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Senior Vice President, Commercial Vaccine Manufacturing,
Vaccines are a safe and effective way to protect children from infectious diseases. Vaccines have reduced and, in some cases, eradicated many diseases that killed millions just even a few decades back.
Unfortunately, despite the continuous innovations of new and effective vaccines, we are yet to achieve our immunization goals as vaccines fail to reach people in the remote corners of the country.
Vaccination has a huge impact on child health yet millions of children die every year from diseases that are preventable through basic immunization. As per WHO, immunizations prevent 2-3 million deaths a year, and an additional 1.5 million lives could be saved by expanding global immunizations. Given the importance of vaccines in child health, the challenges that impair their reach must be dealt stringently.
One big challenge in vaccine reach is faulty and inefficient delivery system. Moreover, wastage of vaccines is a big concern. In low-resource settings, factors like tropical temperature, scarce resources, unreliable power, and long distances between healthcare facilities poses huge risks. Transporting vaccines in the tropical heat of various developing countries – where the vaccine needs to be kept between 2°C to 8°C from the point of manufacture until reaching the recipient – is a big challenge and a major reason of low immunization coverage rates. Temperature changes can shorten the shelf life of vaccines by accelerating their degradation and hamper the delivery of lifesaving vaccines. Studies show that there is a breach of temperature requirements at all stages of supply chain. The World Health Organization (WHO) estimates that annually 10-50 percent of vaccines may be wasted globally because of temperature control, logistics and shipment-related issues.
To measure the exposure to heat, Vaccine vial monitors (VVMs) were introduced, which are attached to vials of the vaccine at the time of manufacture and are temperature and time sensitive. When a vaccine has been exposed to excessive heat, a change in the color of the labels warn the health workers and storekeepers that the vaccine should not be used.
As is evident, temperature sensitive nature of vaccines leads to instability and potency loss during commercial production and distribution across the entire vaccine supply chain from the manufacturer to patient administration. This is a major reason why maintenance of either refrigerated or frozen temperatures, often referred to as the “vaccine cold chain” is essential. Vaccine cold chain is a process that is used to maintain optimal conditions during the transport, storage, and handling of vaccines, starting at the manufacturer and ending with the administration of the vaccine to the client.
Maintaining this cold chain is essential both in the developed and developing world, to ensure that the end-users worldwide receive efficacious vaccines. To this effect, some companies are researching methods to enhance the thermostability of vaccines. They are offering advance technologies that help maintain all quality attributes of the vaccine even under unfavorable temperature conditions. Thermostable vaccines decrease logistics cost by eliminating cold chain and also reduce risk of inactivated vaccine, thereby, maximizing the impact on public health. Thermostability helps in increasing coverage by storing vaccines at facilities which do not have cold chain equipment, reduces costs by minimizing vaccine wastage, reduces cold chain footprints and complexity at all levels.
Moreover, by cutting costs on cold chain, vaccines can be made more affordable, which will help increase the outreach and availability in far-fetched areas. In addition to this, the ease of administration will increase the accessibility aspect of a vaccine. The important thing to be noted is that affordability and accessibility go hand in hand. Focusing on making vaccines affordable from the initial stages of development would make them more accessible and vice versa.
Innovation is the key! Future innovations are essential to continue moving forward in improving and expanding vaccine access. Implementation of computer and cell phone technologies to digitize health information systems provides a feasible method to improve registry management and maximize benefits of an efficient vaccine supply chain. Lastly, better thermostable vaccines are clearly the key to cover the gap as they would address issues related to vaccine stability and cold chain.
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Mühlburg, formerly a town on its own right, is a borough located in the West of Karlsruhe, Baden-Württemberg, Germany. The name Mühlburg could be translated as Mill-castle and refers to a water mill and a water castle located at the site where a Roman road once crossed the small river Alb.
Mühlburg was first mentioned and referred to as Mulenberc in 1248. In 1258 there was the first mentioning of a castle being owned by Rudolf I Margrave of Baden
In 1274 Mühlburg was, as many neighbouring settlements, occupied by Rudolph of Habsburg. In 1670 Mühlbrug received town privileges and just a few years before Karlsruhe a “letter of freedom” was issued, which relaxed the requirements for craftsmen and new citizens to settle down.
It is believed that the Margraves of Baden planned the expansion of Mühlburg. Any plans of such kind came to a halt in 1689. Following the orders of Louis XIV of France to destroy the margravate of Baden („Ruinez les pays de Bade“), Mühlburg and its castle were destroyed by French troops during the Nine Years' War.
The castle was never rebuilt thereafter and the ruins of the castle were used as building material for a newly founded palace nearby out of which the future city of Karlsruhe would develop.
Mühlburg finally became a borough of Karlsruhe in 1886.
- Stadtarchiv Karlsruhe (City Archives); Mühlburg. Streifzüge durch die Ortsgeschichte. Info-Verlag, Karlsruhe 1998, ISBN 3-88190-227-9
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On folio 9v of Manuscript B Leonardo drew a warship equipped with a giant scythe. He cited the source of this invention in his description by explaining that it was used to cut the rigging and masts of enemy ships. He also observed that once the rigging was cut, the sails would fall on the enemies, thus preventing them from effectively defending themselves. A large scythe is placed on a warship with several oars to make it fast and maneuverable. The scythe can be placed vertically or horizontally and the large weight on one end allows it to rotate if vertical or act as a counterbalance if horizontal. The scythe is activated by releasing a rope.
Manuscript B, folio 9v
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# Area of a Circle
## Pi times the radius squared.
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Area of a Circle
Credit: Mary Clark
Source: https://www.flickr.com/photos/marymerry/3122495226
Angelica’s dad is buying a round swimming pool for the yard. The brochure says \begin{align*}\text{diameter} = 24 \ ft\end{align*}. What square footage of the yard will the pool cover?
In this concept, you will learn how to find the area of a circle.
### Guidance
A circle is a set of connected points equidistant from a center point. The diameter is the distance across the center of the circle and the radius is the distance from the center of the circle to the edge.
The number pi, \begin{align*}\pi\end{align*}, is the ratio of the diameter to the circumference. We use 3.14 to represent pi in operations. You can find the area of a circle by taking the measurement of the radius, squaring it and multiplying it by pi. Here is the formula: \begin{align*}A = \pi r^2\end{align*}.
Let’s look at an example.
What is the area of the circle below?
First, write the formula.
\begin{align*}A = \pi r^2\end{align*}
Next, substitute in what you know.
\begin{align*}A=(3.14)(12)^2\end{align*}
Then, following the order of operations, figure out the exponent first and then multiply.
\begin{align*}\begin{array}{rcl} A &=& (3.14)(144) \\ A &=& 452.16 \ sq \ cm \end{array}\end{align*}
The answer is \begin{align*}A = 452.16 \ sq. cm\end{align*}.
Sometimes, you will be given a problem with the diameter and not the radius. When this happens, you can divide the measurement of the diameter by two and then use the formula.
### Guided Practice
Some students have formed a circle to play dodge ball. The radius of the circle is 21 feet. What is the area of their dodge ball circle?
First, write the formula.
\begin{align*}A = \pi r^2\end{align*}
Next, substitute in what you know.
\begin{align*}A=(3.14)(21)^2\end{align*}
Then, following the order of operations, figure out the exponent first and then multiply.
\begin{align*}\begin{array}{rcl} A &=& (3.14)(441) \\ A &=& 1,384.74 \ sq.ft. \\ \end{array}\end{align*}
The answer is \begin{align*}A = 1, 384.74 \ sq. ft\end{align*}.
### Examples
#### Example 1
Find the area of a circle with a radius of 9 inches.
First, write the formula.
\begin{align*}A= \pi r^2\end{align*}
Next, substitute in what you know.
\begin{align*}A=(3.14)(9)^2\end{align*}
Then, following the order of operations, figure out the exponent first and then multiply.
\begin{align*}\begin{array}{rcl} A &=& (3.14)(81) \\ A &=& 254.34 \ sq.in \end{array}\end{align*}
The answer is \begin{align*}A = 254.34 \ sq. in\end{align*}.
#### Example 2
Find the area of a circle with a radius of 11 inches.
First, write the formula.
\begin{align*}A= \pi r^2\end{align*}
Next, substitute in what you know.
\begin{align*}A=(3.14)(11)^2\end{align*}
Then, following the order of operations, figure out the exponent first and then multiply.
\begin{align*}\begin{array}{rcl} A & = & (3.14)(121) \\ A & = & 379.94 \ sq.in. \end{array}\end{align*}
The answer is \begin{align*}A = 379.94 \ sq. in\end{align*}.
#### Example 3
Find the area of a circle that has a diameter of 8 feet.
First, recognize that you have been given a diameter and divide by 2 to get the radius.
\begin{align*}\begin{array}{rcl} r &=& \frac{d}{2} \\ r &=& \frac{8}{2} \\ r &=& 4 \ \text{feet} \end{array}\end{align*}
Next, substitute this value, along with pi, into the formula for the area of a circle.
\begin{align*}A=\pi r^2\end{align*}
Next, substitute in what you know.
\begin{align*}A=(3.14)(4)^2\end{align*}
Then, following the order of operations, figure out the exponent first and then multiply.
\begin{align*}\begin{array}{rcl} A &=& (3.14)(16) \\ A &=& 50.24 \ sq.ft. \end{array}\end{align*}
The answer is \begin{align*}A = 50.24 \ sq. ft\end{align*}.
Credit: Jerald Jackson
Source: https://www.flickr.com/photos/12287146@N04/5070154395
Remember Angelica and the 24-foot diameter pool?
She wants to know how many square feet of ground it would cover.
First, recognize that you have been given a diameter and divide by 2 to get the radius.
\begin{align*}\begin{array}{rcl} r &=& \frac{d}{2} \\ r &=& \frac{24}{2} \\ r &=& 12 \ \text{feet} \end{array}\end{align*}
Next, substitute this value, along with pi, into the formula for the area of a circle.
\begin{align*}A=\pi r^2\end{align*}
Next, substitute in what you know.
\begin{align*}A=(3.14)(12)^2\end{align*}
Then, following the order of operations, figure out the exponent first and then multiply.
\begin{align*}\begin{array}{rcl} A &=& (3.14)(144) \\ A &=& 452.16 \ sq.ft. \end{array}\end{align*}
The answer is \begin{align*}A = 452.16 \ sq. ft\end{align*}. The round swimming pool will cover \begin{align*}452.16 \ sq. ft.\end{align*} of Drayton’s backyard.
### Explore More
Find the area of each circle given the radius or diameter. Round to the nearest hundredth when necessary.
1. \begin{align*}r = 3 \ in\end{align*}
2. \begin{align*}r = 5 \ in\end{align*}
3. \begin{align*}r = 4 \ ft\end{align*}
4. \begin{align*}r = 7 \ m\end{align*}
5. \begin{align*} r = 6 \ cm\end{align*}
6. \begin{align*}r = 3.5 \ in\end{align*}
7. \begin{align*}d = 16 \ in\end{align*}
8. \begin{align*}d = 14 \ cm\end{align*}
9. \begin{align*}d = 20 \ in\end{align*}
10. \begin{align*}d = 15 \ m\end{align*}
11. \begin{align*}d = 22 \ cm\end{align*}
12. \begin{align*}d = 24 \ mm\end{align*}
13. \begin{align*}d = 48 \ in\end{align*}
14. \begin{align*}r = 16.5 \ in\end{align*}
15. \begin{align*}r = 25.75 \ in\end{align*}
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes
### Vocabulary Language: English
TermDefinition
$\pi$ $\pi$ (Pi) is the ratio of the circumference of a circle to its diameter. It is an irrational number that is approximately equal to 3.14.
Area Area is the space within the perimeter of a two-dimensional figure.
Diameter Diameter is the measure of the distance across the center of a circle. The diameter is equal to twice the measure of the radius.
Pi $\pi$ (Pi) is the ratio of the circumference of a circle to its diameter. It is an irrational number that is approximately equal to 3.14.
Radius The radius of a circle is the distance from the center of the circle to the edge of the circle.
Squaring Squaring a number is multiplying the number by itself. The exponent 2 is used to show squaring.
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Students can download Maths Chapter 7 Mensuration Ex 7.3 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.
## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 7 Mensuration Ex 7.3
Question 1.
Find the volume of a cuboid whose dimensions are
(i) length = 12 cm, breadth = 8 cm, height = 6 cm
(ii) length = 60 m, breadth = 25 m, height = 1.5 m
Solution:
(i) Here l = 12 cm, b = 8 cm, h = 6 cm
Volume of a cuboid = l × b × h
= (12 × 8 × 6) cm³
= 576 cm³
(ii) Here l = 60 m, b = 25 m. h = 1.5 m
Volume of a cuboid = l × b × h
= 60 × 25 × 1.5 m³
= 2250 m³
Question 2.
The dimensions of a match box are 6 cm × 3.5 cm × 2.5 cm. Find the volume of a packet containing 12 such match boxes.
Solution:
Length of a match box (l) = 6 cm
Breadth of a match box (b) = 3.5 cm
Height of a match box (h) = 2.5 cm
Volume of one match box = l × b × h cu. units
= 6 × 3.5 × 2.5 cm³
= 52.5 cm³
Volume of 12 match box = 12 × 52.5 cm³
= 630 cm³
Question 3.
The length, breadth and height of a chocolate box are in the ratio 5 : 4 : 3. If its volume is 7500 cm³, then find its dimensions.
Solution:
Let the length of a chocolate be 5x, the breadth of a chocolate be 4x, and the height of a chocolate be 3x.
Volume of a chocolate = 7500 cm³
l × b × h = 7500
5x × 4x × 3x = 7500
5 × 4 × 3 × x³ = 7500
x³ = $$\frac{7500}{5×4×3}$$
x³ = 125 ⇒ x³ = 5³
x = 5
∴ Length of a chocolate = 5 × 5 = 25 cm
Breath of a chocolate = 4 × 5 = 20 cm
Height of a chocolate = 3 × 5 = 15 cm
Question 4.
The length, breadth and depth of a pond are 20.5 m, 16 m and 8 m respectively. Find the capacity of the pond in litres.
Solution:
Length of a pond (l) = 20.5 m
Breadth of a pond (b) = 16 m
Depth of a pond (h) = 8 m
Volume of the pond = l × b × h cu.units
= 20.5 × 16 × 8 m³
= 2624 m³ (1 cu. m = 1000 lit)
= (2624 × 1000) litres
= 2624000 lit
Question 5.
The dimensions of a brick are 24 cm × 12 cm × 8 cm. How many such bricks will be required to build a wall of 20 m length, 48 cm breadth and 6 m height?
Solution:
Length of a brick (l) = 24 cm
Breadth of a brick (b) = 12 cm
Depth of a brick (h) = 8 cm
Volume of a brick = lbh cu.units
Volume of one brick = 24 × 12 × 8 cm³
Length of a wall (l) = 20 m = 2000 cm
Breadth of a wall (b) = 48 cm
Height of a wall (h) = 6 m = 600 cm
Volume of a wall = l × b × h cu. units
= 2000 × 48 × 600 cm³
Number of bricks
= 500 × 50 ( ÷ by 4)
= 25000 bricks
∴ Number of bricks = 25000
Question 6.
The volume of a container is 1440 m³. The length and breadth of the container are 15 m and 8 m respectively. Find its height.
Solution:
Let the height of the container be “h”
Length of the container (l) = 15 m
Breadth of the container (b) = 8 m
Volume of the container = 1440 m³
l × b × h = 1440
15 × 8 × h = 1440
h = $$\frac{1440}{15×8}$$
= 12 m
∴ Height of the container = 12 m
Question 7.
Find the volume of a cube each of whose side is
(i) 5 cm
(ii) 3.5 m
(iii) 21 cm
Solution:
(i) Side of a cube (a) = 5 cm
Volume of a cube = a³ cu. units
= 5 × 5 × 5 cm³
= 125 cm³
(ii) Side of a cube (a) = 3.5 m a³ cu. units
Volume of a cube = 3.5 × 3.5 × 3.5 m³
= 42.875 m³
(iii) Side of a cube (a) = 21 cm
Volume of a cube = a³ cu. units
= 21 × 21 × 21 cm³
= 9261 cm³
Question 8.
A cubical milk tank can hold 125000 litres of milk. Find the length of its side in metres.
Solution:
Volume of the cubical tank = 125000 liters
= $$\frac{125}{1000}$$ m³ (1 cu.m = 1000 lit)
= 125 m³
a³ = 125 ⇒ a³ = 5³
a = 5
Side of a cube = 5 m
Question 9.
A metallic cube with side 15 cm is melted and formed into a cuboid. If the length and height of the cuboid is 25 cm and 9 cm respectively then find the breadth of the cuboid.
Solution:
Side of a cube (a) = 15 cm
Length of a cuboid (l) = 25 cm
Height of a cuboid (h) = 9 cm
Volume of the cuboid = Volume of the cube
l × b × h = a³
25 × b × 9 = 15 × 15 × 15
b = $$\frac{15 × 15 × 15}{25 × 9}$$
= 15 cm
Breadth of the cuboid = 15 cm
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Newswise — As more people become aware of the transgender and gender-nonconforming experience, many may be uncertain about the terminology used by these communities.
Here, a NewYork-Presbyterian expert breaks down some of the terms that are used to describe the spectrum of gender identity to help people better understand both the language and how to create a more inclusive environment for the estimated 1 million adults in the U.S. who identify as transgender.
One of the first steps is understanding the use of a person’s personal pronouns rather than making assumptions. This is widely accepted as a way to treat a transgender person with respect, according to Marianna da Costa, LMSW, the practice care facilitator at NewYork-Presbyterian’s Center for Special Studies and a LGBTQ advocate. For example, when you meet someone, ask which personal pronouns to use to honor them. The most commonly used pronouns are “she” and “her”; “he” and “him”; and “they” and “them.” However, it’s important to recognize that many other pronouns also exist. You can start by sharing your own preferences by saying “Hi, I’m Levi, and my personal pronouns are he and him. What are yours?”
Another good way to learn personal pronouns is to listen to find out if an individual uses pronouns that are masculine, feminine, or neutral, such as “they” and “them.”
If you accidentally use the wrong pronoun, apologize quickly and sincerely, then move on. The bigger deal you make out of the situation, the more uncomfortable it is for everyone.
“People might not realize they make a lot of assumptions about someone’s identity,” says da Costa. “To help make somebody feel welcome, it’s important to step back from assumptions a little bit and speak to people about how they personally identify themselves.”
Here, da Costa explains some common terms that represent a number of identities in the transgender and gender-nonconforming communities.
Agender – someone who identifies as having no gender or being without a gender identity (genderless, gender-free, nongendered, ungendered)
Androgynous – someone whose gender expression is a combination of masculine and feminine characteristics
Bigender, trigender, pangender – someone who identifies with two or more genders
Cisgender – a person whose sense of personal identity and gender corresponds with their sex assigned at birth
Gender expression – refers to the aspects of a person’s behavior, mannerisms, interests, and appearance that are associated with gender in a particular cultural context, specifically with the categories of femininity or masculinity
Gender fluid – someone who does not identify as having a fixed/static gender
Gender nonconforming – gender expression by an individual that does not match masculine and feminine gender norms
Gender queer – someone who does not subscribe to conventional gender distinctions but identifies with neither, both, or a combination of male and female genders
Nonbinary – someone who identifies outside of the gender binary; does not identify with masculinity or femininity as it is culturally defined
TGNC – transgender and gender nonconforming
Transfeminine – describes a person who was assigned male at birth but identifies on the feminine spectrum
Transgender – a person whose sense of personal identity and gender does not correspond with their sex assigned at birth
Transmasculine – describes a person who was assigned female at birth but identifies on the masculine spectrum
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Maglev (magnetic levitation) trains have attracted a lot of interest over the years because of their high speed capabilities. Maglev got off to a slow start; the first passenger Maglev, opened in 1984, was a shuttle in Birmingham International Airport which only traveled at speeds of up to 26 mph (42 kph). Since then the technology has come on leaps and bounds and the fastest passenger train in the world is currently the Shanghai Maglev Train which can reach speeds of up to 268 mph (431 kph).
Now, a team of researchers at Southwest Jiaotong University have built a prototype testing platform to trial a new model called “super-maglev” which could, in theory, reach speeds of up to 1,800 mph (2,900 kph).
The high speeds of this train are achieved by using a vacuum tube to reduce the air resistance that restricts the speed of other maglev trains. The team reduced the air pressure in the testing tube to 10 times less than the atmospheric pressure at sea level which reduced drag substantially and therefore allowed higher speeds.
The speeds attainable by super-maglev are currently limited by the small size of the test platform; however, if longer tunnels are generated they think that it could achieve speeds around three times that of a commercial aircraft. Speeds such as this would allow you to travel from Paris to Moscow in around an hour if a straight tunnel existed, which is pretty impressive to say the least.
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Introduction: Leave It to Beavers (02:01)
Beavers can turn a desert into a garden by controlling water direction and building landscapes. Conservationists try to rehabilitate the species. (Credits)
River Dams (03:46)
Beavers are blind and slow, but they are extraordinary engineers. As vegetarians, they gnaw through bark to get to the sugary substance underneath; their teeth are orange and self-sharpen. Dams made by beavers filter billions of tons of water and prevent droughts.
Beaver Pelts (02:24)
Beaver trapping for over 200 years results in their near extinction. The potential for flooding makes beavers a nuisance to housing developments, farms, and golf courses.
Wildlife Redirection in Canada (06:22)
If a beaver hears a recording of running water, it believes the pond is draining and will start reinforcing its dam. Michel LeClair stops beavers from flooding roads in Gatineau Park by placing posts 15 feet away from a culvert. Wildlife managers need to be plumbers.
Rocky Mountains (03:40)
During spring, birds and mammals feed in beaver created habitats. A tail slap warns of potential threats. Kits supplement their mother's milk with green leaves; offspring do not leave the family until they are over two years old.
Elk Island National Park (02:36)
Dr. Glynnis Hood studies the descendants of seven beavers that were reintroduced in Alberta. Maps demonstrate active and inactive ponds over the past 54 years. Beavers mitigate the effects of drought and keep water on the landscape.
Sierra Nevada Mountains (03:46)
Dr. Suzanne Fouty and Carol Evans discover a beaver habitat with sandhill cranes and mule deer. Cattle are kept away from the damaged sections of streams. Beavers create small pockets of groundwater.
Beavers in Midsummer (05:59)
Kits explore their surroundings while the two-year-old goes upriver to find his own territory. The family relocates after depleting the trees. A beaver named Timber undergoes rehabilitation after being injured and traumatized by teenage boys.
New Beaver Territory (03:43)
The two-year-old begins repairing a disused lodge and half-broken dam. The water level rises. If another male arrives, the two will fight for the territory; a female arrives and courtship begins.
Beaver Reintroduction (06:42)
Five orphaned beavers rescued from a drainage ditch arrive at a valley in Colorado to rehabilitate the landscape. Sherry Tippie explains why the species is the keystone to an aquatic ecosystem. Creeks meander and support life; fathers show the kits how to behave.
Timber's Progress (02:26)
The beaver will undergo a year of training. He begins gnawing sticks, exploring by himself, and breathing underwater for up to a minute. Beavers mature at two-years-old. Timber disappears from the pond.
Beavers in Autumn (02:24)
The two-year-old's lodge has hollowed out areas for eating and sleeping and several underwater entrances. Beavers do not hibernate so they need to create a larder of trees underwater. A moose tries to raid the food supply.
Locating Timber (02:50)
Michele Grant discovers a beaver skull is devastated. At a neighbor's pond, she finds Timber interacting with an adult beaver and her kits. She feels validated about the rehabilitation.
Beavers in Winter (03:14)
Wolves and Coyotes howl; bears hibernate. The male beaver risks exposure to predators to collect food for his pregnant mate. His lodge hosts deer mice, insects, frogs, and muskrats.
Credits: Leave It to Beavers (00:52)
For additional digital leasing and purchase options contact a media consultant at 800-257-5126
(press option 3) or [email protected].
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PS-1-2009
# PS-1-2009 - EE 261 The Fourier Transform and its...
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Unformatted text preview: EE 261 The Fourier Transform and its Applications Fall 2009 Problem Set One Due Wednesday, September 30 1. Some practice with geometric sums and complex exponentials (5 points each) We’ll make much use of formulas for the sum of a geometric series, especially in combination with complex exponentials. (a) If w is a real or complex number, w 6 = 1, and p and q are any integers, show that q X n = p w n = w p- w q +1 1- w . (Of course if w = 1 then the sum is ∑ q n = p 1 = q + 1- p .) Discuss the cases when p =-∞ or q = ∞ . What about p =-∞ and q = + ∞ ? (b) Find the sum N- 1 X n =0 e 2 πin/N and explain your answer geometrically. (c) Derive the formula N X k =- N e 2 πikt = sin(2 πt ( N + 1 / 2)) sin( πt ) 2. Some practice combining simple signals. (5 points each) The triangle function with a parameter a > 0 is Λ a ( t ) = Λ( t/a ) = ( 1- 1 a | t | , | t | ≤ a , | t | > a The graph is ! a a 1 1 The parameter a specifies the width, namely 2 a . Alternately, a determines the slopes of the sides: the left side has slope 1 /a and the right side has slope- 1 /a . We can modify Λ a by scaling the height and shifting horizontally, forming b Λ a ( t- c ). The slopes of the sides of the scaled function are then ± b/a . The graph is: c ! a c c+a b bLa(t ! c) Express each of the following as a sum of two shifted, scaled triangle functions b 1 Λ a 1 ( t- c 1 )+ b 2 Λ a 2 ( t- c 2 ). Think of the sum as ‘left-triangle’ plus a ‘right-triangle’ (‘right’ meaning to the)....
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# how do you turn a decimal to fractions and percents?
10,440 results, page 3
1. ### math fractions and decimals
How do you can you change a decimal to a fraction when the fraction looks like this 0.43 3/4 or .16 2/3 .How can I change this to a fraction?I tried dividing it by 100 but it doesn't give me the right answer.
2. ### math
show how to simplify before you multiply 3 1/2 x 2 2/7 4445456743+38067738476= change both mixed fractions to "improper" fractions 3 1/2 x 2 2/7 = 7/2 x 16/7 =8 (after you cancel)
3. ### math
i am having to add, subtract, multiplication and division on fractions. whloe numbers with fraction. My question is that i do not know how to do fractions at all and i need some help
4. ### Math
Prompt. Use equivalent fractions to order therse fractions from least to greatest: 2/3,1/2, 4/12, 5/6. Explain the steps you took to find your answer.
5. ### Statistics
A total of 16 mice are sent down a maze, one by one. From previous experience, it is believed that the probability a mouse turns right is .38 a) What is the probability that exactly 8 of these 16 mice turn right? b) What is the probability that 8 or fewer turn right? c) What ...
6. ### math
-8 2/3 - -5 1/3 How would you set up? Go here and scroll to 4 http://www.themathpage.com/ARITH/add-fractions-subtract-fractions-1.htm the answer would be -3 1/3
7. ### math
I need to know how to do percents. Example: what is 6% of 18?
8. ### Math
3/4 changed to percents? would it be 75%
9. ### math-percents
what percent is .624?
this is from homework work book . write each fraction or mixed numberas a decimal. use bar notation if the decimal is a repeating decimal
11. ### English
1. We can turn off the water when we are not using it. 1-1. We can turn off the water when we do not use it. 2. We can turn off the water when we are brushing teeth. 2-1. We can turn off the water when we do not brush teeth. ==================== Which ones are grammatical? Do ...
12. ### math
7 1/6 - 6 4/6 = ? could you please show me the steps to do this problem? thank you, ryan 7 1/6 = 6 7/6 - 6 4/6 = -6 4/6 ------- 3/6 = 1/2 mixed fractions are useless in calculations so the first thing you have to do is change them to improper fractions 7 1/6 + 6 4/6 =43/6 + 40...
13. ### math
Describe some practical applications for fractions in your daily life. What are the challenges you have experienced regarding the use of fractions? Explain your answers.
14. ### Math
Describe some practical applications for fractions in your daily life. What are the challenges you have experienced regarding the use of fractions? Explain your answers.
15. ### fractions
How do i add two negative fractions?
16. ### equivalnet fractions
what are two equivalent fractions for 5/15?
17. ### fractions
ordering fractions least to greatest 3/7 1/9 2/3
18. ### Math - fractions
Name 2 fractions between 1/2 and 5/7
19. ### Math - fractions
Name 4 fractions between 1/2 and 5/7
20. ### math
Decimal numbers with digits both before and after the decimal point, such as 16.75, are referred to as: A. the quotient. B. the remainder. C. mixed decimal numbers. D. decimal point numbers.
21. ### Pre-algebra
how do you change interst to percents?
22. ### Percents (Math)
Need help, please. What percent of 30 is 2 1/2?
23. ### math 1350
If the following fractions are arranged from smallest to largest, then which fraction would be in the middle? Explain. Show all work using fractions(NOT DECIMALS). 2/3, 4/5, 3/7, 5/9, 3/4
24. ### Decimal lesson
I need to find a sample lesson plan on rounding decimals using the number line.... and converting fractions to decimals. Do you know where I could find these lessons?
25. ### math
write two decimals that are equivilant to: 0.68 0.9 I think you mean two fractions because the decimal representation is unique (with some exceptions we'll skip for now) 0.68 = 68/100 = 34/50 = 17/25 0.9 = 90/100 = something you can do now
26. ### elementary math
I am going to be a teacher one day. I need help explaining this: A student asks whether it is easier to add fractions or multiply fractions. What my respone should be?
27. ### Math
Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum. 1/7 = ?/? + 3/14 = ?/? __________ ? - ??
28. ### physics
Hi! could anyone help me with this question please, I really don't know how to do this at all. Thank you so much. Question:A 330 turn solenoid with a length of 21.0 cm and a radius of 1.40 cm carries a current of 2.10 A. A second coil of four turns is wrapped tightly around ...
29. ### math
how do you find percents and degrees when there are 50 people and not 100
30. ### math
Can your x-axis values be percents in a bar graph?
31. ### math/fractions
Ok one more question. I had this problem: Kristi jogged for 3/5 of an hour, swam for 1/2 of an hour, and rode her bicycle for 3/4 of an hour. How long did she exercise? I took it to mean you had to add all the fractions together. So I found the lcd of all three numbers which ...
32. ### Algebra I
**Match each word or phrase w/ its definition** Word Bank: A) least common multiple (LCM) B) repeating decimal C) reciprocals D) dimensional analysis E) terminating decimal F) least common denominator (LCD) G) multiple ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ GIVEN QUESTIONS W...
33. ### Physics
A car of mass = 1200 traveling at 60.0 enters a banked turn covered with ice. The road is banked at an angle , and there is no friction between the road and the car's tires.What is the radius of the turn if = 20.0 (assuming the car continues in uniform circular motion around ...
34. ### Geometry
Write an equation of a line in slope intercept form that is parallel to y = 3x+6 and passes through the point (-10, 2.5). Do not use spaces and enter fractions as improper reduced fractions when needed.
35. ### Algebra
3 gears are connected so that the two turns of the first wheel turn ii wheel nine times and the three terms of ii wheel turn the third wheel 5 times. A. If you turn the first wheel once, how many times does the third wheel turn? B. How many times must you turn the first wheel ...
36. ### physic
An SUV is negotiating a horizontal unbanked turn. The radius of the turn is 20m, the center of gravity of the vehicle is 1m above the ground and in the middle between the left and right side. The seperation of the left and right wheels is 1.8m What is is the greatest speed at ...
37. ### Precalculus
Suppose 3 mg of a drug is injected into a person's bloodstream. As the drug is metabolized, the quantity diminishes at the continuous rate of 6 % per hour. Find a formula for Q(t), the quantity of the drug remaining in the body after t hours. Find approximations to two decimal...
38. ### Algebra 1
How do you put percents into degrees? For example: 25%= ?degree
39. ### math
how you figure percents like percent of438 to 789
40. ### Math - Percents
If 200% of a number n is decreased by 12.5%, the result is 28. What is the value of n?
41. ### math
Match the term with it's meaning real numbers irrational numbers rational numbers integers whole numbers natural numbers radical square root perfect squares cube roots terminating decimals repeating decimals truncate radicand a decimal which can be expressed in a finite number...
42. ### math (stats)
Enter your answers as decimals or fractions, rather than percents. In a family with 7 children what is the probability of having 4 boys and then 3 girls, in that order? (Exclude multiple births and assume all outcomes are equally likely). Preview In a family with 7 children, ...
43. ### Math
What is the rotational symmetry as a fraction of a turn and the angle of the smallest turn of letter I
44. ### science
when you turn on a lamp, then turn it off, explain what happens to the circuit.
45. ### algebra
find the L.C.D of each of the following and groups of fractions and then express the fractions of each group in terms of the L.C.D of that group... please show work 1\2,3\4,11\16 2\3,1\8,5\12
46. ### math
find two fractions with a sum that is greater than 1.6 but less than 1.9. write your fractions in simplest form and compute their exact sum.
47. ### Math
From these fractions choose <,>,or= to make a true statement 1. 11/21<2/3 2.1/2=9/18 3. 2 3/8>2 8/24 Order the fractions from least to greatest 3/5 1/4 1/2 2/5 Answer: 1/3 2/5 1/2 3/5 6 3/4, 6 1/2, 6 5/6, 6 3/8 Answer: 3/8 1/2 3/4 5/6
48. ### math
write the pair of the fractions as a pair of fractions with a common denominator : a.) 2/4 and 7/8. b.) 3/10 and 1/2. my answer for the a.) is 16/32-28/32. for b.) is 6/20-10/20 please let me know is my answers is right or not
49. ### Fractions
Is the answer to 3/9 x 4/8 same as the answer to 4/9 x 3/8? Why or why not? 3/9 x 4/8 = 1/6 4/9 x 3/8 = 12/72 (I multiplied straight across after reducing the fractions as much as they could be reduced)
50. ### math
cecile tosses 5 coins one after another a. how many different outcomes are possible b. draw a tree to illustrate the different possibilities c. in how many ways will the first coin turn up heads and the last coin turn up tails d. in how many ways will the second and thrd and ...
51. ### math
identify the rotational symmetry asa fraction of a turn and the angle measure of the smallest turn
52. ### arithmetic
a stock clerk had 600 pads on hand. He then issued 3/8 of his supply of pads to division X,1/4 to division Y and 1/6 to division Z. The number of pads remaining in stock is? I don't get how to solve this problem. In arithmetic problems, the word "of" indicates that you should ...
53. ### math
I forgot how to add and subtract mixed # fractions. How do you do it? ex) 3/7+5/6=1 11/42- How did they get this answer?? ex) 5 6/13-2 8/13=2 11/13- How did they get this answer?? ex) 3/7+5/6=1 11/42 You need to find a common denominator when adding or subtracting fractions. 3...
54. ### percents
If I need to mutliply 80.00 times 8.25%, where do i put my decimals fot the percentage?
55. ### Math
Order the decimals and percents from least to greatest 0.12, 0.21, 1 / 4, 0.4 my answer is 0.12 0.21.0.25 because 1/4 equal. 25 and 0.4
56. ### high school
which one of the fractions contain like fractions A.6/7or 1/5/7,B.3/2or 2/3 C.5/6or10/12,D.3/1/2or 4/3/4
57. ### Math
What is the solution of 1/3 + 3/10 + 1/5? Hi, I don't really know how to add fractions very well yet. Can you explain how to add these 3 fractions? Thanks so much
58. ### fractions
do you have fractions on this website? Yes
59. ### Decimals to Fractions(simplify the fractions)
0.2=1/5? 0.9=9/10 0.80=4/5? 0.55=11/20
60. ### ordering fractions
order these fractions 1/3 1/8 1/6
61. ### fractions
Find 3 equivalent fractions for 4/12.
62. ### physics
A woman is riding a Jet Ski at a speed of 27.9 m/s and notices a seawall straight ahead. The farthest she can lean the craft in order to make a turn is 21.0°. This situation is like that of a car on a curve that is banked at an angle of 21.0°. If she tries to make the turn ...
63. ### physics
A woman is riding a Jet Ski at a speed of 20 m/s and notices a seawall straight ahead. The farthest she can lean the craft in order to make a turn is 20°. This situation is like that of a car on a curve that is banked at an angle of 20°. If she tries to make the turn without...
64. ### physics
A woman is riding a Jet Ski at a speed of 20 m/s and notices a seawall straight ahead. The farthest she can lean the craft in order to make a turn is 20°. This situation is like that of a car on a curve that is banked at an angle of 20°. If she tries to make the turn without...
65. ### Math
Adam wants to compare the fractions 3/12, 1/6, and 1/3. He wants to order them from least to greatest and rewrite them so they all have the same denominator. Explain how adm can rewrite the fractions.
66. ### Math/fractions
I need help with subtracting fractions I have no idea if I'm doing it right. Please help. 3/7-9/21 Fist you find a least common denominator, right? So it's 21 Do you then multiply 3/7 to 3/3 so it will be 9/21 So, 9/21 - 9/21 = 1
67. ### math
will some one please!!!! please!!! help me I'm doing wacky wordies, only have 3 to do!!! decimal decimal decimal ed ot overs pos'-i'-tive' thanks so much!!
68. ### Math
My question is: WRite the percent as a fraction and as a decimal. 0.06% I don't know how many places I need to move that decimal to convert this percent into a decimal.
69. ### Mathematics 1
Find the L.C.D. of each of the following groups of fractions and then express the fractions of each group in terms of the L.C.D. of the group. 1/3, 3/5, 21/25, 13/15
70. ### Calculus - Partial Fractions
What is the integral of 7e^(7t) Divided By e^14t+13e^7t+36 Using partial fractions
71. ### math
caculate the following fractions 1/3+ 2/3+ 5/3 what is the answer to these fractions and show houw you get the answer. please.
73. ### math
the difference between two fractions is 1/10. the smaller fraction is 4/7. what is the sum of the two fractions?
74. ### maths
calculate the area 1.76 and 1.76 writr your 2 decimal answer to the two decimal places. i'm not sure if its 3.0976 and to the two decimal place its 3.10 could someone tell me if im right. thankyou
75. ### Algebra
sorry clicked wrong button. solve: 9 -1=x-11 ____ _____ x-5 x+5 these are supposed to be fractions Your equation is illegible, and can be interpreted too many ways. Try writing it on a single line, using parentheses for clarity and / for fractions
what fraction of a turn does a minute hand turn through between 6:25pm and 7:15pm 10:24pm and 11.58pm
77. ### Physics
Two identical racing horses go around a semicircular turn in a racecourse. The horses have the same speed, but horse A is on the inner side while horse B is on the outer side of the circular turn. Which horse has the greater acceleration while in the turn?
78. ### Math/Fractions
I have this fraction: 6 2/9 + 1 3/4 - 3 5/6= Okay First I changed the mixed numbers into improper fractions. I got this: 56/9 + 7/4 + 23/6 Then I thought you have to find the least common denominator, which for 9,4, and 6 would be 36. Then I muliplied the fractions by 4, 9, ...
79. ### Math
Write 8 fractions equal to one-half (not including one-half) using only the digits 0, 1, 2 and 5. Each digit may be used more than once, but you may not use decimal points or arithmatic operatons. Numerators cannot be larger than 100. You may not use negative numbers.
80. ### math
which of the following percents can also be expressed as a mixed number? a.310% b.49% c.7.4% d.0.001%
81. ### Math percents
a) 2/5 of 80% of 3000 cm b) 3/5 of 150% of 50 mL c) 4/5 of 12.5 % of 10 cm2 please explain how u got the answer thank u!!!!
82. ### Help with math
Explain how you could write 35% as the sum of two benchmark percents or as a multiple of a percent.
83. ### Math
Explain how you could write 35% as the sum of two benchmark percents or as a mutiple of a percent
84. ### Math
2/5=what I assume you are looking for a decimal. Just divide 5 into 2, and the answer will be the decimal. However, if you are looking for a percentage, multiply the decimal by 100. I hope this helps. If not, repost with a clearer question. Thanks for asking.
85. ### Math
How do you rename as a fraction and decimal 55 5/9% You should know that 5/9 is 5 repeating, so the decimal is 55.5%(with a bar over the decimal part). 5/9 is the fraction
86. ### Calculus
State the growth factor in each of the following situations. Newspaper readership is declining by 7 1/3 % per year. A bouncing ball rebounds to 1/3 of its previous height. Dont know how to solve these fractions:\ I just hate working with fractions.
87. ### math I NEED HELP RIGHT KNOW
1. 1/10 x 3/4 A.15/2 B.2/15 C.3/40 D.40/30 2.4/5 of 40 A.32 B.1/32 C.12 D.44/5 3.1/3 of 3 A.1/18 B.1/3 C.1 D.1/9 this is the Lesson 4: Multiplication of Fractions Review Math 6 A Unit 7: Multiplying and Dividing Fractions quiz, so if you know the rest of the answers plz ...
88. ### math
Arrange the fractions in ascending order. Or, if the fractions are equivalent, answer "Equivalent". 7/22,2/5,9/24
89. ### Math
The sum of two fractions is 1. If one of them is 3/8 greater than the other, what are the two fractions?
90. ### equivalent fractions and the numberline
Draw a number line to show how are these fractions are equivalent 3/4=6/8 and 1/4=2/8
91. ### Math
1/6 is the sum of two unit fractions. how may pairs of unit fractions will equal 1/6?
92. ### Math:[
how do you turn decimals to fractions? http://www.webmath.com/dec2fract.html This is a good tutorial. wdwqdr What is an Improper Fraction?
93. ### math 6th
3/8 as a decimal is 7/5 as a decimal is 21/7 as a decimal is 5/3 as a decimal is
94. ### math
what number is 24% of 95. Sorry but i don't understand how to get numbers using percents. another problem im stuck with is what percent of 90 is 60
95. ### Math
Explain how u can write 35% as a sum of 2 benchmarks percents or as multiple of a percent? PLEASE TELL ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:)
96. ### math
Stocks are always quoted in A. quarter lots. B. quarters of a dollar. C. decimals. D. percents. B?
97. ### Math
Stocks are always quoted in A. quarter lots. B. quarters of a dollar. C. decimals. D. percents. c?
98. ### Math
I need help figuring this out, I tried to simplify 3 times this are fractions, I can't express fractions in here.. -4/7x=12/35 (-7/4) x (-4/7) = -7/4 x 12/35 1 times x = 84/140 I am having trouble simplifying I got so far 42/70, 21/35 and are wrong please help
99. ### Physics
A 765-kg car is travelling north and makes a gradual turn to the east at a constant speed of 15 m/s. The radius of the turn is 112 m. I calculated the angular velocity to be 0.135 m/s and the friction force needed to be 1410.86 N. What is the smallest radius for which the turn...
100. ### Calc easy
Having trouble getting the correct solution. The integral of “x squared” in the numerator and “x squared plus x minus 6” in the denominator. S X2 / (X2 + x – 6) dx Thanks! That's a messy one. According to my table of integrals. The answer is -x/6 -(1/72)loge(x^2 +x -...
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Current Global Positioning System
Background and Theory
Stand-Alone GPS Performance
In the GPS positioning problem, a user measures the distance to a satellite and determines the radius of a ‘range ring’ that describes all the possible positions of the user relative to the satellite. Using a minimum of four satellites the user can calculate its position at the intersection of these range rings. Since each one of these range measurements contain errors, the true user position is contained within a region of position error, which varies in size depending on the relative geometry of the satellite constellation. This concept is demonstrated 2-dimensionally in Figures 1 and 2 below. In Figure 1, the two satellites are nearly at right angles to one another, and so this gives a smaller region of position error. In Figure 2, there is a much smaller angle of separation between the two satellites, and as a result, the region of possible user position error is amplified in the direction transverse to the line between the user and the two satellites. Since there is a lack of information of the user position in the ‘transverse’ direction, there is also less certainty about the user position in that direction. In a 3-D application, as with the GPS constellation, the distribution of amplified user position error is described by a geometric Dilution of Precision factor (DOP). Just as in the 2-dimensional case, DOP is a function of the constellation geometry and has axes of information which are generally better than others.
An analysis of the GPS measurement equations can provide insight into the GPS system performance in terms of DOP and the pseudorange measurement errors. A GPS position solution is obtained by varying a linearized estimate of user position until the difference between the estimate and the measured position is minimal. The GPS measurment is described by the following equation:
HDx = Dr (1)
Dx = the offset between measured user position and linearized position
Dr = the offset in pseudorange from the pseudorange values that correspond to the linearization point
H = is a 4x4 matrix describing the direction from the user to the satellite and the user’s time offset from GPS time.
The process of solving for a GPS position solution involves a minimization of the difference between the linearized user position and ‘true’ user position. The offset in user position, Dx , can be expressed as
Dx = xT – xL + dx (2)
xT = the error free position and time
xL = the linearized position and time
dx = the error in the position and time estimate
Solving equation 1 by a method of least squares yields
dx = [(HTH)-1HT]dr (3)
dr = difference between the error-free pseudorange values and the pseudorange values at the linearization point.
By modifying the linearization point until dx is minimized, the final linearization point can be used to describe the measured user position.
The pseudorange errors are considered to be zero mean Gaussian random variables. As a result, the relationship between the GPS position solution error and the pseudorange measurement error can be obtained from the covariance of
cov(dx) = (HTH)-1cov(dr) (4)
The components of dr are usually assumed identically distributed and independent and have a variance equal to the square of the satellite user equivalent range error (UERE). Under this assumption, the covariance of the errors in the computed position and time bias is a scalar multiple of (HTH)-1.
The dilution of precision parameters are defined in terms of the ratio of the components of cov(dx) and sUERE. It is also assumed that local user coordinates are being used in the cov(dx) where the x, y, and z axes correspond to the east, north, and up directions respectively. The vertical and horizontal DOP parameters, VDOP and HDOP, can be expressed in terms of the diagonals of (HTH)-1 by expanding (HTH)-1 in component form
The vertical and horizontal DOP parameters are expressed in terms of (HTH)-1 as follows:
Ultimately, the error in the GPS position solution can be expressed as the product of a DOP geometry factor and a pseudorange error factor.
sp = the standard deviation of the positioning accuracy
DOP = the geometric dilution of precision factor
sUERE = the standard deviation of the satellite pseudorange error
It follows that:
= standard deviation of vertical position (11)
= standard deviation of horizontal position (12)
Expected values for vertical and horizontal position error can be predicted by analyzing VDOP, HDOP, and sUERE.
Pseudorange Errors: sUERE
The GPS measurement errors are caused by corruptions in the time that it takes a signal traveling at the speed of light to traverse the straight-line distance between the user and a satellite. Delays on the signal speed as it passes through the atmosphere, reflections from objects nearby the receiver, and receiver hardware delays all are possible sources of timing error. The total error in the GPS timing measurement can be expressed as:
dtD = dts + dteph + dtatm + dtnoise + dtmp + dthw + dtsa (13)
dts = satellite clock error
dteph = satellite position error
dtatm = atmospheric delays
dtnoise = receiver tracking noise
dtmp = multipath delay
dthw = receiver hardware bias
dtsa = selective availability (if on)
The errors from each of these components are root sum squared to form the total system UERE as is described by Figure 3 below. The result yields that the user equivalent range error is Gaussian distributed with a 1-sigma value of 8 meters. With a Gaussian distribution, 68% of the possible values fall within the ± 1s of the mean; and approximately 95% fall within ± 2s of the mean.
Predicted Horizontal and Vertical Position Error Using VDOP and HDOP
VDOP and HDOP can be directly calculated from GPS observation measurements using equations 8 and 9. Figure 4 shows variation in HDOP and VDOP over a 24-hour period. Note that the average values for HDOP and VDOP are 1.6 and 2.0 respectively. This shows that for a given sUERE, vertical errors will be generally worse than horizontal position errors.
Since the errors in the computed position are assumed to be zero mean Gaussian errors, it follows that 95% of the measurement error will fall within two standard deviations of the position error predicted by equations 11 and 12. Assuming average values of HDOP and VDOP, estimates of the expected vertical and horizontal position error are given by:
Vertical Position Error:
= 32 meters = ± 105 feet (14)
Horizontal Position Error:
= 2*1.5*8 = 24 meters = ± 79 feet (15)
GPS Onboard the Boeing 777
The 777 is equipped with dual (left and right receivers) which the flight management computer (FMC) uses to update the inertial navigation sensors. The benefit of having two receivers is that the FMC can either use the receiver that has a better view of the GPS constellation, or it can average the output of the two receivers and remove some of the uncommon random errors. If one receiver, for example, incurred significant multipath errors during approach, then the averaged output would have a reduced multipath error. The overall effect would be that unpredictable errors due to multipath and receiver tracking noise would be reduced while the common mode errors would remain unchanged. However, the details of how the dual GPS measurements are processed remain unknown.
The processed GPS position solutions were sampled once every second and recorded in latitude, longitude, and height format. Neither the raw pseudorange measurements, nor the time of signal transmission were recorded by the FMC. For this reason, it was impossible to analyze the processing algorithm or to download the corresponding broadcast ephemeris for the time that the measurements were made.
A major difficulty in analyzing the accuracy of GPS measurements made on an aircraft is determining a reliable estimate the truth. In the case of GPS altitude, the aircraft also measures pressure altitude and inertial vertical speed. Even though the pressure altitude is corrected for local variations in mean sea-level pressure, that parameter is known to have decreased accuracy near the ground due to ground effect. So, when the airplane is near the ground, the baro-corrected pressure gives values approximately 50 to 100 feet lower than expected, and the overall accuracy of the baro-corrected pressure is quoted as ± 100 feet. The vertical inertial sensors integrate measured accelerations on the aircraft and output inertial vertical speed as a function of time. This inertial vertical speed can be integrated to obtain estimates of altitude change over short periods of time; however, the inertial vertical sensors are also known to have drifting tendencies and cannot accurately resolve changes in vertical speed below 10 ft/min2. The changes in altitude measured by the inertial vertical sensors were referenced to the transition time when the landing gear sensors indicated the airplane was on the ground. For this reason, all altitude measurements were referenced to this point where the wheels contacted the ground. The associated altitude measurements are termed as: height above takeoff (HATO) and height above touchdown (HAT) respectively.
‘Truth’ values for latitude and longitude were a little more difficult to obtain. In the case of horizontal position, the only time when the location of an airplane is known is when it is in the vicinity of an airport or a DME. It was determined that the simplest way to approximate the airplane’s position was to use the recorded localizer frequency and the landing location during approach. After determining the exact runway that the airplane was using, surveyed values for each end of the runway could be used to estimate the airplane’s approximate position. Although a problem arose due to the fact that there was no way to precisely determine the airplane’s position along the runway at any point in time.
For this reason, GPS position errors were restricted to the direction transverse to the centerline of the runway. When the localizer deviation is near zero, the aircraft is known to be aligned with the center of the runway; and using surveyed positions for each end of the runway, it was possible to determine the GPS horizontal position error transverse to the runway as a function of time. It was assumed that the along-track position error was similar to the transverse position error.
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normal - Maple Help
normal
normalize a rational expression
Calling Sequence normal(f) normal(f, expanded)
Parameters
{f} - algebraic expression
Description
• The expression f is converted to factored normal form. This is the form numerator/denominator, where the numerator and denominator are relatively prime polynomials with integer coefficients.
• The normal command provides basic simplification and recognizes expressions equal to zero in the domain of rational functions. This includes any expression constructed from sums, products and integer powers of integers and variables.
• If f is a list, set, range, series, equation, relation, or function, normal is applied recursively to the components of f. In the case of a series, for example, this means that the coefficients of the series are normalized.
• If f contains subexpressions not in the domain of rational functions, such as square roots, powers, and functions, normal is first applied recursively to these objects. They are then frozen (see the frontend function) to unique names so that the form of f can be simplified. For such cases, normal may not recognize when an expression is equal to zero.
• If normal is called with the second argument, expanded, the numerator and denominator will be expanded polynomials.
Examples
> $\mathrm{normal}\left({x}^{2}-\left(x+1\right)\left(x-1\right)-1\right)$
${0}$ (1)
> $\mathrm{normal}\left(\frac{{x}^{2}-{y}^{2}}{{\left(x-y\right)}^{3}}\right)$
$\frac{{x}{+}{y}}{{\left({x}{-}{y}\right)}^{{2}}}$ (2)
> $\mathrm{normal}\left(\frac{{f\left(x\right)}^{2}-1}{f\left(x\right)-1}\right)$
${f}{}\left({x}\right){+}{1}$ (3)
> $\mathrm{normal}\left(\left\{\frac{2}{x}+\frac{y}{3}=0,\frac{1}{x}-\frac{5}{{x}^{2}}=1\right\}\right)$
$\left\{\frac{{x}{-}{5}}{{{x}}^{{2}}}{=}{1}{,}\frac{{y}{}{x}{+}{6}}{{3}{}{x}}{=}{0}\right\}$ (4)
> $\mathrm{normal}\left(\mathrm{sin}\left(x\left(x+1\right)-x\right)\right)$
${\mathrm{sin}}{}\left({{x}}^{{2}}\right)$ (5)
> $\mathrm{normal}\left(\frac{1}{x}-\frac{1}{{x}^{2}}<5\right)$
$\frac{{x}{-}{1}}{{{x}}^{{2}}}{<}{5}$ (6)
> $g≔\left[\mathrm{seq}\left(\frac{7ix}{{i}^{2}x+1}+\frac{1}{x},i=1..4\right)\right]$
${g}{≔}\left[\frac{{7}{}{x}}{{x}{+}{1}}{+}\frac{{1}}{{x}}{,}\frac{{14}{}{x}}{{4}{}{x}{+}{1}}{+}\frac{{1}}{{x}}{,}\frac{{21}{}{x}}{{9}{}{x}{+}{1}}{+}\frac{{1}}{{x}}{,}\frac{{28}{}{x}}{{16}{}{x}{+}{1}}{+}\frac{{1}}{{x}}\right]$ (7)
> $\mathrm{normal}\left(g\right)$
$\left[\frac{{7}{}{{x}}^{{2}}{+}{x}{+}{1}}{{x}{}\left({x}{+}{1}\right)}{,}\frac{{14}{}{{x}}^{{2}}{+}{4}{}{x}{+}{1}}{\left({4}{}{x}{+}{1}\right){}{x}}{,}\frac{{21}{}{{x}}^{{2}}{+}{9}{}{x}{+}{1}}{\left({9}{}{x}{+}{1}\right){}{x}}{,}\frac{{28}{}{{x}}^{{2}}{+}{16}{}{x}{+}{1}}{\left({16}{}{x}{+}{1}\right){}{x}}\right]$ (8)
> $f≔\mathrm{series}\left(\frac{xy}{x+y}+\frac{1}{x},x=1,3\right)$
${f}{≔}\frac{{y}}{{1}{+}{y}}{+}{1}{+}\left(\frac{{y}{-}\frac{{y}}{{1}{+}{y}}}{{1}{+}{y}}{-}{1}\right){}\left({x}{-}{1}\right){+}\left({-}\frac{{{y}}^{{2}}}{{\left({1}{+}{y}\right)}^{{3}}}{+}{1}\right){}{\left({x}{-}{1}\right)}^{{2}}{+}{O}{}\left({\left({x}{-}{1}\right)}^{{3}}\right)$ (9)
> $\mathrm{normal}\left(f\right)$
$\frac{{2}{}{y}{+}{1}}{{1}{+}{y}}{-}\frac{{2}{}{y}{+}{1}}{{\left({1}{+}{y}\right)}^{{2}}}{}\left({x}{-}{1}\right){+}\frac{{{y}}^{{3}}{+}{2}{}{{y}}^{{2}}{+}{3}{}{y}{+}{1}}{{\left({1}{+}{y}\right)}^{{3}}}{}{\left({x}{-}{1}\right)}^{{2}}{+}{O}{}\left({\left({x}{-}{1}\right)}^{{3}}\right)$ (10)
If normal is called with the second argument, expanded, the numerator and denominator will be expanded polynomials.
> $\mathrm{normal}\left(\frac{1}{x}+\frac{x}{x+1}\right)$
$\frac{{{x}}^{{2}}{+}{x}{+}{1}}{{x}{}\left({x}{+}{1}\right)}$ (11)
> $\mathrm{normal}\left(\frac{1}{x}+\frac{x}{x+1},\mathrm{expanded}\right)$
$\frac{{{x}}^{{2}}{+}{x}{+}{1}}{{{x}}^{{2}}{+}{x}}$ (12)
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# 6.2.2: Convert Pounds and Ounces into Ounces
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
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$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\id}{\mathrm{id}}$$
$$\newcommand{\Span}{\mathrm{span}}$$
$$\newcommand{\kernel}{\mathrm{null}\,}$$
$$\newcommand{\range}{\mathrm{range}\,}$$
$$\newcommand{\RealPart}{\mathrm{Re}}$$
$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$
$$\newcommand{\Argument}{\mathrm{Arg}}$$
$$\newcommand{\norm}[1]{\| #1 \|}$$
$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$
$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$
$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$
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$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
Convert pounds to ounces by multiplying by 16.
## Converting Pounds and Ounces into Ounces - Weight
This page titled 6.2.2: Convert Pounds and Ounces into Ounces is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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Oldest Hominid Remains Offer Clues Of Human Evolution
A 17-year investigation into the discovery of the fragile remains of a small “ground ape” discovered in Ethiopia is described today in a special issue of the journal Science.
The report includes 11 papers about the discovery of the Ardipithecus fossils, which include a partial skeleton of a female nicknamed “Ardi”, the earliest known skeleton from the human branch of the primate family tree. The branch includes Homo sapiens as well as species closer to humans than to chimpanzees and bonobos.
Nearly 15 scientists from 10 different countries were responsible for the 1994 discovery, which provides new insights about how hominids””the family of “great apes” comprising humans, chimpanzees, gorillas and orangutans””may have emerged from an ancestral ape.
The last common ancestor shared by humans and chimpanzees is thought to have lived six or more million years ago. Though Ardipithecus is not itself this last common ancestor, it likely shared many of this ancestor’s characteristics.
Until Ardi’s discovery, the earliest well-known stage of human evolution was Australopithecus, a small-brained, bipedal “ape man” that lived between 4 million and 1 million years ago.
The most famous Australopithecus fossil is the 3.2-million-year-old “Lucy,” discovered in 1974 about 45 miles north of where Ardi would later be found. However, Ardi’s skeleton and associated Ardipithecus ramidus remains are older and more primitive than Australopithecus.
After Lucy’s discovery, there was some expectation that when earlier hominid remains were found, they would converge to a chimpanzee-like anatomy, based on the genetic similarity of humans and chimps. However, the Ardipithecus ramidus did not bear that out.
Ardi’s skeleton contains enough of the skull, teeth, pelvis, legs, feet, arms, and hands to estimate her body weight and height. They also show that she walked on two legs on the ground, but also climbed trees and spent time in them. She was likely omnivorous.
Remarkably, Ardi and her companions did not have limb proportions like chimps or gorillas, but rather like those of extinct apes or even monkeys. Her hands also are not chimpanzee- or gorilla-like, but are rather more closely related to earlier extinct apes.
Los Alamos geologist Giday WoldeGabriel, one of the scientists involved in the discovery of Ardi, led the field geology investigations and sampling of ancient lavas and ashes that were used to determine the age of the fossilized remains. He was also able to precisely characterize the environment in which Ardi lived.
Ardi’s woodland home included fresh-water springs and small patches of fairly dense forest with palm trees at the edges and grasslands extended perhaps many kilometers away.
“It is a privilege to have the opportunity to look back in time into the lives of mankind’s oldest relatives,” said WoldeGabriel.
“This is a fascinating and important discovery.”
Because of its antiquity, Ardipithecus takes us closer to the still-elusive last common ancestor. However, many of its traits do not appear in modern-day African apes.
One surprising conclusion is that it is likely that the African apes have evolved extensively since we shared that last common ancestor, making living chimpanzees and gorillas poor models for the last common ancestor and for understanding our own evolution since that time.
“In Ardipithecus we have an unspecialized form that hasn’t evolved very far in the direction of Australopithecus. So when you go from head to toe, you’re seeing a mosaic creature, which is neither chimpanzee, nor is it human. It is Ardipithecus,” said Tim White of the University of California Berkeley, one of the lead authors of the research.
“With such a complete skeleton, and with so many other individuals of the same species at the same time horizon, we can really understand the biology of this hominid,” said Gen Suwa of the University of Tokyo, Project paleoanthropologist and also a lead author of the Science report.
“These articles contain an enormous amount of data collected and analyzed through a major international research effort. They throw open a window into a period of human evolution we have known little about, when early hominids were establishing themselves in Africa, soon after diverging from the last ancestor they shared with the African apes,” said Brooks Hanson, deputy editor, physical sciences, at Science.
Other fossils associated with Ardi included fig and hackenberry trees, land snails, birds such as owls, parrots, and peafowl, and small mammals such as shrews, mice, and bats. Other animals, such as porcupines, hyenas, bears, pigs, rhinos, elephants, giraffes, two kinds of monkey, and several different types of antelope, were also associated with Ardi.
This research, in the form of 11 detailed papers and more general summaries, will appear in the October 2, 2009 issue of the journal Science, published by the nonprofit science society AAAS.
On the Net:
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#### A student wants to determine the resistivity of the material of a given wire using a meter bridge experiment. The wire is placed on the meter bridge, and various measurements are taken to calculate the resistivity. The known resistors are connected in a ratio of 1 : 9 on one side of the meter bridge. The student balances the bridge by sliding the jockey along the wire. The length of the wire between the jockey and the point of balance is measured to be L = 80 cm. The length of the wire between the jockey and the known resistors is 100 cm, and the known resistance is R = 10 Ω. Calculate the resistivity (ρ) of the material of the given wire.Option: 1 5.81 ×10−7 Ω · mOption: 2 68.9 ×10−7 Ω · mOption: 3 5.45 ×10−7 Ω · mOption: 4 9.81 ×10−7 Ω · m
Given data:
Length of wire between jockey and balance point (L) = 80cm = 0.80 m
Length of wire between jockey and known resistors = 100 cm = 1.00 m ,Known resistance (R) = 10 Ω
Using the principle of the meter bridge experiment, the ratio of resistances is equal to the ratio of lengths:
$\frac{R}{Unkown resistance} = \frac{Length of wire with known resistance }{Length of wire with unknown resistance }$
Substituting the given values:
$\frac{10}{Unkown resistance} = \frac{1.00 }{0.80 }$
Solving for the unknown resistance:
$Unkown resistance = \frac{10 \times 0.80 }{1.00 } = 8\Omega$
Now, we can use the formula for resistivity:
$\rho = \frac{R\times A}{L}$
Where A is the cross-sectional area of the wire. Let’s assume the wire’s diameter (d) is 0.1 cm (0.001 m). Therefore, radius (r) = 0.0005 m. The cross-sectional area (A) is πr2 :
$A= \Pi \times (0.0005)^{2} = 7.85 \times 10^{-7}m^{2}$
Now, substituting the values into the resistivity formula:
$\rho = \frac{10\times 7.85 \times 10^{-7}}{0.80} = 9.81\times 10^{-7}\Omega m$
Therefore, the resistivity (ρ) of the material of the given wire is $9.81\times 10^{-7}\Omega m$
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| null |
Cooperative Extension Service
West Lafayette, IN
Paul C. Pecknold, Extension Plant Pathologist
Fire blight is a bacterial disease that is particularly destructive on
many varieties of apple and pear. It may also damage certain
ornamental plants, such as flowering crabapple, hawthorn, mountain
ash, cotoneaster, pyracantha, and spirea. If not controlled, fire
blight can destroy the blossoms and fruit and may damage or kill the
plant by stem infection.
Fire blight usually first appears during bloom. The blossom clusters
wilt and turn dark brown or black. This is followed by twig blight
infection of the current season's growth. The most obvious symptom of
twig blight is a scorched appearance of affected stems in which the
leaves wilt, turn brown, and cling to the stem. It is this stage that
gives the disease the name "Fire Blight."
Often the tips of blighted twigs have a crooked appearance resembling
a fish hook. Fire blight may continue to spread downward from the
blighted twigs into main scaffolding limbs and trunk. The outer bark
of infected branches becomes shriveled, while the inner bark appears
water-soaked and reddish-brown. There is usually a distinct
separation of the infected (cankered) and healthy tissue. The
cankered areas are often slightly sunken and have a darker appearance
than that of adjacent healthy bark tissue.
Fire blight is caused by the bacterium, Erwinia amylovora. The bacteria
overwinter in cankered limbs, and in spring, droplets of sticky, amber-colored
ooze form from these cankers. These droplets contain large numbers of bacteria.
Insects and spattering rain carry the bacteria from the droplets to blossoms and
twigs. More fire blight bacteria ooze from these new infections, and insects and
rain again carry them to new areas of the tree and orchard. Fire blight is most
damaging in years when spring temperatures are above normal with frequent rains.
During cool springs the blossoms blight phase is usually not significant.
Figure 1: Blighted twig showing typical crooking of the apical
No single practice can insure complete control of fire blight.
However, you can reduce the disease if you employ a combination of
both cultural and chemical control measures as outlined below.
Reference to products in this publication is not intended to be an
endorsement to the exclusion of others which may be similar. Persons
using such products assume responsibility for their use in
accordance with current label directions of the manufacturer.
It is the policy of the Purdue University Cooperative Extension Service,
David C. Petritz, Director, that all persons shall have equal opportunity and
access to its programs and facilities without regard to race, color, sex, religion,
national origin, age, marital status, parental status, sexual orientation, or
Purdue University is an Affirmative Action employer.
This material may be available in alternative formats.
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# Increasing And Decreasing Intervals Calculator
## Increasing And Decreasing Intervals Calculator
The calculator will try to find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, and critical.
## How do you find intervals of increase and decrease?
You can also use the first derivative to find intervals of increase and decrease and accordingly write them. If the function’s first derivative is f’ (x) ≥ 0, the interval increases. On the other hand, if the value of the derivative of (x) ≤ 0, then the interval is said to be a decreasing interval.
## How do you find what interval is increasing?
The derivative of a function may be used to determine whether the function is increasing or decreasing at any interval in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
## How do you find decreasing intervals?
Explanation: To find when a function is decreasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.
## What is increasing interval in math?
Increasing means places on the graph where the slope is positive. [Figure 1] The formal definition of an increasing interval is: an open interval on the axis where every b, c ∈ ( a, d ) with has f ( b ) ≤ f ( c ).
## What is an increasing and decreasing function?
For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function and if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.
## How do you find the interval?
The class interval is the difference between the upper-class limit and the lower-class limit. For example, the size of the class interval for the first class is 30 – 21 = 9. Similarly, the size of the class interval for the second class is 40 – 31 = 9.
## How do you find the interval on a frequency table?
Determine the data range of the data set. Decide the width of the class intervals. Divide the range by the chosen width of the class interval to determine the number of intervals.
## How do you use intervals?
a three-month interval between jobs There might be long intervals during which nothing happens. The sun shone for brief intervals throughout the day. There will be a 20-minute interval between acts one and two.
## What is the difference between increasing and decreasing?
Increasing is where the function has a positive slope and decreasing is where the function has a negative slope.
## What is the interval in a math example?
An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.
## What is the class interval formula?
Class interval refers to the numerical width of any class in a particular distribution. Mathematically it is defined as the difference between the upper-class limit and the lower-class limit. Class interval = upper-class limit – lower class limit.
## What are the 3 types of frequency distributions?
Cumulative frequency distribution. Relative frequency distribution. Relative cumulative frequency distribution.
## How do you find the class interval when given a class mark?
Class interval refers to the numerical width of any class in a particular distribution. It is defined as the difference between the upper-class limit and the lower-class limit. Class Interval = Upper-Class limit – Lower class limit.
## How do you find the interval of concavity?
In determining intervals where a function is concave upward or concave downward, you first find domain values where f″(x) = 0 or f″(x) does not exist. Then test all intervals around these values in the second derivative of the function. If f″(x) changes sign, then ( x, f(x)) is a point of inflection of the function.
Related posts:
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# Math Snap
## One of the following series is convergent a. All b. $\sum_{n=0}^{\infty} \frac{(-i)^{n} 3^{n}}{(2 n+1)!}$ $\sum_{k=0}^{\infty}(1-i)^{k}$ $\sum_{n=0}^{\infty} \frac{(-7)^{n}}{5^{n} i^{n}}$
#### STEP 1
Assumptions 1. We need to determine the convergence of each given series. 2. The series are: a. $\sum_{n=0}^{\infty} \frac{(-i)^{n} 3^{n}}{(2 n+1)!}$ b. $\sum_{k=0}^{\infty}(1-i)^{k}$ c. $\sum_{n=0}^{\infty} \frac{(-7)^{n}}{5^{n} i^{n}}$
#### STEP 2
Consider the first series: $\sum_{n=0}^{\infty} \frac{(-i)^{n} 3^{n}}{(2 n+1)!}$
#### STEP 3
To determine the convergence of this series, we can use the Ratio Test. The Ratio Test states that for a series $\sum a_n$, if $L = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|$ and $L < 1$, then the series converges.
#### STEP 4
Let $a_n = \frac{(-i)^n 3^n}{(2n+1)!}$
#### STEP 5
Compute $a_{n+1}$: $a_{n+1} = \frac{(-i)^{n+1} 3^{n+1}}{(2(n+1)+1)!} = \frac{(-i)^{n+1} 3^{n+1}}{(2n+3)!}$
#### STEP 6
Compute the ratio $\left| \frac{a_{n+1}}{a_n} \right|$: $\left| \frac{a_{n+1}}{a_n} \right| = \left| \frac{(-i)^{n+1} 3^{n+1} (2n+1)!}{(-i)^n 3^n (2n+3)!} \right|$
#### STEP 7
Simplify the ratio: $\left| \frac{a_{n+1}}{a_n} \right| = \left| \frac{(-i) 3 (2n+1)!}{(2n+3)(2n+2)(2n+1)!} \right| = \left| \frac{3}{(2n+3)(2n+2)} \right|$
#### STEP 8
Take the limit as $n \to \infty$: $L = \lim_{n \to \infty} \left| \frac{3}{(2n+3)(2n+2)} \right| = 0$
#### STEP 9
Since $L = 0 < 1$, the series $\sum_{n=0}^{\infty} \frac{(-i)^{n} 3^{n}}{(2 n+1)!}$ converges.
#### STEP 10
Consider the second series: $\sum_{k=0}^{\infty}(1-i)^{k}$
#### STEP 11
This is a geometric series with common ratio $r = 1 - i$.
#### STEP 12
For a geometric series $\sum_{k=0}^{\infty} r^k$ to converge, the common ratio $|r|$ must be less than 1.
#### STEP 13
Compute $|1 - i|$: $|1 - i| = \sqrt{(1)^2 + (-1)^2} = \sqrt{2}$
#### STEP 14
Since $\sqrt{2} > 1$, the series $\sum_{k=0}^{\infty}(1-i)^{k}$ diverges.
#### STEP 15
Consider the third series: $\sum_{n=0}^{\infty} \frac{(-7)^{n}}{5^{n} i^{n}}$
#### STEP 16
Rewrite the general term: $a_n = \frac{(-7)^n}{5^n i^n} = \left( \frac{-7}{5i} \right)^n$
#### STEP 17
Simplify $\frac{-7}{5i}$: $\frac{-7}{5i} = \frac{-7}{5i} \cdot \frac{-i}{-i} = \frac{7i}{5} = \frac{7}{5}i$
#### STEP 18
The series becomes: $\sum_{n=0}^{\infty} \left( \frac{7i}{5} \right)^n$
#### STEP 19
This is a geometric series with common ratio $r = \frac{7i}{5}$.
#### STEP 20
Compute $|\frac{7i}{5}|$: $\left| \frac{7i}{5} \right| = \frac{7}{5}$
#### STEP 21
Since $\frac{7}{5} > 1$, the series $\sum_{n=0}^{\infty} \left( \frac{7i}{5} \right)^n$ diverges.
##### SOLUTION
Conclusion: Among the given series, only the first series $\sum_{n=0}^{\infty} \frac{(-i)^{n} 3^{n}}{(2 n+1)!}$ is convergent.
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# The letters of the word SURITI are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word SURITI.
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Updated On: 18-4-2020
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Text Solution
Solution :
In a dictionary the words at each stage are arranged in alphabetical order. We must consider the words beginning with I,R,S,T,U in order. <br> therefore Number of words starting with I=5! =120 <br> Number of words starting with R=(5!)/(2!)=60 <br> Number of words beginning with S is (5!)/(2!), but one of these words is the word SURITI, So, we first find the number of words beginning with SI,SR,ST <br> Number of words starting with SI=4!""=24 <br> Number of words starting with SR=(4!)/(2!)=12 <br> Number of words starting with ST=(4!)/(2!)=12 <br> Now, the words beginning with SU must follow. There are (4!)/(2!)=12 words beginning with SU, but one of these words is the word SURITI, Number of words starting with SUI=3!=6. The first word beginning with SUR is SURIIT and the next word is SURITI. <br> therefore Rank of SURITI =120+60+24+2xx12+6+2=236
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• ## Related Books
### RC Circuits: Transient Analysis
• The time constant in an RC circuit, tau, is equal to the circuit’s resistance multiplied by its capacitance.
• The time constant indicates the time at which the quantity under observation has achieved 63% of its final value.
• By 5 time constants, the quantity under observation is within one percent of its final value.
### RC Circuits: Transient Analysis
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
• Intro 0:00
• Objectives 0:13
• Charging an RC Circuit 1:11
• Basic RC Circuit
• Graph of Current Circuit
• Graph of Charge
• Graph of Voltage
• Mathematically Describe the Charts
• Discharging an RC Circuit 13:29
• Graph of Current
• Graph of Charge
• Graph of Voltage
• Mathematically Describe the Charts
• The Time Constant 20:03
• Time Constant
• By 5 Time Constant
• Example 1 20:39
• Example 2 28:53
• Example 3 27:02
• Example 4 44:29
• Example 5 55:24
### Transcription: RC Circuits: Transient Analysis
Hello, everyone, and welcome back to www.educator.com.0000
In this lesson we are going to talk about RC circuits, specifically about the transient analysis.0003
What happens as a function of time in these circuits?0010
Our objectives include calculating and interpreting the time constant τ of an RC circuit.0013
Sketch or identify graphs of stored charge voltage for the capacitor or resistor.0020
Write expressions that describe the time dependence of the stored charge voltage or current for elements in RC circuit.0025
Analyze the behavior of circuits containing several capacitors and resistors.0031
As we get into this lesson, please understand this one is going to be pretty math heavy.0036
The transient analysis of RC circuits is one of the more challenging portions of the E and M course.0040
This may get in depth a little bit, probably a great time to pause, to go back, to take really good notes.0047
You may have to come back to this one a couple of times.0053
It is not easy stuff and the first time you see it, it looks like there is a lot a math involved.0055
What you will find as we go through is you will see a bunch of the same patterns repeating and repeating.0060
But the first time you see it, it can look a little bit scary.0064
Do not be daunted, you can get through it.0067
Let us take a look at what happens when we charge an RC circuit.0070
Here I have a basic RC circuit, we have our source of potential difference resistor.0075
We have defined our current direction, our capacitor with the voltage across our capacitor, and the time T = 0 we are going to close the switch.0082
It also had graphs down here of current in the circuit, charge on our capacitor,0090
and the voltage across the capacitor that we are going to be filling out as we go through here.0096
We have done these before, but let us take a minute before we get heavy into the math.0099
Just to think about what these are going to look like.0103
We know the current in the circuit initially is going to be high because the capacitor acts like a wire.0106
So we are going to have all the current I = VT/ R.0112
We are going to start here at this high level of current and by the time we get roughly to 5 τ,0117
the current is going to dwindle down to less than 1% of its initial value because our capacitor starts to act like an open.0123
Our graph is going to have an exponential decay, something like that.0133
The charge on our capacitor is going to start at 0, it is uncharged.0138
After a long time that being again 5 τ, it is going to be CVT.0143
We will have an exponential rise toward that asymptote.0150
The voltage across our capacitor starts at 0 acting like a wire and over time approaches VT.0154
Our graph should look something like that.0166
Our goal here is going to be to mathematically describe those by actually figuring out what happens rather than just quick estimations.0168
To do that, let us start by looking at Kirchhoff’s voltage law.0176
We are going to do that, I'm going to start down here and go clockwise around our circle.0179
As I look at our potential drops, I see - VT first + IR + the voltage across our capacitor, brings us back to our starting point.0185
All of that must equal 0.0197
We also know here that C = Q/ V, therefore, V = Q/ C.0201
I can rewrite my equation now as, let me arrange this a little bit to VT is equal to IR + I’m going to replace VC with Q/ C.0209
This implies then though, Q and I are related because I = DQ DT.0227
We can write this as VT is equal to R × DQ DT, replacing I with DQ DT + we still have our Q/ C.0237
We have a differential equation, we have Q and the derivative of Q in the same equation.0258
How do we deal with something like that?0264
The first thing I’m going to do is called separation of variables.0267
I'm going to try and get all the variables of the same type on the same side.0270
I need to get Q and DQ together.0273
This is going to take a little bit of algebraic manipulation.0275
The reason I know how to do this is I have done it quite a few times.0279
You really just have to practice it and dive in, and do it again and again and again.0282
Let us rearrange this, I'm going to get DQ DT all by itself by dividing both sides by R.0288
I will have VT/ R is equal to, we have our DQ DT + Q/ RC.0293
Rearranging this again, we are trying to get RQ together .0308
We are going to write this as DQ DT is equal to VT/ R -Q/ RC, just a quick algebraic manipulation,0312
which implies then that DQ DT =, I can multiply C down here to combine these on the right hand side.0325
They give us a common denominator of RC so I would get C VT -Q/ RC.0336
Getting those variables separated, I have DQ/ C VT -Q must equal DT/ RC.0346
Just a little bit more algebraic manipulation.0361
I have my Q on one side, I got my variable T on the other, that means I can go when I can try and integrate both sides.0364
Not try, we are going to.0372
Integrate both sides, we will take the left hand side first.0374
The integral and our variable of integration is Q, which is going to go from some value 0 initial charge on our capacitor is 0,0377
to some final charge Q of DQ/ CVT – Q, must equal the integral of the right hand side DT / RC.0383
Our variable of integration on the right hand side T goes from some initial time T = 0 to some final time which we are going to call T.0401
As we integrate this, the left hand side we have got a problem of the form DU/ U.0411
The integral of DU/ U is nat log of U.0418
We have got DU / -U so we are going to get - the log of, we have CVT - Q evaluated from 0 to Q.0422
The right hand side of, 1/ RC is a constant, we are just going to get T/ RC evaluated from 0 to T.0440
A little bit more algebra, this implies then that, we will substitute in our values, our limits here.0452
- the log of CVT -Q - the opposite of the log which is going to be + the log of CVT -0, which is just CVT = T / RC.0458
If we got a difference in the logs, log of that + log of that,0477
we can say that we have the log of CVT - Q/ CVT equal to, we got that negative sign over here to the right, - T / RC.0481
We can simplify this left hand side a little bit too.0504
That means that the log of, that could be 1 -Q/CVT = - T/ RC.0508
I’m starting to run out of room, let us carry this over onto our next screen here.0524
We have the log of 1 -Q/ CVT = - T/ RC.0531
This log is troubling, how do we get rid of a log?0542
We take E and raise it to that power.0545
E ⁺log of 1 -Q/ CVT is what we are going to do.0547
Raise both sides to that, so E ⁺log of 1 -Q/ CVT must be equal to E ⁻T/ RC,0551
doing the same thing on both sides to maintain that equality.0562
E ⁺log of something is just that something.0567
Our left hand side gets a little simpler.0569
We have 1 - Q/ CVT =, right hand side E ⁻T/ RC.0571
Let us see if we can get to that one on that side and do a little bit of rearrangement to say that Q/ CVT = 1- E ⁻T / RC,0583
which implies then that getting just Q by itself, Q is a function of time is equal to CVT × (1 - E ⁻T/ RC).0598
We were able to solve for the charge on the capacitor as a function of time.0612
When you do these types of problems, you are going to see very similar forms come up again and again.0619
Some constant multiplied by either 1 – E ⁻T/ RC or just that constant × E ⁻T / RC.0624
You are going to see this come up again and again and again,0633
to the point where you can almost predict the answer before you go and actually solve it.0637
If that is our charge, let us see if we can find the voltage across C.0642
VC = Q/ C, we just found Q was CVT × 1 - E ⁻T/ RC ÷ C.0648
Our C make a ratio of 1, we get that the voltage across our capacitor or potential difference is just VT × 1 - E ⁻T/ RC.0668
The trick to getting current flow then is realizing that I is the current is equal to the derivative of the charge.0688
Current I is DQ DT which is the derivative with respect to T of our Q which was CVT × 1 - E ⁻T/ RC0696
which is going to be, we can pull our constant out, - CVT × E ⁻T/ RC × -1 / RC E ⁺U DU or DU is –T/ RC.0715
The E ⁺U DU, the derivative is -1/ RC, excuse me.0736
That is going to be, CVT / RC × E ^-¬T/ RC, which implies then,0741
our capacitance is C is going to make a ratio of 1, that our current then = VT/ R E^ -¬T/ RC.0755
By the way, VT/ R that was our initial current.0769
I is actually equal to its initial value × E ¬⁺T/ RC.0772
We were able to find the values for the current, the voltage, and the charge on the capacitor,0783
all as functions of time, much more exactly.0790
You see that the exponential relationship over and over again.0792
Or again, RC is your time constant τ.0796
Sometimes you will actually even see this written as E ⁻T / RC is written as E ^-¬T/ τ.0799
Let us take a look at the opposite side of the storage, discharging an RC circuit.0810
Just like we did in our steady state analysis, we have pulled our source of potential difference out of the circuit.0815
We have our charged up capacitor and at the time T = 0, we are going to close the switch.0821
What happens?0827
We know that our current starts out as V/ R because initially that capacitor0829
is going to act like a source of potential difference, it discharges.0835
We are going to start over here with our current with VC / R and that is going to decay down to 0.0839
Our charge starts at Q0 and also decays down.0848
Our voltage DC starts at its initial value, let us call that V0 and is also going to decay down.0856
We have done that before, now let us fill in the detail.0865
What happens in between?0867
We use KVL again, Kirchhoff’s voltage law.0870
This time I'm going to start here and go this way, counterclockwise.0873
As I write that, that will be -VC + IR = 0, which implies then because we know capacitance = Q/ V, therefore V = Q/C.0878
That Q/ C is equal to IR, just moving it to the other side as well.0895
In this case, we know that I is the rate of change of charge with respect to time0905
but now we are discharging, we are going the opposite way.0911
Do not forget we got to have a negative there, I = – DQ DT.0914
We have Q/ C equal, we still have our R, we will put -R in there because our next piece is that DQ DT.0920
The - coming from our I = –DQ DT.0933
This implies then, let us do our separation of variables again.0940
DQ ÷ Q is going to be equal to - DT/ RC, that piece was a little simpler.0944
But we can integrate both sides now, we integrate the left hand side.0956
The integral of DQ/ Q starting from some Q = 0 all the way to Q =, - the integral from T = 0 to T of DT/ RC.0959
We call that Q₀ to some final value Q.0978
Q = Q₀, whatever the Q initial is to its final value, that is a little bit better.0983
Which implies then that the log of Q, the integral of DU/ U is the natural log,0988
so the log of Q going from some its initial value Q0 to some final value Q.0994
What we are going to have over here is - T/ RC.0998
Taking this left hand side and putting in our limits, we have the log of Q/ Q0 is going to be equal to - T/ RC,1009
which implies that if we raise both of these to the E, that the left hand side becomes Q/ Q₀.1022
The right hand side becomes E ¬⁻T/ RC, and solving for just Q, Q = its initial value Q₀ E ^-¬T/ RC.1029
There we see that exact function, that exponential decay.1043
Once again, same sort of form, we are looking at some constant × E ⁻T/ RC or constant ×(1- E ⁻T/ RC).1051
Just like we did before, let us take a look at voltage.1063
Voltage is Q/C which is going to be in this case, Q₀ E ^-¬T/ RC ÷ C.1066
But we know that our initial value of voltage was Q₀/ C.1081
Really this is just saying that VC = its initial value V₀ × E ^¬T/ RC.1086
Here we see our function that shows the same thing, the same shape that exponential decay.1099
Let us take a look and see if we can do current just to maintain some symmetry here.1105
As I look at current, we have I = – DQ DT, which is - the derivative with respect to time of1113
we had previously Q₀ E ^-¬T/ RC, which is -Q₀ E ^-¬T/ RC × -1/ RC, which will be Q₀/ RC E ⁻T/ RC.1125
We can go a little bit further with that because we know that I initial, I0 was V₀/ R which is Q₀ / RC.1153
This is just saying then that current is a function of time is its initial value I₀ E^ -¬T/ RC.1166
Once again, there is our exponential decay.1177
A pretty heavy stuff in there, and not easy to do the first time you go through it.1182
It take some time but keep working on that until you can do it repeatedly.1186
It is an expectation for the AP Physics C E and M exam but you can do that.1190
Not easy, give it some time, give it some practice.1194
Let us talk for just a minute more about that time constant again.1199
The time constant in RC circuit τ = RC is the time when the quantity has reached 1 – E⁻¹ or 63% of its final value, just like we said.1203
By τ time constant it is more than 99% of the way to its final value.1214
If you want to be sure that your circuit is in pretty close to a steady state condition, wait at least 5 time constants then you will be there.1218
Let us finish this up by, let us do a bunch of old AP problems that involve this process because really it is all about practice.1230
Read it over, give it a shot, then come back here when you are done and hit play again, then we will keep on.1246
This exam question starts off with a circuit and says indicate the position to which the switch should be moved to charge the capacitor.1256
I'm going to draw where it should be, the answer is going to be B,1265
The charge that the capacitor so that you keep the source of potential difference in the loop there.1269
But I'm going to draw that as something like this.1275
We have got our source of potential difference, our resistor R.1280
We come from here over to our capacitor and there we go.1288
There is our basic circuit.1297
It asks on the diagram, draw a voltmeter that is properly connected to the circuit, the line to measure the voltage across the capacitor.1299
Here we need to remember that voltmeters are connected in parallel.1307
I'm just going to put a nice happy little voltmeter right there in parallel with my capacitor and I should be all set for part A.1311
Here it says, it gives us some information of graph.1322
Your partner has does some stuff with the stop watch, it asks you to determine the time constant of the circuit from the slope of the linear graph.1328
How are we going to do that?1335
Let us take a look, as we start to examine what data we have, we have got time and voltage.1338
I'm going to look at the relationship for this as we are discharging the capacitor,1343
realizing that V is equal to its initial value × that exponential decay portion E ⁻T/ RC.1349
I want to see how I can get this into a linear graph based on time and the potential data that we have.1357
If I take the log of both sides, I can say that the log of potential is equal to, the log of that is going to be log of V₀ + - T/ RC.1366
Or with a little bit more manipulation, the log of V will equal -1 / RC × T + log of V₀.1381
Why did I put it that way?1396
I’m trying to make it match the form for a line, the equation of a line that says Y = MX + B.1397
Really, I'm saying that we are going to have log V on the Y.1409
Our X is going to be T, our Y intercept is going to be log of V₀ which means that the slope of that line that we end up with is going to be -1/ RC.1414
We made it match that form.1424
It says use the rows in the table of the data to record any quantities that you indicated that are not given,1427
label each row used and include units.1433
We have got time which is going to go on our X, we do not have is the log of V.1436
I would add a row in there for the log of the potential and put that data in there right under the voltage.1441
The units of that are going to be log volts.1449
Take the value that is in there for B, take the nat log of it and make one more row and you should be all set for part B2.1453
Next we go on to part C and we are actually going to be graphing this.1462
Let us give ourselves a bunch of room here.1469
For part C, let us see if we can do a quick approximation of the graph.1472
Of course, you guys will do a much better job plotting points carefully.1477
We have got time in seconds over here and we have got the log V and log volts over there.1489
On our X, we go 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, something like that.1501
Heading up, we need to make it to about 6V, it looks like something like that 1234567.1513
When we go and actually plot our points, I end up with something that looks roughly,1524
I'm going to draw my rough line first and then fill in the points so I'm not plotting them.1530
But you get the general idea of what the shape of that is going to look like.1537
And I have got a couple of points scattered above and below the line.1540
I’m drawing the best fit line something kind of like this.1544
That would be the data, draw a straight line that best fits your data points.1552
For part D, from your line in part C, obtain the value of the time constant τ from the circuit.1556
We are going to use the fact for part D.1564
Get the slope which is Y2 –Y1/ X2 – X1.1568
As we pick a couple points on our line, that data points, points on our line is, in my case I ended up with something right around -0.079.1577
That slope is also has a meaning, it is -1/ RC, which implies that is -1/ τ = -0.079.1589
Therefore, τ = 1/ 0.079 or about 12.7 s in my calculation.1603
Let us come check out part E, E1 in the experiment that the capacitor had a capacitance of 1.5 µf,1616
calculate an experimental value for the resistance R.1625
That is easy, if τ is 12.7 s and that is RC, it means RC = 12.7 s.1628
Therefore, R = 12.7 s/ C, which it gave us as 1.5 µf, 1.5 × 10⁻⁶ F which is about 8.47 mega ohms with my values from the slope.1635
Part E2, let us go to black here.1657
On the axis that we made already, use a dashed line to sketch a possible graph1665
if the capacitance was greater than 1.5 µf but the resistance R was the same.1669
Let us see, the capacitance was greater then RC would go up if capacitance was greater since C goes up.1678
Our τ, our time constant is also going to go up.1688
The slope is the inverse of τ.1693
Our slope would have to decrease.1701
I would draw a line that has a shallower slope, something like that perhaps.1706
That is part E2 right there and that is how I would answer that one.1719
I think that would leave you in pretty good stead on a problem like that.1724
Let us move on and take a look at the 2012 exam free response number 2.1732
In this one, we have an experimental setup where a student is measuring resistivity of slightly conductive paper.1740
It gives us the thickness and we have got some data there.1747
The first thing we are asked to do is use the grid to plot a linear graph of the data points from which the resistivity can be determined.1750
Include labels and scales for both axis and draw the straight line that best represents the data.1758
The way I would start with this, you have got data for resistance and length.1763
Let us see what we need to graph there.1768
I'm thinking R = ρ L / A, there is a relationship that includes the variables that we have,1770
which by the way is ρ L/ the area, is just the width × the thickness.1778
Then, resistance = ρ/ WT × L.1785
If we want this to fit the equation of a line that is similar to Y = MX.1793
If we plot L on our X axis or on our Y axis, the slope should be ρ/ WT.1799
Let us take a look here and see if we can sketch in that graph.1808
Over here, we are going to have our resistance in ohms.1827
Here we will have our length in meters.1831
We will have you guys pick appropriate, I have 200 J, 400 J, appropriate intervals there, labeled well 600 K.1834
For length in meters, let us say that is 0.1, that is 0.2, and fill in some values in between.1845
When I go and do this and actually plot the data, I get something that, with a couple of data points above, below.1855
You are drawing your best fit line there.1872
That looks remotely like what you should be finding there.1876
In part B, says using the graph, calculate the resistivity of the paper.1879
We have done the hard work there because we just said the slope is ρ/ ω T.1885
If slope is ρ/ WT, that implies then that the resistivity ρ = WT × the slope which is 0.02 × our thickness 10⁻⁴.1889
Our slope Y2 – Y 1/ X2 – X1, picking some points from your line not data points,1911
wherever they happen to be, whatever your slope is, figure that out.1918
I ended up with a value that for the whole thing of the resistivity of about 8.75 ohm meters.1924
It should be somewhere in that ballpark.1937
We are changing things up a little bit in this problem.1945
A student uses those resistors R4 and R5 to build a circuit using wire, a 1.5V battery,1948
an uncharged capacitor, and an open switch as shown.1953
Calculate the time constant of the circuit.1957
I really do not like the way that is drawn, circuit schematics tend make me happy, warm and fuzzy inside.1961
I'm going to draw that in a way that is a little more comfortable for me.1967
We will do that for part C.1970
With a source of potential difference 1.5V, there is the positive and negative side.1973
We then have a couple resistors in parallel, R4 and R5.1979
We have our capacitor C and we have a switch.1991
Something like that.2001
Looking at that as an equivalent, we have two resistors in parallel.2004
If we wanted to do that to find the equivalent resistance, R4 and R5,2009
the equivalent resistance for R4 and R5 is just going to be R4 × R5/ R4 + R5.2013
I should say that that is going to be our equivalent for all of those, we have 370,000 ohms or 440,000 ohms R5/ the sum of those two.2025
What is it going to be, 781000 ohms.2041
Which gives you about 200 kl ohms or 200,000 ohms.2048
If we want to find the time constant of the circuit τ, our time constant is RC, is going to be our 200,000 ohms,2054
the equivalent resistance of our circuit × our capacitance 10 µf or 10 ×⁻⁶ F, which is about 2 s.2067
Part D, at time T = 0, the student closes the switch.2083
On the axis, sketch the magnitude of the voltage across the capacitor2087
and the voltages VR4 and VR5 across each resistors functions of time.2092
The nice thing there is these are going to have the same voltages across them.2097
That is going to be just one plot because they are connected together on the ends.2101
Label each curve according to the circuit element and on the axis explicitly label any intercepts, things like that.2105
Let us make ourselves another nice, happy, little graph.2112
Part D, something like that, where we have our potential and time.2116
If we start uncharged and then we are going to close that circuit,2138
we know that the voltage across the capacitor is going to have an exponential increase to some final value,2141
that is going to be the value of the voltage of our circuit.2147
We can draw an asymptote here with about 1.5V where our voltage across our capacitor is going to do something like that.2151
Where right around here, let us call that around approximately 5 τ or about 10s.2164
That is easy.2172
VR4 and VR5, are all of a sudden going to drop down.2176
They no longer have that voltage across them so they start at 1.5V2181
and they are going to have the corresponding exponential decay.2184
I think I can draw it a little prettier, that was not the best job ever.2188
Something perhaps kind of like that, where this is the voltage across R4 which is equal to the voltage across R5.2194
That should cover you for that one.2209
The general graph above the voltage across our resistors and across your capacitor as a function of time.2211
Let us take a look now at the 2007 exam.2223
Take a minute, printout, look it over.2225
Hit the pause if you need to, come back.2228
E and M number 1 from 2007.2231
Here we have another RC circuit, it says a student sets up that circuit in the lab.2237
The values of the resistance and capacitance are as shown but the constant voltage delivered by the ideal battery is not known.2242
At time T = 0, the capacitor is uncharged and the student closes the switch.2250
It gives us a graph of the current as a function of time measured using a Computer System2254
and you get that nice, happy, little graph that they show you.2258
For part A, using the data, calculate the battery voltage E.2262
The current at time T = 0, we can see right from the graph is about 2.25 milliamps or 0.00225 amps.2268
To find the battery voltage, that is just going to be equal to IR in our circuit by Ohm’s law2282
which will be our current 0.00225 amps × our resistance, we have got 550 ohms there, for a voltage of about 1.24.2290
Part B, calculate the voltage across the capacitor at time T = 4s.2306
Let us take a second and draw our circuit.2313
Here we go, there is E.2316
We have got our switch, we have got our resistor that is 550 ohms, we have our capacitor which is 4000 µf.2319
What I'm going to do is, I'm going to go through and do a KVL around the loop, starting right there going clockwise.2337
I would write that - E +, we will define to the right is the direction of our current - E + IR + the voltage across our capacitor = 0.2344
Therefore, DC = E – IR.2363
But we know that the current at 4s I at T = 4s is equal to 2.35 milliamps.2369
Roughly right from the graph.2382
That then means that VC is going to be equal to, we have got our 1.24V – our I 0.00035 amps × our resistance 550 ohms.2385
So I would get a VC of around 1.05V when I put that into my calculator.2402
That should cover part B.2411
Moving on to part C, calculate the charge on the capacitor at T = 4s.2413
Q on the capacitor is charge × voltage, which is going to be our 4000 µf, 4000 × 10⁻⁶ F × our potential 1.05V or about 0.0042 C.2423
It looks like we are making some headway here.2448
Let us take a look at part D, give ourselves more room here in the next page.2450
It asks us to sketch a graph of the charge on the capacitor as a function of time.2455
Let us draw our axis in here.2461
Our Y axis, our T axis.2470
There we have T, there is our Q.2479
What is that going to look like, the charge on the capacitor as a function of time?2483
We can do this over and over by now.2487
We are going to have that exponential rise as it charges up.2490
There is part D, let us take a look at E.2494
Calculate the power being dissipated as heat on the resistor at 4s.2500
Power = I² R which is going to be our current 4s at 0.00035 amps² × our resistance 550 ohms or about 6.74 × 10 ⁻5W.2504
Onto F, the capacitor is not discharged but it is dielectric of constant K κ = 1 is replaced by dielectric of constant K = 3.2532
It triple the dielectric constant.2543
The procedure is repeated, is the amount of charge on one plate of the capacitor at 4s greater than,2545
less than, or the same as before, and we have to justify our answer.2551
I would start by looking at the formula for capacitance K ϵ₀ A/ D.2555
But in this case, we know that K triples.2563
All those other things are not going to change.2567
It is the same capacitor geometry.2570
Therefore, we can say that our capacitance is going to triple which implies then that we are going to have a greater amount of charge.2572
We can look at that as, with 3 κ, Q3 is going to be E × 3, the initial capacitance, × 1 – E ⁻T/ RC.2587
RC is our initial capacitance still.2602
That would be 3 EC × 1 - E⁻⁴/ 3 × our resistance 550 × our capacitance 4000 × 10⁻⁶.2604
Just to give you a feel for the numbers, complies then that that is going to be,2619
Q3 will be, 3EC 5454 µf × about 1.24V or 6.76 × 10⁻³ C which is 0.00676 C.2624
Which by the way, as we suggested already when we said it was greater,2641
it is greater than what we initially had the initial 0.0042 C.2648
Plug in right through these, let us move on and take a look at the 2006 exam free response number 2.2664
Give it a try, hit pause, comeback.2676
If you have had a few minutes to look it over and we will go through this one.2678
This one is a bit of a doozy.2681
The circuit that they show you has a capacitor of capacitance C, a power supply of EMF given E,2687
two resistors R1 and R2, and a couple of switches.2692
Initially the capacitor is uncharged when both switches are open.2696
Switch S1 then gets close at time T = 0.2700
Part A says, write a differential equation that can be sought to obtain the charge on the capacitor as a function of time T.2705
We started out the lesson with something like this but let us do it.2711
A, let us take a look.2714
We have our source of EMF, our potential difference.2716
I’m just going to redraw this a little bit so it is a little easier to see.2723
R1, we have to capacitor and it should look like that initially based on where the switches are.2727
That both are switches are open and S1 gets close to T = 0.2740
Right at T = 0, this is basically our functioning circuit.2743
Makes it look a little simpler.2746
We also know of course, τ was going to be RC in the circuit.2748
Let us do KVL around the loop again, - E + IR1 + VC = 0.2753
Which implies then, since VC = Q/ C, that we have - E + IR1 + Q/ C = 0.2763
We also know that I is DQ DT, that is charging up.2774
Then, we get - E + R1 DQ DT + Q/ C = 0.2779
There is our differential equation.2792
We have Q and the derivative of Q in the same equation.2794
That should cover us for part of A.2798
Typically, that is as far as they ask you to go on most questions.2801
In this one, they ask you actually go and solve it.2804
In part B, solve the differential equation to determine the charge on the capacitor as a function of time.2806
Exact same thing we have been doing.2811
Chances are you could probably even, based on this tell me what the answer is without even going through the derivation.2814
However, to get full credit you probably got to go through and do all the work.2821
Let us do that.2825
Let us pull the R1, divide everything by r1.2828
We have - E / R1 + DQ DT + Q/ R1 C = 0.2830
A little bit of rearrangement which implies then that DQ DT = E/ R1 -Q/ R1 C, which implies that DQ DT =,2843
we will get a common denominator here, multiply this one by C.2857
We have our 1C in the denominator.2861
That will give us EC -Q/ R1C.2864
Then separating our variables, this implies that DQ/ EC -Q = DT/ R1C.2873
Which implies then that DQ and is going to switch the order here with a negative sign,2886
multiplying through Q - EC = - DT/ R1C.2891
Now we can integrate both sides.2900
We will integrate the left hand side from some Q = 0 to final value Q.2903
The right hand side will be from some T = 0 to final value T2908
which is going to give us the left hand side integral of the DU/ U will be the nat log of U.2914
We will get something that looks like the log of Q - EC evaluated from 0 to Q = - T / R1C.2921
Which implies then that the log of Q - EC - the log of - EC = - T/ R1C.2936
The left hand side, the log of the difference is equal to the log of the quotient.2953
The difference of logs is the log of the quotient.2958
That will give us the log of Q - EC/ -EC = Q – T/ R1C, raising both of these to the E.2961
E ⁺log of that just gives us that piece.2980
We will have Q - EC/ -EC = E ^¬T/ R1C.2983
Multiply it through by that EC so we get Q - EC is equal to – EC E ^¬T/ R1C.2993
Or getting Q by itself, Q = EC × 1 - E ^-¬T/ R1C.3008
You earn your points on that one.3024
Or we could also take a look at that Q = EC 1 - E -T / R1C.3029
I think that works.3035
Let us give ourselves more room before we move on to part C.3040
For part C, it says determine the time at which the capacitor has a voltage of 4V across it.3047
To do that, we know Q, let us see if we can solve for V and then we can back out the time from the voltage.3055
If Q = CV which is equal to EC × 1- E ^-¬T/ R1C, that implies then that V is just equal to E × 1 – E ^-¬T/ R1C.3069
Or V/ E we will pull out that -1, = –E ^-¬T/ R1C.3090
Which implies then that, let us switch our negative signs around.3102
1 - V / E = E ^-¬T/ R1C, which implies then that the log of 1 - V/ E = – T/ RC.3106
Or getting T all by itself, T = – RC × the log of 1 - V/ E.3127
We can substitute in our values to find that time.3138
T is equal to -4700 × 0.06 × our log of 1 - 4/ 12.3142
Put that all on my calculator and I come up with a time of about 114.3s.3157
After switch S1 has been closed for a long time, switch S2 now gets close in new time T = 0.3170
For part D, we have got a new T = 0 configuration which looks kind of like this.3177
We have got our source of potential difference, over here we have got our resistor R1.3185
We come down here, we have our capacitor C.3194
We come down here, we have got R2.3201
There we go, those two are in parallel.3208
Sketch graphs of the current I1 and R1 vs. Time and of the current I2 and R2 vs. Time.3212
Clearly label which is I1 and I2.3220
I guess that is not so bad.3223
Let us draw our axis here.3224
As I look at this, it looks like I1, the current through R1 is going to start at 0,3243
it is going to go to some center point to some final value toward an asymptote.3248
It looks like I2 is going to start at a maximum current when we first do that and approach the same point,3254
so from slightly different directions here.3260
As I take a look at that because those resistors are equal, they are going to split the voltage across them and end up with the same current.3264
I would probably draw this something kind of like this.3271
I would expect that I1 to go like this.3274
I will label my axis here, there is our current, here is our time.3280
I want to do something like that and I2 to come in from about the same point and do something like that,3285
where they are getting closer and closer to each other but not quite meeting.3295
Those should be symmetric but we have got to think you have got the right idea of what that graph should look like.3302
You can perhaps a little closer to that.3309
And that should cover part D.3311
Alright, that finishes up that problem and let us see if we can do one more.3315
Let us look at the 2003 AP physics C E and exam free response number 2.3324
As always, we will have you take a minute, look it up, print it out if you can.3330
Give it a shot, come back here, and we will see how this one goes.3334
In a lab, you can connect a resistor and a capacitor with unknown values in series with a battery of EMF 12V.3342
You include a switch in a circuit, and when the switch is closed the circuit is completed.3348
You measure the current through the resistor as a function of time, as they would show you in a plot below.3351
Using common symbols, draw the circuit that you have constructed that does this.3358
Show the circuit before the switch is closed and include whatever other devices3363
you need to measure the current through the resistor to obtain that plot.3366
Label the components in the diagram.3370
That is not so bad, we need to set up an RC circuit where we can measure the current through the capacitor and the switch S1.3373
We are showing it before the switch has been closed.3381
We have got our source of potential difference E and we will label that.3384
We will label that, we would make it nice and clear.3390
We have some switch S1, we have a resistor R, we have a capacitor C.3398
Somewhere in this series configuration, I will put E in here.3412
Just to be safe, I would probably go through and actually write capacitor, resistor, switch, ammeter.3421
I will let you guys do that.3426
Having obtained the curve shown, determine the value of the resistor at two placed in the circuit.3428
The way I would do that one is I would first look at the point where you have got T = 0 because you can use a ohms law R = VI.3434
At T=0, the voltage across the capacitor is 0.3443
Let me write that at T = 0, VC = 0, which implies that the voltage across R is equal to EMF,3447
which implies that the resistance is just going to be the EMF ÷ the current which is 12V/ 0.01 amps or about 1200 ohms.3456
C, what capacitance you need to insert in the circuit to give that result?3474
I would take a look here and say, our time constant RC must be 4s from the formula3479
that they gave us for the current as a function of time.3490
Therefore, the capacitance must be 4s/ R which is 4s/ 1200 ohms or about 3.3 × 10⁻³ F.3494
Let us check part D, give ourselves some more room here3515
because it looks like we got a significantly different portion of the question.3518
For part D, you are now asked to reconnect the circuit with a new switch so as to charge3524
and discharge the capacitor and be able to get a graph like that when you are switching between positions A and B.3529
Draw that schematic and label anything you might need.3537
It looks like in part A, it is charging in the switches at A and at part B it is discharging.3541
There are bunch of ways you can draw this.3547
Electrically they should all be equivalent though.3549
I would start off with something like our battery.3552
Be good and label this, our battery with an EMF.3558
Let us put this switch over here and we will call that position A.3562
We will put the switch maybe right here, we will call that S1.3566
We will have another position for it down here called B.3574
As we go through here, we need our resistor in the circuit.3580
We need our capacitor, they want to measure the current flow so we will put an ammeter in here in line with that in series.3585
We will connect there so different position B.3599
All we have is this loop to discharge.3601
I will just continue that up here.3604
In position A, this does not make any difference, it is an open circuit.3605
In position B, the whole left hand side is missing.3609
We have got our battery and we have got our ammeter here.3612
We have got our capacitor.3617
If we want to measure the voltage across all of that, let us put our voltmeter in parallel with our capacitor.3622
We have got our resistor up there and there is our switch.3636
I think that should cover all the requirements.3645
Hopefully, you got pretty good feeling for transient analysis of RC circuits.3648
It takes some time, you might want to go back and do some of these analyses a couple of times3654
until it starts to make sense to you, until you start doing the patterns.3659
Thank you very much for watching www.educator.com.3662
We will see again real soon, make it a great day everybody.3665
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Music is one of the glories of sound. When a musician plays a note of a certain pitch, the musical instrument vibrates or RESONATES and produces a complex pattern of sound waves made up of many different frequencies. The most noticeable sound wave is called the fundamental, but there are other waves with higher frequencies, called harmonics. Notes from a flute sound more pure than those from a saxophone because they contain fewer harmonics. Musical instruments often make very quiet sounds, but some are designed to AMPLIFY the sounds they make so we can hear them more easily.
Resonance is the sound made by a vibrating object. If you tap a large wine glass, it produces a low musical note. If you tap a smaller glass, it makes a higher-pitched note. Although objects can vibrate at any frequency, each one has a particular frequency at which it vibrates much more powerfully. This is called its resonant frequency.
Opera singers can shatter a wineglass by singing a note that is exactly the same as the glass's resonant frequency. When the singer sings the note, the glass begins to vibrate and "sing" the same note itself. If the singer holds the note for several seconds, the vibrations become extremely powerful, shaking the glass until it smashes.
Making sounds louder is called amplification. Most musical instruments have a part that vibrates and makes sounds, and another part that makes the sounds louder (amplifies them). On their own, the vibrating parts may make quiet sounds that would be impossible to hear, even from nearby, if they were not increased in volume. Vibrating guitar strings are amplified either by a soundbox or by using electricity.
Under the steel strings of an electric guitar, there are tiny magnets that generate small amounts of electricity as the strings move. These currents are fed into a separate piece of equipment called an electronic amplifier. This increases the current many times and uses it to play the sound of the guitar through a loudspeaker.
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What does “Paraclete” (παράκλητος) mean? In an in-depth look at “the Paraclete” in his commentary on John, Edward Klink says that the term for the Paraclete occurs only five times in the NT, and all five of those occurrences are within John’s writings (14.16, 26; 15.26; 16.7; 1 John 2.1), and the search for an equivalent Hebrew term is a lost cause.1 Klink notes the various ways Paraclete is translated in different translations: “Comforter” (KJV), “Advocate” (NRSV; NEB; JB; NIV), “Counselor” (HCS), and “Helper” (NASB; ESV).
The traditional scholarly opinion has been to see παράκλητος as having a legal or forensic meaning—thus, the term “advocate.” Yet scholars admit that John adds to this meaning by giving the word the connotations of “teacher” and “helper.” To define παράκλητος as “advocate” forces the word into one narrow definition from what John actually means. Some scholars have pushed back against the legal language saying that the term is “better interpreted . . . [for] a prophetic role or office.”2 While the term “‘could appear in legal contexts’ . . . when it did it was used ‘as a supporter or sponsor.’”3 Inevitably translators will have to choose one word as the primary meaning.
Klink, on the other hand, doesn’t translate παράκλητος, but transliterates it as the Paraclete “to avoid limiting or muting aspects of the identity and multifaceted function of the Paraclete that are core to its (his) identity.”4 Instead of looking to a historical or religious background to understand the Paraclete, Klink prefers to look to the foreground. John, and thus, Jesus, is teaching us about the Holy Spirit (John 14.26). He is developing a doctrine for his readers.
“The figure and function of the Holy Spirit cannot be defined by the history of religions, for it requires not only sensitivity to the Gospel’s own multifaceted portrayal but also the foregrounding depiction from the rest of the biblical canon — the primary source for offering a conceptual interpretation of the Spirit’s person and work.”5
In this in-depth section Klink gives three aspects of the Paraclete for his reader to understand ahead of time.
- The Paraclete is still to come.
John 14.26: But the Helper, the Holy Spirit, whom the Father will send in my name, he will teach you all things and bring to your remembrance all that I have said to you.
The Holy Spirit comes (proceeds) from both the Father and the Son and will do so soon at a future time. But the Spirit has surely been at work prior to the future point of his coming (cf. 1 Cor 12.3).
“It is significant that the Paraclete can only come when Jesus departs (16:7), for it suggests that his coming is a direct consequence of the saving work of Christ without which he could have no place or function at all. The Paraclete is therefore symptomatic of the era to come in the new covenant and the new life in Christ, the Spiritual life.”6
- The Paraclete has a special relationship to the disciples. “Without exception, the functions ascribed to the Spirit are elsewhere in this Gospel assigned to Christ.”7
- All will know the Paraclete just as the disciples had the privilege of knowing Jesus (14.7, 9).
- The Paraclete will indwell the disciples and remain with them just as Jesus is to remain in and with the disciples (14.16–17, 20, 23; 15.4–5; 17.23, 26).
- The Paraclete as the Spirit of truth (14.17; 15.26; 16.13) will teach and guide the disciples into “all the truth” (16.13), just as Jesus is the truth (14.6; cf. 1.14).
- The Spirit bears witness to Christ (15.26) and glorifies Christ (16.14), just as it is Christ from whom the Paraclete receives what he makes known to the disciples (16.14).8
- The Paraclete has a unique role in the world to convict the world of sin, righteousness, and judgment (16.8). The world cannot “see” Jesus (5.43; 12.48); the world cannot see the Paraclete. The legal/forensic language comes in to play here because the Paraclete is both witness to Jesus (15.26; 16.14), but he also assists “the disciples in their witness in the world, since his witness takes place through their own.”9 The Paraclete is the Spirit of truth (14.17) who points to the one who is “the way, the truth, and the life; 14.6).
The Mission of the Trinity
There is an extremely close relationship between the Paraclete and Jesus. Not only do they share (some of) the same functions, but Jesus expressly states that the Paraclete is “another Helper” (ἄλλον παράκλητον; 14.16).10 Jesus too was a Paraclete, albeit one different from the Spirit (cf. 1 John 2.1).
Here we see how the Son and the Spirit can belong together (as God) and participate in the same work (the mission of God) and yet be different persons and have different assignments or functions, thus allowing for a distinction in purpose, a unity in function, and an equality in essence. And the relationship among the Trinity is gifted to us by means of the Spirit—the Paraclete, for at his departure (cross, resurrection, ascension) Jesus gives us “a share in his filial relationship with the Father by the indwelling of the Holy Spirit.”11
The title Paraclete “refers to the ministerial office of the Trinitarian God in the world, occupied by both the Son of God and the Spirit of God.”12 It refers to both the Spirit of God and to the Son of God, the one who is “the only God, who is at the Father’s side, he has made him known,” Jesus Christ (1.18). This Jesus is in the Father and the Father is in him. The Father sends the Spirit to his people in Jesus’s name (14.26). It is in this intimate relationship that believers—people, humans—are included. In fact, Jesus concludes his prayer to the Father by saying “I made known to them your name, and I will continue to make it known, that the love with which you have loved me may be in them, and I in them” (17.26). Jesus is in believers, and the love which God shows to his Son is shown to his sons and daughters in Christ.
5 Ibid., 632-33.
6 Ibid., 633.
10 “The adjective ‘another’ (ἄλλον) signifies ‘another of the same kind.’” (634).
12 Ibid., 635.
Amazon Affiliate Disclosure: I receive a percentage of revenue if you buy from Amazon on my blog.
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Prompt: Boston Dynamics is a company that specializes in producing robots that can really do the unimaginable. Take Sand Flea. Sand Flea weighs 11 lbs and can jump to heights of up to 30 ft. Such a feat represents a very attractive design goal across all industries for the coming years: the ability to store massive amounts of energy and release it very quickly. Considering that these high energy-density type systems are in fact the way of the future, using what you know about energy come up with either at least 3 ways of storing/quickly releasing a large amount of usable mechanical energy or come up with one way and describe at least 3 ways to look at your solution.
Almost all land animals have the ability to jump and yet this feat is quite difficult to repeat in the robotic world. This is due to the large amounts of energy that need to be stored and then rapidly released to propel the object off the ground. Directly mimicking the crouching and springing action of many animals requires far too many moving parts to be truly feasible for large jumps, Honda’s Asimo does okay though! This is where we have to get creative. We can use a self-contained method of momentum transfer.
Think of hitting a baseball, the batter has to swing the bat very fast before it hits the ball and transfers all of that energy into sending the ball flying over the outfield. Momentum is the product of mass and velocity, so in this analogy the mass of the bat times the speed of the swing would be it’s total momentum. A lot of this momentum energy is transferred to the ball, some of it is lost in sound and heat. The ball has a substantially smaller mass and therefore must have a much greater velocity to balance out the equation.
We can adapt this baseball metaphor to the robotics world by placing a large mass inside our robot, then launching it forward to smash into the front of the robot. In this instance the mass is acting as the bat and the entire device is acting as the ball. There are a few combinations of components we could use to bring this massive energy transfer into the robotics world.
The first would be a spring and mass, contained inside the device, a small electric motor could slowly compress the spring, storing a large amount of elastic potential energy, then suddenly release the mass. The mass would smash into the front of the robot, boosting it forward.
Another method would look similar to firing a gun. Have a combustion chamber filled with an explosive, something storing a large amount of chemical energy, right behind a large mass. Then simply pull the trigger and launch the mass propelling the robot forward.
A third way, and probably my favorite would be adapting a rail gun idea. This would involve coils of wire surrounding a barrel loaded with the large mass. Once electricity is pushed through these wires a strong magnetic field is generated launching the mass forward and thus the robot. Lithium Polymer batteries can store large amounts of energy and release it very fast making this a feasible idea.
Jumping is just one of the applications for quick release of large amounts of energy. But jumping machines look pretty cool and kinda intimidating, for example, check out Boston Dynamic’s Sand Flea.
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(The following is an article written by Mark Hartsell, editor of the Library of Congress staff newsletter, The Gazette, in honor of the Star Spangled Banner, which celebrates its 200th anniversary this year. To commemorate the anniversary, the Library is hosting a concert featuring baritone Thomas Hampson on July 3.)
The story of “The Star-Spangled Banner,” for many decades, seemed as murky as the smoky haze over Fort McHenry on the morning two centuries ago when Francis Scott Key wrote the lyrics that still inspire a nation.
No one knew for sure who wrote the music. No one fully understood the circumstances of the tune’s creation (but, no, it wasn’t a bawdy English drinking song). No one fully understood how Key’s words became connected to the music or how they were disseminated.
Much of what is known about “The Star-Spangled Banner” now – at the anthem’s 200th anniversary – is known because of research conducted by Music Division librarians or with Library of Congress collections. For more than a century, the Library has served as the principal research center for the national anthem.
“We’ve been collecting, documenting, researching and making available this information since 1909,” Music Division librarian Loras Schissel said. “The piece has been printed and reprinted from 1814 to the Civil War. All the different versions that occurred during that period are here through collecting, purchasing, gift or copyright deposits.”
By Dawn’s Early Light
Key, detained aboard a British warship, watched British ships bombard Fort McHenry in Baltimore Harbor in September 1814. The assault failed, and at dawn on the 14th, Key saw the U.S. flag still there, streaming over the fort’s ramparts. Inspired, he composed the lyrics to what 117 years later became the national anthem.
Key wrote with a particular tune in mind: “To Anacreon in Heaven,” a piece composed as the official song for an 18th-century London club of amateur musicians and, later, widely adapted for other uses.
Key’s lyrics – set to the “Anacreon” melody and soon titled “The Star-Spangled Banner” – over the decades became one of America’s most popular patriotic songs. In 1931, Congress declared the song the official anthem of the United States.
Library collections contain hundreds of pieces related to the “The Star-Spangled Banner,” collectively tracing its evolution from London music club anthem to national anthem of a growing, powerful country an ocean away. The Library holds, for example, the first printed lyrics of “To Anacreon in Heaven”; the first printed sheet music of that song; Key’s own copy of “Anacreon”; the first printing of Key’s lyrics, circulated in Baltimore just days after the battle; the first printed sheet music setting Key’s lyrics to the “Anacreon” tune and bearing the title “The Star-Spangled Banner”; and the lyrics handwritten by Key years later.
“Taken together, we have the whole story,” Music Division librarian Raymond White said.
An Uncertain History
That story, however, remained murky long after Key’s work became one of America’s most popular patriotic songs. Little was known about the London music club, the Anacreontic Society. The identity of the composer of “To Anacreon in Heaven” was unclear; the song frequently, it turned out, was attributed to the wrong composer. It wasn’t clear how Key became familiar with the tune or how his lyrics were spread.
Much of the scholarly work of locating, comparing and evaluating – often contradictory – information about the song was done by researchers using Library resources or by Music Division librarians examining numerous editions of music and lyrics, newspaper reports and other documents.
“What it comes down to is looking at printed sources, which are not unique but extraordinarily rare,” White said. “The story of this thing plays itself out in these printed sources.”
Composer and bandleader John Philip Sousa, conducting research at the Library, in the late 19th century produced the first serious study of the piece. (Sousa also gave “The Star-Spangled Banner” its first official status: On his recommendation, the Navy required the piece to be played each morning as the flag was raised.)
Over the next nine decades, Music Division librarians expanded on Sousa’s work and ultimately wrote the anthem’s definitive story.
A Watershed Report
Oscar Sonneck – Music Division chief from 1902 to 1917 – was perhaps America’s first great musicologist. He wrote a bibliography of American secular music, devised the music-classification system still used by many of the world’s libraries and – determined to make the Library one of the world’s great music repositories – began collecting important material.
“He is, perhaps, the most important music librarian in the world,” Schissel said. “His ideas still are standard.”
In 1909, Librarian of Congress Herbert Putnam asked Sonneck to produce a report on America’s most important patriotic songs: “Yankee Doodle,” “Hail, Columbia,” “America the Beautiful” and “The Star-Spangled Banner.”
Sonneck’s work helped establish, among other things, how Key’s lyrics became connected to the “Anacreon” music, when and how the first editions were printed, and that Key was thinking of “Anacreon” when he wrote the lyrics.
Sonneck also helped resolve the lingering mystery of the “Anacreon” composer. Samuel Arnold, among others, had been prominently suggested as its creator. Sonneck, however, sifted the evidence and concluded that an obscure London church organist, John Stafford Smith, likely was the composer.
Later, Sonneck played a key role in establishing a definitive version of “The Star-Spangled Banner.” At the request of President Woodrow Wilson, Sonneck headed a committee charged with creating a “standard” version that could be taught and performed consistently. (The original manuscript is in the Library collections.)
“That’s the big step toward 1931,” Schissel said. “Wilson’s saying, ‘When it’s appropriate to play a national anthem, I’d like it to be ‘The Star-Spangled Banner.’ That’s another push toward anthemhood.”
Putting it all Together
Music Division librarian Richard Hill carried on Sonneck’s work in later decades, establishing proof of the basic conjectural things Sonneck and Sousa had come up with and adding detail about the Anacreontic Society and Smith.
“He put it all together: This was printed at this time. This edition came out then. The Anacreontic song was first published at this point,” Schissel said. “And, among other things: Who was John Stafford Smith? He was a murky figure in this operation.”
Hill died relatively young, in 1961, leaving his work unfinished.
Music Division librarian William Lichtenwanger took Sonneck’s and Hill’s research, added his own and in 1977 produced the work now considered the anthem’s definitive history: “The Music of The Star-Spangled Banner: From Ludgate Hill to Capitol Hill.”
“It basically should be a three-name book: Sonneck, Hill and Lichtenwanger,” Schissel said. “We’re always looking for new information, we’re always looking for new editions, we’re always adding to our knowledge. But that book still is cited. It’s always used.”
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Last modified on March 16th, 2022 at 3:28 pm
Animals are quite remarkable because they always find ways of adapting to changing seasons to survive. Some, for example, hibernate all winter long to avoid the harsh climate conditions, while others migrate in search of warm weather and food. If you ever have an assignment to write about seasonal effects on animals, or need help with other assignments, Ez Assignment Help, is dedicated to academic help for students.
Many aspects of animal life and biology, especially those related to procreation, depend on seasonal changes. Certain animals that give birth when food is in short supply, for example, often have a difficult time raising and protecting their offspring. Just like human beings, animals tend to change with the changing seasons.
Just like human beings, animals have the basic need to survive. This need drives them to look for places to breed their young and find shelter, water, and food. To improve their chances of survival, animals need to adapt to their habitats in response to different factors, such as seasonal changes. Basically, an adaptation is a change or modification in an animal or organism’s behavior to improve its chances of survival.
Most people choose their diet, activities, and clothing based on the prevailing weather or season. In the same way, animals adapt to seasonal changes to survive and procreate. However, in the animal kingdom, not all changes relate to freezing weather. Some animals, for example, prefer dry and hot environments, rather than wet and cold ones.
Nature has a way of telling every living thing that the season or weather is about to change. Actually, you do not need to listen to the weather report or watch the calendar to know that a seasonal change is about to happen. Nature will give you clues that things are changing. After all, plants and animals do not count down the days or use calendars to prepare for seasonal changes.
- Changing with the Season
Animals need to study their physical environments to determine the time of year. Referred to as an environmental cue, this process often involves determining the length of a day, which tends to change in a regular pattern throughout the year. During spring, for instance, days tend to be longer as opposed to the shorter days in the fall. Summer days are also longer than winter days.
- Reproduction Photoperiodic
Photoperiodic animals adapt their behavior in response to the length of day throughout the year. Various animals are photoperiodic, for example, garden snails. During seasons when days are longer, common garden snails lay eggs depending on the day’s length. Scientists call this process reproductive photoperiodic.
Although certain animals’ reproduction is photoperiodic, different environmental factors may also affect their reproduction. If the common garden snail is too small or young, for example, it may fail to lay eggs even during summer.
Certain species of birds, such as magpies, tend to parade around with nesting materials while exhibiting unique territorial behaviors. Instead of building nests, other species of birds, such as kookaburras, cockatoos, lorikeets, tawny frogmouths, and owls, raise their young in hollows. Therefore, you might notice some power struggles over prime sites.
- Flying Bats
Micro-bats fall into a deep sleep during winter. When the weather starts warming, however, they begin to wake. During the warm season, you will often hear the chirping sounds made by certain species of bats if you live near a local park with bats. Every living thing lives within a unique ecosystem, which is its natural habitat. This habitat consists of many things, such as other competitors or predators, plants that grow in the habitat, climate, and other things. Animals need to learn how to deal with each of these factors to ensure their survival. When it comes to predicting, identifying, and adapting to seasonal changes, some animals seem to have an invisible and accurate radar that humans lack.
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A team of astronomers, including Danai Antonopoulou and Anna Watts from the University of Amsterdam (Uva), has discovered that sudden speed jumps in the rotational velocity of pulsars have a minimum size and that they are caused not by the unpinning and displacement of just one sub-surface superfluid vortex, but by billions. This result is important to our understanding of the behavior of matter under extreme conditions.
Pulsars are rotating neutron stars — remnants of massive stars that end their lives in supernova explosions. They act like cosmic lighthouses whose beams sweep through the universe. Their rotational velocity decreases in time, but can suddenly increase in rare events called glitches. These glitches are caused by the unpinning and displacement of vortices that connect the crust with the mixture of particles containing superfluid neutrons beneath the crust.
The team of astronomers discovered that the glitches of the Crab Pulsar always involve a decrease in the rotational period of at least 0.055 nanosecond. The Crab Pulsar was one of the first pulsars to be discovered and has been observed almost daily with the 42-foot telescope at the Jodrell Bank Observatory over the last 29 years. The huge amount of data makes this object the best choice to study glitches.
The smallest glitch is likely to be caused by the unpinning and movement of billions of vortices. “Surprisingly, no one tried to determine a lower limit to glitch size before,” said Antonopoulou. “Many assumed that the smallest glitch would be caused by a single vortex unpinning. The smallest glitch is clearly much larger than we expected.”
“Astronomers would of course like to know whether the smallest glitches of other pulsars are also caused by billions of vortices. The next step is to sift through the data of other pulsars and to continue observing,” said Cristobal Espinoza from the Institute of Astrophysics Pontificia Universidad Catolica in Chile.
“By comparing the observations with theoretical predictions, we learn about the behavior of matter in these exotic objects,” said Watts. “The precise cause of glitches is still a mystery to us, and this result offers a new challenge to theorists.”
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ananyo writes "A controversial paper published in Nature argues that enigmatic fossils regarded as ancient sea creatures were actually land-dwelling lichen. If true, that would suggest life on land began 65 million years earlier than researchers now estimate. The nature of fossils from the Ediacaran period, some 635 million–542 million years ago, has been fiercely debated by palaeontologists. But where others envisage Ediacaran sea beds crawling with archaic animals, Gregory Retallack, a geologist at the University of Oregon in Eugene, sees these sites in southern Australia as dry, terrestrial landscapes dotted with lichens. He proposes that rock in the Ediacara Member in South Australia — where palaeontologist Reginald Sprigg first discovered Ediacaran fossils in 1947 — represents ancient soils, and presents new geological data. Among other lines of evidence, Retallack argues that the rock's red colour and weathering pattern indicate that the deposits were formed in terrestrial — not marine — environments (abstract). Others strongly disagree."
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# GeoGebra Book: triangle centers
In this book you can learn about some well and less known triangle centers and their coordinates The position of remarkable points in a triangle can be defined relative to the verticles of the triangle by its barycentric coordinates. In a triangle one can identify more remarkable points, called triangle centers. On [url=https://en.wikipedia.org/wiki/Triangle_center]list of triangle centers[/url] you can find the best known. The American mathematician Clark Kimberling indexed more than 10 000 points, identified by their Kimberling number. You can find this index online in the [url=http://faculty.evansville.edu/ck6/encyclopedia/ETC.html]encyclopedia of triangle centers[/url]. For every point you can find its barycentric coordinates. If you know the Kimberling number of one of this points, you can draw it directly in GeoGebra with the command TriangleCenter( Point , Point, Point, Nuber ) in which you can type the coordinates or the names of the verticles of a triangle and the Kimberling nummer of the point up to number 2999. The point with Kimberling number n is written as X(n). In this book you can find applets of all the triangle centers from X(1) up to X(100). This give you an impression of how it's possible to define so many triangle centers, starting just from three points, defining a triangle. Many centers are the result of mathematical operations on earlier defined centers or combinations of some of them. An easy way is calculating e.g. the midpoint of earlier centers. Another way is to costruct triangle centers not of the referention triangle but e.g. to the orthic triangle of it. The interesting thing here is examine if this leads to interesting coordinates. Having passed X(100) we'll make just a selection of the numerous triangle centers in the list, because of their interesting construction or their name. [i]In dit boek kom je meer te weten over een aantal driehoekscentra en hun coördinaten. De positie van een merkwaardig punt in een driehoek kan je beschrijven t.o.v. de hoekpunten van deze driehoek. We spreken dan van barycentrische coördinaten. In een driehoek kan je natuurlijk heel wat merkwaardige punten aanduiden. Deze punten noemt met [b]driehoekscentra[/b]. Op [url=https://nl.wikipedia.org/wiki/Lijst_van_driehoekscentra_met_hun_Kimberlingnummer]lijst van driehoekscentra[/url] vind je een lijst van de meest bekende. De Amerikaanse wiskundige Clark Kimberling gaf meer dan 10 000 punten elk een eigen inventarisnummer: het [b]Kimberling getal[/b]. Je vindt deze inventaris online als de [url=http://faculty.evansville.edu/ck6/encyclopedia/ETC.html]encyclopedie van driehoekscentra[/url]. Voor elk van deze merkwaardige punten vind je ook zijn barycentrische coördinaten. Ken je het Kimberling getal van een van deze punten, dan kan je het rechtstreeks in GeoGebra bepalen met het commando [b]Driehoekscentrum( Punt , Punt, Punt, Getal )[/b] waarin je het de coördinaten of de namen van de hoekpunten van de driehoek invult en het Kimberling getal van het punt, tot het nummer 2999. Het punt met Kimberling getal n noteer je ook als [b]X(n)[/b].[/i] In dit boek vind je applets van alle driehoekscentra van X(1) tot X(100). Zo krijg je een indruk van hoe het mogelijk is om zoveel centra te definiëren, startend vanuit enkel drie hoekpunten. Vele driehoekscentra zijn het resultaat van mathematische operaties op vroeger gedefinieerde centra of maken combinaties van enkele. Een gemakkelijke manier om nieuwe centra te vinden is het midden berekenen van bestaande centra. Een andere manier is gekende centra niet toe te passen op de referentiedriehoek, maar b.v. op de hoogtedriehoek (de driehoek gevormd door de voetpunten van de hoogtelijnen). Het boeiende hier is te onderzoeken of dit ook interessante coördinaten oplevert. Eens X(100) gepasseerd, maken we een selectie uit de lijst, op basis van een interessante constructie of naam.
Material Type
GeoGebra Book
Tags
triangle coordinates number center coordinaten getal barycentric kimberling barycentrische driehoekscentrum diehoekscentra Show More…
Target Group (Age)
3 – 19+
Language
English
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1300_Sec_13_in_class_filled
# 1300_Sec_13_in_class_filled - 15 18 and 36 Use Finding...
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Math 1300 Section 1.3 Prime numbers Write as a product of prime factors. Example 1: Write each as a product of prime factors. A. 28 B. 32 C. 60 D. 15
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Find the greatest common factor (GCF) of a set of numbers (biggest number that divides into each number in the set) Step 1: Write each number in the set as a product of prime factors. Step 2: The GCF is the product of all prime factors common to every number in the set. Example 2: Find the GCF of each set of numbers. A. 32 and 28 B. 32 and 60 C. 18, 30, 48 D. 27, 18, 45
Use: Reducing fractions Example 3: Reduce: 128 1024 Find the least common multiple (LCM) of a set of numbers (smallest number that all of the numbers in the set divide into) Step 1: Write each number in the set as a product of prime factors Step 2: Take the greatest power on each prime number. Multiply the numbers together. Example 4: Find the LCM of each set of numbers. A. 15 and 27 B. 18 and 36
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C.
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Unformatted text preview: 15, 18, and 36 Use: Finding common denominators Example 5: Find the least common denominator (LCM) for 1 5 7 8 6 10 + + • Adding/Subtracting Fractions Step 1: Find a least common denominator Step 2: Change the numerator of each fraction accordingly Step 3: Add or subtract the numerators; keep the denominators unchanged Step 4: Reduce the answer, if possible Example 6: Work each problem. A. 7 2 18 27 + B. 7 11 15 27 + C. 21 13 16 10-D. 7 5 8 8-• Multiplying Fractions Step 1: Multiply numerators. Multiply denominators Step 2: Reduce the answer, if possible. Example 7: Multiply each. A. 1 2 5 3 × B. 5 2 8 3 × C. 8 35 15 16 × D. 1 10 5 3-× ** 3 2 6 5 4 7 × You can use the cancelling method, if you know how to do it. • Dividing Fractions Step 1: Multiply the first number by the reciprocal of the second number. Step 2: Reduce your answer, if possible. Example 8: Find each answer. A. 3 7 2 6 ÷ B. 4 8 9-÷...
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solutions3e
# solutions3e - Stat 651(Winter 2011 Kaizar Homework 3 Extra...
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Stat 651 (Winter 2011) Kaizar Homework 3 Extra Problems Solutions Exercises 1. Lohr, Chapter 3 problem 22 (a) Recall that S 2 h = N h N h - 1 p (1 - p ). Since we are considering the population of Milwaukee, it is reasonable to assume that N h N h - 1 1, and so S 2 h p (1 - p ) Stratum 1 2 p h 0.10 0.03 S h 0 . 09 = 0 . 3 0 . 0291 = 0 . 17 N h /N 0.4 0.6 N h S h /N 0.12 0.102 N h S h / N S 0.54 0.46 n h 1081.0 918.9 n h 1081 919 (b) Allocation: Stratum 1 2 optimal 1081 919 proportional 800 1200 For a SRS, the overall proportion is 0.1*0.4+0.03*0.6 = 0.058 Optimal standard deviation: 0.00497 Proportional standard deviation: 0.00517 SRS standard deviation: 0.00523 2. Lohr, Chapter 3 problem 35 (a) I used the following SAS code to do the allocation and selection. /*first look at the stratification variable = team*/ /*save the counts in a new dataset*/ proc freq data=work.baseball; tables team / out=mylib.baseballteams; run; data mylib.baseballteams; set mylib.baseballteams; _total_=count; keep team _total_; run; /*we see that there are 797 players in 30 teams*/ /*to do proportional allocation, I need to 1. find the proportion of players in each stratum 2. multiply this by the sample size n
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solutions3e - Stat 651(Winter 2011 Kaizar Homework 3 Extra...
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# Thread: substitution method question
1. ## substitution method question
Do can you tell when you can use the substitution method? I just tried it on $\displaystyle \int_{-1}^0(2x+3)^2dx$, but I don't get the right answer unless I square the $\displaystyle (2x+3)$ and then proceed normally.
What about substitution on $\displaystyle \int_3^2\frac{x^2-1}{x-1}dx$?
2. Originally Posted by cinder
Do can you tell when you can use the substitution method? I just tried it on $\displaystyle \int_{-1}^0(2x+3)^2dx$, but I don't get the right answer unless I square the $\displaystyle (2x+3)$ and then proceed normally.
What about substitution on $\displaystyle \int_3^2\frac{x^2-1}{x-1}dx$?
Hello,
to 1.:
use u(x) = 2x+3. Then du/dx = 2. That means du = 2*dx.
So you could use the substitution method if there are the factor 2:
$\displaystyle \int_{-1}^0 \frac{1}{2} \cdot 2 \cdot (2x+3)^2dx=\int_{-1}^0 \frac{1}{2} u^2 du$
$\displaystyle \int_{-1}^0 \frac{1}{2} u^2 du= \frac{1}{6}u^3+c$
Now you can re-substitute and you'll get:
$\displaystyle \int_{-1}^0 \frac{1}{2} \cdot 2 \cdot (2x+3)^2dx=\frac{1}{6} \cdot (2x+3)^3+c$
to 2.:
Factorize (x^2-1) = (x+1)(x-1). Then you can cancel (x-1) and you'll get:
$\displaystyle \int_3^2\frac{x^2-1}{x-1}dx= \int_3^2 (x+1)dx$.
From here on you know what to do!
Greetings
EB
3. Originally Posted by earboth
Hello,
to 1.:
use u(x) = 2x+3. Then du/dx = 2. That means du = 2*dx.
So you could use the substitution method if there are the factor 2:
$\displaystyle \int_{-1}^0 \frac{1}{2} \cdot 2 \cdot (2x+3)^2dx=\int_{-1}^0 \frac{1}{2} u^2 du$
$\displaystyle \int_{-1}^0 \frac{1}{2} u^2 du= \frac{1}{6}u^3+c$
Now you can re-substitute and you'll get:
$\displaystyle \int_{-1}^0 \frac{1}{2} \cdot 2 \cdot (2x+3)^2dx=\frac{1}{6} \cdot (2x+3)^3+c$
to 2.:
Factorize (x^2-1) = (x+1)(x-1). Then you can cancel (x-1) and you'll get:
$\displaystyle \int_3^2\frac{x^2-1}{x-1}dx= \int_3^2 (x+1)dx$.
From here on you know what to do!
Greetings
EB
Okay, so on the first one, could you do:
$\displaystyle \int_{-1}^0(2x+3)^2dx$
$\displaystyle u = (2x + 3)$
$\displaystyle du = 2dx$ which becomes $\displaystyle \frac{1}{2}du=dx$
then
$\displaystyle \int_1^3u^2\frac{1}{2}du = \frac{1}{2}\int_1^3u^2du$
and solve normally, just using $\displaystyle du$?
4. Originally Posted by cinder
and solve normally, just using $\displaystyle du$?
Yes, that what $\displaystyle du$ means, a function in terms of $\displaystyle u$ whose derivative gives you whatever the function is. Or another way of saying the antiderivative in terms of $\displaystyle u$. That is the entire point of substitution because it simplifys the integrand into a simpler one.
5. Originally Posted by ThePerfectHacker
Yes, that what $\displaystyle du$ means, a function in terms of $\displaystyle u$ whose derivative gives you whatever the function is. Or another way of saying the antiderivative in terms of $\displaystyle u$. That is the entire point of substitution because it simplifys the integrand into a simpler one.
Okay, did I do the substitution right?
6. Originally Posted by cinder
Okay, did I do the substitution right?
Yes
7. Originally Posted by ThePerfectHacker
Yes
Thanks.
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The Traffic Signal
As children we learn that red means stop and green means go. Today, traffic signals are as common as the streets we drive on. Rarely considered is the planning and expense which goes into traffic signal control at an intersection.
Traffic signals allow the orderly movement of vehicles and pedestrians through an otherwise challenging intersection. Usually, signals are at intersections of streets with high traffic volumes.
State Law requires that prior to installing a traffic signal an engineering study must be completed. This study should document that the installation of a signal is necessary to improve the over-all operation of the intersection.
The study for installation of traffic signals is based upon the following criteria documented in the national "Manual on Uniform Traffic Control Devices":
- consistently high traffic volume
- an accident rate which may be reduced
- excessive wait time for vehicles or pedestrians to cross an intersection
- restricted visibility
- a high volume of pedestrian traffic
Traffic Signals as a Tool
It is the mission of the Lincoln Public Works and Utilities Department to provide citizens a safe, convenient, accessible and affordable transportation system.
Traffic signals are an important tool in helping traffic move smoothly through Lincoln. Decisions about a signal's optimum timing and operation are unique to each intersection. Most of Lincoln's traffic signals are monitored by a computer and engineers make adjustments to enhance traffic flow.
A traffic signal is not a substitute for an attentive driver. Follow the direction of traffic signals and be alert to other drivers. It's the "Way to Go."
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- Parentalia (day 1) — a festival for honouring/appeasing the dead began on this day with a number of signs: temples were closed, altars did not have fires burn on them, people were forbidden to get married, and magistrates set down the trappings of their office.
- Fornacalia (day 1) — this was actually a “feriae conceptivae”, which means that it probably wasn’t always held on the same day. Originally, it was a feast of the curiae (an early division of the Roman people) which also seems to have involved a sort of banquet for the gods, although scholars are unsure which gods were specifically honoured. Then again, Ovid claims that rural folk would pray to a divinity called Fornax.
- 196 B.C. — dedication of a Temple of Faunus on the Tiber island
- 194 A.D. — Septimius Severus recognized as Emperor in Egypt
- 250 A.D. — martyrdom of Polyeuctus of Melitene
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What is early literacy?
- Teaching children about reading and writing skills before they can actually read and write.
- Includes developing skills and reading components such as vocabulary, letter knowledge, print awareness, and more through five early literacy practices: singing, talking, reading, writing, and playing.
- Based off of the Every Child Ready to Read 2nd edition initiative.
How do we plan to further incorporate early literacy and emerging readers?
- Presenting a new Early Literacy Storytime.
- Adding more early literacy skills to current programming.
- Creating a continually-changing Early Literacy Center featuring games, puzzles, activities, and learning opportunities through play.
- Adding guided-leveled readers to our collection, in conjunction with the District 58 curriculum.
Early Literacy iPads and AWE Computers
Check out the new preschool computers in the Junior Room! These easy-to-use computers are filled with educational games on math, science, early literacy, and more. Engaging graphics and intuitive menus show kids how fun it is to learn!
Kids and parents can also check out iPads from the Junior Room service desk to play with in the library. These iPads are packed with fun and engaging apps designed for kids to have fun learning with their parents.
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##### Introduction: Prerequisite Check
We teach hard concepts with the easiest words we can. Let's make sure you know the words and ideas we need. This course is just right if you get at least 80% on this test, but less than 70% of the place-out test. This test should be very easy for you, since it is only making sure you have the basics to understand.
Time Left:
10:00
1.
Calculate:
$(-2) \times (5 + 3 \times 3 - 20) + 4$
$$-16$$
$$-8$$
$$0$$
$$8$$
$$16$$
2.
What is $$\frac{11}{6} - \frac{6}{4}$$ expressed in simplest form?
$$\displaystyle \frac{1}{2}$$
$$\displaystyle \frac{1}{3}$$
$$\displaystyle \frac{1}{4}$$
$$\displaystyle \frac{2}{3}$$
$$\displaystyle \frac{5}{2}$$
3.
How many different ways are there to make an outfit with exactly one shirt and one pair of pants, if you have 3 different shirts and 4 different pairs of pants to choose from?
$$3$$
$$4$$
$$7$$
$$12$$
$$24$$
4.
What is the area of this triangle?
$$17$$
$$25$$
$$30$$
$$34$$
$$60$$
5.
Which of these is the prime factorization of 30?
$$3 \times 10$$
$$5 \times 6$$
$$2 \times 3 \times 5$$
$$1 \times 2 \times 3 \times 5$$
$$30$$ has no prime factorization
6.
If you pick one marble from a bag which has 3 red marbles and 7 blue marbles, what is the probability that you pick a red marble?
$$\displaystyle \frac{1}{10}$$
$$\displaystyle \frac{3}{7}$$
$$\displaystyle \frac{3}{10}$$
$$\displaystyle \frac{4}{10}$$
$$\displaystyle \frac{7}{3}$$
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The 2004 Sumatra-Andaman earthquake and resulting tsunami are now infamous for the damage they caused, but at the time many scientists believed this area was unlikely to create a quake of such magnitude. In the March 23 issue of the journal Science, a geophysicist from Rensselaer Polytechnic Institute urges the public and policy makers to consider all subduction-type tectonic boundaries to be "locked, loaded, and dangerous."
"Seismologists have long tried to determine which subduction boundaries are more likely than others to break," says Robert McCaffrey, professor of earth and environmental sciences at Rensselaer. "Yet, the great earthquake of 2004 ruptured a segment that was thought to be among the least likely to go."
On Dec. 26, 2004, the earth beneath the Indian Ocean buckled and ruptured, unleashing one of the largest earthquakes in recorded history. Shockwaves from the magnitude 9.2 (M9) quake created a wall of rushing water that devastated communities up to 1,000 miles away.
M9 earthquakes typically occur at a specific type of tectonic boundary called a subduction zone, where one plate is gently slipping underneath another plate, which causes friction, cracking, and lifting of the plates. An M9 earthquake can be created by only 20 meters of slip between two converging plates -- less then the length of an 18-wheeler truck -- but its effects can be global in their impact.
Slips of this length only occur every 200 to 1,000 years or more at a particular boundary, leaving no reliable historic records to track their frequency, McCaffrey notes. Complete records are only available going back 100 years. Scientists had widely accepted that the age and speed of the subducting plate is important in creating M9 earthquakes, based primarily on support from this 100-year historical record.
But this narrow understanding put the Sumatran subduction zone in a very low risk category. McCaffrey suggests that such limited records are incapable of mapping a trend in geological events th3/19/2007at could be several centuries or more apart.
Geologists also focused on the temperature of subduction zones, indicating that temperature at the plate convergence region plays a strong role in the strength of a resulting earthquake. These thermal considerations place the Andaman subduction zone in the high-magnitude class, but one pitfall with this type of classification is that it characterizes some subduction zones as being incapable of producing an M9.
"[The day of the quake], Earth gave us a stark reminder of the important difference between improbability and impossibility," McCaffrey says. "Our understanding of where and when the next great earthquake will happen is in its infancy at best. We have not had enough time to decipher M9 behavior."
In creating new public policy, McCaffrey urges officials to consider all subduction zones as lethal. "Several are near densely populated land areas, and the potential impacts of shaking and tsunamis cannot be overstated," he says.
When crafting warning systems, policy makers should always remember that an earthquake even hundreds of miles removed can create a tsunami capable of widespread destruction, McCaffrey says. Therefore warning systems need to be created with input and support from many countries, in addition to educational outreach to coastal communities. "These systems need to be strong and they need to be maintained over the long term because we have no way of knowing when the next great earthquake will hit," he says.
"We can never forget what happened," McCaffrey continues. "Now is the time to use the knowledge that we have gained and work to save lives should another M9 hit tomorrow or hundreds of years from now. Many didn't know about tsunamis before the quake; we must make sure that now they never fail to remember their destructive force."
Cite This Page:
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A manger scene is the primary decoration in most southern European, Central American, and South American nations. St. Francis of Assisi created the first living nativity in 1224 to help explain the birth of Jesus to his followers.
Over two thousand years ago a young woman by the name of Mary lived in the small town of Nazareth. Mary was to be married to a carpenter named Joseph. She was unaware of the significance of her life until one day an angel sent from God appeared before her. The angel Gabriel had good news for Mary. She had been chosen by God to have a special baby. The baby was to be God’s son and she would name him Jesus. Mary told Gabriel she would do whatever God asked.
Not long after the angel’s visit, Mary and Joseph were married. Together they made a long journey to Bethlehem where Mary was to have her baby. When they arrived in Bethlehem they did not have a place to stay because the inn there was full. The kind innkeeper told them he had a stable where the animals lived that they could stay in for the night. Jesus, God’s Son, was born that night. Mary wrapped baby Jesus in a small cloth and placed him in a manger of hay.
That night there were shepherds staying in the fields nearby, gathering their flocks of sheep. Suddenly, an angel from God appeared before them in a bright light. They were afraid but the angel reassured them. He said he has brought them good news that will bring great joy to all people. He told them that the Son of God has been born today in the city of Bethlehem. The angel told them that they will recognize Him by this sign; he will be wrapped snugly in cloth, lying in a manger.
The shepherds hurried to go to see Baby Jesus. When they found him in the stable in Bethlehem, they were filled with great joy at the sight of God’s Son. They kneeled before the baby and worshipped him. After seeing the baby, the shepherds told everyone what had happened and that the angel appeared to them and told them that Jesus was God’s Son and to be Savior of the World.
The same night far away in the East, wise men were traveling on their camels when they noticed a very strange bright star in the sky. They knew that this star meant that the King of the Jews, the One who would save the world had been born.
During the time that Jesus was born, a very mean king by the name of Herod ruled the land. The three wise men decided to go to the king to learn where they could find this special baby: the King of the Jews. When King Herod heard this, he got very worried as he thought this new king might take his throne away. King Herod called a meeting with all of the other important people in the area and asked them to find this special child so that he too, could worship this special baby.
King Herod told the wise men to go and find this child. After they had spoken to the King, the wise men left to find the baby. They did not know where to find the baby, but at night they followed the star in the east. They followed the star until they found the very place the star hung over in Bethlehem. When they finally arrived, they were excited and happy. They found baby Jesus laying in Mary’s arms and they kneeled down and worshipped Him.
The wise men brought gifts for Jesus of gold, frankincense and myrrh. Mary thanked them for bringing the gifts for Jesus and the wise men left to find a place to sleep for the night. As they were sleeping, they each had the same dream . The wise men were warned by an angel not to go back to King Herod and tell him about where they found the Jesus as King Herod had intended on killing him.
The wise men returned to their country without going to see King Herod. Soon after, Joseph also had a dream where an angel told him to take Mary and the Baby Jesus to Egypt as King Herod was to order to have Jesus be killed. They left Bethlehem for Egypt immediately. When the wise men did not return to King Herod, he ordered that baby boys in Bethlehem be killed. They never found Jesus as he was safe.
The above article is copied in full from http://www.thehistoryofchristmas.com
Luke 1:78 – because of the tender mercy of our God, by which the rising sun will come to us from heaven
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Contents | Index | Previous | Next
That Versus WhichThe traditional approach to this question is to use "that" with restrictive clauses and "which" with nonrestrictive clauses. While some writers seem to have abandoned the distinction entirely, no better rule has come along to replace the traditional rule. Moreover, the rule is easy to master.
1. Use "that" with restrictive clauses. A restrictive clause is one that limits -- or restricts --the identity of the subject in some way. When writing a restrictive clause, introduce it with the word "that" and no comma. (However, if the subject is or was a human being, use "who" to introduce the clause.)
Correct Restrictive Use:The painting that was hanging in the foyer was stolen.
Explanation: The use of "that" in this sentence is correct if the reader intends to single out the one painting that was in the foyer as the stolen painting. However, if there were several paintings hanging in the foyer, this use would be incorrect, since it would mislead the reader into believing that there had been only one painting in the foyer. The restriction here tells us that the one painting that had been hanging in the foyer was stolen -- not the painting in the living room, or the one in the drawing room, or any of those in the parlor.
2. Use "which" with nonrestrictive clauses. A nonrestrictive clause may tell us something interesting or incidental about a subject, but it does not define that subject. When writing a nonrestrictive clause, introduce it with "which" and insert commas around the clause. (However, if the subject is or was a human being, use "who" to introduce the clause and insert commas around the clause.)
Correct Nonrestrictive Use:The painting, which was hanging in the foyer, was stolen.
Explanation: While this nonrestrictive use tells us that the painting was hanging in the foyer, it does not tell us which of the several paintings in the foyer was the stolen painting. It would be incorrect to use this nonrestrictive clause if there had been only one painting in the foyer, as the sentence leaves open the possibility that there were others.
3. Combining Restrictive and Nonrestrictive Clauses. One can provide both limiting and nonlimiting information about a subject in a single sentence. Consider the following.
Correct Use of Both Restrictive and Nonrestrictive Clauses:The Van Gogh that was hanging in the foyer, which we purchased in 1929 for $10,000, was stolen.Explanation: The restrictive clause beginning with "that" tells us that there was only one Van Gogh hanging in the foyer and that it was stolen. The nonrestrictive clause beginning with "which" tells us what the owner had paid for the painting, but it does not tell us that the owner did not pay another $10,000 for another painting in the same year. It does not limit the possibilities to the Van Gogh that was in the foyer.
4. Restrictive and Nonrestrictive Clauses beginning with "Who." When writing about human beings, we use "who" rather than "that" or "which" to introduce a clause telling us something about that human being. Since "who" is the only option, we distinguish between a restrictive use and a nonrestrictive use by the use of commas.
Correct Restrictive Use:The suspect in the lineup who has red hair committed the crime.Note how the subject "suspect" in this sentence is restricted in two ways: we know that this suspect is both in the lineup and has red hair. As a result, we know that the other suspects, who are not in the lineup, could not have committed the crime. Moreover, of those suspects in the lineup, we know that the one suspect in the lineup with red hair committed the crime. If there were more than one suspect in the lineup with red hair, the above usage would be incorrect because it implies a different meaning.
Correct Nonrestrictive Use:The suspect in the lineup, who owns a red car, committed the crime.In this example, the restrictive clause "in the lineup" tells us that of all possible suspects in the world, the one who committed the crime is in the lineup. However, while the nonrestrictive clause "who owns a red car" tells us something about the suspect, it does not foreclose the possibility that there are several different suspects in the lineup with red cars. The car color may tell us something useful, but it does not restrict us to only one possibility.
Cross Reference: Clauses -- Restrictive and Nonrestrictive
to your browser to complete the exercise.
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# Integral of (secx)^3 with eulers formula
## Main Question or Discussion Point
is it possible to integrate (secx)^3 with eulers formula
could we use that cosx = (e^(ix) + e^(-ix)) /(2)
then take it to the -3 power and multiply it out and try to integrate sec(x)^3 this way.
this is not a homework ?
This will only work well if you integrate from zero to 2 pi. But in that case this particular integral will be divergent.
A rational function of cos and sin integrated from zero to 2 pi amounts to a contour integral of a rational function over the unit circle in the complex plane, so you can directly apply the residue theorem.
can u give me an idea on how to start to integrate this.
HallsofIvy
Homework Helper
It's pretty much just algebra, isn't it?
$$sec(x)= \frac{2}{e^x+ e^{-x}}$$
so
$$sec^3(x)= \frac{8}{(e^x+ e^{-x})^3}$$
You can multiply both numerator and denominator by e3x to get
$$\frac{8e^{3x}}{(e^x(e^x+ e^{-x}))^3}= \frac{8e^{3x}}{(e^{2x}+ 1)^3}$$
$$\int\frac{8e^{3x}dx}{(e^2x+ 1)^3}$$
If you let u= ex, du= exdx and we have
$$\int\frac{8u^2 du}{(u^2+ 1)^3}$$
which can be done in terms of partial fractions.
thanks for doing this it must have taken you a long time ,
But when say multiply both top and bottom by e^(3x)
do you mean e^(3ix) or e(3x)
okay i got it now thanks
Pengwuino
Gold Member
Yes it is with the imaginary exponentials. Simply replace everything with i3x and it should still follow
Eh, seems kind of ugly. This integral has a very natural integration by parts solution.
i wouldn't say very natural my whole goal was to find an easier way then by parts , but i think parts is easier
but in the case of like (e^x)sinx dx this is easier with eulers formula then by parts.
Well I meant it was natural in the sense that sec^2(x) is the derivative of tan(x) and sec(x) differentiated gives sec(x)tan(x) and that really lends itself to a clean solution through integrating by parts.
As for (e^x)sinx, I would agree.
yes i agree. but i was hoping eulers formula would yield an easier soultion but appartenlty not.
HallsofIvy
Homework Helper
Sorry about dropping the "i" !
its ok i got it now .
how do i take the arctan(e^(ix)) how do i make it into the real part.
how do i take the arctan(e^(ix)) how do i make it into the real part.
The real part of arctan[exp(ix)] is pi/4 for real x.
if f(z) is an analytic function such that for real z we have that f(z) is real, then:
f*(z) = f(z*)
The real part of f(z) is thus given by:
Re[f(z)] = [f(z) + f*(z)]/2 = [f(z) + f(z*)]/2
If we put z = exp(i x) for real x, then we have z* = 1/z, therefore:
Re[arctan(z)] = 1/2 [arctan(z) + arctan(1/z)] = 1/2 pi/2 = pi/4
The fact that
arctan(z) + arctan(1/z) = pi/2
for all z follows directly from the fact that for real z the above identity is valid using analytic continuation.
i see thanks
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Public Historian and co-author of "Exploring American Girlhood in 50 Historic Treasures" (Rowman & Littlefield, 2021).
Berdache. A strange word, to be sure, but one that has a long and complicated history. The Berdache tradition is a Native American/American Indian tradition that allowed for gender role change.
Gender role change is the adoption, for various reasons, of a culturally defined social role that is dictated to the opposite sex. This means that a man could adopt the social role of a woman and vice versa. In the Berdache tradition, this was almost always a permanent change.
However, unlike the gender role changes of today (as seen in cross-dressers and transvestites), it did not necessarily dictate who you preferred to sleep with. In fact, the berdache tradition rarely - if ever - dictated sleeping with members of one's own sex. Sexuality and gender in Native American societies were two different concepts, which led to some confusion for the poor Europeans who just couldn't understand why a man would dress as a woman yet still sleep with or marry a woman!
The berdache tradition and its specific roles in society were different for each tribe that practiced it. Yet the berdache tradition played a vital role both in the tribe and at the individual level, allowing for the expression of one's preferred way of life without dictating sexuality.
The berdache tradition in North America was as varied as it was extensive, although it was usually practiced strictly by males. Out of the over 150 tribes known to have sanctioned the tradition, only 30 groups - most of whom resided west of the Rocky Mountains - reported the presence of female berdaches.
Before the full imposition of European culture upon Native Americans, it is believed that berdaches existed in numbers that, in most cases, allowed them to inhabit their own social or cultural category within the tribe. They were respected and, although they spent much of their time with women, they had their own separate group within the village. Most were accorded special social status as well, gaining prestige through their spiritual or artistic abilities.
However, despite this R-E-S-P-E-C-T, Native American cultures held a wide range of views about the berdache way of life. These views ranged from the reverent and respectful to teasing, indifference, and scorn or contempt.
Despite these views, berdaches were still a part of tribal culture because Native American worldviews do not typically allow for either/or comparisons. Rather, their worldviews are expresses in terms of various degrees along a continuum between two opposing ideas. Thus, Native Americans did not view gender as either "male or female" but rather as "varying between" male or female. This continuum thus allowed for those who were born one way but inclined the other to be explained and accepted, especially in a world where tribal warfare and harsh environments could exact a costly toll upon a tribe.
In order to explain berdaches, many Native American traditions include explanations for their existence in creation or other myths. Native Americans also recognized the possibility of other explanations. The Inuit viewed berdaches as infants who had been one gender as a fetus but became the opposite gender at birth (called sipiniq). However, at birth one retained the gendered spirit of the fetus, thus showing why a boy could have the "spirit" of a girl. The berdache tradition may also have been created as a means of transferring property or helping in a specific gender role when one lacked the son or daughter dictated by tribal orientation (i.e., one lacked a son in a tribal culture where property was inherited through paternal lines or where only males were allowed to hunt, or vice versa).
A universal characteristic of berdaches was their participation in at least some work reserved for the opposite gender. Female berdaches were allowed to participate in hunting and warfare, while male berdaches were allowed to participate in farming, herding, gathering food, weaving, knitting, basketry, pottery, and leatherwork. Many berdaches gained social acknowledgement and prestige for their accomplishments in these roles.
In fact, berdaches were so well known for their skills that many tribes viewed berdaches as inherently successful, generating both a powerful inspiration for young people to become berdaches as well as for parents to value education and advanced training for children who chose the berdache way of life. However, these skills were typically never valued as much or more than the skills of men (in patriarchal societies, or vice versa in matriarchal societies).
Their intermediate nature also allowed berdaches to become go-betweens in disputes between the sexes, able to resolve spousal conflicts or facilitate romances. In the case of male berdaches, they were also free from the cultural restrictions imposed during women's menstruation, pregnancy, or nursing. This freedom allowed them to help with increased burdens of women's work, when other women were restricted, as well as to become continually productive. Berdaches were also allowed to assume parental roles for orphaned children or for children of large families. A modern contemporary of this is Terry Calling Eagle, a Lakota berdache who adopted children whose parents were drunks and unable to provide for them. Thus, berdaches even offered solutions to social problems within the tribes.
Read More From Owlcation
A common (but not universal) characteristic of berdaches was that they were believed to possess supernatural powers. It was believed that they could mediate between the psychic and physical since they possessed the visions of both sexes (called "double vision" by certain tribes). This was due to both their intermediate status in society as well as the belief that the spirits must have taken great care to create an individual so unique in society.
Some berdaches assumed the role of shaman, although this role was not limited to berdaches. This assumption was commonly seen among the Mohaves, Klamath, Yurok, and other California Indian groups.
Berdaches also occupied roles not associated with shamanism. Navajo berdaches - called nadle - were responsible for preparation and cooking of sacred food at large ceremonial gatherings. Other berdache traditions dictated their involvement in blessing objects, conducting burials, and grooming men before a hunt. It was commonly believed that the berdache's participation would provide the individual or tribe with luck or protection in its endeavors.
Berdaches were not homosexuals in the sense that Americans (and other Westerners) know them. Native American sexuality was distinctly different from European conceptions, which unfortunately led to a lot of misinterpretation about the berdache role in Western literature.
Sexuality in Native American world views as a gift from the spirit world, to be enjoyed and appreciated. While most descriptions of berdaches stress homosexuality, they were not limited to this practice.
For berdaches, homosexual behavior was the most commonly noted type of sexuality, at times being a cultural expectation of the berdache role. Berdaches were often the non-masculine role in these relations. However, these relations did not make non-berdache males into berdaches or require that either refrain from marrying or having sexual relations with a woman. There are some cases where men married male berdaches, and in some tribes this even accorded a special social status (akin to a very good marriage of two rich parties in European traditions). Berdaches also had heterosexual relations and marriages.
Despite this freedom, there are no known accounts of berdaches having sexual relations or marrying other berdaches. This may be due to the fraternity shared by berdaches, and sexual relations or marriage would have violated the kin group ties of berdaches. It may also have been due to the gender-based economy of Native Americans, as having two male berdaches would have meant a lack of someone to continually fill the male role in the family's economic duties. (In other words, you have to have a "husband" and "wife" roles to make a marriage, and having two of one and none of the other can cause problems.)
Berdachism largely disappeared from the written record following the initial European encounters. Many European cultures were unable to fit the berdache role within their already defined concept of gender. While the tradition did continue, it became similar to homosexuality before the mid-1900s: hidden in the closet.
Today, berdachism has re-emerged on the cultural scene, providing a new way of understanding Native American societies. It also provides an outlet for modern-day Native Americans who have been lacking the freedom to express this gender role.
There are two distinct movements as a result. First, anthropologists studying Native America are re-thinking the concept of gender as a whole. Accounting for European bias, we are beginning to understand that gender has meant a multitude of things in different societies and is often distinctly separate from one's sexual orientation.
Second, berdaches have been re-identified as "two-spirits," creating a bridge between modern urban or homosexual Native Americans and their traditional past. The creation of this self-chosen terminology has also enabled Native Americans to separate from their Western homosexual counterparts, bridging the gap between native tribes while providing a unique Native experience.
What lies ahead for the berdache / "two-spirit" tradition is a mystery. Hopefully, the acknowledgement of this tradition - and the European biases which led to widespread discrimination and fear - will provide a meaningful contribution to our modern debates over gender roles, marriage equality, gay rights, and the like. By looking to the past, and clearing up the confusions rife within it, we are able to see a broader, more accepting worldview that could perhaps solve problems we experience today.
If we are able to open our minds to those who choose to live beyond traditional gender roles - just as we have accepted women expanding their traditional roles - perhaps we will be able to accept that gender is a socially-made construct - something alterable and impermeable - that has discriminated against others who would otherwise make meaningful contributions to society if not for the fear and hatred. The Native Americans were able to provide "two-spirits" with a place in their world that did not instill fear and hatred, but rather a society that accepted them and recognized their invaluable contributions both as humans and as part of the societies in which they lived.
Eric Langenthal on January 20, 2020:
I came across the term "berdache", for the first time ever in a novel by Sebastian Barry named, "Days Without End". I had never heard of "two-sprited" American Indians before and i found it illuminating and even a little shocking, considering it comes from a so-called "savage" culture. This article is extremely informative and interesting, thank you so much for writing it!
Cynara on November 25, 2017:
My husband is part Mohawk (Iroquois nation). Our grandson is now 15 and has struggled since he was a wee one with his gender identity. He has always liked to be in the home rather than being out and into sports etc. He has always favored the feminine in action and for the last few years, dress. This has caused him much confusion, but is blessed with a loving & understanding mother, sister and even father. This article will go a long way to help him understand his "two-spirit" nature connected to his own ancestry. Thank you.
Mary Norton from Ontario, Canada on November 19, 2015:
This is really iterating and worth studying further to enlighten our concept of gender. This two-spirit concept intrigues me.
Theophanes Avery from New England on June 21, 2013:
Very interesting read. I have come across the term "two-spirit" before but this article defined it much better than a passing reference! Gender and gender roles can be such fascinating things when you look at how all the different cultures around the world view them. I've written about different forms of marriage, some asexuality articles, and even a few articles on animals and their take on gender roles and sexuality. It is a very complicated and far-reaching topic. I am glad you took on the challenge of writing about just a slice of it. I look forward to see what else you have up your sleeve.
Mr Archer from Missouri on July 26, 2012:
I never expected to view something like this on here. Very nice surprise. I have read in books periodically of such occurring, and in the movie Little Big Man with Dustin Hoffman, one of the charators was a berdache. Well done and informative hub.
Greensleeves Hubs from Essex, UK on June 20, 2012:
Southern Muse; somewhat bizarrely, (because I can't say it's a subject matter of particular specific interest to me!) I really really like this article. That is because it is well written, and because it tells us something about the culture, and philosophy, and indeed practicalities of native Indian life. It's an eye-opener about the liberal nature of native society which would surprise many.
I think it's such a good article of its kind, I have included it as one of my favourites among ten hubs on native Americans which I have just reviewed and published on this site. Hope it attracts a few more viewings and comments on your page! Voted up. Alun
nikki_m from Kansas City, Missouri on August 22, 2011:
Very interesting Hub, I'm glad they posted it on the blog. America, along with much of the rest of the world, seem to have such a close minded view of gender identity. It's so refreshing to learn a little bit about other views and beliefs regarding it. I have to say, I'm surprised by a lot of the information in here! To think that a culture that many people regarded as "savage" when they arrived here, comparing to European society, actually seems to be more open minded and accepting of this is kind of a reality check!
Thanks for writing it!
William J. Prest from Vancouver, Canada on July 15, 2011:
I found this to be a very interesting piece of writing. I have several on the First Nations and I am going to create a link to here.
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Subido por LJ RB
# 1.Density-pycnometer
Anuncio
```Name of student:………………………………
1
DENSITY DETERMINATION BY PYCNOMETER
Task: Determine the densities of one solid material and one liquid
Density
The density () is elementary physical property of matter. For a homogeneous object it is
defined as the ratio of its mass (m) to its volume (V) – Eq.1
m
V
[kg m-3]
[1]
Numerically it represents the mass per unit volume of matter. As it follows from equation
[1], the SI unit of density is kg m-3. However, g cm-3 is another unit commonly used in
a laboratory. Its conversion is:
1 g cm-3 = 1000 kg m-3
[2]
The volume of an object increases with increasing temperature, because of the matter’s
volumetric thermal expansion. Therefore, according to equation [1], the density of an
object depends on its temperature, with higher temperature resulting in lower density.
The density of a gas further depends on the pressure as well. Nevertheless, this effect is
negligible in a case of liquid and/or solid matter.
There are several experimental methods used for density determination of liquids. We
will learn how to use pycnometer in this assignment.
A. Density determination of liquids by pycnometer
Density determination by pycnometer is a very precise method. It uses a working liquid
with well-known density, such as water. We will use distilled water, for which temperature dependent values of density (H2O) are shown in Table 1. The pycnometer (Figure 1)
is a glass flask with a close-fitting ground glass stopper with a capillary hole through it.
This fine hole releases a spare liquid after closing a top-filled pycnometer and allows for
obtaining a given volume of measured and/or working liquid with a high accuracy.
Figure 1 Pycnometer
1
- First we fill pycnometer with distilled water. According to equation [1], the volume of
water that is filling the pycnometer and the stopper is:
V
mH 2O
[3]
H 2O
where: mH2O is experimentally determined weight of water (empty pycnometer weight
subtracted).
- We repeat the procedure for the liquid with unknown density (L) and determine its
weight mL (measured weight minus weight of empty pycnometer). Volume V obtained
in this measurement is the same as the volume of water determined from equation [3].
It follows alternated equation:
m
V L
[4]
L
- Combining equations [3] and [4]:
m H 2O
H 2O
mL
[5]
L
yields a relation that provides the density of measured liquid (ρL):
L
mL
H 2O
mH 2O
[6]
B. Density determination of solid matter by pycnometer
Pycnometer can be also used to determine the density of homogeneous solid object that
does not dissolve in working liquid (water). First, we need to measure the weight of
pycnometer together with inserted object m0+mS. We add water and determine the weight
m´H2O (weight m0+mS+ mH2O). First, we need to measure the weight of pycnometer
together with inserted object m0+mS. We add water and determine the weight mH 2O
(measured weight minus m0+mS). The volume of added water VH 2O can be obtained as:
m
VH 2O H 2O
[7]
H 2O
The volume of measured solid object VS is the difference between the volume of water
that fills the empty pycnometer V and volume VH 2O
m
mH 2O
VT V VH 2O H 2O
[8]
H 2O
Density of measured object S can be then calculated as
m
S S
[9]
VS
2
Experimental procedure:
Accuracy of herein described method for density determination of liquid and/or solid
matter relies on precise measurements of weight and volume. Since it is important to
determine weight of empty pycnometer in its dry state, we do so at the beginning.
1. Determine the weight of empty, dry pycnometer m0 and write value to the Table 2.
2. Fill about 1/3 of pycnometer volume with objects made of examined material and
measure the weight m1.
3. Add water such that pycnometer as well as capillary hole in the stopper is filled with
water. Dry the spare water that leaks through the capillary hole with a filter paper and
measure total weight m2.
4. Empty pycnometer filled with distilled water only. Use the filter paper to dry the
spare water again and measure the weight (m3).
5. Empty pycnometer. Rinse it once with a liquid whose density you are going to
determine next. Fill pycnometer with the liquid as previously and measure the weight
m4.
6. Clean pycnometer carefully after finishing the experiment. Rinse it with distilled
water and let dry.
7. Measure the laboratory temperature t, which determines the temperature of examined
liquids and solid objects.
8. Calculate the weight of water mH2O = m3 – m0, weight of measured liquid mL = m4 –
m0 and determine density of liquid according Equation 6.
9. Calculate objem volume VS following Equation 8 and its density (ρS) according
Equation 9
Table 1 Temperature dependence of distilled water density H2O.
t [C]
H2O [g cm-3]
15
0.99996
16
0.99940
17
0.99990
18
0.99985
19
0.99978
20
0.99820
21
0.99799
22
0.99777
23
0.99754
24
0.99730
25
0.99705
3
Table 2 The weight of empty pycnometer m0, pycnometer with solid object m1,
pycnometer with solid object and added water m2, pycnometer with water
m3 and pycnometer with liquid m4
t = …….°C
m0 [g]
m1 [g]
m2 [g]
m3 [g]
m4 [g]
ρS
ρL
kg m-3
kg m-3
g cm-3
g cm-3
Calculations:
Conclusion:
4
```
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# How to calculate this expected value
How do you calculate this expected value? I have tried everything and I cant seem to get the right answer. The distribution function of a random variable $X$ is given by: $$F(X)=\begin {cases} 0& x\lt -3 \\ \frac38 &-3 \le x \lt 0 \\ \frac12 & 0 \le x \lt 3 \\ \frac34 & 3 \le x \lt 4 \\ 1 & x \ge 4\end {cases}$$
I hope this makes sense, in my practice book it has it all lined up nice and neat if it helps to think of it that way. I know that $E(X)=\frac58$ but I'm just not sure how thats the answer.
-
See if I got the $\LaTeX$ right. You can right click and Show Math as > TeX commands to see what I did. – Ross Millikan Oct 26 '12 at 5:17
Note that the function $F$ is the cumulative distribution function of $X$. The usual notation is $F(x)$, or $F_X(x)$ if we want to be reminded of whch random variable we are working with. Very importantly, it should never be written $F(X)$.
By definition, $$F_X(x)=\Pr(X\le x).$$ With continuous random variables, we can be pretty casual about the use of inequality symbols. With discrete random variables, we have to be much more careful, and cannot casually replace $\le$ by $\lt$.
Look at the first part of the specification of $F$. It tells us, among other things, that $F(-17)=0$. So $\Pr(X\le -17)=0$: there is no "weight" at $-17$ or to the left of it. We also have $F(-\pi)=0$: so $\Pr(X\le -\pi)=0$.
There is a sudden jump in the cumulative distribution function at $-3$. A tiny bit to the left of $-3$, it was $0$. But all of a sudden, at $-3$, $F$ has value $\dfrac{3}{8}$. The jump at $-3$ means that we must have $\Pr(X=-3)=\dfrac{3}{8}$.
Then things are steady until $0$, the cumulative distribution function is $\dfrac{3}{8}$ at $-2$, $-1$, $-0.2$. So $\Pr(X\le -0.2)=\dfrac{3}{8}$, no weight has been added. But at $x=0$, the cdf jumps to $\dfrac{1}{2}$. So $\Pr(X=0)=\dfrac{1}{2}-\dfrac{3}{8}=\dfrac{1}{8}$.
Similarly, $\Pr(X=3)=\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{1}{4}$. similarly, $\Pr(X=4)=\dfrac{1}{4}$.
Now we are at a simple expected value problem. $$E(X)=(-3)\frac{3}{8}+(0)\frac{1}{8}+(3)\frac{1}{4}+(4)\frac{1}{4}=\frac{5}{8}.$$
Remark: For a non-negative integer-valued random variable $Y$, there is a useful way to compute $E(Y)$: $$E(Y)=\sum_{i=1}^\infty \Pr(Y\ge i).$$ We can adapt this to our problem by adding $3$ to $X$, computing the expectation by using the above formula, and subtracting $3$ at the end. One needs to be careful in using the cdf to calculate $\Pr(X\ge i)$.
There is a useful analogue of the above formula for non-negative random variables with continuous distribution. For some details, please look at this.
-
if by definition the $E(X)= \sum_x xP(x)$ how come you dont include the numbers between the steps like for this one -2, and -1 times their probability of (3/8) and so on? – TheHopefulActuary Oct 26 '12 at 12:32
I was worried that if you had not seen the special formula in the comment, it might confuse you. So look only at the main part. Suppose you win $1$ dollar with probability $\frac{5}{6}$, $3$ dollars with probabiity $\frac{1}{9}$, and $7$ dollars with probability $\frac{1}{18}$. Then your mean win is $(1)(5/6)+(3)(1/9)+(7)(1/18)$. The in-between numbers don't figure at all in the calculation. But you know that. The important point is that the fact that the cdf is $3/8$ at $x=-2$, and for that matter at $-2.1234$, does not mean that we get $-2$ with probability $3/8$. (continued) – André Nicolas Oct 26 '12 at 13:27
(Cont) The function of your problem, which should have been called $F_X(x)$, is the cumulative distribution function, it does not give the probability that $X=x$, it gives the probability that $X\le x$. That's crucially important. In our case, $F(-2)=3/8$, and $F(-0.7)=3/8$. So with probability $3/8$, $X\le -2$, and with the same probability $3/8$, $X\le -0.7$. That means that there is probability $0$ that $-2\lt X\le -0.7$. When caps are used, like $F$, it usually means cumulative. The problem should have said cumulative distribution function, for clarity. – André Nicolas Oct 26 '12 at 13:36
@Kyle: Your comment above shows you may have some trouble with (cumulative) distribution function. So I altered the beginning of my answer to try to explain a little more. – André Nicolas Oct 26 '12 at 13:58
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Music is the most universal language that we have, way more so than any dialect or tongue. You can play a melody to a child in China and the same melody to a child in South Africa. And despite the huge differences between those two children, they will still draw some of the same truths from that melody. Now, I think the reason why music has this universality, this way of speaking to each and every one of us, is that somehow it's capable of holding up a mirror to us that reveals, in some small or large way, a little bit of who or what we are. By logical extension of this, if music is this universal force, then surely groups of musicians — let's call them orchestras — should reflect every aspect of the community. Logical, but not necessarily true. At TEDxBrussels today, we've been looking forward to the future — 50 years from now. Well, I'm going to ask you to go in the other direction for a minute, to come back with me 50 years into the past, the early 1960s to be precise. And if you took a look at all the great orchestras of the world at that time, a snapshot, how many women do you think you would find playing in those orchestras? The answer: virtually none. Well, here we are 50 years on, in 2011, and pretty much every orchestra on the planet has a fantastic and healthy balance between the sexes. "Of course!" I hear you say, "Totally logical." But how about another aspect of the community? The disabled community. Do we find them well-represented in the great orchestras of our world? Well, I can tell you as a conductor, I work with orchestras around the world all the time, and I can count on the fingers of one hand the number of disabled musicians I've encountered in any orchestra, anywhere. Why is this? You can't tell me that there aren't millions upon millions of prodigiously gifted musicians of disability around the world. Where is their platform? Where is the infrastructure that creates a space for them so that they can collaborate with other great musicians? So, ladies and gentlemen, as you can probably tell, I'm on a bit of a mission. And this mission has a personal root to it. I have four children, the youngest of whom was born with cerebral palsy. She's now five, and through her glorious existence, I suppose I have now become a fully paid-up member of the amazing, dizzyingly wonderful disabled community. And I find myself looking at the Paralympics and thinking what an incredible model that is. It's taken a good five decades, actually, but I can say with hand on heart that when the Paralympics comes to London next year, there will not be an intelligent person anywhere on the planet who does not absolutely believe in the validity of disabled sportspeople. What an amazing position to be in! So, ladies and gentlemen, where the hell is music in all this? Apologies to any of you who are sports fans, but music is far more universal than sport. Where is the platform? Where is their voice? So, we in the UK are at the very early stages in forming what will be Britain's first-ever national disabled orchestra. We are going to call it the British Paraorchestra, because with the world's eyes on London next year and particularly on the Paralympics, we want to throw down the gauntlet to every single other country that is represented there, to say to them, "Here's our paraorchestra. Where's yours?" Every country should have a multiplicity of paraorchestras of all shapes and sizes, no question. Now, today is a very special day for me, because it is the first time that the first four members of my little embryonic paraorchestra are going to play in public; four extraordinary musicians of which the number will grow and grow. I hope in the end the Paraorchestra could even be as big as 50 musicians. We present to you today a little sonic adventure, a little piece of improvisational whimsy, if you like, a piece on which, of course, the ink is still wet, the clay is still wet. After all, improvisation is never a fixed thing. We decided what we wanted to share with you, at the heart of our improvisation, was a tune which is beloved of British people. It's one of the only folk melodies that we still recognize in our culture. And here's an interesting thing: folk music can tell you an awful lot about the cultural DNA of the country from which it originates. You see, we in Britain are quietly melancholic. You know, the rain ... it does rain. The food's not so good. (Laughter) Quietly melancholic. Not blackly so, just quietly so. And as Shakespeare put it so brilliantly in "Twelfth Night," he loves music that has "a dying fall." So this melody, "Greensleeves," is chock-full of "dying fall." You may know this tune. (Singing) Da, da, da da da da, dying fall. (Laughter) Da da da, da da da da, dying fall. Da dee, da da na na ... dying fall ... na na nee, na ah ah ah ah. Brief burst of sunshine, ladies and gentlemen, the chorus — (Singing) Ya da da da, dying fall ... (Laughter) (Singing) Da da dee, da da da da, dying fall ... Ya da da da, dying fall ... OK? It's like we need some melodic Viagra in our culture, ladies and gentlemen. (Laughter) (Applause) It goes without saying that we are very much at the starting gates with this project. We need your help, we need the global community to help us deliver this dream, so that this orchestra can be full steam ahead by summer 2012. If you think there's any way that you can help us, please, please, get in touch. And so, ladies and gentlemen, it gives me enormous pride, pleasure and joy to introduce to you, with a short improvisation upon that most melancholic tune, "Greensleeves," the first four members of the British Paraorchestra. (Applause) (Cheers) (Music) (Applause) (Cheers) (Applause)
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The debut of the British Paraorchestra
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Dementia isn't a specific disease. Instead, dementia describes a group of symptoms affecting memory, thinking and social abilities severely enough to interfere with daily functioning.
Dementia indicates problems with at least two brain functions, such as memory loss and impaired judgment or language, and the inability to perform some daily activities such as paying bills or becoming lost while driving.
Though memory loss generally occurs in dementia, memory loss alone doesn't mean you have dementia. There is a certain extent of memory loss that is a normal part of aging.
Many causes of dementia symptoms exist. Alzheimer's disease is the most common cause of a progressive dementia. Some causes of dementia may be reversible.
Dementia symptoms vary depending on the cause, but common signs and symptoms include:
- Memory loss
- Difficulty communicating or finding words
- Difficulty with complex tasks
- Difficulty with planning and organizing
- Difficulty with coordination and motor functions
- Problems with disorientation, such as getting lost
- Personality changes
- Inability to reason
- Inappropriate behavior
When to see a doctor
See a doctor if you or a loved one experiences memory problems or other dementia symptoms. Some treatable medical conditions can cause dementia symptoms, so it's important that a doctor determine the underlying cause.
Alzheimer's disease and several other types of dementia worsen over time. Early diagnosis gives you time to plan for the future while you can participate in making decisions.
Dementia involves damage of nerve cells in the brain, which may occur in several areas of the brain. Dementia may affect people differently, depending on the area of the brain affected.
Dementias can be classified in a variety of ways and are often grouped by what they have in common, such as what part of the brain is affected, or whether they worsen over time (progressive dementias).
Some dementias, such as those caused by a reaction to medications or an infection, are reversible with treatment.
Types of dementias that are not reversible and worsen over time include:
Alzheimer's disease. In people age 65 and older, Alzheimer's disease is the most common cause of dementia. People generally may develop symptoms after age 60, but some people may have early-onset forms of the disease, often as the result of a defective gene.
Although in most cases the exact cause of Alzheimer's disease isn't known, plaques and tangles are often found in the brains of people with Alzheimer's. Plaques are clumps of a protein called beta-amyloid, and tangles are fibrous tangles made up of tau protein.
Certain genetic factors also may make it more likely that people will develop Alzheimer's.
Alzheimer's disease usually progresses slowly over about eight to 10 years. Your cognitive abilities slowly decline. Eventually, the affected areas of your brain don't work properly, including parts of your brain that control memory, language, judgment and spatial abilities.
Vascular dementia. Vascular dementia, the second most common type of dementia, occurs as a result of brain damage due to reduced or blocked blood flow in blood vessels leading to your brain.
Blood vessel problems may be caused by stroke, infection of a heart valve (endocarditis) or other blood vessel (vascular) conditions.
Symptoms usually start suddenly and often occur in people with high blood pressure or people who have had strokes or heart attacks in the past.
Several different types of vascular dementia exist, and the types have different causes and symptoms. Alzheimer's disease and other dementias also may be present at the same time as this dementia.
Lewy body dementia. Lewy body dementia affects approximately 10 percent of people with dementia, making it one of the most common types of dementia. Lewy body dementia becomes more common with age.
Lewy bodies are abnormal clumps of protein that have been found in the brains of people with Lewy body dementia, Alzheimer's disease and Parkinson's disease.
Lewy body dementia symptoms are similar to symptoms of Alzheimer's disease. Its unique features include fluctuations between confusion and clear thinking (lucidity), visual hallucinations, and tremor and rigidity (parkinsonism).
People with Lewy body dementia often have a condition called rapid eye movement (REM) sleep behavior disorder that involves acting out dreams.
Frontotemporal dementia. This type of dementia tends to occur at a younger age than does Alzheimer's disease, generally between the ages of 50 and 70.
This is a group of diseases characterized by the breakdown (degeneration) of nerve cells in the frontal and temporal lobes of the brain, the areas generally associated with personality, behavior and language.
Signs and symptoms of frontotemporal dementia can include inappropriate behaviors, language problems, difficulty with thinking and concentration, and movement problems.
As with other dementias, the cause isn't known, although in some cases this dementia is related to certain genetic mutations.
Other disorders linked to dementia
Huntington's disease. This inherited disease causes certain nerve cells in your brain and spinal cord to waste away.
Signs and symptoms usually appear during your 30s or 40s. People may experience personality changes, such as irritability or anxiety.
The condition causes a severe decline in thinking (cognitive) skills over time. Huntington's disease also causes weakness and difficulty with walking and movement.
Traumatic brain injury. This condition is caused by repetitive head trauma, such as experienced by boxers, football players or soldiers.
Depending on the part of the brain that's injured, this condition can cause dementia signs and symptoms such as uncoordinated movement and impaired speech, as well as slow movement, tremors and rigidity (parkinsonism). Symptoms may not appear until many years after the actual trauma.
A person who has experienced a single traumatic head injury could develop a similar condition called posttraumatic dementia, which may cause symptoms such as long-term memory problems.
Creutzfeldt-Jakob disease. This rare brain disorder usually occurs in people without risk factors. This condition may be due to an abnormal form of a protein. Creutzfeldt-Jakob disease sometimes may be inherited or caused by exposure to diseased brain or nervous system tissue.
Signs and symptoms of this fatal condition usually appear around age 60 and initially include problems with coordination, memory, thinking and vision. Symptoms worsen over time and may include the inability to move or talk, blindness, or infections.
- Parkinson's disease. Many people with Parkinson's disease eventually develop dementia symptoms (Parkinson's disease dementia).
Dementia-like conditions that may be reversed
Some causes of dementia or dementia-like symptoms can be reversed. Your doctor may identify and treat these causes:
Infections and immune disorders. Dementia-like symptoms can result from fever or other side effects of your body's attempt to fight off an infection.
People may develop thinking difficulties if they have brain infections like meningitis and encephalitis, untreated syphilis, Lyme disease, or conditions that cause a completely compromised immune system, such as leukemia.
Conditions such as multiple sclerosis that arise from the body's immune system attacking nerve cells also can cause dementia.
- Metabolic problems and endocrine abnormalities. People with thyroid problems, too little sugar in the bloodstream (hypoglycemia), too low or too high amounts of sodium or calcium, or an impaired ability to absorb vitamin B-12 may develop dementia-like symptoms or other personality changes.
- Nutritional deficiencies. Dementia-like symptoms can occur as a result of not drinking enough liquids (dehydration); not having enough thiamin (vitamin B-1), a condition common in people with chronic alcoholism; and not having enough vitamins B-6 and B-12 in your diet.
- Reactions to medications. Dementia-like symptoms may occur as a reaction to a single medication or because of an interaction of several medications.
- Subdural hematomas. Subdural hematomas are caused by bleeding between the surface of the brain and the covering over the brain. They can cause symptoms similar to dementia.
Poisoning. Dementia-like symptoms can occur as a result of exposure to heavy metals, such as lead, and other poisons, such as pesticides.
Dementia-like symptoms may also occur in some people who have abused alcohol or recreational drugs. Symptoms may disappear after treatment, but in some cases symptoms may still be present after treatment.
- Brain tumors. Dementia rarely can result from damage caused by a brain tumor.
Anoxia. This condition, also called hypoxia, occurs when organ tissues aren't getting enough oxygen. Anoxia may occur due to severe asthma, heart attack, carbon monoxide poisoning or other causes.
If you've experienced a severe lack of oxygen, recovery may take longer. Symptoms, such as memory problems or confusion, may occur during recovery.
Normal-pressure hydrocephalus. Sometimes people have a condition caused by enlarged ventricles in the brain (normal-pressure hydrocephalus). This condition can cause walking problems, urinary difficulty and memory loss.
Shunt surgery, which delivers cerebrospinal fluid from the head to the abdomen or heart, may help these symptoms.
Many factors can eventually lead to dementia. Some factors, such as age, can't be changed. Others can be addressed to reduce your risk.
Risk factors that can't be changed
- Age. As you age, the risk of Alzheimer's disease, vascular dementia and several other dementias greatly increases, especially after age 65. However, dementia isn't a normal part of aging, and dementia can occur in younger people.
Family history. If you have a family history of dementia, you're at greater risk of developing the condition. However, many people with a family history never develop symptoms, and many people without a family history do.
If you have specific genetic mutations, you're at significantly greater risk of developing certain types of dementia.
Tests to determine whether you have certain genetic mutations are available.
- Down syndrome. By middle age, many people with Down syndrome develop the plaques and tangles in the brain that are associated with Alzheimer's disease. Some may develop dementia.
Risk factors you can change
You may be able to take steps to control the following risk factors of dementia.
- Heavy alcohol use. People who consume large amounts of alcohol may have a higher risk of dementia. Although studies have shown that moderate amounts of alcohol may have a protective effect, abuse of alcohol increases your risk of developing dementia.
Atherosclerosis. This buildup of fats and other substances in and on your artery walls (plaques) can reduce the blood flow to your brain and lead to stroke. Reduced blood flow to your brain can also cause vascular dementia.
Some research shows there may be an association between blood vessel (vascular) conditions and Alzheimer's disease.
- Blood pressure. Several studies show high or low blood pressure may increase your risk of developing dementia.
- Cholesterol. If you have high levels of low-density lipoprotein (LDL) cholesterol, you may have an increased risk of developing vascular dementia or Alzheimer's disease. Researchers continue to study how cholesterol may affect dementia.
- Depression. Although not yet well understood, late-life depression, especially in men, may be an indication of the development of dementia.
- Diabetes. If you have diabetes, you may have an increased risk of developing Alzheimer's disease and vascular dementia.
- High estrogen levels. Women taking estrogen and progesterone years after menopause may be at greater risk of developing dementia.
- Homocysteine blood levels. Elevated blood levels of homocysteine, a type of amino acid produced by your body, may increase your risk of developing vascular dementia.
- Obesity. Being overweight or obese during the middle of your life may increase your risk of developing dementia when you're older.
- Smoking. Smoking may increase your risk of developing dementia and blood vessel (vascular) diseases.
Dementia can affect the functioning of many body systems and, therefore, the ability to carry out day-to-day tasks. Dementia may lead to several problems, including:
Inadequate nutrition. Many people with dementia will eventually reduce or stop eating and drinking. They may forget to eat or think they've already eaten. Changes in meal times or noise distractions in their environment may affect whether they eat.
Often, advanced dementia causes you to lose control of the muscles used to chew and swallow. This may put you at risk of choking or aspirating food in your lungs. If this happens, it can block breathing and cause pneumonia.
You also lose the feeling of hunger and, with it, the desire to eat. Depression, side effects of medications, constipation and other conditions also can decrease your interest in food.
- Reduced hygiene. In moderate to severe stages of dementia, you'll eventually lose the ability to independently complete daily living tasks. You may no longer be able to bathe, dress, brush your hair or teeth, or use the toilet on your own.
- Difficulty taking medications. Because your memory is affected, remembering to take the correct amount of medications at the right time can be challenging.
Deterioration of emotional health. Dementia changes behaviors and personality. Some of the changes may be caused by the actual deterioration happening in your brain, while other behavioral and personality changes may be emotional reactions to coping with the changes in your brain.
Dementia may lead to depression, aggression, confusion, frustration, anxiety, a lack of inhibition and disorientation.
Difficulty communicating. As dementia progresses, you may lose the ability to remember the names of people and things. You may have trouble communicating with others or understanding others.
Difficulty communicating can lead to feelings of agitation, isolation and depression.
- Delusions and hallucinations. You may experience delusions in which you have false ideas about another person or situation. Some people, especially those with Lewy body dementia, may have visual hallucinations.
- Sleep difficulties. You may experience sleep difficulties, such as waking up very early in the morning. Some people with dementia may have restless legs syndrome or rapid eye movement (REM) sleep behavior disorder, which also can interfere with sleep.
- Personal safety challenges. Because of a reduced capacity for decision-making and problem-solving, some day-to-day situations can present safety issues for people with dementia. These include driving, cooking, falling, getting lost and negotiating obstacles.
Most likely, you'll first see your primary care provider if you have concerns about dementia. In some cases, you may be referred to a doctor trained in nervous system conditions (neurologist).
Because appointments can be brief, and because there's often a lot to talk about, it's a good idea to be well-prepared. If you're a caregiver for someone with more advanced dementia, you'll likely be the one gathering information from the doctor. Here's some information to help you get ready.
What you can do
- Be aware of any pre-appointment restrictions. At the time you make the appointment, be sure to ask if there's anything you need to do in advance.
- Write down any symptoms, including any that may seem unrelated to the reason for which you scheduled the appointment.
- Write down key personal information, including any major stresses or recent life changes.
- Make a list of all medications, vitamins or supplements being taken.
- Take a family member, friend or caregiver along, if possible. Sometimes it can be difficult to soak up all the information provided during an appointment.
Preparing a list of questions will help make the most of your time with the doctor. List questions from most important to least important in case time runs out. For dementia, some basic questions to ask the doctor include:
- What is likely causing my symptoms?
- Are there other possible causes for my symptoms?
- What kinds of tests are necessary?
- Is the condition likely temporary or chronic?
- What's the best course of action?
- What are the alternatives to the primary approach being suggested?
- How can dementia and additional health issues best be managed together?
- Are there any restrictions?
- Is there a generic alternative to the medicine being prescribed?
- Are there any brochures or other printed material that I can take home with me? What websites do you recommend?
In addition to the questions that you've prepared to ask your doctor, don't hesitate to ask questions during your appointment at any time that you don't understand something.
What to expect from your doctor
The doctor is likely to ask you and your caregiver a number of questions such as:
- What symptoms are you experiencing? For example, are you having trouble with finding words or remembering events or with focusing attention? Are you getting lost or developing changes in personality?
- When did symptoms begin?
- Have symptoms been continuous or occasional?
- How severe are symptoms?
- What, if anything, seems to improve symptoms?
- What, if anything, appears to worsen symptoms?
- Is there a family history of dementia or related conditions such as Huntington's or Parkinson's disease?
- Are there any activities that you have had to stop because of difficulty thinking through them?
Memory loss and other dementia symptoms have many causes, so diagnosing dementia and other related conditions can be challenging and may require several appointments.
To diagnose your condition, your doctor will review your medical history and symptoms and conduct a physical examination. Doctors may order a number of tests to diagnose dementia and rule out other conditions.
Cognitive and neuropsychological tests
In these tests, doctors will evaluate your thinking (cognitive) function. A number of tests measure thinking skills such as memory, orientation, reasoning and judgment, language skills, and attention.
Doctors use these tests to determine whether you have dementia, how severe it is and what part of your brain is affected.
In a neurological evaluation, doctors will evaluate your movement, senses, balance, reflexes and other areas. Doctors may use the neurological evaluation to diagnose other conditions.
Doctors may order brain scans, such as a CT or MRI, to check for evidence of stroke or bleeding and to rule out the possibility of a tumor.
Simple blood tests can rule out physical problems that can affect brain function, such as vitamin B-12 deficiency or an underactive thyroid gland.
You may meet with a mental health specialist (psychologist or psychiatrist) who may evaluate whether depression or another psychological condition may be causing your symptoms.
Most types of dementia can't be cured. However, doctors will help you manage your symptoms. Treatment of dementia symptoms may help slow or minimize the development of symptoms.
Cholinesterase inhibitors. These medications — including donepezil (Aricept), rivastigmine (Exelon) and galantamine (Razadyne) — work by boosting levels of a chemical messenger involved in memory and judgment.
Side effects can include nausea, vomiting and diarrhea. Although primarily used to treat Alzheimer's disease, these medications may also treat vascular dementia, Parkinson's disease dementia and Lewy body dementia.
Memantine. Memantine (Namenda) works by regulating the activity of glutamate. Glutamate is another chemical messenger involved in brain functions, such as learning and memory. A common side effect of memantine is dizziness.
Some research has shown that combining memantine with a cholinesterase inhibitor may have beneficial results.
- Other medications. Your doctor may prescribe other medications to treat other symptoms or conditions, such as a sleep disorder.
- Occupational therapy. Your doctor may suggest occupational therapy to help you adjust to living with dementia. Therapists may teach you coping behaviors and ways to adapt movements and daily living activities as your condition changes.
Several dementia symptoms and behavior problems may be treated initially using nondrug approaches, such as:
- Modifying the environment. Reducing clutter and distracting noise can make it easier for someone with dementia to focus and function. It also may reduce confusion and frustration.
- Modifying your responses. A caregiver's response to a behavior can make the behavior, such as agitation, worse. It's best to avoid correcting and quizzing a person with dementia. Reassuring the person and validating his or her concerns can defuse most situations.
- Modifying tasks. Break tasks into easier steps and focus on success, not failure. Structure and routine during the day also help reduce confusion in people with dementia.
People with dementia will experience progression of their symptoms and behavior problems over time. Caregivers may need to adapt the following suggestions to individual situations:
- Enhance communication. When talking with your loved one, maintain eye contact. Speak slowly in simple sentences, and don't rush the response. Present only one idea or instruction at a time. Use gestures and cues, such as pointing to objects.
Encourage exercise. Exercise benefits everyone, including people with dementia. The main benefits of exercise include improved strength and cardiovascular health.
Some research also shows physical activity may slow the progression of impaired thinking (cognitive) function in people with dementia.
Exercise can also lessen symptoms of depression, help retain motor skills and create a calming effect.
- Encourage participation in games and thinking activities. Participating in games, crossword puzzles and other activities in which people are using thinking (cognitive) skills may help slow mental decline in people with dementia.
Establish a nighttime ritual. Behavior is often worse at night. Try to establish going-to-bed rituals that are calming and away from the noise of television, meal cleanup and active family members. Leave night lights on to prevent disorientation.
Limiting caffeine during the day, discouraging daytime napping and offering opportunities for exercise during the day may help prevent nighttime restlessness.
- Encourage keeping a calendar. Keeping a reminder calendar may help your loved one remember upcoming events, daily activities and medication schedules. Consider sharing a calendar with your loved one.
- Plan for the future. Develop a plan with your loved one that identifies goals for care in the future. Several support groups, legal advisers, family members and others can help you. You'll need to consider financial and legal issues, safety and daily living concerns, and long-term care options.
Several dietary supplements, herbal remedies and therapies have been studied for people with dementia. Some may be beneficial.
Dietary supplements, vitamins and herbal remedies
Use caution when considering dietary supplements, vitamins or herbal remedies to slow the progress of dementia, especially if you're taking other medications.
Dietary supplements, vitamins and herbal remedies aren't regulated, and claims about their benefits aren't always based on scientific research.
Some alternative medicine options for Alzheimer's disease and other forms of dementia that have been studied include:
- Vitamin E. Some studies have shown that vitamin E may slow the progression of Alzheimer's disease. Doctors warn against taking large doses of vitamin E because it may have a higher risk of mortality, especially in people with heart disease.
Omega-3 fatty acids. Omega-3s, a type of polyunsaturated fatty acid found in fish and nuts, may reduce the risk of heart disease, stroke and mild cognitive impairment.
However, in studies, omega-3 fatty acids haven't significantly slowed cognitive decline in mild to moderate Alzheimer's disease. More research is needed to understand whether omega-3 fatty acids benefit people with Alzheimer's and other types of dementia.
Coenzyme Q10. This antioxidant occurs naturally in your body. It's also necessary for normal cell reactions.
A synthetic version of this compound, called idebenone, showed some positive results in testing for Alzheimer's disease.
More studies are needed to determine safe dosages and potential benefits of coenzyme Q10.
Ginkgo. Extracts from the leaves of the Ginkgo biloba tree have antioxidant and anti-inflammatory properties that may protect cells in your brain from breaking down.
Some studies have shown that ginkgo may slow the progression of memory problems in people with Alzheimer's or other types of dementia. Other studies have found that ginkgo doesn't slow or delay the onset of dementia.
People with dementia often experience worse symptoms when they're frustrated or anxious. The following techniques may help reduce agitation and promote relaxation in people with dementia.
- Music therapy, which involves listening to soothing music
- Pet therapy, which involves use of animals, such as visits from dogs, to promote improved moods and behaviors in people with dementia
- Aromatherapy, which uses fragrant plant oils
- Massage therapy
Receiving a diagnosis of dementia can be devastating to you and your loved ones. Many details need to be considered to ensure that you and those around you are as prepared as possible for dealing with a condition that's unpredictable and continually changing.
Care and support for the person with the disease
Throughout the disease, you may experience a wide range of feelings. Here are some suggestions you can try to help yourself cope:
- Learn as much as you can about memory loss, dementia and Alzheimer's disease.
- Write about your feelings about having dementia in a journal.
- Join a local support group.
- Get individual or family counseling.
- Talk to a member of your church or another person who can help you with your spiritual needs.
- Stay active and involved, volunteer, exercise, and participate in activities for people with memory loss.
- Maintain contact and spend time with friends and family.
- Participate in an online community of people who are having similar experiences.
- Find new ways to express yourself, such as through painting, singing or writing.
- Delegate help with decision-making to someone you trust.
- Be patient with yourself.
Helping someone with dementia
You can help a person cope with the disease by listening, reassuring the person that he or she still can enjoy life, being supportive and positive, and doing your best to help the person retain dignity and self-respect.
Providing care for a person with dementia is physically and emotionally demanding. Often the primary caregiver is a spouse or other family member.
Feelings of anger and guilt, frustration and discouragement, worry, grief, and social isolation are common. If you're a caregiver for someone with dementia:
- Ask friends or other family members for help when you need it
- Take care of your physical, emotional and spiritual health
- Learn as much about the disease as you can
- Ask questions of doctors, social workers and others involved in the care of your loved one
- Join a support group
- Find out about supportive services in your community, such as respite care or adult care, which can provide you with a break from caregiving at scheduled times during the week
There's no sure way to prevent dementia, but there are steps you can take that might help. More research is needed, but it may be beneficial to do the following:
- Keep your mind active. Mentally stimulating activities, such as puzzles and word games, and memory training may delay the onset of dementia and help decrease its effects.
- Be physically and socially active. Physical activity and social interaction may delay the onset of dementia and reduce its symptoms.
- Quit smoking. Some studies have shown smoking in middle age and older may increase your risk of dementia and blood vessel (vascular) conditions. Quitting smoking may reduce your risk.
- Lower your blood pressure. High blood pressure may lead to a higher risk of some types of dementia. More research is needed to determine whether treating high blood pressure may reduce the risk of dementia.
Pursue education. People who have spent more time in formal education appear to have a lower incidence of mental decline, even when they have brain abnormalities.
Researchers believe that education may help your brain develop a strong nerve cell network that compensates for nerve cell damage caused by Alzheimer's disease.
- Maintain a healthy diet. Eating a healthy diet is important for many reasons, but a diet rich in fruits, vegetables and omega-3 fatty acids, commonly found in certain fish and nuts, may promote overall health and lower your risk of developing dementia.
Nov. 22, 2014
- What is dementia? Alzheimer's Association. http://www.alz.org/what-is-dementia.asp. Accessed Aug. 28, 2014.
- Dementia: Hope through research. National Institute of Neurological Disorders and Stroke. http://www.ninds.nih.gov/disorders/dementias/detail_dementia.htm?css. Accessed Aug. 28, 2014.
- Goldman L, et al. Goldman's Cecil Medicine. 24th ed. Philadelphia, Pa.: Saunders Elsevier; 2012. http://www.clinicalkey.com. Accessed Aug. 28, 2014.
- Halter JB, et al. Hazzard's Geriatric Medicine and Gerontology. 6th ed. New York, N.Y.: The McGraw-Hill Companies; 2009. http://www.accessmedicine.com/resourceTOC.aspx?resourceID=540. Accessed Aug. 28, 2014.
- Marx JA, et al. Rosen's Emergency Medicine: Concepts and Clinical Practice. 8th ed. Philadelphia, Pa.: Mosby Elsevier; 2014. http://www.clinicalkey.com. Accessed Aug. 28, 2014.
- Shadlen MF, et al. Risk factors for cognitive decline and dementia. http://www.uptodate.com/home. Accessed Aug. 29, 2014.
- Press D, et al. Treatment of dementia. http://www.uptodate.com/home. Accessed Aug. 29, 2014.
- Caring for a person with Alzheimer's disease. National Institute on Aging. http://www.nia.nih.gov/alzheimers/publication/caring-person-alzheimers-disease/about-guide. Accessed Aug. 30, 2014.
- Alternative treatments. Alzheimer's Association. http://www.alz.org/alzheimers_disease_alternative_treatments.asp. Accessed Aug. 30, 2014.
- Natural medicines in the clinical management of Alzheimer's disease. Natural Medicines Comprehensive Database. http://www.naturaldatabase.com. Accessed Aug. 30, 2014.
- Preventing Alzheimer's disease: What do we know? National Institute on Aging. http://www.nia.nih.gov/alzheimers/publication/preventing-alzheimers-disease/introduction. Accessed Sept. 2, 2014.
- Lapid MI (expert opinion). Mayo Clinic, Rochester, Minn. Sept. 12, 2014.
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¡Demasiada basura! (Too Much Trash!)
Guided Rd. Level C
Interest Level PK-3
Learn how to keep Earth clean of trash in this informative science reader! Students will learn that trash can be very harmful, causing pollution that harms the water, land, air, birds, fish, and people. Readers will be encouraged not to pollute and to keep the planet clean! The vibrant images and easy-to-read text in this science reader will keep students engaged from cover to cover. This reader also includes instructions for an engaging science activity and practice problems to further students understanding. A helpful glossary and index are also included for additional support.
In this section you can find reviews from our customers, or you can add your own review for this particular product.
Customer reviews help other visitors to read feedback from users who have already purchased and are using TCM’s products.
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# 10.16: Volume of Prisms
Difficulty Level: At Grade Created by: CK-12
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Practice Volume of Prisms
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Let's take another look at Jillian's box.
In the last Concept, you learned how to count unit cubes to figure out the volume of different prisms. Well, there is an easier way. We can use a formula to calculate the volume of a prism. Here are the dimensions of Jillian's box once again.
Jillian's box is a rectangular prism and has the following dimensions: 7" x 6" x 4".
How can we use a formula to calculate the volume of this prism?
Pay attention and this Concept will teach you all that you need to know.
### Guidance
Looking at all of those cubes is a simple, easy way to understand volume. If you can count the cubes, you can figure out the volume. However, not all of the prisms that you will work with will have the cubes drawn in. In this Concept, you will learn how to figure out the volume of a prism when there aren’t any cubes drawn inside it.
How can we figure out the volume of a prism without counting cubes?
Here we have the dimensions written on a rectangular prism. This prism has a height of 5 inches, a width of three inches and a length of four inches.
You can see that a few cubes have been drawn in to show you that if we continued filling the cubes that they would be four cubes across by three cubes wide, and we would build them five cubes high.
That’s right! Here is how it works.
\begin{align*}V = Bh\end{align*}
\begin{align*}B\end{align*} means the area of the base and \begin{align*}h\end{align*} means the height.
The area of the base is length times width.
\begin{align*}A & = 3 \times 4 = 12\\ h & = 5\\ V & = 12 \times 5 = 60\end{align*}
The volume is 60 cubic inches or \begin{align*}in^3\end{align*}.
\begin{align*}V = Bh\end{align*}
The area of the base is 2 \begin{align*}\times\end{align*} 8 = 16
The height is 3 inches.
\begin{align*}V & = 16 \times 3\\ V & = 48 \ in^3\end{align*}
The volume of this rectangular prism is \begin{align*}48 \ in^3\end{align*}.
How can we find the volume of a triangular prism?
We can use the same formula for finding the volume of the triangular prism. Except this time, the area of the base is a triangle and not a rectangle.
\begin{align*}V = Bh\end{align*}
To find the volume of a triangular prism, we multiply the area of the base \begin{align*}(B)\end{align*} with the height of the prism.
To find the area of a triangular base we use the formula for area of a triangle.
\begin{align*}A & = \frac{1}{2}bh\\ A & = \frac{1}{2}(15 \times 6)\\ A & = \frac{1}{2}(90)\\ A & = 45 \ sq. \ units\\ V & = Bh\\ V & = (45)h\\ V & = 45(2)\\ V & = 90 \ cubic \ centimeters \ or \ cm^3\end{align*}
The volume of the prism is \begin{align*}90 \ cm^3\end{align*}.
Now that you know how to find the volume of prisms using a formula, it is time to practice.
#### Example A
Solution: \begin{align*}125 in^3\end{align*}
#### Example B
Solution: \begin{align*}450 in^3\end{align*}
#### Example C
Solution: \begin{align*} 17.5 cm^3\end{align*}
Do you know how to use the formula for finding the volume of a prism? Here is the original problem once again.
Let's take another look at Jillian's box.
In the last Concept, you learned how to count unit cubes to figure out the volume of different prisms. Well, there is an easier way. We can use a formula to calculate the volume of a prism. Here are the dimensions of Jillian's box once again.
Jillian's box is a rectangular prism and has the following dimensions: 7" x 6" x 4".
How can we use a formula to calculate the volume of this prism?
\begin{align*}V = Bh\end{align*}
Now we can substitute in the given values for length, width and height.
\begin{align*}V = (7 \times 6)(4)\end{align*}
The volume of Jillian's box is \begin{align*} 168 in^3\end{align*}.
### Vocabulary
Here are the vocabulary words in this Concept.
Surface area
the outer covering of a solid figure-calculated by adding up the sum of the areas of all of the faces and bases of a prism.
Net
diagram that shows a “flattened” version of a solid. Each face and base is shown with all of its dimensions in a net. A net can also serve as a pattern to build a three-dimensional solid.
Triangular Prism
a solid which has two congruent parallel triangular bases and faces that are rectangles.
Rectangular Prism
a solid which has rectangles for bases and faces.
Volume
the amount of space inside a solid figure
### Guided Practice
Here is one for you to try on your own.
To find the volume of a prism, we use the following formula.
\begin{align*}V = Bh\end{align*}
Now we substitute in the given values.
\begin{align*}V = (16 \times 9)(4)\end{align*}
\begin{align*}V = 576 cm^3\end{align*}
### Video Review
Here is a video for review.
### Practice
Directions: Find the volume of each rectangular prism. Remember to label your answer in cubic units.
1. Length = 5 in, width = 3 in, height = 4 in
2. Length = 7 m, width = 6 m, height = 5 m
3. Length = 8 cm, width = 4 cm, height = 9 cm
4. Length = 8 cm, width = 4 cm, height = 12 cm
5. Length = 10 ft, width = 5 ft, height = 6 ft
6. Length = 9 m, width = 8 m, height = 11 m
7. Length = 5.5 in, width = 3 in, height = 5 in
8. Length = 6.6 cm, width = 5 cm, height = 7 cm
9. Length = 7 ft, width = 4 ft, height = 6 ft
10. Length = 15 m, width = 8 m, height = 10 m
Directions: Find the volume of each triangular prism. Remember that \begin{align*}h\end{align*} means the height of the triangular base and \begin{align*}H\end{align*} means the height of the whole prism.
11. \begin{align*}b = 6 \ in, \ h = 4 \ in, \ H = 5 \ in\end{align*}
12. \begin{align*}b = 7 \ in, \ h = 5 \ in, \ H = 9 \ in\end{align*}
13. \begin{align*}b = 10 \ m, \ h = 8 \ m, \ H = 9 \ m\end{align*}
14. \begin{align*}b = 12 \ m, \ h = 10 \ m, \ H = 13 \ m\end{align*}
15. \begin{align*}b = 8 \ cm, \ h = 6 \ cm, \ H = 9 \ cm\end{align*}
Directions: Answer true or false for each of the following questions.
16. Volume is the amount of space that a figure can hold inside it.
17. The volume of a rectangular prism is always greater than the volume of a cube.
18. The volume of a triangular prism is less than a rectangular prism with the same size base.
19. A painter would need to know the surface area of a house to do his/her job correctly.
20. If Marcus is covering his book with a book cover, Marcus is covering the surface area of the book.
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes
### Vocabulary Language: English
TermDefinition
Net A net is a diagram that shows a “flattened” view of a solid. In a net, each face and base is shown with all of its dimensions. A net can also serve as a pattern to build a three-dimensional solid.
Rectangular Prism A rectangular prism is a prism made up of two rectangular bases and four rectangular faces.
Surface Area Surface area is the total area of all of the surfaces of a three-dimensional object.
Triangular Prism A triangular prism is a prism made up of two triangular bases and three rectangular faces.
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How to Calculate Wire Temperature Resistance When Power is Known
••• Close-up image of an electric range heating element image by Alexey Stiop from Fotolia.com
Print
The resistance of metallic conductors, from metal wire rods, strands, and filaments, depends on a material's composition, cross sectional area, and operating temperature at steady state current flow conditions. The resistance of metallic conductors increases with temperature, which allows for a maximal temperature in relation to power with the nickel-chrome wires used in electric stove elements. Knowing the power flow allows for the calculation of a wire's resistance at a given working voltage, or an approximation of temperature based on comparative resistance values if the type of metal forming the wire is known.
Calculating Electric Stove Operating Resistance at Temperature
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Determine the material's power rating. In this example, a nickel-chrome (nichrome) wire in a large coiled electric stove element is rated for 2400 watts at full operating power when glowing cherry red (about 1600°F). The operating voltage of the stove is 230 volts AC (alternating current). With this information, you can calculate the wire's resistance at a particular temperature.
••• hot gun in hand image by Gintautas Velykis from Fotolia.com
The electrical power equation gives us the power produced by an electric current I passing through a potential difference V
P=VI
We can calculate the steady-state current I of the stove circuit at full power by dividing power P by voltage V to obtain the current.
I=\frac{P}{V}
Since the electrical load is fully resistive and non-reactive (non-magnetic), the power factor is 1-to-1
I=\frac{2400}{230}=10.435\text{ A}
The current through the load is 10.435 A.
Calculate the steady-state resistance of the wire at operating temperature. The applicable formula is
R=\frac{V}{I}
where R is resistance. Therefore,
R=\frac{230}{10.435}=22.04\Omega
The resistance of the nichrome wire at 1600°F is 22.04 Ω.
Calculating Wire Resistance Change with Temperature Decrease
••• burnt house image by pavel siamionov from Fotolia.com
The same stove element at a lower control setting draws 1200 W of power. At this level, the stove's temperature control reduces the voltage across the element to 130 V. With this information, you can calculate the resistance at this setting, and approximate the lower temperature of the element.
Calculate the electrical current flow in amps by dividing power by the voltage
I=\frac{1200}{130}=9.23\text{ A}
Calculate the element wire resistance by dividing the voltage V by the current I
R=\frac{V}{I}=\frac{130}{9.23}=14.08\Omega
Calculate the temperature change resulting in the lower resistance of the element. If the initial condition is 1600°F (cherry red) then the temperature can be calculated from the temperature coefficient of the resistance formula
R=R_{ref}(1+\alpha (T-T_{ref}))
where R is the resistance at temperature, T, Rref is the resistance at a reference temperature, Tref , and α is the temperature coefficient of resistance for the material.
Solving for T, we get
T=T_{ref}+\frac{1}{\alpha}\bigg(\frac{R}{R_{ref}}-1\bigg)
For nichrome wire, α = 0.00017 Ω/°C. Multiplying this by 1.8 and we get the resistance change per °F. For nichrome wire, this becomes, α = 0.00094 Ω/°F. This tells us how much the resistance changes per degree rise. Substituting these values, we get
T=1600+\frac{1}{0.00094}\bigg(\frac{14.08}{22.04}-1\bigg)=1215.8^{\text{o}}\text{F}
The reduced power setting results in a lower nichrome wire temperature of 1215.8°F. The stove's coils will appear dull red in normal daylight compared to glowing cherry red at its highest setting. Though hundreds of degrees lower, it is still hot enough to cause severe burns.
Things You'll Need
• Calculator
• Colors of heated metals chart
• Temperature Coefficients of Resistance for different metals chart
Tips
• Always have the correct size pots with plenty of liquid on moderately powered elements to prevent red hot element temperatures.
Warnings
• Never ever lay objects down on top of electric stoves even when cold and turned off.
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Opposing Viewpoints: Moral Universalism vs. Moral Relativism
Ethics is the branch of philosophy that examines questions of morality, or right and wrong. While applied ethics addresses questions such as “If X happens, what is the ethical thing to do?” meta-ethics takes a step back and looks at even more fundamental questions like “Do moral terms such as 'good' and 'evil' have meaning?” and “What are the basic factors we should use to make moral judgments?”
Philosophers attempting to answer the second question are divided into two basic camps: moral universalism and moral relativism. Moral universalists believe that certain actions are “good” or “evil” regardless of an individual's beliefs. Moral relativists, on the other hand, believe that morality can only be decided by one's cultural or personal beliefs.
Also called moral objectivism, this philosophy argues for the existence of a universal ethic. Certain behaviors are simply wrong regardless of the circumstances. In a 2007 interview Noam Chomsky defined universalism as “If something's right for me, it's right for you; if it's wrong for you, it's wrong for me.”
Universalism is based on the idea of a “rational test” that can be applied to any ethical dilemma. The exact nature of this test varies widely among different factions of universalists. For example, utilitarianism states that the correct rational test is “Does my action create the maximum good for the maximum number of people?” If the answer is yes, then a utilitarianist would say that the action is morally correct.
Moral universalism in the form of human rights has become widely accepted in the past several decades. The Universal Declaration of Human Rights, issued by the United Nations in 1948, and the Geneva Conventions (which define fair treatment of prisoners of war) are based on the theory of moral universalism. In other words, human beings all have certain rights and to deny those rights is always immoral.
Different cultures and individuals have different standards of right and wrong. Moral standards also change over time in the same culture. For example, slavery was considered moral in the United States at one time &ndash but not anymore.
Moral relativists argue that there is no known universal rule that defines right and wrong. Instead, morality is determined by the standards of a person's own authorities. These authorities might be a government, a religion or even a family member.
To carry the argument further, if one society believes that slavery is wrong and another believes that slavery is right, a moral relativist would say that either side may be correct. We have no way of knowing for sure whether slavery is ethically right or wrong, since human beings have not yet found an absolute moral yardstick with which we can judge.
In its most extreme form, moral relativism becomes moral nihilism. Also called amorality, this philosophy takes moral relativism a step further by stating that there is no absolute basis for right and wrong. Therefore, morality is meaningless: a person's or culture's ethical rules are entirely artificial, created to keep a society running smoothly. To a moral nihilist, if a society decides that murder is wrong, this is just as arbitrary a decision as if it decided that a red traffic light means “stop.”
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Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
# How to convert 0.01 mg/ml to mol/L? Thanks
You need to know the identity of the compound.
The only way to go from milligrams, a unit of mass, to moles is by using the molar mass of the given compound.
As you know, the molar mass of a compound tells you the mass of one mole of that compound. Let's say that your compound has a molar mass of M_M grams per mol.
This tells you that one mole of this compound has a mass of M_M grams.
Now, notice that before going from grams to moles you must go from milligrams to grams.
The conversion factor that you come in handy here is
"1 g" = 10^3"mg"
Moreover, you need to go from milliliters to liters, so a similar conversion factor is needed
"1 L" = 10^3"mL"
Now you're ready to convert between milligrams per milliliter to moles per liter
0.01(color(red)(cancel(color(black)("mg"))))/(color(red)(cancel(color(black)("mL")))) * (10^3color(red)(cancel(color(black)("mL"))))/"1 L" * (1color(red)(cancel(color(black)("g"))))/(10^3color(red)(cancel(color(black)("mg")))) * "1 mole"/(M_Mcolor(red)(cancel(color(black)("g")))) = (0.01/M_M) color(white)(a)"mol/L"
So, for a compound that has a molar mass equal to M_M, you have
color(green)("0.01 mg/mL" = (0.01/M_M) color(white)(a)"mol/L")
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About this schools Wikipedia selection
The articles in this Schools selection have been arranged by curriculum topic thanks to SOS Children volunteers. Child sponsorship helps children one by one http://www.sponsor-a-child.org.uk/.
The aldol reaction is an important carbon-carbon bond formation reaction in organic chemistry. In its usual form, it involves the nucleophilic addition of a ketone enolate to an aldehyde to form a β-hydroxy ketone, or "aldol" (aldehyde + alcohol), a structural unit found in many naturally occurring molecules and pharmaceuticals. Sometimes, the aldol addition product loses a molecule of water during the reaction to form an α,β-unsaturated ketone. This is called an aldol condensation. The aldol reaction was discovered independently by Charles-Adolphe Wurtz and by Alexander Porfyrevich Borodin in 1872. Borodin observed the aldol dimerization of 3-hydroxybutanal from acetaldehyde under acidic conditions. The aldol reaction is used widely in the large scale production of commodity chemicals such as pentaerythritol and in the pharmaceutical industry for the synthesis of optically pure drugs. For example, Pfizer's initial route to the heart disease drug Lipitor (INN: atorvastatin), approved in 1996, employed two aldol reactions, allowing access to multigram-scale quantities of the drug.
The aldol structural motif is especially common in polyketides, a class of natural products from which many pharmaceuticals are derived, including the potent immunosuppressant FK506, the tetracycline antibiotics, and the antifungal agent amphotericin B. Extensive research on the aldol reaction has produced highly efficient methods which enable the otherwise challenging synthesis of many polyketides in the laboratory. This is important because many polyketides, along with other biologically active molecules, occur naturally in quantities impractically small for further investigation. The synthesis of many such compounds, once considered nearly impossible, can now be performed routinely on the laboratory scale, and is approaching economic viability on a larger scale in some cases, such as the highly active anti-tumor agent discodermolide. In biochemistry, the aldol reaction is one of the key steps of glycolysis, where it is catalyzed by enzymes called aldolases.
The aldol reaction is particularly valuable in organic synthesis because it produces products with two new stereogenic centers (on the α- and β-carbon of the aldol adduct, marked with asterisks in the scheme above). Modern methods, described below, now allow the relative and absolute configuration of these centers to be controlled. This is of particular importance when synthesizing pharmaceuticals, since molecules with the same structural connectivity but different stereochemistry often have vastly different chemical and biological properties.
A variety of nucleophiles may be employed in the aldol reaction, including the enols, enolates, and enol ethers of ketones, aldehydes, and many other carbonyl compounds. The electrophilic partner is usually an aldehyde, although many variations, such as the Mannich reaction, exist. When the nucleophile and electrophile are different (the usual case), the reaction is called a crossed aldol reaction (as opposed to dimers formed in an aldol dimerization).
The aldol reaction may proceed via two fundamentally different mechanisms. Carbonyl compounds, such as aldehydes and ketones, can be converted to enols or enol ethers. These compounds, being nucleophilic at the α-carbon, can attack especially reactive protonated carbonyls such as protonated aldehydes. This is the "enol mechanism". Carbonyl compounds, being carbon acids, can also be deprotonated to form enolates, which are much more nucleophilic than enols or enol ethers and can attack electrophiles directly. The usual electrophile is an aldehyde, since ketones are much less reactive. This is the "enolate mechanism".
If the conditions are particularly harsh (e.g., NaOMe, MeOH, reflux), condensation may occur, but this can usually be avoided with mild reagents and low temperatures (e.g., LDA (a strong base), THF, -78 °C). Although the aldol addition usually proceeds to near completion, the reaction is not irreversible, since the treatment of aldol adducts with strong bases usually induces retro-aldol cleavage (gives the starting materials). Aldol condensations are irreversible.
When an acid catalyst is used, the initial step in the reaction mechanism involves acid-catalyzed tautomerization of the carbonyl compound to the enol. The acid also serves to activate the carbonyl group of another molecule by protonation, rendering it highly electrophilic. The enol is nucleophilic at the α-carbon, allowing it to attack the protonated carbonyl compound, leading to the aldol after deprotonation. This usually dehydrates to give the unsaturated carbonyl compound. The scheme shows a typical acid-catalyzed self-condensation of an aldehyde.
Acid catalyzed aldol mechanism
Acid catalyzed dehydration
If the catalyst is a moderate base such as hydroxide ion or an alkoxide, the aldol reaction occurs via nucleophilic attack by the resonance-stabilized enolate on the carbonyl group of another molecule. The product is the alkoxide salt of the aldol product. The aldol itself is then formed, and it may then undergo dehydration to give the unsaturated carbonyl compound. The scheme shows a simple mechanism for the base catalyzed aldol reaction of an aldehyde with itself.
Base catalyzed aldol reaction (shown using −OCH3 as base)
Base catalyzed dehydration (sometimes written as a single step)
Although only a catalytic amount of base is required in some cases, the more usual procedure is to use a stoichiometric amount of a strong base such as LDA or NaHMDS. In this case, enolate formation is irreversible, and the aldol product is not formed until the metal alkoxide of the aldol product is protonated in a separate workup step.
More refined forms of the mechanism are known. In 1957, Zimmerman and Traxler proposed that some aldol reactions have "six-membered transition state s having a chair conformation." This is now known as the Zimmerman-Traxler model. E-enolates give rise to anti products, whereas Z-enolates give rise to syn products. The factors which control selectivity are the preference for placing substituents equatorially in six-membered transition states and the avoidance of syn-pentane interactions, respectively. E and Z refer to the cis-trans stereochemical relationship between the enolate oxygen bearing the positive counterion and the highest priority group on the alpha carbon. In reality, only some metals such as lithium and boron reliably follow the Zimmerman-Traxler model. Thus, in some cases, the stereochemical outcome of the reaction may be unpredictable.
Control in the Aldol reaction
The problem of "control" in the aldol addition is best demonstrated by an example. Consider the outcome of this hypothetical reaction:
In this reaction, two unsymmetrical ketones are being condensed using sodium ethoxide. The basicity of sodium ethoxide is such that it cannot fully deprotonate either of the ketones, but can produce small amounts of the sodium enolate of both ketones. Effectively, this means that in addition to being potential aldol electrophiles, both ketones may also act as nucleophiles via their sodium enolate. Two electrophiles and two nucleophiles then potentially results in four possible products:
Thus, if one wishes to obtain only one of the cross-products, then one must "control" the aldol addition.
If one partner is considerably more acidic than the other, then control may be automatic. The most acidic proton is abstracted by the base and an enolate is formed. This type of control only works if the difference in acidity is large enough and no excess of base is used for the reaction. The simplest control is if only one of the reactants has acidic protons and only this molecule forms the enolate. For example, the addition of diethyl malonate into benzaldehyde would only produce one product:
In this case, the doubly activated methylene protons of the malonate would be preferentially deprotonated by sodium ethoxide and quantitatively form the sodium enolate. Since benzaldehyde has no acidic alpha-protons, there is only one possible nucleophile-electrophile combination; hence, control has been achieved. Note that this approach combines two elements of control: increased acidity of the alpha protons on the nucleophile and the lack of alpha protons on the electrophile.
Order of addition
One common solution is to form the enolate of one partner first, and then add the other partner under kinetic control. Kinetic control means that the forward aldol addition reaction must be significantly faster than the reverse retro-aldol reaction. For this approach to succeed, two other conditions must also be satisfied; namely, it must be possible to quantitatively form the enolate of one partner and the forward aldol reaction must be significantly faster than the transfer of the enolate from one partner to another. Common kinetic control conditions involve the formation of the enolate of a ketone with LDA at -78 °C, followed by the slow addition of an aldehyde.
The enolate may be formed by using a strong base ("hard conditions") or using a Lewis acid and a weak base ("soft conditions"):
For deprotonation to occur, the stereoelectronic requirement is that the alpha-C-H sigma bond must be able to overlap with the pi* orbital of the carbonyl:
Extensive studies have been performed on the formation of enolates under many different conditions. It is now possible to generate, in most cases, the desired enolate geometry:
(-- In the above image, the second reaction scheme should say >99% E-enolate, not Z --) For ketones, most enolization conditions give Z enolates. For esters, most enolization conditions give E enolates. The addition of HMPA is known to reverse the stereoselectivity of deprotonation.
The stereoselective formation of enolates has been rationalized with the so-called Ireland model, although its validity is somewhat questionable. In most cases, it is not known which, if any, intermediates are monomeric or oligomeric in nature; nonetheless, the Ireland model remains a useful tool for understanding enolates.
In the Ireland model, the deprotonation is assumed to proceed by a six-membered monomeric transition state. The larger of the two substituents on the electrophile (in the case above, methyl is larger than proton) adopts an equatorial disposition in the favored transition state, leading to a preference for E enolates. The model clearly fails in many cases; for example, if the solvent mixture is changed from THF to 23% HMPA-THF (as seen above), the enolate geometry is inexplicably reversed.
Kinetic vs. thermodynamic enolates
If an unsymmetrical ketone is subjected to base, it has the potential to form two regioisomeric enolates (ignoring enolate geometry). For example:
The trisubstituted enolate is considered the kinetic enolate while the tetrasubstituted enolate is considered the thermodynamic enolate. The alpha hydrogen deprotonated to form the kinetic enolate is less hindered, and therefore deprotonated more quickly. In general, tetrasubstituted olefins are more stable than trisubstituted olefins due to hyperconjugative stabilization. The ratio of enolate regioisomers is heavily influenced by the choice of base. For the above example, kinetic control may be established with LDA at -78 °C, giving 99:1 selectivity of kinetic: thermodynamic enolate, while thermodynamic control may be established with triphenylmethyllithium at room temperature, giving 10:90 selectivity.
In general, kinetic enolates are favored by cold temperatures, relatively ionic metal-oxygen bonds, and rapid deprotonation using a slight excess of a strong, hindered base while thermodynamic enolates are favored by higher temperatures, relatively covalent metal-oxygen bonds, and longer equilibration times for deprotonation using a slight sub-stoichiometric amount of strong base. Use of a sub-stoichiometric amount of base allows some small fraction of unenolized carbonyl compound to equilibrate the enolate to the thermodynamic regioisomer by acting as a proton shuttle.
The aldol reaction is particularly useful because two new stereogenic centers are generated in one reaction. Extensive research has been performed to understand the reaction mechanism and improve the selectivity observed under many different conditions. The syn/anti convention is commonly used to denote the relative stereochemistry at the α- and β-carbon.
The convention applies when propionate (or higher order) nucleophiles are added to aldehydes. The R group of the ketone and the R' group of the aldehyde are aligned in a "zig zag" pattern in the plane of the paper, and the disposition of the formed stereocenters is deemed syn or anti, depending if they are on the same or opposite sides of the main chain.
Older papers use the erythro- threo nomenclature familiar from carbohydrate chemistry.
E vs. Z enolates
There is no significant difference between the level of stereoinduction observed with E and Z enolates:
The enolate metal cation may play a large role in determining the level of stereoselectivity in the aldol reaction. Boron is often used because its bond lengths are significantly shorter than that of other metals such as lithium, aluminium, or magnesium. For example, boron-carbon and boron-oxygen bonds are 1.4–1.5 Å and 1.5–1.6 Å in length, respectively, whereas typical metal-carbon and metal-oxygen bonds are typically 1.9–2.2 Å and 2.0–2.2 Å in length, respectively. This has the effect of "tightening" the transition state:
Stereoselectivity: Alpha stereocenter on the enolate
The aldol reaction may exhibit "substrate-based stereocontrol", in which existing chirality on either reactant influences the stereochemical outcome of the reaction. This has been extensively studied, and in many cases, one can predict the sense of asymmetric induction, if not the absolute level of diastereoselectivity. If the enolate contains a stereocenter in the alpha position, excellent stereocontrol may be realized.
In the case of an E enolate, the dominant control element is allylic 1,3-strain whereas in the case of a Z enolate, the dominant control element is the avoidance of 1,3-diaxial interactions. The general model is presented below:
For clarity, the stereocenter on the enolate has been epimerized; in reality, the opposite diastereoface of the aldehyde would have been attacked. In both cases, the 1,3-syn diastereomer is favored. There are many examples of this type of stereocontrol:
Stereoselectivity: Alpha stereocenter on the electrophile
When enolates attacks aldehydes with an alpha stereocenter, excellent stereocontrol is also possible. The general observation is that E enolates exhibit Felkin diastereoface selection, while Z enolates exhibit anti-Felkin selectivity. The general model is presented below:
Since Z enolates must react through a transition state which either contains a destabilizing syn-pentane interaction or anti-Felkin rotamer, Z-enolates exhibit lower levels of diastereoselectivity in this case. Some examples are presented below:
Stereoselectivity: Merged model for stereoinduction
If both the enolate and the aldehyde both contain pre-existing chirality, then the outcome of the "double stereodifferentiating" aldol reaction may be predicted using a merged stereochemical model that takes into account the enolate facial bias, enolate geometry, and aldehyde facial bias. Several examples of the application of this model are given below:
Evans' oxazolidinone chemistry
Modern organic syntheses now require the synthesis of compounds in enantiopure form. Since the aldol addition reaction creates two new stereocenters, up to four stereoisomers may result.
Many methods which control both relative stereochemistry (i.e., syn or anti, as discussed above) and absolute stereochemistry (i.e., R or S) have been developed.
A widely used method is the Evans' acyl oxazolidinone method. Developed in the late 1970s and 1980s by David A. Evans and coworkers, the method works by temporarily creating a chiral enolate by appending a chiral auxiliary. The pre-existing chirality from the auxiliary is then transferred to the aldol adduct by performing a diastereoselective aldol reaction. Upon subsequent removal of the auxiliary, the desired aldol stereoisomer is revealed.
In the case of the Evans' method, the chiral auxiliary appended is an oxazolidinone, and the resulting carbonyl compound is an imide. A number of oxazolidinones are now readily available in both enantiomeric forms. These may cost roughly $10-$20 US dollars per gram, rendering them relatively expensive.
The acylation of an oxazolidinone is a convenient procedure, and is informally referred to as "loading done". Z-enolates, leading to syn-aldol adducts, can be reliably formed using boron-mediated soft enolization:
Often, a single diastereomer may be obtained by one crystallization of the aldol adduct. Unfortunately, anti-aldol adducts cannot be obtained reliably with the Evans method. Despite the cost and the limitation to give only syn adducts, the method's superior reliability, ease of use, and versatility render it the method of choice in many situations. Many methods are available for the cleavage of the auxiliary:
Upon construction of the imide, both syn and anti-selective aldol addition reactions may be performed, allowing the assemblage of three of the four possible stereoarrays: syn selective: and anti selective:
In the syn-selective reactions, both enolization methods give the Z enolate, as expected; however, the stereochemical outcome of the reaction is controlled by the methyl stereocenter, rather than the chirality of the oxazolidinone. The methods described allow the stereoselective assembly of polyketides, a class of natural products which often feature the aldol retron.
Modern Aldol Chemistry
Recent methodology now allows a much wider variety of aldol reactions to be conducted, often with a catalytic amount of chiral ligand. When reactions employ small amounts of enantiomerically pure ligands to induce the formation of enantiomerically pure products, the reactions are typically termed "catalytic, asymmetric"; for example, many different catalytic, asymmetric aldol reactions are now available.
Acetate Aldol Reactions
A key limitation to the chiral auxiliary approach described previously is the failure of N-acetyl imides to react selectively. An early approach was to use a temporary thioether group:
Mukaiyama aldol reaction
The Mukaiyama aldol reaction is the nucleophilic addition of silyl enol ethers to aldehydes catalyzed by a Lewis acid such as boron trifluoride or titanium chloride. The Mukaiyama aldol reaction does not follow the Zimmerman-Traxler model. Carreira has described particularly useful asymmetric methodology with silyl ketene acetals, noteworthy for its high levels of enantioselectivity and wide substrate scope.
The method works on unbranched aliphatic aldehydes, which are often poor electrophiles for catalytic, asymmetric processes. This may be due to poor electronic and steric differentiation between their enantiofaces.
The analogous vinylogous Mukaiyama aldol process can also be rendered catalytic and asymmetric. The example shown below works efficiently for aromatic (but not aliphatic) aldehydes and the mechanism is believed to involve a chiral, metal-bound dienolate.
Crimmins thiazoldinethione aldol
A more recent version of the Evans' auxiliary is the Crimmins thiazoldinethione. The yields, diastereoselectivities, and enantioselectivities of the reaction are generally high, although not as high as in comparable Evans cases. Unlike the Evans auxiliary, however, the thiazoldinethione can perform acetate aldol reactions (ref: Crimmins, Org. Lett. 2007, 9(1), 149–152.) and can produce the "Evans syn" or "non-Evans syn" adducts by simply varying the amount of (-)-sparteine. The reaction is believed to proceed via six-membered, titanium-bound transition states, analogous to the proposed transition states for the Evans auxiliary.
Organocatalytic aldol reactions
An exciting new development is the use of chiral secondary amine catalysts. These secondary amines form transient enamines when exposed to ketones, which may react enantioselectively with suitable aldehyde electrophiles. This is known as enamine catalysis, a type of organocatalysis, since the catalyst is entirely based on a small organic molecule. In a seminal example, proline efficiently catalyzed the cyclization of a triketone:
This reaction is known as the Hajos-Parrish reaction (also known as the Hajos-Parrish-Eder-Sauer-Wiechert reaction, referring to a contemporaneous report from Schering of the reaction under harsher conditions). Only a catalytic amount of proline is necessary (3 mol%). There is no danger of an achiral background reaction because the transient enamine intermediates are much more nucleophilic than their parent ketone enols. This strategy is particularly powerful because it offers a simple way of generating enantioselectivity in reactions without using transition metals, which have the possible disadvantages of being toxic or expensive.
Interestingly, proline-catalyzed aldol reactions do not show any non-linear effects (the enantioselectivity of the products is directly proportional to the enantiopurity of the catalyst). Combined with isotopic labelling evidence and computational studies, the proposed reaction mechanism for proline-catalyzed aldol reactions is as follows:
This strategy allows the otherwise challenging cross-aldol reaction between two aldehydes. In general, cross-aldol reactions between aldehydes are typically challenging because they can polymerize easily or react unselectively to give a statistical mixture of products. The first example is shown below:
In contrast to the preference for syn adducts typically observed in enolate-based aldol additions, these organocatalyzed aldol additions are anti-selective. In many cases, the organocatalytic conditions are mild enough to avoid polymerization. However, selectivity requires the slow syringe-pump controlled addition of the desired electrophilic partner because both reacting partners typically have enolizable protons. If one aldehyde has no enolizable protons or alpha- or beta-branching, additional control can be achieved.
An elegant demonstration of the power of asymmetric organocatalytic aldol reactions was disclosed by MacMillan and coworkers in 2004 in their synthesis of differentially protected carbohydrates. While traditional synthetic methods accomplish the synthesis of hexoses using variations of iterative protection-deprotection strategies, requiring 8–14 steps, organocatalysis can access many of the same substrates using an efficient two-step protocol involving the proline-catalyzed dimerization of alpha-oxyaldehydes followed by tandem Mukaiyama aldol cyclization.
The aldol dimerization of alpha-oxyaldehydes requires that the aldol adduct, itself an aldehyde, be inert to further aldol reactions. Earlier studies revealed that aldehydes bearing alpha-alkyloxy or alpha- silyloxy substituents were suitable for this reaction, while aldehydes bearing Electron-withdrawing groups such as acetoxy were unreactive. The protected erythrose product could then be converted to four possible sugars via Mukaiyama aldol addition followed by lactol formation. This requires appropriate diastereocontrol in the Mukaiyama aldol addition and the product silyloxycarbenium ion to preferentially cyclize, rather than undergo further aldol reaction. In the end, glucose, mannose, and allose were synthesized:
"Direct" aldol additions
In the usual aldol addition, a carbonyl compound is deprotonated to form the enolate. The enolate is added to an aldehyde or ketone, which forms an alkoxide, which is then protonated on workup. A superior method, in principle, would avoid the deprotonation-aldol-protonation sequence in favour of a "direct aldol addition". The major issue in such a process is that the aldol addition generates an alkoxide, which is much more basic than the starting materials, precluding catalyst turnover:
One approach, recently demonstrated by Evans, is to silylate the aldol adduct:
This method is more cost effective and industrially useful than the more typical enolate-based procedures. A more recent, biomimetic approach by Shair uses beta-thioketoacids as the nucleophile. The ketoacid moiety is decarboxylated in situ (the chiral ligand is a bisoxazoline). Interestingly, aromatic and branched aliphatic aldehydes are typically poor substrates.
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April 15th marks a great man’s birthday. Leonardo da Vinci was born in 1452 and passed away in 1519.
Da Vinci invented so many things that wouldn’t be realized until hundreds of years later, such as the parachute and helicopter. He was a great inventor. To say he was ahead of his time would be a huge understatement!
What might surprised you even more was that Leonardo da Vinci was unschooled. He never received any form of official and formal education. Maybe that’s why his creativity was squished.
Regardless of his lack of schooling, his areas of interest included invention, drawing, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, writing, history, and cartography. He had an unquenchable curiosity and didn’t believe that human beings are born with only one talent or one calling.
One of his most famous painting is the Mona Lisa, which can be found at the Louvre in France. He’s also known for the painting of The Last Supper, which was featured in the movie The Da Vinci Code.
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Dogs are fascinating creatures with complex cognitive processes and behaviors that are shaped by their environment and experiences. Understanding the psychology behind dog behavior can help owners better communicate with their pets and address behavioral issues. In this article, we’ll explore the psychology of dog behavior and how it affects their actions and interactions with the world around them.
Cognitive Processes in Dogs:
Like humans, dogs have complex cognitive processes that shape their behavior. Studies have shown that dogs are capable of understanding cause and effect, learning through observation, and even exhibiting problem-solving skills. They have the ability to learn and retain information through their experiences and interactions with the environment.
Emotions in Dogs:
Dogs are capable of experiencing a range of emotions, including happiness, fear, and anxiety. These emotions can influence their behavior and reactions to different stimuli. For example, fear can lead to aggression, while happiness can lead to more positive and social behaviors.
Socialization in Dogs:
Socialization is an important aspect of dog behavior that begins in puppyhood and continues throughout their lives. Socialization involves exposing dogs to different people, animals, and environments in order to help them develop positive relationships and behaviors. Proper socialization can help reduce fear and anxiety in dogs and promote more positive interactions with their environment.
Learning and Training in Dogs:
Dogs are highly trainable creatures that are capable of learning a wide range of behaviors and commands. Positive reinforcement training techniques, such as rewarding desired behaviors, can be highly effective in teaching dogs new behaviors and reducing negative behaviors. Consistency and patience are key when it comes to training dogs, as it can take time for them to learn and adjust to new behaviors.
In conclusion, understanding the psychology behind dog behavior can help owners better communicate and interact with their pets. From cognitive processes and emotions to socialization and learning, there are many factors that shape dog behavior. By taking the time to understand and address these factors, owners can help their dogs lead happy and healthy lives. Proper training, socialization, and positive reinforcement techniques can all be effective tools in promoting positive behavior in dogs.
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## What is the percent of increase from 4 to 5?
Going from \$4 to \$5 is a 25% increase.
### How do you find percentage increase?
% Increase = Increase / Original Number × 100. This gives you the total percentage change, or increase. To calculate a percentage decrease first, work out the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100.
What is the percent increase from 120 to 150?
Related Standard Percentage Calculations on Percentage Difference for 150, 120
X Y Percentage(P) Difference
147.6 120 23
148.8 120 24
150 120 25
151.2 120 26
What is the percentage increase when 40 is increased to 60?
Related Standard Percentage Calculations on Percentage Increase/Decrease from 40 to 60
X Y Percentage(P) Increase
40 64 60
40 64.4 61
40 64.8 62
40 65.2 63
## How do you find the percentage between two numbers?
Answer: To find the percentage of a number between two numbers, divide one number with the other and then multiply the result by 100.
### What is the percent of increase from 250 to 375?
Related Standard Percentage Calculations on Percentage Increase/Decrease from 250 to 350
X Y Percentage(P) Increase
250 367.5 47
250 370 48
250 372.5 49
250 375 50
What is the percent increase of 80 to 100?
Using the equation, 2080 we get 0.25 and multiply that by 100 to get 25% .
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Question
A triangle has side lengths of 1.9cm, 2.7cm and 3.3cm, all measured to 1 decimal place could this be a right angled triangle
1. Latifah
Yes
Step-by-step explanation:
A triangle is a “right” triangle if its lengths fullfil the Pythagorean theorem:
Here, a and b are the shorter “legs” of the triangle, adjacent to its right angle, while c is the “hypotenuse,” the longest side and the one opposite the right angle.
If we call the 1.9 cm and 2.7 cm our legs, the sum of their squares is:
cm
While squaring our hypotenuse gives us
cm
The fact that we measured the triangle’s side lengths to 1 decimal point of accuracy means that there’s a little margin of error baked into the measurement. The two previous calculations are within 0.01 cm of each other, which is more than close enough, so we can say that yes, this could be a right triangle.
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Circles - Arcs Sectors
# Circles - Arcs Sectors
GCSE(F), GCSE(H),
An arc is part of the circumference of a sector. The amount of the circumference that is described is given by the number of degrees at the centre.
The arc length is a fraction of the circumference of the circle. The circumference of the whole circle is given by 2pir, and the angle at the centre is 360º. The angle of the arc is 83º, or frac(83)(360) of a whole circle:
The arc length is therefore frac(83)(360)pir.
If the perimeter of the arc is required, include the two radii: frac(83)(360)pir + 2.
The area of a whole circle is pir^2. The area of a sector is the same fraction: frac(83)(360)pir^2.
## Examples
1. What is the area of the sector, shown below?
Area = frac(70)(360)πr2
A = frac(70)(360)πx 122
A = 87.92 cm2
2. What is the length of the perimeter of the sector shown below? give the answer to 1 decimal place.
Arc Length = frac(70)(360) x 2 x π x r
Arc Length = frac(70)(360) x 75.36
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TIME for Kids: Frogs!
TIME for Kids: Frogs!
by the Editors of TIME for Kids with Kathryn Hoffman
When working with an informational text in the classroom, it's helpful to use a KWL chart to introduce the topic, access students' prior knowledge, and review what they have learned.
Begin by asking the students what they already know about frogs. Record this information in the "K" section of the chart.
Discuss with the students what types of things they want to learn about them. Record this in the "W" section of the chart. Knowing what the students want to learn can help you guide them through the book and focus on the information they will find most interesting.
At the very end, come back to the KWL chart. Give each student a post-it note and encourage them to write down at least one fact they learned by reading the book. When they are finished, the students can share their fact and stick the post-it in the "L" section of the chart.
A Frog's Life
From egg to tadpole to froglet to frog, and then back to egg again. A frog goes through many changes within its short life. Track the life of a frog in photographs with your students and make observations at every stage. If possible, bring in an aquarium with several tadpoles to your classroom. Have your students observe and record the tadpoles’ development in their science journals.
Pretty, But Poisonous
Many of the most brightly colored frogs are the most poisonous. Does this hold true for other species of animals as well? Discuss with your students why poisonous creatures tend to stand out so much. Brainstorm as many animals as possible, then chart the poisonous versus the non-poisonous.
- What are some facts that you learned about frogs?
- Write a story describing what it would be like if you were a frog.
Slippery Slimy Baby Frogs
Written by Sandra Markle
An introduction to baby frogs from around the world.
by Nic Bishop
Nic Bishop's photographs show all different kinds of frogs, big ones, very tiny ones, frogs with beautiful colors of skin, and one frog you can see inside of.
Face to Face with Frogs
by Mark W. Moffett
Learn about the diverse world of frogs; from metamorphosis to diet, from habitat to distinctive features.
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Vowels are the sounds that are not pronounced by the touch of two organs of vocal tract, rather it is just an air-stream and the difference lies in the manner of its release. We cannot say which vowel is pronounced from where as we can say about consonants simply because of no touch characteristics. Still the linguists offered a diagram explaining that, and that will be discussed later. For present look at the following chart and try to understand the vowels and their sounds.
Few things about the chart need to be explained.
Diacritic and long vowels: diacritic is the colon like two dots symbol (:) as you see in /i:/, /a:/ etc. it prolongs the sound of the vowel, hence the vowel with diacritic is called long vowel.
Short vowels: All those which are without diacritic and one-phoneme vowels are short vowels because their sound is not prolonged like long vowels.
Diphthongs: Two consecutive vowels sounds, like; /ai/, /ei/ etc. these are two vowel sounds joined together and the voice glides from one to another.
The origin of vowel sounds
As it is said earlier that despite the difficulty the linguists have introduced a diagram that explains the origin of different vowel sounds. Just see the following diagram and read the details that follow it.
The diagram of oral cavity about the origin of vowel sounds
Now see the above diagram and you will know about the origin of vowel sounds. There are THREE types of vowels as explained in the above diagram. And they are upper and lower, front and back and rounded and unrounded. Only rounded and unrounded are not shown in the diagram but they are easy to understand as explained later on this page.
i. Upper or closed vowels
They are called upper vowels because they are pronounced somewhere at upper side of oral cavity. Like; /i/, /u:/ etc. They are also called closed because when you pronounce them your mouth doesn’t open wide as compare to other vowels.
ii. Lower or open vowels
They are called lower vowels because they are pronounced somewhere from the lower portion of the oral cavity. And when you pronounce them your mouth opens wider than other vowel sounds that’s why they are called open vowels too. Like; /a:/.
iii. Front vowels:
The front vowels are those that are seemed to be pronounced from the front of mouth near front teeth, like; /i:/ and /a:/ etc.
iv. Back vowels
The vowel sounds that seem to be pronounced from the back side of oral cavity (mouth), like, /u:/
Note: Remember, where ever you find the gap in your oral cavity while pronouncing any vowel that gap indicates its origin once you practice you can easily feel the origin.
v. Rounded vowels
They are such vowels by pronouncing them your lips become rounded, like /u:/ in the word boot.
vi. Unrounded vowels:
The vowels by pronouncing them your lips don’t get
rounded, like; /a:/, /i:/ etc.
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# General Linear Model (GLM)
The equation of the General Linear Model is Y = Xb + e where Y, X, b, and e are matrices. Statistical test such as Analysis of Variance and Regression are special cases of the General Linear Model. These statistical tests can be formulated and solved using the General Linear Model.
# Regression Via Least Squares
The goal of linear regression is to predict the value of a dependent variable, Y, from one or more independent variables, X, where X and Y are observations from multiple subjects.
## Regression Equation
Yi = β0 + β1 * Xi + ε0
• Yi is the dependent variable that is predicted and depends upon the value Xi.
• Xi is the independent variable.
• β0 and β1 are coefficients. Furthermore, β0 is the Y-intercept (value of Yi when Xi is zero) and β1 is the slope of the line.
• εi is random error.
• i ranges from 1 to N, the number of subjects.
It can be shown that:
• ${\beta}_1 = \frac{\sum_{i=1}^N {(X_i - \overline{X}) (Y_i - \overline{Y})}} {\sum_{i=1}^N {(X_i - \overline{X})^2}}$
• ${\beta}_0 = \overline{Y} - {\beta}_1 * \overline{X}$
## Example
Data from Applied Linear Regression Models, page 44.
i Yi Xi
1 73 30
2 50 20
3 128 60
4 170 80
5 87 40
6 108 50
7 135 60
8 69 30
9 148 70
10 132 60
For the data from the table above:
• β0 = 10.0
• β1 = 2.0
so
Y = 10.0 + 2.0X
# Matrices
A matrix is a two dimensional array of numbers. The elements in the matrix are indexed by i and j where i is the row number (starting from the top at zero) and j is the column number (starting at zero from the left). In the matrix below, X01 is the element 2 and X12 is 4.
$\begin{vmatrix} 1 & 2 & 3\\ 6 & 5 & 4 \end{vmatrix}$
$\begin{vmatrix} X_{00} & X_{01} & X_{02}\\ X_{10} & X_{11} & X_{12} \end{vmatrix}$
## Transpose
Given a matrix A, its transpose is A'.
A = $\begin{vmatrix} 1 & 2 & 3\\ 6 & 5 & 4 \end{vmatrix}$
A' = $\begin{vmatrix} 1 & 6 \\ 2 & 5 \\ 3 & 4 \end{vmatrix}$
To add or subtract matrices, the matrices involved MUST contain the same number of rows and columns.
A = $\begin{vmatrix} 1 & 2 & 3\\ 6 & 5 & 4 \end{vmatrix}$
B = $\begin{vmatrix} 17 & 8 & 12\\ 11 & 7 & 15 \end{vmatrix}$
A + B = $\begin{vmatrix} 1 + 17 & 2 + 8 & 3 + 12\\ 6 + 11 & 5 + 7 & 4 + 15 \end{vmatrix} = \begin{vmatrix} 18 & 10 & 15\\ 17 & 12 & 19 \end{vmatrix}$
A - B = $\begin{vmatrix} 1 - 17 & 2 - 8 & 3 - 12\\ 6 - 11 & 5 - 7 & 4 - 15 \end{vmatrix} = \begin{vmatrix} -16 & -6 & -9\\ -5 & -2 & -11 \end{vmatrix}$
## Multiplication
To multiply matrices, the number of columns in the matrix on the left side of the "*" must equal the number of rows in the matrix on the right side of the "*".
A = $\begin{vmatrix} 1 & 2 & 3\\ 6 & 5 & 4 \end{vmatrix}$
B = $\begin{vmatrix} 17 & 8 \\ 11 & 7 \\ 9 & 10 \end{vmatrix}$
A * B = $\begin{vmatrix} (1*17 + 2*11 + 3*9) & (1*8 + 2*7 + 3*10) \\ (6*17 + 5*11 + 4*9) & (6*8 + 5*7 + 4*10) \end{vmatrix} = \begin{vmatrix} 66 & 52 \\ 193 & 123 \end{vmatrix}$
## Identity
An identity matrix is a square matrix (number of rows equals number of columns) with the element one where the row index equals the column index (the diagonal) and zeros for all other elements. Multiplying a matrix by the identify matrix leaves the matrix unchanged (A * I = A).
I = $\begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1) \end{vmatrix}$
## Linear Independence and Rank
A column (row) of a matrix is Linear Dependent if it is some linear combination of another column (row). In the matrix A, below, the elements of column 1 (1 2 3) can be multiplied by 3 producing (3 6 9) which is the third column of the matrix.
A = $\begin{vmatrix} 1 & 4 & 3 \\ 2 & 6 & 6 \\ 3 & 7 & 9 \end{vmatrix}$
The Rank of a matrix is its minimum number of linearly independent rows/columns. For the matrix A, its Rank is 2.
## Inverse
For the matrix A, its inverse is denoted by A − 1and A * A − 1 = A − 1&A = I (multiplying a matrix by its inverse yields the Identity matrix). Only square matrices have an inverse. In addition, a matrix must be nonsingular, that is, its rank must equals its number of rows and columns, to have an inverse. If the rank of a matrix is less than than its number of rows and columns, it is singular. The inverse of a singular matrix can be computed using a pseudoinverse.
A = $\begin{vmatrix} 5 & 3 & 4 \\ -3 & 2 & 5 \\ 7 & 4 & 6 \end{vmatrix}$
$A^{-1} = \begin{vmatrix} -0.533 & -0.133 & 0.466 \\ 3.533 & 0.133 & -2.466 \\ -1.733 & 0.066 & 1.266 \end{vmatrix}$
# Regression Via GLM
Data from Applied Linear Regression Models, page 44.
i Yi Xi
1 73 30
2 50 20
3 128 60
4 170 80
5 87 40
6 108 50
7 135 60
8 69 30
9 148 70
10 132 60
## GLM
$\mathbf{Y} = \mathbf{X} * \boldsymbol{\Beta} + \boldsymbol{\Epsilon}$
$\mathbf{Y} = \begin{vmatrix} 73 \\ 50 \\ 128 \\ 170 \\ 87 \\ 108 \\ 135 \\ 69 \\ 148 \\ 132 \end{vmatrix},~~ \mathbf{X} = \begin{vmatrix} 1 & 30 \\ 1 & 20 \\ 1 & 60 \\ 1 & 80 \\ 1 & 40 \\ 1 & 50 \\ 1 & 60 \\ 1 & 30 \\ 1 & 70 \\ 1 & 60 \end{vmatrix}, ~~ \boldsymbol{\Beta} = \begin{vmatrix} b_0 \\ b_1 \end{vmatrix},~~ \boldsymbol{\Epsilon} = \begin{vmatrix} \epsilon_0 \\ \epsilon_1 \\ \epsilon_2 \\ \epsilon_3 \\ \epsilon_4 \\ \epsilon_5 \\ \epsilon_6 \\ \epsilon_7 \\ \epsilon_8 \\ \epsilon_9 \\ \end{vmatrix}$
## Least Squares Estimation
$\mathbf{X'} * \mathbf{X} * \mathbf{B} = \mathbf{X'} * \mathbf{Y}$
$\mathbf{B} = {(\mathbf{X'} * \mathbf{X})}^{-1} * \mathbf{X'} * \mathbf{Y}$
## Least Squares Estimation Using Example Data
$\mathbf{X'} = \begin{vmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 30 20 & 60 & 80 & 40 & 50 & 60 & 30 & 70 & 60 \end{vmatrix}$
$\mathbf{X'} * \mathbf{X} = \begin{vmatrix} 10 & 500 \\ 500 & 28400 \end{vmatrix},~~ {(\mathbf{X'} * \mathbf{X})}^{-1} = \begin{vmatrix} 0.8353& -0.0147 \\ -0.0147& 0.0003 \end{vmatrix}$
## Result
$\mathbf{B} = \begin{vmatrix} 10 \\ 2 \end{vmatrix}$
# One-Way ANOVA Via Sums Of Squares
A one-way ANOVA determines if the mean values at each node for two or more groups of subjects are statistically different. The groups being compared are allowed to have a different number of subjects.
## Sum of Squares Formulas
K = Number of Groups
N = Total Number of Subjects
Ni = Number of Subjects in Group "i"
dfTotal = N − 1
$df_{Error} = \sum_{i=1}^{K} (N_i - 1) = N - K$
dfTreatment = K − 1
Xij = Measurement for subject "j" in group "i"
Mean of group i, $\bar{X_i} = \frac{\sum_{j=1}^{N_i} x_{ij}} {N_i}$
Grand Mean, $\bar{X_{..}} = \frac{\sum_{i=1}^{K} \sum_{j=1}^{N_i} X_{ij}}{N}$
$SS_{Total} = \sum_{i=1}^{K} \sum_{j=1}^{N_i} (X_{ij} - \bar{X_{..}})^2$
$SS_{Error} = \sum_{i=1}^{K} \sum_{j=1}^{N_i} (X_{ij} - \bar{X_i})^2$
$SS_{Treatment} = \sum_{i=1}^{K} N_i (\bar{X_i} - \bar{X_{..}})^2$
SSTotal = SSWithin + SSTreatment
$MS_{Treatment} = \frac{SS_{Treatment}} {df_{Treatment}}$
$MS_{Error} = \frac{SS_{Error}} {df_{Error}}$
$F = \frac{MS_{Treatment}} {MS_{Error}}$
## Sum Of Squares Example
Data from Statistical Methods for Psychology, page 608.
Treatment 1 Treatment 2 Treatment 3 Treatment 4
8 5 3 6
9 7 4 4
7 3 1 9
SSTotal = 73.00
SSError = 27.333
SSTreatment = 45.667
dfTotal = 11
dfError = 8
dfTreatment = 3
$MS_{Treatment} = \frac{SS_{Treatment}} {df_{Treatment}} = \frac{45.667}{3} = 15.222$
$MS_{Error} = \frac{SS_{Error}} {df_{Error}} = \frac{27.333}{8} = 3.417$
$F = \frac{MS_{Treatment}} {MS_{Error}} = \frac{15.222}{3.417} = 4.46$
# One-Way ANOVA Via GLM
Recall that the equation of the General Linear Model is Y = Xb + e where Y, X, b, and e are matrices.
In the case of a One-Way ANOVA with N total subjects from K groups:
Matrix Dimensions
Y N x 1
X N x (K + 1)
b (K + 1) x 1
e N x 1
## Design Matrix
In the case of ANOVA, X is a Design Matrix that indicates group membership of each subject. In the matrix X, there is one row for each subject and (K + 1) columns. The first column always contains ones. The remaining columns are used to indicate membership in a group with a value of one in column M indicating membership in group (M - 1) and a value of zero indicating not a member of the group.
The matrix Y contains the value from each subject, one per row.
Data from Statistical Methods for Psychology, page 608.
Treatment 1 Treatment 2 Treatment 3 Treatment 4
8 5 3 6
9 7 4 4
7 3 1 9
$\mathbf{Y} = \begin{vmatrix} 8 \\ 9 \\ 7 \\ 5 \\ 7 \\ 3 \\ 3 \\ 4 \\ 1 \\ 6 \\ 4 \\ 9 \end{vmatrix}$ $\mathbf{X} = \begin{vmatrix} 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 & 1 \end{vmatrix}$
Recall from the General Linear Model that $\mathbf{b} = {(\mathbf{X'} * \mathbf{X})}^{-1} * \mathbf{X'} * \mathbf{Y}$
However $(\mathbf{X'} * \mathbf{X})$ is singular so an inverse cannot be computed. To resolve this problem, the design matrix X is modified in two ways. First, the last column, indicating membership in the last group, is removed. Recall that a value of one in a column indicates membership in a group and a value of zero in a column indicates NOT membership in a group. The second modification is to use a value of negative one in a column to indicate membership in the last group (the column that was removed).
$\mathbf{X} = \begin{vmatrix} 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 \\ 1 & -1 & -1 & -1 \\ 1 & -1 & -1 & -1 \\ 1 & -1 & -1 & -1 \end{vmatrix}$
## Computing Sums of Squares using General Linear Model
$SS_{Total} = \mathbf{Y'} * (\mathbf{I} - \frac{1}{n} * \mathbf{J}) * \mathbf{Y}$
$SS_{Error} = \mathbf{Y'} * \mathbf{Y} - \mathbf{b'} * \mathbf{X'} * \mathbf{Y}$
$SS_{Treatment} = \mathbf{Y'} * (\mathbf{H} - \frac{1}{n} * \mathbf{J}) * \mathbf{Y}$
$\mathbf{b} = {(\mathbf{X'} * \mathbf{X})}^{-1} * \mathbf{X'} * \mathbf{Y}$
$\mathbf{I}$ is an NxN identity matrix.
$\mathbf{J}$ is an NxN matrix with all elements having the value 1.
$\mathbf{H}$ is the Hat matrix equal to $\mathbf{X} * {(\mathbf{X'} * \mathbf{X})}^{-1} * \mathbf{X'}$
# Two-Sample T-Test via GLM
A two-sample T-Test is simply a one-way ANOVA with only two groups. Note that T is the square root of F.
## Example Data
Hight Protein Low Protein
134 80
146 118
104 101
119 85
124 107
161 132
107 94
83
113
129
97
123
# References
Neter, J., Wasserman, W., and Kutner, M.H. 1989. Applied Linear Regression Models. IRWIN, Homewood, IL, Second Edition.
Neter, J., Wasserman, W., and Kutner, M.H. Applied Linear Statistical Models. IRWIN, Homewood, IL, Third Edition.
Howell, David C. 2002. Statistical Methods for Psychology. Duxbury, Pacific Grove, CA, Fifth Edition.
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# Samacheer Kalvi 6th Science Solutions Chapter 2 Pdf
## Samacheer Kalvi 6th Science Solutions Chapter 2 Pdf
Tamilnadu Board Samacheer Kalvi 6th Science Solutions Chapter 2: Tamilnadu State Board Solution Class 6 Science Chapter 2 – Force and Motion.
### Samacheer Kalvi 6th Science Solutions Chapter 2: Overview
Board Samacheer Kalvi Class 6 Subject Science Chapter 2 Chapter Name Force and Motion
### Samacheer Kalvi 6th Science Solutions Chapter 2 Pdf
Force and Motion
Chapter 2
1.) Unit of speed is
a.) M
b.) S
c.) kg
d.) m/s
Solution: The unit of speed is m/s. As M, Kg and S are the units of metre, Kilogram and second respectively.
2.) Which among the following is an Oscillatory motion?
a.) Rotation of the earth about Its axis.
b.) Revolution of the moon about the Earth.
c.) To and fro movement of a Vibrating string.
d.) All of these.
Answer: To and fro movement of a Vibrating string.
Solution: To and fro movement of a Vibrating string is an oscillatory motion. On the other hand the rotation of the earth about Its axis and the revolution of the moon about the earth are examples of Circular motion.
3.) The correct relation among the Following is
a.) Speed = Distance × Time
b.) Speed = Distance / Time
c.) Speed = Time / Distance
d.) Speed = 1 / (Distance × Time)
Solution: The formula for calculating the speed of an object is by dividing the distance travelled by time taken by the object to cover the distance.
4.) Gita travels with her father in a bike to Her uncle’s house which is 40 km away From her home. She takes 40 minutes To reach there.
Statement 1 : She travels at a speed Of 1 km / minute.
Statement 2 : She travels at a speed Of 1 km/hour.
a.) Statement 1 alone is correct.
b.) Statement 2 alone is correct.
c.) Both statements are correct.
d.) Neither statement 1 nor statement 2 is correct.
Answer: Statement 1 alone is correct.
Solution: Gita travels 40km in 40 minutes. Speed = distance/time taken , so 40km/40min = 1km/minute.
II.) Fill in the blanks.
1.) A bike moving on a straight road is an Example for ____linear________ motion.
2.) Gravitational force is a ___non contact____ force.
3.) Motion of a potter’s wheel is an Example for ____rotatory_______ motion.
4.) When an object covers equal distances In equal interval of time, it is said to be __periodic_____ In motion.
III.) State True or False. If False correct the statement.
1.) To and fro motion is called oscillatory Motion.
2.) Vibratory motion and rotatory motion Are periodic motions.
3.) Vehicles moving with varying speeds Are said to be in uniform motion.
Answer: False, vehicles moving with a constant speed are said to be in uniform motion.
4.) Robots will replace human in future.
Answer: False because robots are machines that helps in minimising human labour and can make work easier.
IV.) Match the following.
1 Linear motion 2 Rotatory motion 3 Oscillatory motion 4 Circular motion 5 Linear and rotatory motion.
V.) Given below is the distance-travelled by an elephant across a forest with uniform speed. Complete the data of the table given below with the idea of uniform speed.
Distance (m) 0 4 8 12 16 20 Time (s) 0 2 4 6 8 10
VI.) Complete the analogy
1.) Kicking a ball : Contact force :: Falling Of leaf : ?
2.) Distance : metre :: Speed : ?
3.) Circulatory motion : A spinning top :: Oscillatory motion : ?
VII.) Complete the web chart.
VIII.) Answer in a word or two.
1.) The force which acts on an object Without physical contact.
2.) A change in the position of an object With time.
3.) The motion which repeats itself after a Fixed interval of time.
4.) The motion of an object which covers Equal distances in equal intervals of Time.
5.) A machine capable of carrying Out a complex series of actions Automatically.
1.) Define force.
Answer: A force is an applied push or pull upon an object, usually to change its position.
2.) Name different types of motion based On the path.
Answer: The different types of motion based on the path are Linear, Curvilinear, Circular, Rotatory, Oscillatory and Zigzag.
3.) If you are sitting in a moving car, will You be at rest or motion with respect Your friend sitting next to you?
Answer: With respect to the person sitting next to me in the car , I’ll be at rest. But with respect to other things , outside in the surrounding I’ll be in motion.
4.) Rotation of the earth is a periodic Motion. Justify.
Answer: Periodic Motion refers to movements that repeat in uniform interval of time. So, rotation of the earth about Its axis is an example of periodic Motion.
5.) Differentiate between rotational and Curvilinear motion
Answer: Curvilinear motion- movement of an object in a curved path.
Rotational motion – rotating movement of an object about its own axis.
1.) What is motion? Classify different Types of motion with examples.
Answer: When an object changes its position from a state of rest over time is called motion. Motion are of three types.
1) Based on path – Linear, Curvilinear, Circular, Rotatory, Oscillatory and Zigzag.
2) Based on duration – periodic and non periodic.
3) Based on speed – uniform motion and non uniform
XI.) Problems.
1.) A vehicle covers a distance of 400km In 5 hour. Calculate its speed.
Time taken = 5 hours.
Speed = distance/ time taken , 400/5 = 80km/hr
XII.) Give example.
End…
Updated: June 4, 2022 — 3:35 pm
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Norman, OK: There are 4 clear columns on the left side followed by a dash-like sign and 3 columns on the right. The sun and moon were used to distinguish between 1 PM and 4 PM.
The Egyptians used a written numeration that was changed into hieroglyphic writing, which enabled them to note whole numbers to 1,000,000. McIntyre, Loren.
Cuneiform means "wedge shape" in Latin. If you can't figure it out, look at the next step.
Introduction Homepage Math blog Pre-algebra Pre-algebra lessons Algebra Algebra lessons Advanced algebra Geometry Geometry lessons Trigonometry lessons Math by grades Math by grade Math tests Online math tests Math vocabulary quizzes Applied arithmetic Basic math word problems Consumer math Baseball math Math for nurses Interesting math topics Ancient numeration system Set notation Math resources Other math websites Basic math worksheets Algebra worksheets Geometry worksheets Preschool math worksheets First grade math worksheets Basic math formulas Basic math glossary Basic math calculator Algebra solver Educational math software Online educational videos Private math tutors Ask a math question Careers in math The Basic math blog.
They wrote these symbols on wet clay tablets which were baked in the hot sun.
Other methods were invented for means of communication and teaching of numerical systems. In the Arabic form we use the place values of 1, 10, 100, 1,000, and 10,000. It is currently in a British museum.
Century A. One of the strange consequences of the lack of zero comes up in reciprocals. The Greek numbering system was uniquely based upon their alphabet.
Why do we need a symbol that literally means nothing? There was little need for a numeric system until groups of people formed clans, villages and settlements and began a system of bartering and trade that in turn created a demand for currency. The Babylonian Number System. Share Flipboard Email. Our own word "alphabet" comes from the first two letters, or numbers of the Greek alphabet -- "alpha" and "beta.
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The discovery was made at Pachacamac, one of the largest Prehispanic sites in South America, located on the Pacific Coast about 18 miles from Lima, Belgium's Universite libre de Bruxelles reported Tuesday.
In front of the Temple of Pachacamac, a scattering of later period burials was found to conceal an enormous burial chamber 65-feet long, dated to 1,000 years ago, that had survived the pillaging of the colonial period -- particularly intensive on the site -- and was intact, researchers said.
The oval tomb was covered with a roof of reeds supported by carved and shaped tree trunks.
A dozen newborns and infants were distributed around the perimeter, while the main chamber was separated into two sections separated by a wall of mud bricks that served as a base for yet more burials, archaeologists said.
Seventy skeletons and mummies were found inside those sections, representing both sexes and often accompanied by offerings including copper and gold artifacts, masks and ceramic vessels.
Pachacamac is a candidate for inclusion on the United Nations list of UNESCO World Heritage sites.
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# Search by Topic
#### Resources tagged with Theoretical probability similar to Mathsland National Lottery:
Filter by: Content type:
Stage:
Challenge level:
### There are 43 results
Broad Topics > Probability > Theoretical probability
### Mathsland National Lottery
##### Stage: 3 and 4 Challenge Level:
Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.
### Same Number!
##### Stage: 4 Challenge Level:
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
### Probability Resources
##### Stage: 4 Challenge Level:
This set of resources for teachers offers interactive environments to support probability work at Key Stage 4.
### Last One Standing
##### Stage: 3 and 4 Challenge Level:
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
### The Random World
##### Stage: 3, 4 and 5
Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live.
### Win or Lose?
##### Stage: 4 Challenge Level:
A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has. . . .
### Introducing Distributions
##### Stage: 4 Challenge Level:
When five dice are rolled together which do you expect to see more often, no sixes or all sixes ?
### Genetics
##### Stage: 4 Challenge Level:
A problem about genetics and the transmission of disease.
### Like Father Like Son
##### Stage: 4 Short Challenge Level:
What is the chance I will have a son who looks like me?
### Taking Chances Extended
##### Stage: 4 and 5
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
### Coin Tossing Games
##### Stage: 4 Challenge Level:
You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by. . . .
### What Do You Know about Probability? (2)
##### Stage: 3 Challenge Level:
What are the likelihoods of different events when you roll a dice?
### Bet You a Million
##### Stage: 4 Challenge Level:
Heads or Tails - the prize doubles until you win it. How much would you pay to play?
### Tools for Thinking about Probability
##### Stage: 3 Challenge Level:
Can you design your own probability scale?
How do you describe the different parts?
### Can't Find a Coin?
##### Stage: 3 Challenge Level:
Can you generate a set of random results? Can you fool the random simulator?
### At Least One...
##### Stage: 3 and 4 Challenge Level:
Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?
### The Better Bet
##### Stage: 4 Challenge Level:
Here are two games you have to pay to play. Which is the better bet?
### Misunderstanding Randomness
##### Stage: 3 Challenge Level:
Which of these ideas about randomness are actually correct?
### Which Spinners?
##### Stage: 3 and 4 Challenge Level:
Can you work out which spinners were used to generate the frequency charts?
### Distribution Differences
##### Stage: 4 Challenge Level:
How could you compare different situation where something random happens ? What sort of things might be the same ? What might be different ?
### The Birthday Bet
##### Stage: 4 Challenge Level:
The next ten people coming into a store will be asked their birthday. If the prize is £20, would you bet £1 that two of these ten people will have the same birthday ?
##### Stage: 3 Challenge Level:
Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.
##### Stage: 4 and 5 Challenge Level:
Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?
### Fixing the Odds
##### Stage: 4 Challenge Level:
You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .
### The Lady or the Lions
##### Stage: 3 Challenge Level:
The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path. . . .
### Marbles and Bags
##### Stage: 4 Challenge Level:
Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?
### Chances Are
##### Stage: 4 Challenge Level:
Which of these games would you play to give yourself the best possible chance of winning a prize?
### Gambling at Monte Carlo
##### Stage: 4 Challenge Level:
A man went to Monte Carlo to try and make his fortune. Whilst he was there he had an opportunity to bet on the outcome of rolling dice. He was offered the same odds for each of the. . . .
### Interactive Spinners
##### Stage: 3 and 4 Challenge Level:
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
### Experimenting with Probability
##### Stage: 3 Challenge Level:
This package contains environments that offer students the opportunity to move beyond an intuitive understanding of probability. The problems at the start will suit relative beginners to the topic;. . . .
### Taking Chances
##### Stage: 3 Challenge Level:
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.
### Football World Cup Simulation
##### Stage: 2, 3 and 4 Challenge Level:
A maths-based Football World Cup simulation for teachers and students to use.
### Odds and Evens
##### Stage: 3 and 4 Challenge Level:
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
### Who's the Winner?
##### Stage: 3 Challenge Level:
When two closely matched teams play each other, what is the most likely result?
### Scratch Cards
##### Stage: 4 Challenge Level:
To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?
### In a Box
##### Stage: 3 Challenge Level:
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
### Two's Company
##### Stage: 3 Challenge Level:
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
##### Stage: 4 Challenge Level:
A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .
### Card Game (a Simple Version of Clock Patience)
##### Stage: 4 Challenge Level:
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .
### Nines and Tens
##### Stage: 3 Challenge Level:
Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?
### Flippin' Discs
##### Stage: 3 Challenge Level:
Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?
### Cosy Corner
##### Stage: 3 Challenge Level:
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
### What Does Random Look Like?
##### Stage: 3 Challenge Level:
Engage in a little mathematical detective work to see if you can spot the fakes.
|
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Cyber bullying is the use of Internet e-mail, instant messaging, chat rooms, pagers, cell phones, or other forms of information technology to deliberately and repeatedly hurt, taunt, ridicule, threaten or intimidate someone.
- Did you know - Proactive informed parents are the best cyber bullying deterrent .
- Did you know - Cyber bullying incidents have more than quadrupled.
Less than 20 percent tell their parents that they have been cyber bullied out of fear of loosing Internet access. "For a teenager, internet access is nearly as important as oxygen."
It’s a cycle. More than half of students who experience cyber bullying behaviors also display cyber bullying behaviors. Teens tend to respond and escalate.Cyber bullies sometimes leave their “electronic fingerprints” behind.
Parent Cyber Bullying Education Tools Available Right Column of ths Page
- Contract: Internet Behavior Contract - Positive character agreement parents and students
- Glossary - Internet, TXT terms
- Cyber Bully Tracker - finding the bully website location
- Global Cyber Bully In The News
- See right column on this page for these items.
- Cyber Internet Bullying Survival Guide: Video Guide
Glossary Definitions: Cyber Bullying Internet Communication
Bash Board: An online bulletin board on which individuals may post anything they want. The content tends to be malicious, ridiculing, hateful statements directed against another person.
Blog: Interactive web journal or diary (web log) viewable to general audience or specific groups.
Buddy List: Collection of real names, screen names, or handles which represent “friends” or buddies within an instant message, chat program, or cell phone.
Cyberbullying: Cyberbullying is the use of e-mail, instant messaging, chat rooms, pagers, cell phones, or other forms of information technology to deliberately & repeatedly, harass, taunt, ridicule, threaten, or intimidate someone.
Cyber Bullying Victim: The one who is on the receiving end of online social cruelty.
Cyberstalking: Harassment that includes threats of harm or is highly intimidating and intruding upon one’s personal privacy.
Cyberthreats: Online material that either generally or specifically raises concerns that the creator may intent to inflict harm or violence to self or others.
IM/Instant Messaging: The act of instantly communicating between two or more people over a network such as the Internet.
Flaming (via email text etc.): Sending rude, crude, angry or obscene messages directed at a person or persons either privately or to an online group.
Happy Slapping: Extreme form of bullying where physical assaults are recorded on mobile phones and distributed to others. Sometimes they are posted on social networking sites or blogs.
Harassment: Unsolicited words or actions intended to annoy, alarm or abuse another individual.
ISP: Internet Service Provider, the company that provides an Internet connection to individuals or companies.
Offender: The one who instigates online social cruelty.
Social Networking web sites: Online service that bring together people by organizing them around a common interest or by providing an interactive environment of photos, blogs, user profiles, and messaging systems. Examples include Facebook, Twitter and MySpace.
Spam: Unsolicited electronic mail sent from someone you do not know.
Trolling: Deliberately posting false information to entice a genuinely helpful people to respond and contribute to the discussion.
URL: Universal record locator: a string of text that specifies the location of an object accessible through the Hypertext Transfer Protocol (HTTP), typically a World Wide Web address, as of a home page or iplay channel. A Web URL begins with "http://". Differs from a domain name in the sense that the domain name is a part of a URL and corresponds with IP addresses to form a URL.
The security concerns have spawned an industry of touted “software solutions.” At best software tools are reinforcements for your personal child safety campaign.
Tour Kamaron Cyber Bullying Resources Solutions Center Departments
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Reading & writing data
Each permanent magnet (naturally magnetic material) has a "north" and a "south" pole where north poles attract south poles and vice versa.
Electricity circulated through the voice coil creates an electromagnet (a magnetic field produced by an electric current). Current flow direction through the coil changes the orientation of the north and south poles of the electromagnet, which moves the voice coil either toward or away from the north and south poles of the magnets. The intensity and duration of the current determine how quickly and how far the coil moves.
Voice coils move fast enough to pivot the arms from the outside to the inside of the platter (full stroke) over 50 times per second!
The ribbon transports all information and electrical current between the logic board and actuator.
The arms are connected and pivot together.
The disk-facing surface of the slider has specific shapes etched into it that manage air flow and pressurization. As the platters spin, an air pocket or “air bearing” is created and keeps the head ~2 nm (nanometer) from each platter – thinner than a finger print.
The read heads are TMR (tunneling magnetoresistance) devices, which consist of an insulator sandwiched between two sensitive magnetic materials
Magnetic fields from the platter influence the closest magnet, causing electrons to tunnel or travel through the insulator and flip the polarity of the second magnet — thus, "reading" the platter's varying fields without disturbing them.
Write heads create an electromagnetic field that positions the north pole of a domain either up or down. The magnetic field is such that one side of it is much more concentrated, while the other end is more spread out. This allows the field to influence only the atoms on one side of the field (the “right side” of the field in this graphic). A magnetic domain with a north pole up could be a 1 while one with a north pole down could be a 0. Each 1 or 0 is considered a "bit" of data.
Electrons in atoms create magnetic fields, and the direction they “spin” determines the direction of their north and south magnetic poles. Hard disk magnetic domains usually consist of about 100,000 atoms with magnetic poles oriented in the same direction.
Multi-platter writing process
Data is written on both sides of each platter in the same respective location; if something 16 bits in size is written to or read from the platters, 2 bits would be on each of the 8 platter sides to account for the total amount.
For example, the phrase HARD DISK could be written on both sides of four platters as shown in the graphic to the left.
Our 3D animated infographics attract thousands of viewers. We'd love to work with you. Let's chat.
Platters & spindle
Cap & screws
Both sides of the platter can be used, with each side usually able to hold around 500 GB (gigabytes) of data for a total of 4,000 gigabytes (4 terabytes) between 4 platters.
Data storage comparison
If these bits (1's and 0's) were printed on 8.5x11 paper in a 12pt font, it would be 9.6 billion pages – enough pages to fill 957,000 standard four-drawer file cabinets. These file cabinets could completely cover 65 floors of the new One World Trade Center building!
Spacer rings are placed between each platter, and are precisely milled to ensure the platters and arms align properly.
The spindle uses fluid bearings to limit friction, noise, and increase durability. The spindle shaft sits in a tight, airless, sealed chamber within the bearing housing surrounded by a thin layer of lubricant.
This lubricant fills the space around the shaft, and prevents the shaft from contacting the housing
The moving spindle has an attached permanent magnet which forms part of a basic electric motor with the stationary copper coils. Most hard drives spin the platters at 5,400 (90 hertz) or 7,200 (120 hertz) RPMs (Revolutions Per Minute).
A 1-2 nm thick layer of lubrication prevents friction between the protective layer and read / write heads.
A carbon based protective layer is applied, then covered in a 1 nm thick layer of lubrication to protect the media layer of the platter. The protective layer has a smoothness of at least 0.4 nm – like a perfect circle the size of the earth with only 5.7 cm (2.3 in) of variance or imperfection.
The media layer is made of a magnetic material, usually an alloy of Cobalt and other metals, and is about 100 atoms thick.
The base of the platter is non-magnetic and is usually made from aluminum or glass (this layer would be many times thicker than those above if shown at full width).
Hard drives have separate connections for the power and data cables, and a Jumper Block. The pins on the jumper block can be connected to slow data transfer rate to be compatible with older, slower hard drives.
The logic board controls the read/write heads using a built-in map of the platters to determine which areas are available and which areas are occupied. It also controls voice coil positioning, spindle motor speed, overall power management, and the transfer of data to and from the hard drive.
A filter is placed at the edge of the platters to catch any debris created or disturbed by them. Some drives have a breath hole with an Activated Carbon filter that absorbs vapors, and prevents dust or debris from entering the drive. Newer helium drives are sealed and don’t have a breath hole.
Air is naturally circulated within the drive as the platters spin, while a breather hole allows the interior pressure to equalize with air pressure on the outside of the drive.
- Magnetism: Data Storage. (2017). YouTube. Retrieved 7 March 2017, from https://www.youtube.com/watch?v=f3BNHhfTsvk
- MAGNETS: How Do They Work?. (2017). YouTube. Retrieved 7 March 2017, from https://www.youtube.com/watch?v=hFAOXdXZ5TM
- Ferromagnetism. (2017). Hyperphysics.phy-astr.gsu.edu. Retrieved 7 March 2017, from http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c2
- Magnetic domain. (2017). En.wikipedia.org. Retrieved 7 March 2017, from https://en.wikipedia.org/wiki/Magnetic_domain
- Desktop HDD (Barracuda Hard Drive) | Seagate. (2017). Seagate.com. Retrieved 7 March 2017, from http://www.seagate.com/support/internal-hard-drives/desktop-hard-drives/desktop-hdd/
- Advanced 3D Graphics for 3D, 4D and multiple dimension data sets. Visualization solutions for industry, business, healthcare and education.. (2017). Sciencegl.com. Retrieved 7 March 2017, from http://www.sciencegl.com/index.html
- HDD from inside: Hard Drive Main parts. (2017). Hddscan.com. Retrieved 7 March 2017, from http://hddscan.com/doc/HDD_from_inside.html
- How it's made - Seagate Hard Disk Drives. (2017). YouTube. Retrieved 7 March 2017, from https://youtu.be/OPjYRdWmZJA
- A look inside a one terabyte Seagate Hard Drive - fixedByVonnie. (2017). fixedByVonnie. Retrieved 7 March 2017, from http://www.fixedbyvonnie.com/2013/09/a-look-inside-a-one-terabyte-seagate-hard-drive/#.WLDH1xLyuAw
- HDD Spindle Motor. (2017). Hddsurgery.com. Retrieved 7 March 2017, from http://hddsurgery.com/blog/hdd-spindle-motor
- Torres, G. (2017). Anatomy of a Hard Disk Drive - Page 3 of 6 - Hardware Secrets. Hardware Secrets. Retrieved 7 March 2017, from http://www.hardwaresecrets.com/anatomy-of-a-hard-disk-drive/3/
- What’s Inside A Hard Drive? | Tierra Data Recovery. (2017). Tierradatarecovery.co.uk. Retrieved 7 March 2017, from https://tierradatarecovery.co.uk/whats-inside-a-hard-drive/
- Plus, P. (2017). How the humble hard drive is made. TechRadar. Retrieved 7 March 2017, from http://www.techradar.com/news/computing-components/storage/how-the-humble-hard-drive-is-made-667183/2
- Data Sheet: Adsorbent Breather for Disk Drives | Gore. (2017). Gore.com. Retrieved 14 March 2017, from https://www.gore.com/resources/filtration-disk-drive-filters-data-sheet-disk-drive-filters-adsorbent-breather-us?from=%5B%22language%3Aen%22%2C%22categories%3A616%22%5D
- IBM Stores Data on World's Smallest Magnet -- a Single Atom. (2017). Www-03.ibm.com. Retrieved 20 March 2017, from http://www-03.ibm.com/press/us/en/pressrelease/51787.wss
Share / embed code
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## Conversion formula
The conversion factor from centimeters to decimeters is 0.1, which means that 1 centimeter is equal to 0.1 decimeters:
1 cm = 0.1 dm
To convert 0.1 centimeters into decimeters we have to multiply 0.1 by the conversion factor in order to get the length amount from centimeters to decimeters. We can also form a simple proportion to calculate the result:
1 cm → 0.1 dm
0.1 cm → L(dm)
Solve the above proportion to obtain the length L in decimeters:
L(dm) = 0.1 cm × 0.1 dm
L(dm) = 0.01 dm
The final result is:
0.1 cm → 0.01 dm
We conclude that 0.1 centimeters is equivalent to 0.01 decimeters:
0.1 centimeters = 0.01 decimeters
## Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 decimeter is equal to 100 × 0.1 centimeters.
Another way is saying that 0.1 centimeters is equal to 1 ÷ 100 decimeters.
## Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that zero point one centimeters is approximately zero point zero one decimeters:
0.1 cm ≅ 0.01 dm
An alternative is also that one decimeter is approximately one hundred times zero point one centimeters.
## Conversion table
### centimeters to decimeters chart
For quick reference purposes, below is the conversion table you can use to convert from centimeters to decimeters
centimeters (cm) decimeters (dm)
1.1 centimeters 0.11 decimeters
2.1 centimeters 0.21 decimeters
3.1 centimeters 0.31 decimeters
4.1 centimeters 0.41 decimeters
5.1 centimeters 0.51 decimeters
6.1 centimeters 0.61 decimeters
7.1 centimeters 0.71 decimeters
8.1 centimeters 0.81 decimeters
9.1 centimeters 0.91 decimeters
10.1 centimeters 1.01 decimeters
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In this book, students see the scientific method at work in a real-world situation. Readers practice close reading as they look for clues that will lead to a deeper understanding of food, health, and the transfer of energy. The scientific method pushes students to apply critical thinking as they learn new methods of exploration and build on concepts they may already know. Additional tools, including a glossary and index, help students learn new vocabulary and locate information.
Save the Planet:Local Farms and Sustainable Foods applies the NCTE/IRA Standards to science and social studies content. Each book sends the reader on a fact-finding mission, posing an initial challenge and concluding with questions and answers. Through engaging, interactive scenarios, learners can experiment with text prediction, purpose-driven research, and creative problem solving - all critical thinking skills - while learning about ways to care for our planet.
The ability to use the scientific method is key to carrying out experiments, taking measurements, or performing technical tasks. In this book, readers in real-world situations are tasked with following clues and using the scientific method to find out what happens during the spread of an epidemic. Informational text presents evidence and facts in the form of clues and side-bar details to help children develop critical thinking skills. A summary of the situation is included to show how each chapter contributes to the whole and for a solid understanding of the topic.
Using the scientific process, this title provides instructions on how to conduct experiments that help students gain a better understanding of circulatory systems.
Following the scientific process, this title provides instructions on how to conduct experiments that help students gain a better understanding of the body and digestion.
Using evidence-based research and best practices, this informative title provides a thorough introduction to concussions. Content includes causes of concussion, physical, cognitive, and emotional, symptoms, treatments, and the recovery process. Case studies, personal accounts from people who have sustained concussions, and injury-prevention tips encourage readers to advocate for their own health and safety as well as for others.
Your brain has an amazing ability to make changes and reorganize itself throughout your lifetime. This is called neuroplasticity. Supported by the latest in brain research, this motivating title helps readers understand how our brains learn and how each of us has our own personal learning style. Key concepts include brain functions and processes related to learning such as memory, attention, executive functions, and other cognitive abilities, and how neural connections form and grow. Readers are encouraged to take on a growth mindset, which is the belief that we are not just born with certain talents—we can develop them. The book includes several brain-based learning strategies. Each strategy includes a hands-on activity or demonstration to help readers apply the strategy in the real world, be empowered to take more risks in their learning, and to unlock their personal potential.
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# What is the base diameter of 1000 tons of stockpiled 1" rock?
##### Brian Monetti, I spent several years working in home improvement and construction
We will have to make some estimates here, but we can probably get a pretty accurate answer. Lets just assume the pile is a cone, it will make the math easier, and is probably pretty accurate. We will need the volume of rock. Crushed stone is somewhere around 100 lbs/cf. That means our pile has 20,000 cubic feet of stone (1000 tons x 2000 lbs per ton = 2000000 lbs, which divided by 100lbs/cf gives us 20,000 cubic feet.)
The volume of a cone = (pi) x (radius squared) x (height) / 3. We now know the volume, but need to find the radius and height. This is where it gets cool. Whenever you pile a material, it will always have a slope of the same angle. Civil Engineers call this the angle of repose. If the angle of a pile is too steep, it will basically landslide down until it is at the angle of repose. You can learn more about it here: http://en.wikipedia.org/wiki/Angle_of_repose
Now it turns out that 37 degrees is a pretty good estimate for crushed stone. That means the angle between the ground and the slope of the stone pile will be 37 degrees. Now imagine slicing the pile on half. You form a triangle between the bottom corner of the cone, the center, and the top of the pile. The bottom leg of the triangle is the Radius, and the height is the Height.
We have to use some trigonometry here to get the ratio between the height and radius. To do this, we use the Tangent. The tangent of an angle is equal to the opposite side length divided by the adjacent leg length. So, the ratio between the height of the triangle and the radius of cone (the leg thats on the ground) will be the Tangent of 37. Luckily for us, the tangent of 37 is very close to .75, so the ratio is 3 to 4 for height to radius of our cone to height.
So now we plug that into our volume equation for a cone. Volume (20,000) = (pi) x (radius squared) x (height) / 3. We know the ratio of height to radius is 3 to 4, so we can use a variable there and solve for the variable to find the radius. Basically, we set the Radius to equal 4n and the height to equal 3n, and then we can solve for n. So our equation will look like:
20,000 = (pi) x (4n)squared x (3n) / 3
Solving for n, we get 7.35. This means the radius is actually 4 times that because the radius is 4n. Therefore, the radius of the pile will be 7.35 x 4, or 29.4 feet, and the diameter of the pile will be 58 feet.
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Henry Ford was indeed a man ahead of his time. Recognized as the grandfather of the American automobile and the great innovator of the automotive assembly line, few people know that Ford was also an outspoken proponent of alcohol-based fuels. But like most visionaries of his time, his foresight was negated by several historical forces that are increasingly relevant today.
In the early 1900s the world’s first automobile makers searched for efficient fuels to propel their new creations. Rudolph Diesel used peanut oil in the engine he debuted at the World’s Fair in Paris, while most early British car makers preferred kerosene. At that time, gasoline was an unpopular waste product that Rockefeller’s lamp oil refineries dumped straight into the Cleveland River.
Henry Ford, the son of a
And for Ford, who had a farm background and was supportive of agriculture, making what would today be known as biofuel had the potential to alleviate a mounting economic crisis for many mid-western farmers (that would intensify in the Great Depression five years later). Although the economics of American agriculture’s misery were indeed complex, one possible solution could have been the creation of a domestic fuel market from homegrown crops. Through Ford's own financial and political assistance, the idea of creating such a market for farm goods would translate into a broad movement for scientific research labeled "Farm Chemurgy", which also studied the economic viability of hemp and soybean plastic.
In the end, gasoline won out over ethanol even though Henry
Ford actually designed the 1908 engine of his famous Model T to burn a mixture
of these two propellants. Three factors led to gasoline’s emergence as the
dominant transportation fuel -- the ease of operation of gas powered engines,
a growing supply of cheaper petroleum from oil field discoveries, and intense lobbying by petroleum companies to maintain steep alcohol taxes.
Remember alcohol had a very bad reputation in the
It wasn’t that gasoline was considered a miracle fuel; it had a bad reputation too. Gasoline had a lower octane rating than ethanol, was far more toxic, and generally more hazardous. Early refineries were dangerous places - gasoline was famous for spontaneous ignition and catastrophic explosions. Gasoline combustion produced more air pollution and was much more physically and chemically complex than ethanol, necessitating intensive refining procedures to ensure a consistent gasoline product.
Two key reasons have pushed petroleum fuels to forefront of automobile transportation. First, cost per mile of travel is virtually the sole selection criteria at the gas pump, and secondly, large investments made by the oil refining industry in physical capital, human skills and technology made the entry of a new cost-competitive fuel difficult in the existing marketplace.
Unfortunately Ford’s vision was lost to political and economic forces he couldn’t control. In fact, throughout American history any legislation proposing a ‘national energy program’ to employ agricultural resources for fuel production has been extinguished by well funded public relations campaigns launched by petroleum interest groups. One noteworthy claim forwarded by petrol companies in 1928 was that the U.S. government planned to fleece taxpayers to make farmers rich.
If you read some of the websites and blogs on ethanol today you’ll hear the same thing. A common misconception is that large agribusinesses control the ethanol industry. Its a fact however, that over half of the ethanol plants in the United States are owned by local farmers working together in cooperatives or limited liability companies.
The largest producer of ethanol in Canada, GreenField Ethanol works closely with farmers in rural Ontario and Quebec to create jobs and new forms of revenue in these communities.
Henry Ford, long regarded as a genius for
mass producing the automobile, also saw the future; ethanol has now arrived at
many gas stations all over
Just like Henry Ford’s 1908 Model T, most vehicles manufactured after 1980 will tolerate up to 10 per cent ethanol, known as E-10, which is the most common blend in Canada. Some newer vehicles however can tolerate E-85, a blend of 85 percent ethanol and 15 per cent gasoline. In
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In general, writing in biology (or any science) is like writing non-fiction in any other discipline. Writing should be clear, concise, and organized logically. Biological writing need not be dry, but avoid flourishes that distract from the purpose of the paper. Use appropriate scientific vocabulary.
There are some special conventions that are followed in biological writing. These conventions should be followed in any formal paper for a course. Your instructor will give you additional guidelines for specific assignments.
The metric system is the universal system of scientific
measurement. Always use metric units in your writing. If you are
converting your units, don’t artificially inflate the precision of your
measurements. If you measured to the nearest inch, report your answer
in whole centimeters.
Use scientific notation for writing very small or large numbers, and
truncate (round) the number to a maximum of four significant
digits. For example, 3,879,562.34 should be written as 3.88 X 106,
and 0.00000032456 should be written as 32.46 X 10-8.
To avoid confusion, use a leading zero as a placeholder to the left of
the decimal (0.5), but not to the right (do not write 5.0). Leave a
space between a value and its units: 5.6 ml.
Standard scientific names are used internationally to avoid confusion. The scientific name of an organism includes both the genus and the species. It is always underlined or written in italics. The genus is always capitalized, the species (or trivial) name never is. When you use the name of an organism, either use the scientific name consistently or use it the first time you use the common name.
Scientific Citation Style
Any statement of fact that is not considered general knowledge must be followed by a citation. Citations serve two major functions: Allowing the reader to find the original source of information, and giving credit for the ideas or work of others.
Examples of scientific citations:
Examples of references:
Michener, G. R. 1984. Age, sex, and species differences
in the annual cycles of ground-dwelling sciurids: Implications for
sociality. Pp. 81-107, in The biology of ground-dwelling squirrels
(J.O. Murie and G.R. Michener, eds.) University of Nebraska Press,
Lincoln, 459 pp.
Stapanian, M.A. and C.C. Smith. 1978. A model
for scatterhoarding: Coevolution of fox squirrels and black walnuts.
Tizard, I. 1992. Veterinary Immunology: An
Introduction. W. B. Saunders Co. Philadelphia. 498 pp.
Hall, M. H. P.; Fagre, D. B. (2003, February). Modeled
Climate-Induced Glacier Change in Glacier National Park,
1850-2100, Bioscience, 53, 131-140. Retrieved March 27, 2003 from
Plagiarism is a serious academic offense. Briefly, plagiarism is representing the work of another as one's own. One common form of plagiarism is using the words of another without acknowledging the source of those words. This is plagiarism even if the material has never been published or copyrighted. Even text from the internet, from a fellow student, or from an instructor must be immediately preceded or followed by a citation. The quote must be an exact copy of the original and it must be set in quotation marks or in indented text to distinguish it from your own words. Do not merely change a few words of a quote: representing the slightly altered text as your own is still plagiarism. In general, it is best to avoid using quotes because this prevents you from learning to express ideas in your own words. Representing the ideas of another as your own is also plagiarism. Follow the statement of another’s ideas with a citation.
Selecting Appropriate Reference Materials
Scientists must be able to identify appropriate sources of scientific information. One general rule is that the closer one gets to the source of information, the more reliable the information is. A report written by people who actually gathered the information is a primary source. A review of these original research papers is a secondary source of information. A review of reviews, such as one might find in the popular press, is at best a tertiary source. With each step away from the primary source the likelihood of errors and misinterpretation increases. This is why scientific journal papers cite only primary and secondary sources. Advanced students should use primary literature sources whenever possible. Your instructor may give you specific criteria for determining which sources are acceptable for a given assignment. Articles that do not list references are likely to be unacceptable.
Peer-reviewed journals are the preferred source of scientific information. In peer-reviewed journals, papers have been evaluated by other specialists prior to their publication. The goal of this process is to screen out papers that contain faulty experimental design, misinterpretation of data, or other errors. This process is not a guarantee of infallibility, but it does ensure that other experts in the field felt that the work was deserving of scientific attention. You can identify peer-reviewed journals by looking at any volume for the authoring body and the editorial policy.
For help in finding sources of information, see Research tools for biology.
Internet sources are generally less reliable and less accurate than print sources. Anyone can publish documents on the internet; there is no quality control. Errors, fraud, and misrepresentation are common on the world wide web. For that reason, only a small fraction of the total number of documents on the internet are suitable for citations in your biology course work. The convenience of searching and freshness of information on the internet outweigh some of these problems. You will have to be a careful consumer of internet information sources if you choose to use them. While your instructor may have specific criteria for acceptability of internet sources, here are some general points to consider:
Stiner, M. C. N. D. Munro, T. A. Surovell, E. Tchernov,
and O. Bar-Yosef. January 8, 1999. Paleolithic population growth pulses
evidenced by small animal exploitation. Science Online.
Return to Biology Home Page
Last update: 8/26/03 by Rebecca Burton, Dept. of Biology, Alverno College
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# FIND MEAN AND STANDARD DEVIATION OF BINOMIAL DISTRIBUTION
If the probability of mass function of x is given by
Mean = np
Variance = npq
Standard deviation = √npq
Problem 1 :
6 coins are tossed 512 times. Find the expected frequency of heads. Also compute the mean and standard deviation of the number number of heads.
Solution :
Number of coins tossed (n) = 6
Probability of getting heads = 1/2
not getting heads q = 1/2
Getting 0 heads :
Getting 1 head :
Getting 2 heads :
Getting 3 heads :
Getting 4 heads :
Getting 5 heads :
Getting 6 heads :
Expected Frequency :
Mean :
Mean = np
= 6 (1/2)
= 3
Standard deviation :
Variance = npq
Standard deviation = √npq
√6x(1/2)x(1/2)
= √1.5
= 1.22
Problem 2 :
What is the standard deviation of the number of recoveries among 48 patients when the probability of recovering is 0.75 ?
a) 36 b) 81 c) 9 d) 3
Solution :
Number of patients = 48
Probability of recovering p = 0.75
q = 0.25
Standard deviation = √npq
= √48(0.75)(0.25)
= √9
= 3
Problem 3 :
X is a binomial variable with n = 20. What is the mean of X if it is known that X is symmetric ?
Solution :
Here n = 20
Since mean is symmetric p = q
p = q = 0.5
Mean = np
= 20(0.5)
= 10
Problem 4 :
What is the number of trails of binomial distribution having mean and standard deviation as 3 and 1.5 respectively ?
a) 2 b) 4 c) 8 d) 12
Solution :
mean = np = 3 ----(1)
Standard deviation = √npq = √1.5
npq = 1.5
Applying (1)
3q = 1.5
q = 1.5/3
q = 0.5
p = 0.5
np = 3
n(0.5) = 3
n = 3/0.5
n = 6
So, the number of trials is 6.
Problem 5 :
The mean of a binomial distribution with parameters n and p is
a) n(1 - p) b) np (1 - p) c) np d) √np(1 - p)
Solution :
Mean = np
So, option c is correct.
Problem 6 :
The variance of the binomial distribution with parameters n and p is
a) np2(1 - p) b√np(1 - p) c) nq(1 - p) d) n2p2(1 - p)2
Solution :
Variance = npq
p + q = 1
q = 1 - p or p = 1 - q
Applying the value, we get
= np(1 - p) or nq(1 - q)
So, option c is correct.
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The sun dips low over the bay, its fading rays gilding the avocets as they swish their heads through the water. The egrets eye their own reflections as if in profound self-contemplation. A willet flashes past, its black-and-white wings an exclamation in the dusk.
Faced with such beauty, two words come irrepressibly to mind: niche partitioning.
Okay, it’s not a particularly lovely phrase in itself. But niche partitioning is why we can have so many different kinds of long-legged, long-billed shorebirds stalking through the same water, apparently hunting the same food, and yet all coexisting.
Natural selection favors the fittest. This should lead you to expect that one shorebird species would be the fittest—the best at hunting and surviving and reproducing in this shallow-water-and-mud habitat—and, out-competing all other shorebirds, eventually become the only shorebird around. Why doesn’t this happen? Niche partitioning.
A niche is a set of biological conditions: temperature, habitat, types of food, etc. A species’ niche is the set of conditions in which it thrives. Some species have broad niches, being able to do well under a large range of conditions; think of a cockroach, or a pigeon, or the common house mouse. My little buddies the juncos have a fairly broad niche, which is why I was able to study them under a variety of different environmental conditions. Still, there are many things that are outside their niche: juncos could not survive in a punishing desert, or Antarctica, or by trying to live off of nectar from flowers. Other species have narrow niches, specializing in very specific circumstances: cave salamanders, or tubeworms found only next to deep-sea hydrothermal vents.
The niche of shorebirds is, well, the shore. They feed in the same areas and with the same basic strategy: stick your bill in the water (or mud), pull out food, eat, repeat.
Except that this isn’t the whole story. The reason that they can all coexist is that they don’t occupy the same niche; they partition that broad shore niche into narrower, more specific niches, and each species specializes on its own smaller niche. You can see evidence of this in the shapes of their bodies. The shorter-billed Willet won’t be able to reach deep enough into the mud to catch the prey that the Long-billed Curlew can.
The upcurved bill of the avocet is well-suited to its characteristic scything behavior, where it swishes the bill through the water just above the surface of the mud, capturing anything the bill touches as it sweeps. The straight-billed stilt is instead adapted for pecking and grabbing at organisms it sees.
Some of these variations are quite subtle. The bill of the Greater Yellowlegs looks very similar to that of the Willet, but look closely and you’ll see a slight upward curve to the yellowlegs’ bill that the willet’s bill lacks.
It’s not always about the bill. Great and Snowy Egrets have basically identical bills, body plans, and hunting strategies; the difference between them is simply that of size.
Size matters. Here is our snowy, stalking along in the water, looking for prey and then stabbing down to seize it. What kind of prey is she getting?
Worms. Yum! I watched this Snowy Egret catch half a dozen worms in a few minutes, barely taking more than a few steps between each capture. On the same evening, in the same place, I watch a Great Egret stand very still for a long while, barely twitching, then plunge down to make his kill.
It isn’t that the Snowy Egret couldn’t have caught that fish, or that the Great Egret couldn’t catch worms. There are some large prey that the Great Egret can take which are out of the snowy’s repertoire—I have seen a Great Egret eat a vole, which I don’t think a snowy could subdue or fit down its throat—but that little fish is fair game for both of them. The difference here isn’t one of ability but of costs and benefits. For the smaller snowy, the worms are big enough to be a good snack, worth the work of catching them. For the larger Great Egret, the worms are so small relative to his body size that it’s better, instead, to ignore them and wait for something larger. The end result is that these two near-identical species can forage side-by-side, eating different things.
This is niche partitioning: a bay-ful of prey animals divided among predators large and small, visual and tactile hunters, long- and short-billed.
The divisions among the niches aren’t perfect. The Snowy and Great Egrets would both happily eat a small fish, as would pretty much any other bird mentioned in this post. Animals can adjust their behavior, too: stilts usually forage visually, spotting prey and then pecking at it; but at night, or when the wind is so strong that it disturbs the surface of the water and makes it hard to see, stilts switch to scything through the water like avocets. Still, even slight differences in niche allow all of these species to pursue their own specialties most of the time—and let us humans enjoy diverse shores.
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The Set Up
The Articles of Confederation created a “firm league of friendship” between the newly established states. Article III explains that this new confederation would provide for “their common defense” and ensure “their mutual and general welfare.” However, after establishing this new nation, United States merchant ships were under constant attacks from pirates along the coast of the Barbary States. The Continental Congress was unable to sufficiently address these attacks. It became clear that under the Articles of Confederation the states were unable to defend themselves and ensure their general welfare.
Problem with the Prirates
Piracy was critical to the Barbary States economies.1 The Barbary states used both the labor of captive slaves and the money from ransoms and tributesTribute noun money or goods that a ruler or country gives to another ruler or country especially for protection., as means of commerce.2 Once captured or stolen, the Barbary States would then sell slaves and or goods to other countries after capture. The most powerful nations, including England, were able to adapt to these threats to their merchant ships.
During the 18th century the British Empire was arguably the most powerful. Its military, namely it naval forces, protected British and American merchant ships from privateering when traveling to and from the colonies. Moreover, the British Empire had the monetary means to pay tribute to pirates or ransom for captured ships and sailors.3
The American revolution was fought to end British Rule within the colonies. However, the colonial system protected the American colonies through the diplomatic and military might of the British. However, the Treaty of Paris of 1783 not only brought the American Revolution to an end, but it also ended all protection the British provided to American merchant ships. American representatives attempted to ensure continued protection by Britain of American merchant ships, but the British refused.4 Thomas Jefferson claimed that one of the best markets for American exports were the Mediterranean Ports.5 Thus, ships from the United States continued to trade in the Mediterranean following the signing of the Treaty. Trade in the Mediterranean was in part retaliation against restrictions on foreign trade.6 However, he new nation had to face the threats of the Barbary pirates directly and without protection provided by its former colonial power.
Problem with the Articles
Much like the representatives at the signing of the Treaty of Paris, the Continental Congress was aware of the threat the Barbary pirates posed to United States merchant ships. However, Congress' powers were limited under the Articles of Confederation. Congress did not have the power to tax, rather individual states held that power. Therefore, if the United States needed to raise funds for tribute or ransom, the states would need to contribute voluntarily.7 In addition, the Continental Navy was incredibly expensive to maintain and was subsequently disbanded in 1784 to help pay off the nation's debt following the Revolution.8 Although Congress had the authority to re-establish and maintain a navy, the individual states held the authority to enlist sailors and pay for it.9 Thus, under the Articles, Congress was unable to provide adequate tribute and maintain a navy, which subjected merchant ships to threats from Barbary pirates.
The then US Minister to France, Thomas Jefferson, wrote to John Adams on July 11, 1786 with his recommendations for Congress to address concerns about the Barbary pirates. Jefferson believed that a Continental Navy was necessary in order to protect US merchant ships. In response, Thomas Barclay was sent to Morocco to establish a treaty between the United States and the Sultan of Morocco. Barclay wrote to Jefferson on March 23, 1786. The subsequent treaty protected merchant ships with a tribute of 5,000 pounds sterling.10
On July 25, 1785 the schooner Maria was captured by Algerian pirates. Just five days later the ship Dauphin was also captured by Algerian pirates along with its twenty-one person crew.11 The crew was taken hostage and remained captive in Algiers until the United States Constitution was ratified. Only after the ratification, when the United States was able to provided a large enough ransom through collecting taxes and borrowing from foreign states, was the piracy problem addressed. However, both powers were only granted to the federal government after the ratification of the Constitution.
Under the Articles of Confederation, the Continental Congress was unable to fully address the threats posed by the Barbary States. After the Constitution was ratified in 1788, the government was able to provide for the "common defense" and ensure the "general welfare" of the states. Moreover, with a naval force, the United States would engage in a full maritime campaign against the Barbary States during the First Barbary War (1801-1805).
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# Ordinal Numbers Font
A limitless number of sets can be easily enumerated using ordinal numbers as a tool. They can also be used as a way to generalize ordinal numbers.
## 1st
The ordinal number is one the fundamental concepts in mathematics. It is a numerical value that represents the place of an item within the list. The ordinal number is typically an integer between one and twenty. Although ordinal numbers serve many functions, they’re most frequently used to indicate the order of items within the list.
Charts Words, numbers, and even words are all able to represent ordinal numbers. These are also useful to indicate the order in which a collection of pieces is laid out.
The majority of ordinal numbers fall into one of two categories. Transfinite ordinals are represented by lowercase Greek letters, whereas finite ordinals are represented with Arabic numbers.
According to the Axiom of Choice, any set that is organized should include at least one ordinal. The first person in an class, for instance, would receive the highest mark. The winner of the contest was the student with the highest grade.
## Combinational ordinal number
The compound ordinal numbers, which can have multiple digits, are also referred to as. They are generated when an ordinal value is multiplied by its last number. They are typically utilized for ranking and dating purposes. They do not employ an exclusive ending for the final digit like cardinal numbers do.
To identify the order in which elements are placed within a collection, ordinal numerals are used to indicate the order of elements within a collection. These numbers can also be used to identify the items within the collection. Regular numbers come in the form of suppletive and regular.
Regular ordinals can be constructed by prefixing the cardinal number with an -u suffix. The number is next typed in a word and a hyphen is placed after it. There are other suffixes you can use. “-nd”, for numbers that begin with 2 is an example. “-th” is for numbers with endings between 4 and 9, is another.
Suppletive ordinals result from prefixing words with the suffix -u. This suffix, which is used to count, is wider than the normal one.
## Limit of magnitude ordinal
Limit ordinal values that aren’t zero are ordinal numbers. Limit ordinal quantities suffer from one disadvantage: they do not have an element with a maximum. You can make them by joining empty sets, but without the maximum element.
Furthermore, the infinite rules of recursion employ restricted ordinal numbers. Based on the von Neumann model, every infinite cardinal number also functions as an ordinal limit.
A number of ordinals with the limit is in reality equivalent to the total of all the ordinals that are below it. Limit ordinal numbers can be enumerated using mathematics however they also be expressed as a series or natural numbers.
Data are organized according to ordinal number. These numbers are used to explain the nature of the object’s numerical position. They are commonly used in the fields of set theory, arithmetic, and in other settings. While they belong to the same class they are not considered to be natural numbers.
The von Neumann Model uses a well-ordered set, or ordered set. It is assumed that fyyfy represents an element of g’, a subfunction of a function that is described as a singular operation. In the event that g’ fulfills the requirements, g’ is an limit ordinal when there is only one subfunction (i I, the second).
The Church-Kleene oral is an limit order similarly. The Church-Kleene ordinal defines the term “limit” as a correctly ordered collection of the smaller ordinals. It also has an ordinal that is nonzero.
## Examples of stories with ordinary numbers
Ordinal numbers are frequently used to show the order of entities or objects. They are crucial to organize, count, or ranking purposes. They can be utilized to identify the sequence of events and also to indicate the exact position of objects.
The ordinal numbers are typically indicated by the letter “th”. Sometimes though it is possible that the “nd” letter could be used instead of “th”. The titles of books often include ordinal numbers.
Although ordinal numbers are frequently used in list format, they can also be expressed in words. They may also be expressed in the form of numbers and acronyms. In comparison, the numbers are simpler to understand than the cardinals.
There are three kinds of ordinal numerals. Through games and exercises you can be able to learn more about the numbers. A key component to improving your math skills is being educated about them. A coloring exercise is an enjoyable and simple way to build your skills. To assess your progress make use of a handy mark-making page.
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Berlin Airlift Map
After the first weeks of the airlift, the Allied effort to successfully supply Berlin was falling short. Air Force Major General William Tunner arrived to assist General Clay, who was not himself an airman. Tunner has overseen World War II's only successful large scale airlift of thousands of tons of supplies from India to China. Due to his strategic changes, the airlift effort escalated dramatically in scale, culminating in a 24 hour "Easter Parade" in April, 1949 that brought in almost 13,000 tons of supplies.
In late July 1948, the British began expanding this airfield, originally built in 1936 as a German Luftwaffe bombing school. After flying out Dakotas for a number of weeks, the British handed it over to the U.S. Airforce to fly C-54s.
In August 1948, the British moved their air operations from Fassberg to this base, originally built in 1935 for the German Luftwaffe. Only two miles from the border, pilots took great care to avoid Soviet territory in their approaches and departures.
A number of deadly crashes occurred as the frequency and intensity of the airlift increased, many due to adverse weather conditions. The USAF 18th Weather Squadron, based out of Wiesbaden, was responsible for providing around the clock weather forecasting support for the airlift.
On an off day in Berlin, Air Force Lieutenant Gail Halvorsen noticed a group of small children crowded at a fence by Tempelhof airport. He gave them some sticks of gum and promised to bring them some more candy. Halvorsen began dropping small parachutes of sweets from his plane to the growing throngs of children gathered at Tempelhof; the operation became known as "Little Vittles."
In the summer of 1948, Allies begin working on a new airport in the French sector. Forty percent of the civilian work force that built the airport were German women. In November 1948, after the destruction of a Soviet radio tower blocking flight access, Tegel opened as new landing spot for the airlift.
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An inscribed angle is formed when two secant lines intersect on a circle. It can also be formed using a secant line and a tangent line intersecting on a circle. A central angle, on the other hand, is an angle whose vertex is the center of the circle and whose sides pass through a pair of points on the circle, therefore subtending an arc. In this post, we explore the relationship between inscribed angles and central angles having the same subtended arc. The angle of the subtended arc is the same as the measure of the central angle (by definition).
In the first circle, is a central angle subtended by arc . Angle is an inscribed angle subtended by arc . In the second circle, is an inscribed angle and is a central angle. Both angles are subtending arc .
What can you say about the two angles subtending the same arc? Draw several cases of central angles and inscribed angles subtending the same arc and measure them. Use a dynamic geometry software if necessary. Are your observations the same?
In the discussion below, we prove one of the three cases of the relationship between a central angle and an inscribed angle subtending the same arc.
The measure of an angle inscribed in a circle is half the measure of the arc it intercepts. Note that this is equivalent to the measure of the inscribed angle is half the measure of the central angle if they intercept the same arc.
Let be an inscribed angle and be a central angle both subtending arc as shown in the figure. Draw line . This forms two isosceles triangles and since two of their sides are radii of the circle.
In triangle , if we let the measure of be , then angle is also . By the exterior angle theorem, the measure of angle . This is also similar to triangle . If we let angle , it follows that is equal to 2y. In effect, the measure of the inscribed angle and the measure of central angle which is what we want to prove.
The proofs of the second and third case are left as an exercise.
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# What are the charges on plates 3 and 6?
A.) What are the charges on plates 3 and 6?
B.) If the voltage across the first capacitor (the one with capacitance C_{)} is V^{\prime}, then what are the voltages across the second and third capacitors?
C.) Find the voltage { }^{V_{1}} across the first capacitor.
D.) Find the charge { }^{Q} on the first capacitor.
E.) Using the value of Q just calculated, find the equivalent capacitance C_{\mathrm{eq}} for this combination of capacitors in series.
A. the charges on plates 3 and 6 are +Q and -Q
Correct answeris C.+Q and -Q
B. When capacitors are connected in series, the charge on each is same and equal to total charge stored
In series combination, the potential across any capacitor is inversly proportional to its capacity
If thevoltageacross the first capacitor (the one with capacitance C) is V', then
V'=Q /C
The voltage across second capacitor =Q/2C =(1/2)Q/C=V'/2
The voltage across third capacitor =Q/3C =(1/3)Q/C=V'/3
Correct answer is B.V'/2 and V'/3
V= V_1 +V_2+V_3
V= V_1 +V_1/2+V_1/3
V = 11V_1/6
C. The voltage V_1 across the first capacitor= V_1= 6V/ 11
D. The charge Q on the first capacitorQ = cV_1
V= V_1 +V_2+V_3
Q/C_eq =Q/c +Q/2c +Q/3c
1/C_eq =1/c +1/2c +1/3c
E. The equivalent capacitance C_eq for this combination ofcapacitors in series.
C_eq =6c /11
### Raymond Puzio
Raymond Puzio has a PhD in Physics from Yale University. I have been creating PlanetPhysics with Aaron Krowne and Ben Loftin since 2005.
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The change of seasons can bring about a change in people. Allergies hit in the spring, moods change in the sunny summer and dreary cold of winter, but what about vision? Does your vision change with the season? According to new research, it can.
Scientists at the University of York studied the effects of the seasons on how people perceive colour, particularly the colour known as unique yellow. According to the university, there are four unique hues, blue, green, yellow and red. Unique yellow is the most recognized by a cross-section of the population.
Researchers theorized that what we see around us affects how we see the world. To test the theory, they brought in 67 people to a darkened room and used a machine called a colourimeter to pinpoint what they believed was unique yellow. They did this in January and then again in June.
“What we are finding is that between seasons our vision adapts to changes in the environment,” lead author Lauren Welbourne said in announcing the findings. “So in summer when there is a much larger amount of foliage, our visual system has to account for the fact that on average we are exposed to far more green.”
Welbourne says this information shows how much more we are still learning about the way the human eye works and how adaptable we are to changes in our surroundings.
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Any member of the pterosaur suborder Pterodactyloidea, known from Late Jurassic and Cretaceous fossils (159–65 million years ago) in eastern Africa and Europe. Members of the typical genus, Pterodactylus, ranged from the size of a sparrow to that of an albatross. Pterodactyls had slender, delicate teeth that were angled forward (possibly for use as straining devices), long metacarpal bones, and a short tail. They were probably able gliders but not efficient as active fliers, and they apparently lacked feathers. Unlike the archaeopteryx, the pterodactyl was not an ancestor of the birds.
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Researchers photographed this Kandyan dwarf toad in 2009, but the IUCN red list claims this species is extinct. In fact, the last time anybody saw a Kandyan dwarf toad alive was all the way back in 1876. So where did this picture come from?
Writing in the journal Zootaxa, the researchers who rediscovered the toad explain that they came across it during a night-time sampling session on rocks close to a fast-flowing stream. It was discovered among a group of torrent toads (Adenomus dasi), which it strongly resembles — perhaps why several previous extensive searches of the region failed to identify it. However, the researchers write that the Kandyan dwarf toad can be easily recognised by its fully webbed toes and the presence of large warts on its back.
Scientists sometimes refer to rediscovered animals as Lazarus species (though the term is more commonly used among paleontologists to describe the disappearance and re-appearance of fossils in the geological record). Sometimes these Lazarus species re-appear and stick around for a good long while. Others, however, are often at risk of succumbing to real, permanent extinction. The researchers who re-discovered the Kandyan dwarf toad fear it belongs to the latter camp.
Read more at New Scientist.
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Tracheotomy is the surgical creation of an opening from the outside of the neck into the windpipe. Usually a tracheostomy tube is then inserted into the opening to allow for normal breathing.
|Copyright © Nucleus Medical Media, Inc.|
Reasons for Procedure
A tracheotomy is done to bypass obstructions in the upper airway that are interfering with breathing. The opening is called a stoma or tracheostomy. A stoma may be either temporary or permanent.
A tracheotomy is done to restore normal breathing in the following situations:
- The airway is obstructed at or above the level of the larynx, which is also known as the voice box, due to:
Respiratory failure requiring long-term mechanical breathing assistance, as in these cases:
- Spinal cord injury in the neck area
- Severe lung infection or inflammation
- The use of a ventilator for 21 days
- Injury to the respiratory tract due to breathing in smoke or steam or inhaling corrosive substances
- Birth defects of the trachea or larynx
- Foreign object blocking the trachea or larynx
- Severe sleep apnea
- Aspiration related to muscle or sensory problems in the throat
If you are planning to have a tracheotomy, your doctor will review a list of possible complications, which may include:
- Damage to the vocal cords, vocal cord nerves, or esophagus
- Scarring at the site of operation leading to closure of the tracheostomy or tracheal narrowing
- Tracheostomy tube displacement or damage
- Difficulty swallowing
- Air trapped in tissue under the skin of the neck
- Damage to the lungs
- Low blood pressure
- Abnormal connection to esophagus or surrounding blood vessels
Some factors that may increase the risk of complications include:
What to Expect
Prior to Procedure
Your doctor will likely do the following:
- Chest x-ray
- Blood and urine tests
- Review of medications
Talk to your doctor about your medications. You may be asked to stop taking some medications up to one week before the procedure.
General anesthesia will be used. You will be asleep. In emergency situations, local anesthesia may be used. It will numb the area.
Description of Procedure
A cut will be made in the skin of the neck. A small incision will then be made in front of the windpipe between the cartilage. A tracheostomy tube, which will act as the airway, will then be fitted into this opening in the windpipe. The skin will be closed around the tube with stitches or clips.
Immediately After Procedure
You will breathe through this tube as long as it is in place. Oxygen and machines to assist breathing will be provided, if needed. A chest x-ray may be needed.
How Long Will It Take?
About 15-30 minutes
How Much Will It Hurt?
Anesthesia prevents pain during the procedure. You may have some pain and soreness during recovery. Your doctor can prescribe pain medication to help relieve this discomfort.
Average Hospital Stay
The length of stay will depend on the reason for the procedure. Most stays are 1-5 days.
Tracheostomy tubes need to be cared for on a regular basis. The hospital staff will teach you how to care for your tracheostomy tube. It is important follow the staff’s instructions to prevent infection and airway obstruction. Other specialists will help you adjust to the tracheotomy and learn how to speak and eat with the tracheostomy.
Tracheostomy tube care considerations include:
- Regular cleaning
- Regular clearing of secretions
- Keeping the airway open
- How to use oxygen or a humidifier (if needed)
- Learning to keep away from irritants that affect the airway
- Speaking and eating techniques
- Learning cardiopulmonary resuscitation (CPR)
- Knowing when to call for emergency medical services
Call Your Doctor
It is important for you to monitor your recovery after you leave the hospital. Alert your doctor to any problems right away. If any of the following occur, call your doctor:
- Signs of infection, including cough, excessive foul-smelling mucous, fever, and chills
- Redness, swelling, increasing pain, excessive bleeding, or any discharge from the incision site
- Persistent nausea or vomiting
- Pain that you cannot control with the medications you were given
- Cough, shortness of breath, or chest pain
- Symptoms worsen
Call for emergency medical services right away if:
- Your tracheostomy tube falls out and you cannot replace it
- You are having difficulty breathing through your tube
If you think you have an emergency, call for medical help right away.
American Lung Association http://www.lung.org
National Heart Lung and Blood Institute http://www.nhlbi.nih.gov
Canadian Medical Association http://www.cma.ca
The Lung Association http://www.lung.ca
Frequently asked questions about tracheotomy and swallowing. American Speech-Language-Hearing Association website. Available at: http://www.asha.org/slp/clinical/frequently-asked-questions-on-tracheotomy-and-swallowing. Accessed August 29, 2017.
Tracheostomy. National Heart Lung and Blood Institute. Available at: https://www.nhlbi.nih.gov/health/health-topics/topics/trach. Updated December 9, 2016. Accessed August 29, 2017.
Tracheostomy in Adults. American Thoracic Society website. Available at: https://www.thoracic.org/patients/patient-resources/resources/tracheostomy-in-adults-1.pdf. Accessed August 29, 2017.
Tracheostomy tube replacement. EBSCO DynaMed Plus website. Available at: https://www.dynamed.com/topics/dmp~AN~T909881/Tracheostomy-tube-replacement . Accessed August 29, 2017.
What is a tracheostomy? Johns Hopkins Medicine website. Available at: http://www.hopkinsmedicine.org/tracheostomy/about/what.html. Accessed August 29, 2017.
- Reviewer: EBSCO Medical Review Board Michael Woods, MD, FAAP
- Review Date: 09/2018
- Update Date: 08/05/2015
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# Suppose 0.50 g of pure water is sealed in an evacuated 5.0-L flask and the whole assembly is heated to 60 degrees C. Will any liquid water be left in the flask or does all of the water evaporate?
Jul 11, 2016
There will be no liquid water left in the flask.
#### Explanation:
One way to solve this problem is to use the Ideal Gas Law to calculate the moles of water vapour that would be needed to fill the flask.
We could compare this value with the moles of liquid water, to see which is greater.
The Ideal Gas Law is
$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} P V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$
We can rearrange this to get
$n = \frac{P V}{R T}$
The vapour pressure of water at 60 °C is 149.4 torr.
P = 149.4 color(red)(cancel(color(black)("torr"))) ×("1 atm")/(760 color(red)(cancel(color(black)("torr")))) = "0.1966 atm"
$V = \text{5.0 L}$
$R = \text{0.082 06 L·atm·K"^"-1""mol"^"-1}$
$T = \text{(60 + 273.15) K" = "333.15 K}$
n = (0.1966 color(red)(cancel(color(black)("atm"))) × 5.0 color(red)(cancel(color(black)("L"))))/("0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 333.15 color(red)(cancel(color(black)("K")))) = "0.0360 mol"
Thus, it takes 0.0360 mol of water vapour to fill the flask at 60 °C.
The mass of liquid water that we have is 0.50 g.
$\text{Moles of H"_2"O" = 0.50 color(red)(cancel(color(black)("g H"_2"O"))) × (1 "mol H"_2"O")/(18.02 color(red)(cancel(color(black)("g H"_2"O")))) = "0.0277 mol H"_2"O}$
This is less than 0.0360 mol, so all the water will have evaporated in the flask.
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# How do I prove that a matrix is a rotation-matrix?
I have to prove that this matrix is a rotation-matrix $$\begin{pmatrix} \frac12 & 0 & \frac{\sqrt{3}}{2} \\ 0 & 1 & 0 \\ \frac{\sqrt{3}}{2} & 0 & \frac12 \end{pmatrix}$$ How do I do this? My idea is to multiplicate it with $\begin{pmatrix} x \\ y \\ z\end{pmatrix}$ and show that one component will remain unchanged . Is this enough? Do non-rotational transformations exist, which leave one component unchanged ?
• Certainly projection onto one component leaves that component unchanged, but (in dimensions greater than $1$) projections onto a component are singular and so are not orthogonal. Nov 15, 2014 at 11:04
• How do you define rotation matrix? Nov 15, 2014 at 11:16
• No, simply multiplying by (x, y ,z) and showing that one component does not change is not enough. This property would be true for several non-rotational matrices as well. One examples are scaling (diagonal) matrices for the other two components (i.e. all non main-diagonal entries are zero, one main diagonal entry is one, the other ones are arbitrary). Nov 15, 2014 at 17:08
• Also, only matrices for the rotation around a coordinate axis leave one vector component unchanged. But matrices for the rotation around an arbitrary axis (e.g. the axis y=x) do not. Nov 15, 2014 at 17:11
The following characterization of rotational matrices can be helpful, especially for matrix size $n > 2$.
$M$ is a rotational matrix if and only if $M$ is orthogonal, i.e. $MM^T = M^TM = I$, and $\det(M) = 1$.
• Actually, if you define rotation as 'rotation about an axis,' this is false for $n>3$. The matrix $$\left[\begin{array}{cccc} \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} & 0 & 0\\ \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 & 0\\ 0 & 0 & \frac{\sqrt{3}}{2} & -\frac{1}{2}\\ 0 & 0 & \frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right]$$ satisfies all of your conditions, but has no real eigenvalues (and hence, no axis of rotation).
– user88319
Nov 16, 2014 at 1:33
• I don't think that the check det(M) = 1 is relevant to test if a matrix has rotation unless it is to test that it is a pure rotation. A det of 1 means, in 3 dimensions, that the cube formed by the axes given by the matrix as an area of 1 cubic unit. Consequently, this also means that the matrix does not contain scale. It is possible to have a rotation matrix with a det of 1 (eg. 2 flipped axis). Apr 6, 2018 at 11:55
• A rotation matrix $M$ does not need to satisfy $\det(M)=1$. This is only true if $M$ describes a proper rotation; otherwise it describes an improper rotation, and $\det(M)=-1$. Feb 17, 2021 at 22:09
I think there is a minus sign missing. As it is, the determinant is not $1$. After fixing, this specific case is easy.
$$\begin{pmatrix} \frac12 & 0 & -\frac{\sqrt{3}}{2} \\ 0 & 1 & 0 \\ \frac{\sqrt{3}}{2} & 0 & \frac12 \end{pmatrix} = \begin{pmatrix} \cos \frac{\pi}{3} & 0 & -\sin \frac{\pi}{3} \\ 0 & 1 & 0 \\ \sin \frac{\pi}{3} & 0 & \cos \frac{\pi}{3} \end{pmatrix}$$
It is a rotation of $\pi/3$ around the $y$-axis.
• correct. actually, the lower left entry has to be negative Nov 15, 2014 at 12:39
• Then it would be a rotation of $-\pi/3$.. just use that $\cos$ is an even function, and $\sin$ is odd. Nov 15, 2014 at 13:19
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Devices made from plastic semiconductors, like solar cells and light-emitting diodes (LEDs), could be improved based on information gained using a new nanoparticle technique developed at The University of Texas at Austin.
As electrical charges travel through plastic semiconductors, they can be trapped much like a marble rolling on a bumpy surface becomes trapped in a deep hole. These traps of charges are known as "deep traps," and they are not well understood.
Deep traps can be desired, as in the case of plastic semiconductors used for memory devices, but they can also decrease the efficiency of the material to conduct electrical charges. In the case of solar cells, deep traps can decrease the efficiency of the conversion of light into electricity.
To further explore the deep trap phenomenon, a group of scientists led by Professors of Chemistry and Biochemistry Paul Barbara and Allen Bard developed a single-particle technique to study small portions of semiconductor material at the nanoscale.
"Our results strongly suggest that deep traps are formed in plastic semiconductors by a charge induced chemical reaction," says Dr. Rodrigo Palacios, lead author and post-doctoral fellow at the Center for Nano and Molecular Science and Technology. "These traps were not there in the uncharged pristine material."
Deep traps could be caused by defects in the semiconductor material--either native to the material or introduced impurities--with special properties that encourage charge trapping. The traps also could develop over the life of the semiconductor.
Previous techniques used to study deep traps have generally involved completed semiconductor devices, which Palacios says creates complications due to the complexity of a functional device.
For the current study, Palacios used a conjugated polymer (plastic semiconductor) material known as F8BT, which is commercially available and has promising applications in organic LEDs and solar cells.
He produced particles of F8BT with diameters about one-ten thousandth that of a human hair. He then shone light on the nanoparticles and measured changes in intensity of the resulting fluorescence. (This type of semiconductor material takes in light energy and releases part of this energy as light of a different color.)
Palacios observed deep traps forming as he electrochemically charged and discharged the semiconductor nanoparticles. The deep traps led to decreases in light emission from the material.
"With our new technique, we got detailed information on how these deep traps are formed and how long they live," says Palacios. "In principle, this kind of information can be used to improve devices made out of these conjugated polymers, designing new materials that can avoid these deep traps or materials that might be able to form these deep traps better."
The scientists reported their findings in the advanced online issue of the journal Nature Materials.
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Often, tonsils and adenoids are surgically removed at the same time. Although you can see your tonsils by taking a mirror and looking in your throat, adenoids aren't directly visible. Doctors use a special scope to get a peek at the adenoids, and sometimes will order a head X-ray for a better idea of their size.
So, what are adenoids exactly? They're a mass of tissue, located in the passage that connects the back of the nasal cavity to the throat. Adenoids — which are different from the tonsils — filter out bacteria and viruses entering through the nose and produce antibodies to help the body fight infections.
Adenoids begin to shrink after about 5 years of age. They often practically disappear by the time you're a teen.
Because adenoids trap germs that enter the body, adenoid tissue sometimes temporarily swells as it tries to fight off an infection.
Symptoms associated with enlarged adenoids include:
If your doctor thinks you have enlarged adenoids, he or she might:
If an infection is suspected, your doctor may prescribe oral antibiotics.
A doctor may recommend surgical removal of enlarged or infected adenoids if they're bothersome and medicine is not controlling the problem (this procedure is called an adenoidectomy).
Surgery may be recommended if a person experiences one or more of the following:
Having adenoids removed is especially important when repeated infections lead to sinus and ear infections. Badly swollen adenoids can interfere with the ability of the body to ventilate the middle ears. This can sometimes lead to infections or temporary hearing loss. Therefore, people whose infected adenoids cause frequent earaches and fluid buildup may need to get an adenoidectomy at the same time as ear tube surgery.
And although adenoids can be taken out without the tonsils, if someone has tonsil problems, the tonsils may need to be removed at the same time.
During an adenoidectomy:
After an adenoidectomy, the patient will wake up in the recovery area. In most cases, a person can go home the same day of the surgery.
The typical recuperation after an adenoidectomy often involves several days of pain and discomfort.
In less than a week after surgery, everything should return to normal. The area where the adenoids were will be left to heal naturally, which means there are no stitches to worry about.
Reviewed by: Steven P. Cook, MD
Date reviewed: May 2013
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I hate numbers! They’re confusing, hard to keep track of and make my eyes water if I look at them too long. Ugh!
Nevertheless, people insist on throwing them around. They like to talk about them, crunch them, live and die by them, put lots of them in PowerPoint slides and generally find ways to torture me with them.
But I’ve found a way to fight back! I beat them at their own game. How do I do it? I cheat. Hah! There’s really no reason to be oppressed by numbers if you can find simple ways to work around them. In fact, you can win the numbers game if you simply refuse to play it fairly. With that in mind, here’s a few of my favorite math hacks.
### Take off a Zero (or Two) to Calculate Percentages
When I first started out in the media business, the company I worked for had a great training program. Great, that is, except for the numbers.
One day they were teaching us to calculating ratings from a certain report and they had an incredibly convoluted formula that they wanted us to learn. For all the ins and outs, it really boiled down to comparing two numbers like these
Population: 811,756; Audience: 51,184
They put it up on the board, had one of the star pupils work through it and then circled the answer (14%). Then they asked if everybody else agreed. I was still young and dumb enough to answer no.
I didn’t use their crazy formula, just noticed that it was a simple percentage problem. The best way to deal with percentages is to simply take off a zero (or two) to give you 10% (or 1%) and then ballpark. A quick look and it was clear that:
10% = 81,175
That’s a whole lot more than 51,184, so it was clear that 14% was out of the question. While they were patiently re-explaining the formula and generally treating me like an idiot, I did two more quick things in my head:
5% = 81,175 / 2 = about 40,000
7.5% = halfway in between 40,000 and 81,175 = about 60,000
So it wasn’t all that hard to see that 51,184 wasn’t either 5% or 7.5% but somewhere in-between. As they continued to berate me, I finally blurted out, “Look, the answer is somewhere in between 6% and 7%!”.
After some more back and forth, I convinced them put it all in the calculator again. 6.5% jumped out and that launched my reputation as a “numbers guy.” To this day they still probably still think I calculated their crazy formula in my head!
### Compounding Interest with the Rule of 72
Okay, that one was simple (although a surprising number of people don’t do it, because numbers make people freeze). However, compounding interest rates are harder. They seem like they should be straightforward, but the numbers tend to runaway from you. The formula isn’t that tough in Excel, but way too difficult to do in your head.
Luckily, there’s a simple way to cheat here as well. Divide the number 72 by any interest rate and your will get roughly the amount of years it takes to double your money. So at 10% your money will double in about 7.2 years (72 divided by 10).
In the same training program, the instructor remarked that the values for radio stations were going crazy (this was in 1996, right after the new telecom act allowed larger groups to form). He gave the example of some guy who bought a station for \$3 million and sold it for \$75 million thirty years later.
“That’s no big deal” I said, “It’s about 11% annual growth.” This time no long explanations, just amazed looks. They thought I was some kind of Rain Man.
In reality, I just used the “rule of 72” backwards. It was pretty easy to see that the money doubled 4-5 times:
(6, 12, 24, 48, 96) and 75 is somewhere in between 48 and 96
And given that it happened over 30 years:
30 years / 4 = 7.5 years to double= about 10% of 72
30 years / 5 = 6 years to double= exactly 12% of 72
So again, it’s wasn’t that hard to guess 11%. (The actual answer 11.3% – but who cares?). That’s a good return, but not at all unusual. However going from \$3 million to \$75 million makes it seem like it is because 30 years is a long time. Who says numbers can’t lie?
### Sample Size
Sample size is like organic food. Nobody really seems to understand it, but there’s always some little snot around to tell us how important it is. Anytime research is cited, you can be sure someone will ask, “what’s the sample size?” Whatever it is, people who disagree with the study will say it’s too small.
For my part, I’m convinced that the sample size issue is a vast conspiracy cooked up by research companies. You see, it’s really the only source of error that they can’t be blamed for and that they can charge clients big money to correct. That’s a double play in any man’s league!
In actuality, it’s very easy to ballpark sample error: 1/√sample size . So if the sample size is 100:
1/√sample size = 1/√100 = 10% or +/- 5%
If the sample size is 900:
1/√sample size = 1/√900 = 1/30 = 3% or +/- 1.5%
That’s a very small difference given the variance in cost of interviewing an additional 800 people. They usually tell us that anything under 100 respondents yields disaster, what would happen if the sample size was a paltry 50?
1/√sample size = 1/ √49 = 1/7 = 14% or +/- 7%
Again, in most situations that kind of error wouldn’t cause much of a problem. So unless your sample size is very, very low, it shouldn’t affect the outcome of an analysis. Mention this next time someone wants to crap all over your research. The blank stare you get in return will be a thing of beauty!
### Lean back and Tell a Story
We human beings (except for a few freaks) are very bad at calculating. That’s why computers were invented in the first place. We are, however, extremely good at interpreting narratives.
Luckily, most of the numbers we come across in business life tell a story (if they don’t, they’re usually either wrong or irrelevant). They go up or down, left or right or they don’t really go anywhere at all. Keep this in mind and you’re unlikely to be confused by numbers.
Unfortunately, most people do just the opposite. They lean in and actually try to calculate (or worse, remember) numbers, which is how things often get confused. Instead, lean back and watch the story unfold. If there isn’t one, your bullshit alarm should be going off. Chances are, something is very wrong.
### You Don’t Need to Know The Right Answer, Just The Wrong One
Life isn’t like math class. There is rarely a “right” answer. Most of the numbers we come across are aggregations of estimations. No matter how many decimal places they include, they’re not very precise and shouldn’t be taken that seriously.
It is the failure to realize this simple fact that causes people to screw up numbers so royally. They plug numbers into Excel and then take them as Gospel. That’s always a mistake.
You can’t compete with a computer to get the right answer, but you should be able to notice a number that’s wildly off. If it seems wrong, it usually is. If not, you’ve told yourself the wrong story and need to find the right one. Either way, some simple ballparking will save you an enormous amount of time and embarrassment.
You can live by numbers and you can die by numbers. I, however, would much rather cheat them.
- Greg
32 Responses leave one →
1. July 6, 2011
Ha, this is great – thanks!
Thx:-)
July 6, 2011
Hi Greg!
Very good post, like usual. It’s probably not my best day today, but I don’t quite follow your sample size calculation:
1. If the formula is 1/sample size, how is it equal with it’s square root (1/10=1/100, 1/900=1/30, etc)?
2. Sample size 900, what do you mean by “10% or +/-3%”?
Tnx for coping with slow readers!
Dragos,
1/sample size = 1/900 = 1/30 = 3% or +/- 1.5%
Thanks for pointing it out.
- Greg
Greg,
you have a conflict there: elsewhere in another blog item you say it should be 1 / “the square root of the sample size”
i.e. 1 / sqrt (900) = 1/30
which is the true expression of sample error approximations.
Robert,
I’m not sure that I get you. If the sample size is 900, the total sample error is 1/30 or about 3%. The true expression for sample error at 95% confidence is .98/ sqrt sample size, but and at 99% confidence it’s something like 1.29, but using the approximate formula is good enough for just about any practical purpose.
- Greg
Greg
On this site you have used two different formulae to express the deviation.
In another blog item you [correctly] express it as
1/√ 900 = 1/30
but here in THIS blog item you have expressed the formula as
1/900 = 1/30
they cannot both be correct. The first form is the correct one.
Robert,
You’re right. Sorry, I’m in the middle of a trans-continental move and am screwing some things up.
Thanks, I’ll correct.
- Greg
Greg
Norra problem. Good luck with the move
Thanks. I’m returning to the US after nearly 15 years abroad. Lots to do on little sleep:-)
- Greg
3. July 6, 2011
Great post, makes me miss my slide rule (oops I think I just dated myself.)
Calculators and computers are great tools, but without some basic math skills you have no clue if the answer they are giving you is right or wrong.
True:-)
- Greg
4. July 7, 2011
As usual a great article and a damn good lesson for anyone who thinks they need to rely on their CA to tell them 2+2=4!
Thx Megha.
- Greg
5. July 8, 2011
Hi Greg,
As always, a great post!
Having previously studied (nuclear) physics, am a great fun of Raymond Smullyan and his books such as “Lady or the Tiger.” I love math puzzles.
A great read for business savvy peeps who care about numbers could be also, with special emphasis on number sin our lives, economy, etc., book by Leonard Mlodinow – “Drunkard’s Walk.” And of course not to forget the amazing John Allen Paulos with his “Illiteracy.”
Why you moving back to the US, if you don’t mind me asking?
Cheers,
H.
Hayk,
Thanks for the suggestions. As for my move back to the US, after nearly 15 years and with a 2 year old daughter, it really felt like time to come home.
- Greg
July 10, 2011
Greg, greatly enjoyed the read (I know, that sounds geeky ).
When I was in school I loved Trachtenberg Speed Math precisely for some of the reasons you mention. One does not need to be always accurate for the task at hand. Also, as you said folks need to see what the impact of the “error” is going to be and if it is worth laboring to precise decimal places.
Great review and highly recommended for kids & adults alike
Best,
Ned
Thanks, Ned. Have a great week!
- Greg
7. July 11, 2011
I really wish this was more standard in schools – as it is, in my courses (college level) I bring things like this up ALL-THE-TIME to give students that “feel” for what makes sense. Unfortunately, many of them will blindly type into a calculator or computer and write down whatever comes up without thinking about it. This of course is not a reflection on them, but a bad habit picked up over time.
The kind of thinking you are showing here is really about developing your intuition for numbers and not only helps you in day to day “dont need the exact number” situations but also as a check on work when you do.
Thanks Jerimi!
For everyone else, check out Jerimi’s site: http://www.mathbootcamps.com Lots of great stuff there!
- Greg
Hey thanks! It is a work in progress.
Good luck with it!
July 12, 2011
A dumb post and only can impress a guy from US…
9. July 14, 2011
Along with Trachtenberg Speed Math you can take a look at
Vedic Maths which is one of the World’s Fastest Mental Maths System.
Thanks. I’ll check it out.
- Greg
10. July 18, 2011
A funny post, Greg, lmao. Wish my university professors (B.Sc. in math) would have approved your rough linear approximation approach in their exams
Someone up here made a nasty comment saying such a post can only impress US guys. While I disagree with his general conclusion (and tone), that guy has some points about Americans and math.
1. Americans are stats-freaks. You cannot even watch a ball game on TV without hearing a detailed comparison between the teams of the average RBI of left-handed blond batters, who weigh more than 150lb, since the great depression in 1929 (did I mention I hate baseball?
2. When it comes to business, Americans try to translate everything into \$ signs. Even things which cannot be monetized seriously. It’s of course not RBI, but rather ROI. I have lately heard the idiotic question “what is the ROI on social media?”. Can one monetize reputation, market penetration and the like in vast crowds which one doesn’t even know. Yes, you can guesstimate till your Excel sheet will itself dial 911 and file a complaint against abuse, you can fart numbers out of your … as you like, but that’s what these numbers will be – brain-farts that you must present to top management to get what you want, while there’s nothing really serious behind these numbers.
That’s something very deep in the American business culture. Everything must be “measured”, for the false sense of security that “if we measure, we will most likely take the right decisions”. The fact that a lot of these “measurements” are useless are a trivial issue…
Just my 2.71828… cents (yes, you may round it to whatever amount you like .
Thanks Roy, although I’m going to have to disagree with your 2nd observation (the first is spot on). I’ve lived overseas for 15 years and only just returned to the US. The notion that Americans want to quantify everything strikes me as very similar to the idea that “all Americans eat at McDonalds.”
I think people often confuse what is Americans with large organizations. For instance, I certainly don’t think that either Unilever or Nestle is any less metrics driven than P&G, but because they are large, multinational organizations, they are often assumed to be influenced by American trends therefore everything they do is somewhat “American.”
- Greg
I knew that stepping into the twilight zone of generalizations, let alone nationality-based ones, would probably lead to controversy. You cannot be right about everyone, and I know not all Americans eat at that famous establishment I personally dislike quite a bit.
Myself, I have been living – and working in IT – in three different countries (and continents): Israel (wannabe-American business culture), Holland (a very European one) and currently Canada (I should be careful here, my colleagues would hate me for throwing them into the same pot with their Southern neighbours, but the business culture is pretty similar).
I agree with you, Greg, the large organizations – wherever they are – are all metrics-driven. But in North America also the medium-size and the small business are very much so, which is quite different from Europe (that’s at least my observation).
I could see the difference when I had to adapt my European CV into an American-style resume. Except for the fact that an American resume is all “me-me-me” (yes, you have to write you are a team player, but all of the achievements you have achieved alone), things need to be quantified. For example, I have never seen anything like “Fortune 500″ (or the local version thereof) mentioned in a European CV, and I have read quite a lot of these.
In my second job interview in this continent, with a small business, I started to describe the technical details of a recent project (in Holland) I was busy with (and quite proud of). The interviewer cut into me, and bluntly asked what the project budget was. Which was totally irrelevant, in my IT career (nearly two decades) I have had projects of “merely” few hundreds of thousands, in which my technical role was far more significant than in other projects with budgets of 7 or 8 digits. Not to mention that a project budget in a different country, with different labour and other costs, means very little unless you are very familiar with the IT sector in that country (which the interviewer wasn’t).
So I guess we are in disagreement about this one. Which is OK, I promise not to try to convince you with a dazzling presentation strewn with numbers
October 16, 2011
Very interesting point of view. I’ve discovered your blog today and I’ve found it very interesting. Thank you. Only one thing: when you talk about sample error, you should fix the “confidence level” of your estimation. In market research usually we take 95%. A sample size of 100 have a maximum of +/- 10 percentage points of error at 95% CL. That 10 points are +/- 10%, you can’t divide. ;-D
Thanks Manuel. Glad to see you’re enjoying the site.
However, I do believe you are mistaken. If you calculate it out, the two-tailed sample error would be 10%, which means +/- 5%. It doesn’t matter what “market research” or anybody else does. The math is the math.
- Greg
Hi Greg!
You are so assertive that you made me doubt (only a bit). ;-D
You are correct: the math is the math.
If you want, you can check several websites with “margin error calculators” that explain the key concepts better than me. I’ve found this one (http://faculty.vassar.edu/lowry/polls/calcs.html) it’s from an emeritus professor of Vassar College.
Margin of error, confidence limits… related to sample size, are concepts usually misunderstood. I don’t want to polemicize, just pointing out that you can’t oversimplify. A margin of error of 10 percentage points gives you a confidence interval of +/10 percentage points around the estimation.
Another key concept that it’s difficult and usually misunderstood is that the “error margin” of a sample is different regarding to the data you are measuring. If you are measuring the “Proportion of people with Product X” and “Proportion of people with Product Y” and data shows that X is 50%, the margin of error of a sample of a 100 is around 10 percentage points (with 95% confidence), so the “real” value must be between 40% and 60%. In the same study, product Y has only 7% (for the same population and the same sample) the margin of error of this second estimation it’s aprox. 5%, so the real value of product Y in the population have to be between 2% and 12%. The same sample size, different estimation of margin of error.
The first time you are going to study a phenomenon usually you don’t know the proportion of the population that have the product or feature of interest. In this situation, when you have to calculate a margin of error for a given sample size, you should consider the worst case scenario, the maximum error always is that the proportion were 50%. This is “a priory “calculation, and you should check and calculate with the final data.
English is not my mother tongue, forgive my odd writing style.
Manuel
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There's really no such number as "point three seven five." Yet that's how a lot of students say .375, and a big reason for this is that's how a lot of teachers say it--including me until I realized this perpetuated students' difficulties with decimals.
Eventually I referred to rational decimal numbers correctly ("three-hundred seventy-five thousandths," for example), and insisted students do so too. And not only did students' grasp of decimal place value improve, but so did their computational skills. Even better, students became more proficient at a skill many kids struggle with: converting between decimals, fractions, and percents.
So, if your students are having a hard time with decimals, make it a point to stop saying "point," including when referring to mixed numbers (i.e., go with "and" rather than "point;" example: read 15.03 as "fifteen and three hundredths").
Image provided by Phillip Martin with permission
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Talon Mcbride
2022-07-28
Find all the zeros ofthe function and write the polynomial as a product of linear factors:
$f\left(x\right)=5{x}^{3}-9{x}^{2}+28x=6$
Caylee Davenport
$f\left(x\right)=5{x}^{3}-9{x}^{2}+28x+6$
if x=-1/5 is a root of f(x) then f(-1/5) =0.
$f\left(-1/5\right)=5\ast \left(\frac{-1}{5}{\right)}^{3}-9\ast \left(\frac{-1}{5}{\right)}^{2}+28\ast \left(\frac{-1}{5}\right)+6=0$
$\left(5{x}^{3}-9{x}^{2}+28x+6\right)÷\left(x+1/5\right)=30-10x+5{x}^{2}$
$30-10x+5{x}^{2}=0⇒\left(x-\left(1-i\sqrt{5}\right)\right)\ast \left(x-\left(1+i\sqrt{5}\right)\right)=0$
$5{x}^{3}-9{x}^{2}+28x+6=\left(x+1/5\right)\left(x-\left(1-i\sqrt{5}\right)\right)\ast \left(x-\left(1+i\sqrt{5}\right)\right)=0$
Hence
Do you have a similar question?
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What is Big History
What is Big History
Big History is the attempt to understand, in a unified and interdisciplinary way, the history of the Cosmos, Earth, Life and Humanity. Big History is ambitious - it seeks understanding by bringing together and linking the knowledge available in many different scholarly disciplines.
Alexander von Humboldt sought a synthesis of nature and history more than 150 years ago, but was restricted by the limitations of scientific knowledge in his time. H.G. Wells attempted a Universal History in his 'Outline of History'. Today, progress within many different research fields means that it is at last possible to create a rigorous account of the past at multiple scales. Big History surveys the past at all possible time scales, from those of cosmology to those of human history. In its search for understanding Big History explores fields such as astronomy, physics, geology, biology, climatology and archeology.
Big History offers us the possibility to understand our universe, our world, and our humanity in a new way. Big History is a field of vast scope, innovative research, and compelling promise, and may well provide key knowledge to unlock some of the critical challenges of our future.
Van Gogh's Starry Night Over the Rhone...
Van Gogh's' Starry Night Over the Rhone was painted in Arles, in September 1888. It can be seen at the Musee d'Orsay, in Paris. It offers a wonderful icon for big history. The two humans are dwarfed by the immensity of the world and the cosmos, but they also wonder about it. And we, the observers, wonder about them and their place in a vast cosmos. We also see, around them, some of the paraphernalia of civilisation and also water, the key component for any living planet. It captures well a sense of our need to understand our place in a larger universe.
This sense is experienced by astronauts in the 'overview effect' - as they see planet earth from space. For many it has been a transformative experience resulting in a fundamental change in their perspective to understand our planet and the place of humanity's place upon it.
View this beautiful short film to share the thoughts of Apollo astronauts about their experience of travelling into space - and their resulting cognitive shift in understanding their home planet earth.
The image of this astronaut looking at earth is this is a screenshot from the short documentary 'Overview' from Planetary Collective.
Big History Institute
The Big History Institute provides a hub for scholars interested in interdisciplinary research on fundamental scholarly problems. The Institute also provides a focus for Macquarie University's teaching, in-service training, and knowledge dissemination in Big History.
Macquarie University is the intellectual birthplace of Big History. Whilst exploring conceptions of history on very large scales Professor David Christian coined the term "Big History" to argue for an expansion of the temporal and disciplinary limits of history. Big History has since emerged worldwide as an exciting area of interdisciplinary research and teaching.
David Christian taught one of the world's first Big History courses at Macquarie in 1989. He is the author of "Maps of Time", co-founder with Bill Gates of the "Big History Project", inaugural President of the International Big History Association, and Director of the Big History Institute at Macquarie University.
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# Lesson video
In progress...
Hello, everybody, and welcome to today's session.
My name is Miss Hughes and in today's lesson, we're going to be looking at partitioning 2-digit numbers as part of our unit Numbers Within 100.
So let's get going.
For today's lesson you will need a pencil, some paper and some countable objects to represent tens and ones.
Pasta works really well if you've not got dienes or cubes or counters at home.
You can also draw your tens and ones too.
Please pause the video now to go and get these things if you haven't got them already.
Okay, great, team.
Let's have a look at our lesson agenda for today to see our learning journey for today's lesson.
We're going to start off by partitioning numbers into tens and ones as part of our new learning.
Then we're going to partition with dienes in a part whole model.
We'll move on to look at canonical partitioning.
Then you're going to have an independent task and we'll go through the answers.
And finally, of course, you have your quiz where we can remember or we can see everything you have remembered from today's lesson.
Okey-docks.
We are going to start off today's lesson then by looking at an image on the slide.
So it's an image of a market stall.
And I want you to just focus on the bananas on the stall, which are round here.
Have a think about my questions there on the slide.
How many bananas are there altogether? And what might be an efficient way to count the number of bananas that are on the slide.
Or these questions, sorry.
And then play when you are ready to continue.
Okay.
So I'm going to count the number of bananas that we have by counting them in bunches of tens on the single bananas in ones.
It's much more efficient to count the bananas in tens and ones than count them all individually.
So let's get started.
We've got 10, 20, 30, 40, 50, 60, 70, 71, 72, 73, 74, 75, 76, 77, 78.
So there are 78 bananas altogether.
We can show this in a part whole model.
Here is my part whole model.
And we have our whole, which is 78 bananas here.
That was the number of bananas I have altogether in total.
But I'll just count them first one more time to check if that's the right amount.
So 10, 20, 30, 40, 50, 60, 70, 71, 72, 73, 74, 75, 76, 77, 78.
That is a lot of bananas, isn't it? Okay, so great.
I've got my 78 bananas altogether here.
So 78 is my whole.
And I can partition my whole into tens and ones.
So I'm going to put the bunches of 10 bananas into this part.
10, 20, 30, 40, 50, 60, 70 bananas.
And the single bananas can go into this section, in my ones.
One, two, three, four, five, six, seven, eight.
Fantastic.
So now I have partitioned my whole 78 into two parts.
The tens, which are up here, and the ones.
Let's have a look at the value of each part now.
In this section, I have seven bunches of 10.
So this part is worth 70.
The other part is worth eight because there are eight ones in it.
When I add both of my parts together, 70 and eight, I will get the whole amount that I started with.
70 add eight is equal to 78.
I can also, my apologies.
I can also rewrite my equation in this way starting with my whole.
78, which is equal to 70 add eight.
Even if I start with my whole, the values remain the same.
So even if 78 is the beginning here I still am adding 70 and eight.
Let's look at how we can put our oranges.
Let's look at how we can put our oranges in the market stall into a part whole model.
We're going to ignore this big box of oranges at the back and just look at these ones at the front that I've highlighted in red.
Okay, so we've got 10, 20, 30, 31, 32, 33, 34, 35 oranges.
Now we're going to put it into a part whole model.
Which looks like this.
So here is my big part whole model with my 35 oranges in it.
So you can see I've got my 10, 20, 30, 31, 32, 33, 34, 35.
My whole is 35.
Now we can partition our whole into the different paths.
So the bags of 10 oranges will go into this part.
So that's 10, 20, 30.
And the single oranges will go down in this part.
One, two, three, four, five.
So now we've partitioned our whole 35 into two parts, which represent 30 and five.
I can also represent these oranges in this way using dienes.
So in this part, I have three lots of 10 up here.
So that's one lots of 10, two lots of 10, three lots of 10.
And I can put my ones down here to represent my oranges.
One, two, three, four, five.
Now this shows me that 35 is equal to 30 add five.
Or 30 add five is equal to 35.
The whole, in other words, is equal to my two parts added together.
So the whole is 35 and it is equal to 30 add five, which is my separate parts.
Right, team, it's time to put this into practise with a talk task.
So you will be given an image of some fruit, a bit like this one that I've got on the board.
And your task is to partition the amount of fruit into a part whole model like I've got below.
So partitioning it into its tens part and its ones part.
There're going to be some sentence structures that I would like you to use to support your explanation of this.
I'm going to model this one for you and then it will be your turn.
Okay? So let's get up the first sentence structure.
I'm going to count the apples.
10, 20, 30.
31, 32, 33, 34.
There are 34 apples.
The whole is 34.
I've put my 34 in the whole down here.
Let's look at the next sentence structure.
I'm going to make the whole with 10 sticks.
10, 20, 30 and ones.
31, 32, 33, 34.
So I've partitioned 34 into tens and ones.
One part is worth 30.
Sorry.
One part is worth 30, and the other part has a value of four.
34 is equal to 30 add four.
Okay, so you can see that I used my picture.
I used dienes to partition my part whole model.
And I used my sentence structures to give my explanation.
You are now going to use the same sentence structures to have a go at these questions yourself.
So pause the video now to complete your task and then press Play when you are ready to continue.
Okay, welcome back, team.
How'd you guys get on? Are you ready for the answers? Right, let's go through them now then.
So let's have a look at this first one at the top.
I'm going to count the apples.
10, 20, 30, 40, 50, 60, 61, 62, 63, 64, 65, 66, 67.
My whole is 67.
So I'm going to make the whole with 10 sticks.
10, 20, 30, 40, 50, 60.
And I've partitioned them into tens and ones.
61, 62, 63, 64, 65, 66, 67.
So I've partitioned my whole into two parts.
One part is worth 60.
One part is worth four.
Sorry, one part is worth seven.
So 60 add seven is equal to 67.
Let's look at the next one.
So we've counted our carrots.
10, 20, 30, 40, 50, 60, 61.
There are 61 carrots.
The whole is 61.
I'm going to make the whole with six 10 sticks.
10, 20, 30, 40, 50, 60.
And one one.
61.
I'm going to partition the 61 into tens and ones.
One part is worth 60.
One part is worth one.
So 61 is equal to 60 add one.
I'm going to count my carrots.
10, 20, 30, 40, 50, 60, 70, 71, 72, 73, 74, 75, 76.
There are 76 carrots.
The whole is 76.
I'm going to make the whole with 10 sticks.
10, 20, 30, 40, 50, 60, 70.
And ones.
71, 72, 73, 74, 75, 76.
Let's look at this last one then.
So I'm going to count the apples.
10, 20, 30, 40, 50.
There are 50 apples.
The whole is 50.
I'm going to make the whole with 10 sticks.
10, 20, 30, 40, 50.
And no ones because I didn't have any ones left over in that image.
Now I'm going to partition the 50 into tens.
So here are my five tens.
So one part is worth 50.
And the other part has a value of zero because I haven't got any ones down here.
So 50, my whole is equal to 50 add zero.
Let's move on to our develop learning now.
We have a 2-digit number here, which is 45.
Okay.
And I want to know how we can represent this number using dienes.
So let's think about using our part whole model.
Okay, here it is.
Here's my part whole model.
45 has four tens and five ones because the value of the digit four is 40, and the value of the digit five is worth five ones.
So five.
Because 45 is my whole, I'm going to put these into the whole section like this.
Now I can partition 45 into tens and ones.
So there are four tens here, and they are going to go into that part.
And there are five ones, which will go into this part.
The four tens is 40, and the five ones is five.
So 40 add five equals 45 like this.
My two parts, 40 and five.
If I add them together, I will get my whole 45.
Remember I can also write it this way round.
It doesn't matter what way round I say these.
I still end up with the same whole even though my parts are switched around.
So my 40 can be down here, and my five can be up here.
Even though I've switched them over, my whole is still the same.
This is because of something called commutative law, which means that I can change the order of my parts in an equation, but it will not change the whole.
Can you try saying communicative law? I'll go first.
Communicative law.
Awesome.
It's really important to remember that 45 is not five tens and four ones like this.
Okay, so that's five tens and four ones.
If I have five tens, that would be 50, and four ones would be four because 10, 20, 30, 40, 50, five tens is 50, and one, two, three, four is four.
We can also represent our number 45 in a place value chart, which looks something like this.
It's got columns with the two headings, tens and ones.
So if we look back at our part whole model where we've partitioned our whole 45 into tens and ones, we can use that to help us partition our number into tens and ones in our place value chart.
So looking at this representation here, it's really clear to see that 45 is made up of four tens in this part and five ones.
So all I need to do here is put a four in my tens column because that represents four tens.
And you've probably guessed already that five will go in the ones column because that represents five ones.
So I've got four tens and five ones in this representation.
Okay, team, great work.
We're now going to move on to the independent task now.
So just like we were doing in our develop learning, for today's independent task, you are going to be given a number of 2-digit numbers like this one, 54.
And what I would like you to do with those numbers is partition them into tens and ones in a part whole model like this one, in a place value chart like this one, and then write an equation to represent the partitioned parts and how they are together to make the whole.
Okay, for this task you're going to need some countable objects that you can use to represent your tens and your ones.
In the develop learning, you saw that I used dienes, but if you don't have dienes at home, you can use something else.
So maybe you have some counters or some Lego.
You might have some cubes.
Or if you haven't got any of those things you can even use something like pasta, to represent your tens and ones.
Then what I want you to do is write the correct digits in the place value chart and, as I said earlier, write an equation.
So let's go through this one first and then I'm going to let you get on with your own ones.
So I have the 2-digit number 54 here.
So that is my whole.
So I need to put it in the whole section of my part whole model here.
Now I'm going to partition it and use dienes to represent the tens and ones.
So 54 has five tens.
I've got them there.
One, two, three, four, five.
And four ones, one, two, three, four.
You could draw these if you don't have any countable objects and that's fine, too.
Five tens I know represents 50.
And because I've got five tens here, I can put a five in my tens column to represent the five tens.
In my ones column, I'm going to put the digit four because that represents four ones because I've got four ones down here in this partition.
So I know that 50 add four is equal to 54, and that will be that task finished.
Okay? These are the ones that I would like you to try today.
Once you have completed these tasks I have a challenge for you.
So this is the challenge.
For this task, you've been given the parts of a whole and you need to figure out what the whole is.
Okay.
So once you finish your independent task I'd like you to have a go at this challenge.
Pause the video now to complete your task and resume the video once you're finished and ready to continue.
Welcome back team.
Let's have a look at these answers then.
So in this first example, we have the number 64.
So that is my whole.
And I know that 64 is made up of six tens, which is 60, and four ones.
So I'm going to put six in the tens column of my place value chart, four in the ones column of my place value chart, and that represents that 60 add four equals 64.
Let's look at the next one.
46 is the whole, and it's made up of four tens and six ones, which I've put in my place value chart, which means that 40 add six is equal to 46.
72 is the next one.
So 72 is my whole.
72 is made up of seven tens and two ones.
So I put my seven tens in here and my two to represent my two ones in here.
Seven tens is worth 70.
So 70 add two equals 72.
And this one at the bottom.
53 is the whole, which is made up of five tens and three ones.
So I've put five in the tens column and three in the ones column to represent those.
Five tens is worth 50 and three ones is worth three.
So 50 add three together make my whole 53.
35 is the next one that's made up of three tens and five ones.
So I've put that in my place value columns.
30 add five is equal to 35.
Lastly, 27 is the whole, which is made up of two tens and seven ones, and I've put them in my place value chart.
Two tens is worth 20 and seven ones is worth seven.
So 20 add seven is equal to 27.
Okay, and onto the challenge answers.
So remember that in a part whole model, if we add our two parts together we will make our whole.
So what I need to do is add all my two parts together to realise what the whole is.
So 20 add six is 26.
And 90 add five gives me 95 as a whole.
Well done if you got to those challenge questions.
Fantastic.
Okay, team.
That is it for our learning today.
And I'm so impressed with all of the fantastic thinking and listening and hard work that you put into today's session.
I look forward to seeing you on another session soon.
Bye-bye.
Once the video has ended don't forget to go and complete the final quiz.
I'm really excited to see all of the fantastic learning that you've remembered from today's session.
So good luck and see you soon! If you'd like to, please ask your parent or carer to share your work on Twitter tagging @OakNational and hashtag LearnwithOak.
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The Story of Propaganda
The fact that wars give rise to intensive propaganda campaigns has made many persons suppose that propaganda is something new and modern. The word itself came into common use in this country as late as 1914, when World War I began. The truth is, however, that propaganda is not new and modern. Nobody would make the mistake of assuming that it is new if, from early times, efforts to mobilize attitudes and opinions had actually been called “propaganda.” The battle for men’s minds is as old as human history.
In the ancient Asiatic civilization preceding the rise of Athens as a great center of human culture, the masses of the people lived under despotisms and there were no channels or methods for them to use in formulating or making known their feelings and wishes as a group. In Athens, however, the Greeks who made up the citizen class were conscious of their interests as a group and were well informed on the problems and affairs of the city-state to which they belonged. Differences on religious and political matters gave rise to propaganda and counterpropaganda. The strong-minded Athenians, though lacking such tools as the newspaper, the radio, and the movies, could use other powerful engines of propaganda to mold attitudes and opinions. The Greeks had games, the theater, the assembly, the law courts, and religious festivals, and these gave opportunity for propagandizing ideas and beliefs. The Greek playwrights made use of the drama for their political, social, and moral teachings. Another effective instrument for putting forward points of view was oratory, in which the Greeks excelled. And though there were no printing presses, handwritten books were circulated in the Greek world in efforts to shape and control the opinions of men.
From that time forward, whenever any society had common knowledge and a sense of common interests, it made use of propaganda. And as early as the sixteenth century nations used methods that were somewhat like those of modern propaganda. In the days of the Spanish Armada (1588), both Philip II of Spain and Queen Elizabeth of England organized propaganda in a quite modern way.
On one occasion, some years after the Spanish Armada, Sir Walter Raleigh complained bitterly about the Spanish propaganda (though he didn’t use that name). He was angry about a Spanish report of a sea battle near the Azores between the British ship Revenge and the ships of the Spanish king. He said it was “no marvel that the Spaniard should seek by false and slanderous pamphlets, advisoes, and letters, to cover their own loss and to derogate from others their own honours, especially in this fight being performed far off.” And then he recalled that back at the time of the Spanish Armada, when the Spaniards “purposed the invasion” of England, they published “in sundry languages, in print, great victories in words, which they pleaded to have obtained against this realm; and spread the same in a most false sort over all parts of France, Italy, and elsewhere.” The truth of course was that the Spanish Armada suffered a colossal disaster in 1588.
The Spanish claims, though described in the language of Queen Elizabeth’s time, have a curiously modern ring. Make a few changes in them, here and there, and they sound like a 1944 bulletin from the Japanese propaganda office.
The term “propaganda” apparently first came into common use in Europe as a result of the missionary activities of the Catholic church. In 1622 Pope Gregory XV created in Rome the Congregation for the Propagation of the Faith. This was a commission of cardinals charged with spreading the faith and regulating church affairs in heathen lands. A College of Propaganda was set up under Pope Urban VIII to train priests for the missions.
In its origins “propaganda” is an ancient and honorable word. Religious activities which were associated with propaganda commanded the respectful attention of mankind. It was in later times that the word came to have a selfish, dishonest, or subversive association.
Throughout the Middle Ages and in the later historic periods down to modern times, there has been propaganda. No people has been without it. The conflict between kings and Parliament in England was a historic struggle in which propaganda was involved. Propaganda was one of the weapons used in the movement for American independence, and it was used also in the French Revolution. The pens of Voltaire and Rousseau inflamed opposition to Bourbon rule in France, and during the revolution Danton and his fellows crystallized attitudes against the French king just as yarn Adams and Tom Paine had roused and organized opinion in the American Revolution.
World War I dramatized the power and triumphs of propaganda. And both fascism and communism in the postwar years were the centers of intense revolutionary propaganda. After capturing office, both fascists and communists sought to extend their power beyond their own national borders through the use of propaganda.
In our modern day, the inventive genius of man perfected a machinery of communication which, while speeding up and extending the influence of information and ideas, gave the propagandists a quick and efficient system for the spread of their appeals. This technical equipment can be used in the interests of peace and- international good will. Hitler, Mussolini, and Tojo preferred to seize upon this magnificent nervous system for selfish ends and inhumane purposes, and thus enlarged the role of propaganda in today’s world. While the United Nations were slow at first to use the speedy and efficient devices of communication for propaganda purposes, they are now returning blow for blow.
The modern development of politics was another stimulus to propaganda. Propaganda as promotion is a necessary part of political campaigns in democracies. When political bosses controlled nominations, comparatively little promotion was needed before a candidate was named to run for office, but under the direct primary system the candidate seeking nomination must appeal to a voting constituency. And in the final election he must appeal to the voters for their verdict on his fitness for office and on the soundness of his platform. In other words, he must engage in promotion as a legitimate and necessary part of a political contest.
In democracies, political leaders in office must necessarily explain and justify their courses of action to an electorate. Through the use of persuasion, those in office seek to reconcile the demands of various groups in the community. Prime ministers, presidents, cabinet members, department heads, legislators, and other officeholders appeal to the citizens of community and nation in order to make a given line of policy widely understood and to seek popular acceptance of it.
In peacetime the promotional activities of democratic governments usually consist of making the citizens aware of the services offered by a given department and of developing popular support for the policies with which the department is concerned. The purpose is to make these services “come alive” to the everyday citizen, and in the long run official information and promotion tend to make the average man more conscious of his citizenship. If the public is interested in the work done in its name and in its behalf, intelligent public criticism of governmental services can be stimulated.
Recent economic changes have expanded the volume of propaganda. Under the conditions of mass production and mass consumption, techniques of propaganda and public relations have been greatly developed to help sell commodities and services and to engender good will among consumers, employees, other groups, and the public at large.
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The horse in motion
In the 19th century painters typically depicted horses running with all four legs outstretched and off the ground.
But in equine circles there was much debate about how exactly they ran. Were all four hooves actually off the ground at the same time, even if just for an instant? And if this was the case, did this happen when the legs were outstretched or tucked under the body.
In the late 1870s Leland Stanford, the Californian railroad tycoon who founded Stanford University, employed the eccentric British photographer Eadweard Muybridge to settle the question.
Stanford had made a bet that all four hooves did indeed leave the ground at once - termed "unsupported motion" - although he thought they did so while outstretched.
On June 19 1878, Muybridge set up a series of 24 cameras alongside a horse track in Palo Alto, to capture the motion of Stanford's mare Sallie Gardner.
The cameras were set off by trip wires, triggered by the horse's hooves.
The resultant 24 images comprise the first "motion picture" in history.
Rumour has it that Stanford had a $25,000 bet on his supposition of unsupported motion, although whether his gambling adversity ever paid up appears to have been lost in the mists of history.
The bumbling bee
Computer models have said bumble bees shouldn't be able to fly. Their wings are too small and their bodies too heavy. But they do.
Two years ago Oxford University scientists worked out the secret of their success - brute force.
Dr Richard Bomfrey, a zoologist, said: "Instead of the aerodynamic finesse found in most other insects, bumblebees have adopted a brute force approach powered by a huge thorax and fuelled by energy-rich nectar."
Why take such a Rolls-Royce approach to fuel?
Dr Bomfrey said: "This approach may be due to its particularly wide body shape, or it could have evolved to make bumblebees more manoeuvrable in the air at the cost of a less efficient flying style."
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On the PC, partitions traditionally use a structure called Partition Table, located at the end of the master boot record (MBR, Master Boot Record).
This table can not contain more than 4 partition records (also called partition descriptors), specific to its beginning, end and size in different addressing modes, as well as a single number, called partition type, and a flag indicating whether the partition is active or not (there can only be one active partition at a time).
The marker is used during startup, after the BIOS loads the master boot record into memory and run it, check the DOS MBR partition table to a close and locates the active partition.
Then load the boot sector of that partition into memory and executes it. Unlike the master boot record (which is usually independent of the operating system), the boot sector is installed along with the operating system.
After loading the second stage, the boot sector can load any disk partitions (allowing the user to select the partition). Or if the manager knows how to locate the kernel (core) of the operating system on one partition (can allow the user to specify additional kernel options for strategic purposes of recovery).
Extended and logical partitions
Any version of DOS can only read FAT primary partition on the hard drive. This coupled with the deterioration of the FAT with the use and increased size of the disks moved Microsoft to create a relatively simple improved scheme.
One of the entries in the table of main partition was renamed the extended partition and received a number associated with special partition (0x05).
The start field of the location of the partition has first descriptor of the extended partition, which in turn has a similar field with the location of the next, and a linked list of descriptors.
Other fields of an extended partition are undefined, they have allocated space and can not be used to store data. The initial partition of the elements of the linked list are called logical drives that are assigned spaces and can store data.
Older operating systems ignored the extended partitions with type number 0x05. This scheme replaces the old as all partitions on a hard disk can be placed within a single extended partition.
For some reason, Microsoft did not update its DOS operating system to boot from an extended partition, because the need for primary partitions is preserved.
Above this still would have allowed a primary FAT partition per drive, meaning all other primary FAT partitions must have their type numbers prior to changing DOS boot partition so that it is able to proceed.
This technique, used by several popular boot managers is called concealment partition. However, we must take account fifth partition can be compressed but not highly recommended.
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Carbohydrates, found in foods such as bread, fruit, and candy, make your blood sugar rise. So if you have diabetes, you might think you shouldn't eat carbohydrates (carbs) at all. But carbohydrates are one of the three main components of food (the others are proteins and fats). All kids, including those with diabetes, can and should eat carbs as part of a healthy diet.
Kids with diabetes will need to pay closer attention to what they eat, though. Why? Because the more carbs you eat, the more insulin your body will need. Why? Because your body turns carbs into the sugar glucose (say: GLOO-kose), which is used for energy by your cells. And glucose can't get into your cells without insulin (say: IN-suh-lin).
Following a meal plan can help kids balance carbs with medications and exercise so that they maintain a healthy blood sugar level. Like exercising and taking medications, it's just another step many kids with diabetes take to stay healthy.
Why You Need a Plan
It's a little easier for people to control their diabetes if they eat about the same amount of carbs at about the same times each day. That's where a meal plan comes in. Your parents and diabetes health care team can help you create a meal plan that maps out what you will eat.
You might say, "I don't even know what a carbohydrate is!" Don't worry. The adults in your life can help you figure it out and can spell it out in your meal plan. But just to give you a taste of carbohydrate knowledge: Carbs are not found in just one kind of food. Carbs are found in many foods, such as soda, candy, breads, crackers, fruits, vegetables, and milk. Some carb-containing foods, like whole-grain bread, are healthier than others, such as candy. These healthy carbs should be included in your meal plan.
Let's talk a little more about what happens to carbs after you eat them. You know the body turns carbs into glucose. Then the glucose is absorbed into the bloodstream, which makes the sugar level in the blood go up. As the sugar level rises, the pancreas (say: PAN-kree-us) releases the hormone insulin into the blood. Insulin is needed to move glucose from the blood into the cells, where it can be used as a source of energy.
But for kids with diabetes, the pancreas does not make enough insulin (type 1 diabetes) or the body can't respond normally to the insulin that is made (type 2 diabetes). This makes blood sugar levels go up. And when blood sugar is too high, a person won't feel well and his or her body won't work as it should.
In your meal plan, there's no "right" amount of carbs to eat every day. Your meal plan will take into account your age, size, how much you exercise, the medicines you take, and other medical problems you might have. You'll be happy to hear that the meal plan will definitely include plenty of the foods you love to eat. Your meal plan might also suggest when you should eat.
If you're not sure how many carbohydrates a food contains, check the food label or ask your parent. You should also remember to check the labels of diet foods. Sometimes these foods contain extra sugar.
You might be tempted to "cheat" on your meal plan by eating sugary snacks. It's OK to have soda and cookies once in a while, but eating too many sugary foods could be a bad idea. If you overdo it, don't hide it — talk to your mom or dad. Your parent or your doctor can help you get your blood sugar levels back on track.
Better yet, stick to your meal plan. If some foods you like aren't currently in your meal plan, ask your parent or health care team how to include them. By taking a smart approach to balancing carbs with insulin and exercise, you can love your food and stay healthy, too.
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Haemophilia is a genetic disorder, it is characterised by absence of clotting of blood and continuous bleeding. It is a dangerous and life threatening problem. It occurs mostly in males and very rare in females. Read about inherited bleeding disorder.
Haemophilia is a X linked recessive gene therefore males are more likely to suffer from haemophilia than females due to the presence of one single X chromosome whereas females carry 2 X chromosomes. Therefore females act as carriers who pass the defective gene to the next generation.
Queen Victoria was a carrier and passed the mutation to her son Leopold and through several of her daughters to members of the royal families of Spain, Russia, and Germany.
There are three types of haemophilia
- Haemophilia A is a deficiency in Factor VIII
- Haemophilia B is a deficiency in Factor IX.
- Haemophilia C is an autosomal genetic disorder (i.e. not X-linked) involving a lack of functional clotting Factor XI. Haemophilia C is not completely recessive, as heterozygous individuals also show increased bleeding.
The blood clotting mechanism is a series of cascade reactions which involves many clotting factors that generate fibrin which together with platelets stops bleeding and forms a mesh near the bleeding area. If any one of the clotting factors is deficient it leads to haemophilia.
Signs and symptoms
The symptoms of haemophilia can be mild to severe, depending on the level of clotting factors you have. Most cases are mild, but people with severe haemophilia experience symptoms, which require ongoing care.
Some of the signs of haemophilia are, large bruises, bleeding into muscles and joints, spontaneous bleeding, and bleeding for a long time after a cut or surgery.
People with severe haemophilia often experience internal bleeding. This usually occurs around the joints and muscles, causing pain and stiffness. It can also lead to joint damage over time.
Although there’s no cure for haemophilia, treatment usually allows a person with the condition to enjoy a good quality of life.
In recent decades, genetically engineered clotting factor medications have been developed to prevent and treat prolonged bleeding. These medications are given as an injection, the timing of which depends on how severe the condition is. Injections are usually only given in milder cases in response to prolonged bleeding, whereas more severe cases are treated with regular injections to prevent bleeding.
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European Union Law
A PDF of this resource can be accessed here.
European Union law implements the provisions of EU treaties and initiatives. It establishes a series of rights and demands that are recognised by EU member states’ national judiciaries. EU law is governed by the European Court of Justice (ECJ), which has a unique role in developing a European identity and influencing national governments.
The ECJ was originally set up under the Treaty of Paris (1951) and its competences have gradually expanded under the Treaties of Rome (1957), Maastricht (1992),Amsterdam (1997), Nice (2001) and Lisbon (2007).
Legal precedents established by the ECJ have played a large role in shaping the development of EU law. The case of Van Gend en Loos vs. Nederlandse Administratie de Belastingen (1963), in which the Court ruled that the protection of EU law applied to individuals as well as member states, created the principle of direct effect. The case of Costa vs. ENEL (1964) ruled that in the case of a clash between EU and national law, EU law is the higher authority, thus establishing the supremacy of the ECJ.
The British Factortame case (1990) took this further when it was ruled that national courts could actually strike down Acts of Parliament that contravened EU law. The Cassis de Dijon case (1979) laid out the principle of mutual recognition of goods, which underpinned the creation of the single market. In all these cases it was the ECJ interpreting the EU treaties, rather than political arguments, which determined the scope of the EU project.
How does the European Legal System work?
These powers were increased when the Lisbon Treaty came into force in 2009 as it extended the ECJ jurisdiction to Justice and Home Affairs policy for the first time. The ECJ uses three sources for interpreting EU law: the EU treaties, articles of those treaties, and broader principles of law.
The court can act in three ways. First, it can bring about cases called ‘infringement proceedings’ against member states that fail to comply with EU legislation. Secondly, it can review legislative and executive acts passed by EU institutions to ensure their legality. Finally, many national courts hand cases up to the ECJ in what are known as preliminary rulings.
The principles of direct effect and supremacy of EU law guide the implementation of ECJ rulings and the legal framework within which it acts. These joint principles give the ECJ a large amount of judicial power within member states. Supremacy allows the ECJ to establish primacy for European laws while direct effect means that these laws then apply to people as well as to states – making them more like domestic laws then international acts. There has been some resistance to this development. In the 1993 Brunner judgement, the German Courts decided that they could rule acts of the EU to be beyond the EU’s legal authority if the act breached the German Constitution.
- EU law prevents states choosing self-interest over agreed treaty provisions that benefit the entire Community.
- European law allows for greater judicial co-operation between member states in civil and criminal cases, which is important at a time of more cross-border crime.
- It helps to safeguard the agreed economic goals of the EU – like the free movement of goods.
- The intrusion of European law into national judiciaries undermines national control of lawmaking.
- EU law can make constitutional changes to the EU through legal interpretation and judicial precedent without the need for additional treaties.
“What is the really essential feature of the European Union? It is that, in the EU, the guiding principle is law – not force.” – Erkki Liikanen, EU Budget Commissioner, 1994-1999.
“By creating a Community… [with] its own institutions, its own personality, its own legal capacity… the member states have limited their sovereign rights, albeit within limited fields, and have thus created a body of law which binds both their nationals and themselves.” – Costa vs. ENEL, 1964.
Competences: areas of law where the EU has been given control by its member states.
Precedent: previous judicial decisions in similar cases that shape the direction of later legal rulings.
Direct Effect: the principle that EU law creates rights for individuals that must be upheld by national courts.
Supremacy: the principle that EU law is superior to national laws when the ECJ has jurisdiction.
Primacy: the superiority of one law over another.
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Phishing has been a common cyber crime since the 90s, and people are still being targeted by these scams today. Here’s what you need to know about phishing and how to protect yourself from it.
What is phishing?
Phishing is a form of cyber attack that is usually in the form of a deceptive email. The email is often disguised as being sent from someone you know, or a business you may be interested in.
The email is usually asking for personal details such as passwords or credit card details, requiring the receiver to click a link or download an attachment.
Phishing scams can also come in the form of a ‘pop-up’ on a website, asking you to sign up or subscribe to something.
The definition of the term ‘phish’, pronounced like ‘fish’, is similar to the act of fishing. An angler throwing out a hook with bait and hoping for a bite; this is exactly what the cyber criminals (phishers) are doing. They want you to click a link on the scam email and acquire your personal details.
The ‘ph’ beginning of the word probably comes from the older term ‘phone phreaking’; an earlier form of hacking. Phone phreaking was a scam which involved playing sound tones into telephone handsets in order to get free phone calls.
It was hackers in the mid 1990s who established the term ‘phishing’, as they were trying to trick AOL users into sharing their login information.
Signs of a phishing email
- Unusual sender – Phishing emails often say they’re from someone you know… but make sure to look extra closely. There may be something different about the email address e.g. an extra ‘.’ or maybe one letter is different. If anything looks slightly suspicious, don’t click any links or attachments; it’s not worth the risk!
- Surprisingly good offers – We all know about the emails you get from different companies e.g. clothes shops or holiday companies we’ve used before. They send you exclusive deals and offers because you’ve signed up to their mailing list when you made an online order. Yes, these can be annoyingly frequent, filling up your email inbox. But they’re not harmful.
However, cyber criminals jump on this, sending emails that appear to be offers from shops. It’s a common mistake to click on a link on one of these phishing scams and end up giving your personal details to the scammers.
Similarly, offers that seem too good to be true are also dangerous ones. These often come in the form of ‘you’ve won an iPhone’ or ‘you’ve won a holiday’ followed by a link and ‘click here to claim your free prize’. Classic phishing… DO NOT click on emails that look like that.
- Hyperlinks and attachments – phishers put dangerous hyperlinks in emails hoping you click on them. You can hover over a hyperlink and read where it’s going to direct you. Always do this and read the URL carefully! If a website appears to be spelt wrong when you hover on the link, it’s probably a scam site.
Attachments aren’t always as safe as you may think. So if you receive an unexpected email with an attachment on it, do not open it, as it probably contains a virus. The only file you can always click on safely is a .txt file.
- Urgency – phishing emails often rush you into doing a certain action such as clicking on a link. If they’re disguised as an account you’re subscribed to, phishers may send an email saying ‘update your details today before your account is suspended’. This aims to make you quickly give your details, thinking you are saving your account, but have actually fallen for the scam.
Past cases of phishing
- In 2016, employees of the University of Kansas were targeted by a phishing scam. The deceptive email requested that they update their payroll information, which gave phishers the ability to change the account numbers for the direct deposits in the payroll system. Five employees responded to the email in total, and three of them did not receive their paychecks.
- Also occurring in 2016, Hillary Clinton’s campaign chairman, John Podesta, was a victim of a phishing scam. Hackers sent him an email disguised as Gmail’s account services department. The email said his password had been compromised and urged him to click on a link and change it immediately. Podesta eventually clicked this false link, handing over his Gmail account details to the cyber criminals.
The sense of urgency in this email and the inclusion of a hyperlink are both signs of a phishing scam. They essentially scared him into clicking on it by saying his password had been compromised.
How to prevent these cyber scams
- You can use spam filters to protect against phishing emails. These filters are clever little things, working in clever ways… The filters assess the origin of the email and its appearance, as well as the software used to send the message, in order to determine whether the email is spam or not.
- As mentioned previously, you can hover over hyperlinks in an email with your cursor. You should always do this when you receive an email that contains a hyperlink. Secure websites that have a valid Secure Socket Layer certificate will start with ‘https’. Now you know what to look out for…
- You can alter your browser settings so that fraudulent websites don’t open. With this setting activated, your browser will have a list of suspicious websites and will either block you from opening them or show you a warning message first.
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Mental Math with Place Value
Lesson 1 of 10
Objective: Students will be able to complete and compare addition and subtraction equations mentally, using various strategies.
To begin the lesson, I simply ask the students to come to the community area and give me a thumbs up when they have the answer to the solution to the following problems. I explain that they need to only use their minds and be ready to explain how they arrive at their answer.
Some of our equations include:
15 + 45 =
170 - 18 =
94 + 36 =
When students think they have an answer, I ask them to share with their shoulder partner. I then call on several students for each equation to come to the board and "list" their thinking. Below are some examples for 15 + 45.
Student 1: 10 + 40 =50, 5 + 5 = 10, 50 + 10 = 60
Student 2: 45 + 10 = 55, 55 + 5 = 60
Student 3: 45 + 5 = 50, 50 + 10 = 60
I then lead them into the active engagement in which they will also practice their journaling skills. Before sending them off to the activity, we discuss what the prompt asks them to do, and what vocabulary words they think they might use in their responses. The students discuss these terms in small groups of four.
Then as we discuss the possible terms, I write them on the board and leave them up as reference, even though they are also displayed on the math vocabulary board. Having them isolated is helpful for many of my students. You will see in the resources how we set the board up.
As the students work, I pay attention to their place value understanding and listen for their ability to show their thinking in a logical order. Later in the lesson, when they were writing about their strategies, I remind them of the vocabulary terms.
In the following clip, I was pleased with the student's strategy and communication. I am also really impressed when she caught her own mistake, because she was walking me through her thinking.
Many students are able to use their mental strategies, but need work on writing out their train of thought. As you watch this student, you will hear me guide him on how to share his thinking by writing.
Close and Home Practice
As a close, I simply remind students that we all make sense of math in our own way. However, we have to use our knowledge of how numbers work to create our own meaning. We also test our strategies for consistency and efficiency.
I send the journals home as home practice in order for the students to take their time in writing their thinking using our chosen vocabulary terms. In the next lesson, they will share with a partner and compare the terms used.
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Ever since the first prehistoric people began to dig for stone to make implements, rather than collect loose material, humans have modified the landscape through the excavation of rock and soil, the generation of waste and the creation of artificial ground.
An estimated 57 000 million tonnes of earth and rock is shifted annually by humans, whereas only 22 000 million tonnes of sediment is annually transported by our rivers and oceans. The rate and amount of sediment moved correlates with increasing population.
Movement of material can be classified as both deliberate (direct) and unintentional (indirect). Anthropogenic processes where rock or soil is deliberately excavated, transported and deposited by people include:
Unintentional movement of material includes wind and water movement of sediment as a result of the exposure of soil through agricultural activities and the deposition of sediment as a result of dam construction.
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SOLUTION: Tell how to determine whether the system has a unique solution, and solve it with the Cramer method: ax + by = c dx + ey = f The answer is: the system has a unique solution
Algebra -> -> SOLUTION: Tell how to determine whether the system has a unique solution, and solve it with the Cramer method: ax + by = c dx + ey = f The answer is: the system has a unique solution Log On
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Click here to see ALL problems on Matrices-and-determiminant Question 549768: Tell how to determine whether the system has a unique solution, and solve it with the Cramer method: ax + by = c dx + ey = f The answer is: the system has a unique solution if: delta = ae - bd not equal to 0 and the solution is: x = (ce - bf) / (ae - bd) y = (af - cd) / (ae - bd) How do we explain that? Answer by Edwin McCravy(9716) (Show Source): You can put this solution on YOUR website!``` ax + by = c dx + ey = f By Cramer's rule: Delta = = ae - bd Dx = = ce - bf Dy = = af - cd x = = = y = = = Denominators cannot be 0, so Delta = = ae - bd ≠ 0. and both and have unique values when that denominator is not zero. ------------------------------------------------------ In case you need to explain why Cramer's rule works: To eliminate y, multiply the first equation by e and the second equation by -b, and add the equations vertically term by term: aex + bey = ce -bdx - bey = -bf ----------------------- aex-bdx = ce-bf (ae-bd)x = ce-bf x = To eliminate x, multiply the first equation by -d and the second equation by a, and add the equations vertically term by term: -adx - bdy = -cd adx + aey = af ----------------------- aey-bdy = af-cd (ae-bd)y = af-cd y = a and y are the same using the elimination method as they are using Cramer's rule. Edwin```
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the Institute of Electrical and Electronics Engineers
the International Business Machines
This is a lesson plan that engages students in engineering practices as they design, construct, and test a musical instrument that will repeat a pattern of three sounds. Students first examine the construction and operation of the recorder, then work in groups to build instruments from common household items. The driving question of the lesson: How do engineers design musical instruments that will reliably produce notes, tones, and patterns of sound?
The lesson follows a module format that includes objectives and learner outcomes, problem sets, student guides, recommended reading, illustrated procedures, worksheets, and background information about the engineering connections. The lesson plan and student worksheets are available for download. This collection is part of TryEngineering.org, a website maintained by the Institute of Electrical and Electronics Engineers (IEEE).
Editor's Note:This lesson initiates with an examination of the recorder, a type of open-ended column wind instrument. Recorders are easier to study than the better-known transverse flute: they are cheaper to acquire and the dynamics are far less complex. This lesson is appropriate for the upper elementary grades, but can also be adapted for older students by introducing concepts of standing waves and fundamental frequency. See Related Materials for content support in teaching the physics of music.
applied physics, engineering activity, engineering lessons, engineering practices, harmonics, musical instruments, physics of music
Metadata instance created
July 26, 2012
by Gnana Subramaniam
October 20, 2012
by Caroline Hall
Last Update when Cataloged:
December 4, 2010
AAAS Benchmark Alignments (2008 Version)
1. The Nature of Science
1C. The Scientific Enterprise
3-5: 1C/E1. Science is an adventure that people everywhere can take part in, as they have for many centuries.
3. The Nature of Technology
3B. Design and Systems
3-5: 3B/E1. There is no perfect design. Designs that are best in one respect (safety or ease of use, for example) may be inferior in other ways (cost or appearance). Usually some features must be sacrificed to get others.
3-5: 3B/E2. Even a good design may fail. Sometimes steps can be taken ahead of time to reduce the likelihood of failure, but it cannot be entirely eliminated.
4. The Physical Setting
K-2: 4F/P3. Things that make sound vibrate.
6-8: 4F/M4. Vibrations in materials set up wavelike disturbances that spread away from the source. Sound and earthquake waves are examples. These and other waves move at different speeds in different materials.
8. The Designed World
8B. Materials and Manufacturing
6-8: 8B/M1. The choice of materials for a job depends on their properties.
12. Habits of Mind
12C. Manipulation and Observation
3-5: 12C/E1. Choose appropriate common materials for making simple mechanical constructions and repairing things.
6-8: 12C/M5. Analyze simple mechanical devices and describe what the various parts are for; estimate what the effect of making a change in one part of a device would have on the device as a whole.
12D. Communication Skills
3-5: 12D/E2. Make sketches or diagrams to aid in explaining procedures or ideas.
3-5: 12D/E7. Write a clear and accurate description of a real-world object or event.
6-8: 12D/M8. Explain a scientific idea to someone else, checking understanding and responding to questions.
<a href="http://www.thephysicsfront.org/items/detail.cfm?ID=12289">International Business Machines. TryEngineering: Engineered Music. Institute of Electrical and Electronics Engineers, December 4, 2010.</a>
International Business Machines. TryEngineering: Engineered Music. Institute of Electrical and Electronics Engineers, December 4, 2010. http://www.tryengineering.org/lesson_detail.php?lesson=50 (accessed 24 November 2014).
TryEngineering: Engineered Music. Institute of Electrical and Electronics Engineers, 2010. 4 Dec. 2010. International Business Machines. 24 Nov. 2014 <http://www.tryengineering.org/lesson_detail.php?lesson=50>.
%0 Electronic Source %D December 4, 2010 %T TryEngineering: Engineered Music %I Institute of Electrical and Electronics Engineers %V 2014 %N 24 November 2014 %8 December 4, 2010 %9 application/pdf %U http://www.tryengineering.org/lesson_detail.php?lesson=50
Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
This tutorial for teachers explains how various musical instruments generate standing waves to produce tones with a particular pitch. Includes animations of single wave reflection and standing waves to assist with visualization.
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