the transect was discarded, and an equivalent length was added to the end of the transect. Line transects were oriented using a sighting compass from the start point, and cut with a minimum of damage to the understorey. Observers walked slowly (ca. 0.5–0.75 km hr−1) along the line transect, scanning the ground for elephant dung piles. Distance along transects was measured using a hip-chain and topofil to the nearest metre, and the distance of the centre of each dung pile to the centreline were measured to the nearest centimetre using a 10-m tape measure. Survey methods are described in detail in .
In the field, the end of one line transect and the beginning of another were connected by reconnaissance walks following a “path of least resistance” through the forest . On reconnaissance walks, a general heading was maintained in the desired direction of travel, but researchers were free to deviate to avoid thickets and steep hills or to follow elephant trails, human trails, and even logging roads. On reconnaissance walks, a continuous GPS tracklog is maintained, with a fix taken every 10–15 s. Data collection included all elephant dung piles, human sign, and vegetation type, and data records were coded by time (GMT). Data were later reconciled with GMT from the GPS tracklogs and thus geo-referenced and imported into ESRI ArcView 3.2 (Redlands, California, United States). Such reconnaissance walks are particularly useful for assessing the intensity and types of hunting activity if signs of humans are followed when encountered. However data are biased and provide only a general overview of large mammal distributions and human activity in the forest. The Megatransect also used reconnaissance survey methods consistent with the MIKE methods.
Elephant carcasses were defined as poached if evidence of hunting was obtained, which included gunshot holes in the carcass, removal of tusks, and meat on smoking racks. Elephant poaching camps were identified from other hunting camps by the presence of remains of elephant or very large meat-smoking racks.
DISTANCE 4.1 software was used to analyse the perpendicular distance data from the field measurements and to calculate the density of elephant dung piles by survey stratum and by individual line transect as described by Buckland et al. . Different detection functions were fitted to the data sequentially using half-normal, uniform, and hazard rate key functions with cosine, hermite polynomial, and simple polynomial adjustment terms. The best model was selected on the basis of the lowest Akaike's Information Criterion score (AIC) , and χ2 goodness-of-fit tests were used to examine the fit of the model to the data. On-site studies of elephant defecation and dung decay were not carried out due to the logistical and funding difficulties of working over such a large area, thus dung density was converted to elephant density using estimated conversion factors of 19 defecations per day, and mean dung lifespan of 90 d for all sites.
In preparation for the statistical modelling, the centroid of each transect and 5-km Megatransect segment was used to calculate the distance of each “sample unit” from the nearest road or protected area boundary using the ESRI ArcView 3.2 extension “Nearest Feature” . A shapefile of Central African roads was obtained from Global Forest Watch (World Resources Institute, Washington, D. C., United States). The protected areas shapefile was provided by the Wildlife Conservation Society.
Data from two MIKE sites, Dzanga-Sangha and Nouabalé-Ndoki, were pooled for analytical purposes since they are contiguous areas and therefore contained a single elephant population. Generalized Linear Models with a binary response and logistic transformation were used for the logistic regression analyses . The Generalized Additive Models fit to the dung-count data from the MIKE sites have the form where ni denotes the number of dung piles detected on the ith transect, li the length of the ith transect, and ॖ^ is a site-specific estimate of the effective strip half-width calculated using the Distance 4.1 software . The term 2li ॖ^ gives the area effectively surveyed on transect i. β0 is the intercept, and f(zij) is a smooth function of the jth covariate z associated with the ith transect. To deal with the over-dispersion in the data, a quasi-Poisson distribution was assumed. By including area effectively surveyed as an offset term in the model, dung density is, in effect, being modelled. The results are equivalent for elephant density if we assume constant conversion factors of 19 defecations per day and a mean dung lifespan of 90 d for all sites. The models were fit in R using the mgcv package . To avoid over-fitting, the degrees of freedom were restricted to two in the final model. The elephant dung-count data used in the analysis were over-dispersed in part due to the large number of zero counts. Some of these problems were eliminated by conditioning on elephant presence and only using non-zero counts for the analysis. In addition, using a quasi-Poisson model instead of a Poisson allowed for the modelling of over-dispersion by not assuming that the dispersion parameter is fixed at 1. The standard diagnostic plots used in model selection and assessment of fit indicated that the model is consistently giving lower fitted values when these are compared to the response values. The extraordinarily high elephant dung counts for certain areas of Minkébé, and occasionally for Odzala and Ndoki-Dzanga, that are in stark contrast to the counts at other sites or transects within the same site contribute to this problem. The same methods were applied to the Megatransect data except that the offset term representing the area effectively surveyed term was omitted since this dataset does not permit the estimation of the effective strip half-width ॖ^ . Also, to avoid over-fitting, the degrees of freedom were restricted to 3 for both covariate terms in the final model for the Megatransect data. Spatial Analyst from ESRI was used to construct the images in Figure 7A and 7B, and the interpolations of human sign and elephant dung counts for Ndoki-Dzanga shown in Figure 8 were produced using the “Calculate Density” feature of the same extension.
The governments of the Democratic Republic of Congo, Central African Republic, Republic of Congo, Gabon, and Cameroon authorized and promoted the MIKE Programme. Wildlife Directors of each country are thanked for their help and support. The MIKE Programme was directed by Mr. Nigel Hunter. The wise guidance and assistance of Mr. Sébastien Luhunu, Central African MIKE Programme Coordinator, and Dr. Richard Ruggiero of the United States Fish and Wildlife Service, was invaluable. Dr. Ken Burnham provided critical help in reviewing MIKE survey designs. Huge efforts from all field staff in difficult and sometimes dangerous conditions made these surveys possible. Our thanks go to Dr. Fernanda Marques for stimulating discussions on aspects of the analysis. Susan Minnemeyer (World Resources Institute) kindly provided the shapefile of major roads. Drs. Kent Redford, David Wilkie, James Deutsch, Bill Laurance, Emma Stokes, Richard Barnes, and two anonymous reviewers are thanked for constructive comments on earlier drafts of this manuscript.
SB, SS, MF, and JH conceived and designed the experiments. PB, CM, IBI, OI, FG, LBB, BdS, VM, DS, RB, LW, MF, and FM performed the experiments. SB and SS analyzed the data and wrote the paper.
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- 43. Jenness J (2004) Nearest features (nearfeat.avx) extension for ArcView 3.x, v. 3.8a [computer program]. Flagstaff (Arizona): Jenness Enterprises. Available: http://www.jennessent.com/arcview/nearest_features.htm. Accessed 25 February 2007.
- 44. Venables WN, Smith DM, R Development Core Team (2005) An introduction to R. Notes on R: A programming environment for data analysis and graphics. Version 2.2.1 ed. Available: http://www.maths.usyd.edu.au/u/PG/STAT5001/r/R-intro.pdf. Accessed 22 February 2007.
- 45. Wood SN (2006) Generalized additive models: An introduction with R. Boca Raton (Florida): Chapman and Hall. 391 p. | <urn:uuid:ba59746c-1f98-4d98-b2a2-d4a08c361021> | {
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Extreme Environment Mission Operations program (NEEMO)
For astronauts floating hundreds of miles above the Earth in an airless, weightless atmosphere, even the simplest tasks need to be thought out in detail, planning for every step. Thousands of man hours and millions of dollars go into space exploration, and once the rocket has reached the silent depths of space, things absolutely must go as planned. There's no room for error.
The only frontier left on Earth, it is said, is the oceans, and for astronauts of NASA and the European Space Agency, these deep terrestrial environments provide the conditions needed to simulate space missions. It's the perfect place to test the techniques and instrument performance for the future of space exploration, and now NASA is looking at asteroids as their next great space destination.
The NASA Extreme Environment Mission Operations program (NEEMO) project 16 allowed astronauts the chance to train for a manned mission to an asteroid, something NASA has outlined as a core goal, hoping to land a man on a speeding space rock by 2025.
European Space Agency astronaut Tim Peake and his Neemo crewmates, including NASA astronauts, resurfaced last week after spending 12 days underwater. The aquanauts tested equipment and techniques for future space exploration and worked with students above on educational experiments studying the effects of pressurized environments.
The training session off Florida’s Atlantic coast gathered together about 100 European Space Agency astronauts and support crew at the underwater base named Neemo, where the agency ran through the technical aspects of life in space, practicing communications, living in cramped conditions, performing "waterwalks," and engaging in team problem solving.
For these Neemo aquanauts, diving underwater is one of the best ways of simulating weightlessness on Earth. The aquanauts spent hours on "spacewalks," exploring potential methods of retrieving samples from an asteroid, as well as testing tools and techniques.
European Space Agency astronaut Tim Peake talks with students as part of the project's "science under pressure" educational experiments, which involved collaboration with students on science experiments in the underwater habitat.
Educators and scientists from NASA, the European Space Agency, and the Japan Aerospace Exploration Agency proposed science experiments that evaluate whether simple, everyday tasks, such as blowing a bubble or operating a remote controlled device, will be more difficult at a higher pressure environment.
NASA astronaut Dottie Metcalf-Lindenburger (@AstroDot) anchoring a mock-up of Geo-Physical Array into the sea bottom simulating the surface of an asteroid. Metcalf-Lindenburger is secured with her feet locked into a Portable Foot Restraint carried by a mini Sub that's role-playing a Space Exploration Vehicle.
Aquanaut Steve Squyres from Cornell University has been blogging about his adventure beneath the surface. "Just like any other field scientists, we started with reconnaissance, flying above the surface with jet packs and reporting back to Mission Control what we discovered. On the spot, they came up with a science plan for us, just as would happen with a crew at an asteroid. And then it was up to us to use all the tools we had at our disposal, in whatever way we thought best, to carry out that science plan."
Here we see a submersible transporting a Neemo aquanaut to a simulated asteroid. In space, chipping off a piece of asteroid would require that an astronaut hold on to something, otherwise he would float away. The submersible was tested underwater as a means of getting to asteroids as well offering a stable platform for astronauts to work on.
During Neemo missions, aquanauts employ a technique known as saturation diving to live and work in the Aquarius Reef Base underwater habitat for weeks at a time. Aquarius is an ambient pressure habitat, meaning its atmospheric pressure is equal to the surrounding water pressure -- about 2.5 times that of surface level at the habitat’s depth.
Aquarius is an underwater ocean laboratory located in the Florida Keys National Marine Sanctuary. The laboratory is deployed three and a half miles offshore, at a depth of 60 feet, next to spectacular coral reefs. Scientists live in Aquarius during 10–day missions using saturation diving to study and explore our coastal ocean. Aquarius is owned by NOAA and is operated by the University of North Carolina Wilmington.
NASA is actively planning to expand the horizons of human space exploration, and with the Space Launch System and the Orion crew vehicle, humans will soon have the ability to travel beyond low Earth orbit. That opens up a solar system of possibilities, and NASA’s goal is to send humans to explore an asteroid by 2025. But, they say, to accomplish that goal, the planning, experimenting, and training must start now. | <urn:uuid:2e43a1f3-c0d7-40a5-b0e0-d90500e3d30e> | {
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2018 promises great inroads in the realm of “quantum computing.” While conventional computers use binary data or bits (i.e., 0s and 1s) to store and process information (a bit can either store a 0 or 1), a quantum computer operates based on the laws of quantum mechanics and uses quantum bits or “qubits,” which can be in a “superposition” state of zero and one at the same time (e.g., a qubit can store a 0, 1, or a summation of both 0 and 1). Ultimately, it is expected that quantum computers will be able to solve complex computations exponentially faster – as much as 100 million times faster — than classic computers.
While currently not ready for general commercial applications, quantum computers could someday allow scientists and others to solve very complex problems in chemistry, applied mathematics, biology and engineering, and also push huge advances in areas such as artificial intelligence, machine learning, large database searching and big data processing.
How could quantum computing impact blockchains?
Current encryption, cryptography and private/public key systems are premised on the assumption that there are limits to the resources and processing power that can be applied to break such systems. Quantum computers may be powerful enough (perhaps) to break the systems currently in use that protect secure online communications and encrypted data. If the resources of quantum computers are ever generally available or otherwise fall into the “wrong” hands, encryption and cryptography, as we know it today, could be in jeopardy. This has led the National Institute of Standards and Technology to begin the process to standardize so-called post-quantum cryptography. Clearly, basic password protection would appear quaint and merely “a nice try” in light of the resources quantum computing could bring to a “brute force” hack.
Blockchain technology relies on public key cryptography to maintain the security of the ledger. Moreover, bitcoin relies on the work of “miners” to use computing power resources to solve certain complex mathematical problems to verify transactions, a task that could be upended by entities with quantum computing platforms. Again, quantum computing presents a real threat to existing blockchain algorithms. As a result, developers are working on quantum-resistant ledgers.
While widespread use of quantum computing in the commercial context may be a bit far off, significant resources are being applied in that area. When quantum computing becomes readily available, blockchain will have to adapt to this new technological capability. The process is already underway. | <urn:uuid:e7e38b98-0806-4deb-8685-988441f64d8f> | {
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What Is Allodynia?
Allodynia is a medical condition that causes an individual to experience pain from stimuli that do not typically cause pain. For example, a normal everyday touch, such as a sleeve brushing against the arm, a brush combing through the hair, or light pressure applied on the skin from a piece of clothing results in pain. The pain experienced is different for each individual with allodynia.
Types Of Allodynia
Allodynia is classified into three types: static or tactile, mechanical or dynamic, and thermal. Static or tactile allodynia is diagnosed when allodynia pain occurs as a result of pressure applied to the skin. Mechanical or dynamic allodynia is diagnosed when allodynia pain occurs as a result of movement over the skin. Thermal allodynia is diagnosed when allodynia pain occurs as a result of a change of temperature to the skin.
Allodynia can develop on its own or as the result of another condition. The exact reason why allodynia surfaces is not known, but it is thought to involve increased receptiveness or malfunction of nociceptors, a type of nerve.
Medical conditions that may have allodynia as a symptom include, but are not limited to, the following:
- Complex regional pain syndrome
- Postherpetic neuralgia
- Peripheral neuropathy
- Other neuropathies | <urn:uuid:05972068-06f8-454a-868e-1479a36fe847> | {
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Influenza is an infectious disease caused by a constantly varying RNA virus. Natural infections with influenza A viruses can be found in many animals including humans, pigs, horses, sea mammals, mustelids, and birds.1 Capua and Alexander1 said that, in the 20th century, the sudden emergence of antigenically different strains transmissible in humans, termed antigenic shift, had occurred on many occasions, 1918 (H1N1), 1957 (H2N2), and 1968 (H3N2), each time resulting in a pandemic. In 1997, an outbreak of a new potentially devastating influenza strain occurred in Hong Kong.2 The outbreak included 18 cases of avian influenza (bird flu) caused by a novel H5N1 virus and occurred in humans, resulting in 6 deaths.2 Webster3 noted that the separation of aquatic birds from other land-based domestic poultry in Hong Kong after the H5N1 bird flu incident indicated that animal husbandry practices could influence the interspecies transmission of influenza viruses.
In the past year (2004), the revisit of H5N1 infection occurs in Southeast Asia. Since January 2004, the bird flu has been detected in some poultry farms, and the Thai government has launched several attempts to control the infection. Until the present time, more than 100 cases of human infection, with approximately 50% fatal cases, are documented.4 The most recent cases are part of a family under investigation to determine whether human-to-human transmission may have occurred.5 The initial case was a girl in a rural province in northern Thailand who died of pneumonia and finally diagnosed to have H5N1 infection.5,6 Her aunt who resided with the patients has also been confirmed for infection.5,6 Both patients are known to have had contact with infective dead chickens.5,6
The suspected human-to-human transmission case was the mother of the girl, who went back from Bangkok to take care of her daughter in the hospital up to the time of the child's death.5,6 Then this patient went back to Bangkok, developed flu, and died 8 days later.5,6 Continuous attempts are made to proof this possible human-to-human transmission.5,6 Indeed, a similar episode was documented in Vietnam early this year, but final conclusion cannot be made because of lack of patients' specimen. Concerning the probability of the human-to-human transmission, the epidemiology as well as the molecular biology investigations might answer this question.
Kida said that recent outbreaks of highly pathogenic avian influenza in chickens and ducks that occurred in 9 Asian countries alarmed to realize that there was no border for infections and gave a rise to great concern for human health as well as for agriculture.7 Kida also noted that this H5N1 virus jumped the species barrier and caused severe disease with high mortality in humans in Vietnam and Thailand.7 Most infected patients usually developed progressive pneumonia with acute respiratory distress syndrome and consequently died.8
An important reason to have the information on hematologic manifestations of avian influenza is that this is a new disease, and clinicians need to be better able to recognize specific signs suggestive of avian influenza as well as better treat the infection. The hematologic aberration in bird flu infection is noted.
Here, the author performs a summative review to document the impact of bird flu infection on hematologic findings among reported infected patients. A literature review on the papers concerning recent human bird flu in Thailand and Vietnam was performed from database of the published works cited in the Index Medicus, Scopus and Science Citation Index, and in all 256 local Thai journals, which are not included in the international citation index. The hematologic findings on presentation, early in the course of illness, are reviewed. Reports that contained no complete data were excluded for further analysis.
HEMATOLOGIC MANIFESTATION OF H5N1 INFECTION
Effects on White Blood Cell
In 2000, Katz et al said that, in addition to a lethal outcome, H5N1 viruses with a high pathogenicity phenotype exhibited additional features that include rapid and uncontrolled replication in the lungs of infected mice, dissemination and replication of the virus in other organs, and depletion of peripheral blood leukocytes.9 Concerning the leukocyte abnormality in bird flu infection, Tran et al10 reported 10 cases of bird flu infections in Vietnam and showed that all patients had clinically significant lymphopenia (average lymphocyte count, 700 cells/μL; Table 1). Grose and Chokephaibulkit8 also mentioned that lymphopenia was common in the patients infected with bird flu. This can support the finding of Katz et al9 for the lymphocyte suppression effect of H5N1 virus. Concerning 7 reports8,10-15 covering 22 Thai and Vietnamese patients with a firm diagnosis of bird flu, the lymphopenia is common. Indeed, Tam16 summarized the 18 infected cases of H5N1 in Hong Kong and found that all severe cases presented with lower respiratory tract infection and lymphopenia.
The immunohematologic aspect of this viral infection has not been well documented. Of interest, the reported ratios in Thai and Vietnamese patients8,11-15 are varied implying the variability in cellular response to the infection. Generally, viral infection usually induced increased lymphocyte/neutrophil ratio. However, some viral infections such as HIV infection directly attack the lymphocyte and cause decreased lymphocyte/neutrophil ratio. Concerning the average and mean of reported lymphocyte/neutrophil ratios in bird flu cases, the trend of normal to decreased ratio can be seen.8,11-15
Because the absolute neutrophil count is usually within reference range,8,11-15 the change of ratio should be due to the decrease in lymphocyte count. Considering the CD4+ count, the trend of normal level can be seen in the report of Tran et al.10
Effects on Red Blood Cell
There are only a little limited knowledge on the effect of H5N1 infection on red blood cell. According to the retrospective study of Wiwanitkit on 22 Thai and Vietnamese patients with a firm diagnosis of bird flu, the reported hemoglobin ranged from 10.0 to 17.6 g/dL with an average value equal to 13.0 ± 1.7 g/dL (median, 12.9 g/dL).17 Of the 22 cases, 5 cases or 22.7 % according to World Health Organization criteria (hemoglobin, ≤12 g/dL).17 Wiwanitkit17 noted that anemia might be an important manifestation of human bird flu infection, and H5N1 itself might cause red blood cell pathology leading to anemia. However, the conclusion cannot be made from this study because there are many contributing factors that can lead to anemia in the studied patients. Furthermore, there is no report of anisocytosis or poikilocytosis or evidence of disseminated intravascular coagulation on examination of red blood cell, which might be clues as to the etiology of the anemia.
Effects on Platelet
Concerning the platelet change in human bird flu infection, there are only a few reports on this topic. The median of platelet count in cases series in the report of Tran et al10 is low (median, 75,000/μL). Tran et al noted that severe thrombocytopenia was common and could be an important manifestation of H5N1 infection. However, Wiwanitkit18 recently studied the data on 6 Thai cases with H5N1 infection and found that the median of platelet count is within reference range (median, 167,500/μL). According to both studies, the wide range of platelet count can be seen. Further studies to get the conclusion are needed.
Bird flu, H5N1, infection is a new emerging infectious viral disease. The main hematologic manifestation of this infection is lymphopenia with decreased lymphocyte/neutrophil ratio. Anemia can also be observed in this infection. The effects of this infection on platelet are still controversial. Probably, the hematologic abnormalities seen in peripheral blood are the consequences of loss of control of hematopoiesis in individuals infected by bird flu virus as seen in other viral infection. However, some limitations of the analysis in this study should be mentioned. Bacterial coinfection with sepsis could cloud the picture, as could the timing of blood collection of the samples from which the blood cell counts are reported. Sometimes, it is difficult to determine these factors when it is a summarization of other people's reports rather than looking at all patient charts first hand.
1. Capua I, Alexander DJ. Avian influenza and human health. Acta Trop
2. Lin YP, Shaw M, Gregory V, et al. Avian-to-human transmission of H9N2 subtype influenza A viruses: relationship between H9N2 and H5N1 human isolates. Proc Natl Acad Sci U S A
3. Webster RG. The importance of animal influenza for human disease. Vaccine
. 2002;20(suppl 2):S16-S20.
7. Kida H. Avian influenza virus. Uirusu
8. Grose C, Chokephaibulkit K. Avian influenza virus infection of children in Vietnam and Thailand. Pediatr Infect Dis J
9. Katz JM, Lu X, Frace AM, et al. Pathogenesis of and immunity to avian influenza A H5 viruses. Biomed Pharmacother
10. Tran TH, Nguyen TL, Nguyen TD, et al. Avian influenza A (H5N1) in 10 patients in Vietnam. N Engl J Med
11. Chotpitayasunondh T, Lochindarat S, Srisan P. Cases of Influenza A (H5N1)-Thailand, 2004. W Epidemiol Surveill Rep
12. Chotpitayasunondh T, Lochindarat S, Srisan P. Preliminary clinical description of influenza A (H5N1) in Thailand. W Epidemiol Surveill Rep
13. Chokephaibulkit K, Uiprasertkul M, Puthavathana P, et al. A child with avian influenza A (H5N1) infection. Pediatr Infect Dis J
14. Centers for Disease Control and Prevention (CDC). Cases of influenza A (H5N1)-Thailand, 2004. MMWR Morb Mortal Wkly Rep
15. Apisarnthanarak D. FIC Article Center. Atypical avian influenza (H5N1). Available at: http//www.flu.org.cn
. Accessed March 2005.
16. Tam JS. Influenza A (H5N1) in Hong Kong: an overview. Vaccine
. 2002;20(suppl 2):S77-S81.
17. Wiwanitkit V. Anemia in the recent reported cases of bird flu infection in Thailand and Vietnam [e-publication]. J Infect
. July 1, 2005.
18. Wiwanitkit V. Platelet count in the reported cases of bird flu infection in Thailand. Platelets | <urn:uuid:d6696a76-2799-44ba-835f-f25f2ccac511> | {
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# In Fermat's little theorem, if mod is not prime?
Today I learned about Fermat's little theorem
It says -
Fermat's little theorem states that if p is a prime number, then for any integer a, the number a p − a is an integer multiple of p. In the notation of modular arithmetic, this is expressed as $a^p \equiv a \mod p$
It considers "p" as a prime numbers. But what if "p" is not prime? Then if those cases how to solve this type of problems?
There is a generalised form of Fermat, often known as the Fermat-Euler theorem.
Normally we write Fermat as $a^{p-1}\equiv 1 \mod p$
Then the generalised form is $a^{\phi(n)}\equiv 1 \mod n$ for $(a,n)=1$ i.e. $a$ is coprime to $n$
$\phi(n)$ is known as the Euler Totient Function and counts the number of integers between $1$ and $n-1$ which are coprime to $n$. For a prime $p$ this is all $p-1$ of them. In the general case, various proofs including a version of inclusion-exclusion say that if $$n=p_1^{a_1}p_2^{a_2}\dots p_r^{a_r}$$ where the $p_i$ are the distinct prime divisors of $n$ then $$\phi(n)=n\left(1-\frac 1{p_1} \right) \left(1-\frac 1{p_2} \right)\dots \left(1-\frac 1{p_r} \right)$$
One way to see the generalised result is to note that the numbers having $0\lt r\lt n$ and $(r,n)=1$ form group under multiplication $\mod n$ - it is easy to see that they include $1$ and they inherit associativity from the integers. They are closed under multiplication, and a counting argument shows that inverses must exist. $\phi(n)$ is the order of this group.
• Was beaten to it... – George1811 Apr 1 '14 at 14:52
There is the Carmichael Theorem, which provides results stronger than Euler's Theorem, which generalizes Fermat's Little Theorem to non-prime modulo. | crawl-data/CC-MAIN-2021-31/segments/1627046153521.1/warc/CC-MAIN-20210728025548-20210728055548-00629.warc.gz | null |
Widespread microbial mats and the absence of significant bioturbation resulted in a poorly developed mixed layer and extensive cohesive substrates during the Ediacaran-Cambrian transition. Large nonbiomineralized arthropod carapaces overprinted with trails, interconnected burrow systems, narrow-caliber structures with dendritic terminations, and annulated burrows are abundant in the Early Cambrian Sirius Passet Lagerstätte (Greenland). Taphonomic controls were partially responsible for the pronounced association of these structures and carapaces, but ecologic conditions are envisioned as playing a significant role. Although some trace fossils (e.g., annulated structures) may be related to scavenging and/or deposit feeding, morphologic evidence suggests that this is not always the case. Interconnected burrow systems provide evidence for re-use of structures, suggesting grazing on or farming of bacteria. Sulfur bacteria were probably abundant in Cambrian sediments, requiring a source of sulfur or sulfide and limited quantities of oxygen. Anoxic sediment provided a source of hydrogen sulfide, whereas burrow outlets connected to the oxygenated sediment-water interface. Carcasses and molds of nonbiomineralized organisms may have acted as attractors, supporting a community of small invertebrates. Carapaces created a sharp boundary, further decreasing oxygen diffusion into the sediment. This steep oxygen gradient at the organic surface of the carapace promoted the growth of sulfur bacteria that could have served as the primary food for small macrofauna and meiofauna. | <urn:uuid:25199f93-ed08-46c3-b8be-093c35658e4e> | {
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# What fraction of air gets expelled upon heating an empty flask?
A student forgot to add the reaction mixture to the round bottomed flask at $\pu{27 ^\circ C}$ but instead he placed the flask on the flame. After a lapse of time he realised his mistake and using a pyrometer, he found the temperature of the flask was $\pu{477 ^\circ C}$. What fraction of air would have been expelled out?
By solving $$\frac{V_1}{V_1 + V_2} = \frac{T_1}{T_2}$$ I found $$\frac{V_2}{V_1} = \frac{3}{2}.$$ But according to my book it is $\frac 35$. What exactly is this ratio?
## 1 Answer
Your first equation should be: $${V_1\over V_2} = {T_1\over T_2}$$
We want to know what $V_2$ is in terms of $V_1$. Here, I call $V_2$ final volume. Arranging the equation and using the values for temperature in kelvin: $${\rm final\;volume} = {V_1 \times 750\over 300}= {5\over 2}V_1$$
To get the amount that was expelled, we subtract the initial volume ($V_1$) from the final volume: $${\rm amount\;expelled} = {5\over 2}V_1 - V_1 = {3\over 2}V_1$$
The fraction expelled is then: $${{\rm amount\;expelled}\over{\rm final\;volume}} = {3\over 5}$$
• Thanks for the answer. I should've given it a second thought. Commented Jul 17, 2015 at 17:30 | crawl-data/CC-MAIN-2024-26/segments/1718198861741.14/warc/CC-MAIN-20240617215859-20240618005859-00726.warc.gz | null |
Our 5 favorite fifth grade writing worksheets
These handy worksheets will help your fifth grader perfect her prose.
By GreatSchools Staff
W.A. Spooner invented this type of mixed-up phrase, now called a "spoonerism." In this writing worksheet, your child gets practice decoding and editing spoonerisms and then writing the phrases correctly.
Skills your fifth grader will work on: letter sounds (phonemes), fluency, building vocabulary, recognizing common phrases, editing, and writing practice. | <urn:uuid:adc3fd4b-cc34-468c-9933-26b382ecb5aa> | {
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### Pre Math lesson plans that prepares kids to handle preschool math with confidence
A good foundational Math Readiness gives a child a great head start in preschool math. Kids love to learn and are intuitively building their knowledge of numbers and logic. When a teacher or a parent is intentionally creating an environment for pre kindergarten math activities through math games, it opens a child’s mind to the mathematical world.
Here are some different ideas you may introduce in your Math Readiness Lesson Plans:
• Pouring – provides many opportunities to learn division or fraction. Have the child serve drinks to friends or family members. Highlight the concept that a jug of water may be divided into two or more parts. You may like to try Piaget’s experiment on conservation of quantity. Fill 2 glasses with equal amounts. “Do both glasses have the same amount?” Pour one glass of juice into a thinner container. Ask: “Which has more?” According to Piaget, children under the age of 7 cannot understand the theory of conservation. It means they will think that the thinner taller container has more water.
• Sorting – objects helps the child to identify groupings – This is an introduction to the concept of Multiplication and Division. Say: “Here you have 4 green beads, 4 red beads, and 4 blue beads – altogether you have 3 sets/groups of beads – 1,2,3”
• Threading – beads may be used to help the child in understanding the concept of addition as the teacher or parent interacts with him on the number of beads required for each color. Eg “First we thread 2 beads – 1,2. Then we add 3 more – 1,2,3. There, now we have five beads altogether….etc
• Cutting – a banana into pieces gives the concept of division and fraction. "Let's take a banana and cut it into half, and we can share it with 2 people - one for you and one for me"
• Shapes – of various objects may be identified eg. “I spy with my little eyes something that is round – “a clock”…. Something that is rectangular – “a TV”…etc You’ve got the idea. This is the beginning of Geometry, isn’t it ?
• Counting – is best done with something concrete like counting the flight of stairs as you walk up or down, counting the dinnerware on the table, toys….etc Rattling away numbers 1,2,3, and so on till ten or twenty, without associating them with any items will not help the child with number recognition or a real appreciation of its application.
• Art and Craft – Such activities are ideal opportunities to introduce pre math. The teacher may ask the child to choose 3 colors, paint 4 circles, draw a line to divide a square into 2, or cut a pizza picture into 4, crush 10 “balls” from scrap magazines…etc
• Music and Movement – introduces rhythm that requires counting. When a child calls out the beat to the rhythm of a song or dance, he is practicing his numbering as well as associating each number to each step or beat.
• Songs & Poems – with numbers are of great value in preparing a child for math. It is enjoyable, musical, poetical and easy. Eg 1,2,3,4, Mary at the cottage door. 5,6,7,8 Eating cherries off a plate. However, do bear in mind that such songs are fun, it only provides a child with number sequence but not with understanding number concepts.
Try this:
“5 little joeys jumping on the bed, one fell down and broke his head. Called for the doctor, the doctor said, “No more joeys jumping on the bed !” (one child leaves) 4 little joeys jumping…… till no more joeys jumping on the bed.
It will give more depth to learning subtraction.
As you can see, Math Readiness can be incorporated in preschool or homeschooling in a wide choices of activities. All we need is to be intentional, to bring out the concept of math and relate it to the activities. It is a natural interactive learning process that will definitely enrich a child’s logic.
What struggles or success stories do you have with your Math experience as you teach preschool kids? Share it!
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# Video: Finding the Length of the Longest Side of a Triangle given Its Perimeter and the Dimensions of a Similar Triangle
The perimeter of one of two similar triangles is 31.5 cm, and the side lengths of the other are 9 cm, 2 cm, and 10 cm. Find the length of the longest side of the first triangle rounded to two decimal places.
03:02
### Video Transcript
The perimeter of one of two similar triangles is 31.5 centimeters and the side lengths of the other are nine centimeters, two centimeters, and 10 centimeters. Find the length of the longest side of the first triangle rounded to two decimal places.
So we’ve been given different pieces of information about these two triangles. In, one we just know the perimeter, whereas in the second we know the individual side lengths. We were also told that the two triangles are similar, which is a really key piece of information here. Our objective is to find the length of the longest side in the first triangle.
In order to answer this question, we need to recall the proportional perimeters theorem. It tells us that if two polygons are similar, then the perimeters are proportional to the scale factor between them. We know the perimeter of the first triangle, which we’ll refer to as 𝑃 one. It’s 31.5 centimeters. And we can find the perimeter of the second triangle by summing it’s three sides. It’s 21 centimeters.
So if we look at the ratio of these two perimeters, we can then calculate the scale factor between the two triangles. This will then enable us to calculate the length of corresponding sides between the two triangles. So the ratio between the two perimeters, 𝑃 one divided by 𝑃 two, is 31.5 divided by 21. And this simplifies to three over two.
What this means then is that not only is the perimeter of the large triangle three over two or one and a half times as big as the perimeter of the smaller triangle, but the individual sides are also in the same ratio. So the longest side of the larger triangle is three over two or one and a half times as long as the longest side of the smaller triangle.
So in order to calculate the length of the longest side in the first triangle, which we’ll refer to as 𝑥 centimeters, we need to multiply the longest side of the shorter triangle, which is 10, by three over two. So we have that 𝑥 is equal to 10 multiplied by three over two, which is equal to 15. The question actually asked this value rounded to two decimal places, and it’s an exact value. So we just need to add two zeros after the decimal point.
So we have our answer to the problem. The longest side of the first triangle, to two decimal places, is 15.00 centimeters. A sensible check, which you could perform yourself, is to calculate the lengths of the other sides by multiplying the nine-centimeters and the two-centimeter side by this scale factor. You could then check that the perimeter when you add your three values together is indeed 31.5 centimeters. | crawl-data/CC-MAIN-2020-05/segments/1579250610919.33/warc/CC-MAIN-20200123131001-20200123160001-00024.warc.gz | null |
There is an endless literature on the diplomatic circumstances leading up to the outbreak of war between the two great European power blocks in August of 1914. The period between the assassination of Austrian Archduke Franz Ferdinand on June 28, 1914 and the beginning of the war in early August might be THE most studied period of diplomatic history of all time. For our purposes, the key elements to understand are: 1) the creation of the two alliance blocks and 2) the European powers’ perceptions of each other. The imagination of European leaders (and to some extent citizens) played just as great (or perhaps greater) a role in the outbreak of war than any real, direct threat.
The central principle of European politics since the Westphalia Peace of 1648 was balance. This principle of great power balance was reaffirmed in the wake of the Napoleonic wars. No continental power was to grow too strong to threaten its neighbors. Any increase in power within one state would precipitate movements of others to check it. Such was the rationale behind the European intervention to block Russian advancement in the Crimean War. By the middle of the 19th century, the key relationship in this balancing act was between France and Prussia.
The unification of Prussia and surrounding Germanic states into the German Empire in 1871 significantly shifted the balance of power equation in Europe. With Prussia’s easy victory over France in the Franco-Prussian War (1870-1871), the newly unified Germany (under Prussian dominance) was now without doubt the strongest continental land power. Such a status was confirmed by the terms of the peace in 1871, which, among other things, gave the formerly French territories of Alsace and Lorraine, highly industrialized areas, to Germany. Though Germany was an empire and was ruled in large measure by traditional elites, it was also a modern power. It had a well-developed civil bureaucracy. It had strong professional and labor organizations. It had the premier level of educational and technological sophistication in the world by 1900. Though its navy was still dwarfed by England’s, its land forces were the strongest in Europe. Moreover, its historical alliance with the Austro-Hungarian dual empire created a powerful block in the heart of the European continent.
Along with the rise of a powerful and united Germany, the late 19th century witnessed two other important developments from a balance of power point of view. First, the Ottoman Empire—that Early Modern behemoth, which as recently as the late 17th century was threatening to take Vienna—was in the midst of a slow but steady disintegration. North Africa had already begun to break away from Ottoman control, including the strategically important Egypt. By the last decades of the 19th century the Ottomans’ European possessions in the Balkans were peeling away. Second, Ottoman disintegration prompted Russia and Austria to try to expand their influence and/or control over southeastern Europe. These two historic, large, but also relatively outmoded and fragile empires were now embroiled in a region seething with nationalistic ambitions and ethnic and religious rivalries.
Leaving Italy aside for the time being, the constellation of alliances in August, 1914 pitted Germany, Austria, and the Ottoman Empire (the Triple Alliance or Central Powers) against England, France, and Russia (the Triple Entente). The formation of these particular alliances
against the immediate backdrop of German unification and Ottoman disintegration, and a power vacuum in the Balkans, and against the wider backdrop nationalism, imperialism, and the growth of the modern state is key to understand if we are to grasp how war came when and between whom it did.
Understanding all of the dynamics of European alliance-making in the late 19th and early 20th centuries is a daunting task. For our purposes, I will first briefly outline the strategic positions of the major continental powers (England, France, Germany, Russia, Austria) and then how it is that the alliance system resulted in the two opposing camps. The move from the first consideration (strategic position) to the second (alliances) is a twisted path to say the least!England
: The main thrusts of England’s foreign policy in the late 19th and early 20th centuries were principally twofold. 1) England wanted to maintain control over (and productive economic relationships with) its vast network of colonies. The central colonial relationship for England was with India, as we discussed in chapter one. 2) England wanted to use its naval supremacy to control (and keep open
) global trade. Who posed threats or challenges to England? In terms of colonial conflicts, the main threats came, ironically, from Russia and France. Since the mid-19th century, England had been at odds with Russia in central Asia and the Indian borderlands, including Afghanistan. England and Russia squared off in Persia and fought on opposing sides in the bloody Crimean War. England viewed Russia as an expanding imperial land power—one that could have ultimate aims on India and large sections of China. England’s late support for the aging Qing Dynasty in China was in large measure to counter Russian designs on an Asian warm-weather shipping and naval port. Beyond central and western Asia, France was England’s greatest colonial competitor. This had been the case for centuries. The French and British had squared off in a global war of conquest in the 18th century, a war that left the French crown nearly bankrupt. The French had supported the Americans against the British during the Revolutionary War. The two nations fought each other in the Napoleonic wars. By the late 19th century, disputes about numerous colonial possessions fueled new hostility—in Egypt, in central Africa, in West Africa. In both Egypt and Nigeria, colonial conflict nearly led to war.
For an interesting account of the Fashoda Incident written for the American public by a young Winston Churchill, click here
: Despite the long history of anti-British sentiment in France, the unification of Germany forced a new diplomatic calculus to emerge in Paris. The central pillar of French foreign policy after the debacle of the Franco-Prussian War was to establish an alliance to deter future German aggression. This meant, first and foremost, luring Russia out of the so-called Reinsurance Treaty with Germany and Austria and into an alliance with France. Beyond this immediate danger, the French were intent to continue building their colonial empire, which now consisted of a sizable portion of northern and western Africa. This, as noted above, put France primarily in conflict with England.Russia
: The Russian position in the late 19th century was complex—especially given that Russia bordered or was within a quick march from Germany, Austria, the Ottoman Empire, China, and Japan, as well as many British colonial possessions. The only “natural” ally of the Russians might have been the French, though there was little reason why Russia would alienate the Germans by concluding a separate treaty with the French, all things being equal. Of course, all things were not equal and Germany’s steadfast commitment to Austria made the Germans potential enemies by default, especially as tensions heated up around the Balkans. Beyond Europe, the Russians’ chief antagonist was England.Germany
: German motivations, like those of Russia, were complex and shifting. Under the Iron Chancellor Otto von Bismarck, the German Empire operated under the guiding principle of avoiding encirclement. This meant, principally, that France and Russia should never be allied against Germany, forcing it into a two-front war. Such was the thinking that led to the diplomatic success (from the Bismarckian perspective) of the Reinsurance Treaty with Russia. At the same time, however, interests in Germany were shifting. Bismarck’s focus on European power balance started to give way to additional concerns and ambitions. The Germans wanted to forge a colonial empire like the other European powers, which rose tensions with both England and France. The Germans wanted to develop naval power, which struck fear into the heart of Englanders, whose power rested on its control of the seas.Austria
: Austria had perhaps the simplest but also the most perilous foreign policy dynamics. First and foremost, Austria wanted to hold and expand its territory in the Balkans, which put it at direct odds with Russia. Why? Because Russia had formed an alliance with its little brother, the newly independent—and fiercely independent—Serbia. Serbia was not only nationalistic, it was also imperialistic, viewing territories in the Balkans as part of “historic” Serbia, which needed to be liberated from the “tyranny” of Austrian rule. It is no surprise that the clearest antagonism in the European spectrum would ultimately be the fuse that lit the fires of war in 1914.
If Germany’s main goal was not to be encircled, if Britain’s main issues were with Russia and France, if France’s main combatant in world diplomacy was England, if Russia allied with France in order to oppose British coziness with Germany, how on earth do we get the alliances of war in 1914? Far from inevitable, the war as it happened in 1914—at least from the perspective of the late 19th century—was as much counter-intuitive as it was ultimately counterproductive (or a total disaster!). | <urn:uuid:08ab6d3f-f5cc-4469-8336-5bf6e4e32d23> | {
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Heat stress, an annual issue
When the summer comes around, it brings with it the same issues every year: hot days that cause heat stress in production animals. That, and the question whether the animals require additional support through their diet. But what is actually going on inside the animals when they are subjected to heat stress, and what can be done to alleviate it?
Animals can be helped to better deal with heat stress through adjustments in management, especially with regard to ventilation, and through their diet. Adjusting the barn climate can have an effect equal to a 10°C decrease in temperature. The effect that can be achieved through the animals’ feed is more supportive in nature, and its effect extends to approximately 1°C – a small but important difference. In this article, we will discuss the possibilities for additional support through feed. Heat stress occurs when animals are insufficiently able to expel their body heat into the environment and their metabolism is disrupted as a result. The combination of temperature and humidity determines the severity of heat stress. Animals first attempt to lose additional heat by breathing more rapidly (penting), increasing their contact surface with their environment as much as possible, and (if possible) moving to a cooler location. If these measures are not enough, the next step is a decrease in feed consumption. Thanks to the advances in breeding, animals are able to produce more per day, but this also means that they produce more heat, and are therefore more vulnerable to heat stress.
As long as the temperature falls within the thermoneutral zone, no heat stress occurs. When the temperature rises above this comfort zone and animals start to pant in order to get rid of heat, they breathe out more moisture and CO2, causing a decrease of hydrogen ions in the blood, which increases the blood pH (this is called respiratory alkalosis; see Figure 1). The body can partially compensate for this in certain ways, such as by releasing hydrogen bound to hemoglobin in return for potassium.
Consequnces of increased respiratory rate
- Reduction of blood CO2 level
- Increase of blood pH
- Minimal excretion of H+ in urine
- Increased loss of Na+ and K+ minerals
- Reduced osmotic concentration of the cells
- Oxidation of muscles
Among others, this has negative consequences for:
- meat quality
- eggshell quality
- feedconversion ratio (FCR)
Based on our own research and experience around the world, Koudijs has developed HeatStop. HeatStop replenishes the electrolytes that an animal has lost due to heat stress. HeatStop supports the physiological processes in the animal to maximally prevent the damage caused by heat stress. Furthermore, it improves water absorption and can be preventively included in the feed in anticipation of approaching heat waves.
During hot periods, it can be useful to adjust the feed and provide more energy in the form of fats. The metabolization of fat produces less heat than carbohydrates or proteins.
It also helps to add antioxidants to the feed, such as extra Vitamin E. Among other effects, Vitamin E helps limit the drop in production during heat stress. Vitamin C affects several things, including the transport of oxygen. Heat causes Vitamin C levels in the blood to decrease, necessitating replenishment via the feed.
Vitamin C helps prevent the body’s temperature from increasing too much during heat stress. Vitamin C is a very water-soluble antioxidant, while Vitamin E is fatsoluble; both are required to prevent oxidation in all parts of cells, and together they have a positive synergetic effect. Using different kinds of antioxidants together have a broader effect, and is therefore recommendable. By ensuring proper climate control in your barn and
adjusting the feed, supplemented where necessary with specific products such as HeatStop, you can help your animals cope with periods of heat stress with less discomfort.
Advantages of heatstop
- Multi-species application
- Contains active components for full body support
- Attacks heat stress from multiple angles
- Directly affects physiological processes
- Can be used preventively | <urn:uuid:c15f5076-7d16-4c36-8f6b-922172cf4de6> | {
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## Calculus: Early Transcendentals 8th Edition
$f'(x)=2-\frac{15}{4}x^{-1/4}$ $f''(x)=\frac{15}{16}x^{-5/4}$ These functions are reasonable since f' is positive when f is increasing and negative when f is decreasing. The same goes for f'' and f' - since f' is always increasing, f'' is always positive. The slopes of the derivatives are closer to zero wherever the graphs of the original functions appear almost flat.
$f(x)=2x-5x^{3/4}$ Use the Power Rule: $f(x) = x^{n},$ then $f'(x) = nx^{n-1}$ $f'(x)=2(1)-5(3/4)x^{-1/4}$ $f'(x)=2-\frac{15}{4}x^{-1/4}$ $f''(x)=0-(\frac{15}{4})(-\frac{1}{4})x^{-5/4}$ $f''(x)=\frac{15}{16}x^{-5/4}$ | crawl-data/CC-MAIN-2018-17/segments/1524125945037.60/warc/CC-MAIN-20180421051736-20180421071736-00621.warc.gz | null |
Refrigeration is the process in which heat of a certain product is being removed or transfer from one location to another. It also includes the process of reducing and maintaining the temperature of a body below the general temperature of its surrounding. This is done, traditionally, by a mechanical system. But nowadays, it can be driven out by heat, magnetism, electricity laser or by other means.
There are many methods of refrigeration that can be classified, namely: non-cyclic, cyclic, thermoelectric and magnetic.
In this method, the cooling is accomplished by melting the ice or subliming the dry ice. This method is commonly used for small-scale refrigeration such as in laboratories, workshops and portable coolers.
This method removes the heat from a low-temperature space or source and rejected to a high-temperature sink with the help of external work, and its inverse, the thermodynamic power cycle.
Thermoelectric cooling uses the Peltier effect to create a heat flux between the junctions of two different types of materials. This effect is commonly used in camping and portable coolers and for cooling electronic components and small instruments.
This cooling method is based on the magneto caloric effect, an intrinsic property of magnetic solids. The refrigerant is often a paramagnetic salt, such as cerium magnesium dipoles in this case are those of the electron shells of the paramagnetic atoms.
Most of us are mistakenly thinks that refrigeration stops the spoilage of a goods or products. But the truth is that refrigeration does not stop the food spoilage, it just delays it. Most spoilage microorganisms are not active when it is cold, so spoilage takes longer. Some spoilage like in over ripe fruits, may be caused by enzymes and enzymatic activity is also reduced be the colder temperature.
The Main Purpose of Refrigeration
The fundamental reason for having a refrigerator is to keep food cold. Cold temperatures help food stay fresh longer. The basic idea behind refrigeration is to slow down the activity of bacteria (which all food contains) so that it takes longer for the bacteria to spoil the food.
For example, bacteria will spoil milk in two or three hours if the milk is left out on the kitchen counter at room temperature. However, by reducing the temperature of the milk, it will stay fresh for a week or two -- the cold temperature inside the refrigerator decreases the activity of the bacteria that much. By freezing the milk you can stop the bacteria altogether and the milk can last for months (until effects like freezer burn begin to spoil the milk in non-bacterial ways).
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23.1 Relativistic distortion of space and time by Benjamin Crowell,licensed under the .
|`gamma=1/sqrt(1-v^2`||unequal rate of flow (time)|
Let's refer back to the results of the Hafele-Keating experiment described on p. 618. Hafele and Keating were testing specific quantitative predictions of relativity, and they verified them to within their experiment's error bars. Let's work backward instead, and inspect the empirical results for clues as to how time works.
The east-going clock lost time, ending up off by -59±10 nanoseconds, while the west-going one gained 273±7 ns. Since two traveling clocks experienced effects in opposite directions, we can tell that the rate at which time flows depends on the motion of the observer. The east-going clock was moving in the same direction as the earth's rotation, so its velocity relative to the earth's center was greater than that of the clock that remained in Washington, while the west-going clock's velocity was correspondingly reduced. The fact that the east-going clock fell behind, and the west-going one got ahead, shows that the effect of motion is to make time go more slowly. This effect of motion on time was predicted by Einstein in his original 1905 paper on relativity, written when he was 26.
If this had been the only effect in the Hafele-Keating experiment, then we would have expected to see effects on the two flying clocks that were equal in size. Making up some simple numbers to keep the arithmetic transparent, suppose that the earth rotates from west to east at `1000` km/hr, and that the planes fly at `300` km/hr. Then the speed of the clock on the ground is `1000` km/hr, the speed of the clock on the east-going plane is `1300` km/hr, and that of the west-going clock `700` km/hr. Since the speeds of `700`, `1000`, and `1300` km/hr have equal spacing on either side of `1000`, we would expect the discrepancies of the moving clocks relative to the one in the lab to be equal in size but opposite in sign.
In fact, the two effects are unequal in size: -59 ns and 273 ns. This implies that there is a second effect involved, a speeding up of time simply due to the planes' being up in the air. This was verified more directly in a 1978 experiment by Iijima and Fujiwara, figure, in which identical atomic clocks were kept at rest at the top and bottom of a mountain near Tokyo. This experiment, unlike the Hafele-Keating one, isolates one effect on time, the gravitational one: time's rate of flow increases with height in a gravitational field. Einstein didn't figure out how to incorporate gravity into relativity until 1915, after much frustration and many false starts. The simpler version of the theory without gravity is known as special relativity, the full version as general relativity. We'll restrict ourselves to special relativity until chapter , and that means that what we want to focus on right now is the distortion of time due to motion, not gravity.
We can now see in more detail how to apply the correspondence principle. The behavior of the three clocks in the Hafele-Keating experiment shows that the amount of time distortion increases as the speed of the clock's motion increases. Newton lived in an era when the fastest mode of transportation was a galloping horse, and the best pendulum clocks would accumulate errors of perhaps a minute over the course of several days. A horse is much slower than a jet plane, so the distortion of time would have had a relative size of only ≈10-15 --- much smaller than the clocks were capable of detecting. At the speed of a passenger jet, the effect is about 10-12, and state-of-the-art atomic clocks in 1971 were capable of measuring that. A GPS satellite travels much faster than a jet airplane, and the effect on the satellite turns out to be ≈10-10. The general idea here is that all physical laws are approximations, and approximations aren't simply right or wrong in different situations. Approximations are better or worse in different situations, and the question is whether a particular approximation is good enough in a given situation to serve a particular purpose. The faster the motion, the worse the Newtonian approximation of absolute time. Whether the approximation is good enough depends on what you're trying to accomplish. The correspondence principle says that the approximation must have been good enough to explain all the experiments done in the centuries before Einstein came up with relativity.
By the way, don't get an inflated idea of the importance of these atomic clock experiments. Special relativity had already been confirmed by a vast and varied body of experiments decades before the 1970's. The only reason I'm giving such a prominent role to these experiments, which were actually more important as tests of general relativity, is that they were conceptually very direct. It would be nice to have an equally simple and transparent atomic clock experiment in which only the effect of motion was singled out, with no gravitational effect. Exampleon page 662 describes how something along these lines was eventually carried out, forty years after the Hafele-Keating experiment.
Relativity says that when two observers are in different frames of reference, each observer considers the other one's perception of time to be distorted. We'll also see that something similar happens to their observations of distances, so both space and time are distorted. What exactly is this distortion? How do we even conceptualize it?
The idea isn't really as radical as it might seem at first. We can visualize the structure of space and time using a graph with position and time on its axes. These graphs are familiar by now, but we're going to look at them in a slightly different way. Before, we used them to describe the motion of objects. The grid underlying the graph was merely the stage on which the actors played their parts. Now the background comes to the foreground: it's time and space themselves that we're studying. We don't necessarily need to have a line or a curve drawn on top of the grid to represent a particular object. We may, for example, just want to talk about events, depicted as points on the graph as in figure. A distortion of the Cartesian grid underlying the graph can arise for perfectly ordinary reasons that Newton would have readily accepted. For example, we can simply change the units used to measure time and position, as in figure .
We're going to have quite a few examples of this type, so I'll adopt the convention shown in figurefor depicting them. Figure summarizes the relationship between figures and in a more compact form. The gray rectangle represents the original coordinate grid of figure , while the grid of black lines represents the new version from figure . Omitting the grid from the gray rectangle makes the diagram easier to decode visually.
Our goal of unraveling the mysteries of special relativity amounts to nothing more than finding out how to draw a diagram like in the case where the two different sets of coordinates represent measurements of time and space made by two different observers, each in motion relative to the other. Galileo and Newton thought they knew the answer to this question, but their answer turned out to be only approximately right. To avoid repeating the same mistakes, we need to clearly spell out what we think are the basic properties of time and space that will be a reliable foundation for our reasoning. I want to emphasize that there is no purely logical way of deciding on this list of properties. The ones I'll list are simply a summary of the patterns observed in the results from a large body of experiments. Furthermore, some of them are only approximate. For example, property 1 below is only a good approximation when the gravitational field is weak, so it is a property that applies to special relativity, not to general relativity.
Experiments show that:
Most of these are not very subversive. Properties 1 and 2 date back to the time when Galileo and Newton started applying the same universal laws of motion to the solar system and to the earth; this contradicted Aristotle, who believed that, for example, a rock would naturally want to move in a certain special direction (down) in order to reach a certain special location (the earth's surface). Property 3 is the reason that Einstein called his theory “relativity,” but Galileo and Newton believed exactly the same thing to be true, as dramatized by Galileo's run-in with the Church over the question of whether the earth could really be in motion around the sun. Exampleon p. 243 describes a modern, high-precision experiment that can be interpreted as a test of this principle. Property 4 would probably surprise most people only because it asserts in such a weak and specialized way something that they feel deeply must be true. The only really strange item on the list is 5, but the Hafele-Keating experiment forces it upon us.
If it were not for property 5, we could imagine that figurewould give the correct transformation between frames of reference in motion relative to one another. Let's say that observer 1, whose grid coincides with the gray rectangle, is a hitch-hiker standing by the side of a road. Event A is a raindrop hitting his head, and event B is another raindrop hitting his head. He says that A and B occur at the same location in space. Observer 2 is a motorist who drives by without stopping; to him, the passenger compartment of his car is at rest, while the asphalt slides by underneath. He says that A and B occur at different points in space, because during the time between the first raindrop and the second, the hitch-hiker has moved backward. On the other hand, observer 2 says that events A and C occur in the same place, while the hitch-hiker disagrees. The slope of the grid-lines is simply the velocity of the relative motion of each observer relative to the other.
Figure has familiar, comforting, and eminently sensible behavior, but it also happens to be wrong, because it violates property 5. The distortion of the coordinate grid has only moved the vertical lines up and down, so both observers agree that events like B and C are simultaneous. If this was really the way things worked, then all observers could synchronize all their clocks with one another for once and for all, and the clocks would never get out of sync. This contradicts the results of the Hafele-Keating experiment, in which all three clocks were initially synchronized in Washington, but later went out of sync because of their different states of motion.
It might seem as though we still had a huge amount of wiggle room available for the correct form of the distortion. It turns out, however, that properties 1-5 are sufficient to prove that there is only one answer, which is the one found by Einstein in 1905. To see why this is, let's work by a process of elimination.
Figureshows a transformation that might seem at first glance to be as good a candidate as any other, but it violates property 3, that motion is relative, for the following reason. In observer 2's frame of reference, some of the grid lines cross one another. This means that observers 1 and 2 disagree on whether or not certain events are the same. For instance, suppose that event A marks the arrival of an arrow at the bull's-eye of a target, and event B is the location and time when the bull's-eye is punctured. Events A and B occur at the same location and at the same time. If one observer says that A and B coincide, but another says that they don't, we have a direct contradiction. Since the two frames of reference in figure give contradictory results, one of them is right and one is wrong. This violates property 3, because all inertial frames of reference are supposed to be equally valid. To avoid problems like this, we clearly need to make sure that none of the grid lines ever cross one another.
The next type of transformation we want to kill off is shown in figure, in which the grid lines curve, but never cross one another. The trouble with this one is that it violates property 1, the uniformity of time and space. The transformation is unusually “twisty” at A, whereas at B it's much more smooth. This can't be correct, because the transformation is only supposed to depend on the relative state of motion of the two frames of reference, and that given information doesn't single out a special role for any particular point in spacetime. If, for example, we had one frame of reference rotating relative to the other, then there would be something special about the axis of rotation. But we're only talking about inertial frames of reference here, as specified in property 3, so we can't have rotation; each frame of reference has to be moving in a straight line at constant speed. For frames related in this way, there is nothing that could single out an event like A for special treatment compared to B, so transformation violates property 1.
The examples in figuresand show that the transformation we're looking for must be linear, meaning that it must transform lines into lines, and furthermore that it has to take parallel lines to parallel lines. Einstein wrote in his 1905 paper that “... on account of the property of homogeneity [property 1] which we ascribe to time and space, the [transformation] must be linear.” Applying this to our diagrams, the original gray rectangle, which is a special type of parallelogram containing right angles, must be transformed into another parallelogram. There are three types of transformations, figure , that have this property. Case I is the Galilean transformation of figure on page 655, which we've already ruled out.
j / Three types of transformations that preserve parallelism. Their distinguishing feature is what they do to simultaneity, as shown by what happens to the left edge of the original rectangle. In I, the left edge remains vertical, so simultaneous events remain simultaneous. In II, the left edge turns counterclockwise. In III, it turns clockwise.
Case II can also be discarded. Here every point on the grid rotates counterclockwise. What physical parameter would determine the amount of rotation? The only thing that could be relevant would be `v`, the relative velocity of the motion of the two frames of reference with respect to one another. But if the angle of rotation was proportional to `v`, then for large enough velocities the grid would have left and right reversed, and this would violate property 4, causality: one observer would say that event A caused a later event B, but another observer would say that B came first and caused A.
The only remaining possibility is case III, which I've redrawn in figurewith a couple of changes. This is the one that Einstein predicted in 1905. The transformation is known as the Lorentz transformation, after Hendrik Lorentz (1853-1928), who partially anticipated Einstein's work, without arriving at the correct interpretation. The distortion is a kind of smooshing and stretching, as suggested by the hands. Also, we've already seen in figures - on page 654 that we're free to stretch or compress everything as much as we like in the horizontal and vertical directions, because this simply corresponds to changing the units of measurement for time and distance. In figure I've chosen units that give the whole drawing a convenient symmetry about a 45-degree diagonal line. Ordinarily it wouldn't make sense to talk about a 45-degree angle on a graph whose axes had different units. But in relativity, the symmetric appearance of the transformation tells us that space and time ought to be treated on the same footing, and measured in the same units.
As in our discussion of the Galilean transformation, slopes are interpreted as velocities, and the slope of the near-horizontal lines in figureis interpreted as the relative velocity of the two observers. The difference between the Galilean version and the relativistic one is that now there is smooshing happening from the other side as well. Lines that were vertical in the original grid, representing simultaneous events, now slant over to the right. This tells us that, as required by property 5, different observers do not agree on whether events that occur in different places are simultaneous. The Hafele-Keating experiment tells us that this non-simultaneity effect is fairly small, even when the velocity is as big as that of a passenger jet, and this is what we would have anticipated by the correspondence principle. The way that this is expressed in the graph is that if we pick the time unit to be the second, then the distance unit turns out to be hundreds of thousands of miles. In these units, the velocity of a passenger jet is an extremely small number, so the slope `v` in a figure like is extremely small, and the amount of distortion is tiny --- it would be much too small to see on this scale.
The only thing left to determine about the Lorentz transformation is the size of the transformed parallelogram relative to the size of the original one. Although the drawing of the hands in figuremay suggest that the grid deforms like a framework made of rigid coat-hanger wire, that is not the case. If you look carefully at the figure, you'll see that the edges of the smooshed parallelogram are actually a little longer than the edges of the original rectangle. In fact what stays the same is not lengths but areas, as proved in the caption to figure .
m / Proof that Lorentz transformations don't change area: We first subject a square to a transformation with velocity v, and this increases its area by a factor R(v), which we want to prove equals 1. We chop the resulting parallelogram up into little squares and finally apply a - v transformation; this changes each little square's area by a factor R(-v), so the whole figure's area is also scaled by R(-v). The final result is to restore the square to its original shape and area, so R(v)R(-v)=1. But R(v)=R(-v) by property 2 of spacetime on page 654, which states that all directions in space have the same properties, so R(v)=1.
Figureshowed us that observers in different frames disagree on whether different events are simultaneous. This is an indication that time is not absolute, so we shouldn't be surprised that time's rate of flow is also different for different observers. We use the symbol γ (Greek letter gamma) defined in the figure to measure this unequal rate of flow. With a little algebra and geometry (homework problem , page 673), one can use the equal-area property to show that this ratio is given by
When we say, “It's five hours from LA to Vegas,” we're using a unit of time as a unit of distance. This works because there is a standard speed implied: the speed of a car on the freeway. Similarly, the conversion factor c can be interpreted as a speed, so that v/c is the unitless ratio of two speeds. As argued on p. 619, cause and effect can never be propagated instantaneously; c turns out to be the specific numerical speed limit on cause and effect. In particular, we'll see in sectionthat light travels at c, which has a numerical value of 3.0×108 m/s.
Because γ is always greater than 1, we have the following interpretation:
A clock runs fastest in the frame of reference of an observer who is at rest relative to the clock. An observer in motion relative to the clock at speed `v` perceives the clock as running more slowly by a factor of `?`.
q / This figure proves, as claimed in figure `x=1/gamma`. First we slice the parallelogram vertically like a salami and slide the slices down, making the top and bottom edges horizontal. Then we do the same in the horizontal direction, forming a rectangle with sides γ and `x`. Since both the Lorentz transformation and the slicing processes leave areas unchanged, the area γx of the rectangle must equal the area of the original square, which is 1., that the length contraction is
As proved in figuresand , lengths are also distorted:
A meter-stick appears longest to an observer who is at rest relative to it. An observer moving relative to the meter-stick at `v` observes the stick to be shortened by a factor of γ.
What is γ when v=0? What does this mean?
(answer in the back of the PDF version of the book)
r / Example.
Alice stays on earth while her twin Betty heads off in a spaceship for Tau Ceti, a nearby star. Tau Ceti is 12 light-years away, so even though Betty travels at 87% of the speed of light, it will take her a long time to get there: 14 years, according to Alice.
Betty experiences time dilation. At this speed, her `?` is 2.0, so that the voyage will only seem to her to last 7 years. But there is perfect symmetry between Alice's and Betty's frames of reference, so Betty agrees with Alice on their relative speed; Betty sees herself as being at rest, while the sun and Tau Ceti both move backward at 87% of the speed of light. How, then, can she observe Tau Ceti to get to her in only 7 years, when it should take 14 years to travel 12 light-years at this speed?
We need to take into account length contraction. Betty sees the distance between the sun and Tau Ceti to be shrunk by a factor of 2. The same thing occurs for Alice, who observes Betty and her spaceship to be foreshortened.
The correspondence principle requires that `?` be close to 1 for the velocities much less than `c` encountered in everyday life. Let's explicitly find the amount `?` by which `?` differs from 1, when `v` is small. Let `?=1+?`. The definition of `?` gives `1=?^2(1?v^2"/"c^2)`, so `1=(1+2?+?^2)(1?v^2"/"c^2)?1+2??v^2"/"c^2`, where the approximation comes from discarding very small terms such as `?^2` and `?v^2"/"c^2`. We find `epsilon=v^2/(2c^2)`. As expected, this will be small when `v` is small compared to `c`.
Figureshows that the approximation found in example is not valid for large values of `v"/"c`. In fact, `?` blows up to infinity as `v` gets closer and closer to `c`.
Exampleshows that when `v` is small, relativistic effects are approximately proportional to `v^2`, so it is very difficult to observe them at low speeds. For example, a car on the freeway travels at about 1/10 the speed of a passenger jet, so the resulting time dilation is only 1/100 as much. For this reason, it was not until four decades after Hafele and Keating that anyone did a conceptually simple atomic clock experiment in which the only effect was motion, not gravity; it is difficult to move a clock at a high enough velocity without putting it in some kind of aircraft, which then has to fly at some altitude. In 2010, however, Chou et al. succeeded in building an atomic clock accurate enough to detect time dilation at speeds as low as 10 m/s. Figure shows their results. Since it was not practical to move the entire clock, the experimenters only moved the aluminum atoms inside the clock that actually made it “tick.”
t / Apparatus used for the test of relativistic time dilation described in example
(c) 1974 by CERN.
The time dilation effect in the Hafele-Keating experiment was very small. If we want to see a large time dilation effect, we can't do it with something the size of the atomic clocks they used; the kinetic energy would be greater than the total megatonnage of all the world's nuclear arsenals. We can, however, accelerate subatomic particles to speeds at which `?` is large. For experimental particle physicists, relativity is something you do all day before heading home and stopping off at the store for milk. An early, low-precision experiment of this kind was performed by Rossi and Hall in 1941, using naturally occurring cosmic rays. Figureshows a 1974 experiment of a similar type which verified the time dilation predicted by relativity to a precision of about one part per thousand.
Particles called muons (named after the Greek letter `mu`, “myoo”) were produced by an accelerator at CERN, near Geneva. A muon is essentially a heavier version of the electron. Muons undergo radioactive decay, lasting an average of only `?s` before they evaporate into an electron and two neutrinos. The 1974 experiment was actually built in order to measure the magnetic properties of muons, but it produced a high-precision test of time dilation as a byproduct. Because muons have the same electric charge as electrons, they can be trapped using magnetic fields. Muons were injected into the ring shown in figure, circling around it until they underwent radioactive decay. At the speed at which these muons were traveling, they had `?=29.33`, so on the average they lasted 29.33 times longer than the normal lifetime. In other words, they were like tiny alarm clocks that self-destructed at a randomly selected time. Figure shows the number of radioactive decays counted, as a function of the time elapsed after a given stream of muons was injected into the storage ring. The two dashed lines show the rates of decay predicted with and without relativity. The relativistic line is the one that agrees with experiment.
v / Example 5: In the garage's frame of reference, the bus is moving, and fits in the garage due to length contraction. In the bus's frame, the garage is moving, and can't hold the bus due to its length contraction.
Suppose we take a schoolbus and drive it at relativistic speeds into a garage of ordinary size, in which it normally would not fit. Because of the length contraction, it fits. But the driver will perceive thegarage as being contracted and thus even less able to contain the bus.
The paradox is resolved when we recognize that the concept of fitting the bus in the garage “all at once” contains a hidden assumption, the assumption that it makes sense to ask whether the front and back of the bus can simultaneously be in the garage. Observers in different frames of reference moving at high relative speeds do not necessarily agree on whether things happen simultaneously. As shown in figure, the person in the garage's frame can shut the door at an instant B he perceives to be simultaneous with the front bumper's arrival A at the back wall of the garage, but the driver would not agree about the simultaneity of these two events, and would perceive the door as having shut long after she plowed through the back wall.
Figureshows an artist's rendering of the length contraction for the collision of two gold nuclei at relativistic speeds in the RHIC accelerator in Long Island, New York, which went on line in 2000. The gold nuclei would appear nearly spherical (or just slightly lengthened like an American football) in frames moving along with them, but in the laboratory's frame, they both appear drastically foreshortened as they approach the point of collision. The later pictures show the nuclei merging to form a hot soup, in which experimenters hope to observe a new form of matter.
Example: Colliding nuclei show relativistic length contraction.
A: A person in a spaceship moving at 99.99999999% of the speed of light relative to Earth shines a flashlight forward through dusty air, so the beam is visible. What does she see? What would it look like to an observer on Earth?
B: A question that students often struggle with is whether time and space can really be distorted, or whether it just seems that way. Compare with optical illusions or magic tricks. How could you verify, for instance, that the lines in the figure are actually parallel? Are relativistic effects the same, or not?
C: On a spaceship moving at relativistic speeds, would a lecture seem even longer and more boring than normal?
D: Mechanical clocks can be affected by motion. For example, it was a significant technological achievement to build a clock that could sail aboard a ship and still keep accurate time, allowing longitude to be determined. How is this similar to or different from relativistic time dilation?
E: Figurefrom page 665, depicting the collision of two nuclei at the RHIC accelerator, is reproduced below. What would the shapes of the two nuclei look like to a microscopic observer riding on the left-hand nucleus? To an observer riding on the right-hand one? Can they agree on what is happening? If not, why not --- after all, shouldn't they see the same thing if they both compare the two nuclei side-by-side at the same instant in time?
Discussion question: colliding nuclei show relativistic length contraction.
F: If you stick a piece of foam rubber out the window of your car while driving down the freeway, the wind may compress it a little. Does it make sense to interpret the relativistic length contraction as a type of strain that pushes an object's atoms together like this? How does this relate to discussion question?
G: The rod in the figure is perfectly rigid. At event A, the hammer strikes one end of the rod. At event B, the other end moves. Since the rod is perfectly rigid, it can't compress, so A and B are simultaneous. In frame 2, B happens before A. Did the motion at the right end cause the person on the left to decide to pick up the hammer and use it?
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# 2.5: Inserting Dynamic Figures using CalcPlot3D
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## Overview
CalcPlot3D is a free online visualization tool originally developed to help students learn concepts in multivariable calculus, but now offering visual tools that can be useful in many STEM courses. Using CalcPlot3D, authors of LibreTexts can create and insert dynamic figures of two basic types:
1. Rotatable 3D dynamic plots with no external controls
2. 2D and 3D dynamic plots with some scrollbar and other controls
See examples in Figures $$\PageIndex{1}$$ - $$\PageIndex{3}$$ below.
As you can see in these examples, both types of dynamic figures can be helpful. Sometimes a rotatable 3D plot is all that is needed. But in other situations, adjusting various parameters with scrollbars and textboxes can greatly aid student understanding.
## Inserting Pre-made CalcPlot3D Dynamic Figures from the Learning Objects Library
This is the easiest way to get started using CalcPlot3D dynamic figures, since it only requires you to browse the Learning Objects library, find a dynamic figure you'd like to use, and then to use the Content reuse option on the Elements menu to insert it into your LibreTexts page. But this approach does not allow you to adjust the parameters of the interactive figures. You get exactly what's there already. So you may wish to continue to creating your own dynamic figures using CalcPlot3D.
Steps to inserting an existing CalcPlot3D dynamic figure into a LibreTexts page:
1. Browse the CalcPlot3D Interactives library and find a dynamic figure you'd like to use in your custom page.
2. Select Elements > Content reuse from the edit menu. Then click the + in front of Home. You should now see the Learning Objects library. Click on the + in front of Learning Objects and navaigate to find the dynamic figure you found in the previous step.
You should get an object that looks like the following:
And renders as:
If you would like to place a CalcPlot3D dynamic figure from the Learning Objects library in a figure, there is a template for that.
Select Elements > Templates and choose Template:AddFigureCalcPlot3DReuse. It will generate the following placeholder:
You can then follow the instructions at the top of the placeholder to right-click on the content reuse object, select Edit content reuse, and adjust the selection to the CalcPlot3D dynamic figure you want to use. Update the figure caption and remove the instructional text at the top of the figure and you'll be all set!
See examples in the Overview section at the top of this page.
## Creating your own CalcPlot3D Dynamic Figures using CalcPlot3D (without controls)
In this section, we'll discuss how to generate your own CalcPlot3D dynamic figures using the CalcPlot3D app. As stated above, there are two types, a basic rotatable 3D plot with no controls, and a 2D or 3D plot with controls. Since the first type is easiest to implement, we'll start there and then cover the second variety in the section titled Creating your own Dynamic Figures using CalcPlot3D (with controls) below.
1. Open CalcPlot3D and work out the figure you wish to include in your LibreTexts page. See the CalcPlot3D Help Manual for assistance with this.
2. Once you have the 3D plot as you want it to appear in the dynamic figure (including the initial orientation), click on the menu icon (☰) in the upper-left corner of the app, select File and then Encode View in URL. See Figure $$\PageIndex{6}$$ below.
The page will reload with the new URL that will include a script that specifies the initial view. It should match the view you had set up in step 1.
3. Copy the entire query string following the question mark in the URL to the system clipboard. Ctrl-c (cmd-c on a Mac) will help you do this.
4. Use this query string to paste into the HTML code shown below in either the section titled Creating Sharable CalcPlot3D Interactives in LibreTexts or the section titled Using Template:AddFigureCalcPlot3DNew to Insert your New CalcPlot3D Dynamic Figures (without controls). Note that the second approach is easier for beginners, but there are some advantages to organizing your CalcPlot3D dynamic figures in a repository folder (see the next section).
### Creating Sharable CalcPlot3D Interactive Figures in LibreTexts
There is at least one advantage to creating standalone CalcPlot3D dynamic figure pages in your own repository folder (a "Book" in your Campus Hub or Sandbox). It makes your interactive figures much easier to share with others. All they need to do is follow the instructions above to use content reuse to insert your figures into their pages.
It also allows you to easily update the code for all your figures in one place. And if you happen to want a particular figure in multiple places in your LibreTexts, it's a great way to use transclusion to minimize the code you have to maintain moving forward.
This was the approach used to create the library of CalcPlot3D Interactive Figures in the Learning Objects library.
Since the typical user does not have permissions to add new objects there, we will cover how you can create your own repository of CalcPlot3D Interactive Figures. Initially you may practice this process in your Sandbox, but eventually you'll want to move your repository to your Campus Hub, once you have access to it. Note that all links should update when you decide to move this folder. You may wish to make the folder containing these files semi-private using the Permissions menu option on the Options menu for the folder.
The first step in this process is to get a copy of one of the existing CalcPlot3D figures (without controls) into this folder. You have two options to do this for the first time.
1. You can use the Remixer, possibly even using it to create the new "book" which will serve as a repository for your personally created CalcPlot3D dynamic figures, or
2. You can create a new Book in your Sandbox (or Campus Hub), naming it CalcPlot3D Repository (or similar), and then create a new page in this book. Then use Elements > Content reuse to import an existing CalcPlot3D figure into that page. Bee sure there is nothing else in the page.
Once you have a transcluded copy of a CalcPlot3D figure, you will need to fork the page using the Forker option on the Options menu for the page (or the fork symbol to the right of the page title, if you used the Remixer). This should give you a full copy of a CalcPlot3D dynamic figure of your own to edit.
Once you have used either of these approaches, you should have a linked/transcluded copy of a CalcPlot3D dynamic figure in your repository folder. To create additional CalcPlot3D figures, you can just copy this one, giving it a new name!
From this new forked page, click the Edit button on the login bar. Note that the CalcPlot3D figure will still appear in rendered form in Visual edit mode. Click the </> HTML button in the upper-right corner of the edit window to change to HTML mode.
Replace the code shown highlighted in blue in Figure $$\PageIndex{7}$$ with the query string you formed in Step 3 in the previous section. Note that depending on the figure you chose for this placeholder, the code may be longer or shorter than what is shown in this figure.
Clicking of the Visual button to toggle back to view the WYSIWYG mode of the editor will actually let you see how the CalcPlot3D figure looks before you save it. If you need to adjust anything in the code, you can switch back to adjust it using the </> HTML button again. One of the most common options that you may wish to adjust is the zoom option, located about 4 script commands from the end of the query string. Decreasing the decimal number will make the 3D plot smaller. Increasing it will make the 3D plot larger.
You can actually adjust any of the options in the string, many of which are fairly intuitive. But these could also be adjusted using CalcPlot3D and updating the URL query string.
Note that when you create CalcPlot3D figures with this approach, it is very helpful to add a static image of the figure to the page holding the code for it. This makes the figures much easier to quickly browse in your repository, although it takes an extra step on your part.
Once the figure looks as you want it to look, take a screen snip of the figure using a tool like Snip & Sketch on Windows (or Shift-Cmd-4) to create and save an static image to serve as the thumbnail for this figure. Then open the Page Settings at the top of the page by clicking anywhere on this gray bar.
If the Article Type is not Book or Unit or Chapter, change it to one of these. This will allow the Thumbnail option to be shown. Once you have changed the Article Type, reload the page.
Next hover over the thumbnail image (it may be blank) in the upper-left corner and click on the pencil you should see there. This should allow you to load your saved thumbnail image and you will be all set!
### Inserting your own CalcPlot3D Dynamic Figures in LibreTexts Pages
Next we will want to insert our new dynamic figure into a LibreTexts page. There are two basic ways to do this. We can either use Content reuse or the template, Template:AddFigureCalcPlot3DReuse to insert the new sharable CalcPlot3D Interactive figure we created above or we can use the template, Template:AddFigureCalcPlot3DNew, to hard-code the script for our new CalcPlot3D dynamic figure into the page.
#### Using Content Reuse or Template:AddFigureCalcPlot3DReuse to Insert your Sharable CalcPlot3D Dynamic Figures
If you have chosen to create sharable interactive elements for your CalcPlot3D figures, you can use Elements > Content reuse or the template, Template:AddFigureCalcPlot3DReuse to add them into your LibreTexts page, depending on whether you want them in a figure object or not. See the section above titled, Inserting Pre-made CalcPlot3D Dynamic Figures from the Learning Objects Library for instructions for how to do this. The only difference here is where you will look for the CalcPlot3D dynamic figure you wish to reuse. Rather than looking in the Learning Objects library, you'll look in your own Interactive Figure repository in your Campus Hub (or Sandbox, if you are practicing).
#### Using Template:AddFigureCalcPlot3DNew to Insert your New CalcPlot3D Dynamic Figures (without controls)
We can also add a CalcPlot3D dynamic figure using the new template, Template:AddFigureCalcPlot3DNew. This template includes the actual HTML code for the CalcPlot3D object so that you can modify the parameters yourself or copy-and-paste the query string from the CalcPlot3D-generated URL into the provided HTML code. Once you have updated the code, you'll also want to remove the instructions given at the top of the figure.
When you insert the template, you will see the following:
To adjust the actual plot shown, you will switch to HTML edit mode using the button in the upper-right corner of the edit window labeled </> HTML. Then you will copy the query string in the URL generated by CalcPlot3D, as described above (everything after the ?) and paste it into the template code, replacing just the query string starting with ? and ending with "zscalefactor=1". See the highlighted portion of the code in Figure $$\PageIndex{8}$$ below.
One advantage of this method of inserting your CalcPlot3D dynamic figures is that you can see how they look in the Visual mode as you edit the page.
Rendering the default figure (with the instructions line removed):
## Creating your own CalcPlot3D Dynamic Figures using CalcPlot3D (with controls)
Several types of plots in CalcPlot3D can be used to generate dynamic figures that include scrollbars, textboxes or other controls that meaningfully control aspects of the figure.
These are (so far):
1. Any plot that uses parameter sliders
2. Any space (or plane) curve plot can include sliders and an animate button (as shown in Figure $$\PageIndex{3}$$ above).
3. Any volume of revolution figure can include a whole set of controls (as shown in Figure $$\PageIndex{2}$$ above).
4. The trace plane can be shown along with the rotatable 3D plot when contours are shown in the 3D plot, allowing an input point in the trace plane to be moved around while displaying the corresponding output point on the surface. (See Figure $$\PageIndex{11}$$ below.)
If you have other situations that you'd like to animate that are not covered here, please send a detailed request of your idea to Paul Seeburger.
### Creating the URL Query String in CalcPlot3D for a Dynamic Figure with Controls
To make a CalcPlot3D dynamic figure that includes meaningful controls, it does need to include certain things for this to happen.
If you include parameters and parameter sliders are visible on the control panel when in CalcPlot3D, this plot can be converted into a dynamic figure with controls.
Secondly, as mentioned above, any volume of revolution and any plane curve or space curve can be converted into a dynamic figure with controls.
And finally, if you create a contour plot for a function of two variables and save it to the URL when the main plot window is 3D, but still showing the contours on the surface, then this can be converted into dynamic figure like that shown in Figure $$\PageIndex{11}$$ above.
Once you have created your plot in CalcPlot3D, use the process described above in the section titled Creating your own CalcPlot3D Dynamic Figures using CalcPlot3D (without controls). That is, use the Encode View in URL option on the File menu to obtain the query string for the CalcPlot3D plot. Copy the query string to the clipboard, as described above and then follow the instructions below.
### Inserting CalcPlot3D Dynamic Figures with Controls in LibreTexts Pages
#### Creating Sharable CalcPlot3D Dynamic Figures with Controls
First, you will need to either create a copy of a similar CalcPlot3D dynamic figure with controls in your repository folder. If you already have one there, just copy it. If not, copy one from the Learning Objects library, following the steps described in section Creating Sharable CalcPlot3D Interactive Figures in LibreTexts above.
Second, you should check that the figure does indeed use the correct URL to call CalcPlot3D. If it has controls, it should call the following base URL before the query string:
https://c3d.libretexts.org/CalcPlot3D/dynamicFigureWCP/index.html
Note that the only thing that is different here is that the base URL has the characters 'WCP' after 'dynamicFigure' in its path. The WCP represents, "With Control Panel".
Third, you can paste the query string from your CalcPlot3D plot into this new template that you have made.
This means that in order to add a CalcPlot3D dynamic figure with controls, you will either need to copy an existing figure with controls or you will need to modify the HTML base URL by adding these three letters (WCP).
There are a number of special commands you may wish to add to the script in the URL query string to adjust what appears and how it is labeled.
#### Useful Script Commands for CalcPlot3D Dynamic Figures
For CalcPlot3D dynamic figures with controls there are a few options that you may wish to add to the query string by hand. There are even a few commands listed in the last bullet below that can be used for CalcPlot3D dynamic figures with or without controls.
• You can add a name attribute and/or a noanimate attribute to any sliders. For example, “noanimate=true;name=n_x”. Note that each object, including the sliders, starts with “type=” in the query string. To clarify, these attributes must be set in the definition of the relevant slider object.
See:
type=slider;slider=a;value=1;steps=2;pmin=1;pmax=3;repeat=true;bounce=true;waittime=40;careful=true;noanimate=true;name=n_x
The name attribute changes the label of the slider to the supplied name, using MathJAX to format the supplied name. This means you can use LaTeX in the name.
The noanimate attribute allows you to hide the Animate button on the slider control, if you wish.
• For figures showing the trace plane (currently those with contour plots), you can add one or more of the following attributes to the window element at the very end of the query string: “hidexysliders=true; hidetracevalue=true;hidetrancepoint=true;”
See:
type=window;hsrmode=3;anaglyph=-1;center=-7.447051206708178,-2.790794355991455,3.71998429905919,1;
focus=0.5,0.5,0.5,1;up=0.39804763218685024,0.14521777837291014,0.9057979241281567,1;transparent=true;alpha=140;twoviews=false;
showaxes=false;showticks=false;perspective=true;centerxpercent=0.5;centerypercent=0.4;rotationsteps=30;autospin=true;
xygrid=false;yzgrid=false;xzgrid=false;gridsonbox=false;gridplanes=true;gridcolor=rgb(128,128,128);
xmin=0;xmax=1;ymin=0;ymax=1;zmin=0;zmax=1;xscale=1;yscale=1;zscale=1;zcmin=-4;zcmax=4;zoom=3.543529;
xscalefactor=1;yscalefactor=1;zscalefactor=0.5;
hidexysliders=true;hidetracevalue=true;hidetracepoint=true;"
width="90%"></iframe></p>
Here the hidexysliders tag allows you to hide the $$x$$- and $$y$$-sliders that appear below the 2D trace plane by default.
The hidetracevalue tag allows you to hide the trace value normally displayed on the 3D plot when moving a trace point around on the 2D trace plane (and 3D surface).
The hidetracepoint tag allows you to hide the trace point that may otherwise be shown when you click on the 2D trace plane that appears here.
• For figures that include volumes of revolution, you may wish to add the hideaxisofrev command.
See:
type=window;hsrmode=0;nomidpts=false;anaglyph=-1;center=5,3,10;focus=0,0,0,1;up=0,2,0;transparent=false;
faceson=true;showbox=false;showaxes=true;showticks=true;perspective=true;centerxpercent=0.3832428501164356;
centerypercent=0.42;rotationsteps=30;autospin=true;xygrid=false;yzgrid=false;xzgrid=false;gridsonbox=true;
gridplanes=false;gridcolor=rgb(128,128,128);xmin=-1;xmax=5;ymin=-2;ymax=4;zmin=-4;zmax=4;xscale=1;yscale=1;
zscale=2;zcmin=-8;zcmax=8;zoom=0.37;xscalefactor=1;yscalefactor=1;zscalefactor=1;
rotatestart=0;rotatedirectionx=1;rotatedirectiony=0;hidexysliders=true;hidetracevalue=true;
hidetracepoint=true;hideaxisofrev=false" width="90%">
• Note the other commands shown here can be used in any CalcPlot3D dynamic figure (with or without controls).
The rotatestart attribute can have values between $$0$$ and $$100$$ and allows you to set an initial rotation speed. The default speed is 0 which will not cause any initial rotation.
The rotatedirectionx and rotatedirectiony attributes allows you to specify the initial direction of rotation. Typically these values should be between -1 and 1.
Other commands will likely be created as new features are added to CalcPlot3D to accommodate new types of dynamic figures with controls.
2.5: Inserting Dynamic Figures using CalcPlot3D is shared under a CC BY-SA license and was authored, remixed, and/or curated by Paul Seeburger. | crawl-data/CC-MAIN-2022-21/segments/1652662564830.55/warc/CC-MAIN-20220524045003-20220524075003-00255.warc.gz | null |
People considering a career in the medical profession as a doctor most often see themselves as a general practitioner, a pediatrician, or perhaps as a surgeon. But there is another very important field of medical practice that is highly sought-after and those who specialize in it earn one of the highest average salaries in medicine — Radiology.
Radiology is a very highly specialized medical field, requiring extensive training. Most radiologists complete at least 13 years of training following four years of undergraduate study at a university.
This course of study includes medical school, a four-year residency at a hospital working under the supervision of senior radiologists, and an additional one- or two-year fellowship in one of the specialized fields of radiology, such as interventional radiology or oncology, which is the diagnosis of tumors.
Following this long and intensive study and effort, the average U.S. radiologist’s salary is currently about $400,000 per year, making it one of the most highly-paid medical specialties.
Radiologists typically do not work the long hours or odd hours associated with other medical fields. Much of their work involves reviewing and interpreting images, rather than working directly with sick or injured patients. They use cutting-edge technology to identify diseases and conditions, helping to improve patients’ health outcomes. Here’s a closer look at what radiologists do, how someone becomes a radiologist, and the outlook for employment and salaries in the field.
What does a Radiologist do?
Like a general practitioner or a surgeon, a radiologist is a medical doctor, but one who specializes in diagnosing conditions and diseases by using advanced medical imaging.
Most people are familiar with X-ray technology, which is the oldest and most common form of medical imaging. An X-ray machine produces a controlled beam of radiation, which travels through the patient’s body and into a sheet of film. The film then shows an image of the inside of the patient’s body.
Modern medical imaging makes use of techniques such as computed tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), and ultrasound.
CT scans are now a very common feature of the U.S. healthcare system. A CT scan uses x-ray measurements taken from different angles to produce images of the inside of the patient’s body that look like slices. This way, the radiologist and the patient’s doctors can see specific areas inside the patient’s body without cutting. This is also sometimes referred to as a “CAT scan” for computed axial tomography.
MRI scans have also become more common and more convenient for patients. MRI scanners use strong magnetic fields and radio waves to construct pictures of the inside of a patient’s body. MRI and CT are often used in combination, since the different technologies can sometimes yield different diagnostic information.
PET scans are nuclear imaging, using gamma rays to produce 3D images of the inside of a patient’s body.
Latest advances in medical imaging technology allow radiologists to put together full-color 3D images in almost cinematic detail. This allows surgeons to plan surgeries in advance, and allows patients to have a greater understanding of their condition. In the future, artificial intelligence will assist radiologists in detailed and complicated diagnoses.
People might think that radiologists “take x-rays” or operate scanners, but this is not true. These tasks are performed by a radiographers, also known as a medical imaging technologist. A radiographer is not a medical doctor, although they do have to complete an accredited two- or four-year education program to get certified and become a radiology technologist.
Radiologists review the images produced by x-rays or scans and apply their knowledge of anatomy and pathology to interpret the images, looking for signs of conditions or diseases so that they can advise the patient’s physicians as to the proper course of care. In this way, radiologists are part of the patient’s overall clinical care team and assist in selecting the right imaging tests needed to meet the patient’s healthcare needs.
Radiologists also are often called to perform guided procedures, such a biopsies or targeted injections. Importantly, radiologists focus on preventing unnecessary radiation exposure. With the number of scanning capabilities available, selecting the right procedure and limiting the patient’s exposure to harmful radiation is an important part of the radiologists’ job.
Specialties in radiology
Already a very highly specialized field, radiology itself is further broken down into even more detailed subspecialties. Some of these include diagnostic radiologists, interventional radiologists, and radiation oncologists.
Diagnostic radiologists are those most frequently encountered by hospital patients. These are the radiologists who examine radiology findings from such procedures as breast mammograms, heart and lung scans and x-rays, and cardiovascular radiology of the heart and circulatory system.
Diagnostic radiology also includes subspecialties such as gastrointestinal imaging of the stomach, intestines, and abdomen; musculoskeletal imaging of the muscles and bones; neuroradiology of the brain, spine, and nervous system; and pediatric radiology.
Interventional radiologists are those radiologists who use image-guided technology. This involves instruments inserted into the patient’s body through tiny incisions, to deliver treatments targeted to conditions such as cancer or stroke. They use x-rays, MRI, and other imaging technologies to find the right place for the treatment and to guide its delivery. Unlike other radiologists, interventional radiologists will perform these surgeries and consult in the surgery room with the surgical team.
Radiation oncologists oversee the treatment plan for patients with cancer. In addition to imaging, they use radiation treatment to treat cancers. Following the radiation oncologist’s plan, radiation technology is used to deliver internal and external radiation to the cancerous cells. These radiologists also are responsible for the safe use of radiation and for managing the side effects of radiation exposure.
Interaction with patients and working conditions
Because the radiologist is primarily tasked with interpreting scanned images, much of a radiologists’ work day is spent in a room with multiple computer monitors. Examining images for possible diseases and conditions, then compiling their findings and communicating these with referring physicians and surgeons makes up the majority of the typical radiologist’s workday. A typical day might include case conferences with physicians, followed by interpreting images and performing procedures.
Unlike most other physicians, radiologists have limited patient contact. Many have very little face-to-face contact with patients. For some medical students, this can be a drawback. Many students enter the medical field anticipating much greater direct contact with patients. Those who select radiology as their specialty, however, are more likely to crave the challenge of a very highly technical field that is on the cutting edge of medical innovation.
Traditionally, radiologists have done their work in hospitals. But today’s computer technology makes it possible for radiologists to perform their work away from a hospital in an office setting. Today there are many large radiology practices in which the radiologists perform their imaging studies remotely and transmit their findings to physicians.
Radiologists who work in hospitals can expect to work longer shifts and weekends, much the same as other physicians do. Those who work in outpatient centers or in remote locations are much more likely to keep regular business hours.
College, medical school, and training
Radiology is an intensive field of study, requiring more than a dozen years of advanced academic training and guided work. For this reason, radiology tends to attract academic high performers who have an aptitude for math and physics.
The first step to becoming a radiologist is to be accepted to an accredited four-year university and to earn a bachelor’s degree in a scientific field. A high college GPA will be necessary to advance to the next step, medical school. Medical school admissions are highly competitive, and applicants will need not only outstanding undergraduate grades but also a very high score on the MCAT, the Medical College Admission Test. In addition, applicants are more likely to gain admission to medical school if they also have recommendations from faculty and a record of clinical research. While in college, radiologists typically focus on subjects such as chemistry, biology, and physics.
Getting accepted into medical school is the start of the next step in the career path for a radiologist. Medical school in the United States involves a rigorous four-year course of study, and in order to advance to the radiology specialty a student will need to earn grades at or near the top of the class. Medical school topics of study include anatomy, physiology, and other subjects that are required of all physicians.
While in medical school, students must take the United States Medical Licensing Examinations. During the final year of medical school, students will apply for post-graduate residency programs, primarily at academic teaching hospitals around the country. This application process is also highly competitive and students are not guaranteed a shot at admission, let alone their first choice.
Following graduation from medical school, the student is awarded an MD degree. Even while seeking a career in radiology, the new MD must spend the first year of residency practicing general medicine or surgery, which includes caring for emergency patients. During this four-year residency, they then begin their training in radiology. This includes many hours of interpreting images, communicating with physicians, and performing procedures. As their residency ends, they must take even more examinations in order to continue to pursue radiology as a career.
Although not technically required, many radiologists also perform a one- to two-year fellowship following their residencies. Among medical specialties, radiologists are the one most likely to serve a fellowship. Many complete more than one. A fellowship in radiology is similar to a residency, but more advanced. Radiology fellows complete clinical rotations in specialized areas of radiology, such as interventional radiology or pediatric radiology. Radiology fellows also participate in lectures and conferences, as well as scholarly research.
After all the years of college, medical school, and post-graduate training, the new radiologist is finally ready to practice their specialty. Every state requires licensing for radiologists, just as they do for other practicing physicians. This state licensing requires passing a two-part examination. For radiologists, this exam tests knowledge of medicine and anatomy as well as imaging and nuclear physics.
Average salary and job outlook
At the end of the long road of training and certification, radiologists typically earn excellent salaries. In 2018, the average radiologist salary in the United States topped $400,000. According to Medscape’s 2018 Physician Compensation Report, radiologists were the fifth highest compensated medical specialty, behind plastic surgery, orthopedics, cardiology, and gastroenterology.
Not only are radiologists’ salaries comparatively high, some radiology specialties are also quite rare and in high demand. It is not uncommon for an interventional radiologist to be the only one in their region capable of performing certain procedures.
The overall employment outlook for physicians of all types, including radiologists, is quite good. Physician employment is expected to grow by 14 percent from 2014 to 2024, according to the U.S. Bureau of Labor Statistics. The agency also reported that employment prospects could be greater for radiologists who work with elderly populations, who have a greater risk for cancer and heart disease.
As they grow in their careers, radiologists advance by gaining new skills and expertise. It is not uncommon for radiologists at the top of the field to hold multiple advanced degrees in addition to their medical degrees. Many also have masters’ degrees or PhDs in fields such as physics. As one would expect, these professionals command an even higher income and also have opportunities for leadership and research.
If you have the academic skills and a desire to pursue a career in medicine, an analytical mind, and an attention to detail, radiology has a lot to offer as a career path. Many who choose radiology as their medical specialty do so because it consistently offers stimulating intellectual challenges and minimizes patient interaction.
Having reached the pinnacle of achievement at every level of education, radiologists describe their specialty as stimulating and satisfying. Most radiologists are regularly seeing new conditions and sometimes are first to make the diagnosis. They enjoy being on the leading edge in medical technology. While in the tech industry have predicted that artificial intelligence will one day make radiologists obsolete, most in the radiology field disagree. Radiologists view the advance of technology as an advantage and expect that AI will work alongside radiologists to improve workflow and make diagnoses more accurate.
Radiology as a profession has a lot to offer those who can make the steep climb academically and intellectually. Radiologists play a vital role in patient diagnosis and the management of diseases and conditions. It offers unparalleled challenges and significant rewards. | <urn:uuid:1bc3c517-c08f-46f1-8823-25bef073ab94> | {
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What is the vertex of y=-3x^2-4x+2 ?
Dec 4, 2015
$\left(- \frac{2}{3} , \frac{10}{3}\right)$
Explanation:
The vertex of a quadratic equation can be found through the vertex formula:
$\left(- \frac{b}{2 a} , f \left(- \frac{b}{2 a}\right)\right)$
The letters represent the coefficients in the standard form of a quadratic equation $a {x}^{2} + b x + c$.
Here:
$a = - 3$
$b = - 4$
Find the $x$-coordinate of the vertex.
$- \frac{b}{2 a} = - \frac{- 4}{2 \left(- 3\right)} = - \frac{2}{3}$
The $y$-coordinate is found by plugging $- \frac{2}{3}$ into the original equation.
$- 3 {\left(- \frac{2}{3}\right)}^{2} - 4 \left(- \frac{2}{3}\right) + 2 = - 3 \left(\frac{4}{9}\right) + \frac{8}{3} + 2$
$= - \frac{4}{3} + \frac{8}{3} + \frac{6}{3} = \frac{10}{3}$
Thus, the vertex is located at the point $\left(- \frac{2}{3} , \frac{10}{3}\right)$.
This can also be found through putting the quadratic into vertex form $y = a {\left(x - h\right)}^{2} + k$ by completing the square.
y=-3(x^2+4/3x+?)+2
$y = - 3 \left({x}^{2} + \frac{4}{3} x + \textcolor{b l u e}{\frac{4}{9}}\right) + 2 + \textcolor{b l u e}{\frac{4}{3}}$
$y = - 3 {\left(x + \frac{2}{3}\right)}^{2} + \frac{10}{3}$
Again, the vertex is located at the point $\left(- \frac{2}{3} , \frac{10}{3}\right)$. | crawl-data/CC-MAIN-2021-39/segments/1631780057274.97/warc/CC-MAIN-20210921221605-20210922011605-00210.warc.gz | null |
Hypothesis Testing For Proportions
Presentation on theme: "Hypothesis Testing For Proportions"— Presentation transcript:
Hypothesis Testing For Proportions
P-Values of a Hypothesis Test
If the null-hypothesis is true, the P-value (probability value) of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme or more extreme than the one determined from the sample data (farther away).
And then… The smaller the P-Value, the more evidence there is to reject the null hypothesis. A very small P-Value indicates a rare occurrence. If the P-Value ≤ α, then you will reject the null hypothesis. If the P-Value > α, then you will fail to reject the null hypothesis.
Tests… If Ha contains <, the test is a left-tailed test.
P is the area to the left of the test statistic. If Ha contains >, the test is a right-tailed test. P is the area to the right of the test statistic. If Ha contains ≠, the test is a two-tailed test. P is the area to the left of the negative test statistic, and P is the area to the right of the positive test statistic.
Definitions Hypothesis tests for proportions occur (for example) when a politician wants to know the proportion of his or her constituents who favor a certain bill or when a quality assurance engineer tests the proportion of parts which are defective. Z-Test for a Proportion P: A statistical test for a population proportion P. It can be used when np ≥ 5 and nq ≥ 5. (q is 1-p) A test statistic is the sample proportion p-hat. The standardized test statistic is z…formula to follow later.
Steps to follow for a test…
Verify that np ≥ 5 and nq ≥ 5. If these are true, the distribution for p-hat will be normal and you can continue; otherwise you cannot use normal distribution for the problem. State the claim…Identify null and alternative hypotheses. Specify the level of significance (α). Sketch the sampling distribution (make a curve).
More steps… Determine any critical values (see next slide). These will be borders between rejection regions and non-rejection regions (below). They will be the same values each time. Determine any rejection regions. These are a range of values for which the Ho is not probable. If a test statistic falls into this region, Ho is rejected. A critical value separates the rejection region from the non-rejection region.
Critical Values Tailed Significance Level Critical Value Left 0.10
-1.28 Right 1.28 Two ±1.645 0.05 -1.645 1.645 ±1.96 0.01 -2.33 2.33 ±2.575
More steps… Find the z-score (standard score): Make a decision to
reject or fail to reject Ho. Interpret the decision in the context of the original claim.
Example… A medical researcher claims that less than 20% of adults in the U.S. are allergic to a medication. In a random sample of 100 adults, 15% say they have such an allergy. At α = 0.01, is there enough evidence to support the researcher’s claim? n = 100, p = 0.20, q = 0.80 1. np = 20, nq = 80…you can continue. 2. Ho: p ≥ 0.2, Ha: p < 0.2
Example (cont’d)… Since Ha is <, this is a left-tailed test, and since α = 0.01, we will be using the critical value as (they use the symbol zo for this). See drawing on board for sketch. The rejection region is z < The standardized test statistic (z) is:
Example (cont’d)… Since z = -1.25, and this is not in the rejection region, you should decide not to reject the null hypothesis. Interpretation: There is not enough evidence to support the claim that less than 20% of adults in the U.S. are allergic to the medication.
In your groups… USA Today reports that 5% of US adults have seen an extraterrestrial being. You decide to test this claim and ask a random sample of 250 U.S. adults whether they have ever seen an extraterrestrial being. Of those surveyed 8% reply yes. At α = 0.01, is there enough evidence to reject the claim? Your group is to complete and document all the steps to come to the final answer. This will be turned in.
There will be some on Friday
Homework… There will be some on Friday | crawl-data/CC-MAIN-2018-13/segments/1521257647556.43/warc/CC-MAIN-20180321004405-20180321024405-00276.warc.gz | null |
Go Figure! Exploring Figurative Language highlights a variety of common idioms and proverbs for students in grades 5–8. Students will deepen their skills in writing, understanding word meanings, and using context clues with this engaging classroom resource. Based on today's standards, this resource includes 20 content-based lessons in the areas of science, social studies, and mathematics. Teacher overview pages, student activities, and digital resources are included. | <urn:uuid:1d4b9089-10be-46a4-aa74-637ed5c897c5> | {
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# 10 More 10 Less Worksheets
Printable place value worksheets for 1st Grade:
Ten and Ones (eg. 17 = __ ten and __ ones)
Count Tens & Ones (with pictures)
Count Tens & Ones (with place value charts)
Tens and Ones (eg. 73 = __ tens and __ ones)
Add Tens & Ones (with pictures)
Add Tens & Ones (eg. 60 + 4 = )
1 more, 1 less, 10 more, 10 less
### 1 more, 1 less, 10 More, 10 Less Worksheets
Identifying 10 more, 10 less, 1 more, and 1 less than a two-digit number involves understanding the patterns in the base-10 number system.
1. Introduction to Place Value:
Begin by reviewing or introducing the concept of place value. Remind students that each digit in a number has a specific place and value.
2. Visual Representation:
Use visual aids such as place value charts, drawings, or manipulatives to represent two-digit numbers. This helps students visualize the relationship between tens and ones.
3. Identify the Two-Digit Number:
Choose a two-digit number, for example, 45.
4. 10 More:
Explain that to find 10 more than a number, add 10 to the original number.
For 45, 45 + 10 = 55.
Emphasize that only the tens place changes.
5. 10 Less:
Similarly, explain that to find 10 less than a number, subtract 10 from the original number.
For 45, 45 − 10 = 35.
Again, highlight that only the tens place changes.
6. 1 More: For finding 1 more than a number, add 1 to the original number.
For 45, 45 + 1 = 46. Emphasize that this change occurs in the ones place.
7. 1 Less:
For finding 1 less than a number, subtract 1 from the original number.
For 45, 45−1=44.
The ones place is affected in this case.
Understanding the relationships between a two-digit number and its variations (10 more, 10 less, 1 more, and 1 less) helps students develop a deeper grasp of place value and numerical patterns. Regular practice and interactive activities enhance their proficiency in these concepts.
Have a look at this video if you need to review how to find 10 more, 10 less, 1 more, and 1 less than a two-digit number.
Click on the following worksheet to get a printable pdf document.
Scroll down the page for more 10 More 10 Less Worksheets.
### More 1 more, 1 less, 10 More, 10 Less Worksheets
10 More 10 Less Worksheet #1
10 More 10 Less Worksheet #2
10 More 10 Less Worksheet #3 (sprint, practice)
10 More 10 Less Worksheet #4 (sprint, practice)
10 More 10 Less Worksheet #5 (sprint, practice)
10 More 10 Less Worksheet #6 (sprint, practice)
More Printable Worksheets
Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. | crawl-data/CC-MAIN-2024-38/segments/1725700652130.6/warc/CC-MAIN-20240920022257-20240920052257-00839.warc.gz | null |
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Lesson37
Lesson37 - Lesson 37 Examine the following 4 9 = 23 = 6...
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1 Lesson 37 Sections 7.3 & 7.4 Examine the following: 4 9 2 3 6 4 9 36 6 = = = = Since both equal 6, the expressions are equal. Conclusion: 4 9 4 9 = Likewise: 2 4 4 16 2 2 4 4 16 = = = = Since both equal 2, the expressions are equal. Conclusion: 4 16 4 16 = These observations lead to two very important rules: the Product and Quotient Rules for Radicals. Product Rule for Radicals: n n n ab b a = Quotient Rule for Radicals: n n n b a b a = Caution: These rules only apply when the indices (plural of index) are equal! Use the rules above (if possible) to multiply, divide, or otherwise simplify. 1. = ) 6 )( 13 ( 3 3 2. 2 3 4 t = 3. 2 3 2 3 x x - + =
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2 4. = 2 25 x 5. = 3 6 27 2 a 6. = 5 80 7. ( ) ( ) = 3 3 x The product rule can also be used to simplify a radical by using factoring. Look at the following example. 20 4 5 4 5 2 5 = = = To simplify a radical with index n (using factoring or the product rule), use the following steps. 1.
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Lesson37 - Lesson 37 Examine the following 4 9 = 23 = 6...
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Ask a homework question - tutors are online | crawl-data/CC-MAIN-2018-09/segments/1518891812584.40/warc/CC-MAIN-20180219111908-20180219131908-00385.warc.gz | null |
Rabbi Josef Weber (center) with his sons and other Brzozow Jews, in a photograph taken by the Germans. According to testimonies, shortly before the liquidation of the ghetto, the people pictured were led to the Lazenki forests and murdered, Brzozow Ghetto
Jews waiting near the home of Judenrat Chairman Isidor Krumholtz before leaving to perform forced labor outside the ghetto, Andrychów Ghetto, 1942
Since the historiography on the ghettos in Europe during World War II had mainly been limited to the largest ones and that in fact most ghettos had never been systematically researched, the International Institute for Holocaust Research decided to conduct a comprehensive research project on the ghettos with the intention to publish an encyclopedia on the ghettos in Nazi occupied Europe.
This pioneering research project involved a systematic gathering of data from research studies, historical information, testimonies and documents dealing with more than 1,100 ghettos throughout mainly Eastern Europe where Jews were concentrated and whence they were deported. Information on conditions, the type of administration, the leadership, and individual coping methodologies were collected.
As the Nazis never clearly defined “ghettos” themselves, the Institute decided to define “ghetto” for this project in very broad terms, basing it on the phenomenological definition that was obtained through analysis of the historical material.
The data compiled records the stories of the Jews who were herded into and concentrated in various locations through the essential characteristics of the phenomenon. It reflects the differences between each ghetto and reveals the differences between each ghetto and reveals the radical changes in Jewish communal and individual life. Those changes are examined from various perspectives of daily life, coping strategies and the different forms of resistance. Thus, one is able to see the similarities and differences among the various ghettos. Some ghettos lasted only a few weeks, others a month or two, while in Poland and Lithuania some ghettos operated for years. There were different time divisions for the major events that impacted on the confined Jews throughout each ghetto’s existence, such as forced resettlement and adjustment; the sealing and isolation of the ghettos from the rest of the world; signs of imminent doom; and eventual deportation and murder.
In October 2009, the English edition of the encyclopedia was published by Yad Vashem. All entries include the location, the wartime names and geographical coordinates; and, for the larger ghettos, informational sections of the following:
- Pre-World War II
- Soviet occupation
- German (Nazi) occupation
- Ghetto setup
- Ghetto institutions, and internal life
- Murder, terror and killing operations of ghetto inhabitants
- Underground and resistance
- Number of survivors at liberation
The encyclopedia includes pictures and maps of the different ghettos. It also includes a composite of film documentation on DVD.
The Online Hebrew Edition
In the latter half of 2009, Yad Vashem began adapting the Encyclopedia of Ghettos to a new, online Hebrew format, which will be uploaded to the Yad Vashem website. The entries are being translated into Hebrew. Photographs and maps will also be included on the website. The inauguration of the online encyclopedia is forthcoming.
Dr. Lea Prais
Dr. Ruth Shachak
Dr. Nahama Gal | <urn:uuid:c226d087-ac29-4e82-8967-80b4c953e295> | {
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# 96.37 kg to lbs - 96.37 kilograms to pounds
Do you need to know how much is 96.37 kg equal to lbs and how to convert 96.37 kg to lbs? Here you go. You will find in this article everything you need to make kilogram to pound conversion - theoretical and also practical. It is also needed/We also want to point out that all this article is dedicated to a specific number of kilograms - exactly one kilogram. So if you need to know more about 96.37 kg to pound conversion - keep reading.
Before we move on to the practice - this is 96.37 kg how much lbs calculation - we want to tell you a little bit of theoretical information about these two units - kilograms and pounds. So let’s move on.
How to convert 96.37 kg to lbs? 96.37 kilograms it is equal 212.4594818894 pounds, so 96.37 kg is equal 212.4594818894 lbs.
## 96.37 kgs in pounds
We will begin with the kilogram. The kilogram is a unit of mass. It is a basic unit in a metric system, known also as International System of Units (in abbreviated form SI).
At times the kilogram could be written as kilogramme. The symbol of the kilogram is kg.
Firstly, the definition of a kilogram was formulated in 1795. The kilogram was described as the mass of one liter of water. This definition was simply but totally impractical to use.
Then, in 1889 the kilogram was defined using the International Prototype of the Kilogram (in abbreviated form IPK). The IPK was made of 90% platinum and 10 % iridium. The International Prototype of the Kilogram was used until 2019, when it was replaced by a new definition.
Nowadays the definition of the kilogram is build on physical constants, especially Planck constant. The official definition is: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.”
One kilogram is 0.001 tonne. It is also divided into 100 decagrams and 1000 grams.
## 96.37 kilogram to pounds
You know something about kilogram, so now let’s move on to the pound. The pound is also a unit of mass. It is needed to highlight that there are not only one kind of pound. What are we talking about? For instance, there are also pound-force. In this article we want to concentrate only on pound-mass.
The pound is in use in the Imperial and United States customary systems of measurements. To be honest, this unit is used also in another systems. The symbol of the pound is lb or “.
There is no descriptive definition of the international avoirdupois pound. It is defined as exactly 0.45359237 kilograms. One avoirdupois pound can be divided to 16 avoirdupois ounces or 7000 grains.
The avoirdupois pound was implemented in the Weights and Measures Act 1963. The definition of the pound was placed in first section of this act: “The yard or the metre shall be the unit of measurement of length and the pound or the kilogram shall be the unit of measurement of mass by reference to which any measurement involving a measurement of length or mass shall be made in the United Kingdom; and- (a) the yard shall be 0.9144 metre exactly; (b) the pound shall be 0.45359237 kilogram exactly.”
### How many lbs is 96.37 kg?
96.37 kilogram is equal to 212.4594818894 pounds. If You want convert kilograms to pounds, multiply the kilogram value by 2.2046226218.
### 96.37 kg in lbs
Theoretical part is already behind us. In this section we will tell you how much is 96.37 kg to lbs. Now you learned that 96.37 kg = x lbs. So it is time to know the answer. Have a look:
96.37 kilogram = 212.4594818894 pounds.
It is an accurate result of how much 96.37 kg to pound. It is possible to also round off this result. After rounding off your outcome is exactly: 96.37 kg = 212.014 lbs.
You know 96.37 kg is how many lbs, so have a look how many kg 96.37 lbs: 96.37 pound = 0.45359237 kilograms.
Obviously, in this case it is possible to also round off the result. After rounding off your result is as following: 96.37 lb = 0.45 kgs.
We also want to show you 96.37 kg to how many pounds and 96.37 pound how many kg outcomes in charts. Let’s see:
We want to start with a chart for how much is 96.37 kg equal to pound.
### 96.37 Kilograms to Pounds conversion table
Kilograms (kg) Pounds (lb) Pounds (lbs) (rounded off to two decimal places)
96.37 212.4594818894 212.0140
Now see a chart for how many kilograms 96.37 pounds.
Pounds Kilograms Kilograms (rounded off to two decimal places
96.37 0.45359237 0.45
Now you learned how many 96.37 kg to lbs and how many kilograms 96.37 pound, so it is time to go to the 96.37 kg to lbs formula.
### 96.37 kg to pounds
To convert 96.37 kg to us lbs you need a formula. We are going to show you a formula in two different versions. Let’s begin with the first one:
Amount of kilograms * 2.20462262 = the 212.4594818894 result in pounds
The first formula give you the most accurate result. In some cases even the smallest difference can be significant. So if you need a correct result - first formula will be the best for you/option to calculate how many pounds are equivalent to 96.37 kilogram.
So go to the second formula, which also enables conversions to know how much 96.37 kilogram in pounds.
The another version of a formula is as following, have a look:
Amount of kilograms * 2.2 = the outcome in pounds
As you see, this formula is simpler. It could be better option if you need to make a conversion of 96.37 kilogram to pounds in easy way, for instance, during shopping. You only have to remember that final outcome will be not so accurate.
Now we want to learn you how to use these two versions of a formula in practice. But before we are going to make a conversion of 96.37 kg to lbs we want to show you another way to know 96.37 kg to how many lbs without any effort.
### 96.37 kg to lbs converter
Another way to check what is 96.37 kilogram equal to in pounds is to use 96.37 kg lbs calculator. What is a kg to lb converter?
Calculator is an application. Converter is based on longer formula which we gave you above. Due to 96.37 kg pound calculator you can easily convert 96.37 kg to lbs. You only need to enter amount of kilograms which you need to convert and click ‘calculate’ button. The result will be shown in a flash.
So let’s try to calculate 96.37 kg into lbs with use of 96.37 kg vs pound converter. We entered 96.37 as a number of kilograms. It is the result: 96.37 kilogram = 212.4594818894 pounds.
As you can see, our 96.37 kg vs lbs converter is easy to use.
Now we can move on to our chief issue - how to convert 96.37 kilograms to pounds on your own.
#### 96.37 kg to lbs conversion
We are going to begin 96.37 kilogram equals to how many pounds calculation with the first formula to get the most accurate outcome. A quick reminder of a formula:
Amount of kilograms * 2.20462262 = 212.4594818894 the result in pounds
So what need you do to check how many pounds equal to 96.37 kilogram? Just multiply amount of kilograms, this time 96.37, by 2.20462262. It is equal 212.4594818894. So 96.37 kilogram is exactly 212.4594818894.
It is also possible to round it off, for instance, to two decimal places. It is equal 2.20. So 96.37 kilogram = 212.0140 pounds.
It is time for an example from everyday life. Let’s calculate 96.37 kg gold in pounds. So 96.37 kg equal to how many lbs? And again - multiply 96.37 by 2.20462262. It is equal 212.4594818894. So equivalent of 96.37 kilograms to pounds, if it comes to gold, is 212.4594818894.
In this example it is also possible to round off the result. This is the result after rounding off, this time to one decimal place - 96.37 kilogram 212.014 pounds.
Now we can go to examples calculated with a short version of a formula.
#### How many 96.37 kg to lbs
Before we show you an example - a quick reminder of shorter formula:
Amount of kilograms * 2.2 = 212.014 the outcome in pounds
So 96.37 kg equal to how much lbs? As in the previous example you need to multiply number of kilogram, this time 96.37, by 2.2. Let’s see: 96.37 * 2.2 = 212.014. So 96.37 kilogram is exactly 2.2 pounds.
Make another calculation using shorer version of a formula. Now convert something from everyday life, for example, 96.37 kg to lbs weight of strawberries.
So let’s convert - 96.37 kilogram of strawberries * 2.2 = 212.014 pounds of strawberries. So 96.37 kg to pound mass is equal 212.014.
If you know how much is 96.37 kilogram weight in pounds and are able to convert it with use of two different formulas, let’s move on. Now we are going to show you all outcomes in charts.
#### Convert 96.37 kilogram to pounds
We realize that results presented in tables are so much clearer for most of you. It is totally understandable, so we gathered all these outcomes in charts for your convenience. Due to this you can quickly make a comparison 96.37 kg equivalent to lbs results.
Let’s start with a 96.37 kg equals lbs table for the first formula:
Kilograms Pounds Pounds (after rounding off to two decimal places)
96.37 212.4594818894 212.0140
And now look 96.37 kg equal pound table for the second version of a formula:
Kilograms Pounds
96.37 212.014
As you can see, after rounding off, when it comes to how much 96.37 kilogram equals pounds, the results are not different. The bigger number the more considerable difference. Please note it when you need to make bigger amount than 96.37 kilograms pounds conversion.
#### How many kilograms 96.37 pound
Now you know how to calculate 96.37 kilograms how much pounds but we want to show you something more. Are you curious what it is? What about 96.37 kilogram to pounds and ounces calculation?
We want to show you how you can calculate it step by step. Begin. How much is 96.37 kg in lbs and oz?
First thing you need to do is multiply number of kilograms, this time 96.37, by 2.20462262. So 96.37 * 2.20462262 = 212.4594818894. One kilogram is 2.20462262 pounds.
The integer part is number of pounds. So in this case there are 2 pounds.
To convert how much 96.37 kilogram is equal to pounds and ounces you have to multiply fraction part by 16. So multiply 20462262 by 16. It is 327396192 ounces.
So your result is exactly 2 pounds and 327396192 ounces. It is also possible to round off ounces, for instance, to two places. Then your outcome is exactly 2 pounds and 33 ounces.
As you see, conversion 96.37 kilogram in pounds and ounces is not complicated.
The last conversion which we are going to show you is calculation of 96.37 foot pounds to kilograms meters. Both foot pounds and kilograms meters are units of work.
To calculate foot pounds to kilogram meters it is needed another formula. Before we give you this formula, have a look:
• 96.37 kilograms meters = 7.23301385 foot pounds,
• 96.37 foot pounds = 0.13825495 kilograms meters.
Now look at a formula:
Amount.RandomElement()) of foot pounds * 0.13825495 = the result in kilograms meters
So to convert 96.37 foot pounds to kilograms meters you need to multiply 96.37 by 0.13825495. It is equal 0.13825495. So 96.37 foot pounds is 0.13825495 kilogram meters.
You can also round off this result, for example, to two decimal places. Then 96.37 foot pounds will be equal 0.14 kilogram meters.
We hope that this calculation was as easy as 96.37 kilogram into pounds calculations.
This article is a big compendium about kilogram, pound and 96.37 kg to lbs in calculation. Thanks to this conversion you learned 96.37 kilogram is equivalent to how many pounds.
We showed you not only how to do a conversion 96.37 kilogram to metric pounds but also two other conversions - to know how many 96.37 kg in pounds and ounces and how many 96.37 foot pounds to kilograms meters.
We showed you also another way to do 96.37 kilogram how many pounds conversions, that is using 96.37 kg en pound converter. It is the best solution for those of you who do not like calculating on your own at all or this time do not want to make @baseAmountStr kg how lbs conversions on your own.
We hope that now all of you can do 96.37 kilogram equal to how many pounds calculation - on your own or with use of our 96.37 kgs to pounds calculator.
Don’t wait! Let’s calculate 96.37 kilogram mass to pounds in the best way for you.
Do you want to do other than 96.37 kilogram as pounds conversion? For example, for 15 kilograms? Check our other articles! We guarantee that calculations for other numbers of kilograms are so simply as for 96.37 kilogram equal many pounds.
### How much is 96.37 kg in pounds
To quickly sum up this topic, that is how much is 96.37 kg in pounds , we gathered answers to the most frequently asked questions. Here we have for you all you need to know about how much is 96.37 kg equal to lbs and how to convert 96.37 kg to lbs . You can see it down below.
How does the kilogram to pound conversion look? To make the kg to lb conversion it is needed to multiply 2 numbers. How does 96.37 kg to pound conversion formula look? . Check it down below:
The number of kilograms * 2.20462262 = the result in pounds
How does the result of the conversion of 96.37 kilogram to pounds? The accurate result is 212.4594818894 lb.
There is also another way to calculate how much 96.37 kilogram is equal to pounds with another, shortened version of the formula. Have a look.
The number of kilograms * 2.2 = the result in pounds
So this time, 96.37 kg equal to how much lbs ? The result is 212.4594818894 lbs.
How to convert 96.37 kg to lbs in a few seconds? You can also use the 96.37 kg to lbs converter , which will make the rest for you and you will get an accurate result .
#### Kilograms [kg]
The kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side.
#### Pounds [lbs]
A pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms.
Read more related articles:
96.01 kg to lbs = 211.666 96.02 kg to lbs = 211.688 96.03 kg to lbs = 211.71 96.04 kg to lbs = 211.732 96.05 kg to lbs = 211.754 96.06 kg to lbs = 211.776 96.07 kg to lbs = 211.798 96.08 kg to lbs = 211.82 96.09 kg to lbs = 211.842 96.1 kg to lbs = 211.864 96.11 kg to lbs = 211.886 96.12 kg to lbs = 211.908 96.13 kg to lbs = 211.93 96.14 kg to lbs = 211.952 96.15 kg to lbs = 211.974 96.16 kg to lbs = 211.997 96.17 kg to lbs = 212.019 96.18 kg to lbs = 212.041 96.19 kg to lbs = 212.063 96.2 kg to lbs = 212.085 96.21 kg to lbs = 212.107 96.22 kg to lbs = 212.129 96.23 kg to lbs = 212.151 96.24 kg to lbs = 212.173 96.25 kg to lbs = 212.195
96.26 kg to lbs = 212.217 96.27 kg to lbs = 212.239 96.28 kg to lbs = 212.261 96.29 kg to lbs = 212.283 96.3 kg to lbs = 212.305 96.31 kg to lbs = 212.327 96.32 kg to lbs = 212.349 96.33 kg to lbs = 212.371 96.34 kg to lbs = 212.393 96.35 kg to lbs = 212.415 96.36 kg to lbs = 212.437 96.37 kg to lbs = 212.459 96.38 kg to lbs = 212.482 96.39 kg to lbs = 212.504 96.4 kg to lbs = 212.526 96.41 kg to lbs = 212.548 96.42 kg to lbs = 212.57 96.43 kg to lbs = 212.592 96.44 kg to lbs = 212.614 96.45 kg to lbs = 212.636 96.46 kg to lbs = 212.658 96.47 kg to lbs = 212.68 96.48 kg to lbs = 212.702 96.49 kg to lbs = 212.724 96.5 kg to lbs = 212.746
96.51 kg to lbs = 212.768 96.52 kg to lbs = 212.79 96.53 kg to lbs = 212.812 96.54 kg to lbs = 212.834 96.55 kg to lbs = 212.856 96.56 kg to lbs = 212.878 96.57 kg to lbs = 212.9 96.58 kg to lbs = 212.922 96.59 kg to lbs = 212.945 96.6 kg to lbs = 212.967 96.61 kg to lbs = 212.989 96.62 kg to lbs = 213.011 96.63 kg to lbs = 213.033 96.64 kg to lbs = 213.055 96.65 kg to lbs = 213.077 96.66 kg to lbs = 213.099 96.67 kg to lbs = 213.121 96.68 kg to lbs = 213.143 96.69 kg to lbs = 213.165 96.7 kg to lbs = 213.187 96.71 kg to lbs = 213.209 96.72 kg to lbs = 213.231 96.73 kg to lbs = 213.253 96.74 kg to lbs = 213.275 96.75 kg to lbs = 213.297
96.76 kg to lbs = 213.319 96.77 kg to lbs = 213.341 96.78 kg to lbs = 213.363 96.79 kg to lbs = 213.385 96.8 kg to lbs = 213.407 96.81 kg to lbs = 213.43 96.82 kg to lbs = 213.452 96.83 kg to lbs = 213.474 96.84 kg to lbs = 213.496 96.85 kg to lbs = 213.518 96.86 kg to lbs = 213.54 96.87 kg to lbs = 213.562 96.88 kg to lbs = 213.584 96.89 kg to lbs = 213.606 96.9 kg to lbs = 213.628 96.91 kg to lbs = 213.65 96.92 kg to lbs = 213.672 96.93 kg to lbs = 213.694 96.94 kg to lbs = 213.716 96.95 kg to lbs = 213.738 96.96 kg to lbs = 213.76 96.97 kg to lbs = 213.782 96.98 kg to lbs = 213.804 96.99 kg to lbs = 213.826 97 kg to lbs = 213.848 | crawl-data/CC-MAIN-2023-14/segments/1679296949506.62/warc/CC-MAIN-20230330225648-20230331015648-00082.warc.gz | null |
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