Provide a summary to help explain the concepts in "Regarding the Problem of Newborn Piglets in Winter" by Chen Rong.

"Regarding the Problem of Newborn Piglets in Winter" is a short story by author Chen Rong that examines the impact of the Chinese Cultural Revolution. The story takes place at the peak of Mao's power and focuses on the various ways in which the post-revolutionary population of China both resisted and assimilated to the ideology of Mao's regime. The author explores how many people during this time fought quietly against Maoist ideals and offers an often scathing critique of communism and its impractical applications.
In this story, the long-solved problem of keeping piglets from freezing during the winter is turned into a metaphor for the unnecessary interventions of communism. While the elderly pig farmer Mammy Guo has always known exactly what steps to take in order to keep her newborn piglets warm and healthy throughout the winter, Secretary Zhang Dingfan takes it upon himself to issue a national edict on the matter. In this sense, the manufactured problem of freezing piglets is used as an example of what the author views as the inefficiency of the communist system of government. In an attempt to maintain a sense of importance at each level of government, officials place unnecessary restrictions on citizens who are already managing their affairs well on their own. Meanwhile, problems that could be effectively mediated by the government are overlooked or ignored entirely.
As the story progresses, Dingfan's mandate to protect newborn piglets trickles down to all levels of the communist government. The author explores the dysfunction of this system at each level, from Dingfan himself to Xu Quan and his other local-level subordinates. The story also delves into Dingfan's personal life and his distant relationship with his own granddaughter, Babe. While Dingfan insists on intervening in the affairs of private citizens, he is hypocritically disconnected from the concerns of his own family. However, he is shown at one point trying to shelter Babe from Maoist propaganda on television. The story comes to a somewhat melancholic end when Dingfan remarks, "When the time comes, I’ll make up words to suit whatever tune the authority picks." This comment shows that Dingfan has abandoned his passive resistance to communist ideals and will likely continue to perpetuate them.
https://files.eric.ed.gov/fulltext/ED452132.pdf

What is Macbeth's reaction to the witches' "news," and does this change when he finds out he is the Thane of Cawdor?

Initially, Macbeth is incredulous; he cannot believe what the Weird Sisters have told him.  He wants them to keep talking and to tell him more, including how they know the information they claim to know and how they came to meet with Macbeth and Banquo on the heath.  When the witches vanish, Macbeth is awestruck and says that he wishes they had stayed to answer his questions.  Banquo wonders if he and Macbeth were hallucinating when they saw the weird women, and the pair of friends seems to joke about the oddness of the experience. 
However, once Ross and Angus tell Macbeth that he's been named the Thane of Cawdor, Macbeth expresses confusion, but then he begins to hope (privately) that the sisters' other prediction would come true.  He says, "Two truths are told / As happy prologues to the swelling act / Of the imperial theme" (1.3.140-142).  He refers to the fact that the Weird Sisters were right -- he is the Thane of both Glamis and Cawdor now -- and so he begins to think that he cannot but become king (the "imperial theme"), as they said he would.  In other words, he goes from disbelief and shock to acceptance and certainty.

Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 100

Three points that lie on the same straight line are said to be collinear. Consider the points $A(3,1), B(6,2)$ and $C(9,3)$. Use the slope formula to determine whether the point $(0,6), (4,-5)$ and $(-2,12)$.

Let $A$ be the point $(0,6)$

$\phantom{Let}$ $B$ be the point $(4,-5)$

$\phantom{Let}$ $C$ be the point $(-2,12)$

Slope of segment $AB$

$\displaystyle m_{AB} = \frac{-5-6}{4-0} = - \frac{11}{4}$

Slope of segment $BC$

$\displaystyle m_{BC} = \frac{12-(-5)}{-2-4} = - \frac{17}{6}$

Slope of segment $AC$

$\displaystyle m_{AC} = \frac{12-6}{-2-0} = - \frac{6}{2} = -3$

The slope of each segment are not the same. Thus, these three points cannot be collinear.

What do the narrator and three other men do each day?

The American narrator and the three Italian soldiers from Milan go to the hospital each day for treatment on wounds from the war. After working with the machines, which the doctor swears will heal them, they go together to the Café Cova near the famous opera house La Scala in what the narrator labels the "communist quarter" of Milan. People in this part of the city scream insults at the soldiers because they are officers. Another boy, who lost part of his face and now wears a "black silk handkerchief," sometimes accompanies them. Presumably the men spend time in the café drinking and flirting with the girls. Obviously these girls are quite friendly to the soldiers, and the narrator notes that the "girls at the Cova were very patriotic, and I found that the most patriotic girls in Italy were the café girls."
While the three Italians are initially friendly to the narrator, their attitude changes after they learn the narrator basically received his medals because he was an American. It is understood that these men had actually won their medals for extreme bravery in the face of the enemy. This section of the story may be highly biographical, because Hemingway was wounded during the war while working on an ambulance crew. He was hit in the legs while handing out chocolate to Italian soldiers in the trenches. The narrator and the three Italians ultimately "drifted apart," although the narrator remains friends with the boy in the black scarf.

The following sentence is ambiguous. Provide two explanations which illustrate the different meanings of the sentence. "We need more empathetic leaders."

The key word here is the adjective “more.” Does it modify “empathetic,” or does it modify “leaders?”
If “more” modifies the adjective “empathetic,” then it indicates the degree of the emotion. The sentence would refer to the fact that we need leaders who are more empathetic, more understanding, more compassionate, and more connected to us followers and to the situations that we are experiencing. The leaders need to imagine themselves in our shoes sometimes, in order to understand what’s going on with us.
If “more” modifies the noun “leaders,” then it merely indicates quantity. Yes, we do indeed need leaders who are understanding, compassionate, and connected; but we need more of these people than we already have. The implication is that we already have a few of these kinds of leaders; but we don’t yet have enough of them. At least, not in the speaker's opinion.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 5

Express the composite function $y = \sqrt{\sin x}$ in the form $f(g(x))$. [Identify the inner function $u=g(x)$ and the outer function $y = f(u)$.] Then find the derivative $\displaystyle \frac{dy}{dx}$
Let $y = f(g(x))$ where $u = g(x) = \sin x$ and $y = f(u) = \sqrt{u}$

Then,


$
\begin{equation}
\begin{aligned}
y' &= \frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}\\
\\
y' &= \frac{d}{du}(\sqrt{u}) \cdot \frac{d}{dx} ( \sin x)\\
\\
y' &= \left( \frac{1}{2\sqrt{u}} \right) (\cos x) && \text{Substitute value of }u \text{ and simplify}\\
\\
y' &= \frac{\cos x}{2\sqrt{\sin x}}

\end{aligned}
\end{equation}
$

(x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32) Perform the indicated operation(s) and simplify

To be able to perform the indicated operation(s) on (x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32) , we have to express them as similar fractions.
Apply factoring on each expression on the denominator side.
Let:
 x^2-2x-8=(x+2)(x-4)
and
 x^2-12x+32=(x-4)(x-8)
Determine the LCD by getting the product of the distinct factors from denominator side of each term.
Thus, LCD =(x+2)(x-4)(x-8)
                  =(x^2-2x-8)(x-8)
                  = x^3-2x^2-8x-8x^2+16x+64
                   =x^3-10x^2+8x+64
Express each term by the LCD. Multiply top and bottom of each term by the missing factor.
First term:
(x+3)/(x^2-2x-8) =(x+3)/((x+2)(x-4))
                =(x+3)/((x+2)(x-4))*(x-8)/(x-8)
                =((x-8)(x+3))/((x+2)(x-4)(x-8))   
                =(x^2-5x-24)/(x^3-10x^2+8x+64)
Second term:
(x-5)/(x^2-12x+32) =(x-5)/((x-4)(x-8))
                  =(x-5)/((x-4)(x-8)) *(x+2)/(x+2)
                  =((x-5)(x+2))/((x-4)(x-8)(x+2))
                   =(x^2-5x+2x-10)/(x^3-10x^2+8x+64)
                  =(x^2-3x-10)/(x^3-10x^2+8x+64)
Applying the equivalent fraction in terms of LCD, we get:
(x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32)
=(x^2-5x-24)/(x^3-10x^2+8x+64) -(x^2-3x-10)/(x^3-10x^2+8x+64)
=((x^2-5x-24) -(x^2-3x-10))/(x^3-10x^2+8x+64)
=(x^2-5x-24 -x^2+3x+10)/(x^3-10x^2+8x+64)
=(x^2-x^2-5x+3x-24+10)/(x^3-10x^2+8x+64)
=(0-2x-14)/(x^3-10x^2+8x+64) 
=(-2x-14)/(x^3-10x^2+8x+64) or -(2x+14)/(x^3-10x^2+8x+64)
Final answer:
(x+3)/(x^2-2x-8)-(x-5)/(x^2-12x+32)=-(2x+14)/(x^3-10x^2+8x+64) 

What is a detailed analysis of the poem ''This Is My Play’s Last Scene'' by John Donne in terms of language/structure/ tone/imagery/symbols/themes?

In the opening metaphor of this sonnet, Donne imagines life as a play; as he is now approaching his "last scene," the play—the speaker's life—must soon come to an end. This is a euphemistic way to look at life and death, as too are the other metaphors Donne employs: life is variously a "pilgrimage" whose final "mile" is now nearing; a "race" which will soon be over; a "span" and a "minute" both reaching their endpoints. The large number of different metaphors all pointing to the same conclusion seem to emphasize the idea that, however we choose to look at life, it will inevitably end in the same way—with our death.
Death is depicted as "gluttonous," a human attribute suggesting that it will consume all of us. It is not clear whether it is this "face" which the speaker's "ever-waking part," his soul, fears most, or whether Donne is here referring to the devil, but the speaker vividly describes a moment between sleep and the ascension of the soul in which he expects fear to overcome him, shaking "every joint." Only when it becomes clear that his soul—personified with the "her" pronoun—is about to "take[s] flight" can he rest assured that he is escaping the devil. Note the juxtaposition of this imagery, of the soul flying upwards, with the idea of sins falling "down" to where they are "bred," in hell. There is a clear-cut duality to Donne's imagined afterlife: the soul leaves the body, and then must go either up, or down. The speaker anticipates that as his body is purged of its soul, so will he be "purg'd of evil," and ascend to heaven, leaving the realm of sin behind.

In the first few lines of the poem, which is a sonnet, Donne uses a series of metaphors to describe his death. He first compares it to "my play's last scene" and then to "my pilgrimage's last mile," the "last pace" of his "race," his "span's last inch," and "my minute's last point." He repeats the word "my" and emphasizes that death approaches for him. Some of the metaphors he uses are religious, such as "pilgrimage," while others, such as a "span" (which is the distance between two points, such as the ends of a bridge), come from the physical world. He later refers to "sleeping a space," which is also a metaphor for death. The repetition of different metaphors for death emphasizes its inevitability.
He then writes, using personification, that "ever-gluttonous death" (making death into a voracious kind of animal) will "unjoint," or take apart, his body and soul. While his body will remain on earth, his soul will fly to heaven. In this part of the poem, Donne expresses his metaphysical belief that the body is separate from the soul. While his body remains earthbound, his sins will fall into the ground, where they belong, and his body will soar to heaven, free of sin. At the end of the poem, which concludes with a couplet, Donne writes, "For thus I leave the world, the flesh, the devil." The last line includes a series of images that are very powerful, as Donne writes that he will leave the world, his body, and the Devil (a symbol for sin) behind when he ascends to heaven.

How is "La Belle Dame Sans Merci" a romantic poem?

The poem "La Belle Sans Merci" can be considered a romantic poem because of the fleeting love between the fairy lady and the knight. The poem ends tragically, with the knight losing the love of the beautiful fairy woman, but the love still existed, and the knight is sick and forlorn specifically because of his romantic feelings. The poem may be a reflection on the fleetingness of many romantic encounters and may even be a declaration of how, so often, romantic love does not last the length of one's lifetime and often ends in hurt. The knight, even in his sadness and corpse-like state, is still enthralled with the lady and is consumed by the romance that he had with her and the love he has lost.

It's important to keep in mind that Romanticism was, at its core, a reaction against the cold rationalism espoused by the Enlightenment. The Romantics emphasized ideals such as passion, emotion, and beauty. It was a spirit founded in fierce individualism.
"La Belle Dame sans Merci" is certainly a Romantic poem which looks away from Keats's contemporary age—it looks backward toward the Middle Ages and toward British folklore. It's a "fairy story" in which a knight is beguiled by a fairy maiden. Note, however, that the poem's fairy is actually a predatory force. Furthermore, note how the poem resolves: with the magic and beauty stripped away, leaving the knight wandering a deserted hillside.
There is a tension here between beauty and disorientation, and this tension is something that points toward the very heart of Romanticism. The Romantics stressed the intensity of human emotion, and in so doing, they recognized its turbulence. Keats does the same in how he embraces the darker undertones of mythology and leaves his protagonist tormented by his encounter with it.

Keats's "La Belle Dame Sans Merci" has traits both of the romantic, in the modern sense, and of the Romantic in the sense of the Romantic movement. It is romantic in that it paints a picture of the encounter between a young knight and a "full beautiful" lady who "looked at me as she did love / And made sweet moan." I assume, however, your question is really more concerned with the traits of Romanticism which pervade this poem, which served as inspiration for later literary movements, including the pre-Raphaelites, who admired its focus upon a psuedo-Arthurian past.
References to the past, often without specifics, often occur in Romantic poetry. The Romantics frequently alluded to the classical, but an aspect of dwelling in a nebulous past served to further the Romantic preoccupation with a more innocent time, untouched by industry and modern drudgery. The knight in this poem, certainly, exhibits this sort of naivety, allowing the beautiful lady to lure him with her "faery's song" into her "Elfin grot." Lulled to sleep by the lady, the knight sees a vision of "pale warriors," presumably the former victims of the fairy lady, who tell him he too is now "in thrall."
The Romantic preoccupation with nature, too, and the inspirational beauty of nature, permeates this poem. The knight is drawn into his "thrall" by the "wild" eyes of the lady in the "meads," a creature of nature. Accordingly, he decks her in a "garland" of flowers, and she finds him "honey wild, and manna dew." When the knight has been left alone on the "cold hillside" by the lady, by contrast, the natural world around him is withering: the "rose" and "lily" of the knight's own beauty are in decline, and "the sedge is withered from the lake / And no birds sing." Nature seems to reflect the knight's emotional state, an example of pathetic fallacy.
The emotional response of the knight to the faery has left him "cold" and "palely loitering." However, like the "pale kings and princes" who had gone before him, he is now seemingly left with his new wisdom to act as a new "warning" to others, an example of the poet-as-visionary trope also common to Romantic philosophy.

Actually i need some information regarding the popularity of Satire during 18th century. What were the major reasons of its popularity and who were the major satirests of that era. Thanks,

The 18th century was a period of intellectual transformation and of enlightenment. Newer ideas were emerging regarding monarchy, the social structure, and religion. The purpose of satire is to reveal the flaws in established manners and ways of living. Satire also seeks to subvert the existing order of things and especially to discredit political leaders and the ruling class.
The two most prominent satirists in English during the 18th century were Jonathan Swift and Alexander Pope. Swift's Gulliver's Travels is a satire on both the political scene in Britain and, more importantly in Book IV, mankind in general.
In the final section of Gulliver's Travels, Swift has his hero land in a world where human beings have become degraded, animal-like savages, the Yahoos, while intelligent horses, the Houyhnhnms, are the rulers. (It's interesting that the name by which the latter are known is a representation of the sound that horses typically make.) Two centuries later, this scenario was recast by the French writer Pierre Boulle in Planet of the Apes and the countless movies it spawned. By portraying humans as Yahoos, Swift is basically caricaturing the worst sides of human behavior—dirtiness, selfishness, and greed. He also is making a point about the contrast between man and the animal kingdom in the real world, showing that animals, unlike humans, are benign, that they don't make war or kill for sport, and so on.
Swift is aware that his satiric portrayal is an exaggeration, but it is nonetheless a meaningful one. When Gulliver is rescued, the most impressive thing is the kindness with which he's treated by the Portuguese ship captain, belying the totally negative view of humans Gulliver has now adopted after his stay in the realm of the Houyhnhnms and Yahoos. But the impression Swift has given of the worst side of humanity lingers in the mind of the reader.
Swift uses an even more trenchant type of satire in A Modest Proposal, in which he skewers the English attitude toward Ireland. Swift has the "author" of this work suggest, apparently in all seriousness, that the English "eat" the Irish in order to solve the economic problems of Ireland. The bigotry and cruelty toward the Irish by the ruling class in England are thus satirized by Swift's presenting them in an extreme and caricatured form, namely, as cannibals.
Alexander Pope was less focused on holding the general behavior of mankind up to ridicule than on attacking his enemies in the literary world, such as the playwright Colley Cibber. Pope, however, is best known today for The Rape of the Lock, a comparatively gentle work in which he pokes fun at the vanity of men and women in upper-class English society. It is a "mock-heroic" epic in which Pope ironically uses language borrowed from Homer and Virgil to describe trivial and silly events and actions, making his characters look even more ridiculous than they do in real life.
The most important satirist of the period in France, and perhaps in Europe as a whole, was Voltaire. In Candide, Voltaire takes on religion, something the English writers of the period didn't do, at least not so openly. Voltaire presents a parable of recent European history, depicting wars and natural disasters and using these events to ridicule the established monarchical order and the religious and philosophical thinking that could attribute all of this to the workings of a benign God and that could describe this as "the best of all possible worlds."
Both the English writers and Voltaire (and his fellow philosophes in France) saw the injustice and hypocrisy in the whole "system" by which Europe was governed at that time, and in the behavior and attitude of human beings in general. As stated, they lived in a period, later called the Enlightenment, when established ideas were openly and forcefully questioned, and when it became the goal of intellectuals to bring about a transformation in the European world, leading to the American and French revolutions. Satire was an effective method of accomplishing this goal.

How do the rationales of therapeutic approaches for treating somatoform and dissociative disorders compare and contrast?

Somatoform disorders are types of mental health problems in which patients exhibit physical symptoms that cannot fully be explained by medical conditions. Medical test results will be normal or otherwise fail to explain the symptoms. Patients with somatoform disorders will have "higher-than-average levels of anxiety and social dysfunction" (Bauer, M. et al., 2014, "Somatic Symptom Disorder," Consultant). In contrast, dissociative identity disorder (DID), which used to be called multiple personality disorder, is a type of mental health problem in which one person exhibits at least two different personalities. The different personalities will respond with different behaviors, emotions, and reactions. Patients with DID will often have memory lapses, experience losses of time, and be accused of lying. Those with DID often also have post-traumatic stress disorder. Though the two types of disorders are very different in terms of symptoms, one similarity in therapy is that both can be treated, to an extent, with drugs. Studies have shown, especially one conducted by R. Smith et al. (2006), that some drugs can effectively treat patients with somatoform disorders in combination with other therapies. Effective drugs are various types of antidepressants, including serotonin reuptake inhibitors and monoamine oxidase inhibitors ("Somatization Disorder: Top Drugs that Work," Newsmax). Similarly, antidepressants and anti-anxiety drugs can be used to effectively treat DID in combination with other therapies. But, drugs must be used very carefully because drugs can make a person feel controlled, and the feeling of control can lead a patient with DID to feel further traumatized (Dryden-Edwards, R., 2016, "Dissociative Identity Disorder"). In contrast to DID, cognitive-behavioral therapies can be used to treat somatoform disorders, whereas psychotherapy and hypnotherapy can be used to treat DID. One type of cognitive-behavioral therapy that has been used to treat somatoform disorders is mind-body relaxation. To use this method, medical practitioners teach patients relaxation techniques to alleviate symptoms. Techniques include "focused head-to-toe relaxation, abdominal (diaphragmatic) breathing, and mental imagery" (Bauer et al.). Another cognitive-behavior therapy that is effectively used to treat somatoform disorders is cognitive restructuring. Medical practitioners can use cognitive restructuring to "restructure negative thinking patterns" in order to reduce symptoms (Bauer et al.). Methods include asking patients to increase and decrease the severity of their symptoms, teaching patients distraction techniques, and reassuring patients (Bauer et al.). For patients with DID, psychotherapy can be used to help them "improve their relationships with others, preventing crises, and to experience feelings they are not comfortable with having" (Dryden-Edwards). Hypnotherapy can be used to help patients better understand their different personalities, which can in turn help them gain control of their personalities.
https://www.consultant360.com/articles/somatic-symptom-disorder-effective-techniques-diagnosing-and-managing-complex-condition

https://www.medicinenet.com/dissociative_identity_disorder/article.htm

What happened after she got bitten by a snake?

Ty's place in the desert is absolutely crawling with snakes. He tries to reassure Gemma that they're "pretty much" harmless. But bearing in mind that Ty's someone who's actually kidnapped Gemma, we can be forgiven for not trusting him. Besides, we later discover that Ty's been collecting snakes so that he can prepare anti-venom. There'd be point in doing this if the snakes weren't poisonous.
At the point in the story where Gemma gets bitten, she's come to develop an emotional attachment to Ty. She doesn't know it, but it's likely that she's experiencing a form of Stockholm Syndrome, a psychological disorder whereby someone identifies with their captor. So when Ty leaves her a note telling her that he's gone out, instead of trying to escape, Gemma goes looking for him.
That's when she gets bitten by a snake, and it happens to be a deadly poisonous one at that. Ty attempts to treat Gemma using some of the anti-venom he's been collecting, but it's no good. He has no choice but to take Gemma back to civilization, to a hospital where she can receive treatment for the snake bite. Thankfully, she pulls through. And it's at the hospital that she finally realizes the full scale of the physical and mental ordeal she's been put through by Ty.

How does the judicial branch affect me?

The judiciary is one of the three arms of the federal government in the United States. It plays the role of arbitration in both civil and criminal suits. It applies and interprets laws created or passed by the legislature. Through its application and interpretation of the law, the judiciary creates what is known as jurisprudence or precedence in handling future similar cases.
The judicial branch ensures that the law applies equally to all within a particular jurisdiction. The judiciary in certain jurisdictions has the power to review laws that are deemed inconsistent or contradictory to supreme laws, such as those of natural justice or those found in the constitution.
The judicial branch should be a matter of concern for all individuals, because it determines how cases are resolved. It also ensures that everyone is accorded justices and that individual rights are upheld by all under its jurisdiction. Thus, a strong judiciary ensures equality and fairness under the law.
https://www.whitehouse.gov/about-the-white-house/the-judicial-branch/

The judicial branch affects us in several ways. The judicial branch is the branch of our government that interprets the meaning of our laws.
The judicial branch impacts us because it protects us from laws that might violate the Constitution. When a court is asked to review a law, it must determine if the law is constitutional, meaning that it doesn’t violate the principles of the Constitution. You may be attending a school that is or was under a court order to desegregate. For many years, the courts ruled that separate but equal public facilities were legal. However, in 1954, in the Brown v Board of Education case, the Supreme Court ruled that separate but equal schools were illegal. Many schools were then ordered to desegregate.
The judicial branch also hears certain cases. You may be asked to be a juror for a court case. This is one of the responsibilities of being a citizen. The judicial branch will also determine what the punishment is for a person who broke the law. It may determine the damages a person has to pay if that person has harmed another person in some way. It may also determine if a person has to go to jail for breaking a law and for how long.
The judicial branch plays a very important role in our lives.

Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 186

A telephone company estimates that the number $N$ of phone calls made per day between two cities of populations $P_1$ and $P_2$ that are $d$ miles apart is given by the equation $\displaystyle N = \frac{2.51 P_1 P_2}{d^2}$.

Estimate the population $P_1$ given that $P_2$ is $125,000$, the number of phone calls is $2,500,000$, and the distance between the cities is $50$ mi. Round to the nearest thousand.

Solving for $P_1$,


$
\begin{equation}
\begin{aligned}

N =& \frac{2.51 P_1 P_2}{d^2}
&& \text{Given equation}
\\
\\
Nd^2 =& 2.51 P_1 P_2
&& \text{Multiply both sides by } d^2
\\
\\
\frac{Nd^2}{2.51 P_2} =& P_1
&& \text{Divide by } 2.51 P_2
\\
\\
P_1 =& \frac{(2,500,000)(50)^2}{2.51(125,000)}
&& \text{Substitute } N = 2,500,000, d = 50 \text{ and } P_2 = 125,000
\\
\\
P_1 =& 19,920.31873 \approx 20,000
&&

\end{aligned}
\end{equation}
$


The estimated population $P_1$ is $20,000$.

In Shaw's Arms and the Man, why does Bluntschli say that the bet would rob Major Petkoff?

Bluntschli says that the bet would rob Major Petkoff because Catherine is sure to be right about the whereabouts of the major's favorite coat. So, if Major Petkoff bets against both Catherine and Bluntschli, he will be sure to lose a tidy sum of money.
In Act III, everyone is relaxing after lunch, when Major Petkoff exclaims that he would be more comfortable in his old coat. His wife, Catherine, tells him that his coat is probably hanging in the blue closet, but Major Petkoff disagrees with her. He accuses his wife of being obstinate and insists that the only items in the blue closet are two of Raina's old dressing gowns, Catherine's waterproof coat, and his own mackintosh.
Unmoved by her husband's argument, Catherine calls upon their servant girl, Nicola, to fetch the major's coat from the blue closet. In the meantime, Major Petkoff proclaims that he will bet any piece of jewelry Catherine can order at the jeweler's against a week's housekeeping money that the coat isn't in the blue closet. He also calls on Bluntschli to take up the bet, but the latter refuses. Bluntschli replies that Catherine is sure to be right about the coat and he would essentially win the bet, thus "robbing" Major Petkoff of his money. In the end, of course, it is proved that Catherine is right, and Nicola is able to retrieve the major's coat from the blue closet.

Compare and contrast the Enlightenment and the Great Awakening. How did they influence the American colonies?

The Enlightenment's focus on individual rights and empirical science strongly influenced currents of political and economic development in both Europe and the American colonies. Enlightenment thinking treated the existence of both proper science and natural rights as objective facts that could be grasped by any rational person with a proper education.
The Enlightenment's focus on individualized natural rights and the power of reasoned persuasion created the conditions for the British colonists to see themselves as individuals who had the right to self-govern. The work of philosophers like John Locke and Montesquieu was particularly influential. In his Second Treatise, Locke made the case for life, liberty, and property as natural rights. He also argued that a government that did not respect citizens' natural rights could justifiably be overthrown.
The Enlightenment understanding of natural rights and the right to revolution is present in a number of colonial constitutions and treaties as well as the Declaration of Independence.
Empiricism and experimentation in all realms of physical science were also encouraged during the Enlightenment. The Enlightenment's embrace of something more akin to a modern scientific method laid the groundwork for a number of important inventions, like the cotton gin and steamboat engine, that revolutionized economic production and laid the groundwork for the American industrial revolution in the 19th century.
Historians have found that there are commonly reactions against profound political and economic changes, like the ones brought on by the Enlightenment. Most scholars believe both Great Awakenings (the first was in the 1730s and 40s and the second was in the early 19th century) were, in part, reactions to the revolutionary ideas and massive changes of the Enlightenment period.
The First Great Awakening emphasized the importance of subjective and emotional experiences. Faith and passion--which were contrary to the Enlightenment credo of rationality--were prized during these religious revivals. Preachers like George Whitefield and Jonathan Edwards gave spellbinding sermons that used highly charged rhetoric to paint pictures of ecstatic heavenly bliss or incomprehensibly terrifying damnation. (It is important to note that Edwards was also critical of some of the more excessive zealotry.)
The conflict that arose between the "New Lights," who preferred a subjective, emotional orientation in their sermons, and the "Old Lights," who used a more reason-based, analytic approach to religion, is arguably the ancestor of the current conflict between Evangelical and Mainline Protestants.
Another important thing about the First Great Awakening is that it provided some opportunities for women and slaves. The preachers of the Great Awakening took special care to reach out to slaves and promised slaves that they were equal before God (even if they weren't equal on earth). We know that the Black Christian Church was an extremely important force in the civil rights movement, which means the work that preachers like Whitefield did to convert slaves during the time of the Great Awakening had an extremely important historical impact. The Greak Awakening's focus on emotions also gave increased power and legitimacy to women, and more women were able to express themselves via literature and poetry.

Calculus of a Single Variable, Chapter 5, 5.1, Section 5.1, Problem 53

g(t)=ln(t)/t^2
Find the derivative of the function using the quotient rule.
g'(t)={t^2[1/t]-ln(t)[2t]}/t^4
g'(t)=[t-2tln(t)]/t^4
g'(t)=(t(1-2ln(t)))/t^4
g'(t)=(1-2ln(t))/t^3

The derivative of g(t) is (1-2ln(t))/t^3.

Please help me with quotes and chapters on examining the forces that keep Holden from adulthood. Thank you.

The Catcher in the Rye's Holden Caulfield is one of literature's most noteworthy young adult characters, and it is because of his inability to let go of his childhood that he remains so interesting. An important reason as to why Holden rejects entering adulthood is his utter contempt for the hypocrisy and "phoniness" of the adults he meets throughout the novel. He is easily depressed and disturbed by the actions of adults, and because of this he entirely rejects the idea of becoming one.
For example, when Holden meets with a prostitute who solicits him, he finds himself completely unable to feel any true attraction to her. Holden narrates,

I know you're supposed to feel pretty sexy when somebody gets up and pulls their dress over their head, but I didn't. Sexy was about the last thing I was feeling. I felt much more depressed than sexy (95).

He rejects her sexual advances out of empathy. He sees her as a child, like he sees himself, and feels wholly wrong about the whole ordeal. He rejects the adult act of sex, and he refuses to see the prostitute as an object of desire. Instead, he sees her as a peer. Later, Holden is made uncomfortable by the sexual advances of an older man who happens to be his former teacher Mr. Antolini. Holden is embarassed and disturbed by the man's advances and further rejects the sexuality of adults.
Part of the reason Holden seems to reject adulthood is a fondness he has for children, particularly his deceased younger brother Allie and his younger sister Pheobe. This is best expressed in the fantasy Holden reveals near the end from which the novel gets its name,

I keep picturing all these little kids playing some game in the big field of rye . . . I'm standing at the edge of some crazy cliff. What I have to do, I have to catch everybody if they start to go over the cliff (173).

Holden's fantasy serves as a metaphor for protecting children—including himself—from the cruel world of adults, perversion, corruption, and violence. He rejects his adulthood while cherishing the childhood of others. He is ultimately stuck between the two worlds.
At several points in the novel, Holden appears to be dedicated to the idea of becoming an adult and rejecting the standard childhood. When he meets with an old fling, Sally, he suggests they get married in act of mania. Once she rejects this proposal, he once again becomes completely disillusioned with the idea: "I don't even know why I started all that stuff with her . . . I probably wouldn't've taken her even if she wanted to go with me" (134).

What does our legislative branch of government do?

The legislative branch of government in the United States is made up of the House of Representatives and Senate, which together make up the U.S. Congress. The Congress passes legislation in a process that involves the introduction of a bill in either house and the referral of the bill to the subcommittee or committee that handles that area (for example, there are committees related to the budget, agriculture, education, and other areas). Then, the bill is amended and, if the committee votes for it, the bill is sent to the floor of the House or Senate for debate. If both houses of the Congress pass the bill, it is sent to the President, who can either sign it or veto it (if the President vetoes it, the bill can still be passed with a two-thirds majority of the members of Congress).
In addition to creating bills and passing laws, the Congress has the right to declare war. The House has specific powers, such as originating revenue bills and impeaching the President and other federal officials. The Senate has the right to confirm or reject some Presidential appointees, such as Supreme Court justices, and the Senate also tries federal officials, including the President, who have been impeached by the House. The Senate must also approve treaties related to foreign trade. The Congress also has powers of oversight over governmental operations. For example, there is a House Committee on Oversight and Government Affairs to perform checks on governmental operations. 
https://www.whitehouse.gov/about-the-white-house/the-legislative-branch/

Which of the two do you think made the most significant contribution to the ancient world, Greek philosophy or Roman law?

While both historical events have strongly influenced modern thinking, Greek philosophy (more specifically Athenian democracy), beginning with Socrates, then building to Plato’s philosophy, and growing through Aristotle (especially The Poetics) to the military and political accomplishments of Alexander the Great, seem to be the most lasting influences on modern Western thought.  While Roman law was a model for many subsequent legal structures, there have been numerous alterations to the structure of modern legal systems, including influences by other cultures, notably Oriental ideas.  When we use logic, we are employing thinking tools originally designed by the Greek philosopher Socrates more than 2000 years ago; when we divide, discuss, or critique literature, we are using both the definitions and the vocabulary of Aristotle; when we try to imagine the duality of reality and imagination, we are going back to Plato’s allegory of the cave.

How are the city and jungle ethically dependent on one another in Lost City Radio?

In Lost City Radio, people from the jungle stream into the city to find news of their loved ones, so the city functions as a kind of holding pen and relocation center. The jungle is dependent on the city, and particularly on Norma's radio show, to find their loved ones. Alarcon writes:

"Every Sunday night, for an hour, since the last year of the war, Norma took calls from people who imagined she had special powers, that she was mantic and all-seeing, able to pluck the lost, estranged, and missing from the moldering city" (page 9). 

The city, and Norma in particular, function as the nerve center of the country. People regard Norma almost as a god, and they think she is able to see everything and find their loved ones. In the passage above, Norma is represented as an omniscient figure who can find anyone in the vast metropolis. The city represents the hope of the rest of the country. People from the jungle, such as the residents of Victor's town (1797), send people to the city in search of a better life. They write to Norma, "We want a better life for Victor. There is no future for him here." (page 5)
The jungle functions as the heart of the city. Refugees pour their hearts out to Norma. Alarcon writes about the refugees from the jungle:

"They'd dance and drink and sing into the early hours of the morning. Norma greeted them all as they lined up to thank her. They were humble people. Tears would well up in their eyes when they met her--not when they saw her, but when she spoke: that voice" (page 10).

The city depends on the hearts and souls and bodies of the vast numbers of refugees from the jungle to populate it and to give it life and heart. The jungle represents the people who worship Norma and her voice as if she were a god. They are filled with humility and gratitude, and they symbolize the heart and soul of the country. The city is dependent on the jungle for its heart.

My research paper talks about the downsides of love, and argues how it is a source of suffering. I am using British literature, specifically Shakespeare's King Lear, to support my argument. How does love cause conflict in Lear's life?

The entire conflict in King Lear is set off by Lear giving his daughters a test of love, and assuming that their eloquence in describing their love for him matches the affection that they actually feel for him.
Lear is aging, and he attempts to avoid conflict after his death by publicly declaring how he will divide up his kingdom. He has three daughters, and he tells them:

Tell me, mydaughters—Since now we will divest us both of rule,Interest of territory, cares of state—Which of you shall we say doth love us most,That we our largest bounty may extendWhere nature doth with merit challenge (1.1.52-57).


Essentially, Lear has said that he will give the biggest portion of his kingdom to the daughter who loves him most, and is therefore most deserving of this gift. Lear asks his daughters to describe their love for him, and he will decide who gets the biggest piece of the kingdom after hearing what they have to say.

His first daughter, Goneril, gives a hyperbolic description of her love, saying that she loves him


more than word can wield thematter,Dearer than eyesight, space, and liberty,Beyond what can be valued, rich or rare,No less than life, with grace, health, beauty, honor;As much as child e’er loved, or father found;A love that makes breath poor, and speech unable.Beyond all manner of so much I love you (1.1.60-67).


His second daughter, Regan, is equally ridiculous, saying,



I professMyself an enemy to all other joysWhich the most precious square of sensepossesses,And find I am alone felicitateIn your dear Highness’ love (1.1.79-84).


Lear's third daughter, Cordelia, however, only says

I love your Majesty / According to my bond, no more nor less (1.1.101-102).



Cordelia says that she loves Lear as much as she owes him, because he is her father. Lear is outraged and thinks that Cordelia is cold and unfeeling, but only Cordelia has spoken the truth about her feelings.

Lear divides up his kingdom based on the flattery of his first two daughters, but their affection is not true. Neither one of them truly loves him but only cares about herself. Goneril and Regan spend the rest of the play belittling Lear and destroying his kingdom in a series of escalating conflicts. Cordelia was the only one who actually had true affection for her father, and she loved him as a daughter should. However, Lear confuses flattery and words with real love, and by the time he recognizes this it is too late. Cordelia is killed in the string of events that follow from the division of the kingdom, and Lear dies of grief.
https://www.folgerdigitaltexts.org/html/Lr.html

Can anyone provide a critical analysis of the short story "The Taste of Watermelon" by Borden Deal?

Mississippi writer Borden Deal’s “The Taste of Watermelon” (1979) can be critically analyzed as a meditation on ideas about manhood, guilt, and the power of empathy. The sixteen-year-old narrator, new to a watermelon-growing countryside town, is eager to fit in with his new group of friends and is also navigating the transition between boyhood and manhood. He and his friends have a crush on his neighbor Willadeen, a classmate who has begun to “walk differently” over the course of one season. But asking Willadeen out on a date is daunting, because her father is mustached Mr Wills, the most feared farmer in their town, rumored to guard both his daughter and his outstanding watermelon crop with a gun filled with buckshot.
For the narrator, Mr. Wills begin to symbolize a potent masculine power to which he does not have access. Keeper of ripe watermelons and a beautiful daughter, Mr. Wills represents the manhood that still evades the narrator. Thus, the image of Mr Wills holding the gun—another symbol of masculine power—begins to haunt the narrator. He needs to emasculate Mr. Wills to prove his own manhood to himself and his peers. Thus, he steals Mr. Wills’ biggest melon—the seed melon from which he hopes to grow next year’s crop—in plain sight on a night of the full moon.
Though the narrator fulfills the promise of his bravado by stealing, eating, and then wrecking the watermelon, the action does not bring him or his friends a sense of triumph or peace. Thus, Deal suggests that the narrator’s notions about masculinity are misguided and that there is more to being a man than simply stealing power. As Mr. Wills lets out a primal scream of rage and frustration when he discovers the theft, the narrator feels paralyzed by guilt. In a paroxysm of grief, Mr. Wills starts to destroy his watermelon patch, revealing to the narrator and his father that the reason he prized the giant watermelon was that he hoped to feed it to his ailing wife, who loves the taste of the fruit. Shaken by the realization that Mr. Wills is no ogre, but a complex human being like him, the narrator is at a moment of crisis.
Empathy and redefined masculinity come to the narrator’s rescue. Embodying the notion of honor and a deeper bravery, he collects the seeds from the watermelon’s wreckage and brings them to Mr. Wills, admitting his crime. Though Mr. Wills is angry that seeds for next year will not bring back this season’s crop, he forgives the narrator, thus uniting the story’s themes of true masculinity, empathy, and redemption. However, through the story questions certain notions of masculine power, it preserves others. Willadean, whose name itself is a derivative of her father’s, has little agency in the story, and Mr. Wills expresses explicit disappointment that he does not have a son to manage his large farm. Though the feel-good end vindicates notions of goodness and honor, the sphere of their practice largely includes only men.

"The Taste of Watermelon" is a coming-of-age story about a sixteen year-old-boy who goes a long way in maturing from a boy to a man in the course of one evening in which he steals a watermelon.
The narrator is a newcomer to a farming town. Watermelon stealing is a time-honored activity for teenage boys and is not even really considered stealing. The narrator and his two friends look longing at a giant watermelon, the biggest ever seen growing in the middle of Mr. Wills's watermelon patch, and at Mr. Wills's desirable daughter, Willadean. Because Mr. Wills is so fierce and mean, however, they are afraid to approach either of these desired objects. Mr. Wills is especially protective of his watermelon, guarding it at night with his shotgun.
Nevertheless, the narrator decides impulsively one night to steal the melon. He does so successfully, even though it had seemed to be the impossible task. He and his two friends feast on what they can of the delicious melon, but, as narrator says, the sense of glee is short lived. It turns into depression after they destroy what's left of the fruit. The narrator notes:

I did not feel triumph or victory, as I had expected

Shortly thereafter, Mr. Wills realizes his prize melon is stolen and destroys the rest of his melon patch in rage. He also cries over the loss of his melon. He had hoped it would provide seed for a great patch of giant melons.
The narrator had not anticipated Mr. Wills's grief. A teenaged boy, he had not thought through the consequences of stealing the melon. He had lived carelessly in the moment and now regrets what he had done.
As he experiences remorse, the narrator gathers up all the seeds from the watermelon he can find. With his father, he courageously goes and confesses his crime, handing the seeds to Mr. Wills. When Mr. Wills speaks of his regrets, the narrator says:

The seeds are next year.

The theme of the story is maturity. After stealing the watermelon, the narrator both realizes, and more importantly, takes responsibility for what he has done. He has the courage to confess his crime, and the wisdom to realize that bad decisions can be remedied. It's significant that the narrator repeats twice that the seeds are "next year," and offers to help Mr. Wills plant them. The narrator will right the wrong he has done.
In the course of the story, the narrator learns that its not as much fun as he thought to steal someone else's prized possession. The victory he wins is not in the successful theft, though it did take courage to steal a watermelon guarded by a fierce man with gun, which had been said to be loaded with real buckshot, not salt. The real victory comes with the realization that he hurt another person and with having the strength of character to make amends.
As he matures, the narrator also realizes that Mr. Wills is not the fearsome bogyman he once thought, a one-dimensional monster, but a compassionate, caring human being with feelings.
The story is saying that what we do matters and that how we face up to consequences of our actions matters. In the end, the narrator is rewarded with the lovely Willadean, who he has won over not through stealing, but through having the maturity to face up to his actions.
The story is idealized. The narrator is a good and sympathetic person through and through who makes a boyish mistake in high spirits. He then does the right thing. Mr. Wills also turns out to be a good person who appreciates what the narrator has done and sees his worth. The narrator has a supportive father. Willadean also likes the narrator. In really life, the consequences might not work out so neatly or so well, but it is yet heartwarming to witness this successful outcome.

In what way does Joseph Conrad criticize European civilizing missions? How does he address the encounters between African and European peoples?

Look at what Conrad has to say about the various European empires and their role in Africa. Toward the beginning of Heart of Darkness, Conrad discusses the Roman Empire in Britain and then makes some comparisons between how the Romans governed Britain and the rest of Europe, and how the British are doing it today. Pay attention to what Marlowe has to say about the conduct of each of the individual powers, and the nature of an empire based on greed versus one that claims to be doing good in the world.
There are also specific actions in the book which are useful to consider as regards the civilizing mission of the Europeans. Consider the battleship that Marlowe mentions at one point as he heads into the Congo. What is it doing? And based on what it's doing, what can be said about what the Europeans are doing there?
Consider the character of Kurtz. What were Kurtz's intentions in coming to the Congo, and what has been the end result in the story? What's the effect of the European commercial presence in the Congo?
As you consider the interactions between Africans and Europeans, there are a few ways to address this question. How are Africans present in the story? What kind of characters are they? And how are they treated or described by the various European characters, including Marlowe?

How should I go about an essay on the topic "Choose a character you identify with from either The Hunger Games or Catching Fire and explain how you relate to the character"?

It is hard for me to get too specific on this topic since I do not know which character you identify with, but I can give you some general advice. First, to choose a character you identify with, you need to identify a character that means something to you personally. This could be someone that seems to be like you, or someone you admire. For example, you might admire Katniss’s frankness and courage. You might admire Peeta’s loyalty and skill. Either way, the choice of a character is the first step.
The second step is to find a series of reasons why you identify with this character. It is an essay, so you should list three reasons why you identify with whichever character you choose. For each reason, you need to choose a supporting quote and then explain how the quote is relevant to your point.
Let’s say you choose Katniss as the character you admire because she is brave, loyal and intelligent. One of the examples you could give is her famous act of choosing to volunteer as tribute in her sister’s place for the Hunger Games.

I don’t need to shove through the crowd. The other kids make way immediately allowing me a straight path to the stage. I reach her just as she is about to mount the steps. With one sweep of my arm, I push her behind me.
“I volunteer!” I gasp. “I volunteer as tribute!” (Ch. 2)

This quote could be used to describe Katniss’s commitment to her family, her bravery, or her strength of character. You could explain how she is selfless and refused to allow her sister to go into the Hunger Games, choosing to risk her own life instead.

Calculus of a Single Variable, Chapter 8, 8.5, Section 8.5, Problem 20

int x/(16x^4-1)dx
To solve using partial fraction method, the denominator of the integrand should be factored.
x/(16x^4-1)=x/((2x-1)(2x+1)(4x^2+1))
Take note that if the factors in the denominator are linear, each factor has a partial fraction in the form A/(ax+b) .
If the factors are in quadratic form, each factor has a partial fraction in the form (Ax+B)/(ax^2+bx+c) .
So expressing the integrand as sum of fractions, it becomes:
x/((2x-1)(2x+1)(4x^2+1))=A/(2x-1)+B/(2x+1)+(Cx+D)/(4x^2+1)
To determine the values of A, B, C and D, multiply both sides by the LCD of the fractions present.
(2x-1)(2x+1)(4x^2+1)*x/((2x-1)(2x+1)(4x^2+1))=(A/(2x-1)+B/(2x+1)+(Cx+D)/(4x^2+1)) *(2x-1)(2x+1)(4x^2+1)
x= A(2x+1)(4x^2+1) + B(2x-1)(4x^2+1)+ (Cx+D)(2x-1)(2x+1)
Then, assign values to x in which either 2x-1, 2x+1, or4x^2+1 will become zero.
So plug-in x=1/2 to get the value of A.
1/2=A(2(1/2)+1)(4(1/2)^2+1)+B(2(1/2)-1)(4(1/2)^2 + 1) + (C(1/2)+D)(2(1/2)-1)(2(1/2)+1)
1/2=A(4) + B(0)+(C(1/2)+D)(0)
1/2=4A
1/8=A
Plug-in x=-1/2 to get the value of B.
-1/2=A(2(-1/2)+1)(4(-1/2)^2+1) + B(2(-1/2)-1)(4(-1/2)^2+1) + (C(-1/2)+D)(2(-1/2)-1)(2(-1/2)+1)
-1/2=A(0)+B(-4) +(C(-1/2)+D)(0)
-1/2=-4B
1/8=B
To solve for D, plug-in the values of A and B. Also, plug-in x=0.
0=1/8(2(0)+1)(4(0)^2+1) + 1/8(2(0)-1)(4(0)^2+1) + (C(0)+D)(2(0)-1)(2(0)+1)
0=1/8 - 1/8 -D
0=D
To solve for C, plug-in the values of A, B and D. Also, assign any value to x. Let it be x=1.
1=1/8(2(1)+1)(4(1)^2+1) +1/8(2(1) -1)(4(1)^2+1) + (C(1) + 0)(2(1) -1)(2(1)+1)
1=15/8+5/8+C(3)
1=10/4+3C
-3/2=3C
-1/2=C
So the partial fraction decomposition of the integrand is:
int x/(16x^4-1)dx
=int(x/((2x-1)(2x+1)(4x^2+1)))dx
=int (1/(8(2x-1)) + 1/(8(2x+1)) - x/(2(4x^2+1)) )dx
Then, express it as three integrals.
=int 1/(8(2x-1))dx + int 1/(8(2x+1))dx - int x/(2(4x^2+1)) dx
=1/8int 1/(2x-1)dx + 1/8int 1/(2x+1)dx - 1/2int x/(4x^2+1) dx
To take the integral of each, apply substitution method.
For the first integral, let the substitution be:

u=2x-1
du=2dx
(du)/2=dx

For the second integral, let the substitution be:

v = 2x+1
dv=2dx
(dv)/2=dx

And for the third integral, let the substitution be:

w=4x^2+1
dw=8xdx
(dw)/8=xdx

So the three integrals become:
= 1/8 int 1/u * (du)/2 + 1/8 int 1/v *(dv)/2 -1/2 int 1/w * (dw)/8
=1/16 int 1/u du + 1/16 int 1/v dv - 1/16 int 1/w dx
Then, apply the formula int 1/x dx = ln|x| + C .
=1/16 ln|u| + 1/16 ln|v| - 1/16ln|w|+C
And substitute back u = 2x - 1 , v = 2x + 1 and w = 4x^2+1 .
= 1/16ln|2x-1| + 1/16ln|2x+1| -1/16|ln4x^2+1|+C

Therefore, int x/(16x^4-1)dx=1/16ln|2x-1| + 1/16ln|2x+1| -1/16|ln4x^2+1|+C .

Iago is constantly talking about women in derogatory ways, from his joking assessment of women for the amusement of Desdemona in the second act, to his put-downs of Emilia, to his assumption that Desdemona will probably cheat on Othello eventually. Does the play support Iago's opinion of women or refute it?

Shakespeare allows Iago, as the villain, considerable license to say things about respectable women that Elizabethan audiences would have understood as indicative of his disturbed personality.
This is most evident in his condemnation of Desdemona. The relevant information to convey that he is framing her is put right in front of the audience, both in his words and in his talking with Emilia about the handkerchief. Desdemona herself is almost unbelievably perfect, an icon of virtue. There is no ambiguity--to the audience--about her fidelity. That is part of what makes it a tragedy. We know Othello is wrong but we cannot open his eyes.
The question of whether Othello's reaction would be wrong if she had cheated on him is another matter. Iago's fantasy that Emilia was unfaithful is likewise presented as one reason he has become unhinged.
Whether or not these two women were faithful, they still end up dead from domestic violence. It may be that Shakespeare's public would have condoned husbands' violent retribution for adultery, but that is not the situation he presents here.

The play strongly refutes Iago's negative assessment of women as untrustworthy. First, Desdemona is always loyal to Othello and never cheats on him. It's tragic that Othello is manipulated into believing such a good woman has betrayed him.
Second, Bianca shows her feelings for Cassio when she cries at seeing him wounded. Bianca feels compassion for Cassio, while Iago kills him cold-bloodedly.
Finally, Emilia only turns on Iago when she realizes that he has caused Desdemona's death, at which point Iago literally stabs her in the back. However, Emilia has shown her mettle in speaking the truth. She has shown herself loyal to truth and to Desdemona. As she lays dying, she tells Othello that that Desdemona was always faithful to him. All of these are the acts of a courageous woman of character.
Looking at the women in the play, it is clear that Iago projects his own twisted desire to betray and hurt others onto them: it is not women who have a problem but Iago. Shakespeare, who so often sees through misogyny, clearly shows in this play that the women are not at fault, no matter how Iago tries to slander them.

The word explicit means "clearly stated." In "The Cask of Amontillado," does Montresor make his plans explicit to Fortunato as they descend into the vaults? Explain, using the word explicit in your answer

At no time does Montresor explicitly describe his plans to avenge Fortunato by chaining him to the back wall of his family's extensive vaults, building a wall around his enemy, and essentially burying Fortunato alive. At the beginning of the short story, Montresor does not even explicitly state the reason he wants revenge on Fortunato, leaving it up to the reader to interpret the "thousand injuries" and what Fortunato did to offend him. However, Montresor does explicitly inform the reader that he will punish his enemy with impunity and mentions that he carefully disguised his true feelings in Fortunato's presence in order to earn his trust. Poe understood that Montresor's plans of burying Fortunato were horrific and shocking, which is why he purposely omits the explicit details of Montresor's crime. Poe also builds suspense by omitting explicit details as the reader wonders how Montresor will enact his revenge. However, Poe does foreshadow that Montresor will build a wall around Fortunato and bury him alive when Montresor tells his enemy that he is also a "mason" and produces a trowel from his cloak. Overall, Montresor's plans for revenge are purposely vague as Poe builds suspense for the terrifying end of the short story.

No, Montresor does not make his plans for Fortunato totally explicit before they descend into his family's vaults.  He plans, of course, to murder Fortunato by walling him up alive near the bodies of Montresor's ancestors, and he never clearly states his intention to Fortunato.  He lies about the cask of Amontillado, the uncommon Spanish sherry wine, saying that he's anxious to get a true connoisseur's opinion on his recent purchase.  He is honest, on the other hand, about the niter in the vaults, and he warns Fortunato about the effect this will have on him and his terrible cough.  He is honest, as well, about his family's motto, Latin words which translate to "You will not harm me with impunity."  Thus, Montresor does, in many ways, give Fortunato some warning that he should not accompany him into the vaults, that Montresor might have some score to settle and that it could be dangerous for Fortunato.  However, he knows that Fortunato's pride will not permit him to remain above when a chance to embarrass Montresor lies below.

How has the relationship between Islam and other faiths changed through the centuries, and why has this change occurred?

First, we should note that Islam is not monolithic. There are various branches of Islam, and various individual imams or religious leaders and scholars who set forth different opinions about matters of faith and interpretation of the Koran, leading to varying attitudes about other faiths.
The Koran itself distinguishes between the "peoples of the book," or the Abrahamic religions, and other religious faiths, which are considered forms of idolatry. Islam shares a common core of faith with Judaism and Christianity, accepting that the sacred texts and prophets of the other Abrahamic religions represent genuine revelations of Allah, although incomplete, while Mohammed provides a later and more comprehensive revelation; in certain ways, Islam regards Christianity and Judaism the way Christianity sees Judaism. The Zoroastrians were often grouped among the peoples of the book.
In the medieval period, Jews, Christians, and people of certain other faiths were allowed a considerable degree of freedom within Islamic territories, including freedom of worship. In the sixth through twelfth centuries, Baghdad was a refuge for Platonists, Jews, and Christian "heretics" fleeing persecution. As Islam became more legalistic after the twelfth century, in many areas this degree of openness diminished or disappeared.
In more recent times, the Ahmadiyya branch of Islam emphasizes its continuity with other religions of the book, and the Alawites are syncretistic, adopting some Christian traditions. Sufis and Malaysian Muslims are traditionally more open to other religions and accepting of religious diversity than Sunni Salafists.

What are some elements of a dystopian society present in "The Pedestrian"?

One characteristic of a dystopian society is that citizens are thought to be under constant surveillance by a governing force. On the night when Leonard Mead is captured, his solitary walk is observed and noted as suspicious behavior by the police, at a time when only one police car is thought to remain. Leonard's "crime" is considered threatening enough to allocate the primary peacekeeping resources to remove him from the city. The police car also operates solely on technology, down to its "metallic voice." This is another characteristic of dystopian literature: technology seems to overtake humanity in some form and is left to reign over mankind, even making decisions regarding the lives of the citizens.
Another characteristic of dystopian literature is the portrayal of humans living in a dehumanized state. In this story, Leonard notes the very absence of humanity in the world around him. People are sequestered in their houses, focused on the entertainment that their televisions can bring them. Leonard reflects,

In ten years of walking by night or day, for thousands of miles, he had never met another person walking, not once in all that time.

In his society, people have lost the ability to interact with the natural world and, therefore, with each other. This is reflected in the metaphorical way the author links the technology of the daytime to natural images:

He came to a cloverleaf intersection which stood silent where two main highways crossed the town. During the day it was a thunderous surge of cars, the gas stations open, a great insect rustling and a ceaseless jockeying for position as the scarab-beetles, a faint incense puttering from their exhausts, skimmed homeward to the far directions. But now these highways, too, were like streams in a dry season.

The images of nature here are reflective of death and dying: ceaseless, faint, skimmed, dry, silent, thunderous. As humanity has retreated more and more into technology to sustain itself, it has sacrificed life-giving connections.
A final characteristic of dystopian literature is a feeling that conformity is the ultimate goal. In this story, Leonard is seen as standing in direct opposition to the expectation of conformity through this solitary walk around the city. The police voice questions him three times in a row about "walking" when he is stopped and then comes back to question it again. When Leonard confesses that he has no "viewing screen" at home, the police voice stands in silent accusation. Leonard is seen as making individual choices, and that is simply not an option in his society.
In their quests to create a perfect utopia, these societies have actually created innately flawed dystopias, which is the ultimate point Bradbury creates through his various works of dystopian fiction. The freedom of individuality allows for flaws in societies, but the only other option is to remove individuality from society completely—and that presents an even more dire reflection of humanity.

The Merriam-Webster dictionary gives the following definition for "dystopia."  

An imaginary place where people lead dehumanized and often fearful lives.

That definition is fairly narrow in my opinion and does not nearly encompass many of the dystopian novels that exist today.  Take The Giver as an example.  Most literary scholars would certainly classify that society as dystopian; however, the characters in the novel do not lead fearful lives.  They cannot.  That emotion has been eliminated.  
"The Pedestrian" is similar.  The people that are in their homes watching TV are not being forced their by government, nor are they acting out of fear for their lives, and I do not think the story strongly supports the idea of a dehumanized population; therefore, I think we should expand our working definition of "dystopia" to include a few more characteristics.  Let us use the following characteristics of a dystopian society in order to analyze "The Pedestrian."
Propaganda is used to control the citizens of society.
Information, independent thought, and freedom are restricted.
A figurehead or concept is worshiped by the citizens of the society.
Citizens are perceived to be under constant surveillance.
Citizens have a fear of the outside world.
Citizens live in a dehumanized state.
The natural world is banished and distrusted.
Citizens conform to uniform expectations. Individuality and dissent are bad.
The society is an illusion of a perfect Utopian world.
From that list of characteristics, readers can see that "The Pedestrian" fits several quite well.  I definitely see elements of the third criterion in the story.  While there is not a particular person that is being worshiped, it is clear that the general population worships and reveres their "viewing screens."  Nobody comes outside anymore.  Socialization in person just does not happen.  I believe that Leonard's society worships entertainment and that worship functions as a form of control. 

"What is it now?" he asked the houses, noticing his wrist watch. "Eight-thirty P.M.? Time for a dozen assorted murders? A quiz? A revue? A comedian falling off the stage?"

Elements of the fifth criterion are also seen in the story.  Leonard seems to be the only person that goes outside anymore. We are told that he is practically alone in the world.  It appears that people never leave their homes. 

He was alone in this world of A.D. 2053, or as good as alone.

Perhaps the people are simply that addicted to entertainment, or they are fearful of leaving their homes.  We are not told this explicitly, but to the people of 2053, the outside world does not offer anything good. The seventh characteristic  would apply here as well.  Leonard is the only person left that seems to consider time outside beneficial. He is such an anomaly in this regard that he is picked up by a police car and taken to a mental hospital. This is also characteristic eight.  Leonard is punished for being an individual.  He is not breaking any law; however, he is acting so far outside of the norm that he is not allowed to continue walking around his neighborhood.  He is taken to a psychiatric center presumably to be studied and fixed.
http://www.readwritethink.org/files/resources/lesson_images/lesson926/DefinitionCharacteristics.pdf

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 22

Make a table of values and sketch the graph of the equation $y = 9 - x^2$. Find the $x$ and $y$ intercepts.

$ \begin{array}{|c|c|}
\hline\\
\text{Let } x & y = 9 - x^2 \\
\hline\\
-3 & 0 \\
\hline\\
-2 & 5 \\
\hline\\
-1 & 8 \\
\hline\\
1 & 8 \\
\hline\\
2 & 5 \\
\hline\\
3 & 0\\
\hline
\end{array} $

To solve for $x$ intercept, we set $y = 0$


$
\begin{equation}
\begin{aligned}

0 =& 9 - x^2
\\
\\
x^2 =& 9
\\
\\
x =& \pm \sqrt{9} = \pm 3

\end{aligned}
\end{equation}
$


Thus, the $x$ intercept is at $(-3,0)$ and $(3, 0)$


$
\begin{equation}
\begin{aligned}

y =& 9 - 0^2
\\
\\
y =& 9

\end{aligned}
\end{equation}
$


Thus, the $y$ intercept is at $(0, 9)$

What is the purpose of satire in "A Modest Proposal”?

The purpose of Swift's "Modest Proposal" is, first, to expose people's attitudes (particularly those in power) toward the poverty in Ireland and, second, for the author to give his own opinion on the situation.
Swift does this by combining realism with irony, absurdity, and parody. Swift writes the essay in the authoritative tone of an educated person using a structured, seemingly reasonable argument.

I shall now therefore humbly, propose my own thought, which I hope will not be liable to the least objection.

He also backs it up with the use of statistics.

The number of souls in this kingdom being reckoned one million and a half. Of these I calculate there may be about two thousand couples whose wives are breeders, from which number I subtract thirty thousand couples . . .

Most readers are taken in by his argument—up to the point where he starts talking about selling babies for meat. The essay then becomes an exercise in absurdity, but by then, Swift has already made one of his strongest points: just how easily a person in authority can fool the public into participating in something that is actually quite horrific. Yes, at some point the public will realize the authorities have duped them, but by then, it may be too late.

The purpose of the satire in Swift's "A Modest Proposal" is to draw attention to the plight of the poor Irish in 1729 and, by doing so, hopefully improve their lot and change the way the English treat them.  The narrator suggests a plan for the impoverished Irish to sell their one-year-old babies to the wealthy English as a new food source; this would give them a renewable source of income and reduce the number of beggars on the streets. 
To be clear, Swift does not actually want anyone to sell or eat babies.  He does not agree with his narrator. In Swift's time, the English had bought up most of the land in Ireland and had raised rents on their tenant farmers to the point that, although they could afford to pay the rent, they could not purchase any food or means of heat.  They had to beg for their subsistence.  Through his repugnant narrator, Swift suggests that, since the English are already figuratively devouring the Irish—they get fatter, it seems, while the Irish get leaner and leaner—it is not that much of a leap to suggest that the English actually devour the Irish.  

Why does Pegeen refer to Christy as the only playboy of the western world?

First of all, let us define the meaning of the word "playboy" in this context. In contemporary terms, a playboy is a wealthy and privileged man who spends time enjoying life, and he is often sexually promiscuous. Certainly, this definition has relevance in the play; Christy slowly fosters a reputation for daring, and, as a result, becomes a sexualized figure that seems to be pursued romantically by many of the local women. However, that more modern definition of playboy is not completely adequate for us here. Rather, we might think that Pegeen calls Christy a playboy because he becomes an almost mythic figure, a narrative construct who, by perpetuating a fiction of patricide, is seen as a legendary hero by other Irish peasants. Thus, Christy is a playboy in that he can "play" the role of the mythic hero, the hero who accomplishes great tasks, such as toppling a patriarchal tyrant, and who can win any athletic game in which he participates (playboy here especially seems to suggest Christy's new dominance in all kinds of sports). The term is still ambiguous even with this definition, but I think that this ambiguity is part of the reason the play's popularity has endured.
Additionally, I think that we can safely say that "the western world" refers to the west of Ireland, where the play ostensibly takes place.

Calculus of a Single Variable, Chapter 8, 8.7, Section 8.7, Problem 12

Given to solve,
lim_(x->-2) (x^2-3x+10)/(x+2)
as x->-2 then the (x^2-3x+10)/(x+2) =0/0 form
so upon applying the L 'Hopital rule we get the solution as follows,
as for the general equation it is as follows
lim_(x->a) f(x)/g(x) is = 0/0 or (+-oo)/(+-oo) then by using the L'Hopital Rule we get the solution with the below form.
lim_(x->a) (f'(x))/(g'(x))

so , now evaluating
lim_(x->-2) (x^2-3x+10)/(x+2)
=lim_(x->-2) ((x^2-3x+10)')/((x+2)')
=lim_(x->-2) (2x-3)/(1)
now plugging the value of x= -2 then we get
= (2(-2)-3)
= -7

I've never written a critical essay around a poem before and I now need to write one using the poem "One Art" by Elizabeth Bishop. I'm having a tremendous amount of difficulty coming up with a thesis statement. I'm wondering if it's possible to create a thesis statement around the literary pun that Bishop uses in the suggestion that not only is dealing with loss an art but seemingly disastrous losses can be dealt with through art. Beyond that, I'm drawing a blank on a thesis for this critical essay. Any guidance would be greatly appreciated.

The idea you have chosen would make an excellent basis for a thesis statement on this poem. Here are three possible ways you could phrase a thesis statement for a critical essay encompassing the main ideas from the poem and the complex relationship between art and loss:

In the poem "One Art," Elizabeth Bishop uses puns to express the duality of the relationship between loss and art, in which loss is a form of art and art is a form of dealing with loss.
Loss affects everyone, but it is up to the individual to handle it in a way that is artistic and meaningful or to allow it to become a "disaster."
The art of losing is not difficult to master, but the outcome is determined both by the nature of the loss and the way you cope with it.

Elizabeth Bishop is known for her use of puns in the Portuguese language, and the title "One Art" is a pun in and of itself. This pun supports the dual themes Bishop establishes throughout this piece, so it would make a strong topic for an essay. In order to create a solid thesis statement around the pun in the title, here are some important things to consider about the poem:
"One Art" Linguistics and Background
In the Portuguese language, the same word is used as both an article and to denote the number "one." A literal translation of the title in Bishop's native tongue would be "Uma Arte." Due to the gender conventions of Portuguese, uma is the female version of one and um is the male version. In one sense, the title could mean one form or type of art, while in another it could be taken as meaning "it's for you." In this sense, the title is both a reflection of Bishop's call to use art as a means to grieve loss and likely a dedication to her deceased lover.
The lover Bishop is probably referring to is Lota de Macedo Soares, a famous Brazilian architect who was a member of a well-known political family in Rio de Janeiro. Lota and Bishop were together from 1951 to 1967, and much of Bishop's work is dedicated to her. Lota committed suicide in 1967, a tragedy which inspired Bishop to tackle the theme of loss in her work. Understanding the basis of this poem helps us understand the two-pronged and often contradictory approach Bishop takes to describe loss.
Possible Thesis Statements
Using an understanding of the mechanics and background of this poem, it is possible to derive the previous thesis statements I gave earlier from the title. An essay focusing on Bishop's belief that loss is an art while art can be used to navigate loss could expound on the final stanza of the poem:

Even losing you (the joking voice, a gesture
I love) I shan't have lied. It's evident 
the art of losing's not too hard to master 
though it may look like (Write it!) like disaster. 

While brief, this part of the work gives plenty to build off of for a critical essay and it has a strong connection to the title. Throughout most of the poem, Bishop presents loss as something that comes easily and naturally to most people. From losing trivial items like keys to losing an entire continent, likely a reference to Bishop leaving Brazil, the poet considers herself something of an expert at loss. It is in the last stanza that she draws a distinction between the "art" of losing, or the experience of loss we are all destined to have, and the reality of coping with loss. Here Bishop makes the subtle shift from the loss of things and places to the loss of people. She acknowledges, in a somewhat veiled way, that it is harder to lose someone you love than to lose an object. In this sense, we have all been practicing the art of losing on a smaller scale throughout our lives (lost keys and other trivial items), although we reach a level of painful mastery when we inevitably lose someone we love.
When Bishop says the art of losing is "not too hard to master," she is being facetious. This dry humor complements the use of the pun in the title, so your essay could focus on this recurring theme. Bishop uses subtle humor to address tough concepts throughout her works, and this poem is no exception. The parenthetical in the last stanza is also worth noting as it relates to the theme of loss as art and art as a means of coping with loss. When Bishop says "(Write it!)" she is both commanding herself to finish the piece, even though the last line is hard for her to write, and instructing the reader that writing is one possible form of dealing with loss.
To summarize, a critical essay might expound on the following ideas:
The pun in the title reflects Bishop's use of dark humor throughout the poem.
Bishop draws a distinction between losing things and losing people.
Loss is an art, but art can be used to express loss.
Bishop's use of duality, including the two possible meanings of the title and the two interpretations of "(Write it!)" in the last stanza.

In the first line of Brave New World by Aldous Huxley, the reader learns the tri-partite pillars upon which World State is allegedly built: "Community, Identity, Stability." The processes by which these three qualities are achieved and maintained, however, seem completely paradoxical. Using examples from the text, examine each pillar and how Huxley develops his message or warning about how society should be structured.

In "Brave New World," the World State creates community by segregating the population into different social groups. At birth, for instance, children are already categorized into their chosen social group, like Alphas and Epsilons.
Similarly, this strict social hierarchy helps to create a sense of identity. The Alphas, for example, know that they are attractive and highly intelligent, and this contributes to their sense of self. This is also achieved through conditioning, the process by which individuals learn how to behave and what is expected of them.
Stability is created in the World State through the widespread use of soma. By keeping the population in a permanent drugged state, the Controllers ensure that social problems, like rebellion, will never happen.
Through these processes, Huxley warns us that when he focuses on community and a shared sense of identity, we neglect the importance of the self and the individual. Instead of fostering social harmony, all the Controllers have done is create class conflict, create drug dependency, and eradicate social connections that occur through institutions like the family. We see this clearly through the struggles of John the Savage who is unable to integrate into this society and eventually takes his own life.
For Huxley, then, a society should not be structured in a way that ignores the self, the family, and the natural differences which occur between us.

All of these pillars, community, identity, and stability, are achieved and maintained in similar ways. The main process by which these are achieved is conditioning. As the Director explains:

All conditioning aims at  ... making people like their unescapable social destiny.

Babies produced by test tube are genetically engineered to be of one of five social castes. Members of each caste are then conditioned to embrace their role in society. For example, we are shown Delta babies, part of a worker caste, given electric shocks to condition them to hate books and flowers. Betas, who are meant to be major consumers, hear tapes all through their childhood as they sleep encouraging them to shop and buy. Betas, like the other castes, are also conditioned to fear solitude, which reinforces community. 
A strict central control of society is another major way community, identity, and stability are achieved. Economic output is strictly planned in a centralized way. The Director runs the state as a benign dictatorship, banning Christianity, great literature, great art, philosophy, and anything else he fears will disrupt the stable community. He states that after the Nine Years' war people opted for security above all else:

What’s the point of truth or beauty or knowledge when the anthrax bombs are popping all around you? That was when science first began to be controlled-after the Nine Years’ War. People were ready to have even their appetites controlled then. Anything for a quiet life. We’ve gone on controlling ever since.

A third way the society achieves the three pillars is through the use of soma, a drug that keeps people sedated.
This smoothly ordered society runs by encouraging superficial relationships, regulating all aspects of life to avoid any unpleasant surprises or suffering, and encouraging mindless consumption rather than engaged thought.
The paradox of all this is that the Director achieves his vision of a perfectly ordered human society by robbing people of core essentials of their humanity: their ability to suffer, to love deeply, and to fully experience the best that art, literature, and philosophy have to offer. Stability is achieved by conditioning people to accept a superficial life and keeping them drugged. The Director claims this brings "happiness." A reader might argue that this society makes them less than human.

Why is Mrs. Mallard's marriage an oppression?

Mrs. Mallard's marriage is oppressive, it seems, for a couple reasons.
First, she does not truly love her husband. The narrator tells us that "she had loved him—sometimes. Often she had not." He had evidently loved her a great deal, a fact she acknowledges when she considers her new freedom, but she simply could and did not return that feeling in a consistent way. As a result, the relationship felt oppressive to her.
Further, Louise Mallard's relief that she can now enjoy "a long procession of years to come that would belong to her absolutely" provides a clue as to another reason her marriage might have felt oppressive. The narrator says that now, for her, "There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature." Although her husband has been kindly and loving, marriage in this time period (which we can narrow down to the end of the nineteenth century) entitled the husband to rule over the wife. Louise Mallard would not have had her own legal or social identity; rather, her identity would be subsumed under her husband's. Despite his love for her, knowing that she must always submit to him regardless of her own feelings seems to have caused her to feel oppressed by her marriage too.

What caused the South Carolina nullification crisis?

Firstly, let’s discuss what ‘nullification’ means in a legal sense, what brought it about, and then lastly move on to the issue concerning South Carolina.
Nullification refers to a US state suspending federal law within its borders. In other words, the state is declaring that its own law and not that of the federal government will apply to actions within the state. Nullification was first addressed by Thomas Jefferson and James Madison in regards the Alien and Sedition Acts passed by then President John Adams in 1798. Jefferson and Madison viewed these bills as an overreach by the federal government into state matters. The principle of nullification gained traction in New England as well as the southern states, particularly regarding state commerce.
Although the principle of nullification was becoming more popular, what brought the issue to the forefront of politics was the Tariff of 1832. The federal government passed the tariff against the protests of many southern states. South Carolina then passed an ordinance of nullification and went so far as to threaten secession from the US if the federal government attempted to collect tariff duties.  
President Andrew Jackson saw this as a direct threat to the legitimacy of the federal government to regulate affairs within its borders. He sent American warships to Charleston and strengthened federal fortifications. Meanwhile, the US Congress passed a Force Bill in 1833 authorizing Jackson to use federal troops to enforce the tariff.
Senator and former Secretary of State Henry Clay took on the role of the Great Compromiser, similar to the one he had during the Missouri Compromise of 1820 that brought Maine into the Union as a free state and Missouri as a slave state. Clay was able to convince Congress to pass the Tariff of 1833 that would reduce the tariff introduced in 1832 over a ten-year period to the tariff level of 1816. South Carolina accepted the deal and repealed its nullification order. However, the state legislature then nullified the Force Bill, perhaps as a way of sending a message to Jackson regarding federal overreach. Jackson ignored this last action by the state allowing for the potentially explosive tariff matter to finally settle down.
South Carolina was very close to seceding and although the other southern states were sympathetic to its cause, none had gone along with nullification. We can see that federal versus states' rights was a problematic issue long before the American Civil War. Instead of a singular event, South Carolina’s nullification crisis is best viewed as just one in a series of events that finally split the country apart in 1861.  
https://avalon.law.yale.edu/19th_century/ordnull.asp

https://www.history.com/topics/early-us/alien-and-sedition-acts

https://www.presidentprofiles.com//Washington-Johnson/Andrew-Jackson-Nullification.html

What is the theme/idea in the poem "Homage to My Hips"?

A clue to the poem's meaning is found in the word "homage." It is a noun denoting respect or honor demonstrated publicly. The poem's speaker is a woman who is conscious of her feminine physique and appreciative of what nature has given her: large, sensuous hips.
While there are frequently-shifting societal norms about what female body shapes are attractive, the speaker wholeheartedly ignores all of them and revels in the shape and size of her hips, which she describes in glowing terms like "big," "free," "mighty," and "magic."
The speaker embraces her sexuality as well, proudly proclaiming that her hips have a history of entrancing at least one man, on whom they "put a spell." She sets no limits on herself, announcing through the use of synecdoche that her hips "go where they want to go" and "do what they want to do." Her hips are a symbol for the unapologetic physical and sexual freedom she feels as a liberated woman.

What kind of illness did Helen have? What type of experience was it for the child?

According to the first chapter of her autobiography, Helen Keller was suddenly struck with an "acute congestion of the stomach and brain." Modern medical experts have speculated that this illness was likely to have been scarlet fever or meningitis, although it is impossible to be certain.
Helen was only in her second year of life when she became ill. Up to this point, she had been a normal, healthy baby. She could walk and talk, and interact with the world around her.
However, the experience of being sick had a dramatic impact on Helen's life, as we see from the following quote:

Then, in the dreary month of February, came the illness which closed my eyes and ears and plunged me into the unconsciousness of a new-born baby.

In other words, this illness robbed Helen of her sight and hearing, as well as the independence that she had just begun to develop.
In addition, in the next paragraph, Helen talks about the "agony" and "bewilderment" which this illness created. Helen spent all of her waking hours in considerable pain, as well as suffering from "dry" and "hot" eyes. Despite her best efforts, Helen's mother was unable to soothe her daughter's pain or save her sight and hearing.
Fortunately, this illness disappeared as quickly as it came. Helen, however, would never regain her sight or hearing.

How does "The Company of Wolves" by Angela Carter reinforce gender stereotypes?

Although some scholars see "The Company of Wolves" as a feminist rewriting of the story of Little Red Riding Hood, others have criticized "The Company of Wolves" for reproducing dominant patriarchal stereotypes.
First, rather than loyalty to her grandmother and the strength of bonds among women being portrayed as central values, the young girl is depicted as a sexualized heroine for whom heterosexual desire overwhelms even common sense. Even worse, the story portrays a young teenage girl who has just gone through puberty as a sexual object, and most of us would think that a fully adult man (the handsome stranger who turns out to be a wolf) who displays sexual interest in young girls is a pedophile. The girl's complicity is imprudent to say the least.
Although the girl has a knife and some training in using a knife, the girl ends up sleeping with the wolf. The message this sends to girls is that, ultimately, they are sexual objects who can only survive by submitting sexually to powerful men.

Calculus: Early Transcendentals, Chapter 7, 7.3, Section 7.3, Problem 26

intx^2/(3+4x-4x^2)^(3/2)dx
Let's rewrite the denominator of the integrand,
=intx^2/(-(4x^2-4x+1)+4)^(3/2)dx
=intx^2/((2^2-(2x-1)^2))^(3/2)dx
Now let's use the integral substitution,
Let 2x-1=2sin(theta)
=>2x=1+2sin(theta)
=>x=(1+2sin(theta))/2
dx=1/2(2cos(theta))d theta
dx=cos(theta)d theta
Plug the above in the integral,
=int((1+2sin(theta))/2)^2/(2^2-2^2sin^2(theta))^(3/2)cos(theta)d theta
=int1/4((1+2sin(theta))^2cos(theta))/(2^2(1-sin^2(theta)))^(3/2)d theta
=1/4int((1+2sin(theta))^2cos(theta))/((2^2)^(3/2)(1-sin^2(theta))^(3/2))d theta
=1/4int((1+2sin(theta))^2cos(theta))/(2^3(1-sin^2(theta))^(3/2))d theta
Now use the identity:1-sin^2(x)=cos^2(x)
=1/32int((1+2sin(theta))^2cos(theta))/(cos^2(theta))^(3/2)d theta
=1/32int((1+4sin(theta)+4sin^2(theta))cos(theta))/(cos^3(theta))d theta
=1/32int(1+4sin(theta)+4sin^2(theta))/(cos^2(theta))d theta
=1/32int(1/(cos^2(theta))+(4sin(theta))/(cos^2(theta))+(4sin^2(theta))/(cos^2(theta))d theta
=1/32int(sec^2(theta)+4tan(theta)sec(theta)+4tan^2(theta))d theta
Now use the identity:tan^2(x)=sec^2(x)-1
=1/32int(sec^2(theta)+4tan(theta)sec(theta)+4(sec^2(theta)-1)d theta
=1/32int(5sec^2(theta)+4tan(theta)sec(theta)-4)d theta
Now use the standard integrals,
intsec^2(x)dx=tan(x)+C
intsec(x)tan(x)dx=sec(x)+C
=1/32(5tan(theta)+4sec(theta)-4theta)+C
We have used the integral substitution 2x-1=2sin(theta)
=>sin(theta)=(2x-1)/2
theta=arcsin((2x-1)/2)
Now let's find the tan(theta) and sec(theta) using the right triangle with angle theta and opposite side (2x-1) and hypotenuse as 2,
Use pythagorean identity to find the adjacent side A:
A^2+(2x-1)^2=2^2
A^2+4x^2-4x+1=4
A^2=4-1+4x-4x^2=3+4x-4x^2
A=sqrt(3+4x-4x^2)
tan(theta)=(2x-1)/(sqrt(3+4x-4x^2))
sec(theta)=2/(sqrt(3+4x-4x^2))
Now plug these in the above solution,
=1/32(5*(2x-1)/(sqrt(3+4x-4x^2))+4*2/(sqrt(3+4x-4x^2))-4arcsin((2x-1)/2))+C
=1/32((10x-5+8)/sqrt(3+4x-4x^2)-4arcsin((2x-1)/2))+C
=1/32((10x+3)/sqrt(3+4x-4x^2)-4arcsin((2x-1)/2))+C

A 20.0-L nickel container was charged with 0.852 atm of xenon gas and 1.34 atm of fluorine gas at 400°C. The xenon and fluorine react to form xenon tetrafluoride. What mass (g) of xenon tetrafluoride can be produced assuming 100% yield?

The chemical reaction for the given scenario can be written as:
Xe + 2F_2 -> XeF_4
That is, 1 mole of xenon reacts with 2 moles of fluorine to produce 1 mole of xenon tetrafluoride.
In this question, 0.852 atm of xenon gas reacts with 1.34 atm of fluorine gas. Using the ideal gas law, we can calculate the moles of each of the reactants.
Therefore, moles of xenon = PV/RT = (0.852 atm x 20 l)/(0.08205 l atm/mole k  x 673 k) 
= 0.309 moles 
(Do remember to convert the temperature to the Kelvin scale.)
Similarly, moles of fluorine = 0.485 moles
Now, using the stoichiometry, we can see that fluorine is in limited quantity since 0.309 moles of xenon will react with 0.618 moles (= 2 x 0.309 moles) of fluorine gas. And hence, the fluorine gas will dictate how much product will be formed.
From the chemical equation, 2 moles of fluorine produces 1 mole of xenon tetrafluoride. And hence the moles of xenon tetrafluoride produced are:
moles of xenon tetrafluoride = 1/2 x 0.485 moles = 0.243 moles
The molecular mass of xenon tetrafluoride is 207.28 gm/moles and hence the total amount of xenon tetrafluoride that is formed is 50.37 gm (= 0.243 moles x 207.28 g/mole).
Hope this helps.
 

What is the atmosphere of The Lost Symbol by Dan Brown?

I would say that most of the novel's atmosphere is foreboding and tense.  Those won't work for the entire novel, because the concluding chapters bring a return to normalcy and calmness when Peter Solomon explains a bunch of details regarding the Lost Symbol to Robert Langdon.  
The rest of the novel, in typical Dan Brown style, is paced quite quickly and an overall tense and foreboding atmosphere is created.  Mal'akh helps establish the foreboding atmosphere because the guy is equally dangerous and scary.  He has tattoos covering his entire body, and he shows no reservations about killing people.  The sequence when he locks Langdon in the sensory deprivation tank is incredibly tense because readers know that Langdon suffers from extreme claustrophobia.  Another extremely tense part of the book is when Mal'akh is hunting Katherine Solomon through the absolute darkness of her Noetic Science research facility. Darkness has a way of creating tense atmospheres to begin with.  Now add being hunted to it.  It would be terrifyingly tense.  

How does the quote "We were both chumps. But you know what? It's not so bad when you're chumps together" fit into the novel "Okay for Now"?

This quote on page 330 of Gary D. Schmidt's novel "Okay For Now" represents a pivotal point in the life of the protagonist, Doug. In the novel, Doug has just moved to a new town with his abusive father and loser brother, and he is feeling lost. For once, he has a place in life and is experiencing real friendship with a local girl, Lil Spicer. She has procured him a job at the deli her parents own and he has begun to forge relationships with all the locals in Marysville that make him feel connected to the town in a way that he never expected. Lil, it seems, has had an extremely positive influence on his life, and is single-handedly responsible for everything good that is happening to him.
At this point in the book, however, she has experienced a tragic illness and is in the hospital fighting for her life. Doug visits her, but her illness has affected his newfound happiness in unexpected ways that make him feel like a "chump." The use of the word "chump" is significant because it refers to someone who feels stupid or foolish; in this case, Doug feels like a chump for believing that everything could end well for him. He feels foolish for allowing himself to be lead into a false sense of security and for letting himself experience happiness for the first time in a long time.
First, he feels like a chump because even when Mr. Spicer has to fire him to pay Lil's hospital bills, he offers to stay on for free. Then, when the neighbors ask about her, he almost bursts into tears, which makes him feel foolish. When he returns to the deli and sees Mrs. Spicer crying, he cries and feels a little less foolish because they are "chumps together," meaning that they are crying and acting foolish together. 

What are at least four basic beliefs of Puritans?

The Puritans originated as a sect of Protestant Reformers in England who believed that the Church of England was corrupt with Roman Catholic practice. Believing the Anglican Church to be beyond hope for reform, they sought refuge, isolation, and religious freedom in the New World. One of the most famous Puritan communities was that of Salem in the Massachusetts colony. They lived in very strict, religious communities in attempt to purify themselves from the evils of the world.
The Puritans believed in Biblical Absolutism, or that the Bible was the literal word of God and the highest authority. Furthermore, they did not believe in a separation of Church and State. If anything, the Puritans held that the State should adhere to the Church by enforcing laws consistent with Biblical teachings.
The Puritans believed that this world is a constant siege of temptation by the Devil and his demons. It took lots of personal perseverance to remain spiritually pure and overcome worldliness. To minimize temptation by the Devil and emphasize the importance of God, many forms of entertainment or "diversion" were banned. Music was banned from religious services, dancing was considered sinful, theatre and performance were considered a distraction, and even gathering in too large a number was an opportunity for the Devil!
Additionally, the Puritans believed in predestination and covenant theology. This meant that they believed themselves to have been specially chosen by God to live their lifestyle away from the rest of Christianity as truly Godly people.
https://www.britannica.com/topic/Puritanism

In Silent Spring, how was life in terms of biodiversity before the strange blight crept into the imaginary town?

The first chapter of Rachel Carson's Silent Spring is called "A Fable for Tomorrow," and it begins with richly descriptive imagery of "a town in the heart of America where all life seems to live in harmony with its surroundings." The biodiversity of this area is thriving. The narrator of the fable describes a virtual Eden where fields and orchards are fertile and brimming with crops. Roadsides are lush and verdant, and passersby enjoy the sight. In winter, it continues to support life as birds feast on berries and the dried seed heads of weeds not covered in snow. The area is a destination for birdwatchers because of the vibrant migration routes in spring and fall and because of the diversity of species. It is also a destination for fishermen because of the health and abundance of trout. Foxes and deer live there. The narrator observes that this biodiversity has persisted since colonial times.

Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 20

The given problem: ysqrt(1-x^2)y' -xsqrt(1-y^2)=0 is written in a form of first order "ordinary differential equation" or first order ODE.
To evaluate this, we can apply variable separable differential equation in which we express it in a form of f(y) dy= g(x) dx before using direct integration on each side.
To rearrange the problem, we move xsqrt(1-y^2) to the other to have an equation as:ysqrt(1-x^2)y' = xsqrt(1-y^2) .
Divide both sides by sqrt(1-y^2)sqrt(1-x^2) :
(ysqrt(1-x^2)y')/(sqrt(1-y^2)sqrt(1-x^2)) = (xsqrt(1-y^2))/(sqrt(1-y^2)sqrt(1-x^2))
(y*y')/sqrt(1-y^2)= x/sqrt(1-x^2)
Applying direct integration: int(y*y')/sqrt(1-y^2)= int x/sqrt(1-x^2)
Express y' as (dy)/(dx) : int(y*(dy)/(dx))/sqrt(1-y^2)= int x/sqrt(1-x^2)
Express in a form of f(y) dy= g(x) dx : int(y*dy)/sqrt(1-y^2)= int (x*dx)/sqrt(1-x^2)

To find the indefinite integral on both sides, we let:
u = 1-y^2 then du =-2y dy or (du)/(-2) =y dy
v = 1-x^2 then dv =-2x dx or (dv)/(-2) =x dx
The integral becomes:
int(y*dy)/sqrt(1-y^2)= int (x*dx)/sqrt(1-x^2)
int((du)/(-2))/sqrt(u)= int ((dv)/(-2))/sqrt(v)
Apply the basic integration property: int c*f(x) dx= c int f(x) dx .
(-1/2) int((du))/sqrt(u)= (-1/2) int (dv)/sqrt(v)
Apply the Law of Exponents: sqrt(x) = x^(1/2) and 1/x^n = x^(-n) .
Then, the integral becomes:
(-1/2) int((du))/u^(1/2)= (-1/2) int (dv)/v^(1/2)
(-1/2) int u^(-1/2)du= (-1/2) int v^(-1/2)dv
Applying Power Rule of integration: int x^ndx= x^(n+1)/(n+1)
(-1/2) int u^(-1/2)du= (-1/2) int v^(-1/2)dv
(-1/2) u^(-1/2+1)/(-1/2+1)= (-1/2) v^(-1/2+1)/(-1/2+1)+C
(-1/2) u^(1/2)/(1/2)= (-1/2) v^(1/2)/(1/2)+C
-u^(1/2)= - v^(1/2)+C
Note: (-1/2)/(1/2) = -1
In radical form: - sqrt( u)= -sqrt(v)+C
Plug-in u =1-y^2 and v=1-x^2 , we get the general solution of differential equation:
- sqrt( 1-y^2)= -sqrt(1-x^2)+C
Divide both sides by -1 , we get: sqrt( 1-y^2)= sqrt(1-x^2)+C .
Note:C/(-1) = C as arbitrary constant
For particular solution, we consider the initial condition y(0) =1 where x_0=0 and y_0=1 .
Plug-in the values, we get:
sqrt( 1-1^2)= sqrt(1-0^2)+C
sqrt(0)=sqrt(1)+C
0=1+C
C = 0-1
C =-1 .
Then plug-in C =-1 on the general solution: sqrt( 1-y^2)= sqrt(1-x^2)+C .
sqrt( 1-y^2)= sqrt(1-x^2)+(-1)

(sqrt(1-y^2))^2 =(sqrt(1-x^2) -1)^2
1-y^2= (1-x^2) -2sqrt(1-x^2) +1
Rearrange into:
y^2=-(1-x^2) +2sqrt(1-x^2)
y^2=-1+x^2 +2sqrt(1-x^2)
y^2=x^2+2sqrt(1-x^2)-1
Taking the square root on both sides:
y =sqrt(x^2+2sqrt(1-x^2) -1)