What were the effects of the slave revolts?

Slave revolts occurred throughout the New World in the eighteenth and nineteenth centuries. Because your question is very general, I would draw your attention to the important differences between the results of revolts in Brazil and the Caribbean and those which occurred in the United States. There is also a difference between revolts which occurred on ships, which tended to be more effective, and those which occurred on land, which were more likely to be put down by those in power.
Well-known revolts in South America and the Caribbean include the Bahia revolt in Brazil, the Morant Bay Rebellion in Jamaica, and the most successful revolt of all, the uprising in Haiti led by Toussaint L'Ouverture. With the exception of the Haiti uprising, which resulted in independence, these revolts were generally put down swiftly and violently.
Governor Edward John Eyre's response to the Morant Bay Rebellion resulted in the deaths of 439 black people, 600 floggings, and around 1,000 homes being burned to the ground. There was controversy in England over Eyre's actions, with intellectual figures such as Charles Darwin and Thomas Huxley condemning him, while Thomas Carlyle and Charles Dickens defended Eyre's need to restore order. 
In the United States, there was also violent retribution against blacks after slave revolts, though legislation was also enacted to deal with the threat of insurrection. However, most American revolts were foiled before they could be carried out. Gabriel Prosser's intended revolt in Richmond, Virginia in 1803 was spoiled by a black cook who informed on him and other participants. Denmark Vesey's intended revolt in Charleston, South Carolina was also foiled. However, in 1831, Nat Turner did carry out a revolt in Southampton County Virginia which resulted the deaths of 65 whites, including children. 
Before Turner's rebellion there had been talk among legislators of possible abolition of slavery. After the rebellion fear of blacks was palpable, resulting in more severe actions to control black people. The Fugitive Slave Act of 1850 was partially in response to fear of, not only of slaves, but also of free or escaped blacks. Slaves who were found to be off of plantations without written permission from their owners could be severely punished. Prior to Turner's revolt, slaves had more freedom to roam. Also, groups of blacks found to be congregating were deemed suspect and were often broken up and sent back to their respective plantations. Prior to Turner's revolt, blacks were allowed to congregate, particularly for religious services.
Generally, with the exception of Haiti, revolts led to violent retribution against blacks -- both free and enslaved -- and legislation intended to circumscribe their lives (e.g., ability to congregate, leave plantations, learn to read) even further.

What are the consequences of Hester's sin?

One consequence of Hester's sin is that she had to spend at least several months in prison.  We might assume that she was imprisoned once her pregnancy became too obvious to hide. However, she is released shortly after Pearl is born.  Another consequence of Hester's sin is that she is made to stand upon the scaffold, a place of public punishment, in the town square so that all can look upon her and know her sin.  She is questioned publicly about the identity of her fellow sinner, and she is judged harshly by most of the other women in the town: one felt she should have the letter branded on her skin with a hot iron, another felt that she should have been executed for her sin.  The judgment of the townspeople is a third consequence.  Finally, a fourth consequence of Hester's sin is that she is forced to wear the scarlet "A," a symbol of her sin and a constant reminder of it to her and everyone else.

Who is the antagonist and protagonist in Asimov's story "The Machine That Won the War"?

This story doesn't have a clear protagonist or antagonist. If the question is asking for a single protagonist, I don't think one can be provided with strong supporting evidence. That is because "The Machine That Won the War" presents three protagonists to readers: Swift, Henderson, and Jablonski. Each receives relatively equal page time and speaking parts. Additionally, each man plays an equal role in showing readers exactly how Multivac did not win the war. Together, these three men are the heroic figures of the plot, but no one except them will ever know that. 
Finding an antagonist for this story is more difficult. There isn't a real, concrete "bad guy" who is fighting against Henderson, Swift, and Jablonski. I suppose a reader could argue the "Denebians" are the antagonists. We aren't sure if they are aliens or not, but the Denebian force is who is being fought against. I do not believe Multivac is a good choice for antagonist because the three men are not trying to undermine and destroy Multivac.  
I believe that the best choice for antagonist is the abstract concept of being overdependent on technology. By the end of the story, the reader realizes Multivac was nothing more than a hulk of busted computing power. All three men used their own intuition to make war decisions based on the information being given to each of them. Multivac didn't win the war. Human decisions did. The story illustrates to readers that, as good as the technology may be, it still can't compete with human reasoning.   

Explain law of demand, law of supply and how change in demand and change in supply apply to the market condition and discuss how price ceilings and price floors apply in the market.

The law of demand states that, all other things being equal, there will be an inverse relationship between the price of a good or service and the quantity of that product that people are willing and able to buy. This means that when the price of something goes down, people will (ceteris paribus) buy more of it. The opposite applies if the price goes up.
The law of supply states that, all other things being equal, there will be a direct relationship between the price of a good or service and the quantity of that product that people are willing and able to produce and sell. This means when the price of something goes down, people will (ceteris paribus) sell less of it. The opposite applies if the price goes up.
Between them, these two laws tell us how prices will be set in a free market. In such a market, the supply and demand curves intersect. The point where they intersect is called the equilibrium point. It tells us the price that the market will set and the quantity of the good or service that will be bought and sold at that price.
When either demand or supply changes in a market, the equilibrium point also changes, changing the price and the quantity bought and sold. If the demand rises, the price and the quantity bought and sold will (ceteris paribus) rise as well. In other words, more of the product will be sold and the price for the product will be higher. The opposite applies if demand drops. If supply increases, the price of the product will fall, but people will buy and sell more of the good or service. The opposite applies if supply decreases. In these ways, the laws of supply and demand work to set the equilibrium point for every free market.
Price ceilings and price floors disrupt the workings of the free market. They set arbitrary prices that are either below or above the equilibrium that the market would reach if left to its own devices. A price floor exists when the government mandates that the price for something cannot drop below a certain level. The classic example of this is a minimum wage. When a price floor is set, suppliers want to supply more (because they get a high price paid to them) of a good or service than consumers want to buy (because they have to pay the high price). The result is a surplus of that product. A price ceiling exists when the government mandates that the price for something cannot rise above a certain level. The classic example of this is rent control. When a price ceiling is set, consumers want to buy more (because they don’t have to pay very much) of a good or service than producers want to sell (because they do not get as good of a price for their product). The result is a shortage of that product.
On their own, the laws of supply and demand produce equilibrium points in every free market. When the government intervenes and sets price floors or ceilings, the working of the free market is disrupted and shortages or surpluses arise. Please follow the links below for interactive graphs that illustrate these concepts.
http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=demand+and+supply+increase

http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=market+equilibrium

http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=price+floor

What things upset Paul’s mom about the move to Florida?

From the text, we can deduce that there are a few things that upset Paul's mom about the move to Florida. Here are some of them:
The muck fires.
When lightning strikes on the second day in Florida, the lignite field at the end of the street catches fire. The firefighter tells Paul's mother that the field is always on fire. The muck fire, however, can be further exacerbated by lightning strikes. Since there is no conceivable way to put out the muck fire, the smell of smoke in the air is constant. This is one possible source of irritation for Paul's mother.
The lack of storage space in Florida homes.
Paul's mother laments that Florida homes are as "wide open as cathedrals." Because of the lack of storage space, Paul's mother must store most of the family's belongings at a climate-controlled storage space nearby. Paul also hints that his mother's favorite antiques are in storage; the implication is that the cherished antiques are not a good match for the decor and ambiance of the family's new home. Paul speculates that this is one reason his mother may hate the move to Florida.
The lack of a gym and auditorium at Paul's new school.
When Paul and his mother visit Lake Windsor Middle School, Paul's mother is upset to discover that the seventh and eighth-graders are in portable classrooms. There is no gym or auditorium. When it rains (which is often), the students must forgo P.E. and concentrate on academic parts of their health curriculum. Paul's mother also does not like the appearance of the flimsy-looking portable buildings, and she fears that they provide little protection during afternoon lightning storms.

Why do you think the witches tell Banquo his sons will be king?

The way this question is phrased makes it seems like you are being asked to give an opinion on why the witches would tell Banquo he will be the father of kings. The play does not explicitly answer this question. In act 1, scene 3, Macbeth and Banquo are walking across the heath after winning a battle against Norway. Three witches appear out of nowhere and hail Macbeth as "Thane of Glamis," "Thane of Cawdor," and "king hereafter." The entire prophecy given to Banquo by the witches in this same scene reads as follows:

First Witch: Lesser than Macbeth, and greater.
Second Witch: Not so happy, yet much happier.
Third Witch: Thou shalt get kings, though thou be none:

The prophecy reads like a riddle. How can someone be both "lesser" and "greater" than another person? To break down the witches' predictions, we have to actually start with the final one. That Banquo will "get kings" but not "be" one means that he will be the father of kings or ancestor of kings (he will "beget" them), but he will never be king himself. This means that he will be "lesser" and "Not so happy" as Macbeth because Banquo will never be the crowned ruler of Scotland. However, he will, at the same time, be "greater" and "much happier" than his friend. This is because his legacy will live on and he will not be corrupted by power like Macbeth will be.
The question is whether the witches know ahead of time exactly what will happen after telling Macbeth he will be king (this includes trying to kill Banquo and having Banquo's son Fleance killed). Did they set the entire tragedy into motion or did they just know what Macbeth would do with the information, then watch it play out? How you answer this question has much to do with how you would answer the question of why the witches even tell Banquo about his descendants. The information certainly eats away at Macbeth, both leading to the aforementioned murder of Fleance and attempted murder of Banquo in addition to a tantrum once Macbeth sees a vision of the dead Banquo's face multiplied many times in a mirror in act 4. The information adds to Macbeth's paranoia and his feeling that his reign is not that significant because he will not have any heirs. We can either believe that the witches take some sort of sick pleasure in seeing Macbeth's downfall (in which case they would know and enjoy his reaction to the prediction about Banquo) or that they simply provide information and Macbeth is solely to blame for the actions he takes as a result of that information.

Explain how Rainford's initial beliefs compare to Zaroff's statement that "life is for the strong, to be lived by the strong, and, if need be, taken by the strong."

Rainsford's initial comments to Whitney at the beginning of the story correspond to General Zaroff's statement:

Life is for the strong, to be lived by the strong, and, if need be, taken by the strong. The weak of the world were put here to give the strong pleasure (Connell 8).

Before Rainsford swims to Ship-Trap Island, where he meets General Zaroff, he tells Whitney that the world is divided into two classes, namely, "the hunters and the huntees." Essentially, Rainsford's initial perspective regarding competition in life mirrors Zaroff's belief that the strong are meant to take advantage of the weak. However, Rainsford's perspective drastically changes after he becomes the prey on Zaroff's island. As Rainsford runs and hides throughout Ship-Trap Island in order to avoid the general, who is armed and hunting him, he experiences firsthand what it is like to be weak and hunted by a superior being. By the end of the story, Rainsford gains valuable insight into what it is like to be prey. Zaroff's mindset and beliefs prevent him from sympathizing with those less fortunate and support his criminal habit of killing defenseless human beings.

How did the author survive Auschwitz?

The narrator, Tadek, is a Pole sent to the Auschwitz death camp despite not having been involved in any resistance activities against the German occupiers. But then, the Nazis are not renowned for being overscrupulous when it comes to establishing guilt or innocence. As far as they're concerned, Tadek is a Pole, a Slav, and therefore a member of an inferior race. The Germans feel entitled to treat him however they please.
Although Tadek isn't a Jew, conditions at Auschwitz are still unspeakably bad, and he's treated accordingly. Nonetheless, he somehow manages to survive. The main reason for this, as Tadek tells his fiancee in a letter, is that the Germans stopped gassing non-Jewish prisoners over three weeks before he arrived at the camp. With the Soviets fast approaching, Tadek is taken by the SS along with a number of other prisoners to Dachau concentration camp in Germany, where he is eventually liberated.

What is the figurative language in "The Road Not Taken"?

Robert Frost uses "the road" as a metaphor for a course not taken in life. In the first line, the narrator recalls his fateful choice: "Two roads diverged in a yellow wood." "Two roads" are a metaphor for two options. The "yellow wood" signifies an autumn light. Frost's decision to set the moment in the Fall could be a metaphor for a narrator that is in his or her "autumn years."
Like many of those faced with two good options but forced to choose one, the narrator expresses sorrow that he could not choose both—we can only walk down one path. 
In the second stanza, he muses that he initially believed that his choice was the better of the two but later thought differently:

Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that, the passing there
Had worn them really about the same...

The option we choose is always less appealing after it is chosen, for we wonder about the choice that we did not make. Thus, in the end, the narrator realizes that both choices were about equally good.
In the third stanza, the narrator mentions time of day: it is "morning." Morning could signify a new beginning. When we are presented with a new choice, or opportunity, this offers us a chance to do something new—even to start again. It is here, too, that the narrator recognizes the finality of his or her choice:

Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.

The speaker knows that once a choice is made, it cannot be undone. One must continue on the "path" that was chosen.
The final stanza reveals a kind of wistfulness for choices not made:

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I --
I took the one less traveled by,
And that has made all the difference.

The "difference" is not an ode to non-conformity, as so many have thought but instead an acceptance that choices determine the outcome of one's life. The path the speaker chose is "the one less traveled by," not because it was less ordinary, but only because it looked more appealing at first. Yet, both options, or paths, were "really about the same."

2^(3-z) = 625 Solve the equation accurate to three decimal places

For exponential equation:2^(3-z)=625 , we may apply the logarithm property:
log(x^y) = y * log (x) .
This helps to bring down the exponent value.
 Taking "log" on both sides:
log(2^(3-z))=log(625)
(3-z)* log (2) = log(625)
Divide both sides by log (2) to isolate (3-z):
((3-z) * log (2)) /(log(2))= (log(625))/(log(2))
3-z=(log(625))/(log(2))
Subtract both sides by 3 to isolate "-z":
3-z=(log(625))/(log(2))
-3                            -3
------------------------------------
-z=(log(625))/(log(2)) -3
Multiply both sides by -1 to solve +z or z:
(-1)*(-z)=(-1)* [(log(625))/(log(2)) -3]

 
 z~~-6.288       Rounded off to three decimal places.
To check, plug-in z=-6.288 in 2^(3-z)=625 :
2^(3-(-6.288))=?625
2^(3+6.288)=?625
2^(9.288)=?625
625.1246145~~625   TRUE
 
Conclusion: z~~-6.288 as the final answer.
 
 

What are the benefits of studying poetry?

This is a great question! There are definitely many benefits to studying poetry for many groups of people. Here are some:
1) Language learners can greatly benefit from a concentrated immersion in poetry. As poetry emphasizes rhythm and stress patterns, many ESL (English as a Second Language) learners can hone their pronunciation skills by reading poems aloud. Reading-aloud sessions can provide the requisite practice to increase the confidence of language learners.
Additionally, in studying poetry, language learners and other students can begin to appreciate and discover the history behind the poems they read. For example, Shakespearean poems provide a wide context from which to discuss relevant topics such as gender relations, human sexuality, and cultural norms during the Elizabethan era.
The Elizabethan era, as we all know, heralded the golden age of the Renaissance as well as the new age of English exploration and expansion. Therefore, an appreciation of the historical context of the poems can lead to an enriched and stimulating experience in the classroom. For example, students can compare and contrast the differences in gender relations between the modern age and the Elizabethan age.
2) There are emotional and intellectual benefits to studying poetry. For example, a poem may lend itself to many different interpretations. A discussion of these interpretations can help students hone their logic and reasoning skills.
Additionally, an appreciation for the metaphorical or figurative language used in poems can inspire students to view familiar objects in imaginative new ways. Students can increase their emotional and verbal intelligence by immersing themselves in the spirit of the poems they study; thus, the practice of exploring the possible, hidden meanings behind different poems can inspire an openness to new ideas. This approach can only increase a student's sensitivity to the language of poems, a sensitivity that may very well be carried into his/her own writing. Thus, studying poetry can conceivably improve a student's diction immeasurably.
3) In the business world, reading poetry in one's spare time can do one of three things. It can aid in inspiring creativity, improving empathy, and simplifying complexity. For example, reading a complex poem can be frustrating as well as rewarding. Making sense of a poem can be a consuming process, but it can also hone our ability to simplify the kind of complexities that intimidate others. Sometimes, this ability can be a good thing, especially when deadlines loom and solutions are needed.
Poetry also teaches one how to empathize with others. Through poetry, we can begin to appreciate the different perspectives of others. This appreciation can lead to constructive dialogue and perhaps, understanding between different social groups. Last, but not least, poetry inspires the kind of creativity that is unique and often revolutionary, especially if applied to the business world.

Clare Morgan, in her book What Poetry Brings to Business, cites a study showing that poems caused readers to generate nearly twice as many alternative meanings as “stories,” and poetry readers further developed greater “self-monitoring” strategies that enhanced the efficacy of their thinking processes. These creative capabilities can help executives keep their organizations entrepreneurial, draw imaginative solutions, and navigate disruptive environments where data alone are insufficient to make progress. (from The Benefits of Poetry for Professionals by John Coleman).

A great article to read: Why Teaching Poetry is So Important.
Hope this helps!
https://hbr.org/2012/11/the-benefits-of-poetry-for-pro

https://www.theclassroom.com/benefits-reading-poems-11971.html

What are the old man's two pieces of luck?

At the end of the story, the narrator explains that "There was nothing to do about [the old man]" on the bridge. He has tried to encourage the old man to get off the bridge and walk toward where he might find some assistance, but the old man has run out of energy and cannot bring himself to walk farther on. The old man only seems to worry about his animals, the ones he had to leave behind when he was evacuated, and not at all about himself. He says that, because he knows no one in Barcelona, it will not help him to walk in the direction of the trucks that way, and he doesn't seem to realize how much his own life is in danger. Any place would be better than the one he's in.
The narrator says that it was a "gray, overcast day with a low ceiling," and so the Fascists' planes were not up in the sky. "That and the fact that cats know how to look after themselves was all the good luck that old man would ever have." The two pieces of luck, then, are that the enemy planes aren't flying yet—and so the old man is still alive for the time being—and that his cat will probably survive the coming destruction. The implication, of course, is that the old man certainly will not, and his death will likely be a brutal and bloody one.

Although the soldier at the bridge tries to reassure the old man that his animals will be safe—for instance, that his pigeons will fly away since he left their cages open—it becomes clear by the end of the story that the soldier believes the old man's case is hopeless.
He thinks cynically to himself that the old man's two pieces of luck are that his cats will be able to fend for themselves and that it is too overcast for the German soldiers to bomb the bridge and surrounding area this day.
That's a very slender reed of hope. The old man doesn't have much future ahead of him: he could be bombed tomorrow. The story shows the ways war can devastate the lives of simple, innocent beings like the old man, and his animals, who are the collateral damage we might not even consider.

In Hemingway's short story, the old man has evacuated from his town of San Carlos and walked twelve kilometers to avoid artillery fire. Unfortunately, the old man is exhausted and cannot continue to walk away from the bridge where the advancing enemy forces will cross at any moment. The old man laments to the soldier about the fact that he had to leave his cat, two goats, and eight pigeons behind in San Carlos and worries about their well-being. The soldier attempts to comfort the old man by offering him words of encouragement, and the old man feels confident that his cat will survive without his protection. However, the soldier knows that there is not much hope for the old man and the rest of his animals. At the end of the short story, the soldier says,

It was a gray overcast day with a low ceiling so their planes were not up. That and the fact that cats know how to look after themselves was all the good luck that old man would ever have.

Essentially, the only two pieces of luck the old man possesses concern the fact that the Fascists' planes are not in the sky because of the overcast weather and the fact that cats can take care of themselves. The soldier realizes that the enemy forces will eventually cross the bridge and murder the innocent old man as they continue to advance through the country.

Do you think O. Henry himself is the narrator of the story, "The Gift of Magi"? Why or why not?

There are several reasons to think that O. Henry is the narrator of his own story. One is that there is a great deal of authorial input. The author is commenting on his own story with interjections. For example:

There was clearly nothing to do but flop down on the shabby little couch and howl. So Della did it. Which instigates the moral reflection that life is made up of sobs, sniffles, and smiles, with sniffles predominating.

"The Gift of the Magi" is a Christmas story evidently intended to appear in the Christmas issue of a New York newspaper in the days when newspapers printed short stories on a regular basis, especially in their Sunday and holiday editions. O. Henry was a notoriously heavy drinker, said to consume two quarts of whiskey a day. He died at the early age of forty-seven of alcoholim-related diseases. He wrote many of his stories in saloons. The attentive reader will sense that O. Henry must have been half-drunk and writing this, his most famous story, under deadline pressure. He may have turned it in at the copy desk without proofreading it. He would have found that he repeated one bit of exposition several times.

ONE DOLLAR AND eighty-seven cents. 
One dollar and eighty-seven cents. And the next day would be Christmas.
Tomorrow would be Christmas Day, and she had only $1.87 with which to buy Jim a present.
Only $1.87 to buy a present for Jim. 
But what could I do—oh! what could I do with a dollar and eighty-seven cents?”

In addition to having to meet a deadline, O. Henry would have been required to fill up a certain amount of space with a minimum total number of words. He seems guilty of stretching his copy with the simple fact that Della had only $1.87 to buy her husband a Christmas present. His philosophical interjections would also help to stretch his story. 
Another lapse which could be overlooked by many readers occurs near the end, when Jim returns home from work. Della feels sorry for him. She thinks:

Poor fellow, he was only twenty-two—and to be burdened with a family!

What family? Why wouldn't Della think "...to be burdened with a wife" if she were his only obligation? It seems that O. Henry was thinking of introducing the fact that Della is pregnant! That might be appropriate for a Christmas story because it would be a strong allusion to the story of the birth of Jesus on Christmas day about nineteen-hundred years ago. But O. Henry must have had second thoughts. He wrote for a mass audience. Many of his readers might have gotten the notion that he was suggesting that Della's baby (if he said she was pregnant) was the promised second coming of Christ, which many readers would consider sacrilege. The magi were not poor and did not give presents to each other. They were rich kings and could give the baby Jesus gifts of frankincense, gold and myrrh. 
We can detect the workings of the author O. Henry's mind as he was writing "The Gift of the Magi." He might have written a somewhat different story if he had not been under the influence and under deadline pressure, probably writing in a noisy saloon on a cold winter night. 
 
 

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 60

Find the derivative of $\displaystyle y = \frac{(x^3 + 1)^4 \sin ^2 x}{\sqrt[3]{x}}$ by using logarithmic differentiation.

By taking logarithms of both sides..

$\displaystyle \ln y = \ln \left[ \frac{(x^3 + 1)^4 \sin^2 x}{\sqrt[3]{x}} \right]$

If we apply the Laws of logarithm, we have


$
\begin{equation}
\begin{aligned}

\ln y =& \ln (x^3 + 1)^4 + \ln \sin^2 x - \frac{1}{3} \sqrt[3]{x}
&& \text{recall that } \ln (xy) = \ln x + \ln y \text{ and } \ln \left( \frac{x}{y} \right) = \ln x - \ln y
\\
\\
\ln y =& 4 \ln (x^3 + 1) + 2 \ln \sin x - \frac{1}{3} \ln x
&& \text{recall that } \ln (x)^k = k \ln x

\end{aligned}
\end{equation}
$


By taking the derivative implicitly, we have..


$
\begin{equation}
\begin{aligned}

&\frac{\displaystyle \frac{d}{dx} (y)}{y} = 4 \left( \frac{\displaystyle \frac{d}{dx} (x^3 + 1)}{x^3 + 1} \right) + 2 \left(\frac{\displaystyle \frac{d}{dx} (\sin x)}{\sin x} \right) - \frac{1}{3} \left( \frac{\displaystyle \frac{d}{dx} (x)}{x } \right)
\\
\\
& \frac{\displaystyle \frac{dy}{dx}}{y} = 4 \left( \frac{3x^2}{x^3 + 1} \right) + \frac{2 \cos x}{\sin x} - \frac{1}{3} \left( \frac{1}{x} \right)
\\
\\
& \frac{\displaystyle \frac{dy}{dx}}{y} = \frac{12x^2}{x^3 + 1} + 2 \cot x - \frac{1}{3x}
\\
\\
& \frac{dy}{dx} = y \left[ \frac{12x^2}{x^3 + 1} + 2 \cot x - \frac{1}{3x} \right]
\\
\\
& \frac{dy}{dx} = \left[ \frac{(x^3 + 1)^4 \sin ^2 x}{\sqrt[3]{x}} \right] \left[ \frac{12x^2}{x^3 + 1} + 2 \cot x - \frac{1}{3x} \right]



\end{aligned}
\end{equation}
$

You would like to add some decorative slices of apple to the top of a baked dessert. Whenever you’ve tried this, unfortunately, the apples brown before you have the chance to serve them to your dinner guests. While watching a cooking show, you learn that the browning of fruits such as apples is a chemical reaction. It is catalyzed by an enzyme called polyphenol oxidase. To prevent browning, the cooking show suggests that you blanch the fruit by placing it in boiling water or steam for a short time. Explain how blanching affects the enzyme, polyphenol oxidase, to stop the browning process.

The short answer is that under the high-temperature conditions of the boiling water or steam, the polyphenol oxidase enzyme is denatured. Most likely your instructor wants you to give an explanation of what denaturation is, how it occurs, and how it relates to enzyme structure and function.
Biological enzymes such as polyphenol oxidase are proteins—long chains of amino acids joined together by peptide bonds. There are a variety of different amino acids that differ in their R groups. The important thing about these differences is that some are polar, meaning that they have one atom with a slight positive charge and another with a slight negative charge. The chain of amino acids is somewhat flexible and tends to settle into an arrangement where a positive part of one amino acid is near a negative part of another. This arrangement is known as a “configuration,” and protein configurations are generally stable (meaning that they don't change) at room temperature.
The configuration of a protein is important because the “chain” of amino acids is wrapped and condensed into a three-dimensional shape. This shape is essential to a protein’s function. In the case of an enzyme, the shape brings reactants in a chemical reaction together in an orientation that allows the reaction to occur at biological temperatures (many reactions would only occur at much higher temperatures—unsuitable for life—in the absence of enzymes).
The shape of a functional enzyme, however, is only one of many possible configurations that a particular amino acid chain could potentially adopt. Proteins fold as they emerge from ribosomes during synthesis, taking on their one and only possible configuration that is actually functional. If the configuration of an enzyme were disrupted, without breaking any chemical bonds, the chance that it would return to its functional configuration, instead of some other random configuration, would be infinitesimal.
This is what denaturation is. Heating the enzyme causes the atoms in it to vibrate and move, and the energy and motion can overcome the electrostatic attractions between different R groups. We envision the amino acid chain flopping around. When cooled, it settles into one of the millions of possible configurations available to it—but not into the functional configuration. It no longer has the shape needed to promote the oxidation reaction that produces the brown color, so browning does not occur.

Would Rex be considered successful?

Many dictionary definitions of "success" mention the accumulation of wealth in the form of money, property, and other tangible assets. Other looser definitions of "success" mention ideas like personal fulfillment, doing one's best or even simply living according to one's own values. Though Rex is unlikely to be described as successful in terms of wealth and assets, he may fit one of the looser definitions of success mentioned above.
Rex has always lived according to his own standards, and he refuses to play by the seemingly arbitrary rules of society. Though his choices, from an outsider's point of view, might seem selfish, they are all Rex's choices, and he might say that his choice to be independent is a definition of success in and of itself. Rex finds living within the confines of everyone else's expectations suffocating, and he challenges these expectations with determination. He chooses to live by his own rules, and he definitely succeeds in this way.
Success is not an easy word to define, and it is not an idea that exists in black and white terms. Rex's kind of success lives firmly in the gray area, where it can be argued and debated. This is only one way to interpret Rex as a successful person.

What are the Upanishads and the Vedanta? What is their philosophy?

The Vedas are the four sacred texts of the religions of India (often referred to collectively as "Hinduism"). "Veda" is a Sanskrit word meaning "knowledge." The Vedas were regarded by believers as having been revealed to humans through meditation.
Like the sacred texts of most world religions, the Vedas began as oral tradition. They were handed down verbally from generation to generation, beginning around 1400 BCE, and eventually written down. They are known as the Rig Veda, the Yajur Veda, the Sama Veda, and the Atharva Veda.
Each of the four Vedas has four parts: a Samhita (scared hymns) an Aranyaka (rituals), a Brahmana (commentary on rituals), and an Upanishad (meditation and philosophy of how humans are related to the universe).
"Vedanta" also came to refer to one of the six traditional schools of Indian religion, because they focused on the Upanishads.
The central teaching of the Upanishads is that everything in true reality ("Brahman") is unified and connected, and the appearance of individuality and separation (for example, when regarding two different people) is only an illusion. This is summed up in the phrase "Atman (a person's core self, or soul) is Brahman (the cosmos)." The purpose of meditation is therefore to overcome the illusion of separateness and realize the unity of all reality. This is known as "achieving enlightenment."
http://hirr.hartsem.edu/ency/Hinduism.htm

https://library.ucalgary.ca/religiousstudieswebguide

Based on the information in the poem, who was Ozymandias?

By using the text of the poem Ozymandius we can deduce the following about the poem's namesake.  That he was an imperial ruler accustomed to dictatorial control.  In his time he obviously possessed a level of power that induced a self destructive arrogance. We now call such arrogance "hubris".  The wasteland that surrounds his ruined statue, his former kingdom, starkly contradicts the inscription upon his statue.  The grandiose claims for his person, position, and possessions, as the "King of Kings", have a mirror image of devastation that is proportional in degree to his glory at the height of his reign.  While not overtly stated, Ozymandius appears, as a universal archetype revealing the dangers of unchecked power in the ruler. As such the poem can be interpreted as a cautionary warning that is less concerned with the past failure of Ozymandius himself than with humanity's penchant for repeating his mistakes. 

All we learn of Ozymandias from the poem is that he was, according to inscription on his statue, "king of kings." His face on the statue is described as having a "sneer of cold command." HIs "mighty works" are also mentioned. However, since nothing but sand surrounds his broken statue, we can imagine that he reigned over a kingdom that disappeared a long, long time ago. Because his statue is found in the desert, we might surmise he ruled over an ancient Middle Eastern kingdom. He appears to be a narcissist who thought his great works would last forever. 
Though not stated in the sonnet, we know that the poem was inspired by the statue of Egyptian pharaoh Ramesses II, who reigned from 1279-1213 BCE. The British Museum had acquired a large piece of a statue of this pharaoh. This inspired Shelley and his friend, Horace Smith, to write sonnets about it. 

In the book The Witch of Blackbird Pond by Elizabeth George Speare, what is the setting for most of Chapter One?

Most of the first chapter of the book takes place onboard the Dolphin, the ship that Kit takes from Barbados to Wethersfield.  The setting of the book is introduced to us in the first paragraph, where we are told what year it is, where Kit is, and where she is going.

ON A MORNING in mid-April, 1687, the brigantine Dolphin left the open sea, sailed briskly across the Sound to the wide mouth of the Connecticut River and into Saybrook Harbor. Kit Tyler had been on the forecastle deck since daybreak, standing close to the rail, staring hungrily at the first sight of land for five weeks.  (Ch. 1) 

All of this is significant to understanding the book.  First of all, knowing the year is obviously important to appreciating Kit’s situation.  Colonial Connecticut was much different from modern life.  Also, it is significant to know that it is mid-April, meaning that it is just the beginning of spring.  It is still pretty cold.  Kit has not seen land for over a month, and this is clearly a circumstance she is neither used to nor enjoys. 
Kit’s reaction to the first sight of land is also telling. 

She could just make out the row of unimpressive shacks and the Bash of raw new lumber. Her smile was admiring from pure relief. At least this grim place was not her destination, and surely the colony at Wethersfield would prove more inviting. (Ch. 1) 

This tells us that Kit has never been to Connecticut before, and that it is different from what she is used to.  It also tells us a lot about the colony.  Conditions were stark and bleak.  It wasn’t heavily populated, at least not in this part. 
In this chapter, therefore, we learn quite a bit about Kit and the colony of Connecticut before we even get to much plot.  While Kit is still on the ship we learn how different Barbados is from Connecticut, and how different Kit is from the Puritans.  One of the main ways this is illustrated is through Kit jumping in the water for the doll.  The Puritans are shocked.  Kit grew up around water, but in Connecticut it is unheard of for a woman to swim.

Beginning Algebra With Applications, Chapter 2, 2.3, Section 2.3, Problem 70

Translate the phrase "the sum of one-eight of a number and one-twelfth of the number" into a variable expression. Then simplify the expression.

$
\begin{equation}
\begin{aligned}
& \text{The unknown number: } n && \text{Assign a variable to one of the number quantities}\\
\\
& \text{One-eight of the number } \frac{1}{8}n && \text{Use the assigned variable to write an expression for any other unknown quantity.}\\
\\
& \text{One-twelfth of the number } \frac{1}{12}n && \text{Again, by using the assigned variable to write an expression for any other unknown quantity.}\\
\\
&= \frac{1}{8}n + \frac{1}{12}n && \text{Use the assigned variable to write the variable expression.}\\
\\
&= \frac{3n + 2n}{24} && \text{Set the LCD}\\
\\
&= \frac{5n}{24} && \text{Simplify}
\end{aligned}
\end{equation}
$

How is the title "Avarice" appropriate for George Herbert's poem?

The title "Avarice" is appropriate for Herbert's poem because it is about greed. Herbert writes about how money is extracted from dirty mines, and he says of money, "thy parentage is base and low," meaning that gold or other metals that form coins come from dark places. By discussing the money's "parentage," Herbert personifies money and makes it seem like it comes from parents with low status. By digging money out of mines and making the coins bright, Herbert states "thou hast got the face of man," meaning that money has people's faces and impressions on it. In this exchange, "Thou art the man, and man but drosse to thee." In other words, because people are so greedy for money and show such great avarice, money has become the master, while man is lower than money. Herbert believes avarice transforms people into beings who are as low as the base metals that are brought out of the ground and transformed into money. 

How does The Boy in the Striped Pajamas by John Boyne deal with the rise of Hitler?

The Boy in the Striped Pajamas deals with the rise of Hitler by looking at the atrocities Hitler encouraged through the eyes of a child:  Bruno.  By making this particular child our narrator as well as the son of a Nazi commandant, the reader is able to watch the confusion of an innocent boy as he comes upon the evidence of Hitler's rise to power.  One of the most revealing scenes about Hitler's rise to power is the dinner scene where Hitler and Eva come to dinner at Bruno's house.  We have learned to love our narrator by this time, and Bruno already despises Hitler due to his prideful conduct at dinner.  Bruno's innocence continues by calling Hitler "the Fury" instead of the Führer.  Further, Bruno witnesses the treatment of the prisoners of the Auschwitz concentration camp in The Boy in the Striped Pajamas through the character of Shmuel.  When Bruno meets Shmuel, he is dirty, dressed in a striped uniform, thin, gaunt, and without shoes.  Bruno's innocence continues here as he misinterprets life in the concentration camp as life on a brutal farm.  Bruno cannot accept the treatment of Shmuel, so he brings him extra food and company.  Bruno's innocence is lost when he escapes "into" the camp and is killed in the gas chamber.  It is a piece of brutal irony that the son of a Nazi commandant would be killed in this way.

What was Roosevelt trying to achieve with this speech, particularly with his opening discussion of American history from 1789 to the end of World War 1?

In the first section of his Four Freedoms Speech, President Franklin Roosevelt attempted to put into historical context the dangers of fascism and the ongoing conflicts overseas to the United States. World War Two was already in full swing in Europe and Asia and it was clear to him and many others that the United States could not stay neutral for much longer. However, there were still many that hoped that the United States could stay out of the conflict. With only a few exceptions the country had avoided what George Washington had called "foreign entanglements" in the past. Roosevelt wanted to make it clear that this situation was something unprecedented in world history. That is why he traced the country's history to illustrate the extreme circumstances that faced the United States.
In the speech, President Roosevelt mentioned or eluded to the Civil War, the French Revolution, Maximilian I in Mexico, World War I, the War of 1812, and Napoleon. He brought up all these historical episodes to point out that the United States always rises to the occasion to defend democracy. Furthermore, the looming conflict was different than all these other examples that he mentioned. Never before had the United States engaged a nation bent on world domination. He was arguing that this war was a threat to America's very existence, as he says,

"In like fashion from 1815 to 1914—ninety-nine years—no single war in Europe or in Asia constituted a real threat against our future or against the future of any other American nation."

By placing the events of his time in their historical context, Franklin Roosevelt was making it clear that America was facing unique and perilous circumstances. The United States had risen to the occasion in the past and, Roosevelt was arguing, could do it again.
https://www.ourdocuments.gov/doc.php?flash=false&doc=70&page=transcript

The Four Freedoms Speech was Roosevelt's 1941 State of the Union address. At this time, the United States had not entered World War II.
Roosevelt recalled U.S. history from 1789 to 1914 because he wanted to emphasize that the U.S. had, all through our history, gotten involved in a number of conflicts outside our borders. Although George Washington in his Farewell Address had advised Americans to mind their own business and not get involved in Europe's affairs, Roosevelt knew that the United States would almost inevitably get pulled into the second World War. Therefore, he wanted to position the U.S. as having had a non-isolationist history. He hoped for it to seem natural for our country to involve itself in yet another war.
Roosevelt also used the speech to champion the U.S., and democracy in general, as the guardians of freedoms worldwide. He listed the four freedoms as freedom of speech, of religion, freedom from (economic) want and from fear. These freedoms would have been understood as a rebuke to the tyranny of Adolph Hitler in Germany. 

Evaluate the integral int x^2/(4-x^2)^(3/2) dx

I will use trigonometric substitution for this integral. First, substitute to eliminate the square root. Then evaluate the integral. Lastly, convert back to the original variable. Please see the image bellow for the answer.
http://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx

In "The Doll's House" by Katherine Mansfield, it is obvious that she is trying to show the difference between the world of adults and children. What are some specific images/terms that she uses to express this?

When the Burnell children are opening up their doll's house, Mansfield portrays the wonder and perspective of children uncovering a new and mysterious miniature world. When the children open the door to the house, Mansfield writes, "How much more exciting than peering through the slit of a door into a mean little hall with a hat-stand and two umbrellas!" And then the children think, "Perhaps it is the way God opens houses at dead of night when He is taking a quiet turn with an angel." Mansfield conveys the wonder of children through such terms and images as God opening "houses at dead of night," while the adults, on the other hand, concentrate on the smell of the paint coming from the doll's house. Aunt Beryl thinks, " For, really, the smell of paint coming from that doll's house." While the children focus on the wonder of the house, the adults focus on its inconvenience and odd smell.
The symbol of the lamp in the doll house symbolizes the children's wonder. Kezia does not care that the lamp does not work. As Mansfield writes, "the lamp was perfect. It seemed to smile to Kezia, to say, 'I live here.' The lamp was real." The lamp makes the doll's house and its inhabitants come alive to the children.
At the end of the story, Aunt Beryl harshly scolds the Kelvey children for coming to the Burnells' house to look at the doll's house, but the Kelveys quickly forget about her scolding and only care that they have seen the magical little lamp. Mansfield writes of Lil and Else Kelvey:

"But now she [Lil] had forgotten the cross lady. She put out a finger and stroked her sister's quill; she smiled her rare smile. 'I seen the little lamp,' she said, softly."

In this touching episode, Mansfield portrays the Kelveys as only caring about the lamp in the way children do and forgetting the snobbish and cruel world of adults. The lamp symbolizes the children's sense of wonder and magic.

Who is to blame for the unfortunate turn of events in the necklace?

The blame arguably lies with Mathilde. She is a vain, shallow woman who thinks that money and worldly goods will bring her happiness. In borrowing money at an exorbitant rate of interest, she directly contributes to the demise in which she becomes the shambling, pathetic figure that Madame Forestier encounters at the end of the story.
Everything Mathilde does is for show, and the fake necklace neatly exposes the falsity of the world she inhabits. It also symbolizes the real world, a world that is mainly mundane and ordinary, far removed from the tinsel glamor of a society gathering. The everyday world stands in contrast to the glittering facade of the deluded fantasy world she has constructed for herself.
Ultimately, Mathilde has failed to come to terms with her relatively lowly origins. In her heart of hearts, she believes herself a princess. In "The Necklace," De Maupassant is quietly drawing attention to the way in which a hierarchical, class-obsessed society distorts our values and makes us strive to be something we are not. The blame for the "unfortunate turn of events" undoubtedly lies with Mathilde, but her foolish actions can best be understood against the background of a society in which wealth and status are everything.

What did king Leopold assure the world he was trying to do for the Congolese people?

King Leopold II served as king of Belgium from 1865 to 1909, during the height of European colonial expansion. European countries competed for overseas colonies in places such as Africa and Southeast Asia, competing for resources, power, and prestige. Leopold unsuccessfully tried to obtain control of the Philippines twice before turning his attention to Africa. In 1876 he created the International African Society, which was essentially a front for Leopold's colonial exploits. King Leopold claimed it was a humanitarian effort to "civilize" and explore central Africa and convinced African and European leaders that his society was a philanthropic foundation. Instead, in 1879 Leopold created the International Association of the Congo to replace the International African Society. This association allowed Leopold to create his Congo Free State, which he first used to explore and then exploit the Congo. The Congo was particularly rich in resources, such as rubber. At the Berlin Conference in 1885, Leopold convinced European powers that common trade in Africa was in the best interests of all imperial countries. The area controlled by the Congo Society was made its private property, which essentially made it the property of Leopold II.

Cite one parallel in the life of Kurt Vonnegut and the artist Rabo Karabekian.

Some scholars would argue that Karabekian, the artist who also makes an appearance in Breakfast of Champions and Deadeye Dick before his final appearance in the mock-autobiography Bluebeard, is an overarching example of authorial self-insertion. In other words, the fictional character of Rabo Karabekian is but a thinly-veiled version of Vonnegut himself. Not only does Vonnegut cast himself as the central character, but overall, the novel could be seen as a fictional representation of Vonnegut’s life and career, as Karabekian explores many of the themes and ideas that are central to Vonnegut’s work: identity, the role that the artist plays in society, and the question of what art really is, to name just a few. More parallels come to light when comparing the lives of the two men: Karabekian, like Vonnegut, is a married man and former soldier, and both are innovators, however controversial, in their respective fields.

Intermediate Algebra, Chapter 3, 3.1, Section 3.1, Problem 66

Determine the midpoint of the line segment with endpoints $\displaystyle \left( \frac{21}{4}, \frac{2}{5} \right)$ and $\displaystyle \left( \frac{7}{4}, \frac{3}{5} \right)$.

Use the midpoint formula with $\displaystyle x_1 = \frac{21}{4}, x_2 = \frac{7}{4}, y_1 = \frac{2}{5}$ and $\displaystyle y_2 = \frac{3}{5}$

$\displaystyle \left( \frac{\displaystyle \frac{21}{4} + \frac{7}{4}}{2}, \frac{\displaystyle \frac{2}{5} + \frac{3}{5}}{2} \right) = \left( \frac{\displaystyle \frac{28}{4}}{2}, \frac{\displaystyle \frac{5}{5}}{2} \right) = \left( \frac{7}{2}, \frac{1}{2} \right)$

What is the moral lesson of the short story?

I don't think there is only a single moral in this story.  However, I think a major moral lesson of this story is focused on how war affects people.
"The Sniper" does a great job of showing the dehumanizing effects of war. Regardless of the specific conflict, war has a way of driving all humanity out of the people fighting in it and living with it. People are no longer people; they are simply tools that fight, or they are targets to be eliminated. The story helps tell war's impersonal nature by keeping all of its characters impersonal; no names are used. There is a sniper, another sniper, an old woman, and so on. I think readers are lucky to have that much information because to the story's protagonist, who or what a person is doesn't matter. To the sniper, everybody is a target of equal opportunity. It doesn't matter if the person is young, old, man, or woman. They are targets to the protagonist. He doesn't see them as human people.
The shock of the story comes at the end when readers learn with the sniper that he has shot and killed his own brother. Based on all of this, I think that a moral of the story is to be aware of how war affects the men and women who fight it. They form a desensitized, impersonal detachment from humanity that might cause them to do something that they will regret forever.

In I Am Malala, why is there a preface and a prologue?

The preface (“Birmingham, England, June 2015”) introduces the subject of the book and establishes the continued importance of Malala's work through the Malala Fund. In contrast, the prologue describes the events prior to the shooting and thus invites us to read Malala’s story. Basically, the preface establishes Malala's credibility in the area of girls' education, while the prologue provides the background details that led to the shooting. Note that the preface is never a part of the text; it is numbered in Roman numerals rather than the Arabic numerals used in the prologue and the rest of the text.
The preface provides details about Malala's adjustment to life in Birmingham and describes her work with the Malala Fund. From the preface, we learn that Malala played an instrumental role in building a school for the Maasai Mara people in Kenya. The preface also explains why she visited Nigerian schoolgirls on her seventeenth birthday: in 2014, more than 250 schoolgirls in Chibok were abducted by members of Boko Haram. Although many of the girls have been rescued, the Nigerian government is still working on rescuing the rest of the girls. Meanwhile, Malala aims to support girls' education in Nigeria through the Malala Fund. To date, Malala's foundation has funded education projects in Jordan, Kenya, Pakistan, and Nigeria; it has also worked to integrate Syrian refugees into Jordan's schools. So the preface helps us understand why an organization like the Malala Fund is necessary, while the prologue briefly explains the premise behind the shooting (the main event of the book).

The Enlightenment and the Great Awakening reflected the anxieties and tensions of the late seventeenth and early eighteenth century. In a well-written and thoroughly supported essay, discuss the conflicts and anxieties that emerged in both social movements.

The Second Great Awakening, which occurred in the late 1700s and early 1800s in colonial America, brought to the fore religious and social tensions that arose during the tail end of the Enlightenment. Religious fervor had been declining, and people sought a more invigorated and enthusiastic experience with religion that emphasized emotion and a personal connection with God. The religions that began to take root in the U.S. at this time, including Methodism and Baptism, favored this type of enthusiasm and challenged the religions that had developed during the Enlightenment, including Deism (a religion that sought to reconcile Christianity with a belief in rationality). These new forms of religion were often spread through "camp meetings" at which impassioned preachers spoke. This time period marked the end of the Enlightenment, with its emphasis on reason and rationality, in favor of Romanticism and its emphasis on emotion and sensation.
The Second Great Awakening also spread religions that appealed to people on the margins of society and who had less political and economic power, including slaves and women. Newer and more enthusiastic forms of religion appealed to them, in part as a way for them to gain a more central role in the church. These new forms of religion were a challenge to the older forms, and they also ushered in a period of reform in which abolitionists, women's rights campaigners, and other movement leaders tried to right the wrongs they saw in the world. Therefore, the Second Great Awakening was a religious and political upheaval.

Many historians argue that the Great Awakening was a reaction to the Enlightenment. In Europe, the Age of Enlightenment emphasized personal agency in matters of faith. It also promoted rational explanations for the origins of humanity. Science was the order of the day in enlightened Europe, and Deism replaced what many saw as a rigid Christian orthodoxy. People who espoused Enlightenment beliefs emphasized empiricism.
Empiricism is the belief that knowledge can only be acquired through sensory experience. Scientists such as Newton, Copernicus, and Galileo argued that man was born good and that it was only his environment that corrupted him. They resolutely rejected the doctrine of original sin and the depravity of the human soul. Many Enlightenment scientists were also Deists; they believed that God created the world and then largely withdrew from humanity. These scientists believed that it was up to mankind to use rational means to navigate life on earth.
The concepts of the Enlightenment were in direct conflict with those of the Great Awakening, which occurred on the other side of the ocean in the American colonies. In the Middle Colonies, the Presbyterians were especially uneasy about the effects of the Enlightenment across the ocean. As a religious people, they greatly valued a personal religious experience and the biblical precepts they lived by. Their religious fervency soon spread to the Puritan Congregationalists in New England.
There, preachers such as Jonathan Edwards preached about eternal damnation and the forgiveness of sins in sermons such as "Sinners in the Hands of an Angry God." However, Edwards himself was a supporter of the European Enlightenment. Thus, the Great Awakening saw a schism within Puritan Christianity itself. Jonathan Edwards was a proponent of the less formal and more emotional "New Light" experience, while "Old Light" supporters rejected the emotional radicalism of the Great Awakening.
The European Enlightenment certainly caused great anxiety among the faithful in the American colonies. For its own part, the Great Awakening, while a strong response to the movement, came with its own set of conflicts. During this period of revival, great differences of opinion existed between "New Light" proponents and "Old Light" traditionalists. "Old Light" supporters were essentially non-revivalists: they greatly disapproved of what they believed were the excesses of the Great Awakening. This group accepted the depravity of the human soul as religious dogma, and they also rejected undue emotionalism in religious matters.
In due time, the "New Light" modernists further splintered. We can see that both social movements came with their own set of anxieties and conflicts. For more, please refer to the links below.
https://www.colonialwarsct.org/1740_s.htm

https://www.differencebetween.com/difference-between-enlightenment-and-vs-great-awakening/

How would you analyze Elinor Wylie's "Let no charitable hope" in terms of structure, tone, imagery, and language?

Wylie's poem is structured in three stanzas of four lines each. The rhyme scheme in each stanza is end rhyme in an abab pattern (e.g. stanza two: alone, beset, stone, get). The metrical structure is iambic tetrameter, although the first two lines incorporate syllabic variation and read more naturally like trimeter.

The tone of the poem shifts from gentle sarcasm in the first stanza to bitterness in the second stanza then to ridicule in the third stanza. The tone is revealed through subtle contradiction or paradox in the last two lines of each stanza, as in stanza one's "images / Of eagle and of antelope: / I am in nature none of these." We are surprised to learn the images of charitable hope are meant to reveal herself to her in the hope she will rise above her limitations; she contradicts the charitable hope declaring she is "in nature none of these."
 
Wylie's imagery uses concrete objects in surprising associations. Concrete images of eagle and antelope are associated with misguided charitable hope. A stone squeezed is associated with the provision of nourishment. The various outrageous and austere years she has lived are associated with no fear, but all are associated with her gently ridiculing smile: "And none has quite escaped my smile."
 
Regarding language, Wylie's diction is poetic diction in that she uses metaphor, imagery, and symbolism in poetic style. Her vocabulary is ordinary for a person who is educated, as she was, and she uses neither slang nor an elevated vocabulary.
 
An interesting point of language is that Wylie manages, through subtle conjunction of words, to turn "charitable hope" and years being smiled upon into expressions of sarcasm and ridicule. Charitable hope is followed by "confuse my mind," expressing the image that the "charitable hope" is misguided and unfounded, which we find to be true: "I am in nature none of these." "[M]y smile" is preceded by "none has quite escaped," expressing the idea that, could the years do so, they would have been glad to escape her loveless smile of ridicule.
 
It is also interesting that the opening stanza uses "none" in "I am none of these" (she is none of the images conjured, as of powerful eagle or graceful antelope), and the closing stanza uses "none" in "But none has merited my fear, / And none has quite escaped my smile." Wylie provides a closed circle of thought tied together by the "none" that seems to define her sense of being, even to the point where she feels she is "squeezing from a stone / The little nourishment I get."
https://www.britannica.com/biography/Elinor-Wylie

In the book Wonder, when does Amos first show up?

RJ Palacio first introduces Amos on page 122, which is when August's friend Summer arrives at the Halloween party being held by Savanna, who is one of the most popular fifth graders at Beecher Prep.
Summer expresses her surprise at how many couples are at the party, and Amos and his girlfriend Ellie are one of them. This is all we are told about Amos at this stage. We don't hear anything more about what he and Ellie got up to at the party, because Summer became very uncomfortable soon after realizing that Amos was there. Her discomfort was caused by Savanna telling her that Julian (the class bully, who constantly picked on August) thought she was cute and wanted to ask her out on a date.
Summer went and hid in the bathroom, and called her mother to come and fetch her.
Later in the book, we find out that Amos was initially one of Julian's close friends. He was one of the kids who later became disillusioned with Julian's cruelty and ends up later defending August and his friend Jack.

Amos appears for the first time in the chapter "The Halloween Party," told from Summer's point of view. On page 122, Summer speaks about all the couples at Savanna's party, including Ellie and Amos. The character of Amos next appears in the chapter "Back from Winter Break," told from Jack's point of view. Jack describes Amos as "a pretty straight-up kid" (page 168). The fact that even Amos only gives Jack a half nod means that Jack has really become a social outcast because Julian is punishing Jack for his friendship with Auggie. Later, Amos is mentioned as on Julian's side, in the list that Charlotte makes (page 177). Over time, however, Amos is one of the kids who becomes tired of Julian's nastiness. When Julian grabs Jack's backpack and puts pencil sharpener shavings into it, Amos grabs the backpack and hands it to Jack (page 209). Amos grows weary of watching Julian be so cruel, and he realizes that he should treat Auggie well.

int sqrt(9+16x^2) dx Find the indefinite integral

Given to solve,
int sqrt(9+16x^2) dx
by using the trig substitution , we can solve the integral
for sqrt(a +bx^2) dx the x is given as
x= sqrt(a/b) tan(u)
so,
for the integral
int sqrt(9+16x^2) dx
let x=sqrt(9/16) tan(u) = (3/4) tan(u)
=> dx = (3/4) sec^2(u) du
so,
int sqrt(9+16x^2) dx
=int [sqrt(9(1+16/9 x^2))] ((3/4) sec^2(u) du)
= 3 int [sqrt(1+(16/9)x^2)] ((3/4) sec^2(u) du)
= 3 int sqrt(1+(16/9)((3/4) tan(u))^2) ((3/4) sec^2(u) du)
= 3 int [sqrt(1+(16/9)(9/16)(tan^2 u))] ((3/4) sec^2(u) du)
= (9/4) int sqrt(1+tan^2 u) (sec^2(u) du)
= (9/4) int sqrt(sec^2 u) (sec^2(u) du)
= (9/4) int sec u (sec^2(u) du)
= (9/4) int (sec^3(u) du)
by applying the Integral Reduction
int sec^(n) (x) dx
= (sec^(n-1) (x) sin(x))/(n-1) + ((n-2)/(n-1)) int sec^(n-2) (x) dx
so ,
(9/4)int sec^(3) (u) du
= (9/4)[(sec^(3-1) (u) sin(u))/(3-1) + ((3-2)/(3-1)) int sec^(3-2) (u)du]
= (9/4)[(sec^(2) (u) sin(u))/(2) + ((1)/(2)) int sec (u)du]
=(9/4)[(sec^(2) (u) sin(u))/(2) + (1/2) (ln(tan(u)+sec(u)))]
but we know
x= (3/4) tan(u)
= > 4x/3 = tan(u)
=> u =arctan(4x/3)
so,
=(9/4)[(sec^(2) (u) sin(u))/(2) + (1/2) (ln(tan(u)+sec(u)))]
=(9/4)[(sec^(2) (arctan(4x/3)) sin(arctan(4x/3)))/(2) + (1/2) (ln(tan(arctan(4x/3))+sec(arctan(4x/3))))]
 
=(9/4)[(sec^(2) (arctan(4x/3)) sin(arctan(4x/3)))/(2) + (1/2) (ln((4x/3))+sec(arctan(4x/3)))]+c

Single Variable Calculus, Chapter 4, 4.1, Section 4.1, Problem 34

Determine the critical numbers of the function $g(t) = |3t - 4|$

We can rewrite the given function as


$
\begin{equation}
\begin{aligned}

g(t) =& \sqrt{(3t - 4)^2}
\\
\\
g'(t) =& \frac{d}{dt} (\sqrt{(3t - 4)^2})
\\
\\
g'(t) =& \frac{d}{dt} [(3t - 4)^2]^{\frac{1}{2}}
\\
\\
g'(t) =& \frac{1}{2} [(3t - 4)^2]^{\frac{-1}{2}} \frac{d}{dt} (3t - 4)^2
\\
\\
g'(t) =& \left( \frac{1}{\cancel{2}} \right) [(3t - 4)^2]^{\frac{-1}{2}} (\cancel{2}) (3t-4) \frac{d}{dt} (3t - 4)
\\
\\
g'(t) =& [(3t - 4)^2]^{\frac{-1}{2}} (3t - 4) (3)
\\
\\
g'(t) =& \frac{3 (3t - 4)}{[(3t - 4)^2]^{\frac{1}{2}}}

\end{aligned}
\end{equation}
$


Solving for critical numbers


$
\begin{equation}
\begin{aligned}

& g'(t) = 0
\\
\\
& 0 = \frac{3 (3t - 4)}{[(3t - 4)^2]^{\frac{-1}{2}}}
\\
\\
& \sqrt{(3t - 4)^2} \left[ 0 = \frac{3 (3t - 4)}{\cancel{\sqrt{(3t - 4)^2}}} \right] \cancel{\sqrt{(3t - 4)^2}}
\\
\\
& 0 = 3 (3t - 4)
\\
\\
& \text{ or }
\\
\\
& \frac{\cancel{3} (3t - 4)}{\cancel{3}} = \frac{0}{3}
\\
\\
& 3t - 4 = 0
\\
\\
& 3t = 4
\\
\\
& \frac{\cancel{3}t}{\cancel{3}} = \frac{4}{3}
\\
\\
& t = \frac{4}{3}

\end{aligned}
\end{equation}
$



Therefore, the critical number is $\displaystyle t = \frac{4}{3}$.

Why didn't the Age of Exploration start before 1400 AD?

There are many reasons for this. England and France were at war with each other during the Hundred Years' War. This war took up a great deal of resources. The kingdoms of Castille and Aragon in Spain would not be united until the latter part of the 1400s with the marriage of Ferdinand and Isabella, and their first item of business would be to chase out all Muslim influence from Spain. Three of the major exploring powers—Spain, France, and England—were going through their own set of domestic problems. There was also the relative ease and certainty one had of sending trading vessels to Constantinople, which, as of 1453, was still owned by Christians. No one wanted to undertake a voyage around Africa or across the Atlantic in the hopes of getting to China when one could trade with Venetian middlemen who were already doing business in Constantinople and its vast trade networks. There was also the issue of the Black Death, which had wiped out a great deal of Europe in the fourteenth century. It would take the continental economy generations to recover from the loss of all of these people. In many cases the peasants who survived the plague realized that they could ask for higher wages and this put further pressure on societies.

comment on " what man has made of man " in the poem " lines written in early spring " by William Wordsworth

In Wordsworth's "Lines Written In Early Spring," most of the poem is focused on natural phenomena. The narrator begins "in a grove," surrounded by birds, flowers, and plants, and he finds peace and joy in their presence. He explicitly states "That there was pleasure there," and he indirectly reiterates that joyous mood by describing birds that "hopped and played," flowers that "[enjoy] the air," and "a thousand blended notes" of the world around him.
However, the narrator twice repeats the phrase "What man has made of man." In both cases, the reference is prefaced by a line indicating sadness—the first time, "And much it grieved my heart to think"; the second, "Have I not reason to lament."
To fully understand the reason behind the narrator's rueful tone, we need to look at the entirety of the final verse:

And I must think, do all I can,
That there was pleasure there.
If this belief from heaven be sent,
If such be Nature's holy plan,
Have I not reason to lament
What man has made of man?

The narrator believes that the pleasure he takes from Nature (capitalized and personified) is part of a "holy plan." But this understanding brings him sadness. Since the plan itself is clearly a good thing, we can infer that he thinks the plan will not succeed. The narrator's sadness stems from his belief that mankind has collectively rejected the "holy plan," preventing itself from fully appreciating the joy that currently enraptures the narrator. With this context, one can understand that "What man has made of man" refers to modern civilization, society, and/or technology—those things that hold us back from appreciating the natural beauty of the world around us.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 80

Suppose that an air is being pumped into a spherical weather balloon. At any time $t$, the volume of the balloon is $V(t)$ and its radius is $R(t)$.

a.) What do the derivatives $\displaystyle \frac{dV}{dr}$ and $\displaystyle \frac{dV}{dt}$ represent?

$\displaystyle \frac{dV}{dr}$ represents how does the volume changes with respect to its radius. On the other hand, $\displaystyle \frac{dV}{dt}$ represents how quick the volume is changing with respect to time.


b.) Express $\displaystyle \frac{dV}{dt}$ in terms of $\displaystyle \frac{dr}{dt}$.

Recall that the volume of a sphere is $\displaystyle V(r) = \frac{4}{3} \pi r^3$ and by using Chain Rule we have,


$
\begin{equation}
\begin{aligned}

\frac{dV}{dt} =& \frac{dV}{dr} \left( \frac{dr}{dt} \right) = \frac{4 \pi}{3} \frac{d}{dt} (r^3) = \frac{4 \pi}{3} \frac{d}{dr} (r^3) \frac{dr}{dt} = \frac{4 \pi}{\cancel{3}} (\cancel{3}r^2) \frac{dr}{dt}
\\
\\
\frac{dV}{dt} =& 4 \pi r^2 \frac{dr}{dt}

\end{aligned}
\end{equation}
$

Why did the narrator of "The Tell-Tale Heart" kill the old man?

Poe's classic short story "The Tell-Tale Heart" is told by an unreliable narrator, who is clearly mentally unstable. There are numerous clues that suggest the unreliable narrator is insane, which include his continual insistence that he is not "mad," his staccato writing style, and his "sharpened" senses that allow him to hear paranormal sounds. Toward the beginning of the story, the narrator mentions that he had no ill will toward the old man and actually loved him—another example of his insanity. After reading this statement, the reader cannot help but wonder how someone could murder a person they love. The narrator goes on to say that he was not motivated by money to kill the old man and was simply disturbed by the old man's "Evil eye." The insane narrator explains his reason for killing the old man by saying,

I think it was his eye! yes, it was this! He had the eye of a vulture—a pale blue eye, with a film over it. Whenever it fell upon me, my blood ran cold; and so by degrees —very gradually—I made up my mind to take the life of the old man, and thus rid myself of the eye forever. (Poe, 1)

One could argue that the narrator's desire to murder the old man stems from his mental instability. He is clearly mentally ill, and his motivation to kill the old man is not a strong enough reason to commit such a horrific crime, in the eyes of most people. Therefore, one could surmise that the narrator murdered the old man because he was mentally ill and insane.

To answer this question, take a look at the second paragraph of the story. According to the narrator, the old man had an "evil eye" which made him feel very uneasy:

He had the eye of a vulture—a pale blue eye, with a film over it. Whenever it fell upon me, my blood ran cold.

In other words, the narrator felt compelled to kill the old man because this was the only way that he could stop the evil eye from bothering him. As a result, he immediately made plans to murder the old man.
However, if we look a little deeper, it becomes clear that the narrator killed the old man for another reason. Specifically, we can argue that the narrator killed the old man because the narrator was not of sound mind. In the week preceding the murder, he was clearly suffering from some kind of mental illness which caused a deep sense of paranoia about the old man. Although the narrator opens the story by claiming that he is not mad, his motivation for the murder suggests otherwise.

The angular resolution of the Hubble telescope is about .1 arc second (0.1") while that of ACC's (My college) 8 inch reflector is about .5". Could either telescope resolve the individual stars in a binary system 3 parsecs away? Assume the two stars are 1 A.U. apart as measured at right angles to the line of sight from the earth at the time of viewing.

What we're really asking is this: What is the angle subtended by 1 AU at a distance of 3 parsecs? Is it less or greater than 0.1 arcseconds and 0.5 arcseconds respectively?So, let's get everything in the same units: Meters is usually a good choice.A parsec is about 3.1*10^15 m, so 3 parsecs is about 9.3*10^15 m. An AU is about 1.5*10^11 m. For angles this small, we can use the approximation
tan x approx x
where x is measured in radians. So we want to get 0.1 arcseconds and 0.5 arcseconds into radians. 1 arcsecond is pi/180/3600 radians, or about 4.8*10^-6 radians. So 0.5 arcseconds is about 2.4*10^-6 radians, and 0.1 arcseconds is about 4.8*10^-7 radians.Now all we need to do is find the ratio of the two distances, which is the tangent of x, which we've just said is very close to x itself.(1.5*10^11 m)/(9.3*10^15 m) = 1.6*10^-5 radiansThis is larger than both of our given angular resolutions, so we can resolve the two stars with either telescope.

Which country gained the most power during imperialism? Why?

The question considers which country gained the most power during imperialism and why. A good starting point is the definition of imperialism (see reference to Merriam-Webster below). 
The question requires substantial narrowing to be worth addressing, as arguably all nations pursue a certain amount of imperialism as they grow in power. Additionally, the concept of imperialism can be applied to any situation in which a dominant culture uses mechanisms of power and influence to control people in other cultures (i.e. even within a particular nation). That being said, the question most likely refers to the rise of nations during the age of imperialism from the 19th century to the present. In this context, the contenders are Great Britain if we limit ourselves to the period of direct colonization, and the United States if we extend this to the de facto control exercised during the superpower era starting after the Second World War in 1945. The “why” for these statements, that is the proof of them, rests on measures of breadth and depth. That is, how many nations and people came under the control of these powers, and how thorough was/is this control. 
These measures are easier to assess during the colonial era, as clear statistics are available as to who controlled whom, how many people were involved, and how the mechanisms of government were linked between imperial ruler and colonial ruled. In that era, Great Britain’s reach was clearly broadest. As it was said, the sun literally never set on the United Kingdom at the end of the Victorian era. In the 1600’s, England vied with France, Spain and the Netherlands as primary contenders for colonies and resources in the areas of the world which were becoming accessible through ocean travel. Germany and Italy were late entrants to this contest, owing primarily to their not unifying as nation-states until late in the 19th century. However, by 1930, England had evolved into Great Britain, and its pre-eminence in world dominion was clear. In that year, the British Empire comprised over 13 million square miles of territory and over 450 million people. Governance in these areas ran the gamut from democratic institutions in England itself, to representative structures under the ultimate control by the monarchy in others (e.g. Canada and other “dominions”) to tolerance of local control over non-strategic matters as long as they didn’t interfere with the economic and military imperatives of the British rulers (most of the colonies). By comparison, French holdings were also dispersed globally (Asia, Africa) but did not encompass anywhere near the same number of people or resources.
 After World War II, the United States largely took up the mantle of global rule. As the dominant world “superpower” and the only effective counterbalance to the rising power of the post-war Soviet Union, it took it upon itself to engineer world affairs in furtherance of various interests. The application of the term imperialism is harder to measure in direct, tangible statistics in this era, as the mechanisms of control between the US and the rest of the world are not institutionalized in direct legal structures. Instead, relationships between the US and the various other nations are represented as “alliances,” or “friendships.” Arguably, de facto control of high-level domestic and international policies for these countries is exercised through a variety of international institutions (e.g the IMF, the United Nations, and others) in which the “influence” of the US is strong or even dominant. There are also numerous examples of direct US intervention in local political and economic affairs in furtherance of US strategic or business interests (Vietnam, Chile, Central America, and more recently Iraq and Afghanistan).
 It should be noted that this is a highly contentious subject, and the literature arguing the degree of imperial control by the US is massive. The student should acquaint her/himself with this material and form their own opinion as to the extent, impact, and (in)appropriateness of imperialism in the modern era.
https://www.merriam-webster.com/dictionary/imperialism

How did Christopher Columbus contribute to the mythologizing or de-mythologizing of America?

Christopher Columbus played an essential role in defining how the newly discovered Americas would be seen by Europeans. His original intention was to find a new route to India. He thought this was possible due to a mathematical error on his part; if not for the previously undiscovered continent he miraculously ran into, he and his crew would have died at sea. Unfortunately, Columbus's approach to the Americas was to cover up the fact that he had failed to reach India. Hence, Native Americans are routinely referred to as "Indians" even today. Additionally, the cultures of the "new" world were very different from what Europeans were used to. Because of the tropical climate, the indigenous people wore little clothing. Columbus interpreted this as nakedness tied to poverty, because the European custom was to be fully covered. He also described the people he met as almost entirely consisting of young boys, because they didn't have facial hair as the Europeans did. In his "Diario de Abordo" (onboard diary), Columbus noted that they would make "good and intelligent servants" and otherwise described them as easily converted to Christianity. Columbus paints the indigenous people as simple and uncivilized, and these ideas about Native Americans carried on into the accounts of others and shaped European perspectives about the New World.
http://www.historyisaweapon.com/defcon1/diarioofchristophercolombus.html

https://www.britannica.com/biography/Christopher-Columbus/The-first-voyage

In Swift's Gulliver's Travels, what special attributes does the Emperor of Lilliput possess which set him apart from the common folk?

Well, I'd say generally speaking, the Emperor of Liliput is depicted as very much equivalent to the great monarchs of Europe, in terms of his features (he's described with "an Austrian lip" for example), his style of dress, and the opulence of his palace and court. In all these respects, Swift is crafting an image which reflects that of the great princes and monarchs of Europe (and Gulliver describes him accordingly). Physically, he's described as taller than the typical Liliputian with "strong and masculine" features and as being "then past his prime, being twenty-eight years and three quarters old" (Chapter 2). Perhaps more important than his appearance, however, is his pride, and the ways in which Swift uses him as a way of satirizing the ambitions and excesses of European monarchy. After Gulliver destroys the fleet of Blefuscu, the Emperor intends to use Gulliver to conquer them, and when Gulliver refuses to participate in this act of military aggression, the Emperor's relationship with Gulliver takes a stark turn towards the worst.

The emperor of Lilliput is taller, by perhaps a centimeter or so, than anyone else in his court, and Gulliver says that the height difference is enough to impress a beholder.  Likewise, he has "strong and masculine" features, a graceful and regal bearing, and superior posture and proportion.  These seem to set him apart from the rabble, at least for Gulliver.
Besides this, Gulliver tells us that the emperor is almost twenty nine years old, has reigned for approximately seven years, and has been -- for the most part -- victorious and happy all the while.  He is an excellent horseman, quite articulate, and very desirous, at least initially, of showing Gulliver hospitality and courtesy.  He is later revealed to be somewhat less hospitable, especially when thwarted in his plans to defeat Blefuscu.

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 78

A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $\$6$, and the society sells an average of 20 per week at a price of $\$10$ each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 2 sales per week.

a.) Find a function that models weekly profit in terms of price per feeder.

b.) What price should the society charge for each feeder to maximize profits? What is the maximum weekly profit?

a.) If we let $x$ be the price of the feeder and $y$ be the quantity of the feeders sold at price $x$, then by using slope intercept form, then we can now solve the function for the weekly profit. We have two points $(10, 20)$ and $(11, 18)$. The second point is based on the statement that for every dollar increase, the sales loses 2 per week.


$
\begin{equation}
\begin{aligned}

y =& mx + b
\\
\\
y =& \left( \frac{18 - 20}{11 - 10} \right) x + b
\\
\\
y =& -2x + b
\\
\\
& @ (10, 20)
\\
\\
20 =& -2(10) + b
\\
\\
b =& 40


\end{aligned}
\end{equation}
$


Thus,

$y = -2x + 40$

Next, we know that if each feeder cost $\$6$, then the profit from each bird feeder is $x - 6$. Thus, the weekly profit is equal to the profit per bird feeder times the quantities of bird feeders that are sold weekly. So,


$
\begin{equation}
\begin{aligned}

P(x) =& (x - 6)(-2x + 40)
\\
\\
P(x) =& -2x^2 + 52x - 240

\end{aligned}
\end{equation}
$


b.) To maximize the profit, the value of $x$ should be

$\displaystyle x = \frac{-b}{2a} = \frac{-52}{2(-2)} = \$ 13$

Therefore, the maximum weekly profit is


$
\begin{equation}
\begin{aligned}

P(13) =& -2(13)^2 + 52(13) - 240
\\
\\
P(13) =& \$ 98

\end{aligned}
\end{equation}
$

How is the idea of dream deferred related to issues of colour and racism in the context of America ?

In Langston Hughes's famous poem "Harlem" (sometimes referred to as "Dream Deferred"), the speaker ponders what happens to a dream when it is delayed or put off. We don't know precisely what dream it is that the speaker refers to, as it is never explicitly stated in the poem, but the poem's original title of "Harlem" provides a significant clue. It seems likely that the dream referred to is the dream of racial equality, a dream which came dramatically to the forefront of American politics in the mid-twentieth century. Hughes was one of the preeminent poets of the Harlem Renaissance, and Harlem was a community that was primarily comprised of African Americans. The speaker ponders what will happen to a dream deferred, and the final possibility—that it will "explode"—seems the most compelling because it makes use of the only metaphor in the entire poem (which is full of less-powerful similes), because the line is set apart on its own, and because it is typeset in italics. This seems to imply that the effects of a dream deferred, especially the dream of racial equality, will be volatile and violent, like a bomb. It will not only affect the would-be dreamer but entire communities. In other words, the effects of continued racism will be farther-reaching than just African American communities; white America must acknowledge the dream.

Describe the current United States tax system relative to possible reform/alternatives.

The current United States tax system relies on taxes at the municipal, county, state, and federal levels. There are progressive taxes, such as income taxes, which vary based on how much one makes, and there are regressive taxes, such as sales taxes, which tax everyone at the same rate, regardless of income. The tax system is quite convoluted, especially at the federal level. There are various tax brackets for different incomes as well as tax incentives for families, investors, and small-business owners. Tax reform is needed in order to streamline the process and to make the system fair for all.
The government uses tax incentives in order to reward certain behaviors such as investing, starting businesses, and owning homes. However, these are not feasible for Americans who make below a certain amount of money. Some people view tax reform as doing away with tax incentives. Some Republicans have called for the creation of a flat tax which would tax all income at a certain level. Democrats, on the other hand, view tax incentives for the working class as necessary, and they wish to tax goods meant for the upper class, such as stock dividends and high income, at higher rates. They view this as being a way to make taxation more fair and to level the economic playing field for most Americans. Libertarians wish to abolish the federal income tax altogether; however, they also tie this view in with the idea that many federal programs should be abolished.

What makes the US tax system so daunting and complex is that it actually consists of multiple different systems. As well as federal taxes, there are state and municipal taxes. Income taxes can be charged by both federal and state governments, and there is also a wide range of other taxes such as sales tax, property tax, and various special taxes, duties, and fees. The system is so complex that over 80 percent of Americans use either professional tax preparers or tax preparation software.  What drives this complexity is that taxation serves multiple purposes. As well as being a tool to raise revenue, it can serve various ethical and political goals and also attempts to guide behavior. For example, so called "sin taxes" on cigarettes and alcohol are intended to reduce consumption of potentially harmful substances. Tax breaks may be designed to encourage corporate investment, the shift to renewable energy, or home ownership.
While almost everyone agrees on the need for some form of tax reform, there is little consensus on the type of reform needed. A position supported by many members of the Republican party is that the main priority in tax reform is to reduce taxes on corporations and the wealthy because, in theory, this would increase GDP and "trickle down" to everyone else, a theory that has little support from economists. Another potential type of tax reform, favored by Democrats, would aim to reduce the loopholes which allow the very rich and large, multinational corporations to pay extremely little in the way of taxes. The point of such reforms would be to reduce the deficit and increase tax revenue that could be used for infrastructure and social programs.
https://www.taxpolicycenter.org/briefing-book/why-are-taxes-so-complicated

How does Frost employ settings of rural life in "Birches"?

The way that this poem gets readers thinking about rural life is through its descriptions of how people interact with the birch trees themselves or do things that are stereotypically associated with simple, rural life. Line 3 is a good place to start looking for specific rural setting activities.

I like to think some boy's been swinging them.

The narrator is thinking about a boy swinging from the branches of birch trees. It's not like trees don't exist in urban settings. They do, and kids climb those trees as well; however, the notion of spending an afternoon climbing trees and swinging from branches should make most readers think of a rural setting or at the very least family camping trips. The country has more trees, so there is more opportunity for this kind of thing.
About midway through the poem, readers get another example of a boy in the country. Again the narrator comments about the boy bending tree branches, but this time the boy is doing it on his way to fetch the cows. Immediately after this line, Frost is fairly blunt about the boy's setting. He is too far from town to play baseball (presumably on some kind of team).

Some boy too far from town to learn baseball,
Whose only play was what he found himself,
Summer or winter, and could play alone.

If you were Neville Chamberlain, how would you have handled Hitler’s remilitarization of Germany?

In 1938, Adolf Hitler annexed the Sudetenland from Czechoslovakia after Hitler claimed Czech police attacked Germans living in the area. Neville Chamberlain, the British prime minister, flew out to have a conference with Hitler to ask about Hitler's land grabs. Hitler assured Chamberlain that Germany did not desire any more territory. Chamberlain, trying to avoid war, believed Hitler and flew back to Britain where he infamously claimed that Britain had achieved "peace in its time." This was appeasement—Chamberlain gave in to what Hitler wanted.
Before one judges Chamberlain too harshly, remember he had a tough job—the British people had finished WWI within the last twenty years and no one wanted a new fight with Germany. Also, Britain was part of the worldwide financial depression. The British people probably did not want to fight a war to defend a foreign country. If I were Chamberlain, I would have led a propaganda effort showing Hitler as a European madman. This campaign would appear in newspapers and movies.  I would show the Sudetenland's residents' reactions to the takeover and I would have Czechoslovakia appear to be the victim. I would also increase military preparedness by increasing the size of the military budget. I would tell the British people that I was sending arms to Czechoslovakia so Czech people could defend themselves. I would also find a neutral third party to look into whether German citizens were really attacked in the Sudetenland. Of course, my reaction would be different than yours; for example, you may also consider sanctions similar to what the United States did against Russia after the annexation of Crimea from Ukraine.  

Give five reasons to prove that India is a democratic country.

India is considered the world's largest democracy. In short, a democracy is a system of government in which the citizens make governing decisions or elect representatives for that purpose. India became a democracy in 1950 when its Constitution went into effect. Let's look at some of the evidence for India being a democracy.
India practices universal suffrage. This means that all men and women age eighteen and over have the right to vote in elections. This applies regardless of race, religion, or caste. Voter turnout in the 2014 general election was at 66 percent, meaning that over 540 million Indians voted in that election.
India's government is based on a federalist model. This means that the various Indian states have united to form a single country with local, state, and national level of governments. Citizens have the right to elect officials and representatives at each level, although governors are appointed by the president. This is one of the most successful democratic models for any large country.
Since 1947 India has functioned as an independent nation. No foreign power controls the government of India. Like in any democracy, the leaders are answerable to their constituents, not a colonial power.
In an effort to protect the integrity of elections, India has a strong and autonomous election commission. Although it has seen some criticism for failing to safeguard the rights of people with disabilities, the Election Commission is tasked with ensuring free and fair elections in India. It is often regarded as one of the best organizations of its kind worldwide.
The Constitution of India specifically spells out the rights and powers of the citizens of the country. The Supreme Court of India has made a number of rulings specifically to safeguard the rights of its people throughout the history of the Indian republic. This has ensured that democracy has continued in India to this day.

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 64

(a) Prove that the function $F(x) = | x |$ is continuous on $(-\infty, \infty)$
(b) Prove that if $f$ is a continuous function on an interval, then so is $|f|$.
(c) If $|f|$ is continuous, does it follow that $f$ is continuous as well? I so, prove it. If not, find an example.


(a) Based from the definition of absolute value,

$F(x) = |x| = \left\{
\begin{array}{c}
x & \text{ if } & x \geq 0 \\
-x & \text{ if } & x < 0
\end{array}
\right.
$

According to the definition if the function is continuous everywhere, its left and right hand limits should be equal. So,

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \to 0^+} x & = \lim\limits_{x \to 0^-} -(x)\\
0 & = -(0)\\
0 & = 0
\end{aligned}
\end{equation}
$


It shows that $\lim \limits_{x \to a^+} f(x) = \lim \limits_{x \to a^-} f(x)$, therefore $F(x)$ is continuous on $(-\infty, \infty)$


(b) If $f$ is continuous on an interval then $|f| = f$ for $f > 0$ and $|f| = -f$ for $f < 0$. Also, $|f| = 0$ if $f = 0$.
Therefore, if $f$ is a continuous function, $|f|$ is continuous as well.


(c) Suppose that $f(x) = \left\{
\begin{array}{c}
1 & \text{ for } & x \geq 0 \\
-1 & \text{ for }& x < 0
\end{array}
\right.
$

$|f|$ is continuous everywhere such that if we plugin any positive or negative numbers inside the absolute value, we get
a positive value. However, $f$ is not continuous at $x = 0$ because of jump discontinuity.

What are the push and pull factors of European exploration?

"Push" and "pull" factors are usually associated with immigration. "Push" factors are the things that propel people to leave a place (religious persecution, economic downturn, famine) and "pull factors" are the things about a place that make people want to go to a place. These include cheap land, more freedom, and other factors. The factors that "pushed" European nations to explore were mostly economic in nature. They were especially interested in discovering a water route to Asia in order to monopolize the spice trade. They also became involved in exploration as a matter of geopolitical competition that reflected the state of affairs in Europe. What was appealing about colonies (remember that exploration and colonization were two different things) was also economic in nature. Under the economic philosophy of mercantilism, European powers attempted to develop favorable balances of trade with their colonies. They exploited resources (beaver pelts, timber, and precious metals, or example) and cultivated cash crops (sugar, tobacco, and coffee, for example). They also used colonies as outlets for domestic goods. European nations saw colonies as outlets for expanding populations as well, and in Spain especially, there was a powerful desire to convert Native peoples to Christianity.
https://www.history.com/shows/mankind-the-story-of-all-of-us/infographics/age-of-exploration

To boil the water in the kettle, 2400 Coulombs of charge pass through the heating element in 200 seconds. Calculate the current flowing through the heating element and give the unit. Choose the unit from the list below: Amps Volts Watts

By definition, electric current is the amount of electric charge that flows through the cross-section of a conductor in a given unit of time:
I = (Delta Q)/(Delta t)
In SI (International System of units) the charge (Q) is measured in Coulombs, and the time is measured in seconds. The unit for current then equals 1 Coulomb/second, and it is called 1 Ampere, or, sometimes, 1 amp.
In this question, the amount of charge flowing through the heating element is
Delta Q = 2400 C in Delta t = 200 s . This means the current flowing through the heating element is
I = 2400/200 A = 12 A .
Please check out the reference website for the further discussion of the definition and units of measurement of electric current.
The current flowing through heating element is 12 A (Amps)
https://www.physicsclassroom.com/class/circuits/Lesson-2/Electric-Current

What were Zenia's most significant actions and what were the effects of those actions?

Zenia takes a number of actions that the other characters see as significant betrayals. It's best to review her relationship with each of the other female characters and discuss what she does to betray each woman.
Charis is a very sensitive character who tries to help Zenia when she claims to be very ill. Charis allows Zenia to live in her home with her and her boyfriend Billy. Although the women already seem to know that Zenia is not trustworthy and that she possibly lies about her background, Charis takes pity on her. Eventually, Zenia begins an affair with Billy and they run off together. They even violently kill Charis's chickens and leave the mess behind for Charis to find.
Roz is a working woman who seems strong and has a vivacious personality. However, she also falls victim to Zenia's betrayal. Zenia seduces Roz's husband, eventually driving him to commit suicide. Roz also helps Zenia by giving her work at the magazine Roz runs, and Zenia ends up surpassing Roz in some ways, which feels like another betrayal to Roz.
Tony is an intellectual, a professor who studies war and battles. Tony's eventual husband, West, was once in a relationship with Zenia, who treated him poorly. Tony and Zenia meet as students, and Tony writes a paper for Zenia. She uses that against Tony later on, and at one point, when Zenia returns to Tony's life, she rekindles a relationship with West until Zenia discards him yet again and returns to Tony.
Zenia is depicted as a woman who preys on the weaknesses of other women, but she is also someone who seems to enjoy luring men away from those women. We never hear Zenia's perspective in the story, so we cannot know her motivations; she remains a mystery to the reader as well as to the characters, who can only develop an idea of her from the treacherous acts she performs against them.

How did life and landscape change on the Great Plains by 1900?

There were many changes that occurred in the Great Plains by 1900. One change was the status of the Native Americas. The Native Americans had been able to roam the Great Plains since they were relocated there in the 1830s. However, by 1900, the government policy toward the Native Americans had changed. They were placed onto reservations and didn’t roam throughout the area as much.
Two additional changes to the life and landscape of the Great Plains were the growth of the population and the emergence of farming. Many people had viewed the Great Plains as a vast wasteland. However, after the Civil War, people began to move there. With the use of sod houses and the development of new technology, people could live in the area and farm the land. New machines like the steel-tipped plow and the use of the seed drill made it easier to plant crops and farm the land. The mechanical reaper made it easier to harvest the crops. Thus, the population of the area grew.
People also moved to this area to find minerals and to raise cattle. As word spread about the discovery of gold and other minerals, people moved to the Great Plains. As it became more profitable to raise cattle, more people went there to do this. During the Civil War, the demand for meat increased. This helped to make cattle ranching a more profitable economic pursuit.
Another change was the growth of businesses. As more people moved to the Great Plains, businesses began to move there also. Transportation improved allowing businesses to be able to get supplies to the region and to ship products from the region. It also was easier for people to get to and from the Great Plains.
As more people moved to the Great Plains, the number of states in our country increased. Nebraska, Colorado, Montana, North Dakota, and South Dakota are examples of states that entered the Union after the Civil War.
There were many changes that occurred in the Great Plains by 1900.