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Ratios are used to compare quantities. To compare two quantities, the units of the quantities must be the same. Ratios help us to compare quantities and determine the relation between them. We write ratios in the form of fractions and then compare them by converting them to like fractions. If these like fractions are equal, then the ratios are said to be equivalent.
e.g. Cost of 6 pens is Rs 90. What would be the cost of 10 such pens?
Solution: Cost of 6 pens = Rs 90
Cost of 1 pen = 90 ÷ 6 = Rs 15
Hence, cost of 10 pens = 10 × 15 = Rs 150.
When two ratios are equivalent, the four quantities are said to be in proportion.
Ratio and proportion problems can be solved by using two methods, the unitary method and equating the ratios to make proportions, and then solving the equation.
Unitary method is the method of finding the value of one unit (unit rate) at first and then the value of required number of units.
Percentage is another method used to compare quantities. Percent is derived from the Latin word ‘per centum’, which means per hundred. Percentage is the numerator, of a fraction, whose denominator is hundred. Percent is represented by the symbol - %.
e.g. or 21% | <urn:uuid:233e2450-cfd9-416d-8fe5-3583146b6740> | {
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A team of engineers and geo-scientists in the United States say a historic, long-buried seawall in the state of New Jersey played a key role in saving local homes from the wrath of last year’s Hurricane Sandy.
The 1,260-metre seawall, buried beneath the sands of Bay Head on the New Jersey shore, dates back to 1882 and had long been forgotten by local residents.
Despite its venerable age and state of neglect, however, the stone structure was instrumental in enabling local houses to weather the onslaught of Hurricane Sandy - the largest Atlantic hurricane on record and the second costliest in US history.
A comparison with the adjacent borough of Mantoloking highlights the extent to which Bay Head's hidden seawall reduced the damage inflicted by the hurricane.
In Mantoloking the entire dune almost disappeared completely, and the inrush of water was able to create breaches of 165 metres, 59 metres and 35 metres.
In Bay Head, however, only part of the dune situated on the seaward side of the seawall had been eroded, while the dune on the other side of the seawall managed to survive largely intact.
Research conducted by scientists from the College of Engineering at Virginia Tech found that this resulted in dramatic differences in the survival rates for homes in the two areas.
While all the oceanfront homes in the two boroughs suffered some damage, from ground-floor flooding to total leveling, the Virginia Tech team found that only one oceanfront home in Bay Head had been completely destroyed. In Mantoloking, however, over half of the oceanfront homes were classified as damaged or destroyed.
Jennifer L. Irish, associate professor in civil and environmental engineering at Virginia Tech's College of Engineering, says the aged, forgotten seawall was what made all the difference.
"The beach and dunes did their job to a certain point, then, the seawall took over, providing significant dampening of the waves," she says. "It was the difference between houses that were flooded in Bay Head and houses that were reduced to piles of rubble in Mantoloking."
"It's amazing that a seawall built nearly 150 years ago, naturally hidden under beach sands, and forgotten, should have a major positive effect under the conditions in which it was originally designed to perform," said H. Richard Lane, program director with the Division of Earth Sciences of the National Science Foundation (NSF), which was responsible for funding the research.
The research performed by Irish and her team on the impact of the Bay Head stone wall has been published online in the journal Coastal Engineering and is scheduled for publication in the October print edition. | <urn:uuid:a67b48cd-e12f-4bba-b828-3401603f5c18> | {
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Each morning birds join in song to welcome the new day. But did you know:
- The first 15-50 days is the best time for learning a song.
- Male birds sing to attract mates and defend their territories.
- Whereas the Red-eyed Vireo has more than 20,000 songs in his repertoire, and the Brown Thrasher has 2000, the Henslow’s Sparrow has only one song.
- Males do most of the singing in North America while certain tropical male and female birds sing duets.
- Not all use their voices to sing. A Wilson Snipe uses his tail feathers. A noisy woodpecker drums with his beak. A grouse uses his wings.
- While some birds can be taught to sing another species’ song, the flycatcher remains true to his species’ song.
- Some birds sing in flight while others sing perched upon a pedestal.
- Some birds learn their songs from others, and some inherit the appropriate song.
- Mockingbirds and parrot are mimics
- With the loss of hearing, birds lose their ability to sing.
Birds aren’t the only creatures called to sing.
- The younger the person, the easier it is to learn how to lift the voice in praise. But thankfully, people don’t have a window of learning as birds do. You can learn to sing praises no matter your age.
Train up a child in the way he should go: and when he is old, he will not depart from it. Proverbs 22:6
- Your song of praise is for worship and warfare. It’s easy to worship atop a mountain, not so much in the valley. Yet, singing may very well be our Commander’s weapon of choice. If so, sing at the top of your lungs!
And when they began to sing and to praise, the LORD set ambushments against the children of Ammon, Moab, and mount Seir, which were come against Judah; and they were smitten. 2 Chronicles 20:22
- Some may have several songs while others may have one unique song.Whatever the story behind your song, no one can sing it the way you can. If you refuse to lift your voice, the song will be sung, but not in the same key or in the same way! So, sing, children!
But I will sing of thy power; yea, I will sing aloud of thy mercy in the morning: for thou hast been my defence and refuge in the day of my trouble. Psalms 59:16
- Learn to sing a duet with Beloved. When we spend time with Him, we will come away with a sweeter song to share with others.
His mouth is most sweet: yea, he is altogether lovely. This is my beloved, and this is my friend, O daughters of Jerusalem. Song of Solomon 5:16
- We may not always use our voice to sing praise.Whether singing out loud or in your head, clapping your hands, snapping your fingers, or tapping your toe to the rhythm of the beat, do it to the glory of God.
O clap your hands, all ye people; shout unto God with the voice of triumph. Psalm 47:1
- Stay true to the song God has placed within us.There are enough voices screaming “be like me.” There is only one you. Without your voice, the choir is lacking. Stay true to yourself and God.
And he hath put a new song in my mouth, even praise unto our God: many shall see it, and fear, and shall trust in the LORD. Psalm 40:3
- Whether soaring above troubles or resting on the valley floor, sing.
And at midnight Paul and Silas prayed, and sang praises unto God: and the prisoners heard them. Acts 16:25
- With a hearing loss, we lose our song.We lose our hearing when surrounded by continual noise. Rest is a must if we are to keep our song.
My beloved spake, and said unto me, Rise up, my love, my fair one, and come away. Song of Solomon 2:10
Can you imagine our world if everyone was lifting their voice in prayer and praise to our God in Heaven above? | <urn:uuid:2643fecb-5216-45ef-bf66-c735d18940e0> | {
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This book aims to introduce the many cultures the Greeks and Romans encountered and the ways that both Greeks and Romans interacted with, and perceived, these different cultures. It is explicitly addressed to readers “without many years of study behind them” (vii). The author was thoroughly successful in this endeavor: he manages to give an overview on the subject from early Greece until Late Antiquity in a very readable and engaging manner. The book is well illustrated (sometimes with instructions about what to observe especially, e. g. on pp. 51, 66, 105).
Jensen is aware of the historical baggage of the term “barbarian”, but he convincingly defends its use, since it was the word the ancient authors used, and it had not necessarily a pejorative meaning in antiquity (ix). It was initially mainly a linguistic term to designate peoples whose language was unintelligible (1. “Meeting the Barbarians”, pp. 1–22). The ideas behind the concept of “barbarian” were never static, and there are other challenges for modern scholarship as well: markers such as language, religion or proper names do not always reveal identity; in many societies there were different grades of citizenship, and race did not hold equivalent meaning in the ancient Mediterranean.
Chap. 2 (“How the Greeks became Greek”, pp. 23–38) gives an overview of Greek prehistory and shows how myths of invasion and migration were used to “fabricate heritage” (pp. 32–38): they usually tell more about Greek politics of the fifth cent. BC than about population movements a thousand years before. The Greeks encountered societies with cultures older than their own in different ways (3. “The Greeks encounter the World”, pp. 39–60): for instance, the Greeks were mercenaries in Assyrian and Egyptian armies, and founded colonies where they had to accommodate with local peoples; there was also a demand for Greek goods, e. g. in Etruria, where these had to be adapted to local demands. It has to be kept in mind that there were “variations of Greekness” (p. 60); the Greek world had no single center.
The relationships of Greece, especially Athens, with other cultures, especially Persia, did not fundamentally change after the Persian wars (4. “The Greco-Persian Wars”, pp. 61–79), although the conventional Greek narratives after the war often reduced the Persians to stereotypes (with lasting effects until modern times); but Herodotus, Aeschylus or Xenophon offered a more subtly nuanced picture. For the Persians, Greece was probably only a minor spot on the troublesome western frontier; in spite of modern scholarly literature asserting that the battle of Marathon determined the fate of the western world, the arts and culture of Athens probably would have flourished (had the outcome been otherwise) as part of the Persian Empire, which was a tolerant and multicultural state.
The rise of Macedon gave a new urgency to the question of what it meant to be Greek (5. “Greeks, Macedonians and Persians”, pp. 81–99). Greek schemes of ancestry (of which Alexander the Great was well aware) that included or excluded peoples were mostly written by Athenians and in the context of Athenian political and social life.
In the Hellenistic world it was usually a small Greco-Macedonian elite at the top that ruled from urban centers (6. “The Hellenistic Era”, pp. 101–23). The definition of who and what was Greek was open to new interpretations and varied from one context to another; the collaboration of the native elite was necessary, and Ptolemies and Seleucids practiced a model of “limited incorporation” (110) by using local languages as well as Greek for proclamations, and by adapting local deities for a broader, also non-native public (for example, the cult of Sarapis). Greek, however, was the language of authority, as the translation of the Hebrew Bible (Septuagint) shows. But identities could be complex, even at family level, as onomastics often shows (with names composed of Greek and native elements, or parents with Egyptian, but children with Greek, names).
The second part of the book is devoted to Rome, and, like the first, presented as a magisterial historical overview from Rome’s beginnings until about 500 CE. Rome was from the beginning accessible to outsiders and in contact with the surrounding Latins, Sabines, Etruscans and occasionally Greeks (7. “Rome and Italy”, pp. 125–46). The barbarians in the eyes of the Romans were the Gauls (or Celts) of the Po valley, at first a society of mobile warrior bands, for whom Greek literature (in more recent times especially Polybius) had provided the theoretical framework of stereotypes. Even after their defeat they were still perceived as alien and dangerous. A new common enemy rose with Carthage (with whom Rome had in fact been on good terms for almost two hundred years); the Punic wars were a deliberate decision of Rome’s political class, and they also served to create an identity and mobilize allies (pp. 138–45).
It was Caesar who knew how to exploit the persistent anti-Gallic prejudice (8. “An Empire of Barbarians”, pp. 147–65): he fought a war for his own ends affecting enemies and (Gallic) allies alike, but he makes no distinction between the two in his De Bello Gallico. In fact “the Gauls” (as well as “the Germans”) as a coherent ethnic group were Caesar’s invention. His portrayal of Gauls and Germans had a lasting effect, not only on Roman narratives, but until modern times (pp. 152–57). During the civil war following Caesar’s murder, Octavian propagated a “return to romanitas” (pp. 157–61), by, e. g., reviving common traditions not just for the elite. In contrast to Marc Antony he grasped the importance of promoting what it meant to be Roman, which in the end helped him win the war of propaganda.
An altogether different challenge regarding foreign peoples were the Greeks (9. “Greek, Roman, and Greco-Roman”, pp. 167–87), with whom relations were always marked by a lingering sense of uneasiness, although in time a greater equilibrium and an awareness of mutual benefits were achieved. While the Greeks asked whether the Romans were Greeks or barbarians, the Romans, on the one hand, admired Greek education – almost all physicians in Rome were Greeks –, but on the other the suspicion that the Greeks looked down on them never quite died out. Yet in time the awareness of a “shared collection” of values and practices led to what is now called “Greco-Roman” culture (pp. 182–7), characteristics of which are, for example, the adaptation of Greek philosophical traditions, or the avid collecting of Greek art by the Roman elite.
The following chapter focuses on an Empire that stretched from Britain to Arabia (10. “Being Roman”, pp. 189–210), and had foreign contacts, mainly through trade, as far as China and the kingdom of Kush. Rome’s aristocracy had become cosmopolitan, and distinctions of who or what was Roman and barbarian became increasingly blurred, as can be seen e. g. in the works of Tacitus, who uses narratives about barbarians to reflect unflatteringly on his fellow Romans. After Augustus, the frontiers remained mostly stable (11. “The Imperial Frontier”, pp. 211–29), but they were always a sensitive area and occasionally prone to instability as their security also depended on the collaboration of the local population beyond them. They were also an area of trade, exchange, recruitment of soldiers (often from beyond the frontier); in the worst case they were inhabited by restless troops who might either cross the border for plunder or make a bid for the throne. Emperors were therefore well advised not to leave the frontier in anyone else’s hand.
By 500 CE, the Roman world had become a patchwork of states ruled by kings and warlords (12. “Invasions, Migrations, Transformations”, pp. 231–52). Although in scholarly literature the increasing invasions of the “barbarians” and the fall of the empire seem to go together as a matter of course, Jensen points out that the exact relationship and overlap of the two processes are hard to define. The most interesting question he deals with in this chapter seems to me: why did those who successfully acquired political power no longer identify themselves as Romans (pp. 250–2)? They were no strangers to Roman culture, many of them having been Roman soldiers or allies. As Jensen convincingly argues, one of the fatal developments was the split (beginning already in the 3rd cent. CE) between the civil aristocracy formed by an integrated elite, and the military aristocracy, which was recruited increasingly from immigrants who were often the targets of open hostility, even when (or perhaps because) their policies were successful; a case in point is Stilicho, who was eventually murdered.
Jensen gives a fascinating picture of the multicultural world of the ancient Mediterranean 1 and shows in every chapter that the Greeks and Romans and the “barbarians” they encountered often had much in common. Especially to be appreciated is that every chapter contains a summary of the modern scholarship about the subject. The last chapter (13. “Remembering the Barbarians”, pp. 253–261) gives a general, very impressive overview of how far the perception of foreign cultures was shaped by ancient stereotypes and until very recently often described with phrases taken from ancient authors. In turn, modern (ideological or political) contexts often influenced the view of ancient societies. This book is not just about ancient cultures or ethnicities; by showing how stereotypes were forged and used already in antiquity, it is very relevant for present times, too.
1. The only thing to be regretted is that the bibliography (pp. 263–76) consists entirely of literature in English. While I understand that the book is addressed not to specialists but to a more general public, it seems to me that e. g. a work so fundamental as A. Dihle, Die Griechen und die Fremden (München 1994) should have been mentioned. | <urn:uuid:f908b91e-fd85-4bec-ac43-4246419113f8> | {
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# Integral equals to the intermediate value
Let $f$ be twice continuously differentiable. Prove that there exists $\xi\in (-1,1)$ such that $$\int_{-1}^1 xf(x)dx=\frac{2}{3}f'(\xi)+\frac{1}{3}\xi f''(\xi).$$
What I have tried is as follows.
$$\frac{2}{3}f'(\xi)+\frac{1}{3}\xi f''(\xi)=\frac{1}{3}[xf(x)]''|_{x=\xi}.$$
But then how can we do...
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Put $g(x)=xf(x)$, $\displaystyle H(x)=\int_{-1}^x g(t)dt$, and $\displaystyle G(x)=\int_{x}^{1} g(t)dt$. The function $H$ is $3$ time differentiable, and $H^{\prime}(x)=g(x)$, $H^{\prime\prime}(x)=g^{\prime}(x)$ and $H^{\prime\prime\prime}(x)=g^{\prime\prime}(x)$.
We have for all $x$ that there exists $c_x\in ]-1,1[$ (depending on $x$) such that:
$$H(x)=H(0)+xH^{\prime}(0)+\frac{x^2}{2}H^{\prime\prime}(0)+\frac{x^3}{6}H^{\prime\prime\prime}(c_x)$$ Hence, if we put $x=1$, there exists $c_{1}\in ]-1,1[$ such that:
$$H(1)=H(0)+\frac{f(0)}{2}+\frac{g^{\prime\prime}(c_1)}{6}$$
We have that $G^{\prime}(x)=-g(x)$. In the same way,
$$G(x)=G(0)+xG^{\prime}(0)+\frac{x^2}{2}G^{\prime\prime}(0)+\frac{x^3}{6}G^{\prime\prime\prime}(d_x)$$
and there exists $d_{-1}\in ]-1,1[$ such that
$$G(-1)=G(0)-\frac{f(0)}{2}+\frac{g^{\prime\prime}(d_{-1})}{6}$$
Now $\displaystyle I=\int_{-1}^1 xf(x)dx=H(1)=G(-1)=H(0)+G(0)$. We get:
$$I=\frac{1}{6}(g^{\prime\prime}(c_1)+g^{\prime\prime}(d_{-1}))$$
Suppose wlog that $d_{-1} \leq c_1$, and put $J=[d_{-1}, c_1]$.
If $\displaystyle M={\rm Sup}\{g^{\prime\prime}(x), x\in J\}$ and $\displaystyle m={\rm Inf}\{g^{\prime\prime}(x), x\in J\}$, we have:
$$m\leq 3I\leq M$$ As $g^{\prime\prime}$ is continuous, there exists $c\in J\subset (-1,1)$ such that $g^{\prime\prime}(c)=3I$, and we are done.
-
Lemma. Let $g(x)$ is twice continuously differentiable. Then there exists $\xi\in(-1,1)$ such that $$\int\limits_{-1}^1 g(x)\,dx=2g(0)+\frac13 g''(\xi).$$
Proof: Expanding $g(x)$ by Taylor formula we get $g(x)=g(0)+xg'(0)+\frac{x^2}{2}g''(\xi(x))$, where $\xi(x)\in(-1,1)$. Then $$\int\limits_{-1}^1 g(x)\,dx=g(0)\int\limits_{-1}^1\,dx+g'(0)\int\limits_{-1}^1x\,dx+ \frac12\int\limits_{-1}^1x^2g''(\xi(x))\,dx=2g(0)+\frac12\int\limits_{-1}^1x^2g''(\xi(x))\,dx.$$ By the first mean value theorem for integration there exists $x_1\in(-1;1)$ such that $$\int\limits_{-1}^1x^2g''(\xi(x))\,dx=g''(\xi(x_1))\int\limits_{-1}^1x^2\,dx=\frac23g''(\xi(x_1)),$$ since $x^2\geq 0$ and $g''(\xi(x))=\cases{\dfrac{2(g(x)-g(0)-xg'(0))}{x^2},\quad x\neq0 \\ g''(0),\quad x=0}$ is a continuous function. Denoting $\xi=\xi(x_1)$ we obtain the required formula.
To get the result in question we just need to take in this lemma $g(x)=xf(x)$.
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I believe $\xi$ depends on $x$, no? – user1337 Jul 7 '14 at 9:28
YOu cannot factor $g''(\xi)$ out from the integral, as $\xi=\xi(x)$! – daw Jul 7 '14 at 9:28
@daw, user1337, thank you! You're right. I edited the solution, now this is taken into account. – CuriousGuest Jul 7 '14 at 12:11 | crawl-data/CC-MAIN-2016-30/segments/1469257824624.99/warc/CC-MAIN-20160723071024-00243-ip-10-185-27-174.ec2.internal.warc.gz | null |
The Mount Pinatubo eruption on June 15, 1991 eruption the second largest of the twentieth century and the largest near a densely populated area during the century. The 1912 eruption by Novarupta Volcano was the largest but occurred in a remote area of Alaska where very few people lived.
1991 Mt. Pinatubo eruption
The mountain awakes after 500 years
Pinatubo had not erupted for 500 years prior to its climactic eruption in 1991. Scientists had thought the dormant volcano was extinct and would never erupt again. Instead it was a sleeping giant with magma quietly collecting 20 miles beneath the volcano.
The mount awakens
The volcano began awakening in 1990 when a 7.8 earthquake shook the area. The following spring thousands of earthquakes and tons of sulfur dioxide were emitted by the volcano warning scientists and people living near the volcano that an eruption was coming.
Clark Air Force Base evacuated
Scientists used information from the 1980 eruption of Mount Saint Helens to help them predict what might happen on Mount Pinatubo that spring. The Clark Air Force Base was evacuated just five days before the eruption.
Red zone evacuated June 12th
On June 12th just three days prior to the eruption the red zone was extended and 58,000 people evacuated the area. Over 800 people who stayed behind and refused to leave their homes were killed during the eruption.
Typhoon Yunya was moving through the area on June 15 during the eruption. The initial eruption on June 15 sent an ash plume twenty-two miles into the atmosphere.
Rain and ash caused roofs to collapse
Closer to the volcano swirling winds and rain from the storm caused the ash to fall onto the roofs of people living near the volcano. The heavy rain soaked ash caused many roofs to collapse killing over 800 people.
Pyroclastic flows and lahars
Pyroclastic flows deposited pyroclastic material in the valleys below that five years later still measured over 900 degrees fahrenheit. Lahars, volcanic mudflows, carried ash that fell on the upper reaches of the volcano into the valleys covering entire villages near the volcano. Over a billion dollars in damage occurred as a result of the eruption.
Aftermath of the eruption
Sulfur dioxide spewed into the atmosphere during the eruption. It combined with water and oxygen in the atmosphere creating sulfuric acid which triggered ozone depletion over the South Pole. It also lowered temperatures worldwide in 1992 and 1993.
Katmai Volcano Katmia volcano was once thought to be the source of the largest volcanic eruption of the 20th century.
Yellowstone Caldera Yellowstone is a supervolcano that has erupted many times in the past.
Loihi, Hawaii's Newest Volcano Loihi is a seamount lying off the coast of Hawaii.
The Krakatoa Eruption Pyroclastic flows during the Krakatoa Eruption generated tsunamis and swept across the ocean to nearby islands.
Vesuvius Eruption Pliny the Younger wrote about the Vesuvius eruption.
Mount Pinatubo Find out more about the second largest volcanic eruption of the 20th century.
Volcano Facts Find out more volcano facts about these mountains of fire that produce Earth eruptions that can alter the weather on our planet sometimes for several years.
Kids Fun Science The links on our home page include information about volcanoes, science activities, plate tectonics, the rock cycle and much more. | <urn:uuid:e8a22477-84b8-4e19-a0e4-95ea094c8640> | {
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# How to solve logarithms
College algebra students learn How to solve logarithms, and manipulate different types of functions. We can solve math problems for you.
## How can we solve logarithms
In this blog post, we will provide you with a step-by-step guide on How to solve logarithms. It is available for free on both iOS and Android devices. Photomath is able to solve simple mathematical problems by taking a picture of the problem. It can also provide step-by-step instructions on how to solve the problem.
Solving equations is one of the most basic skills you can have as a mathematician. It's also one of the most important, because without it you can't do much in math. Solving equations is all about grouping numbers together and finding the relationship between them. You do that by using addition, subtraction, multiplication, or division to combine the numbers. You can also use inverse operations (like dividing by negative 1) to undo the effects of addition and subtraction. Once you know how to solve equations, you can use them for almost anything! They may seem easy at first, but if you practice solving equations every day, you'll soon be a pro! Here are some tips for solving equations: Group like terms together (like 2 + 5 = 7). Add or subtract one number at a time until you reach your target answer. If you're not sure what to do next, try multiplying both sides by each other (like 12 × 5 = 60). If that doesn't work, try dividing both sides by each other (like 12 ÷ 5 = 4). If none of these works, just look at your answer choices and pick the correct one.
solving equations is a process that involves isolating the variable on one side of the equation. This can be done using inverse operations, which are operations that undo each other. For example, addition and subtraction are inverse operations, as are multiplication and division. When solving an equation, you will use these inverse operations to move everything except for the variable to one side of the equal sign. Once the variable is isolated, you can then solve for its value by performing the inverse operation on both sides of the equation. For example, if you are solving for x in the equation 3x + 5 = 28, you would first subtract 5 from both sides of the equation to isolate x: 3x + 5 - 5 = 28 - 5. This results in 3x = 23. Then, you would divide both sides of the equation by 3 to solve for x: 3x/3 = 23/3. This gives you x = 23/3, or x = 7 1/3. Solving equations is a matter of isolating the variable using inverse operations and then using those same operations to solve for its value. By following these steps, you can solve any multi-step equation.
There are two methods that can be used to solve quadratic functions: factoring and using the quadratic equation. Factoring is often the simplest method, and it can be used when the equation can be factored into two linear factors. For example, the equation x2+5x+6 can be rewritten as (x+3)(x+2). To solve the equation, set each factor equal to zero and solve for x. In this case, you would get x=-3 and x=-2. The quadratic equation can be used when factoring is not possible or when you need a more precise answer. The quadratic equation is written as ax²+bx+c=0, and it can be solved by using the formula x=−b±√(b²−4ac)/2a. In this equation, a is the coefficient of x², b is the coefficient of x, and c is the constant term. For example, if you were given the equation 2x²-5x+3=0, you would plug in the values for a, b, and c to get x=(5±√(25-24))/4. This would give you two answers: x=1-½√7 and x=1+½√7. You can use either method to solve quadratic functions; however, factoring is often simpler when it is possible.
There are many math answers websites available online. These websites allow students to submit questions and receive answers from other students or from tutors. This can be a great resource for students who are struggling with a particular concept or who need extra help outside of class. However, it is important to note that not all of these websites are created equal. Some are more reliable than others, and some may even charge for their services. Before using any math answers website, be sure to do your research to
## Instant assistance with all types of math
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Giuliana Griffin | crawl-data/CC-MAIN-2023-06/segments/1674764494974.98/warc/CC-MAIN-20230127065356-20230127095356-00565.warc.gz | null |
# 2006 AMC 12B Problems/Problem 16
## Problem
Regular hexagon $ABCDEF$ has vertices $A$ and $C$ at $(0,0)$ and $(7,1)$, respectively. What is its area?
$\mathrm{(A)}\ 20\sqrt {3} \qquad \mathrm{(B)}\ 22\sqrt {3} \qquad \mathrm{(C)}\ 25\sqrt {3} \qquad \mathrm{(D)}\ 27\sqrt {3} \qquad \mathrm{(E)}\ 50$
## Solution
To find the area of the regular hexagon, we only need to calculate the side length. a distance of $\sqrt{7^2+1^2} = \sqrt{50} = 5\sqrt{2}$ apart. Half of this distance is the length of the longer leg of the right triangles. Therefore, the side length of the hexagon is $\frac{5\sqrt{2}}{2}\cdot\frac{1}{\sqrt{3}}\cdot2 = \frac{5\sqrt{6}}{3}$.
The apothem is thus $\frac{1}{2}\cdot\frac{5\sqrt{6}}{3}\cdot\sqrt{3} = \frac{5\sqrt{2}}{2}$, yielding an area of $\frac{1}{2}\cdot10\sqrt{6}\cdot\frac{5\sqrt{2}}{2}=25\sqrt{3} \implies \mathrm{(C)}$.
## See also
2006 AMC 12B (Problems • Answer Key • Resources) Preceded byProblem 15 Followed byProblem 17 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
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# Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
Result
S = 23.872 dm2
V = 6.734 dm3
#### Solution:
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#### To solve this example are needed these knowledge from mathematics:
Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.
## Next similar examples:
1. Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
2. Hexagonal pyramid
Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
3. 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
4. Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
5. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
6. Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
7. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
9. Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
10. Pyramid
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
11. Pyramid
The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
12. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
13. Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. | crawl-data/CC-MAIN-2019-22/segments/1558232256215.47/warc/CC-MAIN-20190521022141-20190521044141-00389.warc.gz | null |
Archaeologists continue to debate the reasons for the collapse of many Central American cities and states, from Teotihuacan in Mexico to the Yucatan Maya, and climate change is considered one of the major causes.
A UC Berkeley study sheds new light on this question, providing evidence that a prolonged period of below-average rainfall was partly responsible for the abandonment of one such city, Cantona, between A.D. 900 and A.D. 1050.
At its peak, Cantona, located in a dry, volcanic basin (La Cuenca Oriental) east of today's Mexico City, was one of the largest cities in the New World, with 90,000 inhabitants. The area was a major source of obsidian, and the city may have played a military role alongside an important trade route from the Veracruz coast into the highlands.
To assess the climate in that area before and after Cantona's collapse, UC Berkeley geographers analyzed sediment cores from a lake located 20 miles south of the former city. They found evidence of a 650-year period of frequent droughts that extended from around A.D. 500 to about A.D. 1150. This was part of a long-term drying trend in highland Mexico that started 2,200 years ago, around 200 B.C. The climate became wetter again in about A.D. 1300, just prior to the rise of the Aztec empire.
"The decline of Cantona occurred during this dry interval, and we conclude that climate change probably played a role, at least towards the end of the city's existence," said lead author Tripti Bhattacharya, a UC Berkeley graduate student.
Surprisingly, the population of Cantona increased during the early part of the dry period, perhaps because of political upheaval elsewhere that increased the importance of the heavily fortified city, she said. Teotihuacan, less than 100 miles to the west, was in decline at the time, also possibly because of more frequent droughts.
"In a sense the area became important because of the increased frequency of drought," said UC Berkeley associate professor of geography Roger Byrne. "But when the droughts continued on such a scale, the subsistence base for the whole area changed and people just had to leave. The city was abandoned."
Bhattacharya, Byrne and their colleagues report their findings in an article appearing this week in the early edition of the journal Proceedings of the National Academy of Sciences. The UC Berkeley researchers analyzed lake cores provided by scientists at the National Autonomous University of Mexico in Juriquilla, Querétaro, Mexico and the German Research Centre for Geosciences in Potsdam, Germany.
Political upheaval and climate change
Byrne emphasized that the area's typical monsoon weather with wet summers and dry winters did not stop, but was interrupted by frequent short-term droughts, no doubt affecting crops and water supplies. Today the area is close to the northern limit of maize production without irrigation, and would have been particularly vulnerable to drier conditions, he said.
Byrne, a member of the Berkeley Initiative on Global Change Biology (BiGCB) and curator of fossil pollen in the Museum of Paleontology, has studied sediment cores from many lakes in Mexico and California, and is particularly interested in possible links between climate change and human activities.
Nearly 20 years ago, he learned of Cantona and traveled with students to the areas three times to obtain cores from lakes near the site, most of which are maar lakes created by magma explosions. They are deep and often contain undisturbed and regularly layered sediments ideal for chronological studies.
German colleagues cored this particular lake, Aljojuca, in 2007, and Bhattacharya traveled to Potsdam to collect sediment samples. Oxygen isotope ratios in carbonate sediments are correlated with the ratio of precipitation to evaporation and thus indicate aridity. Organic material in the sediments was used for accelerator mass spectroscopy carbon-14 dating.
"We can show that both the growth and decline of the site took place during a time period of frequent drought, which forces us to think in more nuanced ways about how political and social factors interact with environmental factors to cause social and cultural change," Bhattacharya said. "That makes the study particularly interesting."
Bhattacharya noted that more studies are necessary to reconstruct the prehistoric climate of highland Mexico. Such studies could reveal the causes of prehistoric climatic change and whether they were similar to the factors that regulate the region's climate today, such as the El Niño/Southern Oscillation.
Explore further: Climatic history study suggests pre-Columbian Mesoamerican society's demise was more complex than just weather
"Cultural implications of late Holocene climate change in the Cuenca Oriental, Mexico" Tripti Bhattacharya, PNAS, DOI: 10.1073/pnas.1405653112 | <urn:uuid:fbf67683-1ec5-4d93-b78a-e1fb771090cb> | {
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In our previous post about the 6 Basic Nutrients, we gave a short description of the macronutrient water. Today, we’ll go into more detail about water, its functions in the body, and some information about different strategies to drink enough water.
Surprisingly, there are no recommendations for water in the Dietary Guidelines for Americans. There are some basic guidelines for “Adequate Intake” (AI) of water to replace the amount we lose in everyday functions (breathing, perspiration, and bathroom trips). For adult men, the AI is 15 ½ cups and for adult women, it’s 11 ½ cups. For kids, the AI is 5.5 cups for 1-3 year olds and up to 14 cups for teenage boys. Water is actually the basic nutrient we need the most, by weight and importance!
You can reach these recommendations from both fluids you drink as well as the food you eat. About 20% of your water needs come from food. The rest should be from no-added-sugar beverages, which means water as well as low-fat (1%) or skim milk, coffee, tea, and 100% juice.
Function of Water in Our Bodies
- Water makes up 50-65% of your body weight (more for young children, less for older adults). All of our body’s cells are filled with water-based fluids, even bone cells! Water is a solvent that other materials (nutrients, oxygen, waste products) dissolve in to travel throughout the body.
- Water regulates our body temperature, keeping us near 98.6°F no matter what the temperature is around us. Water is a great insulator. Sweat (made mostly of water) evaporates to cool us off during physical activity or hot weather.
- Water keeps our tissues moist, such as our eyes, nose, and mouth.
- Body fluids (blood, stomach “juice,” saliva, urine, amniotic fluid in the womb) are made of water. Water keeps stools soft to prevent constipation.
- Water lubricates joints and cushions organs and tissues for easy, comfortable motion.
- Water is an ingredient in metabolic processes that produce energy. That’s why we feel tired and lethargic when we get dehydrated.
Drinking Enough Water
- Reach for water first. Anytime you’re thirsty, choose water instead of other beverages. It’s refreshing, hydrating, and calorie free!
- Carry a reusable water bottle. You’ll always have a healthy beverage at hand. No need to buy a beverage or create trash from disposable bottles. Don’t forget to wash it often.
- Drink a glass (or two) before each meal. A Virginia Tech study found this can help with weight management, too!
- Add flavor, not sugar. Fruit infused water makes plain water taste great without added sugar. Kids will love this option. Unsweetened tea and coffee without added sugar or fat count toward your water needs, too.
- Choose sparkling water for a fizzy drink fix. If you love bubbles in your beverages, try a sparkling water. There are many options to choose from that don’t have added sugar or sweeteners.
Water is one of the six nutrients our bodies need. Water has many different important functions in our bodies. Do you have any questions about water, what it does in the body or how it fits into your diet? | <urn:uuid:7120cd16-fdec-4b00-a74f-6bf4561e4b44> | {
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Chapter Table of Contents
Industrial Engineers, and other engineers, often want to perform experiments on real systems, but such experimentation can be difficult. If an IE wants to try a new layout for a production system, moving equipment, furniture, and offices would be difficult and time consuming. Even trying a new procedure may disrupt the production system. Therefore, the IE would create a model of the system, usually a mathematical model.
The following figure shows how models are used.
Let’s look at each piece of the diagram. The first circle is labeled “real world system.” Drawing a line around some system involves deciding which parts are in your system and which are in the environment. For example, to study the arrival and service of customers at a bank, you would probably include the tellers, the drive up window, and the ATM, but not include the roads and traffic system that people use to get to the bank.
The second circle is labeled “model.” Some types of engineers use physical models. For example, a civil engineer might place a scale model of a building on a shaking table to predict how the building will respond to an earthquake. IEs tend to use mathematical models, expressed in equations or sometimes in computer code. For example, an IE might use the mathematics of queuing theory to create a model of the bank.
The top arrow labeled “representation” reminds us that the model represents the real world system but only the relevant parts of the system. Our model of the bank must include information on the time between customer arrivals and the time to serve each customer (both of these times vary from customer to customer), but the model doesn’t have to include descriptions of what color clothing customers wear. Depending on the purpose of our model it might include information on customer’s disabilities so we can predict how many teller windows must be accessible to people in wheelchairs. The M/M/1 queuing model describes the time between arrivals as an exponential random variable with average 1 customer/λ (say 6 minutes) and the time of service as an exponential random variable with average 1 customer/μ (say 4 minutes).
A model is never exactly correct; you should always remember the phrase “it’s only a model.” For example, the M/M/1 queuing model assumes that customers arrive at the average rate of 1 customer every 6 minutes, or 10 customers per hour. Actually, the arrival rate probably varies over the day.
An IE creates a model in order to extract information; the loop from the model to itself is labeled “analysis.” IEs use some models quite frequently and IEs can use mathematical results that others have proven. For example, for the M/M/1 queuing model can be used to compute the average number of people in the queue.
The line labeled “interpretation” is where the IE interprets the mathematical results of the model back to the real world system. Now the IE must again remember “it’s only a model” so the predictions may not be perfect. Since the M/M/1 queuing model assumes a constant average arrival rate, the results using λ = 10 customers per hour can only be applied to the period of the day with that arrival rate. A separate model might be needed for the lunch hour, which is probably busier.
IEs are responsible for efficiency, including the efficient use of time and resources. You already know from calculus class how to find the maximum or minimum of a function and calculus is one tool that IEs use. However, IEs often need to maximize or minimize a linear function, which sounds easy, but finding the solution isn’t easy when there are many variables and also some constraints. The following is an example of such a problem.
Dairy cattle have various nutrient requirements, such as protein, calcium, and potassium, that can be met by different types of feed, such as alfalfa, hominy, and corn cobs. The dairy farmer wants to mix a feed for the dairy cows that will meet the nutrient requirements at the minimum cost. Below is a very simplified version of the Diet Problem as applied to feeding dairy cattle. The following table gives the nutrient content (protein and potassium) of certain feeds (alfalfa, hominy, and corn cobs), as well as the nutrient requirement for protein and potassium (as a percent of the feed) and the cost of alfalfa, hominy, and corn cobs (in $/ton).
For example, alfalfa is 28% protein, 0.26% potassium, and costs $160 per ton. Alfalfa is a good source of protein and a medium source of potassium, but it is expensive. Hominy is a medium source of protein and a good source of potassium, and it is cheaper than alfalfa. Corn cobs are not a good source of either protein or potassium, but since they are otherwise a waste product, they are free. With some thought, you can see that the optimal mix will probably need alfalfa to meet the protein requirement, hominy to meet the potassium requirement, and corn cobs to keep the cost down.
We want to determine how to mix the feed, that is, what fraction should be alfalfa (A), hominy (H), and corn cobs (C). We will use linear programming to solve this problem, by expressing the situation as minimizing a linear objective function (cost) subject to linear constraints (protein and potassium). Because the ingredient’s units are representing percentages of the whole, we also know that A+H+C=1.
Here is the linear programming formulation:
This model is an example of a linear programming model. We can solve it mathematically. There are also computer programs that can help us to solve this type of problem. Excel is one such program although there are better tools for solving LP models.
This problem is an example of how industrial engineers use mathematics to promote efficiency. In this case, we helped the farmer use his or her resources efficiently to keep the cattle healthy while minimizing the cost of feed. This model is an example of an LP model, or, more broadly, an example of a deterministic optimization model. “Deterministic” means the model has no probabilities and “optimization” means we found the optimal, or best, solution.
An LP model is just one type of deterministic optimization model. Actually, in this example we assumed that we can buy any real amount of ingredients. If it were necessary to buy only in integer quantities a LP would not be an appropriate model. An model where the decision variables must be integers is called an integer programming model (IP).
Industrial engineers must be able to recognize situations where a deterministic model can be applied, create an appropriate model, and solve the model using an appropriate tool. The following list describes situations where a deterministic optimization model might be useful.
- Product mix – determine how much of each type of product to make subject to constraints on available resources.
- Production scheduling – determine how much of each type of product to make in different time periods in order to meet specified production amounts by certain times.
- Blending – determine the best blend of inputs to use to minimize the cost of producing a mixture. Our feed example was a blending model.
- Cutting stock – determine the best way to cut resource material to maximize profit. For example, a log can be cut into lumber of various dimensions which can be sold for different amounts.
- Staffing – determine the best way to assign people to jobs to maximize their preference or to maximize the productivity, based on their abilities at different jobs.
- Transportation – determine the best way to route resources through a transportation network to minimize the cost, while delivering the appropriate amount of resources to each location.
- Assignment – determine the best way to assign resources to tasks.
- Traveling salesman problem – determine the best route among a number of points that visits each point at least once. | <urn:uuid:576d19fe-e8a1-4405-a8de-15575fc98569> | {
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• The internet is a good thing.
• Children need to use the internet to be successful in the modern world.
• We need to teach children to use the internet safety to avoid the risks.
• Setup an account/profile.
• Create a virtual friends list by sending and receiving friend requests from others.
• Add personal information such as school details, address, family information etc.
• Share what their ‘status’ is and other friends can comment on this. For example “On my way home from school.”
• Comment on other statuses
• Upload photographs and videos
• Chat to others privately through the use of instant chat and video chat facilities.
• Sign into places and a map will point out where they are.
• They may receive a friend request from somebody they do not know.
• People lie online and may pretend to be someone else.
• People who want to meet with younger children may use their personal information such as their hobbies to build up a relationship with them and ask to meet.
• Cyberbullying – Children can be bullied through the use of technology. They may receive messages, phone calls, photos, videos
• Children may become addicted and may miss out on opportunities.
• Children can share personal information that can be seen by others.
• Future employers, colleges, universities etc. may be able to see their online activities.
• Children should be at least 13 to setup a social networking profile. Social networking sites don’t allow children under the age of 13 to use their services. Some
offer special accounts for younger children such as “SnapKidz.”
• Talk to your child about putting photographs online. They are open for people to see. If somebody copies their photograph then they have this forever.
• Help set up their profile. They can decide how much or how little they want to put on. Discourage your child from adding personal information (e.g. phone numbers etc.). Often social networking sites remind you that you have information missing but you DON’T have to provide everything they want.
• Ensure your child has set privacy settings to maximum. When they set privacy settings to ‘Private’ this is normally only minimum and although some aspects of their profile are set to private not everything is.
• “Friends” need to be people they know and trust in the real world. Try to talk to your child about the friends they have and how they know them.
• Try your very best to be “Friends” with your child on all social networking sites they are using.
• Add your email as the main contact (if possible).
• Make sure your child knows how to block people and how to close down their account in case they wanted to.
• Save www.thinkuknow.co.uk & www.ceop.police.uk/safety-centre to your favourites. Show your child where these are.
• Open up communication – talk to your child about the sites they are using and why they like them.
• Explain that people lie online and they are not always who they say they are .
• Encourage your children to make usernames anonymous. For example SandStorm245 rather than JackSmith1996.
• Use filters and firewall software. Remind them not to respond to popups, junk email and spam.
• Remind your child that everything they do online leaves a ‘Digital Footprint.’ Everything can be traced.
• Turn off location services on your child’s mobile phone.
If anything or anyone online makes you feel suspicious, uncomfortable, bullied or pressurised, you can and should report this. You can:
• Contact your child’s form tutor / head of house.
• Contact the school e-safety lead – Mr Cadwell.
• Report abuse/concerns to CEOP (Child Exploitation and Online Protection Centre) at http://www.ceop.gov.uk.
• Contact Childline at http:/www.childline.org.uk or telephone them on 0800 1111.
The following resources may provide you with additional useful information. They come from third party organisations in the UK and USA.
The aim of the organisations is to education parents/carers to keep children safe online, but some information is limited by the date of publication or the
country or original and should be read in that context. This information has not been produced by Range High School. | <urn:uuid:80335b3e-3c9e-443d-ae31-416fca23041c> | {
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The small fragments of tropical forests left behind after deforestation are suffering extensive species 'extinction', according to new research led by the University of East Anglia (UEA).
Publishing August 14 in the journal PLoS ONE, the researchers carried out a comprehensive assessment to estimate the long-term impact of forest fragmentation and hunting on tropical biodiversity in Brazil.
They studied the Atlantic Forest of eastern Brazil, including the region's largest and least disturbed old-growth forest remnants, and found that remaining habitat fragments had been virtually emptied of their forest wildlife.
White-lipped peccaries were completely wiped out, while jaguars, lowland tapirs, woolly spider-monkeys and giant anteaters were virtually 'extinct'. Defaunation even extended to forest remnants with relatively intact canopy structures.
Widespread agricultural expansion has transformed the world's tropical forests, leaving few remaining blocks of primary forests unaltered by humans. There have been scattered reports of large mammal extinctions throughout Brazil, but the conservation value of a rapidly growing number of small forest remnants in highly-fragmented tropical forest landscapes has been hotly debated.
Senior author Prof Carlos Peres, of UEA's School of Environmental Sciences, said: "You might expect forest fragments with a relatively intact canopy structure to still support high levels of biodiversity. Our study demonstrates that this is rarely the case, unless these fragments are strictly protected from hunting pressure.
"There is no substitute for strict protection of remaining forest fragments in biodiversity hotspots like the Brazilian Atlantic Forest. Protection of forest cover alone is not enough to sustain tropical forest species, as overhunting compounds the detrimental effects of small habitat area and isolation."
Drawing on information from wildlife surveys and local interviews conducted at 196 forest fragments spanning a vast region covering 252.670 km2, Dr Peres worked in partnership with Dr Gustavo Canale of the State University of Mato Grosso (UNEMAT). They investigated the effects of anthropogenic landscape alteration and other impacts, such as hunting, on the survival of large vertebrate species.
The researchers travelled more than 205,000km by treacherous dirt roads to uncover the largest and least disturbed forest fragments left in this vast region of the Atlantic Forest.
"We uncovered a staggering process of local extinctions of mid-sized and large mammals," said Dr Canale.
Around 90 per cent of the original Atlantic Forest cover (about 1.5 million km2) has been converted to agriculture, pasture and urban areas, and most of the remaining forest patches are smaller than a football pitch. On average, forest patches retained only four of 18 mammal species surveyed.
This study -- the first to document the loss of five large tropical forest mammals from one of the world's most endangered tropical biodiversity hotspots -- highlights the critical importance of the few legally protected areas established in the Atlantic Forest.
"We found that the protected areas retained the most species-rich forest fragments in the region," said Dr Canale. "We therefore recommend the implementation of new strictly protected areas, such as National Parks and Biological Reserves, including forest fragments containing populations of endangered, rare and endemic species, particularly those facing imminent extinctions."
However, many of the existing protected areas are far from secure.
Prof Peres said: "A growing number of reserves are being degraded, downsized, if not entirely degazetted, so holding on to the last remaining large tracts of primary forests will be a crucial part of the conservation mission this century."
With the global population projected to surpass nine billion by 2050, tropical forests will face increasing threats posed by anthropogenic land-use change and overexploitation.
"Human populations are exploding and very few areas remain untouched by the expanding cornucopia of human impacts," said Prof Peres. "It is therefore essential to enforce protection in areas that are nominally protected 'on paper'. The future of tropical forest wildlife depends on it."
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“Our study forecasts the science Roman’s spectroscopy survey will enable and shows how various adjustments could optimize its design,” said lead author Wang.
NASA’s Wide-Field Infrared Survey Telescope (WFIRST) is now named the Nancy Grace Roman Space Telescope, after NASA’s first Chief of Astronomy. Credit: NASA
The Roman will conduct a High Latitude Wide Area Survey (HLWAS). The High Latitude Spectroscopic Survey (HLSS) is the spectroscopic part of the HLWAS outlined in this study. The HLWAS is one of the telescope’s featured science objectives, along with novel approaches to
The Roman Space Telescope’s field of view will dwarf the Hubble’s. (No disrespect to the venerable Hubble, The Bringer of Knowledge.) Credit: NASA/GSFC/JPL
Roman’s HLSS relates to Universal expansion, Dark Energy, and Einstein’s Theory of General Relativity (TGR). Obviously, those are all deep and detailed topics, and they won’t fit in a Kurzgesagt-sized nutshell, but here’s how they fit together.
In 1915, when Einstein first put forth his TGR, nobody thought the Universe was expanding. TGR succeeded in explaining things Newtonian Gravity couldn’t. But it had a flaw. Einstein himself realized that his theory predicted that a static Universe was unstable, and it either has to expand or contract to be stable. But he rejected that, and he tripped himself up by introducing the now-notorious ‘cosmological constant’ to compensate. He used it to counteract the effect of gravity and achieve a static Universe. Einstein later called this his greatest blunder.
Then in the 1920s, astronomers discovered that the Universe is expanding. Bye-bye cosmological constant. American astronomer Edwin Hubble played a prominent role in the discovery, and the rule describing the expansion is called Hubble’s Law. (Sidebar: Belgian scientist and priest Georges Lemaître did earlier work on expansion, but he published his work in an obscure journal. Now Hubble’s Law is increasingly referred to as the Hubble–Lemaître law.) They discovered that galaxies are all moving away from each other, with only a very few exceptions. The Universe is expanding.
The expansion of the Universe was and is a mystery. Scientists have a placeholder name for the force that must be driving the expansion: Dark Energy.
For a long time, cosmologists thought the expansion was slowing. But it turns out that’s not true.
In 1998 scientists discovered that the Universe’s rate of expansion is accelerating. It shouldn’t be because the gravity from all the matter should slow the expansion down. With that discovery, the cosmological constant came back into play. It’s now the simplest explanation for the accelerating expansion. The cosmological constant is represented by the Greek capital letter lambda: Λ.
This image shows the expansion of the Universe accelerating. Time flows from bottom to top. Credit: Ann Feild (STScI)
Wouldn’t it be nice if the interminable guessing over the fate of the Universe was over? Wouldn’t it be fun to know how the Universe will end? (Lawrence Krauss thinks so.) It’d be as much fun as knowing what triggered its beginning. Imagine how popular you’d be at cocktail parties.
This brings us to the Roman Telescope and its High Latitude Spectroscopic Survey. The HLSS might be able to tell us about the future of the Universe’s expansion and if the Universe will continue to expand faster and faster and end in a Big Rip.
In their paper, the authors clarify the overall goal of the Survey. There are two top-level questions:
Is cosmic acceleration caused by a new energy component or by the breakdown of general relativity (GR) on cosmological scales?
If the cause is a new energy component, is its energy density constant in space and time, or has it evolved over the history of the universe?
There’s no magic to this. In a way, there’s brute force involved. The more of the Universe you can measure, and the more precisely you can measure it, the more accurate your conclusions are likely to be. This is behind the drive for larger, more precise telescopes like the Roman Space Telescope. The answers to our questions are more complex and harder to find.
In the paper, the authors present a reference design for the HLSS. The Roman’s HLSS will cover nearly 2,000 square degrees or about 5% of the sky in about seven months. This is a considerable improvement over other telescopes like the Hubble. “Right now, with telescopes like Hubble, we can sample tens of high-redshift galaxies. With Roman, we’ll be able to sample thousands,” explained Russell Ryan, an astronomer at STScI.
“Although Roman could execute a shallow and wide-area survey comparable to Euclid’s in approximately 1 yr of observing time, the deeper survey proposed here is a better complement to other surveys and more effectively exploits the capabilities of Roman’s larger aperture,” the paper states. “Per unit observing time, Roman is an extraordinarily efficient facility for slitless spectroscopic surveys, so it is well-positioned to respond to developments in experimental cosmology between now and mission launch in the mid-2020s.”
The new study shows that Roman’s HLSS should precisely measure 10 million galaxies from when the Universe was between three to six billion years old. Astronomers will use that data to map the large-scale structure of the Universe.
Cosmologists have already mapped the large-scale structure, but the Roman Telescope’s HLSS will take that mapping a step further. The HLSS will tell us the distances to about two million galaxies from when the Universe was only two to three billion years old. That’s never been done before and will be new data.
It boils down to measuring as many things as we can as accurately as we can. If the Roman Telescope can bring new depth and breadth to our understanding of the Universe’s large-scale structure over time, we can understand the history of the Universe’s expansion. Then, maybe, we’ll finally have our answer.
“Roman will determine the expansion history of the universe in order to test possible explanations of its apparent accelerating expansion, including dark energy and modification to Einstein’s gravity,” the authors write in their paper. “Roman will determine the growth history of the largest structures in the universe in order to test the possible explanations of its apparent accelerating expansion, including dark energy and modification to Einstein’s gravity…”
This video dissolves between the entire collection of redshift cubes in 55 seconds. As the Universe expands, the density of galaxies within each cube decreases, from 528,000 in the first cube to 80 in the last. Each cube is about 100 million light-years across. Galaxies assembled along vast strands of gas separated by immense voids, a foam-like structure echoed in the present-day Universe on large cosmic scales. This visualization shows the number and clustering of simulated galaxies at different cosmic ages, ranging from 4% to 43% of the Universe’s current age of 13.8 billion years. Each cube represents a fixed volume of space, about 100 million light-years per side. Over the sequence, the expansion of the Universe quickly lowers the density of galaxies. Each cube shows a specific cosmological redshift, from 9 to 1, with earlier cubes cast in redder shades.
That last sentence describes where we’re at now. The Universe is expanding, and the expansion is accelerating. That shouldn’t be the case because the gravity of all the matter in the Universe should be a drag on that expansion. The acceleration means that Einstein’s theory of gravity isn’t exactly correct. Or it means that we need to add a new energy component to the Universe: Dark Energy.
As explained in his TGR, Einstein’s gravity is accurate, to a point. So was Newton’s until we could observe larger portions of the Universe. Newton’s gravity accurately describes what happens with gravity on local scales, and Einstein’s gravity accurately explains what happens on an even larger scale. But now we’re confronting the entire Universe, and our understanding is inadequate.
This study simulates what the Roman can bring to the issue. The Roman Telescope’s vast and deep 3D images of the Universe are a new opportunity to discern between the leading theories that attempt to explain cosmic acceleration: a modified theory of gravity or Dark Energy.
Science can only win. Either result gets us closer.
“In illuminating the unknown nature of cosmic acceleration, we need to measure two free functions of time: the cosmic expansion history and the growth rate of large-scale structure,” the authors write. “These can tell us whether dark energy varies with time and whether it is an unknown energy component (eg, a cosmological constant), or the consequence of the modification of general relativity as the theory of gravity.”
This graphic illustrates how cosmological redshift works and how it offers information about the universe’s evolution. The universe is expanding, and that expansion stretches light traveling through space. The more it has stretched, the greater the redshift and the greater the distance the light has traveled. As a result, we need telescopes with infrared detectors to see light from the first, most distant galaxies. Credit: NASA, ESA, Leah Hustak (STScI)
“We can look forward to new physics in either case – whether we learn that cosmic acceleration is caused by dark energy or we find that we have to modify Einstein’s theory of gravity,” Wang said. “Roman will test both theories at the same time.”
The authors point out that their HLSS reference is an example of how could implement the High Latitude Wide Area Spectroscopic Survey on Roman. “The actual survey that Roman will execute will be defined in an open community process prior to launch, taking into consideration the landscape of dark energy projects and their synergies,” they write.
Will we ever know how the Universe will end? Maybe one day we will, and we can chat about it at cocktail parties. And we can talk about how the Nancy Gracy Roman Space Telescope helped us find our answer. | <urn:uuid:48e0663b-34cf-4331-8a47-10745cc04d79> | {
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discussed in biography
...by a false assumption, then corrected by proportion), extraction of roots, and the properties of numbers, concluding with some geometry and algebra. In 1220 Leonardo produced a brief work, the Practica geometriae (“Practice of Geometry”), which included eight chapters of theorems based on Euclid’s Elements and On Divisions.
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# How Many Ounces Are In 6 Gallons
When you’re doing your weekly grocery shopping, how many ounces of various products do you check? You might go through one bottle of shampoo every week, for example, or one roll of paper towels per wash.
But what about water? We usually assume that the average person needs six (6) bottles of water to stay hydrated, so we never really think about it.
However, this assumption is wrong!
It’s impossible to drink enough water to meet our fluid requirements if we are not drinking enough individual drinks. For example, I would be surprised to find someone who drinks two glasses (0.5 oz.) of milk daily. Almost everyone I know doesn’t drink any either!
So why donut believe the claims that say we need 6-8 cups of liquid a day? Fluid intake has little to do with thirst and everything to do with creating an adequate supply of glucose and salt in your blood.
This article will talk more about the differences between dehydration and thirsty, as well as some strategies for increasing your personal fluid intake.
## Conversion of ounces to liters
To find how many ounces are in a given amount of liquid, you need to know what an ounce is! The definition for ounces varies by source, but most agree that one oz equals 28 grams.
So if you have a bottle that contains six (6) gallons of fluid, then there are just so many times you can multiply 28 grams by six to get how much powder you have.
That would be done using this formula:
Six (lots) x 28 = 168 pounds (or 7,000 kg)
Seven thousand kilograms divided by 30,000 is about two and a half tons of powder!
This seems very high, but it makes sense when you think about it. One gallon of water has a densityof 0.
## Conversion of ounces to pints
Converting fluid ounce measurements into liquid pint measurements is pretty easy, just remember your basics! To do this, you will need to know what an ounce equals as a measurement, and how many inches make up a whole cup or one tablespoon.
The volume of a standard drinky measure like a shot glass or a tall beer bottle is 5 milliliters (0.18 ounces), so we can use that as our base for converting between ounces and pints. A normal size drinking glass has about 4 tablespoons, which means there are 2 tablespoons in a half-cup.
That leaves us with 1/2 a cup to work with, so let’s calculate by breaking down the numbers more slowly. One fourth of a cup is 0.25 cups, and one quarter of an ounce is one third of an ounce, or 0.33 oz. This gives us a total of 0.83 oz per 5 ml = 16 grams (1.6 oz) for 6 fluidounces. We now have enough information to convert another way!
To find out how much water comes in a given amount of vodka, simply divide 16 g by the number of drinks needed, then multiply that by six! The answer here was 3.
## Conversion of ounces to pounds
To find how many pounds there are in a given amount of water, you need to know what an ounce is! An ounce is defined as three hundred grams, or about 30 ml of liquid. A gram is a measure of weight used in both physical education and dieting. One gram equals one thousandths of a pound.
A standard drink is eight grams of alcohol (one eighth of an oz.) which means that one drink is two tablespoons of liquor, four tablespoons of wine, or six tablespoons of clear liquid such as soda, juice, or water. There are also twenty-four points on the alcoholic drinks chart that calculate how much other fluid you should have with each drink to reduce the effect of drinking.
By using these charts, it is easy to see that a normal person needs to consume around five to seven drinks per day to exceed their limit for daily drinking.
## Calculating the number of ounces in a gallon
To determine how many ounces are in a specific amount of liquid, you need to know what a one ounce bottle looks like compared to a full glass bottle. You can also compare it to a total volume of water in a normal person.
A standard length measuring cup is 1/2 cup which equals 250 ml or 0.25 liter. A fluid ounce contains about 5 ml so that is why a one-ounce bottle is actually only half empty!
To find out how many ounces are in a given amount of liquid, simply divide the number of ounces by the density of the liquid. The densest liquids have higher numbers, thus making them take up more space than less dense liquids. Water is pretty heavy per its own definition, so we will use it as an example here.
The easiest way to do this is to measure a small amount of the liquid and see how much space it takes up.
## Calculating the number of ounces in a quart
So how many ounces are in a gallon? It is actually easier to do it the other way around! That is, instead of figuring out what fraction of a gallon is water, we can figure out what fraction of a bottle is water.
By doing this, you will get the same results. All you have to do is divide the amount of bottles by the size of an average bottle cap. The sizes of these bottle caps vary depending on the type of liquid they contain.
For example, if a container does not have any bottle caps, then you would use one glass = 0.5 oz as your normal bottle cap. If there is a half-ounce (0.5oz) bottle cap, then you would use that. And finally, if there is a 1 ounce (1oz) bottle cap, then you would use that for the total weight!
This article will teach you how to find the number of ounces in a six-quart bucket. It is very similar to finding the number ofounces in a one-gallon jug except now we are adding more to the equation.
## Converting ounces to grams
To find how many grams are in one ounce of liquid, you need to know what an ounce is first! An ounce is defined as any amount of pure water that equals exactly 15 ml. One standard drink is determined to be 1 cup or 8 oz of clear liquid.
Based on this definition, it’s easy to calculate the number of grams in a given quantity of liquid. For example, if you want to know how many grams are in six (0.6) cups of your favorite beverage, simply multiply eight (1 cup = 8 oz) by fifteen (15 ml). So, six cups is equal to zero points six times eight times fifteen – so 0 g for six cups!
Sadly, most beverages contain more than five percent alcohol which means they don’t meet our definition of “pure water.” But we can still use our method to determine the number of grams in other liquids! Just remember that dried fruits and some vegetables also contribute towards your total calorie intake so make sure to include those when calculating.
Another important factor to consider is whether or not the fluid in question has been mixed with sugar or milk. For instance, if you mix tea with milk, each serving contains both glucose and fat, making the total calories higher than just adding up the two components separately.
## Converting ounces to milliliters
So how many ounces are in six fluidounces? The easy way to figure this out is by dividing up the number of ounces into half-ounce, one-ounce, two-ounce, and three-ounce increments!
So if you have a liquid that contains 24 ounces then there would be four chunks of liquid that contain six fluid ounces each. To make it simple just divide the number of ounces by eight to get your total amount of liquids in a specific volume.
## Converting ounces to teaspoons
In our food recipes, we often call for an amount of sugar or butter that is measured inounces. These are not liquid measurements like cups or tablespoons, but rather solid measurers such as one cup of sugar or one stick of butter.
If you were to take one ounce of sugar and mix it with three tablespoons of milk, your drink would be one third full of sugar!
To make sure your drinks are balanced, you need to know how much sugar your drinking! Luckily, there is a simple way to do this. You can simply multiply the number of oz by 20 to get the total amount of sugars in the drink. So if one ounce of sugar equals two tablespoons of mixed liquids, then multiplying by twenty gets us the total amount of sugar in the drink.
##### By Ishan Crawford
Prior to the position, Ishan was senior vice president, strategy & development for Cumbernauld-media Company since April 2013. He joined the Company in 2004 and has served in several corporate developments, business development and strategic planning roles for three chief executives. During that time, he helped transform the Company from a traditional U.S. media conglomerate into a global digital subscription service, unified by the journalism and brand of Cumbernauld-media. | crawl-data/CC-MAIN-2024-30/segments/1720763518058.23/warc/CC-MAIN-20240723133408-20240723163408-00593.warc.gz | null |
## Algebra 1
$78$
We start with the given expression: $3m^2+n$ We plug in the values for $m$ and $n$: $3(5)^2+3$ The order of operations states that first we perform operations inside grouping symbols, such as parentheses, brackets, and fraction bars. Then, we simplify powers. Then, we multiply and divide from left to right. We use these rules to simplify the expression: Since there are no grouping symbols, we first simplify powers: $3(25)+3$ Next, we multiply: $75+3$ Finally, we add: $78$ | crawl-data/CC-MAIN-2024-33/segments/1722640365107.3/warc/CC-MAIN-20240803091113-20240803121113-00626.warc.gz | null |
Thanks to German astronomers, we now have the most accurate measurements yet of the giant black hole that sits at the centre of our galaxy.
And what a beast it is: as wide as Earth's orbit around the sun and 4.3 million times more massive than our home star. Lucky, then, that it is 27,000 light years away.
Researchers from the Max Planck Institute for Extraterrestrial Physics used two telescopes operated by the European Southern Observatory in Chile to watch stars as they circled the centre of the Milky Way. The 16-year study, now published in the Astrophysical Journal, has proved beyond doubt that lurking at the very centre of the galaxy is a black hole.
Black holes are clearly intriguing, and not just to scientists. Earlier today, a colleague known more for his in-depth investigations into the wrongdoings of governments and multinationals than his knowledge of quantum gravity, asked what seems like a simple question: "What's inside a black hole?" Sensing my attempt at an answer wasn't good enough, I called Stefan Gillessen, one of the authors of the latest study, for an explanation.
To begin with, he pointed out that scientists should only ask questions that can be answered, and since it is impossible to get information out of a black hole (in the form of light, for example) we can never really know. But let's not give up just yet.
Black holes are created when large stars explode and collapse in on themselves. Many will have masses similar to our own sun, but others grow to much larger masses.
Theoretical physicists have thought long and hard about what goes on inside black holes and their conclusions are mind-bending to say the least. Despite the fact that they suck in material from anything and everything that strays too close, they are empty. The mass of a black hole is confined to an infinitely small point at its centre, called a singularity.
How much blackness surrounds a singularity – in effect, the size of the black hole – is defined by the strength of its gravitational pull. Far away from a black hole, light can zip around as usual, lighting up the heavens as it goes. But closer to a black hole, gravity becomes stronger and stronger until eventually, not even light can move fast enough to escape its pull. This is why a singularity is surrounded by a vast sphere of darkness. The point at which the hole's gravity becomes strong enough to prevent light escaping is known as the event horizon.
"To know what's inside a black hole, we need something to come out from behind the event horizon, and reach us via a telescope. The easiest thing for astronomers would be light, but a black hole is so massive not even light can escape so no information can get out," he said. "You could go and look, but once you're in you never come back out again."
Gillessen admits to feeling uncomfortable about the concept of singularities, but the late John Wheeler, who coined the term "black hole" in 1967, put it nicely in his 1999 autobiography, "Geons, Black Holes and Quantum Foam: A Life in Physics". He said black holes teach us that "space can be crumpled like a piece of paper into an infinitesimal dot, that time can be extinguished like a blown out flame, and that the laws of physics that we regard as sacred, as immutable, are anything but." | <urn:uuid:a817ecb9-2a88-46d2-bb28-1fdf4d34ea4d> | {
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# find sides of right triagle when you know hypoteneuse
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
see attached file. Find a, b and h. know hypotenuese is square root of 3 plus square rrot of 12
https://brainmass.com/math/basic-algebra/find-side-right-triangle-hypoteneuse-453003
#### Solution Preview
The equation to use when dealing with sides and right triangles is known as the Pythagoras' Theorem.
This states that the sum of the square of each side (A,B) is equal to the square of the hypotenuse (C). Mathematically speaking,
A^2+B^2 = C^2
(A^2 means "A squared" and it's A*A)
(sqrt(x) is read as "square root of x")
because there are 3 right triangles in this picture, we can write Pythagoras' Theorem 3 times:
First the large triangle:
a^2+b^2 = (sqrt(3)+sqrt(12))^2 .....(1)
The triangle on the left:
(sqrt(3))^2+h^2 = b^2 .....(2)
The triangle on the right:
(sqrt(12))^2+h^2 = a^2 ...
#### Solution Summary
The expert finds sides of right triangles when you know the hypoteneuse.
\$2.19 | crawl-data/CC-MAIN-2019-30/segments/1563195527396.78/warc/CC-MAIN-20190721225759-20190722011759-00118.warc.gz | null |
The magnitude and distribution of wind velocity are the key elements in determining wind design forces. Mountainous or highly developed urban areas provide a rough surface, which slows wind velocity near the surface of the earth and causes wind velocity to increase rapidly with height above the earth’s surface. Large, level open areas and bodies of water provide little resistance to the surface wind speed, and wind velocity increases more slowly with height. Wind velocity increases with height in all cases but does not increase appreciably above the critical heights of about 950 ft for open terrain to 1500 ft for rough terrain. This variation of wind speed over height has been modeled as a power law:
where V is the basic wind velocity, or velocity measured at a height zg above ground and Vz is the velocity at height z above ground. The coefficient n varies with the surface roughness.
It generally ranges from 0.33 for open terrain to 0.14 for rough terrain. The wind speeds Vz and V are the fastest-mile wind speeds, which are approximately the fastest average wind speeds maintained over a distance of 1 mile. Basic wind speeds are measured at an elevation zg above the surface of the earth at an open site. Design wind loads are based on a statistical analysis of the maximum fastest-mile wind speed expected within a given recurrence interval, such as 50 years. Statistical maps of wind speeds have been developed and are the basis of present design methods. However, the maps consider only regional variations in wind speed and do not consider tornadoes, tropical storms, or local wind currents. The wind speed data are maintained for open sites and must be corrected for other site conditions. (Wind speeds for elevations higher than the critical elevations mentioned previously are not affected by surface conditions.)
Wind speeds Vw are translated into pressure q by the equation
The drag coefficient CD depends on the shape of the body or structure and is less than 1 if the wind flows around the body. The pressure q is the stagnation pressure qs if CD = 1.0, since the structure effectively stops the forward movement of the wind. Thus, on substitution in Eq. (9.2) of CD = 1.0 and air density at standard atmospheric pressure,
where the wind speed is in miles per hour and pressure, in psf.
The shape and geometry of the building have other effects on the wind pressure and pressure distribution. Large inward pressures develop on the windward walls of enclosed buildings and outward pressures develop on leeward walls, as illustrated in Fig. 9.1a. Buildings with openings on the windward side will allow air to flow into the building, and internal pressures may develop as depicted in Fig. 9.1b. These internal pressures cause loads on the over-all structure and structural frame. More important, these pressures place great demands on the attachment of roofing and external cladding. Openings in a side wall or leeward wall may cause an internal pressure in the building as illustrated in Fig. 9.1c and d. This buildup of internal pressure depends on the size of the openings for all walls and the geometry of the structure. Slopes of roofs may affect the pressure distribution, as illustrated in Fig. 9.1e. Projections and overhangs (Fig. 9.2) may also restrict the airflow and accumulate pressure.
These effects must be considered in design.
The velocity used in the pressure calculation is the velocity of the wind relative to the structure. Thus, vibrations or movements of the structure occasionally may affect the magnitude of the relative velocity and pressure. Structures with vibration characteristics which cause significant changes in the relative velocity and pressure distribution are regarded as sensitive to aerodynamic effects. They may be susceptible to dynamic instability due to vortex shedding and flutter. These may occur where local airflow around the structure causes dynamic amplification of the structural response because of the interaction of the structural response with the airflow. These undesirable conditions require special analysis that takes into account the shape of the body, airflow around the body, dynamic characteristics of the structure, wind speed, and other related factors. As a result, dynamic instability is not included in the simplified methods included in this section.
The fastest-mile wind speed is smaller than the short-duration wind speed due to gusting.
Corrections are made in design calculations for the effect of gusting through use of gust factors, which increase design wind pressure to account for short-duration increases in wind speed. The gust factors are largely affected by the roughness of the surface of the earth.
They decrease with increasing height, reduced surface roughness, and duration of gusting.
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The Sugar Act was enacted on April 5, 1764, in order to help reduce the staggering national debt incurred during the French and Indian War and to help pay for the continued presence of British troops in the colonies to defend from any further attacks. The two main thrusts of the Act were to actually collect the taxes that had been in place, but skirted around for so long, and to force the colonists to trade with Britain and her colonies instead of foreign powers, in an effort to boost the ailing British economy.
In April 1763, George Grenville succeeded Lord Bute as Prime Minister and he set about creating a policy to reduce the national debt. Before the French and Indian War, which lasted from 1756 - 1763, the British national debt was only 72,000,000 pounds. By January 1763, the debt had skyrocketed to almost 130,000,000 pounds.
After the French and Indian War, Britain posted 10,000 soldiers in the colonies to protect them from further incursions by Indians or other foreign powers. Lord Grenville's Sugar Act sought to get the colonists to contribute to the costs of this defense, a proposition that wasn't necessarily disagreeable to the colonists, but it was the way in which he went about it that caused them great consternation. The colonists did not mind being taxed by their own elected colonial legislatures, but Parliament was taxing them and they had no representatives in Parliament. This is the origin of the revolutionary battle cry, taxation without representation.
The Sugar Act marked the first time Parliament tried to directly tax the colonists. It was generally considered fair on both sides of the ocean for Parliament to regulate trade within the British Empire. Duties on imported goods were paid by shippers and were not a direct tax on consumption. The Sugar Act, however, was viewed as a direct tax on the consumption of many popular items including sugar, wine, textiles, tropical foods, silk and numerous other items, and had, as its stated purpose, the purpose of raising revenue for the Crown. This intent is stated clearly in the preamble of the Sugar Act:
"It is expedient that new provisions and regulations should be established for improving the revenue of this Kingdom... and... it is just and necessary that a revenue should be raised... for defraying the expenses of defending, protecting, and securing the same."
You can read the entire Sugar Act text here.
This angered the colonists because it seemed that Parliament wanted to use them for its own good. It may seem reasonable to expect that the colonists would be partly responsible for the expenses of their own defense. The colonists were not opposed to this. However, Parliament placed this tax directly on them, which violated the British political principle that taxes could only be levied if they were agreed upon by the common people through their elected representatives. The colonists had no elected representatives in Parliament and had been taxed only by their own colonial legislatures for over a hundred years. Thus the root of the conflict was whether or not Parliament had the right to tax the colonists.
In addition to the right of taxation question, colonists were angered and alarmed because the newly enforced taxes caused great economic hardship by raising the prices of many common goods, reducing foreign markets to which they could export their goods and creating burdensome trade regulations.
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# Prove two sets span the same subspace
I've found here that in order for two sets to span the same subspace, the following must be true:
• Each vector in S1 can be written as a linear combination of the vectors in S2; and
• Each vector in S2 can be written as a linear combination of the vectors in S1.
I don't know why we need the second one, because suppose a vector $$u$$ from $$S_1$$ can be written as a linear combination of vectors from $$S_2$$: $$u = \alpha_1a_1+\cdots+\alpha_na_n$$. Then shouldn't it mean that $$a_i = \frac{u -\alpha_1a_1-\cdots-\alpha_na_n}{\alpha_i}$$, and therefore, this vector in $$S_2$$ can be written as linear combination of $$S_1$$? PS: while writing this I noticed that $$a_i$$ is not written in terms of vectors in $$S_2$$, but in terms of vector in $$S_1$$ and $$S_2$$, so the converse isn't imediately true.
Ok, but,can someone give me na intuition on why these criteria are necessary?
In order to verify that
$$\{(1,-1,2),(3,0,1)\}, \{(-1,-2,3), (3,3,-4)\}$$
generate the same subspace of $$\mathbb R^3$$, I should try to solve
$$(1,-1,2) = \alpha_1(-1,-2,3)+\alpha_2(3,3,4)$$ $$(3,0,1) = \alpha_3(-1,-2,3)+\alpha_4(3,3,4)$$
and
$$(-1,-2,3) = \beta_1(1,-2,3)+\beta_2(3,0,1)$$ $$(3,3,-4) = \beta_3(1,-2,3)+\beta_4(3,0,1)$$
if there is such $$\alpha_1,\alpha_2,\alpha_3,\alpha_4,\beta_1,\beta_2,\beta_3,\beta_4$$, then they generate the same subspace of $$\mathbb R^3$$?
To show $\text{span}\{v_{1}, v_{2} \} = \text{span}\{u_{1}, u_{2} \}$, you need to show these two sets are subsets of each other. But if you show $v_{1}, v_{2} \in \text{span}\{u_{1}, u_{2} \}$, then since the span is a subspace and hence closed under addition and scalar multiplication, it follows that all possible linear combinations of $v_{1}$ and $v_{2}$ are in $\text{span}\{u_{1}, u_{2} \}$, and hence $\text{span}\{v_{1}, v_{2} \} \subseteq \text{span}\{u_{1}, u_{2} \}$.
Similarly, if you show $u_{1}, u_{2} \in \text{span}\{v_{1}, v_{2} \}$, then since the span is closed under addition and scalar multiplication, it follows that all possible linear combinations of $u_{1}$ and $u_{2}$ are in $\text{span}\{v_{1}, v_{2}\}$, and thus $\text{span}\{u_{1}, u_{2} \} \subseteq \text{span}\{v_{1}, v_{2} \}$ | crawl-data/CC-MAIN-2024-26/segments/1718198864850.31/warc/CC-MAIN-20240623194302-20240623224302-00343.warc.gz | null |
Service dogs are dogs that have been trained to carry out a variety of tasks to make life easier for persons with a disability or persons who are suffering from a condition so that they are able to carry out their daily activities like everyone else.
Among other things, service dogs can be trained to:
- alert a person with hearing difficulties when there is a knock on the door or an important noise which requires human intervention such as a smoke alarm or a baby crying – these dogs are called Hearing Dogs;
- pick up objects from the floor or open drawers and doors for someone who is in a wheelchair – these dogs are called Wheelchair Assistance Dogs;
- give persons on the autistic spectrum support and provide them with confidence and a sense of independence – these dogs are called Autism Assistance Dogs;
- alert a diabetic person when their blood sugar level is reaching dangerously high or low levels – these dogs are called Diabetic Alert Dogs;
- alert a person who is prone to seizures that an episode is imminent so that the person can lie down or take other precautions such as stop driving- these dogs are called Seizure Alert Dogs; and
- provide comfort and a sense of peace and security for people with mental health conditions – these dogs are called Therapy Dogs.
There are as many types of service dogs as there are conditions which can be eased by training a dog to perform a task! | <urn:uuid:9e2722ff-be1f-4c3f-933f-1272581f17d9> | {
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A mutation is any change in DNA sequence that can be
passed from parent to offspring. Mutations occur
naturally at a low rate in all living organisms.
fact, mutation is one of the sources of genetic
By inducing mutations, scientists have been
able to increase genetic variation in crop species.
Breeders depend on genetic variation to produce
varieties with desirable traits, such as resistance to
diseases and insects.
Unlike recombinant DNA methods,
induced mutation does not add any genetic material into
the species, although it can remove it by making
deletions of DNA.
To induce mutations, chemicals or
irradiation interact with internal enzymes that
replicate or repair DNA in living organisms.
Essentially, induced mutation produces results that
could have occurred naturally over much longer times
than it takes to induce such results.
Since the 1940s,
over 2,200 crop varieties have been developed by
inducing mutations to alter genetic traits and then
selecting among the progeny for improved types. For
example, semi-dwarf rice, low saturated fat sunflower
seeds, redder grapefruit and many flowers are derived
from induced mutations. | <urn:uuid:7b9fbb1f-9c59-470b-97ca-a87dcf3484ac> | {
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# How Many Trapezoids I Can Draw
I guess this is a good time to give my answer for the challenge of how many different trapezoids there are to draw. At the least it’ll provide an answer to people who seek on Google the answer to how many trapezoids there are to draw. In principle there’s an infinite number that can be drawn, of course, but I wanted to cut down the ways that seem to multiply cases without really being different shapes. For example, rotating a trapezoid doesn’t make it new, and just stretching it out longer in one direction or another shouldn’t. And just enlarging or shrinking the whole thing doesn’t change it. So given that, how many kinds of trapezoids do I see?
I make it out to be six.
Here’s the way I reasoned it. For simplicity, I’m assuming the two parallel bases are horizontal. And I’m assuming the lower base is the longer one; this is the way trapezoids keep getting drawn. I may as well go with the universal standard. I’m also assuming that just making both bases or both legs longer doesn’t by itself change the trapezoid. But I do think there are some differences, and this is how I come up with six.
The difference I was thinking of came about from a comment Chiaroscuro made about how to prove the area formula for a trapezoid. His idea, and a good one, was based on slicing the trapezoid up into three shapes. One of them would be the triangle on the left-hand side, one would be the rectangle in the center, and one would be the triangle on the right-hand side. This proof works just fine for the standard-model trapezoid, where the shorter base is on top, and it’s centered above the longer base. It also works fine if the center of the shorter base is directly above the right end of the lower base, but it falls apart in other cases: if you have a right trapezoid, for example, there’s only the one triangle to lop off. If the upper base isn’t anywhere above the lower base, the proof doesn’t work, but we could repair it.
That inspires the differences that I see, though: How many of the ends of the upper base are above the lower base? And put that way, there are only three possible answers. Either both ends of the upper base are above the lower base, or just one end of the upper base is above the lower, or else neither end of the upper base is above the lower. If both ends of the upper base aren’t above the lower base, they might be either to the left or to the right of the lower base; I’ll draw them going over to the right side. This implies there are three kinds of trapezoids; let me show how we get more of them.
This is the first case with both ends of the upper base above the lower base. And this suddenly shows how to make six cases out of these three possibilities: the ends of the upper base are directly above the ends of the lower base. This is the shape we might more commonly call a rectangle, and we can argue about whether rectangles are trapezoids, but let’s suppose they are or the number of possibilities drops to five.
This is the second case of having both ends of the upper base above the lower base. One end is directly above an end of the lower base; the other is between the ends of the lower base. This is the right trapezoid shape so handy in working out the rules for integration. This is the only example of a right trapezoid that we need, since it wouldn’t really be different if the vertical leg were on the right-hand side rather than the left. And we’re taking by assumption the longer base to be on the bottom, so we don’t need to consider the case of the longer base being above the shorter.
This is the third example of both ends of the shorter base being above the longer base, and it’s also the standard-issue trapezoid, the one shown in textbooks when writing out formulas for areas. This is also one where the area formula could be found by chopping the segment up into three pieces. Do it by dropping vertical lines at the points where the upper base has its ends. You get two triangles and a rectangle.
Figuring out the area of the rectangle should be easy — obvious even — although figuring out the area of each of the triangles may be a bit mysterious. After all, you need the base and the height of each triangle to find its area. The height is obvious; it’s how far apart the parallel bases are. The width, though … that seems to depend heavily on the angle the legs make. It’s worth thinking about how to find the area of these two triangles.
This is the first example of a trapezoid where the upper base has only one end point above the lower base. The right end of the top stretches out past the right end of the bottom. (It wouldn’t be different if the upper base stretched out past the left end instead.) This is probably the second-most-obvious case of a trapezoid at all. The area formula could also be worked out by chopping it up along vertical lines, slicing the trapezoid at the left end of the upper base and at the right end of the lower base.
There’s the same problem in figuring out the areas of both of these triangles, since there’s so much variability in the bases of the two triangles. But if you spotted how to work out the area of the two triangles above then this won’t give you any trouble.
Here’s the second example of just the one end of the upper base being above the lower base. It may not look very different from the previous one, but the difference shows up if you try slicing vertically at the upper-left or the lower-right ends. The left end of the upper base is directly over the right end of the lower base, and so, there’s just the one slice, and it cuts the trapezoid into two triangles, with no rectangle.
This is the example where neither end of the upper base is above the lower base. I don’t see any obvious special cases to this, unless you want to count where the two legs happen to be parallel and make the trapezoid into a parallelogram. If you do try cutting this with vertical slices at the left end of the upper base and the right end of the lower base you come out of it with two short triangles and a brand-new trapezoid, which is just a mess to deal with.
There might be another case worth considering: what about the parallelogram, where the upper base is far enough to the right of the lower base that no point of it is above the lower? And I think we don’t need to pay any special attention to this, because if we rotate that figure a quarter-turn, making what had been the two legs into the bases, then we have a parallelogram with one end of the upper base above the lower base, which I claim we already covered with the fourth kind of trapezoid.
Of course, I claim this, but does that mean I’m right? It may be fun to spend some time convincing yourself of this, or finding a counter-example. Perhaps a seventh kind needs to be added after all.
## Author: Joseph Nebus
I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.
## 55 thoughts on “How Many Trapezoids I Can Draw”
1. ivasallay says:
Reblogged this on Find the Factors and commented:
A trapezoid is often defined for young students as a four-sided shape with EXACTLY two parallel sides. Once a person studies higher level math, the definition changes: A trapezoid is a four-sided shape with AT LEAST two parallel sides. How many different kinds of trapezoid can a person draw? It depends on which definition you use. If you use the second definition, you can also include parallelograms, rectangles, rhombuses, and squares. Either definition will allow the standard isosceles trapezoid and several others. But how many? Whichever definition you use, figuring out how many different ones can be drawn is a nice puzzle to solve. This blog post does a nice job explaining the different ones, and it even came up with ones I hadn’t considered!
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2. I like this post because I was just trying a different approach to my writing today now of course you speaking about something totally different but in my mind the process is some what the same,how do you think outside the box to arrive at the answer,so it took some doing but I took a bare bone idea that I had written a turned it on its ear,you took a shape and wanted to see how many more,to me it’s the same,
As always Sheldon
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1. Well, ah, thank you, I believe. I don’t know that I was trying anything particularly outside-the-box when I tried thinking how many different trapezoids there were. It amounted to more thinking about what sorts of things stand out to me as trapezoids, and how I might describe them to someone who wasn’t looking at the same picture I was.
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3. This is the one I was speaking about,how I took it and reworked it
Thank you for visiting
As always Sheldon
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4. this was interesting but i find myself wondering, what is the underlying rule that is being used to define what makes a different type. i feel like there is one, but not sure how to express it mathematically.
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1. This is a good question and I’m not sure how to characterize it exactly. I may have to write a follow-up post to say how I came to figure on these trapezoids rather than another set.
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# 160.9 pounds to stones
## Result
160.9 pounds equals 11.4929 stones
You can also convert 160.9 pounds to stones and pounds.
## Conversion formula
Multiply the amount of pounds by the conversion factor to get the result in stones:
160.9 lbs × 0.0714286 = 11.4929 st
## How to convert 160.9 pounds to stones?
The conversion factor from pounds to stones is 0.0714286, which means that 1 pounds is equal to 0.0714286 stones:
1 lbs = 0.0714286 st
To convert 160.9 pounds into stones we have to multiply 160.9 by the conversion factor in order to get the amount from pounds to stones. We can also form a proportion to calculate the result:
1 lbs → 0.0714286 st
160.9 lbs → m(st)
Solve the above proportion to obtain the mass m in stones:
m(st) = 160.9 lbs × 0.0714286 st
m(st) = 11.4929 st
The final result is:
160.9 lbs → 11.4929 st
We conclude that 160.9 pounds is equivalent to 11.4929 stones:
160.9 pounds = 11.4929 stones
## Result approximation
For practical purposes we can round our final result to an approximate numerical value. In this case one hundred sixty point nine pounds is approximately eleven point four nine three stones:
160.9 pounds ≅ 11.493 stones
## Conversion table
For quick reference purposes, below is the pounds to stones conversion table:
pounds (lbs) stones (st)
161.9 pounds 11.56429 stones
162.9 pounds 11.635719 stones
163.9 pounds 11.707148 stones
164.9 pounds 11.778576 stones
165.9 pounds 11.850005 stones
166.9 pounds 11.921433 stones
167.9 pounds 11.992862 stones
168.9 pounds 12.064291 stones
169.9 pounds 12.135719 stones
170.9 pounds 12.207148 stones
## Units definitions
The units involved in this conversion are pounds and stones. This is how they are defined:
### Pounds
The pound or pound-mass is a unit of mass used in the imperial, United States customary and other systems of measurement. A number of different definitions have been used; the most common today is the international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms, and which is divided into 16 avoirdupois ounces. The international standard symbol for the avoirdupois pound is lb; an alternative symbol is lbm (for most pound definitions), # (chiefly in the U.S.), and ℔ or ″̶ (specifically for the apothecaries' pound). The unit is descended from the Roman libra (hence the abbreviation "lb"). The English word pound is cognate with, among others, German Pfund, Dutch pond, and Swedish pund. All ultimately derive from a borrowing into Proto-Germanic of the Latin expression lībra pondō ("a pound by weight"), in which the word pondō is the ablative case of the Latin noun pondus ("weight"). Usage of the unqualified term pound reflects the historical conflation of mass and weight.
### Stones
The stone or stone weight (abbreviation: st.) is an English and imperial unit of mass now equal to 14 pounds (6.35029318 kg). England and other Germanic-speaking countries of northern Europe formerly used various standardised "stones" for trade, with their values ranging from about 5 to 40 local pounds (roughly 3 to 15 kg) depending on the location and objects weighed. The United Kingdom's imperial system adopted the wool stone of 14 pounds in 1835. With the advent of metrication, Europe's various "stones" were superseded by or adapted to the kilogram from the mid-19th century on. The stone continues in customary use in Britain and Ireland used for measuring body weight, but was prohibited for commercial use in the UK by the Weights and Measures Act of 1985. | crawl-data/CC-MAIN-2021-04/segments/1610704843561.95/warc/CC-MAIN-20210128102756-20210128132756-00135.warc.gz | null |
While not all neurons look the same, the basic structure of a motor neuron is represented in the image.Each specific part of the neuron plays an important role, allowing the neuron to send information throughout our entire body. Key terms listed below are labeled in blue on the neuron image above.Neural communication depends on the ability of our neurons to respond to incoming stimulation and then pass signals to other neurons. Neurons send information electrochemically, which means half of this process is electrical and the other half is chemical. The chemicals cause an electrical signal.How do neurons communicate to one another?Our neurons are surrounded by a membrane that allows some ions to pass through and blocks the passage of other ions, such as a gate to a pool. This type of membrane is calledsemi-permeableorselectively permeable.When a neuron is inactive, hanging out in our bodies not sending signals, it is calledresting potential. There is a slightly negative charge inside the neuron, during resting potential because at rest, there are relatively more sodium ions outside the neuron and more potassium ions inside that neuron. We call thispolarization.When a neuron decides to communicate and go to work, it is calledaction potential(the process by which a neuron fires). During action potential, an electrical signal passes along the axon and causes a release of neurotransmitters (chemicals) that transmit signals to other neurons. A depolarizing current creates this explosion of electrical activity. This means that a stimulus caused the resting potential to fire an action potential. This is what we callthreshold. If the neuron does not reach threshold, then no action potential will fire.In addition, when the threshold level is reached, an action potential will always fire. There are no large or small action potentials in a neuron – all action potentials are the same size. Therefore, the neuron either fires an action potential or does not. This is the “all-or-none principle”.Action potentials are caused by an exchange of ions across the neuron membrane. A stimulus first causes the sodium channels to open. Since there are many more sodium ions on the outside, sodium ions rush into the neuron. Remember, sodium has a positive charge, so the neuron becomes more positive for this brief moment and becomes depolarized. As this occurs, potassium channels open, and potassium rushes out of the cell, reversing thedepolarization.When the neuron fires, the depolarization of the cell membrane moves along the axon like a wave at a concert. When the next gates along the axon open, allowing positive sodium ions in, the previous gates close and begin to pump the positively charged sodium ions out of the axon and potassium ions back inside. As each section of the axon is depolarizing, the preceding section is going through the process ofrepolarization. This step is called therefractory periodand the axon cannot fire again until it returns to resting potential.The entire process is like falling dominoes all the way down the axon except these dominoes can set themselves back up as soon as they fall over.What role do neurotransmitters play in communication between neurons?Just like there are several different types of ice cream flavors, there are differentneurotransmittersin the body! Just as each flavor affects our taste buds differently, various neurotransmitters do different things to our body. We cannot underestimate how important these chemicals, neurotransmitters, are to our body. Everything we do, we need a neurotransmitter to do it. Every time we think, move, laugh, or feel emotion; we are relying on our neurotransmitters.Neurotransmitters are made in the cell body of the neuron and then transported down the axon to the terminal buttons (axon terminals). Molecules of neurotransmitters are stored in small “packages” called vesicles.Neurotransmitters are released from one neuron at thepresynapticterminal button into the synaptic gap due to action potential. Neurotransmitters then cross the synapse where they may be accepted by the next neuron (postsynapticneuron) at a specialized site called a receptor. Neurotransmitters will bind only to specific receptors on the postsynaptic dendrite’s membrane that recognize them. The action that follows activation of a receptor site may be either depolarization (an excitatory postsynaptic potential) or an inhibitory postsynaptic potential. (This means once the neurotransmitter binds onto the receptor site of the dendrite, either action potential will take place, or it will not allow action potential to take place because it is an inhibitor.) Neurotransmission is then terminated byreuptakein which the neurotransmitter is taken back into the presynaptic terminal buttons that released it.How do neurotransmitters influence behavior, emotion, and thoughts?As you have learned, neurotransmitters act to either enhance or inhibit action potentials. Many substances such as drugs can alter the action of neurotransmitters in several ways. Substances such as toxins or drugs can either raise or lower the amounts of neurotransmitters released into the synapse, and change the reuptake process by either blocking reuptake or preventing it. Drugs that mimic or enhance the actions of neurotransmitters are known asagonists. Drugs that inhibit or block actions of neurotransmitters areantagonists.A neurotransmitter’s effect is a function of the receptors to which it binds. The same neurotransmitter can be both excitatory and inhibitory, or produce different effects depending on the receptor site. Neurotransmitters can be broken into four categories: acetylcholine, monoamines, amino acids, and peptides.Sensory neuronsSensory neurons, also known as afferent neurons, carry information from our sensory receptors to our spinal cord or brain.Your sensory neurons communicated how painful touching the hot stove was!Motor neuronsMotor neurons, also known as efferent neurons, carry messages from the spinal cord and brain and distribute it to our muscles and glands.Your motor neurons are what made your hands move away as fast as you could!InterneuronsInterneurons connect and communicate between the afferent and efferent neurons. As you can imagine, this occurs rapidly. Motor neurons and sensory neurons refuse to communicate with each other, so they use the interneurons to help communicate back and forth to each other.Central nervous system (CNS)Thecentral nervous system (CNS)includes our brain and spinal cord. These are the nerves that are encased in bone. The brain performs nearly all functions of the CNS. Behavior and mental processes are produced within specific locations in the brain that we will discuss in future lessons. The main function of the spinal cord is to receive sensory signals from the body and transmit them to the brain and then receive signals from the brain and relay them to the specific body parts. The spinal cord is also capable of reflex action.Peripheral nervous system (PNS)Theperipheral nervous system (PNS)consists of all the other nerves in our body or all nerves that are not encased in bone. The PNS is divided into two categories, the Somatic and Autonomic Nervous Systems.Somatic nervous systemThesomatic nervous systemcontrols all of our voluntary muscle movements. Every time we choose to move our body to dance, kick a soccer ball, write a haiku, or text message someone, we are using motor neurons located in the somatic nervous system.Autonomic nervous systemTheautonomic nervous systemcontrols all of the automatic functions of our body such as our heart rate, lungs, and internal organs. Pretend you just consumed a pizza! The pizza enters into your stomach. Do you need to think about squirting stomach acid on the pizza? No! Do you press a switch to turn the food into energy your body can use? No! Did you even think about breathing while readying this? Although it would be really interesting if we could control every function of our body, they happen automatically, therefore named the autonomic nervous system. The autonomic system is broken down into two nervous systems: the sympathetic and parasympathetic.Sympathetic nervous systemWhether it is a fire alarm ringing or someone attractive coming into view, we experience nervous symptoms. Whenever our body feels stress, thesympathetic nervous systemautomatically releases epinephrine to attempt to prepare ourselves.When activated, the sympathetic nervous system will speed up your heart rate, increase your blood sugar and oxygen levels, dilate your pupils, and decrease your digestive process. Why does our body do this? It prepares the body for action to either fight to protect ourselves or run from danger. We call it thefight or flight response, which is activated by psychological states such as anxiety or unhappiness, as well as sexual arousal.Chronic activation of the sympathetic nervous system is associated with ulcers and heart disease.Parasympathetic nervous systemAs soon as we know that the fire alarm was false, our heart starts to return to its normal rate, breathing slows, pupils contract, and digestive process resumes. This is a result of theparasympathetic nervous systemreturning your body to normal resting state after sympathetic activation.In 1848, the case study of Phineas Gage’s accident led scientists to hypothesize that specific regions of the brain were responsible for our personality and behavior. Watch a video aboutthe case of Phineas Gage. When the page loads, scroll down and click on Video 25: “Frontal Lobes and Behavior: The Story of Phineas Gage.” Also watch and take notes on Video 1: “Organization and Evaluation of Brain Function.”Today’s neuroscientists no longer need to wait for injuries or accidents to study the brain. Recent technology has enabled neuroscientists to see inside the living brain. They can now surgically lesion tissue in specific brain areas in animals, or electrically, chemically, or magnetically stimulate the brain in order to study the effects of specific areas.These brain-imaging techniques help neuroscientists to understand the relationships between specific brain regions and what functions they serve. Neuroscientists are also able to locate regions of the brain affected by neurological disorders, and develop new strategies to treat brain disorders.LesionsScientists surgically remove or destroy tissue in a specific region of the brain to understand the function of the specific area.Lesions are also conducted by neurosurgeons during brain surgery to remove tumors.EEGResearchers position electrodes on the scalp of subjects to record the waves of electrical activity that sweep across the brain’s surface. EEG orelectroencephalogrammeasures brain activity to determine a relationship to cognitive or perceptual tasks.CAT/ CT ScanCAT/CT Scans orComputerizedAxialTomography Scans, are sophisticated x-rays of the brain. Cross-sectional 3-D images of the brain are taken and used to show the structure of the brain, but not activity or function. CAT/CT Scans are particularly useful in locating brain tumors damage to brain regions.ET ScanPET,positronemissiontomography, scans depict brain activity by locating and measuring radioactivity after a person is given a radioactive form of glucose. The PET scan reveals areas of the brain that “light up” while using the glucose, allowing researchers to know which brain areas are most active during a specific activity.MRIThe MRI,MagneticResonanceImaging, provides neuroscientists with the most detailed picture/ image of the brain. MRI scans use magnetic fields and radio waves to produce computer generated images that distinguish between the structures within the brain as well as different types of soft tissue.fMRIThe fMRI,functionalMRI, is a technique that shows blood flow and brain activity by comparing successive MRI scans. The fMRI reveals brain structure as well as functioning and activity when areas light up due to increased blood flow while a subject is performing different mental functions. | <urn:uuid:a040f11c-e428-41fb-97d3-edc01d9a55df> | {
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organometallic chemistry, the reactions and use of a class of compounds (R-M) that contain a covalent bond between carbon and metal. They are prepared either by direct reaction of the metal with an organic compound or by replacement of a metal from another organometallic substance. Their use is based on the polar R-M bond, in which the carbon atom carries a partial negative charge, and on the nature of the metal atom. In synthesis they act as nucleophiles that can bond with relatively positive carbon atoms in compounds such as alkyl halides, aldehydes, and ketones. For example, the Grignard reagent, RMgX (where X equals Br, Cl, or I), and organolithium compounds react with ketones to give secondary alcohols. In industry, butyllithium is used for the polymerization of isoprene in the manufacture of synthetic rubber; metalloorganic compounds serve as catalysts. The semimetals, boron, and silicon are important organometallics; organoboranes are used in synthesis, while organosilicones are polymerized to manufacture plastics and elastomers. Many organometallics are toxic primarily because of the toxicity of the metal. For example tetraethyl lead has been banned as gasoline additive and the conversion of mercury to mercury alkyls by fish has had serious consequences in Japan.
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.
See more Encyclopedia articles on: Organic Chemistry | <urn:uuid:a9404463-c11a-48b1-b74b-d7c83b0805ee> | {
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The word ‘squeeze’ sounds like one of those passwords that are used by the printing world simply to add to the mystique of letterpress. It’s true that it has been used in the past by some printers to justify some very imprecise practices. That said, squeeze is something for printers to think about, especially those concerned with precision.
After World War II the general drive for greater productivity and quality meant printers needed to adopt ever more precise ways of working to avoid problems during printing and also increase the productive hours of each machine. Where once objects like furniture and blocks could be points adrift from their stated size, they now had to be correct.
‘Squeeze’ is the term to describe the difference between the length of a line of type as sat in the composing stick; and the same line when locked up in a chase ready to print. The accepted view was that a compositor should set type a little longer than the measure (line length) but the forces of quoins would squeeze the type together and bring it back to the intended size.
Knowing that type metal itself cannot usually be compressed, we have to look at what else could cause this phenomena –
- Dirt and other deposits on the walls of type might be compressible
- Bent spaces might be brought back in to true
- Type that is not straight in the stick (‘off its feet’) may be corrected to an upright position
- Basic equipment, like the composing stick, might be inaccurate
It follows, then, that if clean new type is used in an accurately made and set composing stick and the line is properly justified then there is no room at all for compression and so squeeze is eliminated. Remember that the pressure of the quoins on the specific lines will be around the same as the pressure of the composing stick ends.
The problem then becomes ‘how can the line be accurately filled’, for the endless combinations of character widths and standard spaces will always leave some room at the end of a line. As an example, a line of 14pt type is set and a gap at the end of the line is too small to be filled with a thick space, and too big to be filled with a middle space. The difference between the two is 1 and 1/6 of one point.
Naturally spaces cannot be made in each possible size, so if we are using the precision approach above every line will be short because an irregular space will exist at the end of each line. Our answer now is to make sure that, on average, each line is correct.
To do this we have to establish a common space: what is the average difference between any two standard sizes of space. Just how big is the jump between mid and thick; or thin to mid; or mid + thin to nut?
Saving you the maths, the answer is 7/120ths of an em, and converting this to points the average is 7/12th of a point. That is to say that any given combination of type and standard spacing will be between 7/24th over line length and 7/24th under line length. We have to further round this to a usable unit, and the key point is to set your composing stick to ½pt over the desired line length.
To make the best of this, the following points should be observed –
- Composing sticks should be periodically checked for accuracy
- Precision, milled, em gauges should be used to set the stick along with a half-point gauge. All sticks should be set from the same gauges
- When using type over 14pt, use half-point ‘hair’ spaces
- Leads should be cut to the line length minus one point
- Reglet should be used down the sides to pages to take any remaining irregularity in justification | <urn:uuid:2f1c5bd0-f3bf-42d7-95e2-9390ed9e2f4e> | {
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# Lecture 7
Another common variant is known as strong induction. This allows you to assume all previous cases in your induction step, rather than just the last one.
It looks like the following:
Definition: [Strong induction] Let $P(n)$ be a statement that depends on a natural number $n$. Then if
1. $P(0)$ is true, and
2. for all $k$, if $P(0), P(1), \ldots P(k)$ are all true, then $P(k+1)$ is also true,
then $P(n)$ is true for all $n\in\mathbb{N}$.
Again, this can be viewed as a cleverly disguised version of ordinary induction: if we define the statement $Q(n)$ as follows: \begin{aligned} Q(n) &= P(0)\wedge P(1)\wedge\cdots\wedge P(n-1)\wedge P(n)\\ &= \text{all the statements P(0),\ldots,P(n) are true'',}\end{aligned} then proving $Q(n)$ by ordinary induction works out to be effectively the same thing as proving $P(n)$ by strong induction.
Indeed, the base case $Q(0)$ is the same thing as the base case $P(0)$. The induction step $Q(k)\Rightarrow Q(k+1)$ looks like $P(0)\wedge\cdots\wedge P(k)\Rightarrow P(0)\wedge\cdots\wedge P(k)\wedge P(k+1).$
In order to prove this, we assume $P(0),\ldots,P(k)$ are all true and have to prove that $P(0),\ldots,P(k+1)$ are all true. But then all of these except the last are assumptions: what is left is to prove $P(k+1)$ assuming $P(0),\ldots,P(k)$, and that’s exactly the induction step of a strong induction.
Here’s an example of strong induction in practice. First we’ll need a definition:
Definition: The Fibonacci numbers $F_0, F_1, \ldots$ are defined by taking $F_0 =0$ and $F_1 = 1$, and then for $n\geq 2$ by $F_{n} = F_{n-1} + F_{n-2}.$
Now for the result in question:
#### Proposition
For all $n\in\mathbb{N}$ we have $F_n<2^n$.
#### Proof
Let $P(n)$ be the statement $F_n<2^n$. We know that $P(0)$ is true, since $F_0 = 0<1 = 2^0.$ We also know that $P(1)$ is true, since $F_1 = 1<2 = 2^1.$
Now we’ll show that for all $k\geq 1$ we have that if $P(0),\ldots,P(k)$ are all true, then $P(k+1)$ is true. So suppose that $P(0),\ldots, P(k)$ are all true.
We now have that \begin{aligned} F_{k+1} &= F_k + F_{k-1}\\ &< 2^k + 2^{k-1}\qquad\text{(using P(k) and P(k-1))}\\ &< 2^k + 2^k\\ &= 2^{k+1},\end{aligned} which is exactly $P(k+1)$. This completes the induction step, and so finishes the proof.
That strong induction argument really had two base cases before the induction step.
So we proved $P(0)$, and we proved $P(0)\Rightarrow P(1)$ by proving $P(1)$, and then we proved $P(0)\wedge\cdots\wedge P(k)\Rightarrow P(k+1)$ by proving $P(k-1)\wedge P(k)\Rightarrow P(k+1)$.
I like to think that the proof was arranged according to the shape of the definition of the Fibonacci numbers: that definition has two base cases $F_0 = 0$ and $F_1 = 1$, and a step $F_{n+2} = F_{n+1} + F_n$. This is not a rare coincidence.
## Why induction works
In this section we make a few comments on why induction works. They may be helpful in thinking about when you can and when you can’t generalise induction to other settings.
Let’s introduce a definition:
Definition: A set (of numbers) is well-ordered if every nonempty subset has a least element.
For now, our main use of that is to say this:
Definition: The well-ordering principle for $\mathbb{N}$ says that $\mathbb{N}$ is well-ordered.
This is a very special property of $\mathbb{N}$. The integers $\mathbb{Z}$, for example, are not well-ordered. Indeed, the subset $\mathbb{Z}\subset\mathbb{Z}$ of all integers does not have a least element: there is no least integer.
The main interest is this:
#### Theorem
The well-ordering principle for $\mathbb{N}$ and the principle of strong induction are equivalent.
#### Proof
We’ll show first that we can derive the principle of strong induction from the well-ordering principle.
So suppose we had a statement $P(n)$ for each $n\in\mathbb{N}$, and we had a base case (that $P(0)$ was true) and an induction step (that, for all $k\in\mathbb{N}$ if we have $P(i)$ for all $i, we also have $P(k)$). We need to show that $P(n)$ is true for all $n$.
We might argue as follows. Let $A$ be the set of natural numbers $n$ for which $P(n)$ does not hold: $A = \left\{n\in\mathbb{N}\mid \neg P(n)\right\}.$ So $A$ is the set of “counterexamples”.
If $A$ has any elements at all, it has a smallest element $a$. But $a$ can’t be $0$, because we have $P(0)$. But $a$ can’t be bigger than $0$ either: because $a$ is minimal, we have $P(i)$ for all $i. Hence we have $P(a)$ also, by the induction step. But that’s a contradiction: we assumed that $\neg P(a)$.
Hence $A$ doesn’t have any elements, which is the same as saying that $P(n)$ holds for all $n$.
Now we’ll show the other half of the equivalence: that we can derive the well-ordering principle from the principle of strong induction.
Let $Q(n)$ be the statement, “any subset of $\mathbb{N}$ which contains $n$ has a smallest element”. We’ll prove $Q(n)$ for all $n$ by strong induction.
Firstly, for a base case, we must prove $Q(0)$ (“any subset of $\mathbb{N}$ which contains $0$ has a smallest element”). This is clearly true, as $0$ is the smallest natural number of all, so any such subset has $0$ as its smallest element.
Now we must prove the induction step: we assume for some $k$ that $Q(i)$ is true for all $i, and we prove that $Q(k)$ is true. Consider a subset $S\subset\mathbb{N}$ which contains $k$. If it contains some element $i, then by $Q(i)$ it has a least element. If, however, it contains no element $i, then $k$ is its least element: so in particular, it has a least element. This proves $Q(k)$.
Hence we have $Q(n)$ for all $n$ by strong induction. So if $S$ is a nonempty subset of $\mathbb{N}$, it has at least one element: call it $n$. But then by $Q(n)$, the set $S$ has a least element: this proves the well-ordering principle.
Part of the reason this is such good news is that there are other well-ordered sets, besides the natural numbers. Whenever you find a well-ordering, you get a notion of induction for free.
For example, consider the set of pairs $(m,n)$ of naturals, where we say that $(m,n)<(m',n')$ if $m, or if $m=m'$ and $n. (This is called the lexicographic ordering, because it’s inspired by the way that words in dictionaries are ordered).
It is not too hard to prove that that is well-ordered: any set of pairs of natural numbers has a “least” element with respect to this ordering. Hence we can do (strong) induction on pairs of naturals! | crawl-data/CC-MAIN-2023-23/segments/1685224649193.79/warc/CC-MAIN-20230603101032-20230603131032-00308.warc.gz | null |
- A child counts each of four objects, pointing to each while saying . . . "1, 2, 3, 4"
Help your student become a(n) Corresponder
These activities focus on saying one number word for each object. Rhythmic and playful games such as "Simon Says" lay the ground work, and others such as "Counting Wand" demonstrate and discuss the concept that we must have one and only one number word for each object. Because there are really two correspondence – between saying the counting words and pointing, and between pointing and the objects – multiple experiences over a considerable time are often needed.
Counting Wand [Corresponder]
Scoops for Everyone
Ding Clink Bam
Jack in the Box
Dice Movement Game
Get Ready to Go: Object Count | <urn:uuid:9d587a96-aa26-4dc5-a4ed-1476606d0e10> | {
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# Simplify: $$\frac{1}{2\space+\space\frac{1}{1\space-\space\frac{1}{2}}}\times \frac{1}{\frac{1}{6}\space of\space{36}\space \div\space 3}\space +\space\frac{1}{2\space+\space\frac{1}{1\space+\space\frac{1}{4}}}$$
1. 27/56
2. 37/56
3. 17/56
4. 47/56
Option 1 : 27/56
## Detailed Solution
Given:
$$\frac{1}{2\space+\space\frac{1}{1\space-\space\frac{1}{2}}}× \frac{1}{\frac{1}{6}\space of\space{36}\space \div\space 3}\space +\space\frac{1}{2\space+\space\frac{1}{1\space+\space\frac{1}{4}}}$$
Calculation:
$$\frac{1}{2\space+\space\frac{1}{1\space-\space\frac{1}{2}}}× \frac{1}{\frac{1}{6}\space of\space{36}\space \div\space 3}\space +\space\frac{1}{2\space+\space\frac{1}{1\space+\space\frac{1}{4}}}$$
⇒ [1/(2 + 2)] × (1/2) + [1/(2 + 4/5)]
⇒ (1/4) × (1/2) + (5/14)
⇒ (1/8) + (5/14)
⇒ 54/112
⇒ 27/56
∴ The required answer is 27/56. | crawl-data/CC-MAIN-2023-06/segments/1674764499713.50/warc/CC-MAIN-20230129112153-20230129142153-00820.warc.gz | null |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Fractional Exponents
Relate fractional exponents to nth roots
Levels are CK-12's student achievement levels.
Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.
At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.
Advanced Students matched to this level are ready for material that requires superior performance and mastery.
• Read
Applying the Laws of Exponents to Rational Exponents
by CK-12 //at grade
This lesson applies the laws of exponents to rational exponents.
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• Read
Fractional Exponents
by CK-12 //at grade
Simplify exponential expressions that involve terms being raised to a zero or fractional power.
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• Read
Rational Exponents and Roots
by CK-12 //at grade
This lesson introduces rational exponents and how to relate them to nth roots.
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• Read
Evaluate Radical Expressions and Fractional Powers
by CK-12 //at grade
Learn to evaluate radical expressions and fractional exponents.
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• Video
Zero and Negative Exponent Properties
by CK-12 //at grade
This is a short tutorial on zero and negative exponent properties.
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• Video
Fractional Exponents: A Sample Application
by CK-12 //at grade
This video demonstrates a sample use of fractional exponents.
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Zero and Fractional Exponents: An Explanation of the Concept
by CK-12 //at grade
This video provides an explanation of the concept of fractional exponents.
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• Downloadable Quiz
Fractional Exponents Quiz
by CK-12 //at grade
Quiz for Fractional Exponents.
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• Critical Thinking
Fractional Exponents Discussion Questions
by CK-12 //at grade
A list of student-submitted discussion questions for Fractional Exponents.
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• Real World Application
Beaufort Scale
by CK-12 //at grade
Students will apply their knowledge of fractional exponents to better understand how the Beaufort Scale is used to measure the intensity of tornadoes and storms.
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Follow the Rules
by CK-12 //at grade
Use rational exponents to determine the maximum distance of each planet from the Sun.
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• Study Guide
Properties of Exponents Study Guide
by CK-12 //at grade
This study guide reviews properties of exponents and the exponential form: product rule, quotient rule, power rule for exponents, power rule for quotients. It also looks at how to evaluate zero, negative, and fractional exponents.
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Please wait... | crawl-data/CC-MAIN-2017-13/segments/1490218193284.93/warc/CC-MAIN-20170322212953-00322-ip-10-233-31-227.ec2.internal.warc.gz | null |
Conversion formula
The conversion factor from meters to decimeters is 10, which means that 1 meter is equal to 10 decimeters:
1 m = 10 dm
To convert 676.4 meters into decimeters we have to multiply 676.4 by the conversion factor in order to get the length amount from meters to decimeters. We can also form a simple proportion to calculate the result:
1 m → 10 dm
676.4 m → L(dm)
Solve the above proportion to obtain the length L in decimeters:
L(dm) = 676.4 m × 10 dm
L(dm) = 6764 dm
The final result is:
676.4 m → 6764 dm
We conclude that 676.4 meters is equivalent to 6764 decimeters:
676.4 meters = 6764 decimeters
Alternative conversion
We can also convert by utilizing the inverse value of the conversion factor. In this case 1 decimeter is equal to 0.0001478415138971 × 676.4 meters.
Another way is saying that 676.4 meters is equal to 1 ÷ 0.0001478415138971 decimeters.
Approximate result
For practical purposes we can round our final result to an approximate numerical value. We can say that six hundred seventy-six point four meters is approximately six thousand seven hundred sixty-four decimeters:
676.4 m ≅ 6764 dm
An alternative is also that one decimeter is approximately zero times six hundred seventy-six point four meters.
Conversion table
meters to decimeters chart
For quick reference purposes, below is the conversion table you can use to convert from meters to decimeters
meters (m) decimeters (dm)
677.4 meters 6774 decimeters
678.4 meters 6784 decimeters
679.4 meters 6794 decimeters
680.4 meters 6804 decimeters
681.4 meters 6814 decimeters
682.4 meters 6824 decimeters
683.4 meters 6834 decimeters
684.4 meters 6844 decimeters
685.4 meters 6854 decimeters
686.4 meters 6864 decimeters | crawl-data/CC-MAIN-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00721.warc.gz | null |
3.3 Effects of Shooting Uphill or Downhill
When a gun is sighted in on a level or nearly level range and then is fired either uphill or downhill, the gun will always shoot high. This effect is well known among shooters, particularly hunters, but how high the gun will shoot is a subject of considerable controversy in the shooting literature. In fact, at the present time some literature has information that is simply erroneous. In this subsection, we will try to explain the physical situation carefully so that it can be understood clearly, and then provide some examples using Infinity to perform precise calculations.
Throughout this subsection the terms “bullet drop” and “bullet path” will be used frequently, so we will review the definitions of those terms before we begin to explain the physical situation. One may refer back to Figure 3.0-1 concerning these definitions. Bullet drop is always measured in a vertical direction regardless of the elevation angle of the trajectory. At any range distance measured along either a level range or a slant range, drop is then the vertical distance between the extended bore line and the point where the bullet passes. Drop is expressed as a negative number, denoting that the bullet falls away from the extended bore line as the bullet travels.
Bullet path, on the other hand, is always measured perpendicular to the shooter’s line of sight through the sights on the gun. Thus, it would be where the shooter would “see” the bullet pass at any instant of time while looking through the gun sights, if that were possible. At the gun’s muzzle, the bullet path is negative because the bullet starts out below the line of sight of the shooter. Somewhere near the muzzle, the bullet will follow a path that rises and crosses the line of sight, then travel above the line of sight until the target is reached. The bullet path is then positive throughout this portion of the trajectory. The bullet will arc over and cross the line of sight at the zero range. So, the bullet path is zero at the zero range, and then becomes negative at distances greater than the zero range.
The explanation of the physical situation for uphill/downhill shooting begins with a simple observational fact — that bullet drop at any given range from the muzzle is almost independent of firing elevation angle. What this means is that if the drop of a bullet trajectory at, say, 150 yards is measured when the gun is fired on a level range, then the drop at a slant range distance of 150 yards will be almost the same value when the gun barrel is elevated at +45 degrees, – 15 degrees, – 60 degrees, or any other positive or negative elevation angle. It is very important to remember that we use “start range” because that is the range that the bullet must actually travel to reach the target. This is true for all range distances practical for small arms fire.
To illustrate this point, Table 3.3-1 has been prepared for a group of five cartridges, three for rifles and two for handguns. The table shows drop numbers at a specific range distance for each cartridge, as a function of the bore elevation angle of the gun at the firing event. These drop numbers have been computed with Infinity. These trajectories have been computed for a firing point altitude of 2500 feet above sea level. The selected cartridges in Table 3.3-1 illustrate typical behavior of drop at a specific (and relatively long) range distance versus the bore elevation or depression angle. The 338 Winchester Magnum cartridge exhibits the worst case in the table. At a range distance of 600 yards, there is only about 0.5 inch difference in drop value between a level trajectory and a trajectory elevated 60 degrees or depressed 60 degrees. This is because the major driving cause of bullet drop is gravity acting over the bullet’s time of flight. There are two other smaller effects on drop as the bullet travels. When a bullet is traveling upward on an elevated trajectory, there is a component of gravity that adds to the drag deceleration of the bullet, but the bullet is traveling into less dense atmosphere that reduces the aerodynamic drag. So, these small effects tend to offset one another. The opposite small effects occur when the bullet is traveling downward along a depressed trajectory.
This result is true in general. At practical range distances for small arms fire the change in vertical drop with firing elevation or depression angle is very small, even for very steep angles. However, the bullet path can change dramatically, particularly at steep angles.
Figure 3.3-1 shows how this happens. Ordinarily, a shooter will sight his gun in on a target range that is level or nearly level. Figure 3.3-1 (a) shows this situation. When sighting in, the shooter adjusts his sights so that the line of sight intersects the trajectory at the range (Ro in the figure), which is the range where he wants his gun zeroed in. Ro is called the zero range for level fire. The vertical distance between the line of departure (extended bore line) of the bullet and the point where the bullet passes is the drop (do). This symbol is used to denote the drop at the range where the gun is zeroed in.
Note that the angle between the bullet’s line of departure (extended bore line) and the line of sight is very small. This angle is greatly exaggerated in Figure 3.3-1 for purposes of illustration. Even for very long-range target shooting (1000 yards or more), the angle A is much less than 1.0 degree, and it is typically less than 10 minutes of arc for sporting rifles and handguns.
Table 3.3-1 Bullet Drop at a Specific Range Distance versus Bore Elevation Angle for a Selection of Cartridges
|Cartridge and Load Range Distance||Elevation Angle||Bullet Drop|
|22 Hornet, Sierra’s 200 yds||0 deg (level)||– 13.39 in|
|45 gr. Hornet bullet,||20||– 13.38|
|2700 fps Mzl Vel||45||– 13.36|
|– 20||– 13.40|
|– 45||– 13.41|
|270 Winchester 400 yds||0 deg (level)||– 39.98 in|
|Sierra’s 140 gr.||20||– 39.94|
|SBT GameKing,||45||– 39.90|
|2900 fps Mzl Vel||60||– 39.89|
|– 20||– 40.01|
|– 45||– 40.05|
|– 60||– 40.06|
|338 Winchester 600 yds||0 deg. (level)||– 109.05 in|
|Magnum, Sierra’s||45||– 108.66|
|250 gr. SBT GameKing,||60||– 108.57|
|2700 fps Mzl Vel||– 45||– 109.44|
|– 60||– 109.53|
|44 Magnum, Sierra’s 150 yds||0 deg (level)||– 28.34 in|
|240 gr. JHC bullet,||20||– 28.33|
|1300 fps Mzl Vel||45||– 28.32|
|– 20||– 28.36|
|– 45||– 28.37|
|38 S&W Special, 100 yds||0 deg (level)||– 16.04 in|
|Sierra’s 125 gr.||20||– 16.03|
|JSP bullet,||45||– 16.03|
|1100 fps Mzl Vel||– 20||– 16.04|
|– 45||– 16.05|
Now consider the situation where the shooter fires his gun uphill at a steep angle, as shown in Figure 3.3-1 (b), with no changes in the sights. Since the true bullet drop changes very little, at a slant range distance Ro from the muzzle the bullet has a vertical drop nearly equal to do, as shown in the figure. However, the line of sight at slant range distance Ro still is located a distance do in a perpendicular direction away from the line of departure. Because of the firing elevation angle, the bullet trajectory no longer intersects the line of sight at the slant range Ro. In fact, the bullet passes well above the line of sight at that point, as Figure 3.3-1 (b) shows. In other words, the bullet
shoots high from the shooter’s viewpoint as he or she aims the gun, and at steep angles it may shoot high by a considerable amount at longer ranges.
Figure 3.3-1 (c) depicts the situation when the shooter fires the gun downhill. Again the vertical drop at the slant range distance Ro changes a very small amount from the value do for level fire, but the line of sight and line of departure are still separated by the perpendicular distance do at that range point. Compared to the case of level fire, the bullet again shoots high from the shooter’s viewpoint as he or she aims the gun. Furthermore, if the gun is fired uphill at some elevation angle, and then fired downhill at an equivalent depression angle, the two bullets will shoot high by nearly the same amount at the same slant range distances.
A careful look at Figure 3.3-1 (a) or (b) shows us that the amount by which the bullet shoots high at the slant range distance Ro is equal (approximately) to the perpendicular distance do from the line of sight to the extended bore line minus the projection of the drop do on that same perpendicular line. From plane trigonometry, the distance by which the bullet shoots high at Ro is:
Amount by which the bullet shoots high = do [1.0 – cosine A]
where A is the elevation angle (or depression angle). Now, if you have forgotten or never studied trigonometry in school, don’t worry. The Infinity program will make exact calculations for you, and two examples of these calculations will be shown below.
First though, let us point out that this explanation of the physics of uphill or downhill shooting has been given specifically for a slant range distance equal to the zero range distance for level fire, and this has been done just for convenience. The sketches are easier to draw and to understand for that situation. The result, however, applies for all slant range distances. At any range distance from the muzzle, the amount by which the bullet will shoot high at any elevation or depression angle A is very nearly equal to the drop for level fire at that range distance multiplied by the quantity [1.0 – cosine A].
Two examples for uphill or downhill shooting have been prepared using Infinity, and they are shown in Tables 3.3-2 and 3.3-3. The first example is for a 7 mm Remington Magnum, a flat-shooting rifle cartridge. The second example is for a 44 Remington Magnum handgun cartridge that has a trajectory with much more arc. It is presumed that both the rifle and the handgun have telescope sights and are sighted in at an altitude of 2500 feet. Then, they are fired uphill or downhill while at the same altitude. The tables show the reference bullet path for level fire together with the changes in bullet path depending on the elevation angle and slant range distance. When reviewing Tables 3.3-2 and 3.3-3, keep in mind that a depression angle is a negative elevation angle.
Two conclusions are evident from these examples. First, shooting uphill or downhill can have a strong effect on the trajectory of any bullet, always causing the bullet to shoot high relative to the bullet path for level fire. This effect grows larger as the slant range distance grows longer and the elevation angle grows steeper. The second conclusion is that a bullet always shoots slightly higher when it is fired downhill than when it is fired uphill at the same angle. The reason for this, as explained above, is that when the bullet travels upward, there is a component of gravity acting as drag on the bullet that increases the drop slightly. When the bullet travels downward, on the other hand, there is a component of gravity acting as drag on the bullet that decreases the drop slightly.
Table 3.3-2 Example of Bullet Path Changes for a Rifle Bullet Fired Uphill or Downhill
Cartridge: 7 mm Remington Magnum with Sierra’s 140 grain Spitzer Boat Tail bullet at 3000 fps muzzle velocity Zero range: 300 yds for level fire Shooting environment: 2500 ft altitude with standard atmospheric conditions
|Elevation||Parameter||Slant Range Distance (yds.)|
|0||Bullet Path (in)||3.71||4.45||0.0||– 10.49||– 28.06|
|+ 15||Bullet Path Change (in)||0.07||0.29||0.68||1.26||2.08|
|– 15||Bullet Path Change (in)||0.07||0.29||0.70||1.32||2.19|
|+ 30||Bullet Path Change (in)||0.27||1.13||2.68||5.03||8.31|
|– 30||Bullet Path Change (in)||0.27||1.15||2.73||5.13||8.50|
|+ 45||Bullet Path Change (in)||0.59||2.49||5.89||11.05||18.27|
|– 45||Bullet Path Change (in)||0.59||2.50||5.94||11.17||18.48|
Table 3.3-3 Example of Bullet Path Changes for a Handgun Bullet Fired Uphill or Downhill
Cartridge: 44 Remington Magnum with Sierra’s 240 grain Jacketed Hollow Cavity bullet at 1300 fps muzzle velocity Zero range: 100 yds for level fire Shooting environment: 2500 ft altitude with standard atmospheric conditions
|Elevation||Parameter||Slant Range Distance (yds.)|
|0||Bullet Path (in)||2.40||0.0||– 9.88||– 28.35|
|+ 15||Bullet Path Change (in)||0.09||0.38||0.89||1.63|
|– 15||Bullet Path Change (in)||0.10||0.42||1.04||2.01|
|+ 30||Bullet Path Change (in)||0.37||1.55||3.67||6.84|
|– 30||Bullet Path Change (in)||0.37||1.61||3.92||7.49|
|+ 45||Bullet Path Change (in)||0.80||3.42||8.16||15.28|
|– 45||Bullet Path Change (in)||0.81||3.50||8.44||16.03| | <urn:uuid:db063147-6d5f-4ff1-bd46-e7cd9d1a036e> | {
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Charts and graphs are a way to present numerical data in a reader-friendly way, but they are more like pictures than tables in the way they represent visual information.
Source: MapStats for Kids, FedStats.gov
### Pie Charts
A pie chart or graph depicts data as parts of a whole. The whole pie (or circle) represents the total of something, while each sliver represents a percentage of that total. Let’s take a look at the pie chart on the right.
The chart tells us that of the people who ordered dessert at a local pie shop, 36% ordered apple pie, while only 3% ordered coconut cream pie. By looking only at the shapes, we can see that three of the pies sold by the shop were very popular, and two were not so popular. What might the pie shop owner do with this information? Perhaps the owner could offer the most popular pies on the daily menu and the least popular pies as specials.
To see how easy it is to read and use a pie chart, complete the activity that follows with your classmates or friends.
Source: IPSI
Ask a group of 10 students to tell you what their favorite electronic device is (i.e., tablet, phone, MP3 player, computer, or TV). Write down their preferences. Once you have all 10 responses, figure out the percentages. For example, if five students said they preferred their tablet computers, you could make a pie chart showing that half (50%) of the students prefer “tablet computers,” while the other half prefer “other devices.” Your pie chart would look like the first example on the right. What if you want to specify the “other devices” preferred by half of the students? Perhaps three students said they can’t live without their MP3 players (30%), and two said they prefer their phones (20%). Your pie chart would look like the second example on the right. You can now easily see that most of the students who responded prefer to use their tablets over phones or MP3 players.
Source: Mobile devices DSC 0988, HLLundgaard, Wikimedia
All you have to do is reread the explanation to the left of the charts to see that the pie chart is a much easier way to explain and represent the same information. Learning to read the information contained in pie charts and graphs helps you gain information in an efficient and accurate way.
### Bar Graphs
A bar graph is used to track changes over time or to make comparisons. Let’s look at the bar graph below from the U.S. Bureau of Labor Statistics, the department that tracks information about employment. This graph illustrates how more education made it less likely for certain groups of people to be unemployed during the recession in 2011 and presents information about how much money those groups earned over the same time period.
Source: Bureau of Labor Statistics, Department of U.S. Labor, http://www.bls.gov/emp/ep_chart_001.htm
and Technology, Wikimedia
This graph not only shows which groups were less likely to be unemployed during the recession, but it also shows that those with a bachelor’s degree or higher made more money per week than the national average. Those with less than a bachelor’s degree made less money per week than the national average. The left side of the graph shows that those with an associate degree or higher were less likely to be unemployed than the national average, while those with less than an associate degree were more likely to be unemployed. In case you missed it, the average for all groups is shown at the bottom on each side of the graph.
Using your notes, respond to the following question:
What conclusions can we draw about the importance of education?
Sample Response:
People with more education make more money and are less likely to be unemployed than those who have less education.
### Line Graphs
Source: FoodMeat, Wikimedia
Line graphs are most often used to depict changes over time. Sometimes these graphs may look confusing, but if you take your time and read them carefully, you will find that reading line graphs is not that difficult.
The graph below illustrates changes in meat consumption in the United States from 1910 to 2008. Take your time and locate the “beef” line, the “pork” line, and the “chicken” line. Notice that the years are listed along the bottom. If you read from left to right, you can tell whether the consumption of a particular meat has risen or declined for the decades between 1910 and 2008. The graph also shows the consumption of eggs, fish and shellfish, lamb, turkey, and veal.
Source: New York Times Knowledge Repository, http://www.nytimes.com/imagepages/2011/03/15/science/15food_graphic.html
This graph shows that the consumption of chicken has risen sharply since the 1950s. On the other hand, the consumption of beef has been erratic, peaking in the late 1970s and dropping significantly in the early 1980s.
Using your notes, respond to the questions that follow. When you’re finished, check your understanding to see some possible responses.
1. What happens to pork consumption after the “The Other White Meat” ad campaign begins?
2. What happens to chicken consumption after the 1950s? Can you think of a reason for the change?
3. How would you summarize the information on the graph that compares beef, chicken, and pork over the last fifty years? | crawl-data/CC-MAIN-2019-04/segments/1547584334618.80/warc/CC-MAIN-20190123151455-20190123173455-00315.warc.gz | null |
Nanotechnology and nanomaterial are expected to be very vital in environmental protection. Not only will they save raw materials, but they will also provide clean energy and reduce hazardous waste. Using manufactured nanomaterial promises potential environmental sustainability significance. However, limited industries use this technology mostly for a subordinate role and innovative applications. Some of the potential ecological benefits of these technologies are:
Batteries are used in many IoT devices, from watches, remotes, and mobile phones. These batteries, however, pose a significant threat to not only the environment but also human health. Their primary raw materials in manufacture are heavy metals such as lead, mercury, and cadmium. Moreover, landfills of batteries also lead to loss of valuable raw materials. Researchers have identified a way to recover pure zinc oxide from disposed of batteries. The process uses manufactured nanomaterial to extract these particles. Although the process has been successful with zinc oxide, similar procedures can be used to recycle other batteries, including nickel-cadmium and lithium-ion.
Radioactive Waste and Oil Spills Clean-Up in Water
Experts are working on a solution for radioactive wastes in water using titanate nanofibers. According to the research, the nanofibers’ structure makes it possible for them to bond with radioactive components in water and remove them. The elements include Cesium and iodine ions. Oils spills can also be economically extracted from water using the same method. Traditional methods for spillage control are not suitable for massive oil spills. The process is still in a new stage, but it provides great promise for years to come. Many countries have put researchers to work on suitable ways to solve spillages, and nanotechnology might be a breakthrough.
Hydrogen Production for Green Power
Hydrogen is a clean source of energy that many companies use. However, the origins of hydrogen are potent pollutants. Hydrogen cannot be mined or trapped; it has to be industrially produced using several raw materials. Hydrogen production’s most efficient method, yet environmentally unfriendly, is the gasification of coal. A cleaner way will be electrolysis, which entails using renewable energy to split water into hydrogen and oxygen. Nanotechnology can be used to clean the materials in cases where coal is used. Moreover, on a nanoscale, inorganic light-harvesting nanocrystal can be reacted with cheap electrocatalyst with several elements to provide stable hydrogen.
Water might be the best beneficially from nanotechnology. It benefits in three major categories: pollution prevention, treatment and remediation, and sensing and detection. Remediation is the process of removing harmful materials that threaten human health and the environment at large. Manufactured nanomaterial provides a more natural and cheaper gateway to treating these areas. The procedures used are safe, including the byproducts. Desalination processes are used to remove excess sodium chloride contents in areas close to the ocean. Nanotechnology can also be used to disinfect water. The technique can create Chlorine-free biocides to kill pathogens for safe water to drink.
Researching on nanotechnology has shown a significant impact on the environment. It provides an economical way to perform specific procedures and lessen, if any, pollution after the processes. | <urn:uuid:acd00cdb-16bf-419c-a0de-939b8f44a45b> | {
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A team in China led by researchers from the University of California, Davis have discovered the first fossil of an amphibious ichthyosaur. Ichthyosaurs were dolphin-like marine reptiles that thrived for around 150 million years during the Age of the Dinosaurs. The discovery dates to the Lower Triassic period and marks the creature’s transition from land back to the sea. As the first evidence linking the marine ichthyosaur to its terrestrial ancestors it fills a significant gap in the fossil record.
The discovery of the fossil, named Cartorhynchus lenticarpus, is described in a paper recently published in the journal Nature. The fossil is about 248 million years old and measures roughly 16 inches (40 cm) long. UC Davis professor Ryosuke Motani and his colleagues discovered the specimen in China’s central-eastern Anhui Province. Unlike the later ichthyosaurs that were fully adapted to living in the sea, the fossil has unusually large flippers with flexible wrists, which could have allowed it to move around on land like a seal. Most ichthyosaurs also had long, beak-like snouts, but the new discovery shows a nose as short as that of land reptiles. It also appears adapted for suction feeding from the sea floor.
The fossil also has thicker bones than previously discovered ichthyosaurs. This is in keeping with the theory that most marine reptiles that moved back to the sea from land first became heavier by developing thicker bones, in order to swim through rough coastal waters before entering the deeper sea. Professor Motani says, “Cartorhynchus represents a stage of the land-to-sea transition that was somehow lacking in the fossil record of the ichthyosaur lineage, while known in most other marine reptile and mammal lineages.”
Motani also notes that the study’s implications go beyond evolutionary theory because the animal lived about four million years after the worst mass extinction in Earth’s history. Scientists have long wondered how long it took life on Earth to recover from the mass die-off 252 million years ago, particularly since it was associated with global warming. Montani says, “This was analogous to what might happen if the world gets warmer and warmer. How long did it take before the globe was good enough for predators like this to reappear? In that world, many things became extinct, but it started something new. These reptiles came out during this recovery.” | <urn:uuid:b04cab67-83da-4667-8c32-aa0a99c5f8a4> | {
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Union of a set
• Sep 3rd 2009, 12:51 PM
Union of a set
This is from a proof in my book:
If $A = \{ x : f(x) > 0 \}$, define $A_n = \{ x : f(x) > \frac {1}{n} \}$, then $A = \bigcup ^ \infty _ 1 A_n$
Why is this true?
• Sep 3rd 2009, 12:59 PM
siclar
Quote:
This is from a proof in my book:
If $A = \{ x : f(x) > 0 \}$, define $A_n = \{ x : f(x) > \frac {1}{n} \}$, then $A = \bigcup^\infty_1 A_n$
Why is this true?
To show set equality we just need to show inclusion, right? One inclusion is obvious:
Clearly $A_n\subseteq A$ for each $n$ so
$A \supseteq \bigcup^\infty_1 A_n$.
The other inclusion is not much harder. Let $x\in A$. Then $f(x)>0$ so by the Archimedean principle there exists an integer $M$ such that $Mf(x)>1$, and so $f(x)>\dfrac{1}{M}$ thus $x\in A_M\subseteq \bigcup^\infty_1 A_n$. Therefore $A \subseteq \bigcup^\infty_1 A_n$ and so $A = \bigcup^\infty_1 A_n$!
• Sep 3rd 2009, 01:00 PM
Plato
Quote:
If $A = \{ x : f(x) > 0 \}$, define $A_n = \{ x : f(x) > \frac {1}{n} \}$, then $A = \bigcup ^ \infty _ 1 A_n$
$a \in A\, \Rightarrow \,f(a) > 0\, \Rightarrow \,\left( {\exists n} \right)\left[ {\frac{1}{n} < f(a)} \right]\, \Rightarrow \,a \in A_n$ | crawl-data/CC-MAIN-2017-30/segments/1500549423222.65/warc/CC-MAIN-20170720141821-20170720161821-00506.warc.gz | null |
# Chapter 13 Magnetic Effects of Electric Current
## NCERT Solutions for Class 10th Science: Chapter 13 Magnetic Effects of Electric Current
Question 1:
Why does a compass needle get deflected when brought near a bar magnet?
A compass needle is a small bar magnet. When it is brought near a bar magnet, its magnetic field lines interact with that of the bar magnet. Hence, a compass needle shows a deflection when brought near the bar magnet.
Question 1:
Draw magnetic field lines around a bar magnet.
Magnetic field lines of a bar magnet emerge from the north pole and terminate at the south pole. Inside the magnet, the field lines emerge from the south pole and terminate at the north pole, as shown in the given figure.
Question 2:
List the properties of magnetic lines of force.
The properties of magnetic lines of force are as follows.
(a) Magnetic field lines emerge from the north pole.
(b) They merge at the south pole.
(c) The direction of field lines inside the magnet is from the south pole to the north pole.
(d) Magnetic lines do not intersect with each other.
Question 3:
Why don’t two magnetic lines of force intersect each other?
If two field lines of a magnet intersect, then at the point of intersection, the compass needle points in two different directions. This is not possible. Hence, two field lines do not intersect each other.
Question 1:
Consider a circular loop of wire lying in the plane of the table. Let the current pass through the loop clockwise. Apply the right-hand rule to find out the direction of the magnetic field inside and outside the loop.
Inside the loop = Pierce inside the table
Outside the loop = Appear to emerge out from the table
For downward direction of current flowing in the circular loop, the direction of magnetic field lines will be as if they are emerging from the table outside the loop and merging in the table inside the loop. Similarly, for upward direction of current flowing in the circular loop, the direction of magnetic field lines will be as if they are emerging from the table outside the loop and merging in the table inside the loop, as shown in the given figure.
Question 3:
How much energy is given to each coulomb of charge passing through a 6 V battery?
The energy given to each coulomb of charge is equal to the amount of work required to move it. The amount of work is given by the expression,
Where,
Charge = 1 C
Potential difference = 6 V
Work Done = 6×1 J = 6 J
Therefore, 6 J of energy is given to each coulomb of charge passing through a battery of 6 V.
Question 3:
Choose the correct option.
The magnetic field inside a long straight solenoid-carrying current
(a) is zero
(b) decreases as we move towards its end
(c) increases as we move towards its end
(d) is the same at all points
(d)The magnetic field inside a long, straight, current-carrying solenoid is uniform. It is the same at all points inside the solenoid.
Question 1:
Which of the following property of a proton can change while it moves freely in a magnetic field? (There may be more than one correct answer.)
(a) mass
(b) speed
(c) velocity
(d) momentum
(c) and (d)
When a proton enters in a region of magnetic field, it experiences a magnetic force. As a result of the force, the path of the proton becomes circular. Hence, its velocity and momentum change.
Question 2:
In Activity 13.7 (page: 230), how do we think the displacement of rod AB will be affected if (i) current in rod AB is increased: (ii) a stronger horse-shoe magnet is used: and (iii) length of the rod AB is increased?
A current-carrying conductor placed in a magnetic field experiences a force. The magnitude of force increases with the amount of current, strength of the magnetic field, and the length of the conductor. Hence, the magnetic force exerted on rod AB and its deflection will increase if
(i) current in rod AB is increased
(ii) a stronger horse-shoe magnet is used
(iii) length of rod AB is increased
Question 3:
A positively-charged particle (alpha-particle) projected towards west is deflected towards north by a magnetic field. The direction of magnetic field is
(a) towards south (b) towards east
(c) downward (d) upward
(d) The direction of the magnetic field can be determined by the Fleming’s left hand rule. According this rule, if we arrange the thumb, the centre finger, and the forefinger of the left hand at right angles to each other, then the thumb points towards the direction of the magnetic force, the centre finger gives the direction of current, and the forefinger points in the direction of magnetic field. Since the direction of positively charged alpha particle is towards west, the direction of current will be the same i.e., towards west. Again, the direction of magnetic force is towards north. Hence, according to Fleming’s left hand rule, the direction of magnetic field will be upwards.
Question 1:
State Fleming’s left-hand rule.
Fleming’s left hand rule states that if we arrange the thumb, the centre finger, and the forefinger of the left hand at right angles to each other, then the thumb points towards the direction of the magnetic force, the centre finger gives the direction of current, and the forefinger points in the direction of magnetic field.
Question 2:
What is the principle of an electric motor?
The working principle of an electric motor is based on the magnetic effect of current. A current-carrying loop experiences a force and rotates when placed in a magnetic field.
The direction of rotation of the loop is given by the Fleming’s left-hand rule.
Question 3:
What is the role of the split ring in an electric motor?
The split ring in the electric motor acts as a commutator. The commutator reverses the direction of current flowing through the coil after each half rotation of the coil. Due to this reversal of the current, the coil continues to rotate in the same direction.
Question 1:
Explain different ways to induce current in a coil.
The different ways to induce current in a coil are as follows:
(a) If a coil is moved rapidly between the two poles of a horse-shoe magnet, then an electric current is induced in the coil.
(b) If a magnet is moved relative to a coil, then an electric current is induced in the coil.
Question 1:
State the principle of an electric generator.
An electric generator works on the principle of electromagnetic induction. It generates electricity by rotating a coil in a magnetic field.
Question 2:
Name some sources of direct current.
Some sources of direct current are cell, DC generator, etc.
Question 3:
Which sources produce alternating current?
AC generators, power plants, etc., produce alternating current.
Question 4:
Choose the correct option.
A rectangular coil of copper wires is rotated in a magnetic field. The direction of the induced current changes once in each
(a) two revolutions (b) one revolution
(c) half revolution (d) one-fourth revolution
(c) When a rectangular coil of copper is rotated in a magnetic field, the direction of the induced current in the coil changes once in each half revolution. As a result, the direction of current in the coil remains the same.
Question 1:
Name two safety measures commonly used in electric circuits and appliances.
Two safety measures commonly used in electric circuits and appliances are as follows:
(i) Each circuit must be connected with an electric fuse. This prevents the flow of excessive current through the circuit. When the current passing through the wire exceeds the maximum limit of the fuse element, the fuse melts to stop the flow of current through that circuit, hence protecting the appliances connected to the circuit.
(ii) Earthing is a must to prevent electric shocks. Any leakage of current in an electric appliance is transferred to the ground and people using the appliance do not get the shock.
Question 2:
An electric oven of 2 kW is operated in a domestic electric circuit (220 V) that has a current rating of 5 A. What result do you expect? Explain.
Current drawn by the electric oven can be obtained by the expression,
Hence, the current drawn by the electric oven is 9.09 A, which exceeds the safe limit of the circuit. Fuse element of the electric fuse will melt and break the circuit.
Question 3:
What precaution should be taken to avoid the overloading of domestic electric circuits?
The precautions that should be taken to avoid the overloading of domestic circuits are as follows:
(a) Too many appliances should not be connected to a single socket.
(b) Too many appliances should not be used at the same time.
(c) Faulty appliances should not be connected in the circuit.
(d) Fuse should be connected in the circuit.
Question 1:
Which of the following correctly describes the magnetic field near a long straight wire?
(a) The field consists of straight lines perpendicular to the wire
(b) The field consists of straight lines parallel to the wire
(c) The field consists of radial lines originating from the wire
(d) The field consists of concentric circles centred on the wire
(d) The magnetic field lines, produced around a straight current-carrying conductor, are concentric circles. Their centres lie on the wire.
Question 2:
The phenomenon of electromagnetic induction is
(a) the process of charging a body
(b) the process of generating magnetic field due to a current passing through a coil
(c) producing induced current in a coil due to relative motion between a magnet and the coil
(d) the process of rotating a coil of an electric motor
(c) When a straight coil and a magnet are moved relative to each other, a current is induced in the coil. This phenomenon is known as electromagnetic induction.
Question 3:
The device used for producing electric current is called a
(a) generator
(b) galvanometer
(c) ammeter
(d) motor
(a) An electric generator produces electric current. It converts mechanical energy into electricity.
Question 4:
The essential difference between an AC generator and a DC generator is that
(a) AC generator has an electromagnet while a DC generator has permanent magnet.
(b) DC generator will generate a higher voltage.
(c) AC generator will generate a higher voltage.
(d) AC generator has slip rings while the DC generator has a commutator.
(d) An AC generator has two rings called slip rings. A DC generator has two half rings called commutator. This is the main difference between both the types of generators.
Question 5:
At the time of short circuit, the current in the circuit
(a) reduces substantially
(b) does not change
(c) increases heavily
(d) vary continuously
(c) When two naked wires of an electric circuit touch each other, the amount of current that is flowing in the circuit increases abruptly. This causes short-circuit.
Question 6:
State whether the following statements are true or false.
(a) An electric motor converts mechanical energy into electrical energy.
(b) An electric generator works on the principle of electromagnetic induction.
(c) The field at the centre of a long circular coil carrying current will be parallel straight lines.
(d) A wire with a green insulation is usually the live wire of an electric supply.
(a) False
An electric motor converts electrical energy into mechanical energy.
(b) True
A generator is an electric device that generates electricity by rotating a coil in a magnetic field. It works on the principle of electromagnetic induction.
(c) True
A long circular coil is a long solenoid. The magnetic field lines inside the solenoid are parallel lines.
(d) False
Live wire has red insulation cover, whereas earth wire has green insulation colour in the domestic circuits.
Question 7:
List three sources of magnetic fields.
Three sources of magnetic fields are as follows:
(a) Current-carrying conductors
(b) Permanent magnets
(c) Electromagnets
Question 8:
How does a solenoid behave like a magnet? Can you determine the north and south poles of a current-carrying solenoid with the help of a bar magnet? Explain.
A solenoid is a long coil of circular loops of insulated copper wire. Magnetic field lines are produced around the solenoid when a current is allowed to flow through it. The magnetic field produced by it is similar to the magnetic field of a bar magnet. The field lines produced in a current-carrying solenoid is shown in the following figure.
In the above figure, when the north pole of a bar magnet is brought near the end connected to the negative terminal of the battery, the solenoid repels the bar magnet. Since like poles repel each other, the end connected to the negative terminal of the battery behaves as the north pole of the solenoid and the other end behaves as a south pole. Hence, one end of the solenoid behaves as a north pole and the other end behaves as a south pole.
Question 9:
When is the force experienced by a current-carrying conductor placed in a magnetic field largest?
The force experienced by a current-currying conductor is the maximum when the direction of current is perpendicular to the direction of the magnetic field.
Question 10:
Imagine that you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally from back wall towards the front wall, is deflected by a strong magnetic field to your right side. What is the direction of magnetic field?
The direction of magnetic field is given by Fleming’s left hand rule. Magnetic field inside the chamber will be perpendicular to the direction of current (opposite to the direction of electron) and direction of deflection/force i.e., either upward or downward. The direction of current is from the front wall to the back wall because negatively charged electrons are moving from back wall to the front wall. The direction of magnetic force is rightward.
Hence, using Fleming’s left hand rule, it can be concluded that the direction of magnetic field inside the chamber is downward.
Question 11:
Draw a labelled diagram of an electric motor. Explain its principle and working. What is the function of a split ring in an electric motor?
An electric motor converts electrical energy into mechanical energy. It works on the principle of the magnetic effect of current. A current-carrying coil rotates in a magnetic field. The following figure shows a simple electric motor.
When a current is allowed to flow through the coil MNST by closing the switch, the coil starts rotating anti-clockwise. This happens because a downward force acts on length MN and at the same time, an upward force acts on length ST. As a result, the coil rotates anti-clockwise.
Current in the length MN flows from M to N and the magnetic field acts from left to right, normal to length MN. Therefore, according to Fleming’s left hand rule, a downward force acts on the length MN. Similarly, current in the length ST flows from S to T and the magnetic field acts from left to right, normal to the flow of current. Therefore, an upward force acts on the length ST. These two forces cause the coil to rotate anti-clockwise.
After half a rotation, the position of MN and ST interchange. The half-ring D comes in contact with brush A and half-ring C comes in contact with brush B. Hence, the direction of current in the coil MNST gets reversed.
The current flows through the coil in the direction TSNM. The reversal of current through the coil MNST repeats after each half rotation. As a result, the coil rotates unidirectional.
The split rings help to reverse the direction of current in the circuit. These are called the commutator.
Question 12:
Name some devices in which electric motors are used?
Some devices in which electric motors are used are as follows:
(a) Water pumps
(b) Electric fans
(c) Electric mixers
(d) Washing machines
Question 13:
A coil of insulated copper wire is connected to a galvanometer. What will happen if a bar
magnet is (i) pushed into the coil, (ii) withdrawn from inside the coil, (iii) held stationary
inside the coil?
A current induces in a solenoid if a bar magnet is moved relative to it. This is the principle of electromagnetic induction.
(i) When a bar magnet is pushed into a coil of insulated copper wire, a current is induced momentarily in the coil. As a result, the needle of the galvanometer deflects momentarily in a particular direction.
(ii) When the bar magnet is withdrawn from inside the coil of the insulated copper wire, a current is again induced momentarily in the coil in the opposite direction. As a result, the needle of the galvanometer deflects momentarily in the opposite direction.
(iii) When a bar magnet is held stationary inside the coil, no current will be induced in the coil. Hence, galvanometer will show no deflection.
Question 14:
Two circular coils A and B are placed closed to each other. If the current in the coil A is changed, will some current be induced in the coil B? Give reason.
Two circular coils A and B are placed close to each other. When the current in coil A is changed, the magnetic field associated with it also changes. As a result, the magnetic field around coil B also changes. This change in magnetic field lines around coil B induces an electric current in it. This is called electromagnetic induction.
Question 15:
State the rule to determine the direction of a (i) magnetic field produced around a straight conductor-carrying current, (ii) force experienced by a current-carrying straight conductor placed in a magnetic field which is perpendicular to it, and (iii) current induced in a coil due to its rotation in a magnetic field.
(i) Maxwell’s right hand thumb rule
(ii) Fleming’s left hand rule
(iii) Fleming’s right hand rule
Question 16:
Explain the underlying principle and working of an electric generator by drawing a labelled diagram. What is the function of brushes?
An electric generator converts mechanical energy into electrical energy.
The principle of working of an electric generator is that when a loop is moved in a magnetic field, an electric current is induced in the coil. It generates electricity by rotating a coil in a magnetic field. The following figure shows a simple AC generator.
MNST → Rectangular coil
A and B → Brushes
C and D → Two slip rings
X → Axle, G → Galvanometer
If axle Xis rotated clockwise, then the length MN moves upwards while length ST moves downwards. Since the lengths MN and ST are moving in a magnetic field, a current will be induced in both of them due to electromagnetic induction. Length MN is moving upwards and the magnetic field acts from left to right. Hence, according to Fleming’s right hand rule, the direction of induced current will be from M to N. Similarly, the direction of induced current in the length ST will be from S to T.
The direction of current in the coil is MNST. Hence, the galvanometer shows a deflection in a particular direction. After half a rotation, length MN starts moving down whereas length ST starts moving upward. The direction of the induced current in the coil gets reversed as TSNM. As the direction of current gets reversed after each half rotation, the produced current is called an alternating current (AC).
To get a unidirectional current, instead of two slip rings, two split rings are used, as shown in the following figure.
In this arrangement, brush A always remains in contact with the length of the coil that is moving up whereas brush B always remains in contact with the length that is moving down. The split rings C and D act as a commutator.
The direction of current induced in the coil will be MNST for the first rotation and TSNM in the second half of the rotation. Hence, a unidirectional current is produced from the generator called DC generator. The current is called AC current.
Question 17:
When does an electric short circuit occur?
If the resistance of an electric circuit becomes very low, then the current flowing through the circuit becomes very high. This is caused by connecting too many appliances to a single socket or connecting high power rating appliances to the light circuits. This results in a short circuit.
When the insulation of live and neutral wires undergoes wear and tear and then touches each other, the current flowing in the circuit increases abruptly. Hence, a short circuit occurs.
Question 18:
What is the function of an earth wire? Why is it necessary to earth metallic appliances? | crawl-data/CC-MAIN-2017-34/segments/1502886103910.54/warc/CC-MAIN-20170817185948-20170817205948-00674.warc.gz | null |
A safe and supportive learning environment can improve student attendance and achievement—including rates of high school graduation—for students in both community schools and juvenile justice facilities. Such environments and appropriate discipline policies also can assist in reducing juvenile justice system involvement. The pages throughout offer resources to help providers improve learning environments through discipline, behavior and classroom management, student engagement, and school safety.
NDTAC Brief: Improving Conditions for Learning for Youth Who Are Neglected or Delinquent
Learning is not just a cognitive process; research shows that powerful social and emotional factors affect learning. By providing students with support that addresses these needs and building positive social and emotional conditions for learning, staff in facilities and schools can help improve learning outcomes that cannot be addressed through academic remediation alone. | <urn:uuid:60b4faa7-822d-4c0c-853a-88763ed75b00> | {
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# roots of polynomial equations (complex #s)
• May 6th 2008, 08:07 PM
phthiriasis
roots of polynomial equations (complex #s)
so im just starting to learn about roots of polynomial equations with roots that are complex numbers and i dont understand them at all.. i hope you can help
A. Use the quadratic formula to find the roots of the equation x^2+4x+5=0. Simplify and compare the roots. what do you notice?
B. write a quadratic equation with integral coefficients such that one of its roots is 4-5i
C. Write a quartic equation with integral coefficients and with roots 7i and -3i
.....
so for A i think its x= -2+i and x=-2-i but i dont "notice" anything and have no idea how to do the other questions.
im thinking its something simple and im going to feel stupid once i find out the answer -.-
• May 6th 2008, 08:23 PM
Solan
The roots are conjugate pairs
• May 6th 2008, 08:25 PM
TheEmptySet
Quote:
Originally Posted by phthiriasis
so im just starting to learn about roots of polynomial equations with roots that are complex numbers and i dont understand them at all.. i hope you can help
A. Use the quadratic formula to find the roots of the equation x^2+4x+5=0. Simplify and compare the roots. what do you notice?
B. write a quadratic equation with integral coefficients such that one of its roots is 4-5i
C. Write a quartic equation with integral coefficients and with roots 7i and -3i
.....
so for A i get x= -2+i and x=-2-i but i dont "notice" anything and have no idea how to do the other questions.
im thinking its something simple and im going to feel stupid once i find out the answer -.-
What they wanted you to notice is that $-2+i \mbox{ and } -2-i$
are conjugates two complex numbers are conjugate if
$a+bi \mbox{ and } a-bi$ the numbers are the same, but the immaginary parts have opposite signs.
Now with this new knowlege(Wink)
we can find the roots of the other quadratic.
since we know that 4-5i is a root then 4+5i must also be a root.
If c is a root of a polynomial then x-c is a facor of the polynomial
now comes the fun part
We multiply out our two factors.
$[x-(4-5i)][x-(4+5i)]=x^2-(4+5i)x-(4-5i)x+(4-5i)(4+5i)=$
$x^2-4x-5ix-4x+5ix+16+20i-20i-25i^2=x^2-8x+16-25(-1)=$
$x^2-8x+41$
I hope this helps
see what you can do with the next one.
(Rock)
• May 6th 2008, 08:48 PM
phthiriasis
thanks a lot TheEmptySet
so i tried the next one..
since 7i and -3i are roots the other roots are -7i and 3i
so i multiplied it all out..
(x-7i)(x+7i)(x-3i)(x+3i) and ended up with
x^4+58x^2+441
is this right?^^
thanks again! | crawl-data/CC-MAIN-2018-05/segments/1516084891705.93/warc/CC-MAIN-20180123012644-20180123032644-00650.warc.gz | null |
Location and General Description
There are five inhabited islands in the Tubuai group: Rimatara, Rurutu, Tubuai, Raivavae, and Rapa. The largest is Tubuai, with an area of 44 km2. The chain also includes an uninhabited island group, Ilots de Bass (Marotiri), and an uninhabited atoll named Maria.
The islands are the expression of a geologic hot spot track and are similar in ages and rock composition to the Hawaiian Islands. The islands at the southeastern end are the youngest, and have highly dissected volcanic summits. The islands to the northwest become progressively older, more weathered, and eroded. In areas where uplift has occurred, the flanks of the islands are covered by coral limestone. Uninhabited Marotiri, the youngest island located at the southeastern end of the chain, has been eroded or has subsided almost to a high point of approximately 100 m. It is steep-sided and rugged, with no flat land or adjacent reefs (Mueller-Dombois & Fosberg 1998).
Next in line is Rapa Island, an ancient volcanic caldera open on the east side that rises to an elevation of 633 m. The deep bays and drowned valleys of the island suggest that it has subsided, possibly because of post-Pleistocene sea level rise. The lower interior slopes of the caldera have outcrops of lignite, a low grade coal, which suggests a long history of floral growth on the island. Rapa is one of only two oceanic Pacific Islands to have coal deposits, the other being Babeldaob in Palau. The flora of this island shows some relationship to that of New Zealand, and includes the genera Hebe, Olearia, Haloragis, and Corokia. There are many endemic species, and some strictly Pacific genera such as Fitchia, Bidens, and Sclerotheca (Mueller-Dombois & Fosberg 1998).
The vegetation on Rapa has been highly disturbed by anthropogenic activities, including the introduction of goats. Of the remaining native vegetation, the dominant type is a moist to wet broadleaf evergreen forest that is remarkably rich in species considering the small size of the island. This forest hosts numerous ephiphytes, and there is a rich fern flora, including Marattia and Angiopteris, in the understory. Scrub forests of Metrosideros collina are found on high crests and ridges with associated tree species and numerous epiphytic bryophytes and ferns (Mueller-Dombois & Fosberg 1998).
The volcanic peaks of Raivavae, located 600 km north of Rapa, are strongly dissected and the topography is rugged, rising to a maximum elevation of 437 meters. The flanks of the island include some areas of elevated reef limestone, and there is a surrounding barrier reef. The vegetation includes lowland and montane rain forest, with several important endemic plant species (Dahl, 1986).
Tubuai Island is characterized by two mountain masses that rise to elevations of more than 400 meters. These mountains are surrounded by a raised coral limestone platform which extends across the island and between the two ranges. Patches of native forest remain around the higher peaks, and are characterized by Metrosideros, Aleurites, Celastrus vitiensis, Myrsine, Ixora, Psychotria, Cantium barbatum, and Charpentiera. There are also the large ferns Cyanthea and Angiopteris and many smaller species. Ferns are the dominant flora in some areas. About 150 species of flowering plants have been documented on Tubuai (IUCN, 1993).
Rurutu Island is surrounded by an almost continuous limestone rim 50 to 60 meters high in elevation. This rim surrounds the inner volcanic hills which have elevations of up to 400 meters and are mantled with a red clay soil. The hills are cut by several ravines containing small streams that shelter scattered remnants of limestone forest (Mueller-Dombois & Fosberg 1998).
Rimatara Island is also surrounded by a limestone rim, but the central peak is topographically lower and more weathered. The low hills of the interior are cut by small streams. Patches of marshy ground have developed in the flat land between the hills and on the surrounding limestone rim. Endemism rates are more than 20 percent among the native plants on Rimatara (IUCN 1993, Mueller-Dombois & Fosberg 1998).
Maria is a small coral atoll with four islets, and is the oldest island of the Tubuai group. The islets support a dense atoll forest with nearly original vegetation (Mueller-Dombois & Fosberg 1998).
Several islands still have remnants of native montane rain forests with Metrosideros, Weinmannia, Celtis, Myoporum, Elaeocarpus, Psychotria, and Myrsine. Also, tall ferns such as Cythea, Angiopteris, and Marattia remain.
Invertebrates of conservation interest include Endontidae and two Partiluidae, which have been threatened by catastrophic snail extinctions (IUCN 1993).
The Austral Islands harbor a few endemic bird species. The Endangered Kuhl’s lorikeet (Vini kuhli) is found on 4 islands in the Pacific, but is considered to be native to the Australs. It is now found on Rimatara but was apparently once found on Rurutu. The bird is also found on three islands in Kiribati. The Rimatara reed-warbler (Acrocephallus rimatarae) is strictly endemic to Rimatara. It is common and widespread on the island, but is considered Vulnerable due to the small size of the island (Stattersfield et al. 1998, Birdlife International 2000).
Rapa Island harbors the Vulnerable Rapa fruit-dove (Ptilonopus huttoni), which is confined to 3km2 mid- to high elevation forest fragments. While it has a small population and its habitat has diminished, there has been no ‘serious’ decline since 1974 (Staattersfield et al. 1998, Birdlife International 2000).
The lowlands of the Tubuai Islands are more open than the higher island interiors, and are strongly altered by cultivation, anthropogenic fires, and uncontrolled grazing. Low elevations on the main high islands consists of secondary thickets of Hibiscus tiliaceus and orange trees, Psidium guajava, or Dicranopteris fernlands and grasslands, with some scattered secondary ravine forests. In fact, with the exception of remote Maria Atoll, the vegetation of the islands is considered ‘profoundly altered.
Types and Severity of Threats
The remaining indigenous vegetation on Tubuai is threatened by clearing and burning of forests for agricultural development, as well as by the development of an airport and hotels for the tourism industry. Remaining forest areas are in need of protection and extension. On many of the islands, there is a serious problem with feral goats, pigs, cattle, and horses (Mueller-Dombois & Fosberg 1998, Birdlife International 2000).
Norway rats (Rattus norvegicus) are considered the key threat to remaining populations of Kuhl’s lorikeet on Rimatara – thus far none of the more dangerous black rats (Rattus rattus) have been detected (Birdlife International 2000).
Justification of Ecoregion Delineation
This ecoregion includes the Austral Islands group stretching from Illes Maria to Rapa and Marotiri. Van Balgooy et al. (1996) lump the Cooks, Niue, Societies, Tuamotus, Tubaui, and Marquesas based on floristic affinities. However, Birdlife International (Stattersfield et al. 1998) separate two distinctive areas in the Austral Islands (Tubaui). This includes the island of Rimatara Endemic Bird Area, with 2 endemic bird species, and the Rapa Island Secondary Endemic Bird Area, with its one endemic fruit dove. On the basis of these three endemic bird species, we have separated out the Tubuai Islands as a distinct ecoregion.
Birdlife International. 2000. Threatened birds of the world. Lynx Edicions, Cambridge & Barcelona.
Cahiers de L’Indo-Pacifique. Tubuai. 1980. Direction des Centres D’Experimentations Nucleaires, Service Mixte de Controle Biologique. Paris.
Dahl, A.L. 1986. Review of the protected areas system in Oceania. International Union for Conservation of Nature and Natural Resources, Commission on National Parks and Protected Areas, in collaboration with the United Nations Environment Programme.
Mueller-Dombois, D. and F.R. Fosberg. 1998. Vegetation of the tropical Pacific islands. Springer-Verlag, New York.
Stattersfield, A, M.J. Crosby, A.J. Long, and D.C. Wege. 1998. Endemic Bird Areas of the World, Priorities for Biodiversity Conservation. Birdlife International, Cambridge, UK.
Van Balgooy, P.H. Hovenkamp, and P.C. Van Welzen. 1996. Phytogeography of the Pacific – floristic and historical distribution patterns in plants. Pages 191-213 in Keast, A. and S.E. Miller, editors. The origin and evolution of Pacific island biotas, New Guinea to Eastern Polynesia: Patterns and processes. SPB Academic Publishing, Amsterdam.
Prepared by: Sandra Zicus
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Build-A-Body Assessment Tips
You can use the Build-A-Body: Digestive System simulation as both a pre- and post-assessment tool. Have students explore the simulation prior to your unit of instruction on the digestive system to build background knowledge. You can then project the simulation for the class to see during your instruction to illustrate your points and help students recall what they have learned. When your unit is finished, have students complete the simulation independently. You can evaluate the results in conjunction with students’ scores on the game quiz. | <urn:uuid:2c81b29b-ee37-456f-8456-0c7e91fb7347> | {
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A composer is someone who writes (composes) music. Some composers work by writing music down on paper; this is called 'written notation'. Classical music writers work this way. Writers for TV and movie music also usually write this way, so that an orchestra or other players can read the music and play it.
Some musicians are very good at improvisation. This means that they think up (invent) the music as they play it. Some church organists are good at improvising. During a service they may need to play some organ music to fill in the gaps while people are collecting money or taking communion. Jazz musicians are usually excellent at improvising. Improvisation is not written down, so each time it is different.
Popular and rock or soul music writers are often not able to read and write music down. Many pop and rock composers compose their songs on a guitar or piano. Cole Porter and Irving Berlin usually composed at the piano.
Many songs are written by two or more people. It is common for two people to work together to write songs. Sometimes, one person writes the music and one writes the words (the lyrics). Some songs such as folk songs were composed many years ago and no one knows who wrote them.
Related pages[change | change source] | <urn:uuid:3565a10a-8b4a-4bd4-a36a-5cb704f9449f> | {
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In undergraduate physics, the ideal gas model is usually the end of the line when it comes to discussing the properties of real gases. But in fact – as is often the case with people – it is only when we consider deviations from ideal behaviour that things get really interesting.
The ideal gas model is exactly applicable to real gases in the limit of low density, but that is rarely where we need to understand the properties of gases in detail. The defining equation of the ideal gas is:
PV = nRT (1)
where P is the pressure in pascals; V is the volume in m3; n is the number of moles of gas under consideration; T is the temperature in kelvin and R is the molar gas constant. Another,slightly more meaningful, way to write this is:
P = ρRT (2)
where ρ is the molar density (mol/m3).
[Aside: Just in case you are interested, and most people aren’t, in 2013 I published the most accurate measurement of R ever made!]
The mathematical derivation of this equation is covered in Chapter 4 of Understanding the Properties of Matter. In this article I just wanted to cover asome of the ideas which are passed over quickly at the end of that Chapter.
At room temperature and atmospheric pressure the typical density of gases is P/RT which evaluates to 100000/(8.31 x 293) ≈ 41 mol/m3. And as we saw in Chapter 5, this is correct to within typically 1%.
You might think that is good enough for most purposes, and indeed it is. So why bother going further? The reason is that if these small deviations from ‘ideal’ behaviour can be measured they give clues about the way the gas molecules interact that simply cannot be obtained in any other way.
So it turns out that by making precision measurements of a ‘mundane’ property of real gas such as its density, speed of sound, or thermal conductivity, we can infer details the way in which the molecules interact! And that makes almost every property of a gas interesting when one looks at it detail.
But after the precision measurements have been made, we need some idea of what factors might have been neglected in the ideal gas model that might explain the deviations from the simple theory.
The two most important of the ‘neglected details’ turn out to be the finite size of the molecules and their mutual interactions. These can be taken account of in two wuite different ways
In the first way – the subject of the next article – we follow the astonishing Johannes Diderik van der Waals. In the second and much more general way, we discuss the so called ‘Virial’ approach. | <urn:uuid:45ac8bd0-2cd4-416a-a3dc-151e3c55317c> | {
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## 1 Capacitor overview
### 1.1 What is capacitance
What is capacitor? Before explaining this question to you,let’s first understand the capacitance.As the name suggests, it is the ability to store electricity. The university physics book says that “for any ‘isolated’ conductor that is not affected by the outside world, when the conductor is charged, the ratio of the charge q carried by the conductor to the corresponding potential U is C. This ratio C is a physical quantity that has nothing to do with the charge carried by the conductor , known as the “capacitance of the ‘isolated’ conductor” that is
C=q/U
The capacitance characteristic of a conductor is a unique property of a conductor, which is equal in magnitude to the electric charge carried by the conductor when the potential of the conductor is one unit.
In the International System of Units, the unit of capacitance is farad(F). If the electric charge carried by the conductor is 1 coulomb(C), and the corresponding potential is 1 volt (V), the capacitance of the conductor is 1 farad, which can be represented by the capital letter F. If you feel that the unit of farad is too large, you can also express it in smaller units such as mF, uF, nF, pF, etc. Their relationship is as follows
1F=1000mF=106uF=109nF=1012pF (1.2)
1mF=103uF=106nF=109pF=10-3F (1.3)
1uF=103nF=106pF=10-3mF=10-6F (1.4)
1nF=103pF=10-3uF=10-6mF=10-9F (1.5)
### 1.2 What is capacitor
What is capacitor? As the name suggests, it is a device that holds charges. When there are other objects around the conductor, the capacitance of the conductor will be affected. Therefore, it is necessary to design a conductor combination with a large capacitance value and a geometric size as small as possible without being affected by other objects. Such a combination of conductors is a capacitor. The concept of a capacitor in physics can be expressed as: “a conductor system composed of two conductors when there are no other charged conductors around it.” The capacitance (or capacitance) of a capacitor is defined as: when the two plates of the capacitor have the same electric charge q, the ratio of the electric charge q to the corresponding potential difference UA-UB between the two plates, that is
C=q/UA-UB (1.6)
An isolated conductor can actually still be considered a capacitor, except that the other conductor is at infinity and has zero potential. Formula (1.6) becomes formula (1.1). Therefore, it can be seen that the capacitance of the so-called “isolated conductor” is actually the capacitance between two conductors. Unlike ordinary capacitance, the other conductor is only at infinity. But capacitance is a characteristic between conductors after all. Conductor capacitance is virtually non-existent. | crawl-data/CC-MAIN-2024-22/segments/1715971058560.36/warc/CC-MAIN-20240522163251-20240522193251-00158.warc.gz | null |
I had about five minutes before I was set to deliver a talk to a bunch of business owners about visibility and being on camera. After all, I was the so-called expert there, the former 20-year television news anchor and life and business coach. I happened to take a look down at my cell phone just to catch the time, and I noticed that I had a missed call from my ex-husband. I can still hear his voice. "Darieth, what is going on? I just got a call from some strange man who told me to go to this website, and now I'm looking at all of these photos of you naked. Your private parts are all over this website. Who's seen this?" I couldn't think. I couldn't breathe. I was so humiliated and so embarrassed and so ashamed. I felt like my world was coming to an end. And yet, this began for me months of pain and depression and anger and confusion and silence. My manipulative, jealous, stalker ex-boyfriend did exactly what he said he would do: he put up a website with my name on it, and he posted this. And this. And several explicit photos that he had taken of me while I was asleep, living with him in Jamaica. For months prior to that, he had been sending me threatening text messages like this. He was trying to make me out to be some sleazy, low-life slut. He had even threatened to kill me. He told me that he would shoot me in my head and stab me in my heart, simply because I wanted to end the controlling relationship. I couldn't believe this was happening to me. I didn't even know what to call it. You might know it as cyberharassment or cyberbullying. The media calls it "revenge porn." I now call it "digital domestic violence." It typically stems from a relationship gone bad, where a controlling, jilted ex-lover can't handle rejection, so when they can't physically put their hands on you, they use different weapons: cell phones and laptops. The ammunition? Photos, videos, explicit information, content — all posted online, without your consent. I mean, let's face it — we all live our lives online. And the internet is a really small world. We show off our baby photos, we start and grow our businesses, we make new relationships, we let the world in, one Facebook like at a time. And you know what I found? An even smaller world. One in 25 women say they have been impacted by revenge porn. For women under the age of 30, that number looks like one in 10. And that leaves a few of you in this audience as potential victims. You want to know what's even more alarming? Lack of legislation and laws to adequately protect victims and punish perpetrators. There's only one federal bill pending; it's called the ENOUGH Act, by Senator Kamala Harris. It would criminalize revenge porn. But that could take years to pass. So what are we left with in the meantime? Flimsy civil misdemeanors. Currently, only 40 states and DC have some laws in place for revenge porn. And those penalties vary — we're talking $500 fines. Five hundred dollars? Are you kidding me? Women are losing their jobs. They're suffering from damaged relationships and damaged reputations. They're falling into illness and depression. And the suicide rates are climbing. You're looking at a woman who spent 11 months in court, thirteen trips to the courthouse and thousands of dollars in legal fees, just to get two things: a protection from cyberstalking and cyberabuse, otherwise known as a PFA, and language from a judge that would force a third-party internet company to remove the content. It's expensive, complicated and confusing. And worse, legal loopholes and jurisdictional issues drag this out for months, while my private parts were on display for months. How would you feel if your naked body was exposed for the world to see, and you waited helplessly for the content to be removed? Eventually, I stumbled upon a private company to issue a DMCA notice to shut the website down. DMCA — Digital Millennium Copyright Act. It's a law that regulates digital material and content. Broadly, the aim of the DMCA is to protect both copyright owners and consumers. So get this: people who take and share nude photos own the rights to those selfies, so they should be able to issue a DMCA to have the content removed. But not so fast — because the other fight we're dealing with is noncompliant and nonresponsive third-party internet companies. And oh — by the way, even in consenting relationships, just because you get a nude photo or a naked pic, does not give you the right to share it, even [without] the intent to do harm. Back to my case, which happens to be further complicated because he was stalking and harassing me from another country, making it nearly impossible to get help here. But wait a minute — isn't the internet international? Shouldn't we have some sort of policy in place that broadly protects us, regardless to borders or restrictions? I just couldn’t give up; I had to keep fighting. So I willingly, on three occasions, allowed for the invasion of both my cell phone and my laptop by the Department of Homeland Security and the Jamaican Embassy for thorough forensic investigation, because I had maintained all of the evidence. I painstakingly shared my private parts with the all-male investigative team. And it was an embarrassing, humiliating additional hoop to jump through. But then something happened. Jamaican authorities actually arrested him. He's now facing charges under their malicious communications act, and if found guilty, could face thousands of dollars in fines and up to 10 years in prison. And I've also learned that my case is making history — it is the first international case under this new crime. Wow, finally some justice. But this got me to thinking. Nobody deserves this. Nobody deserves this level of humiliation and having to jump through all of these hoops. Our cyber civil rights are at stake. Here in the United States, we need to have clear, tough enforcement; we need to demand the accountability and responsiveness from online companies; we need to promote social responsibilities for posting, sharing and texting; and we need to restore dignity to victims. And what about victims who neither have the time, money or resources to wage war, who are left disempowered, mislabeled and broken? Two things: release the shame and end the silence. Shame is at the core of all of this. And for every silent prisoner of shame, it's the fear of judgment that's holding you hostage. And the price to pay is the stripping away of your self-worth. The day I ended my silence, I freed myself from shame. And I freed myself from the fear of judgment from the one person who I thought would judge me the most — my son, who actually told me, "Mom, you are the strongest person that I know. You can get through this. And besides, mom — he chose the wrong woman to mess with." (Laughter) (Applause) It was on that day that I decided to use my platform and my story and my voice. And to get started, I asked myself this one simple question: Who do I need to become now? That question, in the face of everything that I was challenged with, transformed my life and had me thinking about all kinds of possibilities. I now own my story, I speak my truth, and I'm narrating a new chapter in my life. It's called "50 Shades of Silence." It's a global social justice project, and we're working to film an upcoming documentary to give voice and dignity to victims. If you are a victim or you know someone who is, know this: in order to be empowered, you have to take care of yourself, and you have to love yourself. You have to turn your anger into action, your pain into power and your setback into a setup for what's next for your life. This is a process, and it's a journey of self-discovery that might include forgiveness. But it definitely requires bravery, confidence and conviction. I call it: finding your everyday courage. Thank you. (Applause) | How revenge porn turns lives upside down | null |
# ‘KEY 528’ and mi LIFE PATH NUMBER
Originally Posted by wiz-oz
Like take your birthday to work a life path number and punch it into a calculator and divide by 9 the first number after the decimal place is the reduced number, except when it’s zero in which case it’s a 9.
eg 23/05/2008 would add to 20 or 2 in a calculator 23,052,008/9 = 4.222 any string of numbers will work, try it!
you won’t find this in any math book
Thank you for sharing wiz.
I just want to confirm a successful result re: the life path number = birthday formula.
The following is far more than just coincidental.
My birthday is July 3rd, 1957 similar to Tom Cruise, same day but Tom Cruise was born in 1962.
So according to your Life Path formula I would key in day/month/year and then divide by 9.
3071957/9 = 341328.555555…..to infinity
I can’t help notice the numbers 28.5
I have written a few blogs about 528.
Is that what you mean about finding your life path wiz, through numbers that make you numb with an awakening but not dumb?
Numbers that can help define you, and get this…they can help you zero in on your life purpose, assist you in finding your path too?
That was a cool acknowledgment wiz.
WOW I just noticed more ‘coincidences’.
My journey has been a fourfold exploration of archetype these past 4+ years.
Starting with the number 4.
Which lead me to 4 specific numbers 11, 2, 5, 8 found on this Card X, the Wheel of Fortune.
## 11, 2, 5, 8
Back to the life path formula.
My birthday 3/07/1957 converts to 3071957/9 (divide by 9) = 341328.55555555 ….. to infinity
Take the first 4 numbers from the result and add them together.
3 + 4 + 1 + 3 = 11
11 … followed by 285 followed by an infinite string of 5s
LIFE PATH number = 11285
11285 anticipates Card X being associated with my life path.
Would you believe me if I told you I am tingling just a little right now?
Find out your life path number(s).
I am proof of its validity, that there is something to it.
IMHO
namaste
Raphael
## 8 thoughts on “‘KEY 528’ and mi LIFE PATH NUMBER”
1. Jim says:
hey im having trouble understanding this… i put my birthday and i came out with a perfect number whats next?
2. mind if I see the ‘formula’ of your birthday?
if you mean that your number was 1234.00000?
then .00000 = .999999
sorry I didn’t mention that.
namaste
3. Jim says:
thnx for the response my bday is 11/16/1989
4. Jim I see your script looking something like this….
1240221.0 = 1240221.9
though 9 is the main number … the image is 124O221
🙂
namaste
5. Zephyr1369 says:
Love your blog, I get it (i do)!
my birthday is August, 6, 1977
life path 11
Truly,
Z*
6. monique says:
Here is mine
800,219.11111111
20.11111111
8 1s.
2.8
Where’s my 5 lol?
Monique
• as soon as somebody sits down, you will get your dues
… and don’ts | crawl-data/CC-MAIN-2018-30/segments/1531676589752.56/warc/CC-MAIN-20180717144908-20180717164908-00471.warc.gz | null |
### The marked price of a radio is 20% more than its cost price. If a discount of 10% is given on the marked price, the gain per cent is:
A. 15 B. 12 C. 10 D. 8 Answer: Option D
### Solution(By Apex Team)
Let CP = 100 Then, MP = 100 + 20% of 100 = 120 Now, SP = 120 – 10% of 120 = 108 Gain = 108 – 100 = 8 %Gain $\Large=\frac{8 \times 100}{100}$ = 8% Short-cut 100(CP) == 20%(up) ⇒ 120(MP) == 10%(disc.) ⇒ 108 % gain = 8%
## Related Questions on Profit and Loss
A. 45 : 56
B. 45 : 51
C. 47 : 56
D. 47 : 51
A. Rs. 2600
B. Rs. 2700
C. Rs. 2800
D. Rs. 3000
### A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:
A. A neither losses nor gains
B. A makes a profit of 11%
C. A makes a profit of 20%
D. B loses 20% | crawl-data/CC-MAIN-2022-21/segments/1652663021405.92/warc/CC-MAIN-20220528220030-20220529010030-00226.warc.gz | null |
Confusing Words in English Language. Free Reading..
Ideas To Improve Student Motivation
Simple Ideas To Improve Student Motivation. by TeachThought Staff.
1. Give students a sense of control
While guidance from a teacher is important to keeping kids on task and motivated, allowing students to have some choice and control over what happens in the classroom is actually one of the best ways to keep them engaged. For example, allowing students to choose the type of assignment they do or which problems to work on can give them a sense of control that may just motivate them to do more.
2. Define the objectives
It can be very frustrating for students to complete an assignment or even to behave in class if there aren t clearly defined objectives. Students want and need to know what is expected of them in order to stay motivated to work. At the beginning of the year, lay out clear objectives, rules, and expectations of students so that there is no confusion and students have goals to work towards.
3. Create a threat free environment
While students do need to understand that there are consequences to their actions, far more motivating for students than threats are positive reinforcements. When teachers create a safe, supportive environment for students, affirming their belief in a student s abilities rather than laying out the consequences of not doing things, students are much more likely to get and stay motivated to do their work. At the end of the day, students will fulfill the expectations that the adults around them communicate, so focus on can, not can t.
4. Change your scenery
A classroom is a great place for learning, but sitting at a desk day in and day out can make school start to seem a bit dull for some students. To renew interest in the subject matter or just in learning in general, give your students a chance to get out of the classroom. Take field trips, bring in speakers, or even just head to the library for some research. The brain loves novelty and a new setting can be just what some students need to stay motivated to learn.
5. Offer varied experiences
Not all students will respond to lessons in the same way. For some, hands on experiences may be the best. Others may love to read books quietly or to work in groups. In order to keep all students motivated, mix up your lessons so that students with different preferences will each get time focused on the things they like best. Doing so will help students stay engaged and pay attention.
6. Use positive competition
Competition in the classroom isn t always a bad thing, and in some cases can motivate students to try harder and work to excel. Work to foster a friendly spirit of competition in your classroom, perhaps through group games related to the material or other opportunities for students to show off their knowledge.
7. Offer rewards
Everyone likes getting rewards, and offering your students the chance to earn them is an excellent source of motivation. Things like pizza parties, watching movies, or even something as simple as a sticker on a paper can make students work harder and really aim to achieve. Consider the personalities and needs of your students to determine appropriate rewards for your class.
8. Give students responsibility
Assigning students classroom jobs is a great way to build a community and to give students a sense of motivation. Most students will see classroom jobs as a privilege rather than a burden and will work hard to ensure that they, and other students, are meeting expectations. It can also be useful to allow students to take turns leading activities or helping out so that each feels important and valued.
9. Allow students to work together
While not all students will jump at the chance to work in groups, many will find it fun to try to solve problems, do experiments, and work on projects with other students. The social interaction can get them excited about things in the classroom and students can motivate one another to reach a goal. Teachers need to ensure that groups are balanced and fair, however, so that some students aren t doing more work than others.
10. Give praise when earned
There is no other form of motivation that works quite as well as encouragement. Even as adults we crave recognition and praise, and students at any age are no exception. Teachers can give students a bounty of motivation by rewarding success publicly, giving praise for a job well done, and sharing exemplary work.
Test your English Language
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Benefits of Passion fruits | <urn:uuid:a5c7ab24-99ac-439b-b4fe-4a36d3679ef4> | {
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```Partial Solutions for Appendix G
Michael Roy
2257&itemId=0471472441&resourceId=8026
p
5. Plug in to our formulas for distance and midpoints: d = (−2 − (−7))2 + (−6 − (−4))2 =
√
29. Midpoint = ( −2+(−7)
, −6+(−4)
) = ( −9
2
2
2 , −5).
9. Use the distance formula
to show that the distance from each of the three
√
each is the same distance from the center,
listed points to (−2, 3) is 29. Since√
they all lie on the circle with radius 29.
23. Answers can be read off using the general equation for a circle. Note
that the first part, x2 + y 2 = 25 is equivalent to (x − 0)2 + (y − 0)2 = 25 Thus the
centers in (a) through (d) are (0, 0), (1, 4), (−1,
√ −3) (note these are negative),
and (0, −2). The corresponding radii are 5, 4, 5, and 1.
25. Plug in to our equation for a circle: (x − 3)2 + (y − (−2))2 = 42 , which
simplifies to (x − 3)2 + (y + 2)2 = 16.
33. Using algebra to complete the square, this simplifies to (x − 1)2 + (y −
2)2 = 4. 4 > 0, so this represents a circle with center (1, 2) and radius 2. If
you don’t recall how to complete the square, don’t worry about it: it probably won’t come up again. If you’re curious check http://en.wikipedia.org/
wiki/Complete_the_square.
39. Divide both sides by 9, so x2 + y 2 = 91 . 19 > 0, so this represents a circle
q
with center (0, 0) and radius 31 (note 19 = 31 ).
61, 63. See the graphs on Wiley. They’re using the formula x = −b
2a to
find the x-coordinate of the vertex and setting x = 0 and y = 0 to find the
y-intercept and x-intercepts.
EOF
1
``` | crawl-data/CC-MAIN-2020-40/segments/1600400190270.10/warc/CC-MAIN-20200919044311-20200919074311-00741.warc.gz | null |
February is I Love to Read Month, which promotes and celebrates reading.
However, there are children and adults who don’t enjoy reading, who can’t read very well, or just choose not to. We may call these types of readers, reluctant readers.
There are varied factors among reluctant readers as to why they choose not to read or don’t enjoy reading. The website, www.connectingya.com, tells us that for adolescent reluctant readers, books may be inadequate entertainment compared to other media sources, such as the Internet and television.
Some adolescents may not enjoy sitting long enough to read for a long period of time. There may be some students who just equate reading with schoolwork, and thus, are turned off by it.
Experts stress that it is important for children to read for enjoyment. We, as parents and adults, should encourage this.
There are many types of reading material, including nonfiction books and articles, magazines, directions to games and toys, and the newspaper. Find something that piques your child’s interest.
Some children, including adolescents may grow up in non-reading homes that don’t contain reading materials or reading role models. Reading may not be valued among family members.
It is important to be good role models for our children. We need to value reading if we want them to value reading.
Have a variety of reading materials in your home. Bring your children to the library regularly. Read to your children. When your children can read, take turns reading with them, using material that is not above their reading level so they can feel comfortable when reading. If material is too hard and they have to struggle, they will not enjoy it. We want to instill the love of reading.
It is extremely important that we read aloud to our children and make it a part of their daily lives, so they grow up being exposed to books, vocabulary, and the love of reading.
These are the books that National Education Foundation has listed as great reading for children and young people:
For preschoolers, “The Snowy Day” by Ezra Jack Keats, “The Runaway Bunny” by Margaret Wise, “The Rainbow Fish” by Marcus Pfister are popular picks.
These books were picked for children ages 7 to 8: “The Polar Express” by Chris Van Allsburg, “Green Eggs and Ham,” “The Cat in the Hat,” “Oh, The Places You’ll Go,” “How the Grinch Stole Christmas,” “The Lorax,” and “Horton Hatches the Egg” by Dr. Seuss, “Strega Nona” by Tomie De Paola, “Amazing Grace” by Mary Hoffman, and “The Napping House” by Audrey Wood.
Top picks for children ages 9 through 12 included, “Charlotte’s Web” by E. B. White, “Hatchet” by Gary Paulsen, “The Lion, the Witch, and the Wardrobe” by C.S. Lewis, “Maniac Magee” by Jerry Spinelli, “The Watsons Go to Birmingham-1963” by Christopher Paul Curtis, “Walk Two Moons” by Sharon Creech, and “Mr. Popper’s Penguins” by Richard Atwater. | <urn:uuid:6e27ed6d-0167-48fc-a1e9-1223ce0ef38a> | {
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The monumental architecture of the Ancient Greeks and Romans continues to influence and inspire modern culture. If you have never studied the Classics it can be hard to tell the difference. However, there are subtle (and not-so-subtle) differences. Knowing them can enhance your understanding of the ancient world, or at least give you something to talk about at your next dinner party.
All About The Angles
Greek temples are often constructed up on a mountain or on high ground. The approach to the temple is itself an experience - a winding path can keep the temple out of view. It is only emerging from a front gate or a path that a tourist experiences the structure in its majesty – seeing the long and the short sides simultaneously. Greek temples are often rectangular in form, the entrance isn’t necessarily clear and they are best approached at an angle.
The ingress to a Roman temple is quite obvious. Roman priests ascended a distinct staircase into a temple which was built upon a pedestal. The Temple of Isis in Pompeii, Italy is dedicated to an Egyptian goddess but its Roman construction is apparent. The Temple is set on a platform with a precise main entrance and is a little boring to look at from certain angles. Roman temples are best appreciated from the front.
The Columns On The Temple Go Around and Around
Generally, the columns of a Greek temple are peripteral – constructed around the temple on all sides. The Temple of Hera (II) at Pestum, Italy is located in a former Greek colony called Poseidonia. Although built using local tufa (not marble) this structure is easily identified as Greek due to its use and placement of columns. If columns are the first feature you notice when looking at a structure – Greek is your safe bet.
Roman temples often feature columns in the front. The large Corinthian (fanciest type) columns of the Temple of Artemis in Jerash, Jordan are so large they make the visitor lose their natural sense of scale. Jerash was a Hellenistic (Greek) town, which later became Roman territory in 63 BC so it is a good location to compare the two building styles. Sometimes the sheer size of Roman columns is enough to characterize a structure was built with a Roman eye.
Remember the Romans conquered vast stretches of land so you will see Roman-built structures outside of Italy. Some Roman emperors (like Hadrian) admired the Hellenistic world so much they copied Greek architecture, making this topic a little more complicated than I have treated it here. From the use and placement of columns to the scale and entrance of these buildings the architects of the ancient world left us with a wide array of structures to enjoy.
Disclaimer: This post is intended to aid non-classicsts and non-architects identify ancient buildings. This is by no means a replacement for actual education. | <urn:uuid:d4f2f510-54ae-4134-977c-c606e4679530> | {
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Medical Dictionary Definitions A-Z List
Medical Dictionary Definitions A - Z - «I»:
Interneuron: A neuron that exclusively signals another neuron....
Internist: A physician who specializes in the diagnosis and
medical treatment of adults. This specialty, called internal medicine, is dedicated to
adult medicine. A minimum of seven years of medical school and postgraduate training are
focused on learning the prevention, diagnosis, and treatment of ...
Interpersonal therapy: A form of psychotherapy in which the focus is on a patient's relationships with peers and family members and the way they see themselves. Interpersonal psychotherapy (IPT) is based on exploring issues in relationships with other people. The goal is to help people to identify a...
Interphase: The interval in the cell cycle between two
cell divisions when the individual chromosomes cannot be distinguished, interphase was
once thought to be in resting phase but it is far from a time of rest for the cell. It is
the time when DNA is replicated in the cell nucleus....
Intersex: A group of conditions sometimes referred to as disorders of
sexual development (DSDs) in which there is a discrepancy between the appearance
of the external genitalia and the type of internal (testes and ovaries)
genitalia. The condition was formerly termed hermaphroditism or
Intersexual genitalia: Genitalia that are neither typically female nor typically male. Known in clinical medicine as ambiguous genitalia. See:
Interstice: A small space between things, especially between things that are usually closely spaced, such as cells. Interstices are the cracks and crevices, the breaks, the gaps.
The word "interstice" comes from the Latin "interstitium" which was derived from "inter" meaning "between" + "sistere" me...
Interstitial: Pertaining to being between things, especially between things that are normally closely spaced.
The word "interstitial" comes from the Latin "interstitium" which was derived from "inter" meaning "between" + "sistere" meaning "to stand' = to stand between.
The word "interstitial" is muc...
Interstitial cystitis (IC)
Interstitial cystitis (IC): Disease that involves
inflammation or irritation of the bladder wall. This inflammation can lead to scarring and stiffening of the bladder, and even ulcerations and bleeding. Diagnosis is based on symptoms, findings on cystoscopy and biopsy, and eliminating other treatabl...
Interstitial radiation: Radiation therapy in which a radioactive
material is placed directly into a tumor. ...
Interstitial radiation therapy
Interstitial radiation therapy: Radiation treatment given by placing radioactive material directly into the target, often a tumor.
For example, in treating prostate cancer, radioactive seeds are implanted in the prostate gland. The seeds might be titanium-encased pellets containing the radioisotope...
Intertrigo: A superficial skin disorder involving any area of the body where opposing skin surfaces may touch and rub, such as the creases of the neck, the skin folds of the groin, axilla (armpit) and breasts (especially if large and pendulous) and between the toes.
Intertrigo is characterized by sk...
Interval malignancy: In mammography, a malignancy that becomes evident during the period between annual screening mammograms. The finding of an interval malignancy indicates that it either went undetected on the prior breast imaging scan or that it developed during the interval since that last scan...
Intervening sequence: Part of a gene that is
initially transcribed from the DNA into the primary RNA transcript
but then is excised (removed) from it when the so-called exxon
sequences on either side of it are spliced together.
Intervening sequences, which are also called introns, are genetic
Intervention: The act of intervening, interfering or interceding with the intent of modifying the outcome. In medicine, an intervention is usually undertaken to help treat or cure a condition. For example, early intervention may help children with autism to speak. "Acupuncture as a therapeutic inter... | <urn:uuid:9c8e0cf4-2c8a-4cfb-9e0c-7d9bd60a56af> | {
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# 009A Sample Final 2, Problem 9
A plane begins its takeoff at 2:00pm on a 2500-mile flight. After 5.5 hours, the plane arrives at its destination. Give a precise mathematical reason to explain why there are at least two times during the flight when the speed of the plane is 400 miles per hour.
Foundations:
Intermediate Value Theorem
Let ${\displaystyle f(x)}$ be a continuous function on the interval ${\displaystyle [a,b]}$ and
without loss of generality, let ${\displaystyle f(a)
Then, for every value ${\displaystyle y,}$ where ${\displaystyle f(a)
there is a value ${\displaystyle c}$ in ${\displaystyle [a,b]}$ such that ${\displaystyle f(c)=y.}$
Solution:
Step 1:
On average the plane flew
${\displaystyle {\frac {2500{\text{ miles}}}{5.5{\text{ hrs}}}}\approx 454.5{\text{ miles/hr}}.}$
Step 2:
In order to average this speed, the plane had to go from 0mph, up to full speed, past 454.5mph, and then it had to go back down to 0mph to land.
This means that there will be at least two times where the plane of the speed is 400mph by the Intermediate Value Theorem. | crawl-data/CC-MAIN-2021-49/segments/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00585.warc.gz | null |
Cross a crow and it'll remember you for years.
Crows and humans share the ability to recognize faces and associate them with negative, as well as positive, feelings. The way the brain activates during that process is something the two species also appear to share, according to new research being published this week.
"The regions of the crow brain that work together are not unlike those that work together in mammals, including humans," said John Marzluff, University of Washington professor of environmental and forest sciences. "These regions were suspected to work in birds but not documented until now.
"For example it appears that birds have a region of their brain that is analogous to the amygdala of mammals," he said. "The amygdala is the region of the vertebrate brain where negative associations are stored as memories. Previous work primarily concerned its function in mammals while our work shows that a similar system is at work in birds. Our approach could be used in other animals such as lizards and frogs to see if the process is similar in those vertebrates as well."
Marzluff is the lead author of a paper being published the week of Sept. 10 in the online edition of the Proceedings of the National Academy of Sciences.
Previous research on the neural circuitry of animal behavior has been conducted using well-studied, often domesticated, species like rats, chickens, zebra finches, pigeons and rhesus macaques and not wild animals like the 12 adult male crows in this study.
The crows were captured by investigators all wearing masks that the researchers referred to as the threatening face. The crows were never treated in a threatening way, but the fact they'd been captured created a negative association with the mask they saw. Then for the four weeks they were in captivity, they were fed by people wearing a mask different from the first, this one called the caring face. The masks were based on actual people's faces and both bore neutral expressions so the associations made by the crows was based on their treatment.
In most previous neurological studies of animals, the work usually starts by sedating the animals, Marzluff said. Instead the approach developed by the UW involved injecting a glucose fluid commonly used in brain imaging into the bodies of fully alert crows that then went back to moving freely about their cages. The fluid flooded to the parts of the crow brains that were most active as they were exposed for about 15 minutes to someone wearing either the threatening or caring mask.
Then the birds were sedated and scans made of their brains. All the birds were returned to the wild once all the work was completed.
"Our approach has wide applicability and potential to improve our understanding of the neural basis for animal behavior," wrote Marzluff and co-authors Donna Cross, Robert Miyaoka and Satoshi Minoshima, all faculty members with the UW's radiology department. The department funded the preliminary work while the main project was conducted using money from theUW's Royalty Research Fund.
Most neurological studies to date in birds have concerned their songs how their brain registers what they hear, how they learn and come up with songs of their own. This new approach enables researchers to study the visual system of birds and how the brain integrates visual sensation into behavioral action, Marzluff said.
Among other things the findings have implications for lowering the stress of captive animals, he said.
"By feeding and caring for birds in captivity their brain activity suggests that the birds view their keepers as valued social partners, rather than animals that must be feared. So, to keep captive animals happy we need to treat them well and do so consistently," he said.
Intriguingly, Marzluff said the findings might also offer a way to reduce conflict between birds and endangered species on which they might be feeding. In the Mojave Desert, for instance, ravens prey on endangered desert tortoises. And on the West and East coasts, crows and ravens prey on threatened snowy plovers.
"Our studies suggest that we can train these birds to do the right thing," Marzluff said. "By paring a negative experience with eating a tortoise or a plover, the brain of the birds quickly learns the association. To reduce predation in a specific area we could train birds to avoid that area or that particular prey by catching them as they attempt to prey on the rare species."
The partnering of neuroscientists with ecologists could be used to better understand the neural basis of cognition in widely diverse animals, said co-author Cross. For example, her suggestion to use the glucose technique prior to brain scans, so the crows could be fully awake, could be used for other animals.
"This was a true collaboration that would never be possible without the people that were involved with very different areas of expertise," she said.
|Contact: Sandra Hines|
University of Washington | <urn:uuid:a95ff027-4b68-4945-ba32-849c7b7c2ce3> | {
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# Decimal to Binary
Binary to Decimal
Different techniques can be used to convert from decimal to binary. Recursively dividing a given decimal value by two is one way to convert it from decimal to binary. The remainders are then recorded until the final quotient is equal to 0. Following this, these leftovers are written in reverse order to produce the provided decimal number's binary equivalent. The mathematical representation of numbers using a set of digits or symbols is known as a number system. The decimal number system, the binary number system, the octal number system, and the hexadecimal number system are only a few examples of the various number systems. These are recognised with the aid of the base they possess. From one base to another, converting numbers is simple.
Binary to Decimal Conversion
When we translate a number from the decimal number system to the binary number system, we are converting it from decimal to binary. The total amount of digits employed in the number system determines the base, which is a property shared by all number systems. For instance, the binary number system, which only employs two digits to express numbers, has a base of 2. Similar to this, the base of the decimal number system, which uses 10 digits to express numbers, is 10. Before we convert numbers from decimal to binary, let's first learn the decimal and binary number systems. | crawl-data/CC-MAIN-2023-40/segments/1695233510149.21/warc/CC-MAIN-20230926043538-20230926073538-00183.warc.gz | null |
# Factorise:
Question:
Factorise:
(i) 9x3 − 6x2 + 12x
(ii) 8x3 − 72xy + 12x
(iii) 18a3b3 − 27a2b3 + 36a3b2
Solution:
(i) H.C.F. of $9 x^{3}, 6 x^{2}$ and $12 x$ is $3 x$.
$\therefore 9 x^{3}-6 x^{2}+12 x=3 x\left(3 x^{2}-2 x+4\right)$
(ii) H.C.F. of $8 x^{3}, 72 x y$ and $12 x$ is $4 x$.
$\therefore 8 x^{3}-72 x y+12 x=4 x\left(2 x^{2}-18 y+3\right)$
(iii) H.C.F. of $18 a^{3} b^{3}, 27 a^{2} b^{3}$ and $36 a^{3} b^{2}$ is $9 a^{2} b^{2}$.
$\therefore 18 a^{3} b^{3}-27 a^{2} b^{3}+36 a^{3} b^{2}=9 a^{2} b^{2}(2 a b-3 b+4 a)$ | crawl-data/CC-MAIN-2024-38/segments/1725700651523.40/warc/CC-MAIN-20240913133933-20240913163933-00493.warc.gz | null |
Tip #37 to Get a Top ACT English Reading Science Score
You've now learned all the skills that you need for the ACT Science section. The Mantras remind you what to do when, what that girl who got a 36 does automatically. In Skill 37, let's make sure you've integrated the Mantras. Drill them until you are ready to teach them. Then do that. Once you're sure you've got'em, check off the box next to each Mantra. Learning Mantras is like learning martial arts. Practice until they become part of you, until you follow them naturally: when you see a Science question, you know which type it is, you confidently find the appropriate graph, and you find the answer. Your ACT score and probably even your science class grades will go way up.
- Skill 30. Read ACT passages quickly, just to get the gist of what the experiment is generally about. Then glance at the graphs and go to the questions.
- Skill 31. The most common ACT Science question asks you to find a value or a fact from the tables or graphs. And usually the question tells you exactly which table or graph to look back at!
- Skill 32. The second most common type of ACT Science question asks you to look at a chart or graph and decide what happens to one thing as another changes.
- Skill 33. The third type of ACT Science question asks you to use the graph or table to determine the value for a data point that is not shown, but is above, below, or between points that are shown.
- Skill 34. When you see a question that refers to a graph and you don't see the terms from the question in the graph, look at the paragraphs.
- Skill 35. Don't get intimidated. If the wording of a question is confusing, reread it a few times and then do the thing that seems most obvious. That's usually correct for ACT Science questions!
- Skill 36. For a "fight" passage, read the first scientist/student opinion and circle or jot down the main idea and then read the second scientist/student opinion and circle or jot down the main idea. Then consider for a moment the similarities and differences. That will answer the questions of the passage.
- Skill 37. If a question does not tell you which table or graph to use, scan the figures for the one that has the terms from the question.
- Coats and Car Seats: A Lethal Combination?
- Kindergarten Sight Words List
- Child Development Theories
- Signs Your Child Might Have Asperger's Syndrome
- 10 Fun Activities for Children with Autism
- Why is Play Important? Social and Emotional Development, Physical Development, Creative Development
- The Homework Debate
- First Grade Sight Words List
- Social Cognitive Theory
- GED Math Practice Test 1 | <urn:uuid:6b8b908d-4f39-4a66-a899-544951e111d6> | {
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# 19 Times Table- Learn Table Of 19 : Multiplication Table Of 19
Safalta expert Published by: Yashaswi More Updated Thu, 19 May 2022 10:48 PM IST
## Highlights
Check out how to learn the 19 Times table easily here at Safalta.com
19 Times Table: Sam asked Joy, "Do you know that there is a Chinese game of Go which is played on a grid of 19 x 19 lines?" He then asked Joy if he could recite the 19 times table. Joy and Sam together recited the multiplication table of 19 which consists of the multiplication of 19 with various whole numbers. You can refer to the chart shown below for the 19 times table. Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty. Our online school aims to help students prepare for Board Exams by ensuring that students have conceptual clarity in all the subjects and are able to score their maximum in the exams.
Table of 19 Chart:
## Multiplication Table of 19
Learning the multiplication table of 19 helps you in solving mathematical problems related to the two basic operations, i.e., multiplication and division. Go through the 19 times table that is given below and try to memorize it.
### 19 Times Table
19 Times Table up to 10 19 × 1 = 19 19 × 6 = 114 19 × 2 = 38 19 × 7 = 133 19 × 3 = 57 19 × 8 = 152 19 × 4 = 76 19 × 9 = 171 19 × 5 = 95 19 × 10 = 190
## Tips for 19 Times Table
Here are some tips for you to memorize the 19 times table:
1. Table of 19 has a pattern for every ten multiples.
### Free Demo Classes
Source: Safalta.com
Let's write the 1st 10 odd numbers in a sequence in the ten's place. Now from the reverse side, start writing the numbers from 0 to 9 in the unit's place.
• 19 × 1 = 19
• 19 × 2 = 38
• 19 × 3 = 57
• 19 × 4 = 76
• 19 × 5 = 95
• 19 × 6 = 114 and so on.
2. There is another way to write down the table of 19. First, we need to memorize the 9 times table. The first 10 multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. . . .
3. To obtain the multiples of 19, add natural numbers to the tens digit for the multiples of 9. Hence, the 19 times table is obtained as follows: (1+0)9, (2+1)8, (3+2)7, (4+3)6, (5+4)5, (6+5)4, (7+6)3, (8+7)2, (9+8)1, (10+9)0 = 19, 38, 57, 76, 95, 114, 133, 152, 171, 190.
4. There is another short method to obtain the table of 19 with the help of an 18 times table. By adding 1-10 natural numbers to the multiples of 18, we can obtain the table of 19.
### 19 Times Table up to 20
Here is the 19 times table for the numbers 11 to 20.
## Worksheet on Table of 19
1. ### Example 1: Evaluate using 19 times table: 19 times 8 times 9
Solution:
First, we will write 19 times 8 times 9 mathematically.
Using the table of 19, we have: 19 times 8 times 9 = 19 × 8 × 9 = 1368
Thus, 19 times 8 times 9 is 1368.
2. ### Example 2: If one coconut candy costs 10 cents, Using the table of 19, estimate the cost of 19 coconut candies?
Solution:
Since, 1 candy = 10 cents, Therefore, by using 19 times table:
19 candies = 19 x 10 = 190 cents
Thus, the cost of 19 coconut candies is 190 cents.
## Multiplication Tables
2 Times Table 11 Times Table 3 Times Table 12 Times Table 4 Times Table 13 Times Table 5 Times Table 14 Times Table 6 Times Table 15 Times Table 7 Times Table 16 Times Table 8 Times Table 17 Times Table 9 Times Table 18 Times Table 10 Times Table 20 Times Table (Soon)
## What is the times table of 19?
Hence, the 19 times table is obtained as follows: (1+0)9, (2+1)8, (3+2)7, (4+3)6, (5+4)5, (6+5)4, (7+6)3, (8+7)2, (9+8)1, (10+9)0 = 19, 38, 57, 76, 95, 114, 133, 152, 171, 190.
...
19 Times Table up to 20.
19 × 11 = 209 19 × 16 = 304
19 × 14 = 266 19 × 19 = 361
19 × 15 = 285 19 × 20 = 380
## What is the value of 19 x 10?
The value of 19 x 10 is 190.
## What is the importance of learning Table 2 to 20?
For making mathematical section easier, memorising table 2 to 20 is important.
## How can I learn tables easily?
Daily recite the table as mentioned in the article twice and thrice. | crawl-data/CC-MAIN-2023-14/segments/1679296943625.81/warc/CC-MAIN-20230321033306-20230321063306-00192.warc.gz | null |
# Determining Thévenin voltage using nodal analysis
Here I want to determine $$\V_{th}\$$ without using mesh analysis and just by using nodal analysis. Now, $$\V_{th}\$$ is the same as the voltage across the $$\6\ \Omega\$$ resistor since no current passes through the outer $$\2\ \Omega\$$ resistor. Now, let us the set the ground reference voltage as $$\0\$$. Now, $$\V-V_x=2V_x\$$ or $$\V=3V_x\$$ due to the dependent voltage source.
So our $$\V_{th}\$$ is now $$\(3V_x-0=3V_x)\$$. Now, if we try to apply KCL at node $$\V_x\$$ (upper side of $$\4\ \Omega\$$ resistor), we see that $$\-5\ \mathrm{A},\frac{V_x}{4},\frac{V_x-3V_x}{2}\$$ currents are exiting the node, but there is one more current we need to take into consideration which is the current flowing across the dependent source.
So I need some insights on how to solve this question using KCL and nodal analysis.
• let us the set the ground reference voltage as 0 <-- a ground reference voltage is not set to be 0 volts; it is 0 volts but, unfortunately you haven't shown that node on your diagram. You then mention $V$ but, I'm not sure what that refers to. Dec 3, 2023 at 9:44
• You have a voltage source (dependent voltage source) in parallel with 2-ohm resistor. And you do not have to include this resistor in your equations. Because we have a supernode. The only equation you need is this $-5A + \frac{V_X}{4\Omega} + \frac{3 V_X}{6\Omega} = 0$ Becouse no mate what Vth will be 3Vx.
– G36
Dec 3, 2023 at 9:55
First, I will present a method that uses Mathematica to solve this problem. I know that this approach is not 'smart' but this method will work all the time, even when the circuit is (way) more complicated than this one. Also, this method will check your work.
Well, we are trying the analyze the following circuit:
simulate this circuit – Schematic created using CircuitLab
When we use and apply KCL, we can write the following set of equations:
\begin{cases} \begin{alignat*}{1} \text{I}_\text{s}&=\text{I}_0+\text{I}_1+\text{I}_3\\ \\ \text{I}_0+\text{I}_3&=\text{I}_2+\text{I}_4\\ \\ 0&=\text{I}_2+\text{I}_4+\text{I}_5\\ \\ \text{I}_1&=\text{I}_\text{s}+\text{I}_5 \end{alignat*} \end{cases}\tag1
When we use and apply Ohm's law, we can write the following set of equations:
\begin{cases} \begin{alignat*}{1} \text{I}_1&=\frac{\displaystyle\text{V}_1-0}{\displaystyle\text{R}_1}\\ \\ \text{I}_2&=\frac{\displaystyle\text{V}_2-0}{\displaystyle\text{R}_2}\\ \\ \text{I}_3&=\frac{\displaystyle\text{V}_1-\text{V}_2}{\displaystyle\text{R}_3}\\ \\ \text{I}_4&=\frac{\displaystyle\text{V}_2-\text{V}_3}{\displaystyle\text{R}_4}\\ \\ \text{I}_4&=\frac{\displaystyle\text{V}_3-0}{\displaystyle\text{R}_5} \end{alignat*} \end{cases}\tag2
We also know that $$\\displaystyle\text{V}_2-\text{V}_1=\text{n}\cdot\text{V}_1\$$.
Now, we can set up a Mathematica code to solve for all the voltages and currents:
In[1]:=Clear["Global*"];
FullSimplify[
Solve[{Is == I0 + I1 + I3, I0 + I3 == I2 + I4, 0 == I2 + I4 + I5,
I1 == Is + I5, I1 == (V1 - 0)/R1, I2 == (V2 - 0)/R2,
I3 == (V1 - V2)/R3, I4 == (V2 - V3)/R4, I4 == (V3 - 0)/R5,
V2 - V1 == n*V1}, {I0, I1, I2, I3, I4, I5, V1, V2, V3}]]
Out[1]={{I0 -> (Is R1 ((1 + n) R2 R3 +
n R2 (R4 + R5) + (1 + n) R3 (R4 + R5)))/(
R3 (R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5))),
I1 -> (Is R2 (R4 + R5))/(R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)),
I2 -> (Is (1 + n) R1 (R4 + R5))/(
R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)),
I3 -> -((Is n R1 R2 (R4 + R5))/(
R3 (R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)))),
I4 -> (Is (1 + n) R1 R2)/(R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)),
I5 -> -((Is (1 + n) R1 (R2 + R4 + R5))/(
R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5))),
V1 -> (Is R1 R2 (R4 + R5))/(
R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)),
V2 -> (Is (1 + n) R1 R2 (R4 + R5))/(
R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)),
V3 -> (Is (1 + n) R1 R2 R5)/(
R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5))}}
Now, we can find:
• $$\\text{V}_\text{th}\$$ we get by finding $$\\text{V}_3\$$ and letting $$\\text{R}_5\to\infty\$$: $$\text{V}_\text{th}=\frac{\displaystyle\text{I}_\text{s}\text{R}_1\text{R}_2\left(1+\text{n}\right)}{\displaystyle\text{R}_1\left(1+\text{n}\right)+\text{R}_2}\tag3$$
• $$\\text{I}_\text{th}\$$ we get by finding $$\\text{I}_4\$$ and letting $$\\text{R}_5\to0\$$: $$\text{I}_\text{th}=\frac{\displaystyle\text{I}_\text{s}\text{R}_1\text{R}_2\left(1+\text{n}\right)}{\displaystyle\text{R}_1\left(\text{R}_2+\text{R}_4\right)\left(1+\text{n}\right)+\text{R}_2\text{R}_4}\tag4$$
• $$\\text{R}_\text{th}\$$ we get by finding: $$\text{R}_\text{th}=\frac{\displaystyle\text{V}_\text{th}}{\displaystyle\text{I}_\text{th}}=\text{R}_4+\frac{\displaystyle\text{R}_1\text{R}_2\left(1+\text{n}\right)}{\displaystyle\text{R}_1\left(1+\text{n}\right)+\text{R}_2}\tag5$$
Where I used the following Mathematica codes:
In[2]:=FullSimplify[
Limit[(Is (1 + n) R1 R2 R5)/(
R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)), R5 -> Infinity]]
Out[2]=(Is (1 + n) R1 R2)/(R1 + n R1 + R2)
In[3]:=FullSimplify[
Limit[(Is (1 + n) R1 R2)/(R2 (R4 + R5) + (1 + n) R1 (R2 + R4 + R5)),
R5 -> 0]]
Out[3]=(Is (1 + n) R1 R2)/(R2 R4 + (1 + n) R1 (R2 + R4))
In[4]:=FullSimplify[%2/%3]
Out[4]=((1 + n) R1 R2)/(R1 + n R1 + R2) + R4
`
$$\text{V}_\text{th}=20\space\text{V}\space\wedge\space\text{I}_\text{th}=\frac{10}{3}\approx3.33\space\text{A}\space\wedge\space\text{R}_\text{th}=6\space\Omega\tag6$$
You can keep the sum of the currents of R2 and the controlled source as one. I named it to I2.
Write the ordinary "nodal method" current summing equations for the top ends of resistors R1 and R3. Note that the node voltage at the top end of R3 must be 3Vx because the controlled 2Vx is in series with the unknown node voltage Vx.
The equations are
(I1) + (I2) = (Vx)/(R1) and (I2) + (3Vx)/(R3) = 0
Eliminate unknown I2 and solve Vx. The wanted no-load Voc is 3Vx.
This all can be found in a short form from already given comments. | crawl-data/CC-MAIN-2024-18/segments/1712296816879.25/warc/CC-MAIN-20240414095752-20240414125752-00578.warc.gz | null |
A clean definition
In 2004, REEEP, the Renewable Energy & Energy Efficiency Partnership, proposed a definition of sustainable energy as “the provision of energy such that it meets the needs of the future without compromising the ability of future generations to meet their own needs. Sustainable energy has two key components: renewable energy and energy efficiency.”
Technologies are key
The move towards sustainability in energy generation, transmission and consumption can only happen through an array of technological advances that promote renewable energies – wind, solar, geothermal, hydro, marine (wave and tidal) – and energy efficiency.
Smart systems, using two-way communication technology and computer processing, are making their way into electricity networks, from power plants to homes and businesses. Smart and sustainable energy has many benefits for utilities and consumers alike: day-to-day generation, distribution and consumption monitoring, cost reduction, electricity storage and much more.
Smart gets smarter everyday
Today’s world is as smart as it is thanks to the extensive use of electronic components of all types. Smart energy environments rely heavily on information and communication technology (ICT) for transmitting and processing signals and data smoothly and providing communication between devices or systems. They also depend on power electronics for the conversion of electrical power.
The role of power electronics
Power electronics is the phrase used to define the application of solid-state electronics for the efficient control and conversion of electrical power. Power electronics comes into play whenever there is a need to modify voltage, current or frequency. In modern systems the conversion is performed using semiconductor switching devices such as diodes, thyristors and transistors.
Power electronics is used in a wide range of applications in industry, transportation, utilities, power supply for electronic equipment, commercial and residential appliances. For instance, many consumer electronic devices, such as cell phones, personal computers and battery chargers, contain an AC/DC converter, probably the most popular converter of all. In industry a common application is the variable speed drive (VSD), which controls induction motors. The power range of VSDs goes from a few hundred watts to tens of megawatts.
Power electronics also plays a major role in low-voltage direct current (LVDC) projects such as micro grids used for electricity distribution in rural or remote areas. Direct current in the electrical network combined with power electronics reduce power cuts and enable the intelligent use of the electrical network. This is of particular importance for developing country where access to electricity is still limited or non-existent.
Trust throughout the supply chain
Manufacturers and suppliers of electronic components and manufacturers of electronic devices and systems have to ensure that their products are of the highest quality and performance. For their part, utilities that install smart meters or retailers who sell devices and equipment need to make sure that those are safe and reliable – and the consumers who acquire them will also want to know this.
For all, trust is essential. One way to build that trust is through testing and certification. IECQ, the IEC Quality Assessment System for Electronic Components, is a major player and a leader in this field, working relentlessly to develop Schemes that cover not just electronic components but also associated materials, assemblies and processes.
IECQ – a building block
As a worldwide approval and certification system covering the supply of electronic components, assemblies and associated materials and processes, IECQ provides a certification system that enables manufacturers and suppliers to provide independent verification that the claimed specifications (including IEC International Standards) have been met. This gives end manufacturers the reassurance of knowing that suppliers holding IECQ certification do not need stringent second party assessment or monitoring.
The plethora of electronic components and processes covered by IECQ are used in all kinds of technologies, from the smallest device to the most complex piece of equipment. IECQ’s contribution to a safer and more reliable world can only increase with the development of new technologies and state-of-the-art electronic devices.
IECQ offers several Schemes for specific industry sectors or that address issues that raise concerns:
- IECQ AP (Approved Process)
- IECQ AP-CAP (Counterfeit Avoidance Programme)
- IECQ AC (Approved Component)
- IECQ AC-TC (Technology Certification)
- IECQ AC-AQP (Automotive Qualification Programme)
- IECQ Scheme for LED Lighting (LED components, assemblies and systems)
- IECQ Avionics
- IECQ HSPM (Hazardous Substances Process Management)
- IECQ ITL (Independent Testing Laboratory)
The IECQ Schemes help facilitate trade, reduce industry costs and eliminate duplication of assessments because certificates are recognized globally in the member countries. This means that once a device, a piece of equipment or an installation has been tested by a recognized certification body, the certificate is valid everywhere, making it highly valuable. It also provides those components, processes and materials that have been certified with the potential to access international markets.
To learn more about IECQ and its Schemes, please visit: www.iecq.org | <urn:uuid:acc46d4c-3da2-4e67-a962-d2aa15b424df> | {
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a. Suppose that throughout some region of space. Can you conclude that in this region? Explain.
b. Suppose that throughout some region of space. Can you conclude that in this region? Explain.
(a) No, is not necessarily .
(b) Yes, is zero
Theory used :
In the region of constant electric potential, electric field is zero so there is no charge inside the region.
Electric field is the negative slope (“derivative” or “gradient”) of the potential.
However, you can deduce that , implying that the potential in that region of space is constant.
(b) The answer is yes.
Because , when is constant in a region of space, .
Consider a uniformly charged sphere of radius R and total cAlC charge Q. The electric field outside the sphere is simply that of a point charge Q. In Chapter 24, we used Gauss's law to find that the electric field inside the sphere is radially outward with field strength
a. The electric potential outside the sphere is that of a point charge Q. Find an expression for the electric potentialat position r inside the sphere. As a reference, let at the surface of the sphere.
b. What is the ratio
c. Graph V versus r for 0 r 3 R.
94% of StudySmarter users get better grades.Sign up for free | <urn:uuid:9e64d517-eb18-411a-b5b7-bc71cf1ab54c> | {
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Question
Mathematics
Evaluate $\left(f\circ g\right)\left(x\right)$(f@g)(x) and write the domain in interval notation. Write the answer in the intervals as an integer or simplified fraction.
$f\left(x\right)=\frac{x}{x-1}\phantom{\rule{1em}{0ex}}g\left(x\right)=\frac{13}{{x}^{2}-36}$f(x)=(x)/(x-1)quad g(x)=(13)/(x^(2)-36)
Part: $0/2$0//2
Part 1 of 2
$\left(f\circ g\right)\left(x\right)=$(f@g)(x)=
Solve problem with AI
To evaluate $\left(f\circ g\right)\left(x\right)$(f@g)(x), we need to first find $g\left(x\right)$g(x) and then evaluate $f$f at $g\left(x\right)$g(x).
Given that $f\left(x\right)=\frac{x}{x-1}$f(x)=(x)/(x-1) and $g\left(x\right)=\frac{13}{{x}^{2}-36}$g(x)=(13)/(x^(2)-36), we have
$\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)=f\left(\frac{13}{{x}^{2}-36}\right)=\frac{\frac{13}{{x}^{2}-36}}{\frac{13}{{x}^{2}-36}-1}.$(f@g)(x)=f(g(x))=f((13)/(x^(2)-36))=((13)/(x^(2)-36))/((13)/(x^(2)-36)-1).
$\begin{array}{rl}\left(f\circ g\right)\left(x\right)& =\frac{\frac{13}{{x}^{2}-36}}{\frac{13}{{x}^{2}-36}-1}\cdot \frac{{x}^{2}-36}{{x}^{2}-36}\\ \\ & =\frac{13}{\left({x}^{2}-36\right)-13}\\ \\ & =\frac{13}{{x}^{2}-49}\\ \\ & =\frac{13}{\left(x-7\right)\left(x+7\right)}\end{array}${:[(f@g)(x)=((13)/(x^(2)-36))/((13)/(x^(2)-36)-1)*(x^(2)-36)/(x^(2)-36)],[],[=(13)/((x^(2)-36)-13)],[],[=(13)/(x^(2)-49)],[],[=(13)/((x-7)(x+7))]:}
Therefore, $\left(f\circ g\right)\left(x\right)=\frac{13}{\left(x-7\right)\left(x+7\right)}$(f@g)(x)=(13)/((x-7)(x+7)).
Now, let’s find the domain of $\left(f\circ g\right)\left(x\right)$(f@g)(x). The function is undefined when the denominator $\left(x-7\right)\left(x+7\right)$(x-7)(x+7) equals zero. This happens when $x=7$x=7 or $x=-7$x=-7. So, the domain of $\left(f\circ g\right)\left(x\right)$(f@g)(x) is all real numbers except for $x=7$x=7 and $x=-7$x=-7.
In interval notation, the domain of $\left(f\circ g\right)\left(x\right)$(f@g)(x) is $\left(-\mathrm{\infty },-7\right)\cup \left(-7,7\right)\cup \left(7,\mathrm{\infty }\right)$(-oo,-7)uu(-7,7)uu(7,oo).
Answer: $\left(f\circ g\right)\left(x\right)=\frac{13}{\left(x-7\right)\left(x+7\right)}$(f@g)(x)=(13)/((x-7)(x+7)) with domain $\left(-\mathrm{\infty },-7\right)\cup \left(-7,7\right)\cup \left(7,\mathrm{\infty }\right)$(-oo,-7)uu(-7,7)uu(7,oo). | crawl-data/CC-MAIN-2024-10/segments/1707947473472.21/warc/CC-MAIN-20240221102433-20240221132433-00533.warc.gz | null |
How many ways to arrange $20$ items on $4$ towers
Suppose you have $20$ different rings and $4$ display towers. On each tower the rings are stacked one above another. In how many ways can they be arranged if:
[a]: The order of rings on each tower does not matter:
[b]: The order of rings on each tower matters, and there are exactly 5 rings on each tower?
[c]: The order of rings on each tower matters, and each tower can hold any number of rings?
Here is what I am thinking, not sure if it's right:
[a]:
Order does not matter - standard combination question:
$$Ni = # of rings on tower i$$ then: $$N1+N2+N3+N4 = 20$$ and we find number of solutions to this problem I.E (Stars and bars): $$\binom{20+3} {3} = 1771$$
[b]: I know that this is a permutation question since order is important, but I am not sure if I am doing it right: $$20P5 * 4$$ [c] have no clue
For [a], what matters is what tower each ring is put on. The first ring can go on each of the four towers, so can the second, and so on. So the result is $4^{20}$.
For [b], you can just order all $20$ rings in a single row, then put the first five on the first stand, rings number 6 through 10 on the second stand, and so on. So the answer is $20!$
For [c], it's a stars and bars solution, only the internal order of the stars and of the bars matter. The answer then comes out to be $23!$ | crawl-data/CC-MAIN-2020-45/segments/1603107881640.29/warc/CC-MAIN-20201024022853-20201024052853-00260.warc.gz | null |
“Frederick the Great Playing the Flute at Sanssouci” by Adolph Menzel
“Frederick the Great Playing the Flute at Sanssouci” by Adolph Menzel depicts the King of Prussia, a keen flutist, playing on the occasion of a visit from his sister.
The King is shown keeping time with his left foot and facing the chamber ensemble. Menzel has portrayed the scene, with great attention to the historical accuracy in the dress, musical instruments, and furnishings.
The concert room in Sanssouci is filled with the warm candlelight creating a theatrically atmospheric portrayal of Frederick the Great playing the flute at Sanssouci. (The music is available below.)
Adolph Menzel’s attention to details includes the inclusion of the following historical figures:
- Johann Joachim Quantz, the King’s flute teacher in the far right,
- Franz Benda, standing up with a violin and wearing dark clothing,
- Gustav Adolf von Gotter is the leftmost in the foreground,
- Jakob Friedrich von Bielfeld is behind him in the far left,
- Pierre Louis Maupertuis is looking at the ceiling,
- Wilhelmine of Bayreuth in the background, sitting on a pink sofa, and
- Carl Philipp Emanuel Bach is at the harpsichord:
Menzel produced numerous illustrations related to the history of Frederick the Great and German history, which transformed his subjects by subtly introducing parochial patriotism.
Frederick the Great
Frederick II (1712 – 1786) ruled the Kingdom of Prussia from 1740 until 1786, the longest reign of any Hohenzollern king.
His accomplishments included his military victories, his reorganization of Prussian armies, his patronage of the arts, and the Enlightenment.
In his youth, Frederick was more interested in music and philosophy than the art of war. Nonetheless, upon ascending to the Prussian throne, he attacked Austria and claimed Silesia.
Frederick acquired Polish territories in the First Partition of Poland. He was an influential military theorist.
Frederick reformed the judicial system and made it possible for men not of noble status to become judges and senior bureaucrats.
Frederick also encouraged immigrants of various nationalities and faiths to come to Prussia. Frederick supported arts and philosophers he favored, as well as allowing complete freedom of the press and literature.
The Nazis glorified him as a great German leader pre-figuring Adolf Hitler, who personally idolized him.
Associations with Frederick became far less favorable after the fall of the Nazis, primarily due to his status as one of their symbols. However, recent re-evaluations of his legacy have positioned him as a great general and enlightened monarch.
Sanssouci was the summer palace of Frederick the Great, King of Prussia, in Potsdam, near Berlin. Sanssouci is in the more intimate Rococo style and is far smaller than its French Baroque Versailles.
The palace’s name derives from the French phrase “sans souci,” which translates “without worries” or “carefree,” symbolizing that the palace was a place for relaxation.
After World War II, the palace became a tourist attraction in East Germany. Following German reunification in 1990, Frederick’s body was returned to the palace and buried in a new tomb overlooking the gardens he had created.
Sanssouci and its extensive gardens became a World Heritage Site and a significant tourist attraction.
Adolph Menzel (1815 – 1905) was a Realist artist considered one of the two most prominent German painters of the 19th century (along with Caspar David Friedrich).
Menzel was the most successful artist of his era in Germany and was knighted in 1898.
Adolph Menzel’s popularity in Germany, especially with his history paintings, was such that museums quickly acquired many of his works.
He received many honors, and in 1898 became the first painter to be admitted to the Order of the Black Eagle and raised to the nobility, becoming “Adolph von Menzel.”
He was also made a member of the Académie des Beaux-Arts in Paris and the Royal Academy in London. After his death, the Kaiser attended his funeral and walked behind his coffin.
Frederick the Great Playing the Flute at Sanssouci
- Title: Frederick the Great Playing the Flute at Sanssouci
- German: Flötenkonzert Friedrichs II. in Sanssouci.
- Artist: Adolph Menzel
- Medium: Oil on canvas
- Date: 1851
- Dimensions: Height: 142 cm (55.9″); Width: 205 cm (80.7″)
- Type: History Painting
- Museum: National Gallery (Berlin) – Alte Nationalgalerie
- Name: Adolph Friedrich Erdmann von Menzel
- Born: 1815 – Breslau, Prussian Silesia (now Poland)
- Died: 1905
- Nationality: German
- Notable works:
Adolph von Menzel painting – Concert for flute with Frederick the Great in Sanssouci
Explore Alte Nationalgalerie – National Gallery, Berlin
- “In Summer” by Pierre-Auguste Renoir
- “In the Conservatory” by Édouard Manet
- “Moonrise by the Sea” by Caspar David Friedrich
- “Cromwell in Battle of Naseby” by Charles Landseer
- Frederick the Great Playing the Flute at Sanssouci by Adolph Menzel
Frederick the Great
Explore History Paintings
- “Washington Crossing the Delaware” by Emanuel Leutze
- “The Family of Darius before Alexander” by Paolo Veronese
- “Las Meninas” or “The Ladies-in-Waiting” by Diego Velázquez
- “The Third of May 1808″ by Francisco Goya
- “The Fighting Temeraire” by Joseph Mallord William Turner
- “Westward the Course of Empire Takes Its Way” by Emanuel Leutze
- “The Capture of the Hessians at Trenton, December 26, 1776″ by John Trumbull
- “The March to Valley Forge” by William B. T. Trego
- “The Massacre at Chios” by Eugène Delacroix
- “The Execution of Lady Jane Grey” by Paul Delaroche
- History Paintings
Bach meets Frederick the Great
- The Pergamon Museum
- Neues Museum
- Altes Museum
- Alte Nationalgalerie – National Gallery (Berlin)
- Bode Museum
- Gemäldegalerie, Berlin
- Spy Museum Berlin
- Jewish Museum, Berlin
- Deutsches Historisches Museum – German Historical Museum
- DDR Museum
- German Resistance Memorial Center
“Diplomacy without arms is like music without instruments.”
– Frederick the Great
Photo Credit: Adolph von Menzel [Public domain] | <urn:uuid:f3c23073-e939-4464-b33b-a56ba8d4c366> | {
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# CLASS-6CONVERTING PERCENTAGE INTO FRACTION
CONVERTING PERCENTAGE INTO FRACTION -
Converting a percentage into a fraction involves expressing the percentage as a fraction with a denominator of 100. Here's how you can do it:-
1. Write the Percentage as a Fraction:- Let's say you have a percentage, such as 25%.
2. Express as a Fraction:- To convert 25% to a fraction, you write it as 25/100.
3. Simplify the Fraction:- You can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 25 and 100 is 25.
25 25 ÷ 25 1
--------- = ------------ = -------
100 100 ÷ 25 4
So, 25% is equivalent to 1/4 as a fraction. (Ans.)
Let's take another example:-
Example.2) If you have 60% and you want to convert it to a fraction:-
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 20:
60 60 ÷ 20 3
--------- = ------------ = -------
100 100 ÷ 20 5
So, 60% is equivalent to 3/5 as a fraction. (Ans.)
In general, to convert a percentage p% to a fraction:
p
---------
100
And then simplify the fraction if possible. This fraction represents the ratio of the given percentage to the whole (which is 100 in terms of percentages). | crawl-data/CC-MAIN-2023-50/segments/1700679100909.82/warc/CC-MAIN-20231209103523-20231209133523-00536.warc.gz | null |
Watch your tire pressure.
Your tire is (supposed to be) the only part of your car that contacts the road. The specific part of the tire that touches the road is called the contact patch. Changing your tire pressure changes the way that contact patch touches the road.
- Too little air pressure will cause inconsistent wear, unnecessary drag between the tire and the road and can cause the sidewall (the part between the edge of the tread and the wheel) to soften, negatively affecting the way your car handles.
- Too much air pressure will cause your tire to balloon, which means only the center of your tire’s tread will contact the road. This causes it to wear faster than the rest of the tire. Also, because only the center of the tread is touching the road, your contact patch is reduced, leading to less overall grip and poor handling.
Tires on all vehicles are produced to be run at a specific air pressure to optimize their capabilities. Most passenger cars run around 30-35psi of pressure in each tire. Monitoring your tires will help you keep your car handling like it’s supposed to and result in the best gas mileage. Be sure to always carry a tire pressure gauge in your car and check your pressures every few weeks, your wallet will thank you! | <urn:uuid:728b52bc-9b78-42e3-ab31-14db5f1d3f65> | {
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In the 19th century, in the United States, Tribal nations were rounded up and placed on reservations. There Tribal people were subjected to the forces of assimilation that worked to change Tribal culture and make the people into Americans. The national policy of this time was to assimilate American Indians into the “melting pot” of the United States.and eliminate the need for reservations.
First the Tribes needed to be removed and dispossessed from their land, then the children were removed, and imprisoned in schools to remove their culture. Gradually the tribes changed, survived in many ways, but changed to American culture. This process worked well as population counts on reservations were dropping.
In fact, early anthropologists were so alarmed at the population losses that they feared that very soon there would be no Native culture for them to study. The future looked dim for the tribes.
In the late 19th century a series of wars and conflicts, Modoc war (1872-1873), Nez Perce War (1877), Geronimo (1873-1886), Wounded Knee (1890) were significant points of resistance to United States colonization and imperialism in Indian Country. Coupled with the numbers of escapements of individual tribal people from the reservations, and it appeared that the tribes were not simply giving up and accepting their fates. They were not being the depressed end-of-the-trail Indians as many Americans hoped they would be. They were instead defiant and planting seeds of pride within the hundreds of thousands of Native peoples on reservations.
Out of this spirit of defiance, came a generation of energized partially-assimilated Indians who excelled in intramural sports. Football, baseball, track and long distance runners, and basketball were common games then played and excelled at by young native athletes.
The plans and desires of the mid-19th century American Politicians to eliminate Indians was not occurring. Even though reservation populations were declining as Indians left to go to school, to find work, or died,the reservations were in no danger of completely disappearing.
By the 1880s, a plan was hatched to allot the Indians with land. The Dawes, or, General allotment act was created to give individual Indians a permanent farm, an allotment, and to sell off the remainder acreage to white settlers who needed land. By the 1880s, most of the frontier was claimed and the last remaining lands not claimed by whites were on the large reservation holdings. White settlers were thought to to be able to more efficiently make use of the land, and the tribes were wasting the land on the reservations, and the new generation of pioneers needed their opportunities as well.
So the Dawes allotment act (1887) was passed and presented to the tribes. A few tribes refused to accept it, understanding that through the bill, they would lose a good portion of their remaining lands. the tribes had given up 100’s of millions of acres to get a few hundred thousand acres for their permanent reservations. But most tribal people wanted their allotments. They had already been through one or two generations of assimilation by the 1880s, most of their peoples had been to school and knew how to read and write. And they too wanted their piece of the American dream. Such was their education in American boarding schools, that they all deserved opportunity, even if few were American citizens. (American citizenship was not given to all until 1924.)
The Dawes Act did a few other things to the tribe. First Dawes instilled the notion of individualism among the tribes. Tribal people learned to understand that in order to get ahead in American society they had to be individuals and not simply part of a community. And Dawes taught the tribes about the value of blood quantum. In order to receive am allotment under Dawes, tribal people, those defined as “Indian”under other federal policies, had to have one half Indian blood or better (even though this was not a stipulation in the treaties). In this manner, through this bill thousands of Indian people were dispossessed of the rights of citizenship in their nation because they had too much non-Indian ancestry. The real effect was felt in the following generation as thousands more people who were even further assimilated and because they were more likely to marry out of the tribe were dispossessed of their and their children’s rights to be a part of their tribes. In this manner, the federal government had no further reason to re-allot the Tribal reservation lands, there were too few “official” Indian people (1/2 Indian blood or better) who could get allotments.
Literally in a few generations, the tribes went from owning thousands of acres down to almost nothing. In 1856, the tribes at the Grand Ronde reservation had between 60 thousand acres and 69 thousand (we have yet to find the actual number). In 1901 the acreage was reduced to 33,000 acres after the Dawes Act, By 1920, thousands of acres went out of tribal hands by either sale, or through decisions made by the BIA. In about 1911, the BIA began a series of heir-ship investigations to find out who were the direct relations of the people who had died with allotments. By 1918 these were concluded and the original allotments were sold, and the proceeds given to the descendants. Also under Dawes, allottees received their fee simple titles in 20 years, then many turned around and sold their land. In this manner by 1950 there were 497 acres remaining in Tribal hands at Grand Ronde.
Perhaps the most egregious effect the practice of allotting from the Dawes Act had, was instilling the notion of blood quantum in the tribes, based on the definition of an “Indian” used in federal law, as a person of 1/2 Indian blood or better. Tribes began accepting blood quantum as a measure of citizenship. Under the Wheeler-Howard act (1934), many tribes wrote their own constitutions and wrote into their membership requirements that they had to maintain a certain blood quantum of tribal blood.
Sec. 19. The term “Indian” as used in this Act shall include all persons of Indian descent who are members of any recognized Indian tribe now under Federal jurisdiction, and all person who are descendants of such members who were, on June 1, 1934, residing within the present boundaries of any reservation, and shall further include all other persons of one-half or more Indian blood. For the purposes of this Act, Eskimos and other aboriginal peoples of Alaska shall be considered Indians. The term “tribe” wherever used in this Act shall be construed to refer to any Indian tribe, organized band, pueblo, or the Indians residing on one reservation. The words “adult Indians” wherever used in this Act shall be construed to refer to Indians who have attained the age of twenty-one years.
Its clear that the tribes wanted to maintain their Indian-ness. Many tribal people had the belief that people had to be active participants in the community to be members. In 1905 when the Applegate Report was submitted to Congress, there were statements from tribal elders about individuals who had moved away. They believed that those who had moved away had willingly stopped being a member of the tribe. This is a traditional value in many tribes. In American ethnography there are many stories of how tribal peoples could move to different communities and they would eventually be accepted into the community if they remained long enough. People had the autonomy to chose what was their community and they could decided to leave a tribe and integrate with another tribe if they chose that route.
In this period of late 19th and early 20th centuries, the people were under extreme pressure to assimilate. Many had little choices but to leave the tribe and find opportunity elsewhere. If their blood quantum was too low, or they had learned a skill in boarding school that they could not practice at the reservation, many chose to leave, move to a city and never returned. Some of these people maintained contact and may visit the res on the weekends or a few times a year, but much of the population loss was due to people being forced to move away to find more opportunities.
So by the time the tribes were forming governments of elected officials, with official rolls of members, under the Indian Reorganization Act, (Grand Ronde was 1936), many of their people were no longer around. At this time, it was not negative to marry outside the tribe, it was actually looked on favorably as your children would have more opportunity. But the IRA inculcated Blood quantum within the bill,
When the Grand Ronde tribe was undergoing restoration in the 1970s, Several generations of people have now lived under blood quantum as being the measure of Indian-ness and citizenship. There had been several more generations of people, in the termination era that had married outside the tribe. And now, after restoration in 1983, many people could not join because their blood quantum is too low. Today we are in a situation were every single family at the Grand Ronde Tribe, like many other tribes in the USA, have descendants who can not be members. The children and grand children of the people who worked to restore the tribe, many, cannot join because of blood quantum.
Remember, this is an imposed federal policy that was never a traditional measurement of citizenship. There is not a tribe before treaties and removal to reservations that measured someone’s blood quantum. This was a policy imposed upon an imprisoned and heavily managed people, which was designed and worked to Eliminate legal Indians. Discussions at the federal and Congressional level during their people was about the overwhelming cost of Indian Affairs, and the need to eliminate Indians and eliminate the overhead in the federal budget for Indian affairs. This is the same reasoning that was used against the Grand Ronde Tribe in the 1950’s when National Termination policy was imposed, because of the need of the federal government to eliminate Indians, that their budgets.
Dawes was successful in dispossessing thousands of Indians, and the next effort, Termination, was successful in eliminating many thousands more Indians. Now that tribes have some rights for self-determination, and have the rights to have casinos, the generations of assimilation are now working to dissociate many thousands of more Indians from the tribes. Now Indians from assimilated tribes want their individual rights, a piece of the profits for being Indian in a tribe. Now blood quantum works in their favor, as the less number of Indians in each tribe, the more money each member makes in per cap and services.
The Federal Government now does not need to lift a finger or say a word or make a decision. They planted the seeds of extinction of tribes in the 1850’s with forced education, and then planted the notion of Blood quantum as a measurement of Indian identity. Blood quantum is not even written into the treaties yet many tribes continue to accept it as a traditional characteristic of being Indian and allowed thousands of people to be dispossessed of their rights by Indian agents. (I am not sure the tribes in 1887 or 1934 knew how to challenge the notion of Blood Quantum.)
Continuing to accept blood quantum is a death sentence for tribes, as each generation a good percentage of the tribal members will marry outside of their tribe. In 100 years, unless things change, more Tribes will have half or less the members than they have today. In effect the tribes are self-terminating, and the federal government could not have planned it better.
Tribes appear to be in effect continuing to participate in this grand experiment of colonization in the United States. Every couple of generations there is a new challenge to tribes, from the federal government, which places their very survival are stake. The federal government is not our friend and their policies are not friendly to the tribes. We have accepted a new version of colonization that will continue to work to eliminate all Tribes unless it is directly challenged. Our challenge in this generation is to instill a spirit of Tribal sovereignty in the people so they act to take back from the federal government our rights to true sovereignty within our homelands. As long as we continue to accept these imposed policies we are a colonized people. | <urn:uuid:0eefb6e4-7ee5-4c8a-a7bf-7231cf10507a> | {
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South Georgia and the South Sandwich Islands lie more than 1,700 kilometers (1,050 miles) from the southern tip of South America in a remote expanse of the South Atlantic Ocean. While mostly uninhabited by humans, the area hosts what could be the single largest concentration of marine species in the world.
In the past, the wildlife of South Georgia and the South Sandwich Islands was seriously depleted by overexploitation, mostly in the form of whaling. The Pew Bertarelli Ocean Legacy Project and its partners are exploring the feasibility of enhancing marine protections in the waters around South Georgia and the South Sandwich Islands.
Forming part of the Antarctic ecosystem, the rich waters are full of plankton and krill which support one of the largest and most varied populations of seabirds and marine mammals on earth. Overall, they have a higher diversity of species than the more temperate Galapagos Islands.
The islands, a British overseas territory, provide habitat for more than four million Antarctic fur seals—more than 95 percent of the world’s population—and more than half of the world’s southern elephant seals. Sperm, humpback, and other whale species are also frequently seen in the islands’ waters.
South Georgia has as many as 100 million seabirds, including vast numbers of penguins, albatross, prions, and petrels. The Antarctic’s only songbird, the South Georgia pipit, of which only 6,000 remain, is found only on that island. The continued existence of this species is threatened by the spread of introduced rats on South Georgia. Zavodovski Island in the South Sandwich Islands has more than one million chinstrap penguins, the largest colony in the world.
The South Sandwich Islands have no permanent inhabitants, while South Georgia has a transitory population of scientists, government officials and military personnel. Both are mountainous and capped by glaciers. Volcanic in origin, the islands are surrounded by nutrient-rich waters. The South Sandwich Trench, which at more than eight kilometers (five miles) is one of the deepest parts of the ocean, includes thermal vents which are yet to be fully explored.
Captain James Cook, a Briton, first landed on South Georgia in 1775. In the early 20th century, it was the destination of Sir Ernest Shackleton’s epic mission to save the crew of his ship, the Endurance. In 1916, after an 800-mile voyage in a lifeboat, he reached South Georgia. Crossing its ice cap on foot, he famously remarked: “We had seen God in His splendours, heard the text that Nature renders. We had reached the naked soul of man.”
The Pew Bertarelli Ocean Legacy Project is calling for enhanced protection of this spectacular region.
Did you know?
- The islands have a higher diversity of species than the Galapagos Islands.
- Zavodovski Island is home to the largest colony of chinstrap penguins in the world.
- South Georgia Island is believed to have as many as 100 million seabirds.
- This region is home to more than 95 percent of the world’s Antarctic fur seals. These waters include the South Sandwich Trench, one of the deepest parts of the ocean.
Pew Bertarelli Ocean Legacy Project
The Pew Charitable Trusts and Dona Bertarelli joined forces in 2017 to create the Pew Bertarelli Ocean Legacy Project, with the shared goal of establishing the first generation of ecologically significant, large, and effective marine protected areas (MPAs) around the world. Today, the Pew Bertarelli Ocean Legacy Project also seeks to connect MPAs and help conserve key migratory species and entire marine ecosystems. These efforts build on more than a decade of work by Pew and the Bertarelli Foundation, led by Dona Bertarelli, to create large-scale highly or fully protected MPAs. Between them, they have helped to obtain designations to safeguard nearly 9 million square kilometers (3.5 million square miles) of ocean by working with communities, local leaders, philanthropic partners, Indigenous groups, government officials, and scientists. Dona Bertarelli is a philanthropist, investor, sportswoman, and strong advocate for ocean conservation. The Pew Charitable Trusts addresses the challenges of a changing world by illuminating issues, creating common ground, and advancing ambitious projects including the need for effective marine conservation. | <urn:uuid:8e3f3a29-ccfe-4170-93fb-aad97613ccb0> | {
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One the great surprises about heat energy is that the transfer of heat can occur by any or all of three very different mechanisms.
In conduction, heat transfer occurs by a process of molecular collision. If you heat up one end of a bar of iron, the energy is transferred from the hot end to the cold by atoms or molecules bumping into one another i.e. while there is a net drift of energy from hot to cold, the molecules do not change their respective positions. This is the primary method of heat transfer in solids and it works best of all in metals (because loosely bound electrons play a role). It is also an efficient method of conduction in liquids, but occurs hardly at all in gases. In gases, a low density of atoms or molecules inhibits conduction very effectively – hence air is an excellent insulator.
This fact is used to good effect in double glazing; a layer of air between two panes of glass allows one to have good light and views in a house without too much heat loss. Similarily, modern mountaineers keep warm by wearing many thin layers as the air trapped between each set of layers acts as an effective insulator.
Conduction in a solid: the molecules do not change position much
Heat transfer can also occur by the process of convection. In this case, heat energy is transferred by a movement of molecules. The classic example is hot air rising: on a hot day, air close to ground absorbs heat from the earth’s surface, expands, and rises because it has become less dense than other air. Cooler and denser air then rushes down from above to fill its place, only to be heated in turn and a cycle is set up. As you might expect, this an important method of heat transfer in gases, and convection currents are responsible for everything from sea breezes at shore to major wind patterns around the globe.
Sea breeze close to shore on a hot day
Convection also occurs in liquids: indeed, convection currents are of great importance in the oceans of the world. For example, the seas around Ireland are warmer than might be expected for our latitude. This warming is a result of the famous North Atlantic Drift, a huge ocean current that is part of a giant conveyor belt that delivers heat from the seas off South America all the way up to the seas near Greenland. One of the concerns of global warming is that as the ice caps melt, this current may weaken or even shut down: in which case Ireland and Britain could become very cold indeed!
The North Atlanic Drift keeps Ireland’s climate mild
What is the third process of heat transfer? Well, that is a different story altogether… | <urn:uuid:cfda15f5-9f33-4001-a691-a2716e664c92> | {
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A Cryptocurrency, also known as cryptogram, is any digital currency that is created through an algorithm. It is generally created by governments or regulatory groups as a method of regulating the transfer and ownership of monetary assets. A Cryptocurrency is not backed by a commodity, such as gold. A Cryptocurrency is generally considered valuable because it has some sort of government backing from a regulating body. A few examples of Cryptocurrects include the digital currency used on the Silk Road, the Forex market, and the Litecoin network.
In order for Cryptocurrects to be created, there needs to be a certain amount of computing power and memory space dedicated to running the algorithm or computer code that creates them. After this, a certain amount of real-time data must be stored on servers in order to ensure that there will be accurate updates made to the Cryptocurrency’s ledger at all times. Some Cryptocurrencies have been combined with other currencies, such as the Litecoin network, and others have been entirely separate from all others.
A typical Cryptocurrency consists of a group of computer codes that are programmed to perform specific tasks when they are executed. The execution of these codes is done by a network of servers, computers, and the internet. A typical Cryptocurrency will include a currency unit, a digital asset, a database, a network of internet nodes, and a central authority. This central authority keeps track of all transactions and the balances of each Cryptocurrency.
The reason why there are many currencies in the world is because each currency is backed by real goods or assets. When you send money to another person, you are actually transferring physical real goods or assets to that person. When you trade in the Cryptocurrency market, you are trading assets or commodities for a digital currency. This type of trading can be done at a number of different speeds and in a variety of different environments, but the most common environment for Cryptocurrences is a peer-to-peer basis.
There are many aspects to the workings of a typical Cryptocurrency. One of the most important aspects of the modern day Cryptocurrency market is the ledger of accounts. These Ledgers are used to keep track of all the transaction that has taken place. In order for a Cryptocurrency to be successful, it must be able to attract investors and users who will then in turn pay for its growth in the Cryptocurrency market. In order for this to happen, the ledger must be well-known and well-organized.
Fortunately, there are several good examples of Cryptocurrencies that work well in a network like the bitx. Several distinct Cryptocurrencies are being utilized around the world right now. A few of the more well-known Cryptocurrencies being utilized include Dash, Zcash, Doge, Peercoin, Litecoin, and FAP Turbo. As more new technologies emerge for use with Cryptocurrency, we should continue to see an increase in the number of well-known and well-organized blockchains as well as the number of unique tokens that are being launched. | <urn:uuid:28a574d6-655e-4cd3-8257-a12c87df5068> | {
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Using fruit flies as a model to study embryo formation, scientists report in Nature Cell Biology that molecular breakdown of a protein called Bicoid is vital to normal head-to-tail patterning of the insect's offspring.
Published online by the journal Dec. 19, the study shows how Bicoid is targeted for molecular degradation by a newly identified protein the researchers named Fates-shifted (Fsd). Without the interaction between Bicoid and Fsd, fruit fly embryos are improperly formed and misshaped, according to scientists at Cincinnati Children's Hospital Medical Center.
The findings are another example of how genetic and molecular studies of embryonic development in fruit flies (known formally as Drosophila melanogaster) help inform medical research into human disease and birth defects. Over half of the genes known to cause disease in humans have a recognizable match in the fruit fly's genetic code.
"Although there is no direct medical impact, this study has critical relevance for medical research into birth defects," said Jun Ma, Ph.D., senior investigator and a researcher in the divisions of Biomedical Bioinformatics and Development Biology. "For tissues in the developing embryo to form properly, cells have to know what their proper locations are. This study looks at the location cues cells receive in early Drosophila embryos."
The cues are delivered through a process that scientists still don't completely understand. It's controlled by molecules called morphogens, which form concentration gradients along the head-to-tail axis, or other axes, of developing embryos. Scientists think these gradients enable cells to know their locations when cells evaluate whether the chemical signals they receive are above or below specific threshold levels. The cells' knowledge of their locations leads them to choose different developmental paths and form distinct tissue types in embryos.
"There are really two sides of the morphogen problem," Dr. Ma explained. "The first is how such concentration gradients are formed in the first place, and the second is how cells respond to such gradients. Our current study looks into the first question at a molecular level."
Bicoid is a morphogen protein critical to fruit fly embryos in forming the head and thorax. The new findings suggest the protein's molecular breakdown is important for establishing a correct concentration gradient and the formation of appropriate tissues at their correct embryo locations.
Collaborating with Dr. Ma on the study is first author, Junbo Liu, Ph.D., a researcher in the division of Biomedical Informatics. Funding support came from the National Institutes of Health and National Science Foundation.
Materials provided by Cincinnati Children's Hospital Medical Center. Note: Content may be edited for style and length.
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First off, if you are looking into learning modes I can only assume you have at least some musical theory background and know a little about scales and the musical alphabet. This knowledge will be required to better understand this lesson. I will not be explaining how scales and the musical alphabet works or where they/it comes from, rather, I will focus entirely on the concept and origin of modes. I suggest you look into lessons on basic scales and the musical alphabet if you still do not feel confident in that area yet. No let's go!
To start, we must define what a "Mode" is. A mode is simply a variation on the major scale. When I say "variation" on the major scale, I do not mean the notes in the scale changes, but rather the note you start on does change within the scale.
There are a total of 7 modes we use (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian) which intentionally coincide with the 7 notes in the major scale.
It is much easier to understand modes in a visual way I find, rather than trying to picture it in your head by reading text so hopefully this example will help you!
We will use the C Major scale for this example: (C D E F G A B)
First off, the major scale is called Ionian and is the first mode. So in C Major we would call the sequence of notes from C to C (C D E F G A B C), C Ionian.
To get the next mode (Dorian) we simply take the next note in the C Major scale (D) and go octave to octave of that note.
So, the Dorian scale in C Major would be: (D E F G A B C D) and is called D Dorian.
You then simply continue this pattern and start on the next note of the major scale and play octave to octave (or beyond if desired of course) of that particular note. Here is what the whole C major scale would look like when broken down into modes:
C Ionian: C D E F G A B C
D Dorian: D E F G A B C D
E Phrygian: E F G A B C D E
F Lydian: F G A B C D E F
G Mixolydian: G A B C D E F G
A Aeolian: A B C D E F G A
B Locrian: B C D E F G A B
See the pattern? Not too difficult! Notice we did not change any of the notes in C major, but we simply started at a different point within the scale at that's it. Now, you're probably wondering what the point of knowing modes is, and a lot of it has to do with chord progressions and following those chords with the "best" sounding notes. For instance, we know that C Ionian or "Major" has a very happy sound, so playing C Ionian and targeting those notes will make for a nice sound when playing over a C Major chord progression. On the other hand, if you had an A minor chord progression you would probably want to stick to playing A Aeolian, but all in all it's all about TARGET notes. If you play jazz or have studied it at all you will know the importance of this. I will cover more of chord progressions and how modes fit into certain ones specifically in a future lesson, but hopefully for now this will help get those new to modes a jump start into the world of them and will wipe away any small confusion! Hope this little lesson was somewhat helpful and keep playing! Rate, Comment, Friend me, any support is very much appreciated! | <urn:uuid:c076de6d-f00a-4271-ac0b-ffc6ae130aa4> | {
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Constipation is defined as:
- a decrease in frequency of bowel movements, compared to a child's usual pattern (some physicians define constipation as fewer than three bowel movements per week).
- the passage of hard, often times large caliber, dry bowel movements.
- bowel movements that are difficult or painful to push out.
Click Image to Enlarge
Sometimes, there is no identifiable reason for constipation in children. However, some of the causes may include:
- Some children eat too much of foods that are high in fat and low in fiber (such as fast foods, "junk" foods, and soft drinks).
- Some children do not drink enough water and liquids.
- lack of exercise
Children who stay inside, watching TV and playing video games, do not get enough exercise. Exercise helps move digested food through the intestines.
- emotional issues
- Pre-school and school-aged children are sometimes embarrassed to use public bathrooms and hold in their bowel movements, causing constipation.
- Toddlers can be overwhelmed by toilet training, especially when a parent is more anxious for the child to be out of diapers than the child is.
- Toddlers can also become involved in power-struggles with their parents as they learn to assert their independence, and may intentionally, hold bowel movements in.
- Some children who experience stress at school, with their friends, or in the family, may have constipation.
- busy children
- Some children ignore signals their intestines give them to have a bowel movement. This can happen when children are too busy playing and forget to go to the bathroom.
- Constipation can also be a problem when children start a new school year, since they are no longer able to go to the bathroom whenever the urge strikes and have to change their bowel routine.
- Once a child becomes constipated, a vicious cycle can develop. Hard, dry stools can be painful to push out, and the child can avoid using the bathroom to avoid the discomfort. Eventually, the intestine will not be able to sense the presence of stool.
Physical problems that can cause constipation include the following:
- abnormalities of the intestinal tract, rectum, or anus
- problems of the nervous system, such as cerebral palsy
- endocrine problems, such as hypothyroidism
- certain medications (i.e., iron preparations and narcotics such as codeine)
Hard stools can irritate or tear the lining of the anus (fissure), making it painful to have a bowel movement. The child may avoid having a bowel movement, which can cause further constipation.
The following are the most common symptoms of constipation. However, each individual may experience symptoms differently. Symptoms may include:
- not having a bowel movement for several days, or passing hard, dry stools
- abdominal bloating, cramps, or pain
- decreased appetite
- clenching teeth, crossing legs, squeezing buttocks together, turning red in the face as the child tries to hold in a bowel movement to avoid discomfort
- small liquid or soft stool smears that soil the child's underwear
The symptoms of constipation may resemble other conditions or medical problems. Always consult your child's physician for a diagnosis.
A physician will examine your child and obtain a complete medical history. Depending on the age of your child, you might be asked questions such as:
- How old was your baby when he/she had their first stool?
- How often does your child have a bowel movement?
- Does your child complain of pain when he/she has a bowel movement?
- Have you been trying to toilet train your toddler recently?
- What does your child's diet consist of?
- Have there been any stressful events in your child's life lately?
- How often does your child soil his/her pants?
Occasionally, your child's physician may want to perform other diagnostic tests to determine if there are any problems. These tests may include:
- digital rectal examination (DRE) - a physician or healthcare provider inserts a gloved finger into the rectum to feel for anything unusual or abnormal.
- abdominal x-ray - a diagnostic test to evaluate the amount of stool in the large intestine.
- barium enema - a procedure performed to examine the large intestine for abnormalities. A fluid called barium (a metallic, chemical, chalky, liquid used to coat the inside of organs so that they will show up on an x-ray) is given into the rectum as an enema. An x-ray of the abdomen shows strictures (narrowed areas), obstructions (blockages), and other problems.
- anorectal manometry - a test that measures the strength of the muscles in the anus, nerve reflexes, ability to sense rectal distention, and coordination of muscles during defecation.
- rectal biopsy - a test that takes a sample of the cells in the rectum to be examined under a microscope for any problems.
Do not hesitate to contact your child's physician if you have any questions or concerns about your child's bowel habits or patterns. The National Institutes of Health recommends that you talk to your child's physician if:
- episodes of constipation last longer than 3 weeks.
- the child is unable to participate in normal activities because of constipation.
- normal pushing is not enough to expel a stool.
- liquid or soft stool leaks out of the anus.
- small, painful tears appear in the skin around the anus.
- hemorrhoids develop.
Specific treatment for constipation will be determined by your child's physician based on the following:
- your child's age, overall health, and medical history
- extent of the condition
- type of condition
- your child's tolerance for specific medications, procedures, or therapies
- expectations for the course of the condition
- your opinion or preference
Treatment may include:
Often, making changes in your child's diet will help constipation. Consider the following suggestions:
- Increase the amount of fiber in your child's diet by:
- adding more fruits and vegetables.
- adding more whole grain cereals and breads (check the nutritional labels on food pack ages for foods that have more fiber).
||Whole wheat bread, granola bread, wheat bran muffins, Nutri-Grain® waffles, popcorn
||Bran Flakes®, Raisin Bran®, Shredded Wheat®, Frosted Mini Wheats®, oatmeal, Muslix®, granola, oat bran
||All-Bran®, Bran Buds®, Corn Bran®, Fiber One®, 100% Bran®
||Beets, broccoli, brussel sprouts, cabbage, carrots, corn, green beans, green peas, acorn and butternut squash, spinach, potato with skin, avocado
||Apples with peel, dates, papayas, mangos, nectarines, oranges, pears, kiwis, strawberries, applesauce, raspberries, blackberries, raisins
||Cooked prunes, dried figs
||Peanut butter, nuts
||Baked beans, black-eyed peas, garbanzo beans, lima beans, pinto beans, kidney beans, chili with beans, trail mix
- Offer your child fruit juice instead of soft drinks.
- Encourage your child to drink more fluids, especially water.
- Limit fast foods and junk foods that are usually high in fats and offer more well-balanced meals and snacks.
- Limit drinks with caffeine, such as cola drinks and tea.
- Limit whole milk to 16 ounces a day for the child over 2 years of age, but do not eliminate milk altogether. Children need the calcium in milk to help their bones grow strong.
Plan to serve your child's meals on a regular schedule. Often, eating a meal will stimulate a bowel movement within 30 minutes to an hour. Serve breakfast early so your child does not have to rush off to school and miss the opportunity to have a bowel movement.
Increasing the amount of exercise your child gets can also help with constipation. Exercise aids digestion by helping the normal movements the intestines make to push food forward as it is digested. People who do not move around much are often constipated. Encourage your child to go outside and play rather than watch TV or engage in other indoor activities.
Proper bowel habits
Have your child sit on the toilet at least twice a day for at least 10 minutes, preferably shortly after a meal. Make this time pleasant; do not scold or criticize the child if they are unable to have a bowel movement. Giving stickers or other small rewards, and making posters that chart your child's progress can help motivate and encourage him/her.
If these methods do not help, or if your physician notices other problems, he/she may recommend laxatives, stool softeners, or an enema. These products should ONLY be used with the recommendation of your child's physician. DO NOT use them without consulting with your child's physician first.
The outlook depends on what type of condition caused the constipation. Those children with diseases of the intestine, such as Hirschsprung's disease, may have chronic problems. However, most of the time, constipation is a temporary situation.
Click here to view the
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# M01 #35 clarification
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31 Oct 2010, 11:32
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Find the number of divisors of 90 and then the number of divisors of that result.
The following formula can be used to find the number of divisors of any given number. Factor 90 ( $$90= 2*3^2*5$$ ) and then multiply the powers+1 $$2*3*2=12$$ . Therefore, $$@90=12$$ .
Another approach is to write out all of the distinct divisors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90; the answer is 12, not 10 because 1 and 90 are also included.
The explanation says there is a formula to determine the number of divisors rather than counting them out, I can't follow the formula can the club please define if your familiar with it? Thanks
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31 Oct 2010, 11:36
gettinit wrote:
Find the number of divisors of 90 and then the number of divisors of that result.
The following formula can be used to find the number of divisors of any given number. Factor 90 ( $$90= 2*3^2*5$$ ) and then multiply the powers+1 $$2*3*2=12$$ . Therefore, $$@90=12$$ .
Another approach is to write out all of the distinct divisors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90; the answer is 12, not 10 because 1 and 90 are also included.
The explanation says there is a formula to determine the number of divisors rather than counting them out, I can't follow the formula can the club please define if your familiar with it? Thanks
Discussed here: m01-78589.html?hilit=finding%20factors#p786451
MUST KNOW FOR GMAT:
Finding the Number of Factors of an Integer
First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.
The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.
Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$
Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.
Back to the original question:
If $$@x$$ is the number of distinct positive divisors of $$x$$ , what is the value of $$@@90$$?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
The question defines $$@x$$ as the number of distinct positive divisors of $$x$$. Say $$@6=4$$, as 6 have 4 distinct positive divisors: 1, 2, 3, 6.
Question: $$@@90=?$$
$$90=2*3^2*5$$, which means that the number of factors of 90 is: $$(1+1)(2+1)(1+1)=12$$. So $$@90=12$$ --> $$@@90=@12$$ --> $$12=2^2*3$$, so the number of factors of 12 is: $$(2+1)(1+1)=6$$.
For more on these issues check Number Theory chapter of Math Book: math-number-theory-88376.html
Hope it helps.
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04 Nov 2010, 17:24
Thanks Bunuel, very helpful and really appreciate the responsiveness!
Re: M01 #35 clarification [#permalink] 04 Nov 2010, 17:24
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14 Re: M01-Q35 Please help with this question. thanks 17 04 Apr 2009, 05:39
19 M01-Q15 20 16 Jul 2008, 20:25
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# M01 #35 clarification
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Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | crawl-data/CC-MAIN-2017-09/segments/1487501173866.98/warc/CC-MAIN-20170219104613-00026-ip-10-171-10-108.ec2.internal.warc.gz | null |
Hectometer to Furlong (US) converter | hm to fur conversion
# Hectometer to Furlong (US) converter| hm to fur conversion
Are you struggling with converting Hectometer to Furlong (US)? Don’t worry! Our online “Hectometer to Furlong (US) Converter” is here to simplify the conversion process for you.
Here’s how it works: simply input the value in Hectometer. The converter instantly gives you the value in Furlong (US). No more manual calculations or headaches – it’s all about smooth and effortless conversions!
Think of this Hectometer (hm ) to Furlong (US) (fur) converter as your best friend who helps you to do the conversion between these length units. Say goodbye to calculating manually over how many Furlong (US) are in a certain number of Hectometer – this converter does it all for you automatically!
## What are Hectometer and Furlong (US)?
In simple words, Hectometer and Furlong (US) are units of length used to measure the size or distance of something. It helps us understand the length of objects, spaces, or dimensions. The short form of Hectometer is “hm” and the short form for Furlong (US) is “fur”
In everyday life, we use length units to express the size of anything in various contexts, such as measuring furniture, determining the length of a room, or specifying the dimensions of an object. Hectometer and Furlong (US) are also two common units of length.
## How to convert from Hectometer to Furlong (US)?
If you want to convert between these two units, you can do it manually too. To convert from Hectometer to Furlong (US) just use the given formula:
fur = Value in hm * 0.4970959596
here are some examples of conversion,
• 2 hm = 2 * 0.4970959596 fur = 0.9941919192 fur
• 5 hm = 5 * 0.4970959596 fur = 2.485479798 fur
• 10 hm = 10 * 0.4970959596 fur = 4.970959596 fur
### Hectometer to Furlong (US) converter: conclusion
Here we have learn what are the length units Hectometer (hm ) and Furlong (US) (fur)? How to convert from Hectometer to Furlong (US) manually and also we have created an online tool for conversion between these units.
Hectometer to Furlong (US) converter” or simply hm to fur converter is a valuable tool for simplifying length unit conversions. By using this tool you don’t have to do manual calculations for conversion which saves you time. | crawl-data/CC-MAIN-2024-10/segments/1707947475311.93/warc/CC-MAIN-20240301125520-20240301155520-00626.warc.gz | null |
Chagas disease, a tropical parasitic disease that can lead to life-threatening heart and digestive disorders, may be more widespread in Texas than previously thought, according to research from The University of Texas at Austin.
"We've been studying this for four years now, and this year the number of disease-causing insects is quite amazing," says Sahotra Sarkar, professor of integrative biology and philosophy at The University of Texas at Austin and lead author of a paper on the disease published in PLoS Neglected Tropical Diseases.
Endemic to rural areas of Latin America, Chagas disease is often transmitted by triatomine bugs, also known as "kissing bugs."
In order to assess the prevalence of Chagas disease in Texas, Sarkar is working with a network of health professionals and researchers around the state. After collecting and classifying insects from the field, Sarkar sends them to Philip Williamson, an assistant professor at The University of North Texas Health Science Center. Williamson determines how many of the bugs carry the protozoa Trypanosoma cruzi, which causes the disease.
From the data Sarkar creates epidemiological maps showing the number and location of carrier insects, recorded human Chagas infections and hospitable habitats for the insects.
The maps suggest South Texas is an area of high risk for Chagas infection. Sarkar says there may already be hundreds of undiagnosed cases of the disease.
Chagas can be hard to detect because it can look like the flu at first, with symptoms similar to pains and fever. The symptoms appear to go away but the disease can live in a person for decades, sometimes reappearing in the form of digestive or heart failure.
In Texas, where most doctors are not familiar with the disease and are not required to report it to public health officials, they may misinterpret its late-onset symptoms as an old age problem, says Sarkar.
"So it doesn't get diagnosed at the beginning, and it doesn't get diagnosed at the end," he says.
Until further research is done, Sarkar and his colleagues won't be able to say for sure how widespread the disease is. They believe the risks are high enough, however, to recommend a few low-cost, low-impact changes to the way the Texas public health system deals with Chagas.
They say Chagas should be designated as a reportable disease, which would require health professionals to report incidences of it to the Texas Department of State Health Services. Efforts should be launched in South Texas to more thoroughly determine the prevalence of Chagas in humans, dogs and wild species (particularly rats) that often act as reservoirs of the disease. And there should be mandatory screening of blood donations for the presence of Chagas. Currently, screening is voluntary and only done with about 65 percent of samples.
In the future, Sarkar would like to see Mexico and the U.S. collaborate on a multi-layered attack on the disease. He points to the success of the Southern Cone Initiative in South America as a model. Simple changes in lifestyle, such as keeping piles of wood away from the home and encouraging people to switch from adobe or wooden houses to concrete, have been effective. Selective spraying for the insects has also been key to decreasing the burden of the disease in South America. | <urn:uuid:acdd691f-05cd-434e-ad16-2648466bd787> | {
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# What is the value of $\int^\infty_{-\infty} \cos^2 x\, dx$?
For the given expression, I can make the following steps:
$$\int^\infty_{-\infty} \cos^2x \,dx = \frac{1}{2}\int^\infty_{-\infty} \cos 2x\, + 1\, dx\\ \hspace{19mm}= \frac{1}{2} \left\{ \frac{1}{2}\sin2x + x \right\}\bigg\rvert^\infty_{-\infty}\\ \hspace{13mm}= \frac{1}{4} \sin2x \, \bigg\rvert^\infty_{-\infty} + x\,\bigg\rvert_{\infty}$$
I understand that $\lim_{x \rightarrow 0} \sin x$ is not defined. Thus the last line indicates that the integral is not defined.
Given that $1 \geq \cos^2 x \geq 0\, \forall \, x \in \mathbb{R}$. Should not the integral be $\infty$ instead of not defined?
• Where did the $x$ in your second line go? – Arthur Jun 29 '18 at 9:01
• Why did you kill the "$+x$" in the last equality? – Crostul Jun 29 '18 at 9:01
• my apologies for missing out the last term, I have made an edit – Tian Jun 29 '18 at 9:04
$\int _{2k\pi } ^{2(k+1)\pi } \cos ^{2} (x) \, dx =\pi$. Add these integrals over $k$.
Note that$$\int_{-\infty}^{+\infty}\cos^2(x)\,\mathrm dx=\int_0^{+\infty}\cos^2(x)\,\mathrm dx+\int_{-\infty}^0\cos^2(x)\,\mathrm dx.$$This way, you can prove that integral $\int_0^{+\infty}\cos^2(x)\,\mathrm dx$ and $\int_{-\infty}^0\cos^2(x)\,\mathrm dx$ is indeed $+\infty$. | crawl-data/CC-MAIN-2019-51/segments/1575540488870.33/warc/CC-MAIN-20191206145958-20191206173958-00260.warc.gz | null |
## Calculus: Early Transcendentals (2nd Edition)
$${x^2} + x + 1$$
\eqalign{ & \frac{d}{{dx}}\int_3^x {\left( {{t^2} + t + 1} \right)dt} \cr & {\text{Using The Fundamental Theorem }}\left( {{\text{part 1}}} \right) \cr & A\left( x \right) = \int_a^x {f\left( t \right)dt{\text{ }} \to {\text{ }}} A'\left( x \right) = \frac{d}{{dx}}\int_a^x {f\left( t \right)dt} = f\left( x \right) \cr & {\text{In this exercise}} \cr & f\left( t \right) = {t^2} + t + 1,{\text{ and }}a = 3 \cr & then \cr & \frac{d}{{dx}}\int_3^x {\left( {{t^2} + t + 1} \right)dt} = {\left( x \right)^2} + \left( x \right) + 1 \cr & \frac{d}{{dx}}\int_3^x {\left( {{t^2} + t + 1} \right)dt} = {x^2} + x + 1 \cr} | crawl-data/CC-MAIN-2018-30/segments/1531676592420.72/warc/CC-MAIN-20180721071046-20180721091046-00063.warc.gz | null |
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Lec13 - Convex hulls Gift wrapping d > 2 Problem definition...
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Convex hulls Gift wrapping, d > 2 Problem definition CONVEX HULL, D > 2 INSTANCE. Set S = { p 1 , p 2 , … p N } of points in d -space ( E d ). QUESTION. Construct the convex hull H ( S ) of S . The coordinates of the points p i S will be referred to as p i = ( x 1 , x 2 , …, x d ). For d = 2, the constructed hull was given (represented) as a sequence of hull vertices. How is the hull represented for d > 2? To answer that, and describe the algorithm, more definitions are needed.
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Convex hulls Gift wrapping, d > 2 Polyhedron In E 3 a polyhedron is defined by a finite set of planar polygons such that every edge of a polygon is shared by exactly one other polygon and no subset of the polygons has the property. Polyhedra is plural for polyhedron. The polygons that share an edge are adjacent . The vertices and edges of the polygons are the vertices and edges of the polyhedron. The polygons are the facets of the polyhedron. A polyhedron is simple if there is no pair of nonadjacent facets sharing a point. A simple polyhedron partitions 3-space into two domains, the interior (bounded) and the exterior (unbounded). The term polyhedron often means boundary interior. A simple polyhedron is convex if its interior is a convex set. A polyhedron is the 3-dimensional equivalent of a polygon.
Convex hulls Gift wrapping, d > 2 Polytope A half-space is the portion of E d lying on one side of a hyperplane. A polyhedral set in E d is the intersection of a finite set of closed half-spaces. Note that a polyhedral set is convex, since a half-space is convex, and the intersection of convex sets is convex. Plane polygons ( d = 2) and space polyhedra ( d = 3) are 2- and 3-dimensional instances of bounded polyhedral sets. A bounded d -dimensional polyhedral set is a polytope . Note that polytopes are convex by definition. The terms “convex d -polytope”, “ d -polytope”, and “polytope” are all equivalent. Theorem. The convex hull of a finite set of points in E d is a convex d -polytope. Conversely, a polytope is the convex hull of a finite set of points. For d = 3, the convex hull is a convex polyhedron. For arbitrary d , the convex hull is a d -polytope.
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Convex hulls Gift wrapping, d > 2 Affine set Given k distinct points p 1 , p 2 , …, p k in E d , the set of points p = α 1 p 1 + α 2 p 2 + . . . + α k p k ( α j , α 1 + α 2 + . . . + α k = 1) is the affine set generated by p 1 , p 2 , …, p k , and p is an affine combination of p 1 , p 2 , …, p k . We have seen this before. If k = 2, this is the parametric equation of a line, i.e., a line is an affine set. For k = 3, the affine set is a plane. In general, an affine set for given k is a “flat” object of k - 1 dimensions. Given a subset
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Ask a homework question - tutors are online | crawl-data/CC-MAIN-2018-09/segments/1518891813431.5/warc/CC-MAIN-20180221044156-20180221064156-00445.warc.gz | null |
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You are reading an older version of this FlexBook® textbook: CK-12 Basic Algebra Concepts Go to the latest version.
# Chapter 12: Rational Equations and Functions
Difficulty Level: Basic Created by: CK-12
## Introduction
The final chapter of this text introduces the concept of rational functions; that is, equations in which the variable appears in the denominator of a fraction. A common rational function is the inverse variation model, similar to the direct variation model you studied in a Concept in chapter 4. We finish the chapter with solving rational equations and using graphical representations to display data.
## Summary
This chapter begins by talking about inverse variation models, the graphs of rational functions, and the division of polynomials. It then moves on to discuss rational expressions in detail, including the multiplication, division, addition, and subtraction of rational expressions. Next, instruction is given on solving rational equations by using proportions and by clearing denominators. Finally, surveys and samples in statistics are highlighted.
### Rational Equations and Functions; Statistics Review
Define the following terms used in this chapter.
1. Inverse variation
2. Asymptotes
3. Hyperbola
4. Points of discontinuity
5. Least common multiple
6. Random sampling
7. Stratified sampling
8. Biased
9. Cherry picking
10. What quadrants are the branches of a hyperbola located if k<0\begin{align*}k<0\end{align*}?
Are the following examples of direct variation or inverse variation?
1. The number of slices n\begin{align*}n\end{align*} people get from sharing one pizza
2. The thickness of a phone book given n\begin{align*}n\end{align*} telephone numbers
3. The amount of coffee n\begin{align*}n\end{align*} people receive from a single pot
4. The total cost of pears given that nectarines cost \$0.99 per pound
For each variation equation:
1. Translate the sentence into an inverse variation equation.
2. Find k\begin{align*}k\end{align*}, the constant of variation.
3. Find the unknown value.
1. y\begin{align*}y\end{align*} varies inversely as x\begin{align*}x\end{align*}. When x=5,y=215\begin{align*}x=5, y=\frac{2}{15}\end{align*}. Find y\begin{align*}y\end{align*} when x=12\begin{align*}x=- \frac{1}{2}\end{align*}.
2. y\begin{align*}y\end{align*} is inversely proportional to the square root of y\begin{align*}y\end{align*}. When x=16,y=0.5625\begin{align*}x=16, y=0.5625\end{align*}. Find y\begin{align*}y\end{align*} when x=18\begin{align*}x=\frac{1}{8}\end{align*}.
3. Habitat for Humanity uses volunteers to build houses. The number of days it takes to build a house varies inversely as the number of volunteers. It takes eight days to build a house with twenty volunteers. How many days will it take sixteen volunteers to complete the same job?
4. The Law of the Fulcrum states the distance you sit to balance a seesaw varies inversely as your weight. If Gary weighs 20.43 kg and sits 1.8 meters from the fulcrum, how far would Shelley sit, assuming she weighs 36.32 kilograms?
For each function:
1. Graph it on a Cartesian plane.
2. State its domain and range.
3. Determine any horizontal and/or vertical asymptotes the function may have.
1. y=4x\begin{align*}y=\frac{4}{x}\end{align*}
2. f(x)=24x\begin{align*}f(x)=\frac{2}{4-x}\end{align*}
3. g(x)=1x+1\begin{align*}g(x)=\frac{-1}{x+1}\end{align*}
4. y=63x+12\begin{align*}y=\frac{6}{3x+1}-2\end{align*}
5. f(x)=3x5\begin{align*}f(x)=\frac{3}{x}-5\end{align*}
Perform the indicated operation.
1. 5a65b4b\begin{align*}\frac{5a}{6}-\frac{5b}{4b}\end{align*}
2. 43m+4m5\begin{align*}\frac{4}{3m}+\frac{4m}{5}\end{align*}
3. 3x2xy+43\begin{align*}\frac{3x}{2xy}+\frac{4}{3}\end{align*}
4. 25n2+2n2\begin{align*}\frac{2}{5n-2}+\frac{2n}{2}\end{align*}
5. 2x+13x+9x+53x+9\begin{align*}\frac{2x+1}{3x+9}-\frac{x+5}{3x+9}\end{align*}
6. 5m+n30n44m+n30n4\begin{align*}\frac{5m+n}{30n^4}-\frac{4m+n}{30n^4}\end{align*}
7. r64r212r+8r+64r212r+8\begin{align*}\frac{r-6}{4r^2-12r+8}-\frac{r+6}{4r^2-12r+8}\end{align*}
8. 216x3y2+x2y16x3y2\begin{align*}\frac{2}{16x^3 y^2}+\frac{x-2y}{16x^3 y^2}\end{align*}
9. n6n+2+2n5\begin{align*}\frac{n-6}{n+2}+\frac{2n}{5}\end{align*}
10. 84x+5x+8\begin{align*}\frac{8}{4}-\frac{x+5}{x+8}\end{align*}
11. 3x2(x+1)+67x6\begin{align*}\frac{3x}{2(x+1)}+\frac{6}{7x-6}\end{align*}
12. 11820x22\begin{align*}\frac{11}{8} \cdot \frac{20x^2}{2}\end{align*}
13. 17r167r416\begin{align*}\frac{17r}{16} \cdot \frac{7r^4}{16}\end{align*}
14. 15181417t\begin{align*}\frac{15}{18} \cdot \frac{14}{17t}\end{align*}
15. 2(b11)14bb+5(b+5)(b11)\begin{align*}\frac{2(b-11)}{14b} \cdot \frac{b+5}{(b+5)(b-11)}\end{align*}
16. 17w2w+418(w+4)17w2(w9)\begin{align*}\frac{17w^2}{w+4} \cdot \frac{18(w+4)}{17w^2 (w-9)}\end{align*}
17. 10s330s230s210s3s38\begin{align*}\frac{10s^3-30s^2}{30s^2-10s^3} \cdot \frac{s-3}{8}\end{align*}
18. 1f5÷f+3f2+6f+9\begin{align*}\frac{1}{f-5} \div \frac{f+3}{f^2+6f+9}\end{align*}
19. (a+8)(a+3)4(a+3)÷10a2(a+10)4\begin{align*}\frac{(a+8)(a+3)}{4(a+3)} \div \frac{10a^2 (a+10)}{4}\end{align*}
20. 1(h10)(h+7)÷(h4)4h(h10)\begin{align*}\frac{1}{(h-10)(h+7)} \div \frac{(h-4)}{4h(h-10)}\end{align*}
21. 2(5x8)4x2(85x)÷64x2\begin{align*}\frac{2(5x-8)}{4x^2 (8-5x)} \div \frac{6}{4x^2}\end{align*}
22. 2(q7)40q(q+1)÷140q(q+1)\begin{align*}\frac{2(q-7)}{40q(q+1)} \div \frac{1}{40q(q+1)}\end{align*}
Solve each equation.
1. 33x2=1x+13x2\begin{align*}\frac{3}{3x^2}=\frac{1}{x}+\frac{1}{3x^2}\end{align*}
2. 25x2=12x3\begin{align*}\frac{2}{5x^2}=-\frac{12}{x-3}\end{align*}
3. 7xx6=34x+16\begin{align*}\frac{7x}{x-6}=\frac{3}{4x+16}\end{align*}
4. 4c2=3c+4\begin{align*}\frac{4}{c-2}=\frac{3}{c+4}\end{align*}
5. \begin{align*}\frac{d-4}{4d^2}=\frac{1}{4d^2}+\frac{1}{4d}\end{align*}
6. \begin{align*}\frac{1}{2}=\frac{2z-12}{z} - \frac{z+1}{4z}\end{align*}
7. \begin{align*}\frac{1}{n}=\frac{1}{n^2} +\frac{6}{n}\end{align*}
8. \begin{align*}\frac{1}{2a}=\frac{1}{2a^2}+\frac{1}{a}\end{align*}
9. \begin{align*}\frac{k+4}{k^2} =\frac{5k-30}{3k^2}+\frac{1}{3k^2}\end{align*}
10. It takes Jayden seven hours to paint a room. Andie can do it in five hours. How long will it take to paint the room if Jayden and Andie work together?
11. Kiefer can mow the lawn in 4.5 hours. Brad can do it in two hours. How long will it take if they worked together?
12. Melissa can mop the floor in 1.75 hours. With Brad’s help, it took only 50 minutes. How long would it take Brad to mop it alone?
13. Working together, it took Frankie and Ricky eight hours to frame a room. It would take Frankie fifteen hours doing it alone. How long would it take Ricky to do it alone?
14. A parallel circuit has \begin{align*}R_1=50 \Omega\end{align*} and \begin{align*}R_t=16 \Omega\end{align*}. Find \begin{align*}R_2\end{align*}.
15. A parallel circuit has \begin{align*}R_1=6 \Omega\end{align*} and \begin{align*}R_2=9 \Omega\end{align*}. Find \begin{align*}R_T\end{align*}.
16. A series circuit has \begin{align*}R_1=200 \Omega\end{align*} and \begin{align*}R_t=300 \Omega\end{align*}. Find \begin{align*}R_2\end{align*}.
17. A series circuit has \begin{align*}R_1=11 \Omega\end{align*} and \begin{align*}R_2=25 \Omega\end{align*}. Find \begin{align*}R_T\end{align*}.
18. Write the formula for the total resistance for a parallel circuit with three individual resistors.
19. What would be the bias in this situation? To determine the popularity of a new snack chip, a survey is conducted by asking 75 people walking down the chip aisle in a supermarket which chip they prefer.
20. Describe the steps necessary to design and conduct a survey.
21. You need to survey potential voters for an upcoming school board election. Design a survey with at least three questions you could ask. How will you plan to conduct the survey?
22. What is a stratified sample? Name one case where a stratified sample would be more beneficial.
### Rational Equations and Functions; Statistics Test
1. True or false? A horizontal asymptote has the equation \begin{align*}y=c\end{align*} and represents where the denominator of the rational function is equal to zero.
2. A group of SADD members wants to find out about teenage drinking. The members conduct face-to-face interviews, wearing their SADD club shirts. What is a potential bias? How can this be modified to provide accurate results?
3. Name the four types of ways questions can be biased.
4. Which is the best way to show data comparing two categories?
5. Consider \begin{align*}f(x)= -\frac{4}{x}\end{align*}. State its domain, range, asymptotes, and the locations of its branches.
6. \begin{align*}h\end{align*} varies inversly as \begin{align*}r\end{align*}. When \begin{align*}h=-2.25, r=0.125\end{align*}. Find \begin{align*}h\end{align*} when \begin{align*}r=12.\end{align*}
7. Name two types of visual displays that could be used with a frequency distribution.
8. Tyler conducted a survey asking the number of pets his classmates owned and received the following results: 0, 2, 1, 4, 3, 2, 1, 0, 0, 0, 0, 1, 4, 3, 2, 3, 4, 3, 2, 1, 1, 1, 5, 7, 0, 1, 2, 3, 2, 1, 4, 3, 2, 1, 1, 0
1. Display this data with a frequency distribution chart.
2. Use it to make a histogram.
3. Find its five-number summary.
4. Draw a box-and-whisker plot.
5. Make at least two conclusions regarding Tyler’s survey.
1. Find the excluded values, the domain, the range, and the asymptotes of:
Perform the indicated operation.
1. \begin{align*}\frac{4}{21r^4}+\frac{4r+5t}{21r^4}\end{align*}
2. \begin{align*}\frac{a-v}{12a^3}-\frac{a+5v}{12a^3}\end{align*}
3. \begin{align*}\frac{8}{g+8}+\frac{g-3}{g-5}\end{align*}
4. \begin{align*}\frac{4t}{5t-8}+\frac{24}{12}\end{align*}
5. \begin{align*}\frac{4}{5} \cdot \frac{80}{48m}\end{align*}
6. \begin{align*}\frac{1}{d-8} \div \frac{d+7}{2d+14}\end{align*}
7. \begin{align*}\frac{1}{u-3} \div \frac{u-4}{2u-6}\end{align*}
Solve.
1. \begin{align*}\frac{7w}{w-7}=\frac{7w}{w+5}\end{align*}
2. \begin{align*}\frac{p-6}{3p^2-6p}=\frac{7}{3}\end{align*}
3. \begin{align*}\frac{2}{x^2} =\frac{1}{2x^2}-\frac{x+1}{2x^2}\end{align*}
4. \begin{align*}\frac{1}{2}-\frac{1}{4r}=\frac{3}{4}\end{align*}
5. \begin{align*}\frac{y-5}{3y^2}=-\frac{1}{3y}+\frac{1}{y^2}\end{align*}
6. Working together, Ashton and Matt can tile a floor in 25 minutes. Working alone, it would take Ashton two hours. How long would it take Matt to tile the floor alone?
7. Bethany can paint the deck in twelve hours. Melissa can paint the deck in five hours. How long would it take the girls to paint the deck, working together?
8. A parallel circuit has \begin{align*}R_t=115 \ \Omega\end{align*} and \begin{align*}R_2=75 \ \Omega\end{align*}. Find \begin{align*}R_1\end{align*}.
9. A series circuit has \begin{align*}R_1=13 \ \Omega\end{align*} and \begin{align*}R_t=21 \ \Omega\end{align*}. Find \begin{align*}R_2\end{align*}.
#### Texas Instruments Resources
In the CK-12 Texas Instruments Algebra I FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9622.
Basic
8 , 9
Feb 24, 2012 | crawl-data/CC-MAIN-2016-07/segments/1454701160950.71/warc/CC-MAIN-20160205193920-00037-ip-10-236-182-209.ec2.internal.warc.gz | null |
Between a quarter and a half of all birds, along with around a third of amphibians and a quarter of corals, are highly vulnerable to climate change. These findings have emerged from the most comprehensive assessment to date of the impact of global warming on life. Its results have led some researchers to warn of the need for unprecedented conservation efforts if we don’t cut our emissions.
The new assessment of climate change risk was performed by scientists from the International Union for Conservation of Nature (IUCN), the organisation that produces the Red List of Threatened Species. “When the Red List was invented, it was long before anyone worried about climate change,” says Wendy Foden of the IUCN in Cambridge, UK.
Red List assessments of extinction risk do consider climate change, but in a limited way. The main tools used in these earlier assessments are species distribution models, says Foden. These map out the climate conditions where a species lives now, then estimate how that liveable area will alter as the climate changes. In many cases, species’ habitable ranges will move and shrink, putting them at risk.
But that’s not enough to assess risk. Some species may be able to cope if their environment changes. Others may be particularly suited to evolving new adaptations that will allow them to acclimatise to the changing environment. And yet more species may simply move to new areas.
Pace of reproduction
Foden and colleagues tried to take all that into account in their new assessment. They considered how quickly species could relocate, and whether they were barriers like mountain ranges in their way. They also examined how rapidly species could evolve. For instance, species that reproduce quickly have a better chance of evolving new adaptations than those that do not.
“If you’re a narwhal and only breed once every two years, it’s not going to happen,” says Foden. Species with low genetic diversity are also slow to evolve.
“These ideas have been milling around,” says Chris Thomas of the University of York in the UK. “But the way they’ve clarified them will be really helpful.”
So far, the team has applied their criteria to all birds, amphibians and corals. Species were classed as highly vulnerable if their local climate is changing rapidly, they are sensitive to these changes, and have little ability to adapt or relocate.
The results make for grim reading. Among birds, 24 to 50 per cent of species are highly vulnerable, according to the team’s most optimistic and pessimistic forecasts, as are 22 to 44 per cent of amphibians and 15 to 32 per cent of corals. The figures are similar to those obtained in a 2004 study by Thomas, which estimated that 15 to 37 per cent of species will be “committed to extinction” by 2050 due to climate change (Nature, doi.org/c34wgp). “These are high percentages,” says Thomas.
“Safe” species at risk
What’s more, many of these species are not currently classed as threatened. Foden says that 17 to 41 per cent of birds are highly vulnerable to climate change despite being considered safe by the Red List.
Certain areas are hotspots of threatened species. For instance, the Amazon rainforest contains huge numbers of birds and amphibians that are highly vulnerable to climate change. Most Arctic birds are also highly vulnerable, as are corals in the Caribbean and the Coral Triangle in south-east Asia.
“The moment you start thinking about the magnitude of the conservation programme we might need to put in place, it’s mind-boggling,” Thomas says. Protected areas would need to be much bigger than at present to safeguard relocating species. Also, we would have to intervene to move many species, often to new countries. Such translocations are difficult and expensive, and in any case many countries don’t allow them.
The best thing we can do is cut greenhouse gas emissions. “Minimising the rate and extent of climate change will reduce the amount of action required,” says Thomas.
Journal reference: PLoS ONE, DOI: 10.1371/journal.pone.0065427
More on these topics: | <urn:uuid:89d1e62a-cf58-4e5d-b162-a5baab818154> | {
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The retina is the light-sensitive tissue lining the back of our eye. Light rays are focused onto the retina through our cornea, pupil and lens. The retina converts the light rays into impulses that travel through the optic nerve to our brain, where they are interpreted as the images we see. A healthy, intact retina is key to clear vision.
The middle of our eye is filled with a clear gel called vitreous (vi-tree-us) that is attached to the retina. Sometimes tiny clumps of gel or cells inside the vitreous will cast shadows on the retina, and you may sometimes see small dots, specks, strings or clouds moving in your field of vision. These are called floaters. You can often see them when looking at a plain, light background, like a blank wall or blue sky.
As we get older, the vitreous may shrink and pull on the retina. When this happens, you may notice what look like flashing lights, lightning streaks or the sensation of seeing “stars.” These are called flashes.
Usually, the vitreous moves away from the retina without causing problems. But sometimes the vitreous pulls hard enough to tear the retina in one or more places. Fluid may pass through a retinal tear, lifting the retina off the back of the eye — much as wallpaper can peel off a wall. When the retina is pulled away from the back of the eye like this, it is called a retinal detachment.
The retina does not work when it is detached and vision becomes blurry. A retinal detachment is a very serious problem that almost always causes blindness unless it is treated with detached retina surgery.
Vitreous gel, the clear material that fills the eyeball, is attached to the retina in the back of the eye. As we get older, the vitreous may change shape, pulling away from the retina. If the vitreous pulls a piece of the retina with it, it causes a retinal tear. Once a retinal tear occurs, vitreous fluid may seep through and lift the retina off the back wall of the eye, causing the retina to detach or pull away.
Vitreous fluid normally shrinks as we age, and this usually doesn’t cause damage to the retina. However, inflammation (swelling) or nearsightedness (myopia) may cause the vitreous to pull away and result in retinal detachment.
People with the following conditions have an increased risk for retinal detachment:
• Previous cataract, glaucoma or other eye surgery;
• Glaucoma medications that make the pupil small (like pilocarpine)
• Severe eye injury;
• Previous retinal detachment in the other eye;
• Family history of retinal detachment;
• Weak areas in the retina that can be seen by an ophthalmologist during an eye exam.
If you have risk factors for retinal detachment, know the warning signsand seek immediate medical attention if you have any of these signs.
If you are very nearsighted or if you have a family history of retinal problems, be sure to have complete dilated eye exams on a regular basis. And always wear protective eyewear when playing sports or engaging in any other hazardous activities. If you have a serious eye injury, see your ophthalmologist right away for an exam.
Symptoms of a retinal tear and a retinal detachment can include the following:
• A sudden increase in size and number of floaters, indicating a retinal tear may be occurring;
• A sudden appearance of flashes, which could be the first stage of a retinal tear or detachment;
• Having a shadow appear in the periphery (side) of your field of vision;
• Seeing a gray curtain moving across your field of vision;
• A sudden decrease in your vision.
Floaters and flashes in themselves are quite common and do not always mean you have a retinal tear or detachment. However, if they are suddenly more severe and you notice you are losing vision, you should call your ophthalmologist right away.
Some retinal detachments are found during a routine eye examination. That is why it is so important to have regular eye exams.
Your ophthalmologist can diagnose retinal tear or retinal detachment during an eye examination where he or she dilates (widens) the pupils of your eyes.
An ultrasound of the eye may also be performed to get additional detail of the retina.
Only after careful examination can your ophthalmologist tell whether a retinal tear or early retinal detachment is present. | <urn:uuid:81f89d09-c5ad-4612-b3be-f994df37ef1e> | {
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Until now, the existing technique for genetically reprogramming adult cells and converting them into stem cells required time — roughly several weeks — and had a dismal success rate of about one percent. Today, a team of Japanese scientists have published their research supporting a much simpler method, referred to as stimulus-triggered acquisition of pluripotency (STAP), which is more efficient, more rapid, and more successful than the existing technique. In fact, the new method, tested within mice, requires only that blood cells be dipped into an acid bath as a way of exposing them to a low pH.
Despite the seeming ease of this groundbreaking technique, the development process took years — nearly five — since Haruko Obokata, a stem cell biologist at the RIKEN Center for Developmental Biology in Kobe, Japan, first came up with the initial idea. One reason such a long delay spread between conception and birth was the fact that she needed to fully convince her scientific colleagues of the value of her technique. But that, as they say, is science.
Stem cells are unspecialized cells that have the remarkable ability to turn into any cell in the human body and for this reason they are a significant area of research for scientists seeking to develop personalized medicine. The technique of genetically reprogramming cells and creating stem cells, known as induced pluripotent stem cells (iPSC), was first reported in 2006 and demonstrated in human cells one year later. Since then, iPSCs have been very useful to scientists in drug development and modeling of diseases, though the process of creating these cells, which took and was not often successful, left much to be desired.
How, then, did the new STAP cell technique come about? One day while culturing cells, Obokata saw how some cells, after being squeezed through a capillary tube, shrunk to a similar size as stem cells. She wondered: Could simply stressing cells make them pluripotent? To investigate, she began a series of experiments where she applied different kinds of stress, including heat, starvation, and a high-calcium environment. Soon, she found that three stressors — perforating the cell membrane with a bacterial toxin, physical squeezing, and exposing a cell to low pH — induced signs of pluripotency in the cells.
Having made this significant discovery, Obokata next had to prove these cells were indeed capable of turning into any and all cell types in the manner of a true stem cell. To accomplish this, she turned to mouse-cloning pioneer Teruhiko Wakayama at the University of Yamanashi, Japan, who helped her by developing mice into which she could introduce her STAP cells. Next, she worked in the laboratory of Charles Vacanti, a tissue engineer at Harvard University. With his help, Obokata uncovered a biological explanation for her method: that generation of cells in this manner occurs in nature as a response to injury.
Today, Obokata has already genetically reprogrammed a dozen cell types, including those from different organs in the body. Although she believes the STAP method does not work on all cell types, it works with most and, on average, 25 percent of the cells survive the stress and 30 percent of those convert to pluripotent cells. Her research appears in two papers published simultaneously in Nature, along with an editor’s summary stating, “Extensive analysis of the molecular features and developmental potential of STAP cells suggests that they represent a unique state of pluripotency — and provide an alternative source of pluripotent cells…”
Obokata H, Wakayama T, Sasai Y, Kojima K, Vacanti MP, et al. Stimulus-triggered fate conversion of somatic cells into pluripotency. Nature. 2014.
Obokata H, Wakayama T, Sasai Y, Niwa H, Kadota M, Takata N, et al. Bidirectional developmental potential in reprogrammed cells with acquired pluripotency. Nature. 2014. | <urn:uuid:0d075f8d-023d-42fa-ae42-0159b7196f83> | {
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# Complex solutions of ordinary differential equation of order 2
I'm trying to understand the math notes detailing the way to obtain the complex solution:
If the problem is homogeneous we have :
$$ay''(t) + by'(t) + cy(t) = 0$$
to know all solutions for this use the ansatz
$$y(t) = e^{\lambda t}$$
and plug it into the ODE to find
$$ay''(t) + by'(t) + cy(t) = a \lambda^2e^{\lambda t} + b\lambda e^{\lambda t} + ce^{\lambda t} = 0$$
This problem can be solved using the characteristic equation:
$$a\lambda^2 + b\lambda +c = 0$$
Dependeing on the value of the discriminant $$D = b^2 - 4ac$$ we find different types of solutions:
$$1.$$ $$D < 0$$: $$\lambda_1 \neq \lambda_2$$ and both real.
Then we have two linearly independent solutions
$$y_1(t) = e^{\lambda_1t} \quad \text{and}\quad y_2(t) = e^{\lambda_2t}$$ and thus the general solution is
$$y(t) = c_1y_1(t) + c_2y_2(t) = c_1e^{\lambda_1t} + c_2e^{\lambda_2t}$$
$$2.$$ $$D = 0$$: $$\lambda_1 = \lambda_2 \in \mathbb{R}$$
One solution is immediate from the previous case
$$y_1(t) = e^{\lambda_1t}$$
One can verify that the second solution is given by
$$y_2(t) = te^{\lambda_1t}$$ Thus the general solution is
$$y(t) = c_1y_1(t) + c_2y_2(t) = c_1e^{\lambda_1t} (c_1 +tc_2)$$
$$3.$$ $$D < 0$$: $$\lambda_{1,2} = \alpha \pm i\beta$$ with $$\alpha$$, $$\beta \in \mathbb{R}$$ and $$\beta \neq 0$$
Using the idea from the first case we end up with complex sotluions
$$u_1(t) =e^{\lambda_1t} = e^{(\alpha + i \beta)t} = e^{\alpha t}(\cos(\beta t) + i \sin(\beta t)) \tag{1}\label{eq1}$$ $$u_2(t) =e^{\lambda_2t} = e^{(\alpha + i \beta)t} = e^{\alpha t}(\cos(\beta t) - i \sin(\beta t)) \tag{2}\label{eq2}$$
My Question:
I guess the statement $$(1)$$ and $$(2)$$ have to do with the properties of complex numbers. However can you give me a link to understand those $$2$$ statements.
• That's Euler's formula: en.wikipedia.org/wiki/Euler%27s_formula Oct 27, 2018 at 15:07
• Actually, it's 1 and 3 which are easily linked through complex numbers: $y(t)=Ae^{\lambda_1t}+Be^{\lambda_2 t}$ works for both of them, and there is no real reason to consider them two distinct cases. As for how to link (2) to the other two, I asked about that here. You can see what you think about the answers given there. Oct 27, 2018 at 15:07
• thank you @EthanBolker!
– ecjb
Oct 27, 2018 at 15:08
$$e^{i\theta}=\cos\theta+i\sin\theta$$
However, to summarize, the function $$f(t)=e^{i\beta t}$$ for some constant $$\beta$$ is a complex function that starts at $$f(0)=1$$ and then rotates around the unit circle at $$\beta$$ radians per second (assuming $$t$$ is a variable of time in seconds). Then, the function $$f(t)=e^{(\alpha+i\beta)t}=e^{\alpha t}e^{i\beta t}$$ for $$\alpha > 0$$ is a function that starts at $$f(0)=1$$ and then rotates around the unit circle at $$\beta$$ radians per second while also getting exponentially farther away from the origin because of the exponentially growing magnitude $$e^{\alpha t}$$. However, if $$\alpha < 0$$, then $$f(t)=e^{\alpha t}e^{i\beta t}$$ gets closer and closer to the origin because of the exponentially decaying magnitude $$e^{\alpha t}$$. | crawl-data/CC-MAIN-2024-18/segments/1712296819273.90/warc/CC-MAIN-20240424112049-20240424142049-00015.warc.gz | null |
One of the most popular ways to compose your photographs is to use the “Rule of Thirds”. Although this compositional rule is frequently used by photographers, not everyone understands exactly what it is or when it works. This article introduces the rule of thirds and explains when to use it for composition (or not). Keep in mind that this rule is a suggestion for beginners and those who struggle with properly composing their pictures, and it is far from the only way to take good images.
Table of Contents
What is the Rule of Thirds?
The Rule of Thirds is a type of off-center composition where important elements of a photograph are placed along a 3×3 grid, which equally divides the image into nine parts. For many photographers, this type of composition is a basic way to give structure to photographs and make them more appealing. With the rule of thirds, photographers envision four lines across their photographs, which also creates four intersecting points. Take a look at the illustration below:
The important elements within a frame should be placed at the intersection points of these lines, as shown in the above diagram. Or, when photographing subjects like a tree or horizon, which are comprised of straight lines, the rule of thirds suggests placing them along one of the four lines instead. Take a look at the below photograph:
As you can see, both the horizon line and the primary subject are placed along this grid:
You can apply the rule of thirds to any genre of photography. In the portrait example below, the subject’s eyes are placed about two thirds up the photograph, and her nose aligns with the rule of thirds grid as well:
When to Use the Rule of Thirds
So, when should you use the rule of thirds? The basic value of this rule is to remind yourself that off-center compositions can work well and be successful. Most of the time, beginner photographers will place their subjects in the dead center by default, forming central compositions. Although central composition can be a very strong way to compose photographs, using it for every photo can be boring. If you find that you are doing this, you can add more interest and variety by using the rule of thirds.
To use the rule of thirds, start by imagining a 3×3 grid (or use one that is built into your camera) and place your subjects along those lines and intersections points. When you evaluate the result, you may find that you like it more than with your subject in the center.
So, if you are struggling to compose your images, you might find that the rule of thirds can be a quick way to make your photos more dynamic.
When Not to Use the Rule of Thirds
The biggest problem with the rule of thirds is that it doesn’t change, even when your subjects do. It simply does not take into account what you are photographing. For example, in some scenes, you might be compromising your composition and excluding important elements just to adhere to the rule of thirds. So, in a way, it is a cookie-cutter composition.
The whole idea of the rule of thirds is that it introduces beginners to off-center composition. However, it might lead you to think that your subjects always (or often) need to be placed along the exact lines and intersections of the 3×3 grid in order to capture a successful composition.
In reality, any type of off-central composition – not just the rule of thirds – can work well. Instead, try framing your subject just slightly off center, or even in the extreme corners. Sometimes, the scene itself will dictate the type of composition which will work best for your photograph. In the image below, you can see that I purposefully placed the subject close to the edge of the frame in order to convey a sense of isolation with a negative space composition:
While taking this photo, I wanted it to be somewhat striking and unexpected. If I had framed it using the rule of thirds, it would not have conveyed that emotional message.
Along with that, do not underestimate central composition. Although it can be boring if you use it too much, it also can be the most powerful way to compose and frame photographs. Personally, I use central composition quite a bit, especially if there is a single, strong subject in the scene:
The rule of thirds is certainly worth exploring, especially for those who are just starting to learn composition in photography. However, as you get more advanced, you will start to realize that good composition is not about adhering to strict rules, but rather about composing each photo for its own merits. Different compositions will be ideal in different situations. While the rule of thirds works well for some photographs, it is not the only way to capture a good image. Indeed, any type of composition can be beautiful, and you will miss many opportunities if you never go beyond the rule of thirds. | <urn:uuid:ff4649c1-854d-4777-9b63-3f33b93408e4> | {
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USING OUR SERVICES YOU AGREE TO OUR USE OF COOKIES
# Is 67 A Prime Number?
• Yes the number 67 is a prime number.
• It's a prime because sixty-seven has no positive divisors other than 1 and itself.
## Prime Factorization Of 67
• Prime factors of 67: 1 * 67
## How To Calculate Prime Number Factors
• How do you calculate natural number factors? To get the number that you are factoring just multiply whatever number in the set of whole numbers with another in the same set. For example 7 has two factors 1 and 7. Number 6 has four factors 1, 2, 3 and 6 itself.
• It is simple to factor numbers in a natural numbers set. Because all numbers have a minimum of two factors(one and itself). For finding other factors you will start to divide the number starting from 2 and keep on going with dividers increasing until reaching the number that was divided by 2 in the beginning. All numbers without remainders are factors including the divider itself.
• Let's create an example for factorization with the number nine. It's not dividable by 2 evenly that's why we skip it(Remembe 4,5 so you know when to stop later). Nine can be divided by 3, now add 3 to your factors. Work your way up until you arrive to 5 (9 divided by 2, rounded up). In the end you have 1, 3 and 9 as a list of factors.
## Mathematical Information About Numbers 6 7
• About Number 6. Six is the smallest composite number with two distinct prime factors, and the third triangular number. It is the smallest perfect number: 6 = 1 + 2 + 3 and the faculty of 3 is 6 = 3! = 1 * 2 * 3, which is remarkable, because there is no other three numbers whose product is equal to their sum. Similarly 6 = sqrt(1 ^ 3 + 2 + 3 ^ 3 ^ 3). The equation x ^ 3 + Y ^ 3 ^ 3 + z = 6xyz is the only solution (without permutations) x = 1, y = 2 and z = 3. Finally 1/1 = 1/2 + 1/3 + 1/6. The cube (from the Greek) or hexahedron (from Latin) cube is one of the five Platonic solids and has six equal areas. A tetrahedron has six edges and six vertices an octahedron. With regular hexagons can fill a plane without gaps. Number six is a two-dimensional kiss number.
• About Number 7. Seven is a prime number. It is the lowest natural number that cannot be represented as the sum of the squares of three integers. The corresponding cyclic number is 142857. You can use this feature to calculate the result of the division of natural numbers by 7 without a calculator quickly. A seven-sided shape is a heptagon. One rule for divisibility by 7 leads to a simple algorithm to test the rest loose divisibility of a natural number by 7: Take away the last digit, double it and subtract them from the rest of the digits. If the difference is negative, then you're leaving the minus sign. If the result has more than one digit, so you repeat steps 1 through fourth. Eventually results are 7 or 0, then the number is divisible by 7 and not otherwise.
## What is a prime number?
Prime numbers or primes are natural numbers greater than 1 that are only divisible by 1 and with itself. The number of primes is infinite. Natural numbers bigger than 1 that are not prime numbers are called composite numbers. Primes can thus be considered the basic building blocks of the natural numbers. There are infinitely many primes, as demonstrated by Euclid around 300 BC. The property of being prime (or not) is called primality.
In number theory, the prime number theorem describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger.
Primes are used in several routines in information technology, such as public-key cryptography, which makes use of properties such as the difficulty of factoring large numbers into their prime factors.
© Mathspage.com | Privacy | Contact | info [at] Mathspage [dot] com | crawl-data/CC-MAIN-2022-21/segments/1652662594414.79/warc/CC-MAIN-20220525213545-20220526003545-00301.warc.gz | null |
This is part 60 of a series of articles featuring the book Beyond Connecting the Dots, Modeling for Meaningful Results.
The first step in using historical data to calibrate the model parameters is to understand what is meant by “the best fit” between historical and simulated data. Conceptually, the idea of a “good fit” seems obvious. A good fit is one where the historical and simulated results are very close together (a perfect fit is when they are the same, but that is generally more than we can hope for). However, putting a precise mathematical definition on the concept is not trivial.
Many commonly used ‘goodness of fit’ measures exist; some key measures are listed below.
Squared error is probably the most widely used1. To calculate the squared error we carry out the following procedure. For each time period we determine the difference between the historical data value and the simulated value, and square that difference. We then determine the sum of these differences to obtain the total error for the fit. Higher totals indicate worse fits, and lower totals indicate better fits.
The following equation could be placed in a variable to calculate the squared error between a primitive named Simulated and one named Historical:
Please note that maximizing the R2 measure we described earlier is equivalent to minimizing the squared error.
Absolute Value Error
A characteristic of squared error is that outliers have high penalties compared to other data points. Outliers are points in time where the fit is unusually bad. Since the squared error metric squares the differences between simulated and historical data, large differences can cause even larger errors when they are squared. This can sometimes be a negative feature of squared error if you do not want the outliers to have special prominence and weight in the analysis.
An alternative to squared error that treats all types of differences the same is the absolute value error. Here, the absolute value of the difference between the simulated and historical data series is taken. The following equation could be placed in a variable to calculate the absolute value error between a primitive named Simulated and one named Historical:
Many other techniques are available for measuring error or assessing goodness of fit. Most statistical approaches function by specifying a full probability model for the data and then taking the goodness of fit not as a measure of error, but rather as the likelihood of observing the results we saw given the parameter values2. To be clear, the issue of optimizing parameter values for models is one that is more complex than what we have presented here. Many sources of error exist in time series, and analyzing them is a very complex, statistical challenge. The basic techniques we have presented are, however, useful tools that serve as gateways toward further analytical work.
|You have a model simulating the number of widgets produced at a factory. The model contains a stock, Widgets, containing the simulated number of widgets produced. You also have a converter, Historical Production, containing historical data on how many widgets were produced in the past.
Write two equations. One to calculate squared error for the model’s simulation of historical production, and one to calculate the absolute value error of the same.
|You like the idea of penalizing outliers in your optimizations. In fact, you like this idea so much that you would like to penalize outliers even more than squared error does. Create an equation to calculate error that penalizes outliers more than squared error.|
|Describe why this is not a valid equation to calculate error:
Next edition: Optimization and Complexity: Multi-Objective Optimizations.
- The main reason is that regular linear regression (ordinary least squares, the most widely used modeling tool) uses squared error as its measure of goodness of fit. Doing so simplifies the mathematics of the regression problem greatly in the linear case. ↩
- Likelihood is a technical statistical term. It can be roughly thought of as equivalent to “probability”, though it is not precisely that. ↩ | <urn:uuid:5ae17a59-0739-4e81-a4e3-cbb406cf7f4e> | {
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# Probability
• Jul 30th 2008, 08:16 AM
hrunup
Probability
Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
What is the probability that you will receive a Merit scholarship?
What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?
What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?
Need help
• Jul 30th 2008, 09:04 AM
Plato
$P(M \cup A)\quad {\mbox{means at least one}}$ and $P(M \cap A)\quad {\mbox{means both}}$.
You know that $P(M \cup A) = P(M) + P(A) - P(M \cap A)$.
Now solve for $P(M)$.
• Jul 30th 2008, 04:57 PM
mr fantastic
Quote:
Originally Posted by hrunup
Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
What is the probability that you will receive a Merit scholarship?
What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?
What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?
$\Pr(A | M) = \frac{\Pr(A \cap M)}{\Pr(M)}$.
$\Pr(M | A) = \frac{\Pr(M \cap A)}{\Pr(A)} = \frac{\Pr(A \cap M)}{\Pr(A)}$. | crawl-data/CC-MAIN-2017-47/segments/1510934807650.44/warc/CC-MAIN-20171124104142-20171124124142-00277.warc.gz | null |
They say slow and steady wins the race, and that’s especially true of human developmental timing. Turns out that, in terms of development, humans are like the tortoise that started the race late and slow—yet still won!
Scientists have long suspected that delays in gene expression play a part in the obvious delays observed in human physical development compared to (other) animals. Developmental delay (known as “neotony”) in humans is not entirely surprising. We’ve all seen movies of the wobbly colt that finds its legs and walks within minutes of its birth. Yet human babies require about a year before they take their first steps.
Recently, scientists postulated that the delayed timing of gene expression in a newborn baby’s brain is, to some degree, responsible for humans’ increased intellectual ability.1 A team of 15 scientists from around the world set out to determine if humans experience postponement in early infancy in the gene expression required for brain development. They began by obtaining brain tissue from humans, chimpanzees, and rhesus macaques. The human samples ranged in age from 0 to 40 years; samples from other species were the equivalent ages.
In the first phase of the study, the researchers identified 7,598 genes expressed in the three species as indicated by the presence of the same mRNA. They then analyzed each gene’s expression pattern with regard to age, sex, and species. Their first astounding discovery was that in all three species, gene expression in the brain underwent enormous change during infancy. In humans, 71 percent of the genes underwent a change in expression level during the first few years of life, with 50 percent undergoing a change in expression level during the first year. Following infancy, the changes were much less dramatic. In this sense, all three species showed the same general pattern with regard to the gene expression in the brain. However, in humans 48 percent of the genes showing an age-dependent expression pattern were either expressed at a significantly different level or showed a significantly different pattern of expression compared to chimps.
In order to categorize the difference in the species’ genes expression timing, the researchers chose to use the rhesus macaques as the outgroup (a reference group). In other words, if at least one of the species has the same expression pattern for a particular gene as the macaques, that pattern will be deemed to be the “standard” pattern of expression for that gene. Doing this allowed the scientists to establish four categories of gene expression:
- Human neotony: human gene expression was delayed relative to chimp and macaque expression
- Human acceleration: human gene expression was accelerated relative to chimp and macaque expression
- Chimp neotony: chimp gene expression was delayed relative to human and macaque expression
- Chimp acceleration: chimp gene expression was accelerated relative to human and macaque expression
Of the 7,598 genes, 299 could be assigned unambiguously to one of these categories. In round numbers, human neotony occurred twice as much as the other categories.
What is the significance of all this data? Does it really make a difference when a gene is expressed? Actually, it does. For example, experiments have demonstrated that mice form an additional vertebra due to a one day delay (out of a 20-day gestation period) in expressing some of the genes involved in vertebrae formation. The additional vertebra resulted in shifting the beginning of the sacrum region toward the mouse’s posterior.2
How does this relate to human uniqueness and intelligence? One theory suggests that the delay in expressing genes in the brain means that the brain remains in a “plastic” state for an extended time. In this state, additional synaptic connections can be formed, resulting in the acquisition of knowledge and memories. Additional time spent in the plastic state may explain some of the biological basis for humanity’s vast intellectual abilities.
Another example of the “timing is everything” principle can be observed in the mid phase of human embryogenesis (17 to 23 weeks)—a critical period for the process of brain development. Though electrical activity can be detected in the brain as early as the fifth or sixth week after conception, synaptic connections begin to form in earnest at the beginning of the mid phase. By the end of this phase, the baby’s brain is stable, thus, marking the beginning of the time at which a premature baby has a chance of surviving outside the womb. In a recent paper, scientists reported that 76 percent of human genes are expressed in the developing brain during the mid phase.3 This is the most radical known example of a complex organism expressing this much of its genome4 in one organ (the brain) at one time. It does not occur in other human tissues and it is not believed to occur in any other organism.
Clearly, gene expression timing in fetal and infant brains plays an important role in the development of human intellect. However, scientists are identifying yet many more factors essential in developing that intellect. In future Today’s New Reasons to Believe, I will discuss some of these other factors.
Dr. Patricia Fanning
Patricia Fanning is an RNA biochemist with a PhD from North Carolina State University and formerly a consultant for software companies. As a visiting scholar to Reasons To Believe in 2011, she specialized in human embryology and evolutionary development and regularly contributed to RTB’s podcasts and publications. | <urn:uuid:0fee2ba0-c1cf-4be1-a2f8-9a9c879a028e> | {
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for Health Care Providers
Glossary of HIV/AIDS Terms
A simple set of effective practices designed to protect health workers and patients from infection with a range of pathogens, including blood-borne viruses. These practices are used when caring for all patients regardless of diagnosis.
Usually, the numbers of individuals who agree to a procedure such as the number of pregnant women who agree to take an HIV test or agree to participate in prenatal care.
Inoculation of a substance (i.e. vaccine) into the body for the purpose of producing active immunity against a disease. Initially associated with smallpox vaccination but now often used interchangeably with immunization.
A substance that contains antigenic components from an infectious microorganism. By stimulating an immune response--but not the disease--it protects against subsequent infection by that organism. There can be preventive vaccines (e.g. measles or mumps) as well as therapeutic (treatment) vaccines.
Infection of the vagina caused by the yeastlike fungus Candida (especially Candida albicans). Symptoms include, pain, itching, redness, and white patches in the vaginal wall. It can occur in all women, but it is especially common in women with HIV infection. The usual treatment is a cream applied locally to the vagina. Women with HIV infection may experience frequent reoccurrence of symptoms and may require systemic medications in order to treat these symptoms successfully.
Varicella Zoster Virus (VZV)
A virus in the herpes family that causes chicken pox during childhood and may reactivate later in life to cause shingles in immunosuppressed individuals.
The puncture of a vein (usually in the arm) with a hollow-bore needle for the purpose of obtaining a blood specimen.
Transmission of a pathogen such as HIV from mother to fetus or baby during pregnancy or birth.
Viral Burden/Viral Load
The amount of HIV in the circulating blood. Monitoring a person's viral burden is important because of the apparent correlation between the amount of virus in the blood and the severity of the disease. Sicker patients generally have more virus than those with less advanced disease. A sensitive, rapid test--called the viral load assay for HIV-1 infection--can be used to monitor the HIV viral burden. This procedure may help clinicians decide when to give anti-HIV therapy or to switch drugs. It may also help investigators determine more quickly whether experimental HIV therapies are effective.
Viral Load Test
In relation to HIV, a test that measures the quantity of HIV RNA in the blood. Results are expressed as the number of copies per milliliter of blood plasma. Research indicates that viral load is a better predictor of the risk of HIV disease progression than the CD4 count. The lower the viral load, the longer the time to AIDS diagnosis and the longer the survival time. Viral load testing for HIV infection is being used to determine when to initiate and/or change therapy.
See Nevirapine (NVP).
The presence of virus in the bloodstream.
Organism composed mainly of nucleic acid within a protein coat. When viruses enter a living plant, animal, or bacterial cell, they make use of the host cell's chemical energy, protein, and nucleic acid-synthesizing ability to multiply. Some viruses do not kill cells but transform them into a cancerous state. Some cause illness and then seem to disappear, while remaining dormant and later causing another, sometimes much more severe, form of disease. In humans, viruses cause measles, mumps, yellow fever, poliomyelitis, influenza, and the common cold, among others. Some viral infections can be treated with drugs.
Voluntary HIV Testing
An individual is usually counseled regarding HIV prevention and how HIV infection occurs. Participants have the opportunity to accept or refuse HIV testing. | <urn:uuid:21ef4985-89d7-4900-a5d0-5f17a3f725bb> | {
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Facts about Generalized Anxiety Disorder
Generalized anxiety disorder (GAD) is characterized by 6 months or more of chronic, exaggerated worry and tension that is unfounded or much more severe than the normal anxiety most people experience. People with this disorder usually expect the worst; they worry excessively about money, health, family, or work, even when there are no signs of trouble. They are unable to relax and often suffer from insomnia. Many people with GAD also have physical symptoms, such as fatigue, trembling, muscle tension, headaches, irritability or hot flashes.
When their anxiety level is mild, people with GAD can function socially and hold down a job. Although they don’t avoid certain situations as a result of their disorder, people with GAD can have difficulty carrying out the simplest daily activities if their anxiety is severe.
Fortunately, through research supported by the National Institute of Mental Health (NIMH) and by industry, effective treatments have been developed to help people with GAD.
How Common Is GAD?
- About 3.1% of the adult U.S. population ages 18 to 54 – approximately 6.8 million Americans – have GAD during the course of a given year.
- GAD most often strikes people in childhood and adolescence, but can begin in adulthood, too.
- It affects women more often than men.
What Causes GAD?
Some research suggests that GAD may run in families, and it may also grow worse during stress. GAD usually begins at an earlier age and symptoms may manifest themselves more slowly than in most other anxiety disorders.
What Treatments Are Available For GAD?
Treatments for GAD include medications and cognitive-behaviour therapy.
Can People With GAD Also Have Other Illnesses?
Research shows that GAD often coexists with depression, substance abuse, or other anxiety disorders. Other conditions associated with stress, such as irritable bowel syndrome, often accompany GAD.
Patients with physical symptoms such as insomnia or headaches should also tell their doctors about their feelings of worry and tension. This will help the patient’s health care provider to recognize that the person is suffering from GAD.
Source: National Institute of Mental Health | <urn:uuid:02829be7-6811-4540-ae4a-a9cad61aa276> | {
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# How To Find X And Y Intercepts Of A Quadratic Function References
How To Find X And Y Intercepts Of A Quadratic Function References. The notation is the same for any value of x, whether a number or symbol: The y intercept if given by f(0) = c.
This function can be plotted giving a parabola (a curve in the shape of an upward or downward u) to find the x intercepts you must put y=0; The solutions of a quadratic equation of the form a x 2 + b x + c = 0 are given by the quadratic formula. To find the x intercepts of a quadratic function, means to find those values of x for which y equals zero, graphically, it implies to find the values that pass through the x axis.;
### And Y Intercept Is 2?
So, the equation can be changed as ax2 + bx + c = 0. X = − b ± b 2 − 4 a c 2 a. , where a is the coefficient of the quadratic term, b is the.
### The Intercept Form Of The Equation Is Completely Different From The Standard Quadratic Equation.
Here, the expression b 2 − 4 a c is called the discriminant. Related posts of how to find x and y intercepts of a quadratic function references To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x.
### This Function Can Be Plotted Giving A Parabola (A Curve In The Shape Of An Upward Or Downward U) To Find The X Intercepts You Must Put Y=0;
One can find out only one intercept at a time in a given equation. The notation is the same for any value of x, whether a number or symbol: How to find x and y intercepts of a quadratic function.
### Consider You Have The Following Quadratic Function:
A quadratic function is one of general form: F(x) = a x 2 + b x + c. In this given equation we can consider x=p and x=q as the intercepts of x.
### For Example, We Have Quadratic Function.
The y intercept if given by f(0) = c. How to find a quadratic equation from 2 points? A parabola is the shape of the graph of a quadratic equation.
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This is a video of a teacher sharing an example of the PALS math curriculum in action. The pedagogy in this video though frustrates me though, and although the idea of Peer Assisted Learning Strategies (PALS) seems good, I don’t think the approach this teacher took is very good.
- She’s using rewards to encourage kids to work with each other. Alfie Kohn does a good job of explaining why this is problematic. "The smiley faces help you remember to mark points." She also spends nearly a minute describing to the kids how to do the task. My experience with kids this young (or any age really) is that they don’t have the attention span to remember something as complex and essentially arbitrary as the instructions necessary to this task "the teacher’s way."
- The students actually have very little interaction in this video with the numbers themselves. The symbols aren’t the numbers. In fact, I think they are an unnecessary layer of abstraction on the concept of number at this young age. Kids need representations of numbers that are more concrete, and once they have a concrete understanding of the concept, then you can move into the abstraction. The entire objective of this lesson seems to be to connect one abstraction (the verbalization of the numbers) with another abstraction (the symbols that represent the numbers).
If you want kids to learn about these two abstract representations, then you should pair them with a concrete representation with which the kids are more familiar. For example, the symbols should be paired with objects (ie 8 blocks paired with the symbol for 8). You should also teach the two abstractions independently of each other, if at all possible, at least when introducing them.
- It’s clear from the way the kids are reciting facts after this teacher asks questions that they do a lot of this. Reciting something verbatim doesn’t mean you understand what you are doing. In this entire clip, the teacher doesn’t give a single piece of feedback to the students about their learning. Learning is a process through which you incorporate feedback from the world into your existing schema of the world. The only feedback the kids get is the voices of the other children saying the same thing as them, which is minimal at best.
- Not a single kid gets to ask a question, like "why do the numbers look like that?" What would be the harm in the kids spending some time creating their own number system, and then matching it to our existing one?
- It seems like the interaction between the kids is forced. I’m sure there must be more natural ways of discussing the numbers and providing feedback to each other on understanding of the numerals than this contrived activity.
In fairness, I cannot tell from this video anything more than this particular 5 minute segment of this one teacher’s class could use improvement. There does seem to be some evidence that this is a typical 5 minute period, at least at the beginning of class, but it could be that the rest of her class is wonderful. I do think that I wouldn’t share this particular 5 minute clip as example of good pedagogy. | <urn:uuid:db159f18-b025-4a28-8714-0c89bf73bd55> | {
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1. Chapter 1 Class 11 Sets
2. Concept wise
3. Subset
Transcript
Ex 1.3, 2 Examine whether the following statements are true or false: (i) {a, b} ⊄ {b, c, a} Since, each element of {a, b} is also an element of {b, c, a}. So, {a, b} ⊂ {b, c, a} So, the statement is False ⊂ - is a subset ⊄ - is not a subset A ⊂ B if all elements of A are in B Ex 1.3, 2 Examine whether the following statements are true or false: (ii) {a, e} ⊂ {x: x is a vowel in the English alphabet} {x: x is a vowel in the English alphabet} = {a, e, i, o, u} Since, each element of {a, e} is also an element of {a, e, i, o, u}. So, the statement is True ⊂ - is a subset A ⊂ B if all elements of A are in B Ex 1.3, 2 Examine whether the following statements are true or false: (iii) {1, 2, 3} ⊂ {1, 3, 5} Since, 2 is in set {1, 2, 3}; but not in {1, 3, 5} So, {1, 2, 3} is not a subset of {1, 3, 5} So, the statement is False. ⊂ - is a subset A ⊂ B if all elements of A are in B Ex 1.3, 2 Examine whether the following statements are true or false: (iv) {a} ⊂ {a, b, c} Each element of {a} is also an element of {a, b, c}. Thus, {a} ⊂ {a, b, c} So, the statement is True. ⊂ - is a subset A ⊂ B if all elements of A are in B Ex 1.3, 2 Examine whether the following statements are true or false: (v) {a} ∈ {a, b, c} Given set {a} belongs to {a, b, c} Here, set {a} is not an element of {a, b, c} as elements of {a, b, c} are a, b, c So, the statement is False. ⊂ - is a subset ⊄ - is not a subset ∈ - belongs to ∉ - not belongs to Ex 1.3, 2 Examine whether the following statements are true or false: (vi) {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36} Natural number = 1, 2, 3, 4, 5, 6, 7, 8,…. Even natural number = 2, 4, 6, 8,… {x: x is an even natural number less than 6} = {2, 4} ⊂ - is a subset A ⊂ B if all elements of A are in B {x: x is a natural number which divides 36} 36 = 1 × 36 36 = 2 × 18 36 = 3 × 12 36 = 4 × 9 36 = 6 × 6 Thus, {x: x is a natural number which divides 36} = {1, 2, 3, 4, 6, 9, 12, 18, 36} So, {1, 2, 3, 4, 6, 9, 12, 18, 36} has all the elements of {2, 4}. ∴ {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36} So, the statement is True
Subset | crawl-data/CC-MAIN-2021-17/segments/1618038066981.0/warc/CC-MAIN-20210416130611-20210416160611-00285.warc.gz | null |
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# a and b are positive integers. What is the remainder of of
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a and b are positive integers. What is the remainder of of [#permalink]
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a and b are positive integers. What is the remainder of of (6*10^b + a - 1)/3 ?
S1) a = 2
S2) b = 5
Senior Manager
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25 Jun 2005, 20:14
AJB77 wrote:
a and b are positive integers. What is the remainder of of (6*10^b + a - 1)/3 ?
S1) a = 2
S2) b = 5
A would suffice. The remainder is 1.
B insufficient.
HMTG.
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25 Jun 2005, 20:15
It is A
(6*10^b + a - 1)/3 = 2*10^b + (a - 1)/3
So if we know a thats enough
25 Jun 2005, 20:15
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While ancient history was the buzzword of the Olympic Games' return to their birthplace, history was also made in a very modern way: these were the first Olympics with women in the key leadership roles, including the first-ever woman head of a national Olympic organizing committee and the first woman mayor of an Olympic city.
Having women fill these roles is remarkable in itself, say Greeks, but even more so given that this is a European nation without a strong tradition of feminism or gender equity. Though Greece was the birthplace of democracy, Greek women weren't able to vote until 1952. The practice of obligatory dowries wasn't outlawed until 1983. Today, there are only 39 women in Greece's 300-member Parliament, and Greece routinely ranks at the bottom of female representation in government, trade unions, and political parties among the 25 nations of the European Union.
But the success of the Games could be a catalyst for change here.
"Greek society is still very patriarchal and unequal. I think the image of seeing these women in power, the symbol, will be a very important thing for Greeks. This is an indication that we'll see more women in public office. It will get a younger generation used to the idea of women in powerful posts," says Maria Stratigaki, a sociologist at Athens' Panteion University.
Analysts say it's hard to overestimate the political and psychological effect of the successful Olympics to the Greeks, especially after Athens' much maligned preparations. The successful completion of the most high-profile and expensive endeavor in the country's recent history has given Greece a desperately needed surge of confidence, a moment on the world stage that showed the transformation of a poor developing country into a competent modern European state. Experts say that any public figure associated with these Games would be lionized; that they were women in a male-dominated culture may well go far towards changing attitudes here.
Of the women leaders, the most prominent is Gianna Angelopoulos-Daskalaki, who headed the Athens Olympic Committee. Known simply as "Gianna" to most Greeks, she cuts a colorful and imposing figure - at once revered, hated, admired, and satirized. She is credited with getting the mired Olympic Games off the ground, but also with using a ruthless approach to do so, which earned her the sobriquet "Iron Lady." But she injected more glamour into the role than the original Iron Lady, Margaret Thatcher. Ms. Angelopoulos-Daskalaki seldom appeared without flashy, form-fitting designer suits, diamonds, spike heels, and Cuban cigars.
Her Olympic legacy began in 1997, when the former lawyer and member of Parliament headed Athens' successful Olympic bid, redeeming Greece from its humiliating failure to get the centennial 1996 Games. Shortly afterward, however, the conservative party member was shunted aside by Greece's ruling Socialist government, and she left the country. But by 2000, preparations were so far behind schedule, Greece was faced with with losing the Olympics. The government begged Angelopoulos-Daskalaki to return. Today, she's given full credit for salvaging the train wreck, and producing an acclaimed Olympic Games.
Now it's widely speculated that she'll run for president. Greeks say that while she's tough to love as a politician, no one can deny her effectiveness. "Gianna is perceived as an 'iron lady' - but she is also perceived as very effective at her job. We've never had a female leader like her so far, but she could change that," says Myrto Boutsi, a journalist at the Greek daily Eleftheros Typos.
Civil engineer Constantine Papaconstantinou admits that a leader like Angelopoulos-Daskalaki might be tough for him to take. "In Greece we've never before had women in significant roles," he says. "Someone like Gianna - well, I don't like people who will do anything to succeed, to get ahead. But in this case, it was advantageous for Greece."
Athens' mayor, Dora Bakoyianni, who worked closely with Angelopoulos-Daskalaki, says the fact that she was elected to office in 2003 shows that Greek attitudes are already starting to shake up.
"Greeks have gone through an evolution in society the last years," she says. "They said that in Athens, a woman could never be elected - it was proven wrong." Indeed, since she took office, opinion polls have frequently named Ms. Bakoyianni as the most popular politician in the country.
Bakoyianni has been credited with doing much to clean up Athens, promoting pedestrian parks, tree-planting, improving handicapped access and hiring a municipal force to crack down on littering and illegal peddlers - mostly aesthetic projects that polished Athens' image for the millions of Olympic visitors and billions of Olympic television viewers, not to mention the quality of life of Athenians themselves.
The third prominent woman of the Greek Games, deputy culture minister Fanni Palli-Petrallia, only came on board in March of this year, after national elections brought her conservative New Democracy party into power. She is credited with overseeing the successful completion of the major Olympic works, as the country desperately dashed towards the finish line. | <urn:uuid:c64890fc-8ac5-4c5f-a06f-5ad4dd55805f> | {
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