Calculus: Early Transcendentals, Chapter 4, 4.9, Section 4.9, Problem 7

The most general antiderivative F(x) of the function f(x) can be found using the following relation:
int f(x)dx = F(x) + c
int (7x^(2/5) + 8x^(-4/5))dx = int (7x^(2/5))dx + int (8x^(-4/5))dx
You need to use the following formulas:
int x^n dx = (x^(n+1))/(n+1)
int x^(-n)dx = (x^(-n+1))/(-n+1)
int (7x^(2/5))dx = (x^(2/5+1))/(2/5+1) = (5/7)*x^(7/5) + c
int (8x^(-4/5))dx = (x^(-4/5+1))/(-4/5+1) = 5*x^(1/5) + c
Gathering all the results yields:
int (7x^(2/5) + 8x^(-4/5))dx = (5/7)*x^(7/5) + 5*x^(1/5) + c
Hence, evaluating the most general antiderivative of the function yields F(x) = (5/7)*x^(7/5) + 5*x^(1/5) + c.

How did the congressional election of 1866 illustrate the sentiments of the American people regarding Andrew Johnson?

The congressional elections of 1866 were effectively a referendum on Andrew Johnson's presidency. Johnson was deeply unpopular with large sections of the Republican Party over his Reconstruction policies. He was strongly opposed to what he saw as the extremism of the Radical Republican agenda, favoring a more piecemeal, conciliatory approach to incorporating rebel states back into the Union. Unable to close the gaping chasm between himself and Radical Republicans, Johnson used the congressional elections to put his vision of Reconstruction before the American people.
On the campaign trail, Johnson viciously assailed his opponents within the GOP, resorting to the kind of language normally reserved for Southern rebels during the Civil War. In fact, Johnson openly equated the Radical Republicans' alleged extremism with the treachery of Southern secessionists. Johnson's intemperate language, combined with his aggressive demeanor, alienated large swaths of the electorate. The president further damaged both his campaign and his credibility by playing upon racist fears, accusing his Radical Republican opponents of inciting African Americans to murder whites.
When the results came in, they were a disaster for Johnson. Republicans opposed to the president won two-thirds of the seats in both houses of Congress. This meant that not only could anti-Johnson Republicans thwart his legislative program, they could also begin the process that would eventually culminate in his impeachment.

I need a short plot overview of Emma by Jane Austen, please.

The story is told from the point of view of Emma Woodhouse, a rich, snobbish (but in the end lovable) young woman whose life is upended as the novel begins with the marriage of her governess Miss Taylor to their neighbor, Mr. Weston.
Emma fills the hole left by Mrs. Weston's marriage with a new companion, the young and pretty Harriet Smith. Emma plots a marriage between Harriet and the local clergyman, Mr. Elton.
The notable fact about Emma is her cluelessness. The novel is famous because it is channeled through the perceptions of a heroine who misses what is right in front of her eyes. First, she fails to see what we as readers do: Mr. Elton wants to marry the rich and established Emma, not the penniless Harriet of unknown parentage. Emma's mix up over this leads to the dark comedy of the first part of the novel.
Later in the novel, Jane Fairfax and Frank Churchill arrive on the scene. Jane is beautiful and accomplished but penniless. Frank, the son of Mr. Weston, is wealthy, having been adopted and raised by his rich Churchill relations. He is dependent on Mrs. Churchill for his money and does not dare offend her.
Frank is secretly engaged to Jane. He can't marry her without Mrs. Churchill's approval. That approval is not likely to be coming, hence the secrecy. We don't know of this engagement until the end of the novel.
In the meantime, Franks flirts with Emma, using her as a decoy so that nobody will suspect he is in love with Jane. Because Emma is clueless, she falls for the idea of Frank being in love with her. We as readers usually do too because we see the world through Emma's eyes.
After the shock of the Jane and Frank engagement quickly wears off, Emma turns to Mr. Knightley, her brother-in-law. Though they have had a quarrelsome relationship throughout the novel, they realize they are in love, and so the novel ends happily: Jane ends up with Frank, Emma with Mr. Knightley, and Harriet with her first love interest, Mr. Martin.

How does the Duke of Albany feel about his wife’s action against the king and what is Goneril’s response to the duke in scene 4 of King Lear?

In act1, scene 4 of King Lear, Lear goes on a furious rampage after his eldest daughter, Goneril, refuses to follow the aging king's orders in her own home. Lear insults Goneril, telling Albany to think twice before impregnating a strong-willed woman like Goneril.
Albany, meanwhile, plays the role of a diplomat. He speaks to the mad king, assuring Lear that it not his own choice but Goneril's to defy him:

My lord, I am guiltless, as I am ignorant,
Of what hath moved you

Albany continues to attempt to calm the king while paying respects to him. He also refuses to take the king's side too confidently at the risk of upsetting his wife. When he attempts to address Goneril, hoping to take the king's side, he is meek and unconfident, and he is quickly shushed by his wife:


I cannot be so partial, Goneril,
To the great love I bear you—



Goneril then silences her husband and quickly criticizes his diplomacy:


Though I condemn not, yet under pardon
You are much more attasked for want of wisdom
Than praised for harmful mildness.



Here, Goneril is saying that Albany's indecisiveness, as well as his lack of political strategy, is far more obvious and noticeable than his tenderness and love for the king. While Albany attempts to make suggestions as to how Goneril should deal with the king, he is immediately shot down by her.

In "The Bet," does the bet resolve the issue for which the bet had been made?

The original issue was whether the death penalty was better or worse, more or less humane, than imprisonment for life. It somehow got confused with solitary confinement, which had not previously been discussed at all. This was evidently because the lawyer could hardly agree to be imprisoned for the rest of his life, and the banker could hardly be expected to propose such a thing. It might mean keeping the lawyer locked up somewhere for as long as fifty years. He would have to be dead to win the bet. Meanwhile, the banker, a middle-aged man, would certainly have died. A dead man would be collecting from a dead man! So the original issue was never resolved from the very beginning. For plot purposes, Chekhov had to change the terms of the bet, without any explanation, into solitary confinement for fifteen years. That in itself seems questionable, since the banker had only specified a term of five years.


"It's not true! I'll bet you two million you wouldn't stay in solitary confinement for five years."
"If you mean that in earnest," said the young man, "I'll take the bet, but I would stay not five but fifteen years."

No one has been able to explain why the lawyer should have gratuitously added ten years to his ordeal. It was a big all-male party and no doubt a lot of vodka was being drunk. The quoted dialogue sounds as if the two men were showing off for the others and then were too proud to call the bet off when they were sober. The story opens the night before the fifteen years is up, and the banker himself is reflecting that the bet was senseless and proved nothing.


"What was the object of that bet? What is the good of that man's losing fifteen years of his life and my throwing away two million? Can it prove that the death penalty is better or worse than imprisonment for life? No, no. It was all nonsensical and meaningless."

Technically, the banker wins the bet because the lawyer deliberately loses it by leaving his confinement before the full fifteen years is up. Morally, the lawyer has won the bet because he could easily have remained imprisoned for a few more hours. However, he would never have collected the two million rubles because the banker intended to kill him. So the unforeseeable ending has the winner losing and the loser winning. And the issue for which the bet had been made is left unresolved. 

A neutron in a reactor has kinetic energy of approximately 0.020 eV. Calculate the wavelength of this neutron.

The de Broglie relation is
eq. (1) -> P=h/lambda
Now get the momentum P in terms of the kinetic energy K_E .
K_E=1/2 mv^2
K_E=P^2/(2m)
eq. (2) -> P=sqrt(2mK_E)
Therefore the wavelength can be found by equating eq. (2) and eq. (1) and solving for lambda .
h/lambda=sqrt(2mK_E)
lambda/h=1/sqrt(2mK_E)
lambda=h/sqrt(2mK_E)
Plug in numerical values. You will find the units are much easier if you convert the neutron mass into energy with units of eV by E=mc^2 . Hence,
lambda=h/sqrt(2mc^2K_E)
lambda=(1240 eV*nm)/sqrt(2(940 *10^6 eV)(0.020 eV))=0.20 nm
http://hyperphysics.phy-astr.gsu.edu/hbase/debrog.html

Why did the Puritan settlements surround a village green?

The Puritans built their villages with a village green in the middle because it gave the town a community space that was accessible to everyone. People could gather in the village green for all kinds of reasons, from trade to everyday socializing. It was very like the public parks that we have today, combined with the mall and town hall. It could even also be used as a space for horses and other livestock to graze, and even get water if there happened to be a pond. In general, the village green served as a center of community life for a Puritan town. This was important because Puritan communities valued giving every citizen a voice in the direction of the community, and the village green made this easy by giving the town a place where everyone could congregate.

What was the religious object that Ultima gave Antonio?

In the story, Ultima gives Antonio her scapular.
A scapular was originally worn by priests and monks. It consists of two pieces of woolen cloth joined together by narrow strips of cloth. One piece is worn in the front, and the other piece goes in the back.
Modern worshippers wear smaller scapulars. These scapulars consist of smaller squares of woolen cloth joined by very thin, connecting strips. From the description in the text, this is likely the type of scapular Ultima bequeaths to Antonio.
Ultima tells Antonio that he will likely receive his own scapular when he participates in his first Communion. However, she wants Antonio to have hers so that he will not be without protection from evil. Ultima's scapular is a unique one. It does not have religious images on the cloth, and her scapular holds a small pouch of mixed herbs. Ultima promises that the "helpful herbs" will keep Antonio safe. She also asks Antonio not to tell anyone about her gift.

Calculus of a Single Variable, Chapter 7, 7.4, Section 7.4, Problem 8

Arc length (L) of the function y=f(x) on the interval [a,b] is given by the formula,
L=int_a^b sqrt(1+(dy/dx)^2)dx , if y=f(x) a <= x <= b,
Now y=x^4/8+1/(4x^2)
Now we need to differentiate the above function with respect to x,
dy/dx=1/8(4)x^(4-1)+1/4(-2)x^(-2-1)
dy/dx=1/2x^3-1/2x^(-3)
dy/dx=x^3/2-1/(2x^3)
dy/dx=(x^6-1)/(2x^3)
Now arc length L=int_1^3 sqrt(1+((x^6-1)/(2x^3))^2)dx
=int_1^3sqrt(1+(x^12-2x^6+1)/(4x^6))dx
=int_1^3sqrt((4x^6+x^12-2x^6+1)/(4x^6))dx
=int_1^3sqrt((x^12+2x^6+1)/(4x^6))dx
=int_1^3sqrt(((x^6+1)/(2x^3))^2)dx
=int_1^3(x^6+1)/(2x^3)dx
=int_1^3(x^6/(2x^3)+1/(2x^3))dx
=int_1^3(x^3/2+1/2x^(-3))dx
=[1/2x^4/4+1/2(x^(-3+1)/(-3+1))]_1^3
=[x^4/8-1/(4x^2)]_1^3
=[3^4/8-1/(4(3)^2)]-[1^4/8-1/(4(1)^2)]
=[81/8-1/36]-[1/8-1/4]
=[(729-2)/72]-[(1-2)/8]
=[727/72]-[-1/8]
=727/72+1/8
=(727+9)/72
=736/72
=92/9
So, the Arc length=92/9

I am going to write an explication of "The Black Cat," and I need a thesis statement. Can you help me with some ideas for that? I was thinking maybe something surrounding the perverseness in his short story but maybe something else?

When analyzing a literary work, there are multiple potential arguments a writer could make. Based on your interest in the "perverseness" of the story, I would suggest you focus on the narrator's character and the way he evolves throughout the story. You might make an argument about his descent into madness and how it affects his reliability as a narrator.
We know, for example, that when he was younger, the narrator was an animal lover. In the second paragraph, the narrator explains,

From my infancy I was noted for the docility and humanity of my disposition. My tenderness of heart was even so conspicuous as to make me the jest of my companions. I was especially fond of animals, and was indulged by my parents with a great variety of pets. With these I spent most of my time, and never was so happy as when feeding and caressing them.

Here, he dwells on his calm and humane demeanor and his love of animals. You might even say his kindness toward his family pets was his defining characteristic. How does this kind of person change so much that he tortures and kills his pet cat?
In your essay, you can trace the development of the narrator from his youth, described above, to his growing hatred for the black cat. We know that his feelings are partially related to his alcoholism, but is that really enough to make someone commit such a senseless and violent act? Why is the narrator so paranoid about the cat? What further atrocities and character devolution do his paranoia and guilt lead him to? Why does he murder his wife? What does it mean that another black cat reveals his guilt to the police?
All of these questions can be discussed in an analysis of how the narrator's character devolves over the course of the story. "The Black Cat," like many Poe stories, can be viewed as a study of how a person speaks and behaves when he has lost his sanity; the story provides us with a look into both the possible causes and the progression of the narrator's madness.

What are Delia's characteristics in "A Service Of Love"?

In the story, Delia is loving, loyal, and caring. Delia marries Joe even though she knows that he is a struggling artist.
When they experience straitened circumstances, Delia takes a job at a laundry-shop. She doesn't complain but sets to work to earn enough for Joe's art lessons with Mr. Magister. Although Joe feels guilty that Delia is shouldering the financial load in their little family, he cheers up when he hears that Delia has found a paying piano student.
Delia tells Joe that her new student is a little girl named Clementina. Accordingly, she is the daughter of one General A. B. Pinkney, and the Pinkneys appear to be a wealthy family. Of course, none of what Delia tells Joe is true. She tells a white lie because she wants to spare Joe the humiliation of knowing that his wife is supporting him financially.
In the end, Joe discovers what Delia has really been doing when she accidentally injures her hand at the laundry-shop. Ironically, it is Joe who sends up the "cotton waste and oil from the engine–room...for a girl upstairs who had her hand burned with a smoothing–iron." So, in the story, Delia's loving and loyal nature is clearly demonstrated through her actions.

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 26

Solve $\displaystyle 3x^2 - 6x - 1 = 0$ by completing the square.


$
\begin{equation}
\begin{aligned}

3x^2 - 6x - 1 =& 0
&& \text{Given}
\\
\\
3x^2 - 6x =& 1
&& \text{Add 1}
\\
\\
x^2 - 2x =& \frac{1}{3}
&& \text{Divide both sides by 3 to eliminate the coefficient of } x^2
\\
\\
x^2 - 2x + 1 =& \frac{1}{3} + 1
&& \text{Complete the square: add } \left( \frac{-2}{2} \right)^2 = 1
\\
\\
(x - 1)^2 =& \frac{4}{3}
&& \text{Perfect square}
\\
\\
x - 1 =& \pm \sqrt{\frac{4}{3}}
&& \text{Take square root}
\\
\\
x =& 1 \pm \sqrt{\frac{4}{3}}
&& \text{Add 1}
\\
\\
x =& 1 + \frac{2}{\sqrt{3}} \text{ and } x = 1 - \frac{2}{\sqrt{3}}
&& \text{Solve for } x
\\
\\
x =& \frac{3 + 2 \sqrt{3}}{3} \text{ and } x = \frac{3 - 2 \sqrt{3}}{3}
&& \text{Rationalize}



\end{aligned}
\end{equation}
$

Why do you think Stanley lied about camp in his letter to his mom?

Stanley lied in order to spare his mother pain and worry.
In the story, we learn that Stanley has been sent away to a camp for "bad boys." At Camp Green Lake Juvenile Correctional Facility, Mr. Sir tells the boys that they are responsible for digging one hole each, every single day.

"You are to dig one hole each day, including Saturdays and Sundays. Each hole must be five feet deep, and five feet across in every direction. Your shovel is your measuring stick. Breakfast is served at 4:30."

On Stanley's first day, he begins to realize how difficult it is to dig a hole that is five feet deep and five feet across in every direction. The surface (about eight inches deep) is the hardest to break through. By the time Stanley breaks through the surface, he has a blister on his right thumb. This makes it painful for Stanley to hold on to the shovel.
Unfortunately, the worst is yet to come. By the time Stanley is finished, his blisters have broken open, and his hands are openly bleeding. Every part of his body is aching. At the end of the day, Stanley is so exhausted that he can only stand still as he showers. He is too tired to lather up with soap.
So, this is what Stanley tells his mother when he writes to her:

Dear Mom, Today was my first day at camp, and I've already made some friends. We've been out on the lake all day, so I'm pretty tired. Once I pass the swimming test, I'll get to learn how to water-ski . . .

Stanley knows that he is lying, but his primary goal is to spare his mother pain and worry. From the text, we can infer that Stanley loves his mother and has a reasonably good relationship with her.

What are some of the barriers to self-reliance in “Self-Reliance” by Emerson?

According to Emerson, some of the barriers to self-reliance are:
The Overwhelming Need To Conform In Order To Fit In
In his treatise, Emerson contends that society is a "joint-stock company, in which the members agree, for the better securing of his bread to each shareholder, to surrender the liberty and culture of the eater." The need to conform is especially strong, because membership in such a society confers certain benefits. These benefits may either be material or abstract in nature; nevertheless, they are "real" benefits people value.
Thus, Emerson argues that conformity is the enemy of self-reliance. He maintains that conformity "loves not realities and creators, but names and customs."
A Society That Confers Respectability On Those Who Abide By Its Strictures
By extension, Emerson argues that society is perhaps the greatest barrier to self-reliance. When people conform to societal expectations, society confers on them social respectability. Emerson complains that this unfairly gives an "angry bigot" a good reputation (albeit one he does not deserve).

If an angry bigot assumes this bountiful cause of Abolition, and comes to me with his last news from Barbadoes, why should I not say to him, "Go love thy infant; love thy wood-chopper: be good-natured and modest: have that grace; and never varnish your hard, uncharitable ambition with this incredible tenderness for black folk a thousand miles off. Thy love afar is spite at home."

Emerson argues that social respectability hides many evils, so to speak. He especially resents the fact that society gets to decide the definition of a "good" man. For his part, Emerson sees no reason to give to "miscellaneous popular charities" and the "thousandfold Relief Societies" that confer respectability on anyone who donates. Emerson will only align with those who share his spiritual values:

I tell thee, thou foolish philanthropist, that I grudge the dollar, the dime, the cent, I give to such men as do not belong to me and to whom I do not belong. There is a class of persons to whom by all spiritual affinity I am bought and sold; for them I will go to prison, if need be.

The Almost Overpowering Need For Consistency
According to Emerson, the need for consistency is another barrier to self-reliance. He suggests that people are motivated by their need for consistency. Our nature is drawn to the familiar. We trust in our social, political, and religious institutions because they fill our need for uniformity and stability. In contrast, self-reliance is seen as a position that embraces volatility; this is unsettling to many people.
However, Emerson argues for self-reliance anyway. He contends that each individual is capable of greatness.

Why all this deference to Alfred, and Scanderbeg, and Gustavus? Suppose they were virtuous; did they wear out virtue? As great a stake depends on your private act to-day, as followed their public and renowned steps. When private men shall act with original views, the lustre will be transferred from the actions of kings to those of gentlemen.

Describe the murder scene in the play “Duchess of Malfi.”

This is during Act 5, Scene 5 of the play. At the beginning of the scene, the Cardinal is pondering the nature of hell when Bosola enters, along with a servant carrying Antonio's body. Bosola tells the Cardinal, "I am come to kill thee." The Cardinal cries, "We are betrayed!" and Pescara, Malatesti, Roderigo and Grisolan then enter.
The Cardinal tries to tell them that he is being attacked, but they don't believe him, thinking it to be a ruse. To ensure nobody will enter to help him, Bosola kills the servant and then stabs the Cardinal. However, Ferdinand breaks in and gives Bosola his death wound. In retribution, the dying Bosola kills Ferdinand. When Pescara, Malatesti, Roderigo and Grisolan come in and find the carnage, Bosola explains that it was done in revenge for the Duchess of Malfi. The Cardinal finally dies; Bosola gives a soliloquy on the nature of life and then also dies. When Delio and Antonio's son arrive, they are "come too late" to offer any assistance.
https://www.bartleby.com/47/4/55.html

What is the resolution to Ray Bradbury's "All Summer in a Day"?

The resolution of a story comes right after the climax. After the climax when the outcome of the conflict is revealed, the resolution usually shows how the characters move forward or react afterward. For Ray Bradbury's "All Summer in a Day," the conflict is person vs. society as one little girl is bullied by her classmates because she has seen the sun before and they haven't. At first, the conflict revolves around Margot and William. Margot believes the sun will shine that day as the scientists predict; however, William dispenses negativity and doubt in the classroom. All of the children want to see the sunshine because they have never experienced it—or at least they don't remember it. Margot probably wants to see it shine more because she misses it. 
When the kids shove Margot into a closet before the sun shines, the reader wonders if she will escape in time to enjoy the rays of the sun. Maybe someone will remember Margot in the closet and free her in time to play in the sun. Unfortunately, the climax of the story comes when the clouds cover up the sun again, and a little girl remembers her and screams, "Margot!" It is at this point that everyone knows Margot's fate and that she won't be able to see the sun that day or for another seven years. The resolution, then, is when the class goes back into the building to free Margot from the closet after the sun goes away. The text seems to suggest that the kids know they have done something wrong to Margot because it says the following: 

They walked slowly down the hall in the sound of the cold rain. . . They walked over to the closet door slowly and stood by it. Behind the closed door was only silence. They unlocked the door, even more slowly, and let Margot out.

The fact that the children proceed very slowly when freeing Margot suggests that they know what they did is wrong. They are not happy, joyful, skipping, or shouting because of a fun day in the sun. The moment is diminished because of their hateful actions toward a classmate. Therefore, the resolution is that Margot is freed, but she doesn't get to enjoy the sun; sadly, the children recognize that they did something they can never take back, change, or rectify.

How is Moscow, the big town, contrasted with the village where Vanka lives?

In the story, Chekhov contrasts the village and Moscow by highlighting the latter's detachment from nature.
Vanka tells us that Moscow is a "big town." It is filled with "gentlemen's houses." There are also plenty of horses and dogs there. However, there is an absence of sheep. In contrast, sheep are an intrinsic part of the village landscape. In the story, we are told that Konstantin Makaritch (Vanka's grandfather) keeps warm with a sheepskin wrap.
In the village, the people are deeply connected to nature. They hunt for their meat and know the origins of their food. In contrast, nobody knows where the meat comes from in a Moscow butcher shop. Vanka proclaims that there are plenty of "grouse and woodcocks and fish and hares" in the meat shops. However, the "shopmen" cannot tell who shot the game. In the city, people are detached from nature and from the source of their food.
Vanka prefers the village. There, the air is always crisp and fresh. In the nighttime, he can see the stars and the clear silhouette of village houses.

How do the poems "The Lovesong of J. Alfred Prufrock," "The Wasteland" by T. S. Eliot, and "Dulce et Decorum Est” by Wilfred Owen relate to T. S. Eliot's theory of impersonality? How are these poems "an escape from emotion" and how must a poet refrain from channeling his own emotions into his poems?

These poems are not so much an escape from or denial of emotion as they are mode of expressing it that is different from that of most poetry written prior to the year 1900.
Eliot, in both "Prufrock" and "The Waste Land," does in fact deal with emotional themes: regret, loss, alienation, embarrassment. But he uses an impersonal style of conveying them. Prufrock is presented as a little man who frets over little things which reveal his self-abasement and, by extension, the disordered and despairing world of the modern age. But Eliot distances himself, personally, from this through the remoteness of the Prufrock persona and the deliberately un-poetic language, as in the famous opening:

Let us go then, you and I,When the evening is spread out against the sky,Like a patient etherized upon a table.

This poem, with its epigraph from Dante and its references to "eating a peach" and women who come and go "talking of Michelangelo," is one of alienation. Similarly, "The Waste Land" is filled with remote allusions and descriptions of ghost-like populations with whom the poet cannot commune:

A crowd flowed over London bridge, so many,I had not thought death had undone so many.

Wilfred Owen's verse is more "conventional" and less modernist, but the horrors of war are described in an impersonal, matter-of-fact way that drives home the point of the brutality of war even more strongly than personal outrage, more emotionally expressed, would do. Compare "Dulce et Decorum Est" with Thomas Hardy's "The Man He Killed." Both are anti-war poems, but even Hardy, as bleak and pessimistic as he is, presents a more gently regretful tone than that of Owen's despairing, hell-like vision.

T. S. Eliot developed his theory of impersonality in his essay "Tradition and the Individual Talent." In this essay, he states:

Poetry is not a turning loose of emotion, but an escape from emotion; it is not the expression of personality, but an escape from personality.

In this statement, he is articulating a combination of ideas. First, he does not think that poetry should resemble a diary in the sense of simply being an outpouring of what a person happens to be feeling at a given time. Instead, it exists at an intersection of the poetic tradition, the objective external objects or specific images that can evoke an emotion in a reader, and the particular emotion or experience.
Thus in "Prufrock," we do not simply get an outpouring of Eliot's own feelings. The poem connects to tradition through its frequent uses of allusion as well as its formal character, which moves back and forth between modernist free verse and traditional forms such as the heroic couplet and Shakespearean song. 
Although "The Wasteland" may have originated in Eliot's personal feelings (instead of being purely autobiographical), it addresses fragmentation as a modern condition and grounds itself in poetic and religious tradition in its central figure of the Fisher King. 
"Dulce et Decorum Est” is a more intensely personal poem, but the poet distances himself by use of the concrete imagery and details that are "linguistic objective correlatives" of the emotions experienced. Rather than telling us that war is horrible, Owens shows its horrors by means of precise descriptions of soldiers enduring trench warfare and gas attacks in World War I. Its title and conclusion link it to the poetic tradition.

Calculus of a Single Variable, Chapter 9, 9.10, Section 9.10, Problem 64

From the basic list of power series, we have:
ln(x) =sum_(n=0)^oo (-1)^(n) (x-1)^(n+1)/(n+1)
= (x-1)-(x-1)^2/2+(x-1)^3/3 -(x-1)^4/4 +...
We replace "x " with "x+1 " to setup:
ln(1+x) =sum_(n=0)^oo (-1)^n ((x+1)-1)^(n+1)/(n+1)
=sum_(n=0)^oo (-1)^n x^(n+1)/(n+1)
=x-x^2/2+x^3/3 -x^4/4+...
Note: ((x+1)-1) = (x+1-1) = x
Then,
x ln(1+x) =sum_(n=0)^oo (-1)^n x^(n+1)/(n+1) *x
=sum_(n=0)^oo (-1)^n x^(n+2)/(n+1)

Note: x^(n+1) * x = x^(n+1+1) =x^(n+2)
Applying the summation formula, we get:
x ln(1+x)= x*[x-x^2/2+x^3/3 -x^4/4+...]
or
= x^2 -x^3/2+x^4/3-x^5/4 +...
Then the integral becomes:
int_0^(1/4) xln(x+1) = int_0^(1/4) [x^2 -x^3/2+x^4/3-x^5/4 +...]dx
To determine the indefinite integral, we integrate each term using the Power Rule for integration: int x^n dx= x^(n+1)/(n+1) .
int_0^(1/4) [x^2 -x^3/2+x^4/3-x^5/4 +...]dx
= [x^3/3 -x^4/(2*4)+x^5/(3*5)-x^6/(4*6) +...]_0^(1/4)
= [x^3/3 -x^4/7+x^5/15-x^6/24 +...]_0^(1/4)
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
F(1/4) or F(0.25) =0.25^3/3 -0.25^4/7+0.25^5/15-0.25^6/24 +...
=1/192-1/1792+1/15360 -1/98304+...
F(0)=0^3/3 -0^4/7+0^5/15-0^6/24 +...
= 0-0+0-0+...
All the terms are 0 then F(0) =0 .
We may stop at 4th term (1/98304~~0.00001017) since we only need an error less than 0.0001 .
F(1/4)-F(0) = [1/192-1/1792+1/15360 -1/98304]-[0]
= 0.00470522926
Thus, the approximated integral value:
int_0^(1/4) xln(x+1) dx ~~0.0047

Is Bassanio a selfish friend in The Merchant of Venice?

I would argue that Bassanio is indeed a selfish friend to Antonio. He takes advantage of Antonio's generosity in trying to obtain some ready cash with which he plans to woo the lovely Portia. At no point does he seem to acknowledge that perhaps Antonio might end up in serious financial trouble as a result. To be fair to Bassanio, he doesn't force Antonio to cough up the money or resort to emotional blackmail; Antonio's a soft touch, and his excessive generosity has encouraged his friend to come looking for another hand-out.
Nevertheless, it's Bassanio's fecklessness that gets Antonio into serious debt and almost ends up killing him. Bassanio's not a bad person, by any means, but he lacks maturity when it comes to financial affairs. And this immaturity is indissolubly linked to a certain selfishness on his part. In seeking money from Antonio, Bassanio never stops to consider his friend's needs.

Much has been made of the friendship between Bassanio and Antonio in Shakespeare's The Merchant of Venice. Often, readers note that both Bassanio and Antonio go to great lengths to help each other. While this fact is true, it's also worth considering that Bassanio is, in fact, quite selfish. For instance, Bassanio convinces Antonio to fund his efforts to woo Portia (which, it's worth mentioning, Bassanio does because he's broke and thinks Portia's fortune will help him financially), thus forcing his best friend to go into debt. While it's true that Bassanio then rushes to Antonio's aid when things with Shylock go sour, it's hard to avoid thinking that it was Bassanio's self-interested desire for money and love that got his friend into such a sticky situation. As such, even if Bassanio is at times a good friend, it's entirely reasonable to also consider him to be selfish.  

What is Anglo-Saxon poetry? Discuss the features and themes of this period.

Anglo-Saxon poetry is the poetry of England attributed to the Anglo-Saxons, Northern Germanic tribes who immigrated to England in the wake of the removal of Roman soldiers needed to defend Rome at its fall. The Anglo-Saxons became the principal group in England, dominating between the mid-400s and 1066 when William of Normandy entered England to take over the throne of King Edward after his death left it unclear who was to be the successor, Godwinson or William of Normandy. Since the 1066 invasion was successful and Godwinson was conquered, the successor was William and the Anglo-Saxon era closed but not without a double legacy: the Anglo-Saxons left us the roots of Modern English in Old English and they left the corpus of Anglo-Saxon poetry, including Beowulf and The Wanderer.
Some features and themes of Anglo-Saxon period poetry include the (1) caesura, (2) alliteration, (3) stressed and unstressed syllables, (4) absence of end-rhymes, (5) kenning, (6) the elegiac theme and (7) the dream vision.
(1-3) Lines are constructed around alliterative stressed syllables and a strong mid-point caesura (strong break between the two halves of each line). There are four stressed syllables in each line. The number of unstressed syllables is variable. There are various patterns possible for alliterated caesura lines.
The overall principle is that there are two stressed and alliterated syllables before the caesura and two stressed syllables after the caesura. One or both of the post-caesura stressed syllables will be alliterated with the pre-caesura stressed syllables. This example from The Wanderer shows the four stressed syllables and related alliteration on both sides of the caesura, which is marked with a comma in this line: "the Measurer’s mercy, though he must." Here, "must" is the second stressed syllable after the caesura, and "must" alliterates /m/ with "Measurer's mercy" before the caesura.
(4) A few random lines from Widsith show that end-rhyme is not a feature of Anglo-Saxon poetry (bearing in mind that Old English has been translated into Modern English). The lines end with the non-rhyming words sprung, Ealhild, time, Hreth-king, Eormanric:

with agreeable treasures. His descent had sprungfrom up among the Myrgingas. He with Ealhild,an unfailing peace-weaver, for the first timeseeking the home of Hreth-king,east of the Angle, of Eormanric,...

(5) Kenning is a feature of Anglo-Saxon poetry that compounds substitute words to foreground certain identities or concepts expressed as nouns. The substituted compound words convey the same meaning as the original noun but in a metaphoric imagery that elevates one feature to represent the whole (perhaps the precursor to synecdoche and metonymy).
One popular example of kenning (the compounding of two words to substitute for one important noun) is the metaphorical compound "whale-road" in Beowulf to substitute for "sea" or "ocean." The feature of whales, ocean inhabitants, is elevated to foreground the mystery and importance of the ocean: "until all of them had to obey him, / those lying about him across the whale-road,...."
(6) The elegiac theme in Anglo-Saxon poetry honors a hero who has faced tremendous odds. In the elegiac theme, the hero has a happy past that is thrown into stark contrast with the desolation of a horrific present. Think of Beowulf who has a glorious youth but faces Grendel in a desolate and horrific present. Or think of the Wander who, "accustomed as he is to joys," now finds himself alone, desolate and friendless, seeking someone who might wish to comfort him:

... deprived of my homeland,far from freeborn kindred, since years agoI concealed my gold-friend in the earth’s darkness,and went forth from there abjected,winter-anxious over the binding waves,hall-wretched, ... [seeking] who wishes to comfort a friendless me,... (The Wanderer)

(7) The dream vision theme is an Anglo-Saxon poetic feature that continued to be popular into the Middle English era and was used to great effect by Chaucer in poems like The Book of the Duchess.
The dream vision theme places the dreaming hero in a beautiful garden or garden-like location as a result of having fallen asleep during some psychologically disturbing unhappiness or turmoil. The dream vision theme attunes with the belief that some dreams connect the dreamer to supernatural wisdom or Providential intervention. A dream guide escorts the dreamer through allegorical situations but the process of explaining what the dream means is interrupted when the dreamer awakens, leaving a philosophical or spiritual mystery to be sorted out by dreamer and reader. The Anglo-Saxon dream vision poem The Dream of the Rood starts out with the dreamer dreaming:

What I wish to say of the best of dreams,what came to me in the middle of the nightafter the speech-bearers abode at rest! (1-3)
It seemed to me that I saw the greatest treeconducted to the sky, bewound in light,the brightest of beams. That beacon was entirely adorned with gold.

Although Chaucer's Middle English dream vision poetry is much later than Anglo-Saxon Old English dream visions, it serves to further illustrate the dreamer mechanism used in dream vision theme poetry. The following is from The Book of the Duchess and describes the dreamer falling asleep ["niste" is  contraction for "ne wist" or "knew not"; "swich" is "such"; "sweven" and "sweveninge" are "dream" and "dreaming"; "mette" is the verb "dream"; "trowe" is "believe"; "conne" is "know"; "rede" is "explain"; "hit yow" is "it you"]:

Right thus as I have told hit yow,    That sodeynly, I niste how,    Swich a lust anoon me took    To slepe, that right upon my book    I fil aslepe, and therwith even    Me mette so inly swete a sweven,    So wonderful, that never yit    I trowe no man hadde the wit    To conne wel my sweven rede;... (The Book of the Duchess) 

Middle English Dictionary extracts
Dr. Aaron K. Hostetter, Anglo-Saxon Narrative Poetry Project, Rugers
The Columbia Encyclopedia, available on encyclopedia.com
http://www.bbc.co.uk/history/ancient/anglo_saxons/saxons.shtml

https://hugohouse.org/how-to-write-your-own-anglo-saxon-poetry/

Why does Cole think the bear attacked him?

Angry, delinquent teen Cole Matthews is the main character in Ben Mikaelsen's novel Touching Spirit Bear. When Cole first arrives at the island he is supposed to spend a year on as a part of his contract with Circle Justice, Edwin tries to have a conversation with him about surviving on the island by himself. Cole brushes off the wisdom and advice he is given, telling Edwin that he's "not afraid of dying." When Edwin tells him about a "special black bear called the Spirit Bear," which is "pure white, and has dignity, pride, and honor," the following exchange happens:

"If I saw a Spirit Bear, I’d kill it," Cole said.
Edwin tightened his grip as if in warning. "Whatever you do to the animals, you do to yourself. Remember that."

The first time Cole sees the Spirit Bear, standing on the shoreline, he gets angry at the fact that the animal is staring at him "without any sign of fear." Once the bear disappears, he says, "I ever see you again, you're dead. I'll teach you to be afraid of me." Upon the bear's second appearance, Cole actually makes a spear to attack it with, but the creature disappears once again before he can make any sort of move towards it.
The third time the Spirit Bear appears, Cole goes to try and kill it. It's clear to the reader that this animal is not afraid of Cole, but Cole believes that because the bear is not moving or trying to attack him, it must be afraid. As soon as Cole makes a move to throw his spear, the bear viciously attacks him, clawing, biting, and breaking many bones with its strength. The Spirit Bear stands over Cole for what seems like "an eternity" and eventually walks away, leaving Cole alive but severely wounded.
As Cole lays on the ground, essentially unable to move, with seagulls picking at his torn flesh, he refers to the Spirit Bear as a "stupid bear that didn't have brains enough to run away." Because Cole is used to bullying and terrorizing people and having everyone be afraid of him, he cannot understand why the bear wasn't afraid of him. Cole thinks that the Spirit Bear attacked him because the creature was too dumb to understand that Cole should be feared.

Calculus of a Single Variable, Chapter 9, 9.1, Section 9.1, Problem 56

a_n=(-2/3)^n=(-1)^n(2/3)^n={(-(2/3)^n if n=2k-1),((2/3)^n if n=2k):}
This tells us that odd-numbered terms are negative, while even-numbered terms are positive. Since the terms alternate in sign, the sequence is alternating. In other words, the sequence is not monotonic.
All terms of the sequence are in [-2/3,4/9].
This is because -(2/3)^n< -(2/3)^(n+1), forall n in NN and lim_(n to infty)-(2/3)^n=0
Also, (2/3)^n>(2/3)^n, forall n in NN and lim_(n to infty)(2/3)^n=0
Clearly -2/3 is the smallest term of the sequence and 4/9 is the greatest.
Therefore, the sequence is bounded.
The image below shows the first 20 terms of the sequence. We can see that the sequence is also convergent even though it is not monotonical

What is the crux of her argument in,"Eating the other" and a critical analysis of the passage: Microsoft Word - Assignment Description Midterm Paper fem theory.docx Currently, the commodification of difference promotes paradigms of consumption wherein whatever difference the Other inhabits is eradicated, via exchange, by a consumer cannibalism that not only displaces the Other but denies the significance of that Other's history through a process of decontextualization. Like the "primitivism" Hal Foster maintains ''absorbs the primitive, in part via the concept of affinity" contemporary notions of "crossover" expand the parameters of cultural production to enable the voice of the non-white Other to be heard by a larger audience even as it denies the specificity of that voice, or as it recoups it for its own use (hooks 31).

This essay from bell hooks' book Black Looks: Race and Representation goes into great depth on a number of points, but the main point she makes is that people that fall under the category of "the Other" are considered by white people as something to be consumed. White people want the foods, music, and words of the Other—and to have sex with the Other—but will not un-Other the Other. As bell hooks puts it herself, 
"The commodification of Otherness has been so successful because it is offered as a new delight, more intense, more satisfying than normal ways of doing and feeling. Within commodity culture, ethnicity becomes spice, seasoning that can liven up the dull dish that is mainstream white culture."
She is essentially stating that white people do not want to have real human interactions or relationships with people they deem the Other. Instead, they want to consume them, in order to add a sense of "spice," "exoticness," or "experience" to their lives. 
In the specific passage you mention, bell hooks writes about commodification of the Other. For a specific example, a film, TV show, piece of theatre, or some other work of art may be marketed to the world as being something wonderful and new because it was created by a minority/person of color, who has given the medium new "spice," new insight with their voice. However, with straight white people in charge (as they often are), that voice is often changed and made less radical or less specific to a cultural narrative in order to pander to more white people. Difference of race is often promoted in order to sell something, but the difference that has been promoted is often erased so that the white people who supposedly wanted said difference will enjoy and consume it. In this sense, the Other and their voice have become a commodity for white people to use as they please.

What were the strategic factors, operational setting, and reviewed tactical situation of the Battle of Seven Pines/Fair Oaks Station?

The Battle of Seven Pines, also known as Fair Oaks, was the climax of Union Army of the Potomac commander George McClellan's famous Peninsula Campaign. McClellan's strategic vision was to use an amphibious movement to outflank the Confederate Army of Northern Virginia, Joseph Johnston commanding, and advance with a significant force on Richmond, the capitol of the Confederacy.
McClellan's advance was met with greater resistance than he had expected, and his pace was slowed enough that Johnston's force was able to effect a withdrawal from its advanced position near Washington to position itself to defend Richmond against the Army of the Potomac. Several tactical Union victories at Yorktown, Williamsburg, and Norfolk gave McClellan the confidence to continue the advance, albeit at a much slower pace than he had originally anticipated.
Johnston, knowing that he could not sustain a protracted siege if McClellan was to advance on Richmond, opted instead to go on the offensive, and he organized an assault on the Federal position at Seven Pines in Henrico County, Virginia.
McClellan's line was bifurcated by the Chickahominy River, as he expected reinforcements from Fredericksburg to the south, and at the opening of the battle, two of his corps were isolated on the southern bank of the river while the majority of his force was deployed to the north. Johnston opted to attack the two isolated corps on the Federal left, or southern, flank and turn the flank, leaving the northernmost three Federal corps to be pinned against the river and overwhelmed.
Johnston's plan was to divert McClellan's focus by engaging the three corps north of the river while allowing James Longstreet to coordinate the main action on the isolated two corps, commanded by General Erasmus Keyes on the left flank. The plan was confusing, and Johnston failed to effectively communicate his intentions to his corps commanders, Longstreet included. The result was a badly mismanaged and costly engagement.
Longstreet, by virtue of a wrong turn, ended up engaging the Federal left on a narrower front than the overall plan allowed for, and delaying the opening of the offensive by some 5 hours. Confederate General D.H. Hill became impatient and intiated the action without word from his superiors. Despite these early blunders, Hill was able to dislodge the Federals from their defensive line at Fair Oaks Station and force them to withdraw to a secondary position at the Seven Pines crossroads.
Longstreet reinforced Hill several hours later, and he renewed his assault on the Federal left, forcing another withdrawal.
As Longstreet renewed his assault, he send word to Johnston to join the attack. Johnston took several brigades from General William Whiting's division and attacked the right of Keyes' line. Keyes resisted, and were reinforced by Gen. John Sedgwick after a treacherous crossing of the last bridge over the Chickahominy. The other bridges had been burned by the Confederates, and heavy rains in the preceding days had caused the river to swell.
Sedgwick's division supported the defenders of Keyes' right, still at their positions near Fair Oaks Station.
The fighting that ensued was prolonged, desperate, and bloody. Joseph Johnston himself was wounded and taken to the rear, and the following day, as the Confederates renewed their assaults against now-reinforced Federal positions, President of the Confederacy, Jefferson Davis, appointed General Robert E. Lee to command the Army of Northern Virginia.
The continued Confederate attacks made no progress, and the Federals counterattacked in the late morning, forcing the battle-weary Confederates to retire from the field.
The fighting exacted a toll of roughly 5,000 Union and 6,000 Confederate casualties, and both sides claimed a victory. The Army of Northern Virginia withdrew to Richmond, and Lee reorganized to launch a counteroffensive against McClellan's stationary army. The Confederates launched a series of attacks known as the Seven Days Battles, which pushed the Federals off the Virginia Peninsula, back to the James River.
Richmond would not fall for three more years.
https://www.nps.gov/rich/index.htm

Does the US government today meet the democratic, social, and deliberative mandates developed at its inception?

Yes, and it meets them more today than it did at the founding of the government.  In 1787, America still had slaves.  Women could not vote.  There was a constant fight between Native Americans and whites over land use and ownership.  While it was not written into the Constitution, many states had property requirements one had to meet to vote or to run for public office.  The government of 2016 is much more democratic than the government of 1787.  Minorities can vote.  Young people who are over the age of eighteen can vote.  There are no property requirements to vote, and in many states you do not even need proof of identity.  Slavery has long since been abolished.  
The original government had little in the way of social responsibility.  The Founders believed that small government was ideal.  However, due to demographic changes and changes to the way Americans work, this changed.  The government has gotten involved in civil rights and workers' rights.  It is also involved in environmental protection and public education.  These additions to the federal government's responsibilities continue to adapt as people feel a need to get government involved.  While some critics of large government are wary of federal oversight, this is one of the consequences of living in a democracy--people vote to uphold their best interests.  

The U.S. Government does meet the democratic, social, and deliberative mandates developed at it's inception.  We cannot deny that even in it's inception, what we know to be government, was even then divided by those who sought justice and fairness for all, and those who wanted to quiet down the outcriers. 
Not much has changed today in that aspect.  What has changed, is the involvement of many other countries, and their influence on our decisions as a lawful country, sometimes taking away from our focus on independent growth as a unified Nation.  
With exponential population growth, we have seen amazing advancements in intelligence by humans, technology growth, and social demands. What started out as a way for the people to be heard in regards to the wants and needs of communities to work harmoniously, has turned into ways for people to get rich, manipulate, and abuse the communities they are "chosen" to protect. Which by any intelligent eye, can be seen as the easiest way to handle an enormous group of people who essentially cannot be "handled." 
 

How does Sandburg defend Chicago in the poem "Chicago"?

In 2011, Chrysler released their two-minute-long "Born of Fire" commercial during the Super Bowl. The following is the script.

Narrator: I got a question for you.
What does this city know about luxury, hm?
What does a town that’s been to hell and back know about the finer things in life?
Well I’ll tell you.
More than most.
You see, it’s the hottest fires that make the hardest steel.
Add hard work and conviction.
And a know how that runs generations deep in every last one of us.
That’s who we are.
That’s our story.
Now it’s probably not the one you’ve been reading in the papers.
The one being written by folks who have never even been here.
Don’t know what we’re capable of.
Because when it comes to luxury, it’s as much about where it’s from as who it’s for.
Now we’re from America—but this isn’t New York City, or the Windy City, or Sin City, and we’re certainly no one’s Emerald City.
Eminem : This is the motor city—and this is what we do.

The commercial was ranked as one of the top Super Bowl commercials of all time, and it is very similar to Sanburg's "Chicago" poem. Both the poem and the commercial are unapologetic about the rough sides of their respective cities. Sandburg doesn't even try to hide the fact that Chicago is full of corrupt behaviors and practices.

They tell me you are wicked and I believe them, for I have seen your painted women under the gas lamps luring the farm boys.
And they tell me you are crooked and I answer: Yes, it is true I have seen the gunman kill and go free to kill again.

But that is exactly Sandburg's point. Yes, Chicago has all kinds of rough edges, but it is those rough edges that make Chicago great. It is a city that doesn't posture and try to be something that it isn't. The city itself is strong because of the hard working, blue-collar people that live there. The city is made stronger because it has gone through rough patches, and it wasn't killed because of them. Chicago, like Eminem's Detroit, has been through the hottest fires and has been made harder and stronger because of that. Sandburg even goes so far as to insult other cities by calling them "soft."


Come and show me another city with lifted head singing so proud to be alive and coarse and strong and cunning.
Flinging magnetic curses amid the toil of piling job on job, here is a tall bold slugger set vivid against the little soft cities . . .

In the second stanza of "Chicago," Sandburg lists the insults that have been aimed at Chicago, including that it is wicked, crooked, and brutal. While he admits that these qualities are true of Chicago, he defends the city by saying that it is also vital, clever, and strong. He refers to Chicago as a "tall bold slugger set vivid against the little soft cities." It is a city that is constantly building and rebuilding, and it has the kind of liveliness and energy that the smaller cities around it don't have. The city is like a callow youth that laughs. As Sandburg writes, Chicago is "laughing even as an ignorant fighter laughs who has never lost a battle." It has a kind of brashness because the city is proud to offer so much to the rest of the country. As Sandburg writes, Chicago plays many roles, including those of "Hog Butcher, Tool Maker, Stacker of Wheat, Player with Railroads and Freight Handler to the Nation." So, while what people say to vilify the city might be true, Chicago is also a proud producer of many goods and services that the rest of the nation needs.

Based on Chapters 5-9 of Ian Haney López's Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class: In Chapter 8, what does the author say about common sense racism and cognitive response?

In his book Racism on Trial: The Chicano Fight for Justice, Haney Lopez defines common sense racism as "action arising out of racial common sense that furthers social hierarchy" (page 128). Common sense racism does not necessarily have the intention of doing harm, as overt racism does, but it still results in helping keep whites on top of the social hierarchy.
In his book Dog Whistle Politics, Haney Lopez writes that whites have some seemingly rational reasons to engage in common sense racism, but their belief is largely guided by "the delusion that that racial superiority will restore a mythical middle-class wonderland" (page 173). In other words, white working-class voters believe that their common sense racism will help restore their lost incomes and lost economic status. However, the reasons that whites support common sense racism runs deeper than that. As Lopez Haney writes, white working-class voters engage in commonsense racism, even if it overtly goes against their economic interests, because "what's economic and what's social cannot be neatly separated" (page 172). As the author explains, whites blame nonwhites for the economic hardships they have faced, and they use non-whites as a scapegoat for the larger economic forces that have caused recessions, job losses, declining opportunities, and shrinking savings. Common sense racism allows working-class whites to hold onto the myth that they will regain economic ground, and working class whites' cognitive response to the economic situation is not always rational.

Malcolm X is eventually sent to reform school because of his deliberate decision to wear a hat in his classroom. Do you agree with the teacher's handling of the situation?

In The Autobiography of Malcolm X, the author recounts his decision to wear a hat in the classroom of his school, a calculated act of defiance that results in his being exiled to a reform school. However, the wearing of the hat is only part of the cycle of events that gets Malcolm exiled, and the nature of the story, combined with both the details we have and the details that are denied us, makes it difficult to determine precisely whether Malcolm's teacher was justified in his decision to oust the student.
In the Autobiography, Malcolm makes it clear that his decision to wear the hat was a deliberate one. He confesses that he was acting in direct defiance of school policy and his teacher's orders. He also makes it plain through the remainder of the story that it is not the hat-wearing that is the principle reason for his expulsion. First of all, as punishment for his hat-wearing, Malcolm is forced by the teacher to walk around the classroom until he is told to stop, so, the teacher says, "'everyone can see you.'" While he is doing so, the teacher continues writing on the blackboard, and while his back is turned, Malcolm, on his round-the-room circuit, plants a tack on the teacher's chair. By the time the educator returns to his seat, Malcolm, still walking around the room, is far away from the "scene of the crime." The teacher sits on the tack, and Malcolm sees him "spraddling up" as he runs out of the room, implicating himself for the planting of the tack. Even then, it's not merely the tack-planting, or even the wearing of the hat, that gets Malcolm expelled. He admits that the decision, after this incident, to send him to the reform school was not surprising to him "with my deportment record." This clearly suggests that Malcolm's exile is not punishment for wearing a hat in class, or for planting a tack on the teacher's chair. It's the culmination of a long record of such incidents, done deliberately and with calculated desire to cause trouble, that causes the teacher to send Malcolm on his way.
However, it is difficult to be certain that the teacher's actions in the Autobiography are just due to several mitigating circumstances. First of all, this is a literary work that takes as one of its central themes the balance of injustice in the way black men are treated versus white men. Throughout the book, there are numerous instances of black men being punished all out of proportion to their crimes (both real and supposed) for reasons that have more to do with the color of their skin than with the content of their characters. This culminates in Malcolm, grown up, out of school, and living "like an animal" by robbing and stealing, being given a prison sentence for burglary that is far higher than that normally given for the crimes he committed. He speculates openly in the book that the stiff sentence was not in fact for the house robberies, but for the fact that he and his partner in crime were at the time engaged in sexual relationships with white women, which was indeed still illegal in numerous parts of the country. So the entire book generates an atmosphere in which black men suffer far fiercer consequences for their crimes than white men do, even if the crimes of the whites exceed those of their black counterparts.
Therefore, in order to determine whether or not the teacher's behavior was just, we would need to answer one question: what would happen to a white student in similar circumstances? Since we do not get to see a white student engaging in the same behavior and being disciplined for it, we cannot for certain say that the teacher is acting outside the bounds of classroom justice, or from motivations that are less than pure or in defiance of the rules his position sets forth for him. But by positioning this anecdote within a story steeped in disproportionate white-on-black punishment, it is strongly inferred that Malcolm's punishment outweighs the consequences a white student would have received for the same infractions. So, based purely on the evidence of the story itself, Malcolm's punishment may seem acceptable in some lights. But placed in the context of a world in which whites routinely mete out disproportionate judgment to blacks for the "crimes" they commit, one can only assume that Malcolm's punishment is based as much on his complexion as on his crime.
Of course, the Autobiography is a work of non-fiction, so Malcolm is commenting as much on the reality of white-on-black injustice in the real world as in the "story" he has chosen to tell. These situations do indeed find numerous common parallels in life today. It is also worth noting that Malcolm's statement that his expulsion and reformatory incarceration are based as much on his "deportment record" as on the hat-wearing and tack-planting also has contemporary parallels. The significant number of fatal shootings of unarmed black men by police officers has raised questions about the responses of the media, the police, and society as a whole. Recent shootings have provoked a number of attempts to find evidence of past crimes as a means to "justify" police use of deadly force. The suggestion would be that, just like Malcolm, Trayvon Martin and Michael Brown were punished for their "deportment records"—not the incidents that immediately preceded their deaths.
https://books.google.com/books?id=EtVfCgAAQBAJ&pg=PT34&lpg=PT34&dq=malcolm+x+hat+in+class&source=bl&ots=TvuVEJFHTh&sig=Mann0hV3PB7pbcKqK-mYDzJzo-Q&hl=en&sa=X&ved=0ahUKEwiC89Xg6P3PAhVo0FQKHV7hARAQ6AEIWjAO

London represents home to Clarissain in Mrs. Dalloway Explain ?

On a very fundamental level, London is home to Clarissa Dalloway because she lives there (and has lived there for quite some time when the book begins). However, London is home to Clarissa for more complex reasons. Indeed, the hustle and bustle of London is actually an integral part of Clarissa's identity. Early in the book, Woolf identifies the love Clarissa has for enjoying the present moment of her urban existence, and that in this exhilarating experience, "in the streets of London, on the ebb and flow of things, here, there, she survived" (9). This quote suggests that life in London sustains, at least in a symbolic sense, Clarissa's existence, allowing her to find vitality not only in the present, but in the future as well. The implication here is that London affords Clarissa a certain "immortality," with the activity of the busy city promising to preserve her memory long after she ceases to exist. Thus, though London is simply the place that Clarissa lives, it is her home because the city gives her the opportunity to self-actualize on a very complex level, finding a sense of metaphysical meaning in the ebb and flow of urban life.

In the poem "How It Is" by Maxine Kumin, explain the use of all metaphors, lexical deviations, grammatical deviations and semantic deviations found in the poem. How do these contribute to the meaning of the poem? What are examples of parallelism (lexical, sound, grammatical) found in the poem, and how do they affect the meaning of the poem? Is "they swell like wine bags" a semantic deviation?

Let's start with Kumin's deviations in language and grammar, which are numerous. I also think that we can talk about lexical and semantic deviations simultaneously. There is, after all, the field of lexical semantics, which deals specifically with the meanings of words and phrases in text.
To illustrate the feelings of the narrator in the wake of a loved one's death, Kumin upturns our traditional understanding of what words mean, what they ought to do, and how they ought to be organized. This reshuffling of language parallels the reorganization that occurs in life in the aftermath of a loved one's death.
The first example of semantic deviation occurs at the end of the first stanza: "My skin presses your old outline. / It is hot and dry inside." The narrator has reduced her old friend's jacket, the one she wears "a month after [her] death," to an "old outline." The reference to an outline is especially macabre, as we know that the police make chalk outlines of the deceased in homicide investigations. The narrator's loved one has also died an "unnatural death": a suicide resulting from "the death car idling in the garage." The narrator gives the outline a temperature and interiority: it is hot and dry inside.
Other examples of semantic deviation include the following: "praying hands unlaced" and "a ceremony of sandwich." Choosing the word "unlaced" instead of "folded" gives the friend's hands a limp and fragile quality. The "ceremony of sandwich" occurs on the last day of his or her life, giving something as mundane as the tuna sandwich he or she makes a mortal significance it would not otherwise have. Both phrases occur in a stanza that, grammatically, is a run-on sentence (grammatical deviation):
      I think of the last day of your life,
      old friend, how I would unwind it, paste   
      it together in a different collage,
      back from the death car idling in the garage,   
      back up the stairs, your praying hands unlaced,   
      reassembling the bits of bread and tuna fish   
      into a ceremony of sandwich,
      running the home movie backward to a space   
      we could be easy in, a kitchen place
      with vodka and ice, our words like living meat.
 
The last day of the friend's life is unwound like a piece of disassembled celluloid that, in reality, cannot be pieced together anywhere except for in the narrator's imagination. She pastes together "a different collage," one in which the friend is still alive, one in which they sit in a kitchen over cocktails, talking, their "words like living meat." The grammatical deviation, in the form of a run-on sentence, reflects the stream-of-consciousness state that allows the narrator to enter this scenario.
 
Simile is a more common use of figurative language in this poem than metaphor. I would encourage closer attention to those, particularly the one which ends this stanza: "words like living meat." Meat is, of course, the carcass of a dead animal, which makes the use of the modifier "living" a bit oxymoronic here. However, she imagines that, if her friend had lived, their conversation would be as textured and as nourishing as meat.
 
In the first stanza, the narrator says: "In my heart, a scatter like milkweed, a flinging from the pods of the soul." In this line, there is both simile and metaphor. The simile is "a scatter like milkweed." Reminders of the friend—the parking ticket and a hole in the pocket—resurrect a presence that is not physically there. Thus, her heart becomes fragile in response to the memory, as fragile as milkweed. The feeling is a "flinging"—this motion, which is sudden and violent, is both a lexical deviation and a metaphor in this context, as is the phrase "pods of the soul." "Pod" parallels "heart." A pod is an anatomical pouch from which a life form emerges. A heart, anatomically, resembles a pouch, and, figuratively, contains memories of our loved ones.
 
The line you cite, "They swell like wine bags," is an example of simile. This is preceded by an example of sound parallelism: "Dear friend, you have excited crowds with your example." The words "excited" and "example" sound similar, and both words stress the first syllable "ex," whose sound suggests, very subtly, 'X,' or the prefix 'ex-," which indicate elimination or the evocation of something taboo. Suicide remains a taboo in our culture.

What are some “markers” that indicate what is happening in part IX?

St. John of the Cross identifies three signs that signify a person is experiencing a dark night of the soul. At first glance, these share a striking similarity with modern signs and symptoms of clinical depression: lack of interest in things that formerly provided joy and/or comfort in one’s life, especially physical pleasure; the inability to concentrate on ordinary tasks of daily life or upon one’s spiritual endeavors; and a profound sense of disconnection from the everyday, and ultimately, from God. The dark night of the soul differs from depression, however, in that it comes directly from God, instead of being triggered from a traumatic event or biochemical imbalance. Therefore, it is not an affliction of body and mind, but a divine gift. Through divesting oneself of all previous attachments to the physical and material, one undergoes a purification, a preparatory stage that is necessary for transcending to a higher plane of consciousness and a deeper, more meaningful relationship with God.

How does American realist Kate Chopin depict upper-class marriage at the turn of the 19th century? What does she suggest about relationships between married men and women?

In "The Story of an Hour," Chopin portrays the role of servitude in upper-class marriages and the effect that has on a woman's soul. In the story, Louise Mallard is told that her husband has died, and her primary emotion is one of relief. Finally, there is no one else to serve. Finally, she no longer has to bend her will to her husband's desires instead of pursuing her own. She has played the role of a good wife for so many years, always taking care of her husband's needs. When she thinks she is finally released from this role, she feels light:

Her fancy was running riot along those days ahead of her. Spring days, and summer days, and all sorts of days that would be her own. She breathed a quick prayer that life might be long. It was only yesterday she had thought with a shudder that life might be long.

Chopin suggests that simply because women fill the roles required of them in marriage does not mean that they are happy doing so. Many times, this means giving up on dreams of their own. She also suggests that women forced into roles of servitude will lose their passion and even love for their husbands along the way. Louise Mallard reflects on these conflicting emotions, as well:

And yet she had loved him--sometimes. Often she had not. What did it matter! What could love, the unsolved mystery, count for in the face of this possession of self-assertion which she suddenly recognized as the strongest impulse of her being!

Louise Mallard sees a brief glimpse of opportunity to live in self-fulfillment instead of husband-fulfillment. Although she has served her role, she did so in obligation and not out of love; Chopin suggests that marriages which hope to persist in love should allow for the self-fulfillment of both parties and not place one partner in a role of servitude of the other.

Kate Chopin depicts upper class marriage at the turn of the 19th century as confining and largely loveless.  When Mrs. Mallard is told her husband dies, the impression given to the reader is that she is grief-stricken.

“She wept at once, with sudden, wild abandonment."

When she goes upstairs, however, she undergoes a change.  Suddenly, the reader realizes that on some level she is glad her husband has died. Mrs. Mallard feels free. 

“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."

This quotation shows that Mrs. Mallard feels oppressed in her marriage—as if a powerful will is bending hers.   Her realization that she will no longer have to live under her husband’s rule makes her feel free. 

“But she saw beyond that bitter moment a long procession of years to come that would belong to her absolutely. And she opened and spread her arms out to them in welcome." 

Mrs. Mallard reflects that her husband had always been loving toward her and that she had loved him—sometimes.

“And yet she had loved him—sometimes. Often she had not."

Chopin shows the reader the tradition of upper class arranged marriages of convenience.  Women had little choice and even less freedom.  Mrs. Mallard is overjoyed at the idea of freedom for the rest of her life, which she now hopes will be long. 

“It was only yesterday she had thought with a shudder that life might be long."

As a result, the shock of seeing him again kills her—a fact of which her husband is blissfully unaware. 
https://archive.vcu.edu/english/engweb/webtexts/hour/

What are the legacies of the American Revolution?

Some of the obvious points include the separation of powers, Bill of Rights, property rights, and limited government. However, the American Revolution was arguably the consecration of the principles of the Enlightenment by way of force. The Founding Fathers and the documents they created (Declaration of Independence, Bill of Rights, and Constitution) were products of the Enlightenment. Although the American Revolution was unique in forcing these issues to the forefront and putting them into effect through revolutionary means, the issues themselves were not unique to the American colonies, but were well established as ideals that had not been achieved.
But the real legacy of the American Revolution can be seen in the effect it had throughout the Americas and broader world. In North and South America, the American Revolution served as a model of independence. Likewise, the former colonies of Africa and Asia also looked on the American Revolution and its ideals as a model during decolonization. What's more, countless constitutions around the world have been modeled after the US Constitution. The Revolution's legacy therefore is probably seen best in the way it inspired other nations to build liberal, democratic governments.

int xarcsec(x^2+1) dx Use integration tables to find the indefinite integral.

Indefinite integral are written in the form of int f(x) dx = F(x) +C
 where: f(x) as the integrand
           F(x) as the anti-derivative function 
           C  as the arbitrary constant known as constant of integration
For the given problem int xarcsec(x^2+1) dx, it has a integrand in a form of  inverse secant function. The integral resembles one of the formulas from the integration as :  int arcsec (u/a)du = u*arcsin(u/a) +-aln(u+sqrt(u^2-a^2))+C .
where we use: (+)  if 0ltarcsec (u/a)ltpi/2
                    (-) if pi/2ltarcsec(u/a)ltpi
Selecting the sign between (+) and (-) will be crucial when solving for definite integral with given boundary values [a,b] .
 For easier comparison, we may apply u-substitution by letting:
u =x^2+1 then du = 2x dx or (du)/2
Plug-in the values int xarcsec(x^2+1) dx , we get:
int xarcsec(x^2+1) dx=int arcsec(x^2+1) * xdx
                                        = int arcsec(u) * (du)/2
Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int arcsec(u) * (du)/2= 1/2int arcsec(u) du
                         or 1/2 int arcsec(u/1) du
Applying the aforementioned formula from the integration table, we get:
1/2 int arcsec(u/1) du=1/2 *[u*arcsin(u/1) +-1ln(u+sqrt(u^2-1^2))]+C
                                =1/2 *[u*arcsin(u) +-ln(u+sqrt(u^2-1))]+C
                                =(u*arcsin(u))/2 +-(ln(u+sqrt(u^2-1)))/2+C
Plug-in u =x^2+1 on (u*arcsin(u))/2 +-(ln(u+sqrt(u^2-1)))/2+C , we get the indefinite integral as:
int xarcsec(x^2+1) dx=((x^2+1)*arcsin(x^2+1))/2 +-(ln(x^2+1+sqrt((x^2+1)^2-1)))/2+C
=(x^2arcsin(x^2+1))/2+arcsin(x^2+1)/2 +-ln(x^2+1+sqrt(x^4+2x^2))/2+C
=(x^2arcsin(x^2+1))/2+arcsin(x^2+1)/2 +-ln(x^2+1+sqrt(x^2(x^2+2)))/2+C
=(x^2arcsin(x^2+1))/2+arcsin(x^2+1)/2 +-ln(x^2+1+|x|sqrt(x^2+2))/2+C
 
 

How is Frankenstein an amalgam of Enlightenment and Romantic philosophies?

One way in which the novel blends and comments on Enlightenment and Romantic philosophies is through its characters. Initially, Victor is very much aligned with the Enlightenment while his childhood friends, Elizabeth Lavenza and Henry Clerval, are much more associated with Romanticism. Victor is interested in discovery, with learning about the natural world and how it works. As a child, Henry writes his own fairy tale and is interested in fictional tales of knights and chivalry while Elizabeth prefers to create her own worlds and stories. Both Henry and Elizabeth are more passionate, but their passions are more short-lived; Victor doesn't burn with same emotion, but his ambitions are of longer duration. When Victor goes to Ingolstadt and turns his attentions toward the creation of a human being, his interest in discovery and experimentation (and personal glory) outstrips even his human nature which he claims "turns with loathing" from his activities (stealing body parts and dissecting creatures). In other words, Victor's association with the Enlightenment and obsession with scientific discovery far outweigh any emotional concerns, relationships, or even professional ethics, and Mary Shelley seems to imply that this sort of science, science without forethought, can be dangerous.
The creature, with whom we seem meant to sympathize (at least, at times), is born a tabula rasa (a blank slate): we seem him testing out his senses, learning to distinguish between them, developing an understanding of his emotions, reveling in nature's sublimity, and developing a moral code of his own (helping the DeLacy family, sympathizing with their sufferings, and so forth). His beginning as a blank slate seems to indicate that Shelley doesn't condemn Enlightenment ideas out of hand (as John Locke, the philosopher who coined the term, was of this movement); she seems to convey that our emotions and logic are of equal importance to our humanity and that, as we see from Victor, if a person's drive for discovery strips them of everything else, it becomes destructive. On the other hand, when the creature allows himself to become totally driven by his emotions, he also becomes destructive and unsympathetic in his maliciousness. Shelley seems to claim that a balance of humanity's emotions and intellect is best: one should not take precedence over the other, and it is to our and humanity's detriment if one does.
Captain Walton, however, seems to be associated with both Enlightenment (his quest to discover the secret of the compass and find the Northwest Passage at, perhaps the cost of his own life) and Romantic values (as a child, he wanted to become a poet, he is affected by nature, and his most significant desire is companionship -- a need he associates with the heart). Hearing Victor's story eventually compels him to give up his quest for discovery (unlike Victor) and protect the lives of his men. He exercises forethought and places the well-being of others before his own desire for personal glory. Though he is deeply frustrated and disappointed, he allows his heart to check his head -- his Enlightened ambitions do not run away with him.

In Shoeless Joe, who is the antagonist and who is the protagonist? Why?

Shoeless Joe was actually the basis for one of the most popular baseball movies of all time: Field of Dreams. The story is about a man who hears a voice telling him to build a baseball field in the middle of his corn field. He does this, and the field becomes a place where legendary baseball players, including (eventually) his hero, Shoeless Joe Jackson, come to play.
The protagonist in this story is the narrator, Ray Kinsella, the owner of the farm who is "touched by the land." He hears the voice that tells him to build the baseball field, and he sets the entire story in motion. He is responsible for the action in the story and is thus the protagonist.
It could also be argued that the fictionalized version of author J. D. Salinger is a secondary protagonist, as he helps Ray in his mission. Specifically, he helps him track down a player named Moonlight Graham.
The antagonist in the story is Mark, Ray's brother-in-law. He is the one who opposes Ray's dream at every turn: he wants to shut down all the baseball field nonsense (he cannot see the ghosts of the players on the field like the others can, because he doesn't believe in them) and modernize the farm so that it will bring in more money. The fact that he is the opposing force to Ray's protagonist makes him the antagonist.

What are the language techniques used in the poem “Afternoons” by Philip Larkin?

In "Afternoons," Philip Larkin uses a poem in three stanzas to describe the inevitable degeneration of youth into early middle age as couples have children, who will "push them / to the side of their own lives." The poem is written in blank verse, without rhyme, but its rhythm is regular, lending the poem cohesion and enforcing the sense of life's monotony Larkin is conveying.
Larkin's language choices both set the scene and emphasize his theme of emptiness. An "estateful" of washing awaits the women who were once young lovers: the quantifier indicates that the people described are living on a council estate, one of many new developments that grew up in the UK after World War II to house the working class, many of whose old neighborhoods had been lost to bombings. The men are "in skilled trades," such as carpentry and plumbing. Larkin sets this description in juxtaposition to the fact that the albums labeled "Our Wedding" are now gathering dust on top of televisions. The "skilled trades" comes first, the men's lives as lovers behind them.
Now, the "hollows of afternoons" are for collecting children from school, the couples' identities lost to parenthood as "the wind ruins their courting-places." The summer of their lives "is fading." Larkin repeats the motif of weather to highlight the movement of life towards its autumn, symbolized by the leaves falling "in ones or twos" by the recreation ground. At the end of the poem, the children are intent on finding "unripe acorns," which we may infer symbolize the beginning of other lives which will progress in the same fashion as their parents' did.

What is the connection between Mrs. Dalloway and The Hours? How does Michael Cunnningham use characters, ideas, and themes from Virginia Woolf's Mrs. Dalloway to create his contemporary novel?

Michael Cunningham superimposes certain characters from Virginia Woolf's Mrs. Dalloway into The Hours. For example, Cunningham's Clarissa Vaughn is essentially Virginia Woolf's Clarissa Dalloway. In the beginning of their respective stories, both women are preparing to host parties.
Clarissa Vaughn is hosting a party to honor her poet/writer friend, Richard, who is dying from AIDS. She goes flower shopping, and so does Virginia Woolf's Clarissa Dalloway. Both women happen upon old friends during or after running their respective errands. Cunningham's Clarissa Vaughn bumps into Walter Hardy during her excursion, while Woolf's Clarissa Dalloway is surprised by her old suitor, Peter Walsh, when she returns home.
Like Richard in The Hours, Walter Hardy is a writer and a homosexual; unlike Richard, however, Walter is not suffering from AIDS. Instead, his partner, Evan, is the one grappling with the prospect of dying from AIDS. Here, we can see that Cunningham has utilized similar types of characters to highlight Woolf's themes of mortality, homosexuality, and disillusionment in his own novel. Woolf's Clarissa Dalloway is unhappily married to Richard Dalloway, while Cunningham's Clarissa Vaughn is equally disillusioned about life with her live-in lover, Sally. Both women wonder if alternate choices could have given them greater happiness in life.
Cunningham also highlights Woolf's theme of mortality and death by exploring the idea of suicide in his novel.  In Woolf's novel, Septimus (a World War One veteran) suffers from depression; he is numbed by his battle experience, and memories of war atrocities have destroyed his faith in human nature. Septimus lives with his wife, Lucrezia, but contemplates suicide daily. His psychiatrist, Sir William Bradshaw, believes that he will be better served in a mental institution. However, Septimus cannot contemplate such a dehumanizing existence and eventually jumps to his death.
Similarly, Clarissa Vaughn's friend, Richard, jumps to a desperate death because he cannot reconcile his physical suffering with his will to live. Septimus and Richard are victims of life; both decide that suicide is preferable to a slow, agonizing death. Thus, in deciding the time and context of their deaths, both men believe that they have retained some semblance of control over their respective fates. Cunningham also explores the theme of disillusionment through the character of Laura Brown. Laura is married to her World War Two veteran husband, Dan (there's that war motif again-it helps us explore the themes of disillusionment and emotional paralysis in Cunningham's novel). Laura and Dan live a superficially normal existence, but Laura is privately unhappy.
She feels constrained by her responsibilities to her husband and son. Similarly, Cunningham's Virginia Woolf and Clarissa Vaughn experience frequent bouts of doubt and disillusionment. From these examples, we can see how Cunningham used characters, ideas, and themes from Virginia Woolf's Mrs.Dalloway to create his unique, contemporary novel. 
 
 

What are some examples of foreshadowing in the story "Charles"?

Shirley Jackson's classic short story "Charles" first appeared in Mademoiselle in 1948 and contains many examples of foreshadowing. 
The story is told in the first person point of view of the mother of a boy named Laurie, who is just beginning kindergarten. Laurie comes home from kindergarten every day with stories of the awful things his classmate, Charles, has done. His parents are appalled by the influence of Charles and worry that it will affect Laurie negatively. The irony is that at the end of the story, Laurie's parents discover there is no boy named Charles in Laurie's kindergarten class. A close look at the foreshadowing in this story reveals that Charles was invented by Laurie as a scapegoat for his own heinous actions.
The first example of foreshadowing is the manner in which Laurie returns from his first day of kindergarten. Jackson describes the scene when Laurie comes home from his first day of kindergarten, slams the door, throws his cap on the floor, and shouts "Isn't anybody here?" Laurie proceeds to speak rudely to his father and spill his sister's milk. This suggests that Laurie has changed from the sweet preschooler his mother describes in the first paragraph.
The next example of foreshadowing is when Laurie, after telling the story of Charles' spanking, slides off his chair, takes a cookie and walks off when his father is still talking to him.  
Another example of foreshadowing occurs when Laurie comes home with another story about Charles and tell his father: "Look up....look down, look at my thumb, gee you're dumb." He then laughs "insanely." 
After this, Laurie once again comes home with a story about Charles and says to his father "Hi, Pop, y'old dust mop." By this time, Laurie's parents are so involved in the stories about Charles they appear not to notice the insolent behavior of their son. 
When the mother describes a confusing positive change in Charles' behavior, the father tells her to wait and see if there is really a change, saying "When you've got a Charles to deal with, this may mean he's only plotting." This foreshadows the pinnacle of Charles' deviant behavior, who tells a girl to say a naughty word, and a few days later, says the naughty word in class himself.  

How does Edwards use repetition at the end to heighten the effect of his sermon?

Near the end of his sermon, Edwards says,

And now you have an extraordinary opportunity, a day wherein Christ has thrown the door of mercy wide open, and stands in calling and crying with a loud voice to poor sinners; a day wherein many are flocking to him, and pressing into the kingdom of God. Many are daily coming from the east, west, north and south; many that were very lately in the same miserable condition that you are in, are now in a happy state, with their hearts filled with love to him who has loved them, and washed them from their sins in his own blood, and rejoicing in hope of the glory of God. How awful is it to be left behind at such a day! To see so many others feasting, while you are pining and perishing! To see so many rejoicing and singing for joy of heart, while you have cause to mourn for sorrow of heart, and howl for vexation of spirit! How can you rest one moment in such a condition? Are not your souls as precious as the souls of the people at Suffield, where they are flocking from day to day to Christ? (all emphases are mine)

He repeats the phrase "a day wherein" twice near the beginning of this excerpt, as though to emphasize the tremendous import of this day, this day when his listeners have the opportunity to join with Christ, and to imply that there may not be another such day for them to make this choice.
The words "daily" and "day" are repeated several more times throughout the paragraph, presumably in order to draw attention to the passage of time and the wasting of one's chances with each day that passes: he says, in other words, days keep passing and other people keep taking Jesus up on this deal, and yet YOU still have not. How many more days will YOU let go by, while others flock to him, and you remain distant and apart? How many more chances do you think you will get?
Edwards then repeats certain phrases and even uses parallel sentence structures to emphasize the fact that these others will be feasting and rejoicing while YOU are yearning and wishing and howling because you will have missed your chance—unlike these other happy believers.

In the discipline of rhetoric, repetition and restatement are staples, and Jonathan Edwards makes great use of both in this iconic sermon from 1741. Accomplished orators and students of rhetoric understand that the first and last things a speaker says are usually what stay with an audience; this phenomenon is known to educators as "primacy" and "recency."
Edwards's thesis was, of course, that sinners who did not act quickly to reform themselves faced an agonizing afterlife in the fires of hell, where God's wrath would hurl them for their impiousness. 
In the last paragraph of the sermon, Edwards use the word "fly" twice to describe what sinners must do: escape God's wrath and (metaphorically) leave Sodom.  He uses the words "every one" twice to emphasize that no one in the congregation should feel complacent about their salvation.  And lastly, Edwards uses the word "wrath" twice to hammer his point home: God is angry with all sinners.
 
 

What were some challenges for Thomas Jefferson while he was writing the Declaration of Independence?

Jefferson had to deal both with the contradictions within his own life and thought, as well as with the possible objections by much of Congress either to his saying too much on "sensitive" topics or not saying enough.
As is well known, his initial draft included a paragraph criticizing the King for allowing the slave trade to continue. This, as Jefferson later indicated, was not acceptable to those members of Congress who themselves held enslaved people. But Jefferson himself, of course, was a practitioner of slavery. My guess is that he must have realized, at least on a subconscious level, that it was hypocritical for him to blame the King for the continuance of either the slave trade or the institution of slavery itself. The only allusion to slavery in the final version of the Declaration is a euphemistic one, saying of the King that "he has incited domestic insurrections among us." This refers to the sporadic recruiting by the British of enslaved people as troops with the promise of freedom to them. One also must ask if Jefferson might have struggled inwardly over the clause concerning the indigenous Americans in which they are described as "merciless savages." Jefferson was an admirer in general of the spirit and character of Native Americans, as he expressed in other writings.
A second major issue, though this has received less attention by commentators over the years, involves religion. Jefferson and many others in Congress were deists, rejecting not only organized religion but also, for the most part, the belief that God actively influences human affairs. Interestingly, however, Jefferson's original version stated, "We hold these truths to be sacred and inviolable: that all men are created equal." Most scholars believe that when Franklin and Adams made their preliminary review of the draft, it was Franklin who amended "sacred and inviolable" to "self-evident." Though there is not necessarily anything "spiritual" or based on religious belief in the use of the word "sacred" in this context, Franklin's word choice is more purely secular and "human." It is also more eloquent.
It was when Congress as a whole reviewed the draft that more extensive changes were made. Jefferson had already written that men "are endowed by their Creator with certain inalienable rights," but Congress made additional references to God which, in my opinion, actually improved the document. The phrases "appealing to the Supreme Judge of the world for the rectitude of our intentions" and "with a firm reliance on Divine Providence" lend a gravity to passages which in Jefferson's original seem more lightweight and dry.

In Fahrenheit 451, what does Beatty criticize about schools, universities,and printed material? To what extent are these criticisms true for today’s world?

Captain Beatty is the head "fireman" in Ray Bradbury's classic sci-fi novel Fahrenheit 451. He is a contradiction. Paradoxically, as a result of his job he's actually read quite a few books and memorized many passages, and yet at the same time he doesn't see the value in the knowledge produced through the written word.
Beatty's view is that schools and universities create too many differences between people, and that the talented student brings about jealousy and hatred from others. He doesn't see the value of education and reading because he believes it doesn't make anybody happier. In fact, all it does is confuse people. Books are either fictions about people who never existed and things that never happened, or they are contradictory and lack consensus, leading to debate, difference, and disorder. Besides this, he argues that most people stopped reading long before the fireman started burning books.
Beatty's view is ultimately very dogmatic and totalitarian. He sees order as more important than ideas. While some of his criticisms may have merit and books and ideas can create tremendous confusion and difference of opinion, this is not a bad thing. In fact it's of the essence of democracy and the human experience.

Single Variable Calculus, Chapter 7, 7.4-2, Section 7.4-2, Problem 42

Differentiate $y = (\ln x)^{\cos x}$


$
\begin{equation}
\begin{aligned}

\ln y =& \ln (\ln x)^{\cos x}
\\
\\
\ln y =& \cos x \ln (\ln x)
\\
\\
\frac{d}{dx} \ln y =& \frac{d}{dx} [\cos x \ln (\ln x)]
\\
\\
\frac{1}{y} \frac{dy}{dx} =& \cos x \frac{d}{dx} \ln (\ln x) + \ln (\ln x) \frac{d}{dx} (\cos x)
\\
\\
\frac{1}{y} y' =& \cos x \cdot \frac{1}{\ln x} \frac{d}{dx} (\ln x) + \ln (\ln x) (-\sin x)
\\
\\
\frac{y'}{y} =& \frac{\cos x}{\ln x} \cdot \frac{1}{x} - \sin x \ln (\ln x)
\\
\\
y' =& y \left( \frac{\cos x}{x \ln x} - \sin x \ln (\ln x) \right)
\\
\\
y' =& (\ln x)^{\cos x} \left[ \frac{\cos x}{x \ln x} - \sin x \ln (\ln x) \right]



\end{aligned}
\end{equation}
$

Precalculus, Chapter 5, 5.5, Section 5.5, Problem 8

sin(2x)sin(x)=cos(x) ,0<=x<=2pi
sin(2x)sin(x)-cos(x)=0
=2sin(x)cos(x)sin(x)-cos(x)=0
=cos(x)(2sin^2(x)-1)=0
=cos(x)(sqrt(2)sin(x)-1)(sqrt(2)sin(x)+1)=0
solving each part separately,
cos(x)=0 , (sqrt(2)sin(x)-1)=0 , (sqrt(2)sin(x)+1)=0
General solutions for cos(x)=0 are,
x=pi/2+2pin , x=(3pi)/2+2pin
solutions for the range 0<=x<=2pi are,
x=pi/2 , x=(3pi/2)
(sqrt(2)sin(x)-1)=0
sin(x)=1/sqrt(2)
General solutions are,
x=pi/4+2pin , x=(3pi)/4+2pin
solutions for the range 0<=x<=2pi are,
x=pi/4 , x=(3pi)/4
sqrt(2)sin(x)+1=0
sin(x)=-1/sqrt(2)
General solutions are,
x=(5pi)/4+2pin, x=(7pi)/4+2pin
solutions for the range 0<=x<=2pi are,
x=(5pi)/4 , x=(7pi)/4
Combine all the solutions,
x=pi/2 ,x=(3pi)/2 , x=pi/4 , x=(3pi)/4 , x=(5pi/4) , x=(7pi)/4

What did Alexander Hamilton fear?

Alexander Hamilton was concerned that America would not develop as a modern, industrialized economy. He felt that if the United States retained a system of government in which ultimate sovereignty resided with the states, then the country as a whole would not progress economically.
If the United States was to take its place in the world economy, Hamilton thought, it needed to have the requisite institutional framework in place, such as a strong central government and a federal banking system. The latter was especially crucial for Hamilton's vision, as it would oil the wheels of commerce, proving loans to help businesses get started. A federal banking system would also enable the United States to pay off the enormous debts it had accrued during the Revolutionary War. This would show that the new Republic could be taken seriously as an economic power. Paying off the national debt would also enhance America's credibility as a country with which to do business.

One of Alexander Hamilton’s biggest fears was having a weak federal government. He saw the struggles that the federal government had with the plan of government that was created by the Articles of Confederation. He knew it was hard for the federal government to raise money and to pay its debts because the federal government couldn’t levy taxes. He knew the financial stability of the country suffered, because there was no national banking system. As a result, states printed money, which caused inflation. He also was concerned about the federal government’s ability to protect and defend itself because the federal government couldn’t require people to join the military. This is partially why the federal government was unable to deal with aggressive actions toward the United States by Spain and Great Britain.
Alexander Hamilton feared the new federal government created by the Constitution might not have enough power to resolve these issues. This is why Alexander Hamilton and the Federalists wanted to create a strong federal government when the Constitution was being written.
https://www.encyclopedia.com/people/history/us-history-biographies/alexander-hamilton

What are the factors that encourage land pollution?

Land pollution is the long term damage, degradation or destruction of the soil and the surface of the earth by the direct or indirect activities of human beings.
Several factors encourage the activities resulting in land pollution. Waste generation is an inevitable end product of several human activities. An unwanted consequence of urbanization is the generation of huge amounts of garbage and industrial waste from factories, offices, homes, schools and hospitals. In spite of the utilization of sophisticated waste processing plants, unrecyclable items still end up in landfills, increasing the degree of land pollution.
An increase in demand for food and shelter to meet the needs of a growing population leads to the generation of more waste. Over-intensive agriculture through the use of agricultural pesticides and fertilizers lead to soil contamination and poisoning.
Mining activities and crude oil extraction for economic gains lead to oil spillage and contamination of arable land by toxic chemicals causing land pollution. Nuclear waste produced by energy generating nuclear plants are buried beneath the earth, but the harmful effects of radioactive material to the soil and other living things above it cannot be entirely eliminated.
https://www.explainthatstuff.com/land-pollution.html

College Algebra, Exercise P, Exercise P.4, Section Exercise P.4, Problem 92

Simplify $\left( 1.062 \times 10^{24} \right) \left( 8.61 \times 10^{19} \right)$ using scientific notation, the laws of exponents, and a calculator.

$
\begin{equation}
\begin{aligned}
\left( 1.062 \times 10^{24} \right) \left( 8.61 \times 10^{19} \right) &= (1.062)(8.61) \times 10^{24+19}\\
\\
&= 9.14382 \times 10^{43}
\end{aligned}
\end{equation}
$

I do not understand what this question means: "Explain what most readers surmise Alexie proposes by juxtaposing Victor and Thomas."

Most readers surmise from the way in which Alexie juxtaposes Victor and Thomas that Victor and Thomas are two halves of the same whole and represent what the other needs. In helping Victor get to Phoenix to make arrangements for Victor's father's funeral, Thomas is literally the means by which Victor can do what he needs to do and achieve closure after his father's death. Thomas pays for the trip to Phoenix, and Victor, after claiming his father's savings account, pays for the trip home, symbolizing the way in which they are two halves of a whole.
In addition, Thomas provides the dreams and stories that Victor, a less spiritual soul, needs. For example, when Victor is young, Thomas tells him the story of a modern-day Indian warrior who steals a car and delivers it to the police station. Victor says, "That's a good one. I wish I could be a warrior." Thomas's stories inspire Victor. Later, Thomas says of himself:

"I have no brothers or sisters. I have only my stories which came to me before I even had the words to speak. I learned a thousand stories before I took my first thousand steps. They are all I have. It's all I can do."

Now that Victor has lost his father, he will also need these stories for sustenance, and he needs Thomas for spiritual guidance.
Later, Thomas tells Victor a story about Victor's father. Thomas had gone to Spokane to wait for a vision when Victor's father appeared and told him to go home before he got mugged. Thomas says, "Your dad was my vision. Take care of each other is what my dreams were saying. Take care of each other." By telling this story, Thomas reminds Victor about the caring parts of Victor's father, which Victor needs to hear. The story is about the importance of people looking out for each other, which is what Thomas does for Victor. At the end of the story, Victor gives Thomas half his father's body, as they share memories of Victor's father. When he gets home, Victor "heard a new story come to him in the silence afterwards." In other words, Victor has been inspired by Thomas to hear stories and think about life in more spiritual terms. The realist and the idealist have become one.