Who is the most important character in "The Canterville Ghost" and why?

This is an opinion question, so feel free to state any character from the story.  The important part is adequately defending your answer.  The explanation for your choice should be more in depth than a single reason.  
For example, I could claim that the most important character is Lord Canterville. He is the most important character because he sold the haunted house to the Otis family.  If he didn't sell the house, there wouldn't be a story.  That's the only reason I can come up with though, so Lord Canterville is probably not a good choice.  
I would go with Virginia or Sir Simon for the most important character.  If I was forced to choose between the two, I would go with Sir Simon.  He gets more page time, so he is an easier choice to defend because there's more information to use.  Additionally, he is a deeper and more dynamic character than Virginia.  Virginia is super important because without her Sir Simon is still forever doomed to haunt the mansion, but Virginia doesn't quite shape events of the story as powerfully as the ghost.  If Sir Simon wasn't in the story, Virginia's help wouldn't be necessary anyway.  Sir Simon propels the story forward as he tries to antagonize just about everybody in the house, and he fails every single time.  We see him go through a range of emotions during that time too.  We see him angry, scared, and sad.  Readers really get to know Sir Simon, his motivations, and his emotions.  Virginia, on the other hand, stays a mystery.  Even her own husband can't get her to explain how she helped the ghost.  Sir Simon is definitely the character that I feel is most important to the story. 

In The Sympathizer, a) Nguyen's unnamed narrator is, in many ways, a complex example of how all of us navigate statuses that constantly change. How do the experiences of the narrator reveal his fluctuating insider/outsider statuses? b) Explain how the narrator can make the claim that nonwhite immigrants and refugees to the United States know white people better than they know themselves (see Nguyen 2015, page 258). Is this something anthropologists would agree with? Why?

a) The narrator's experience as a double agent definitely reveals his fluctuating outsider/ insider status. In the novel, the unnamed narrator (referred to as the Captain) is a South Vietnamese general's most trusted aide; he's also a North Vietnamese communist mole, and he has been assigned to spy on the general.
The narrator negotiates his double role with finesse, objectivity, and discretion. He exhibits compassion for both the North Vietnamese position and the South Vietnamese one. Even as he reports tidbits of information to his handler, Man, the Captain finds himself sympathizing with the South Vietnamese people. He realizes that no South Vietnamese citizen ever asked to be brutalized in his own country by his Northern cousins. In short order, he must also finalize transportation logistics for the general and a small group of patriots who wish to flee the country. The captain works with Claude, the general's CIA liaison in South Vietnam.
In the novel, we can see that the Captain must negotiate the complexities of his relationship with the South Vietnamese general, Claude, and Man with a certain amount of detachment. He relates how precarious his double life is: in order to keep from blowing his spy cover, he ends up condemning a fellow communist agent to an indefinite period of torture and incarceration. Later, he must assassinate a college acquaintance, Sonny, on the general's orders. In his position of duality, he cannot afford the privilege of grief or emotional catharsis. Even as he decides who the general's ninety-two fellow passengers will be on the flight out of South Vietnam, the Captain must ignore the dictates of his conscience and perform his task with detached precision.
In the story, the Captain is both an insider and an outsider. He has two "faces." As an outsider, he must repress his reservations about the war in order to function credibly in his role as a South Vietnamese/ American ally. Simultaneously, he must ignore his personal inclinations as a Vietnamese citizen in order to obey the dictates of his communist loyalties. He is both an insider and outsider in his own country. Of his two blood brothers, one is a communist (Man), while the other (Bon) is a patriot. He must protect Bon without arousing Man's suspicion about his motives. Both the Captain and Man resort to subterfuge to deceive Bon about their communist loyalties.
Later, the Captain is ordered by the general and his communist handlers to accept a consultant role on a movie project. Although he is faced with conflicting interests, the Captain remains focused on his ultimate goal. The movie is a Hollywood production about the Vietnam War, and the Captain hopes to influence how the filmmaker portrays the war. He is disappointed when he discovers that the filmmaker has little interest in telling the Vietnamese side of the story. When pressed, the filmmaker consents to three speaking parts for Vietnamese actors; sadly, he uses Filipino actors for those parts. For his part, the Captain is constrained by his need to keep his cover, so he has few options in terms of making substantive changes. Through this distressing experience, the author shows how the Captain must consistently vacillate between his insider and outsider status in order to retain his sanity and survive in mutually exclusive environments.
b) The narrator feels that he can make the claim because he has been on both sides of the equation. As both an insider and outsider, the narrator feels that he approaches the matter from a more objective vantage point. He sees Vietnamese history through the lens of impartiality, and sees the civil war in his country as a conflict between two opposing forces that often entertain ambivalent goals. These are the same forces that rage in every human soul, and as an immigrant, the narrator feels that he recognizes this on a more intrinsic level than the typical westerner.

Our country itself was cursed, bastardized, partitioned into north and south, and if it could be said of us that we chose division and death in our uncivil war, that was also only partially true. We had not chosen to be debased by the French, to be divided by them into an unholy trinity of north, center, and south, and to be turned over to the great powers of capitalism and communism for a further bisection, then given roles as the clashing armies of a Cold War chess match played in air-conditioned rooms by white men wearing suits and lies.

As for whether anthropologists agree with the narrator's claim, you might be interested to know what many anthropologists conclude about race. I suggests reading Newsweek's article "There Is No Such Thing As Race." The anthropologists conclude there "is no inherent relationship between intelligence, law-abidingness, or economic practices and race, just as there is no relationship between nose size, height, blood group, or skin color and any set of complex human behaviors." So, when the narrator asserts that non-white peoples know white people better than themselves, he is really reiterating the anthropologists' claim: we are more alike than we realize.

How are the protagonists similar and different in When the Sleeper Wakes and 1984? Examine the view that idealized figures are used as mechanisms of control in dystopian societies.

Winston (1984) and Graham (When The Sleeper Wakes) are both idealized figures in the respective novels.
Both men are avowed revolutionaries, and both rebel because of their conscientious natures. Both are also drawn to treacherous men who betray them. Additionally, Winston and Graham experience individual epiphanies that alert them to the dangers that surround them. Graham awakes from more than two centuries of a "cataleptic trance" to face the fight of his life. Similarly, Winston comes to realize that Big Brother is malevolent in nature and that he must be defeated.
On the surface, Winston appears to be a confirmed loyalist, but internally, he is a rebel. Graham differs here slightly in the sense that he leads an open revolt against the Council (albeit in a confused state of mind) and later, against Ostrog himself. In Winston's case, however, he consistently cherishes a pessimistic view of the rebel effort. By the time the novel begins, Winston is in a state of full-blown paranoia, sequestering himself at regular intervals in order to scribble "DOWN WITH BIG BROTHER" into his diary. His paranoia is a debilitating influence; he feels that, no matter what he does, the "Thought police would get him just the same."
On the other hand, Graham firmly and unequivocally stands his ground in the rebel fight. Both Winston and Graham fight courageously to save their societies; however, Graham fights overtly while Winston fights in the shadows.
Both men fall into the same trap of trusting faithless mentors. Winston puts himself in O'Brien's hands, and Graham initially trusts Ostrog implicitly. However, both O'Brien and Ostrog use their proteges' idealized natures against them. O'Brien tricks Winston into committing the ultimate crime against Big Brother, and he oversees Winston's torture. For his part, Ostrog secretly plots Graham's downfall while beguiling his protege into thinking that he has his best interests at heart. With the full force of the Black Police at his disposal, Ostrog tries to enslave the rebels and to topple Graham from power.
In the end, both men experience similarly despairing fates. Winston is tortured to mental oblivion, and he betrays his lover, Julia, during his ordeal. By the end of the novel, he is a broken man, enamored with Big Brother and effectively transformed into a shell of his former self. O'Brien has essentially manipulated, molded, and tortured Winston into an instrument of the state. Winston's idealism has been distorted purposefully; the torture of innocents is the mechanism by which the state controls the masses. Similarly, Graham meets a devastating end. His plane is shot down by Ostrog's plane, and the novel ends on an ominous note. The author leaves no indication that Graham survives his crash.

In "Rikki-Tikki-Tavi," what does Nagaina do alone to try and complete her and Nag's original plan?

In “Rikki-Tikki-Tavi,” Nag and Nagaina are a married pair of cobras living in the garden of an English family in India. They want to get rid of the English family because they believe that, if they do so, Rikki-Tikki-Tavi, who is a mongoose that lives with the family, will leave the area. They know that mongoose and snakes are enemies and they believe that the presence of Rikki-Tikki will be dangerous for them.
In order to get rid of the family, the two snakes plan that Nag will kill them. He will start by killing the father when he comes for his morning shower. Then he will kill the others.  Nag says,

I will kill the big man and his wife, and the child if I can, and come away quietly. Then the bungalow will be empty, and Rikki-tikki will go.

This is their original plan. However, Rikki-Tikki hears of it and ends up killing Nag. This means that Nagaina is left to carry out the plan on her own. The next morning, she goes to where the family will eat breakfast and waits there.  When Rikki-Tikki gets there,

Nagaina was coiled up on the matting by Teddy's chair, within easy striking-distance of Teddy's bare leg, and she was swaying to and fro singing a song of triumph.

Teddy is the child of the family. Nagaina has come to kill him and then kill the rest of the family. This is how she plans to complete her and Nag’s original plan.
http://www.cs.cmu.edu/~mongoose/rtt.html

Discuss whether the practice of price discrimination benefits consumers or not.

The practice of price discrimination is to charge different prices for the same good or service; the reasons for this price change can vary based on who is buying the product or service or on certain circumstances such as how or when the product or service is sold.
Depending on the specific circumstances, price discrimination can benefit consumers. In other situations, however, it does not. Take, for example, a discount offered to students on a train. This specific group gets the benefit of a lower price and will receive the same service as others who are paying full price. In this example, students benefit and gain a consumer surplus from the discount. Price discrimination is not always fair, however, and who receives the lower price and consumer surplus could be based on factors race, gender, political affiliation, and so on.
Price discrimination can also have disadvantages for consumers. Take, for example, an airline that charges different prices based on when someone buys a ticket. A consumer might see a low price for a ticket one day and decide not to buy it only to check the next day to see that the exact same ticket has gone up in price. The airline has used price discrimination here, because they changed the price for an identical service based on when a consumer buys the product. Having to pay a higher price for the same service is obviously a disadvantage for the consumer.
Sometimes it is not clear whether price discrimination benefits consumers or not and may depend on the specific thoughts and opinions of the individual. For example, take a highway that charges a higher toll during rush hour compared to the rest of the day. Drivers must pay a higher price for the same service (use of the highway). However, this is done with the intention of relieving congestion on the highway during the busiest time of day. Some drivers might feel that the toll is good because it reduces traffic, while others might not like having to pay a higher fee to use the highway.
Generally speaking, price discrimination is used by producers to benefit themselves more so than consumers. Sometimes consumers can benefit, but other times they do not; it also may depend on how the individual thinks about the different price.
https://academicarchive.snhu.edu/bitstream/handle/10474/2412/snhu_00169.pdf?sequence=1

Allows an unprofitable business to avoid going bankrupt. In some cases, it may be possible that there is no one price that would enable a firm to make normal profits. (i.e. average costs would always be higher than demand curve) However, price discrimination may enable the firm to turn a loss into a small profit. This means that a business activity can keep going, rather than closing down. This is obviously beneficial for consumers because it increases their choice of goods and services. An example might be train services. Without price discrimination (off-peak, peak) train companies would make a bigger loss and may be discontinued.

Some groups benefit from cheaper prices. Price discrimination means that firms have an incentive to cut prices for groups of consumers who are sensitive to prices (elastic demand). For example, firms often offer a 10% reduction to students. Students typically have lower income so their demand is more elastic. This means they benefit from lower prices. These groups are often poorer than the average consumer. The downside is that some consumers will face higher prices.

Avoid Congestion. Price discrimination is one way to manage demand. If there were no price discrimination rush hour trains would be more overcrowded. Price discrimination gives an incentive for some people to go later in the day. This means that those who have to travel at rush hour benefit from less congestion.

Investment. Price discrimination helps a firm to become more profitable. This may enable the firm to invest in increased capacity. For example, an airline which maximizes profits from price discrimination can invest in updating its aircraft to the latest technology.

Price discrimination means the selling one product in different price on different customer in different region. This way used by consumers to maximize his profit. Through this way he can sell same product on different class peoples. Some peoples can afford high price where some cannot afford that price. So consumer sell out his product by decreasing the price. There also came the weather effect which can decrease the demand of product so to maintain demand constant the consumer decrease the price. If there is shortage of some product which is basic need of every one in that region then the consumer increase the price to get maximum product. In any way if consumer increase or decrease the price it just for the maximum profit.

Calculus and Its Applications, Chapter 1, 1.7, Section 1.7, Problem 90

Differentiate $\displaystyle g(x) = \sqrt{\frac{x^2 - 4x}{2x +1}}$

By using Quotient Rule and Chain Rule, we get

$
\begin{equation}
\begin{aligned}
g'(x) &= \frac{d}{dx} \left[ \left( \frac{x^2 - 4x}{2x + 1} \right)^{\frac{1}{2}} \right]\\
\\
&= \frac{1}{2} \cdot \left( \frac{x^2 - 4x}{2x + 1} \right)^{\frac{1}{2}- 1} \cdot \frac{d}{dx} \left( \frac{x^2 - 4x}{2x + 1} \right)\\
\\
&= \frac{1}{2} \left( \frac{x^2 - 4x}{2x + 1} \right)^{-\frac{1}{2}}
\left[ \frac{(2x +1) \cdot \frac{d}{dx}(x^2 - 4x) - (x^2 - 4x) \cdot \frac{d}{dx} (2x + 1) }{(2x + 1)^2} \right]\\
\\
&= \frac{1}{2 \left( \frac{x^2 - 4x}{2x + 1} \right)^{\frac{1}{2}}} \left[ \frac{(2x + 1)(2x - 4) - (x^2 - 4x)(2)}{(2x + 1)^2} \right]\\
\\
&= \frac{1}{2 \left( \frac{x^2 - 4x}{2x + 1} \right)^{\frac{1}{2}}} \left[ \frac{4x^2 - 8x + 2x - 4 - 2x^2 + 8x}{(2x + 1)^2} \right]\\
\\
&= \frac{1}{2 \left( \frac{x^2 - 4x}{2x + 1} \right)^{\frac{1}{2}}} \left[ \frac{2x^2 + 2x- 4}{(2x + 1)^2} \right]\\
\\
&= \frac{1}{2 \left( \frac{x^2 - 4x}{2x + 1} \right)^{\frac{1}{2}}} \left[ \frac{2(x^2 + x - 2)}{(2x + 1)^2} \right]\\
\\
&= \frac{x^2 + x - 2}{(2x + 1)^2 \left( \frac{x^2 - 4x}{2x + 1} \right)^{\frac{1}{2}}}\\
\\
&= \frac{x^2 + x - 2}{(2x +1)^{\frac{3}{2}}(x^2 - 4x)^{\frac{1}{2}} }
\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 9, 9.9, Section 9.9, Problem 10

To determine the power series centered at c, we may apply the formula for Taylor series:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) =f(c)+f'(c)(x-c) +(f''(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f'^4(c))/(4!)(x-c)^4 +...
To list the f^n(x) for the given function f(x)=3/(2x-1) centered at c=2 , we may apply Law of Exponent: 1/x^n = x^-n and Power rule for derivative: d/(dx) x^n= n *x^(n-1) .
f(x) =3/(2x-1)
=3(2x-1)^(-1)
Let u =2x-1 then (du)/(dx) = 2
d/(dx) c*(2x-1)^n = c *d/(dx) (2x-1)^n
= c *(n* (2x-1)^(n-1)*2
= 2cn(2x-1)^(n-1)
f'(x) =d/(dx) 3(2x-1)^(-1)
=2*3*(-1)(2x-1)^(-1-1)
=-6(2x-1)^(-2) or 2/(2x-1)^2
f^2(x) =d/(dx) -6(2x-1)^(-2)
=2*(-6)(-2)(2x-1)^(-2-1)
=24(2x-1)^(-3) or 24/(2x-1)^3
f^3(x) =d/(dx) 24(2x-1)^(-3)
=2*(24)(-3)(2x-1)^(-3-1)
=-144(2x-1)^(-4) or -144/(2x-1)^4
Plug-in x=2 for each f^n(x), we get:
f(2)=3/(2(2)-1)
=3/ 3
=1
f'(2)=-6/(2(2)-1)^2
=-6/3^2
= -2/3
f^2(2)=24/(2(2)-1)^3
=24/3^3
=8/9
f^3(2)=-144/(2(2)-1)^4
=-144/3^4
= -16/9
Plug-in the values on the formula for Taylor series, we get:
3/(2x-1) = sum_(n=0)^oo (f^n(2))/(n!) (x-2)^n
= sum_(n=0)^oo (f^n(2))/(n!) (x-2)^n
=1+(-2/3)(x-2) +(8/9)/(2!)(x-2)^2 +(-16/9)/(3!)(x-2)^3 +...
=1-2/3(x-2) +(8/9)/2(x-2)^2 +(-16/9)/6(x-2)^3 +...
=1-2/3(x-2) +4/9(x-2)^2 +8/27(x-2)^3 +...
= sum_(n=0)^oo (-(2(x-2))/3)^n
To determine the interval of convergence, we may apply geometric series test wherein the series sum_(n=0)^oo a*r^n is convergent if |r|lt1 or -1 ltrlt 1 . If |r|gt=1 then the geometric series diverges.
By comparing sum_(n=0)^oo (-(2(x-2))/3)^n with sum_(n=0)^oo a*r^n , we determine: r = -(2(x-2))/3 .
Apply the condition for convergence of geometric series: |r|lt1 .
|-(2(x-2))/3|lt1
|-1|*|(2(x-2))/3|lt1
1*|(2(x-2))/3|lt1
|(2(x-2))/3|lt1
|(2x-4)/3|lt1
-1lt(2x-4)/3lt1
Multiply each sides by 3 :
-1*3lt(2x-4)/3*3lt1*3
-3lt2x-4lt3
Add 4 on each sides:
-3+4lt2x-4+4lt3+4
1lt2xlt7
Divide each side by 2 :
1/2lt2x/2lt7/2
1/2ltxlt7/2
Thus, the power series of the function f(x) =3/(2x-1) centered at c=2 is sum_(n=0)^oo (-(2(x-2))/3)^n and has an interval of convergence: 1/2ltxlt7/2 .

What allusions does Hawthorne make in The Scarlet Letter?

Because Hawthorne used so many allusions in the novel, the only way not to miss any is to read a well-footnoted edition such as the Norton Critical Edition. I will give you two examples from chapter one to get you started.
The second paragraph in the novel alludes to Sir Thomas Moore's 1515 Utopia, a fictional work with which both the colonists Hawthorne writes about and his readers in the nineteenth century would have been very familiar. Moore mean to contrast English or European society with what an ideal society would be like. Hawthorne's narrator points out the irony that a theocratic colony, a Utopia (ideal society), has decided one of its first buildings should be a prison. 
Another allusion—this one in the chapter's final paragraph—is a reference to Anne Hutchinson. Hawthorne's narrator speculates that the rose bush that grows beside the prison door "sprung up under [her] footsteps" as she entered the prison. Anne Hutchinson, like the fictional Hester Prynne, dared to defy the belief system of the paternalistic Puritan elders.

How did audiences behave in The Globe Theater?

The Globe Theater, famous for having hosted the plays of Shakespeare, was one of the first purpose-built playhouses. Prior to this, plays were frequently performed in public houses and squares; the novelty of coming to a theater like The Globe appealed to all echelons of society, and audiences at The Globe represented a cross-section of London at the time.
The Globe could accommodate around 3,000 people, although all were not seated. The lower classes could buy a "groundling" ticket for a penny, which meant a play spent standing by the stage. Other gradations of ticket entitled the bearer to a bench seat in the open air, while the wealthier theater-goers would purchase a ticket in the enclosed theater boxes.
A visit to the theater was an experience: food and drink were for sale during the performance, and the audience would frequently be drunk. A visit to the theater was intended to be an all-day (or at least, all-afternoon) experience and was meant to be fun. It is for this reason that Shakespeare's plays generally take up to four hours to perform, and even the tragedies and histories include "light" scenes (mainly bawdy humor) to rejuvenate audiences. Crowds were very large and would generally behave towards the actors in a way that would only be seen now in a pantomime—indeed, traditional British pantomimes give us a general understanding of how all theater was once received. Villains would be booed and heroes cheered, and the audience would not shy away from attempting to "influence" the action onstage—calling "it's behind you!" and attempting to clue in the hero as to the machinations of the villain, for example. This gives some explanation as to why Shakespeare's characters so often address the audience as if conspiring with them.
You can read more in The Globe's own very useful factsheet, linked below.

College Algebra, Chapter 3, 3.1, Section 3.1, Problem 58

Determine the domain of the function $\displaystyle g(x) = \frac{\sqrt{x}}{2x^2 x -1}$
The function is not defined when the radicand is a negative value and when the denominator is 0. Since,
$\displaystyle g(x) = \frac{\sqrt{x}}{2x^2 + x -1} = \frac{\sqrt{x}}{(2x-1)(x+1)}$
Then,

$
\begin{equation}
\begin{aligned}
2x^2 + x - 1 &> 0\\
\\
(2x-1)(x+1) &> 0
\end{aligned}
\end{equation}
$

We have,

$
\begin{equation}
\begin{aligned}
2x -1 &> 0 &&\text{and}& x +1 &> 0 \\
\\
x &> \frac{1}{2} &&\text{and}& x &> -1 && \text{(However, negative values are not defined in square root)}
\end{aligned}
\end{equation}
$


So, the domain is...
$\displaystyle \left[ 0, \frac{1}{2} \right)\bigcup \left( \frac{1}{2}, \infty \right)$

The prevalence of warfare in West Africa increased with the expansion of trade with Europe. What was the main reason for this?

In the 16th century, the demand for African slaves by European colonial powers increased as England and Spain officially legalized international slave trade. One effect of this in West Africa was the expansion of warfare. Some local leaders, viewing the slave trade as an opportunity for profit, began engaging in constant warfare with neighboring groups in order to take captives to sell to European traders. A few West African states developed a thriving economy due to constantly taking prisoners of war from nearby states. Additionally, these leaders sometimes used the profit from selling war prisoners to buy guns and other weapons from European traders, which facilitated their ability to engage in constant war. Ultimately, the economic advantage experienced by some West African leaders was short-lived, as the slave trade devastated local populations and eventually the economy of all of West Africa.

Is there consistency in the Wife of Bath's arguments?

There is consistency in the Wife of Bath's arguments regarding marriage. She claims that there is nothing wrong with her five marriages and that choosing to marry can make one as morally or spiritually sound as choosing chastity. Her contemporary medieval society would have the Wife join a convent after the death of her first husband, but she argues that she can be just as religious while marrying again. She is certainly defending her actions and her successive marriages more than marriage itself, yet she is consistent in the arguments she makes.
She uses the Bible to justify marriage and even to justify intimacy. She tells the pilgrims that marriage can be beneficial for women, though in her examples, it is not so beneficial for men. Women can gain independence and even land and money through marriage, and they can use sex to have power over their husbands as well. She demonstrates this with the stories of her five husbands. The actual story she chooses to tell the pilgrims for her tale is a medieval romance that emphasizes that the key to a happy marriage is for the man to allow his wife to have control.
Her arguments are consistent with her story, though they are not consistent with the moral and social expectations of the times. She is anachronistic in her overt feminism, yet she still charms the narrator and some of the other pilgrims on the journey as she looks for her next husband.

Did Martin Luther King and Malcolm X agree?

Of the many misfortunes caused by each leader's death is the fact that they were each moving closer to one another ideologically, but never had a chance to meet and discuss those shifting ideologies. Malcolm X was killed in Harlem at the Audubon Ballroom on February 21, 1965; Dr. Martin Luther King, Jr. was killed on April 4, 1968. 
Early in the Civil Rights Movement, King advocated civil disobedience, which meant, even if physically attacked, black protesters should not retaliate. Malcolm X, and the Nation of Islam, to which he belonged at the time, was sharply opposed to this. Malcolm X advocated for self-defense. In 1964, he advocated for justice "by any means necessary." He never supported non-violent protest. 
The non-violent approach, coupled with King's favor for integration, caused Malcolm and other more militant leaders to identify King as an "Uncle Tom"—that is, an obsequious figure more interested in putting whites at ease than in justice and dignity for his community. This, of course, was untrue. 
Malcolm X had been indoctrinated by the Nation of Islam with the notion of white people as "devils" while still in prison. Therefore, any thought of working with them or seeing them as allies was impossible to Malcolm. In 1963, after his brief ostracism from the Nation of Islam, due to his controversial comments about the assassination of John F. Kennedy, Malcolm made discoveries about Elijah Muhammad that disillusioned him.
In response, he left the United States and embarked on a world tour, which included a pilgrimage to Mecca. There, he saw men of all races united under Islam. This experience revealed the fallacy of the Nation of Islam's rhetoric, and brought him closer to understanding King's ideas about "brotherhood."
When he returned to the States, his set up the Organization for Afro-American Unity (OAAU). Malcolm still advocated for self-reliance, but he welcomed white allies. In its nascence, the organization accepted help from whites but would not allow white membership. He insisted that, first, black people had to determine for themselves what justice and equality should look like.
Because he was rooted in Harlem, Malcolm X was more associated with poor and working-class black people. The Nation of Islam also had a tendency to find its members among these classes, in addition to seeking out social rejects, such as ex-convicts—which Malcolm was. 
In contrast, Dr. King is more often associated with the black middle-class Civil Rights movement, rooted in Southern Christian churches. Some of this has to do with King's background, which was middle-class and highly educated, contrary to Malcolm's. However, toward the end of his life, King focused more on the needs of the working-class and became involved in labor organizing. He traveled to Memphis, Tennessee, where he was killed, to help organize sanitation workers.
All of this suggests that, had Malcolm X lived and had the two had another opportunity to meet, they might have merged in class consciousness. This would include the understanding that white people should be included in the struggle for civil rights, but should not be permitted to co-opt the movement.

What was Tommy's behavior like in "Gryphon"?

Tommy, the first-person narrator in the short story “Gryphon,” is a student in fourth grade. When his teacher, Mr. Hibler, catches a cold, the eccentric Miss Ferenczi is brought in as a substitute to teach the class. Miss Ferenczi is very different from the other teachers that the students have had, and her lesson plans blend fact and fiction in a way that mesmerizes the students. 
Tommy quickly begins to admire Miss Ferenczi, and he defends her half-truths to his classmate Carl Whiteside. While Tommy is one of the first students to be swayed by Miss Ferenczi’s eccentricities, the other students are also mesmerized when she returns the following day. Tommy attempts to imitate her, but Carl tells him that he should not and that he will only sound foolish in comparison.
Mr. Hibler returns and some time passes before Miss Ferenczi substitute teaches for the class again. When she does, she decides to perform tarot card readings. She tells one boy, Wayne Razmer, that he will die soon, and Wayne reports her to the principal. The principal fires Miss Ferenczi, and Tommy attacks Wayne, telling him that “she was right” and that he was “just scared.”
Tommy admires Miss Ferenczi throughout the story, and his behavior reflects this. He is perhaps attracted to her teaching style because it is so different from anything else he has seen in his rural life. We get the sense that his home life is mundane: while the story does not show us much of it, what we do see is Tommy being told to do chores. In comparison, Miss Ferenczi provides a sense of magic and fantasy through her griffin-like stories and lies.

Why does Bud think ideas are like trees?

The answer to this question can be found in chapter 9. Technically speaking, Bud does not say that ideas are like trees. He says that ideas are like seeds.

IT'S FUNNY HOW IDEAS ARE, in a lot of ways they're just like seeds.

The idea and seed comparison comes up throughout the novel, but chapter 9 is the location where Bud explains the comparison. Bud says that both ideas and seeds start out small, and they both are capable of growing into something that is unfathomably larger than the original seed.

Both of them start real, real small and then . . . woop, zoop sloop . . . before you can say Jack Robinson they've gone and grown a lot bigger than you ever thought they could.
If you look at a great big maple tree it's hard to believe it started out as a little seed.

Bud goes on to explain that the idea of Calloway being his father started out just like that little maple seed. Bud explains that the initial seed of the idea was so small that it was likely to blow away with the first little breeze. It's fitting, then, that the idea itself began with a paper flyer of Calloway. That is an item that quite literally would blow away in any kind of breeze. Eventually, the idea that Calloway is his father is the only thing that fills Bud's entire field of vision. The idea is massive and powerful like a huge maple tree.
Once Bud finds Calloway and the rest of the band, he begins to feel accepted, and another seed gets planted, which quickly moves Bud from laughing to crying in an instant:

but sometime whilst I was sitting in the Sweet Pea another seed got to sprouting . . .

He has finally come home and found a loving family.

Bud thinks that ideas are like trees because they have the potential to grow, just like trees grow from tiny seeds.
To Bud, an idea is like a seed. It has the potential to grow into reality. He relates that the idea of Herman E. Calloway being his father began when he first spied one of Herman E. Calloway's flyers. That small idea soon burst "out of the dirt" when Billy Burns teased the boys at the Home. 
Bud remembers how Billy teased him and his friends, challenging them to reveal who their parents were. Billy Burns bet a nickel that none of the boys could reveal who their fathers and mothers were. Upon hearing this, Bud told Billy that his father was Herman E. Calloway. Bud maintains that this is how the idea of Herman E. Calloway being his father was born. That idea then grew and became the impetus for him to travel across the state of Michigan. So, to Bud, ideas are like trees because they have the potential to grow into reality.

How did "interchangeable parts" change the production of weapons, warfare, and eventually the Industrial Revolution?

Think of your own experiences fixing things. When a screw comes loose, you can easily just grab a screwdriver and pop it back in. When something in a car is damaged, you can simply go and find a replacement and likely know what's going to work and what won't. If you lose your phone charger, you can ask a friend. And if you've ever been in a situation where you need that one special little tool or cable, odds are it's been frustrating, time consuming, and expensive going from place to place searching for just one tiny little item. Before interchangeable parts, everything had to be special order.
The introduction of interchangeable parts is the sort of thing that was revolutionary but also relatively understated compared to flashier inventions. Before, each item had to be made specially, start to finish, by the same individual or group of people. Mass production was impossible beforehand. The idea of assembling IKEA furniture would have been unheard of—without standardization, only those with craftsman skills knew how to build, for instance, a table. And if that table was to be damaged, such as a leg being broken, someone couldn't just go and ask for a replacement part or order an entirely new table with the same specifications to ensure it fits in their tiny kitchen. You would have to wait to get everything custom made by special people that knew what they were doing.
Interchangeable parts allows production of items to occur on a much larger and faster scale. Workshops of artisans/craftsmen and their apprentices began to move aside in favor of less skilled workers. This later lead to the assembly line and automated machines.
This production method was used to make weapons in the 19th century. The logic is simple—you can build more weapons faster and cheaper. More weapons equals more firepower. More firepower should give more of an edge over an enemy who has to wait for each gun to be built one by one. The same pattern followed with the industrial revolution. More goods and cheaper prices meant even more people had greater access to new developments and higher standards of living. These developments could be put back into the production process, making it even more efficient.
Some additional benefits included unskilled laborers being able to find more work possibilities, particularly in cities. Also with more people enjoying these goods, there was more demand and opportunity to study these items and develop them even further, leading to greater technological boom (including weapons development). It's difficult for a young, budding scientist with little means to study how electricity works if they have no access to it. Like many things in history, it's a domino effect.
https://www.eliwhitney.org/7/museum/about-eli-whitney/factory

What points can you include in a letter from a commoner to Brutus in order to convince him he should be the ruler instead of Caesar?

I'm assuming the letter would be presented to Brutus before Caesar's assassination.
You could mention that Brutus, as a man of the people, would act for the people, unlike Caesar, who only seems to care about himself. 
Secondly, Brutus displays deeply entrenched values, whereas Caesar's morals seem to be suspect.
Also, Brutus does not display the kind of supercilious arrogance that seems to be an attribute of Caesar's character. Brutus comes across as humble and caring.
Fourthly, Brutus commands great respect among the common folk because of the above-named qualities, whereas Caesar generates skepticism and suspicion since he focuses only on his victories and thrives on adulation.
Furthermore, Brutus presents an image of courage and strength, whereas Caesar could come across as frail and infirm. Caesar is prone to fainting spells brought about by his supposed epilepsy, while Brutus is physically robust. It is easier to be inspired by a leader who presents an image of resilience and power than one who comes across as weak and unstable.
The general image of Brutus, therefore, much favors him as one suitable to lead, as Cassius so cleverly and slyly suggests during their speech in Act I, Scene 1.

What were the political goals of the Urban League? How did they differ from the political goals of the NAACP?

The Urban League, founded only a year after the NAACP, championed equality and integration in much the same way as its predecessor. There were slight nuances, however, that distinguished their actions. Most importantly, the types of cases that each organization undertook to try and bring about racial equality is what led to their differentiation.
The Urban League is echoed in the modern day efforts for ubran development and cost-effective housing. This organization tried to improve the lives of impoverished minorities by fighting for their rights to equal housing opportunities. Additionally, they vied for better job opportunities to try and improve the overall economic situation of African Americans. Because of the harsh inequality in jobs and housing, African Americans ended up in a cycle of poverty that the Urban League was determined to overcome.
The NAACP was more concerned with social issues such as education and voting rights, particularly with their famous case Brown v. Board of Education. Both of these causes are extremely important, and progress was necessary on all fronts. Because of their specialization, the two organizations worked in tandem, focusing on their areas of expertise and exacting change for the African-American community at large. Fortunately, much good has come from their efforts, and their partnership has been largely effective.

The National Association for the Advancement of Colored People (NAACP) was founded in 1909 by W.E.B. Du Bois and a group of white and black reformers, while the National Urban League (NUL) was founded in 1910 in New York City. Both groups aimed to combat racial segregation and improve civil rights in different ways. The focus of the NAACP was engaging people in grassroots campaigns for equality and using the judicial system to bring about racial justice through the passage of laws that struck down desegregation. The organization also tried to ensure equality in education. Through the Legal Defense Fund, the NAACP pursued many cases to create racial equality, including the landmark 1954 Supreme Court case Brown v. Board of Education that ruled that "separate but equal" black and white schools were unconstitutional. In contrast, the National Urban League sought to fight segregation and unfairness for African Americans in housing and jobs (first in New York City and later in communities across the country), and it was vital in helping African Americans who arrived in northern cities during the Great Migration and afterward. The organization still works to help African American communities with issues related to jobs, education, housing, and healthcare.
https://www.naacp.org/

The Urban League had several political goals. Their main purpose was to advocate on behalf of African Americans and to combat racial discrimination in the United States. This group was specifically interested in ending employment and housing discrimination. The Urban League believed that if employment opportunities were available to African Americans, they would be able to achieve social and political equality.
In contrast, the NAACP (National Association for the Advancement of Colored People) used the strategy of confronting civil rights violations directly. The official goal of the organization was to ensure the educational, social, and political rights of all people and to eliminate racial hatred and discrimination. W.E.B. Dubois started the NAACP with the goal of ending racial discrimination of all types. The NAACP favored using the courts as a battleground to decide civil rights issues instead of focusing on the economic freedoms of African Americans as the Urban League had done.

Why is Porter's story entitled "The Grave"?

The title of Katherine Anne Porter’s story “The Grave” at first glance seems to be something of a misnomer. The story, contrary to the singular implication of the title, is full of graves. There is the grave of Miranda and Paul’s grandfather, on which the story opens. That single grave has been joined over the years by other members of the family in a cemetery plot on the family farm. At the time the story takes place, however, all of the bodies have been removed to the public cemetery, leaving behind in their places nothing but “just a hole in the ground.” (Though, even empty, two of them yield treasures: a small hollow-breasted silver dove and a gold ring.)
Later on, there is the tragic and faintly gruesome grave of the unborn baby rabbits—the doe’s body, into which Paul replaces them after Miranda becomes distressed. The doe herself is presumably subsequently buried when Paul takes her away into the bushes.
But this is a story full of echoes and repeated imagery, and these are just shadows of the true grave—that of the memory of the rabbits. As Porter writes of Miranda, the memory “sank quietly into her mind and was heaped over by accumulated thousands of impressions.” Just like the graves of her grandfather and family members, the memory lay undisturbed for years, until the chance trigger of animal-shaped sweets upon a tray in a foreign marketplace. And like the hollow graves that begin the story, this metaphorical grave has a small treasure in it: the memory of her brother’s face as it was when he was a child.

Which is the largest muscle in the human body?

Great question! The largest muscle in the human body would be the gluteus maximus, which is also one of the human body's strongest muscles. 
There are three gluteal muscles: the gluteus maximus, the gluteus medius, and the gluteus minimus. All of these make up the area of the body which we usually refer to as the buttocks. This trio of muscles is what people are talking about if you ever hear someone say they're working out their "glutes".
The gluteus maximus muscle is connected to multiple bones, and, along with the other gluteal muscles, is responsible for the body being able to move its legs and hips, as well as keep the trunk of the body in an upright position. The gluteus maximus helps you sit down, stand up, climb stairs, and so much more. 

Describe Dill and the influence he has on Scout and Jem.

When Jem and Scout first meet Dill, also known as Charles Baker Harris, Scout describes him as a "curiosity." He has white hair, blue eyes, and although shorter than Scout, he is a year older. Dill lives in Meridian, Mississippi, but spends summers with his Aunt Rachel in Maycomb County. Dill proudly announces that he can read and shares that he is the winner of a "Beautiful Child contest." By telling Jem about the movie Dracula, it seems as though Dill earns Jem's respect. In chapter 5, Scout recalls Dill asking her to marry him but says that he "promptly forgot about it."
Dill influences Scout and Jem through his interest in Boo Radley. Chapter 1 of To Kill a Mockingbird begins with Scout looking back on the events that lead to Jem's broken arm. Jem believes the events begin with Dill giving them the "idea of making Boo Radley come out." Dill seems to be fixated on Boo Radley the way "the moon draws water." On a dare from Dill, Jem runs and slaps the side of the Radley house. The children believe they see a movement of one of the window shutters inside the house thus beginning their events with Boo. Dill is involved when Jem loses his pants while trying to escape the Radley property, and he accompanies Scout and Jem to the trial of Tom Robinson.

College Algebra, Chapter 7, 7.4, Section 7.4, Problem 52

Solve for $x$ if the matrix $\displaystyle \left| \begin{array}{ccc}
x & 1 & 1 \\
1 & 1 & x \\
x & 1 & x
\end{array} \right| = 0$.

For this matrix we have


$
\begin{equation}
\begin{aligned}

0 =& x \left| \begin{array}{cc}
1 & x \\
1 & x
\end{array} \right| - 1 \left| \begin{array}{cc}
1 & x \\
x & x
\end{array} \right| + 1 \left| \begin{array}{cc}
1 & 1 \\
x & 1
\end{array} \right|
&& \text{Expand}
\\
\\
0 =& x (1 \cdot x - x \cdot 1) - 1 (1 \cdot x - x \cdot x) + 1 (1 \cdot 1 - 1 \cdot x)
&& \text{Simplify}
\\
\\
0 =& x(0) - (x - x^2) + 1 -x
&& \text{Distributive Property}
\\
\\
0 =& -x + x^2 + 1 - x
&& \text{Combine like terms}
\\
\\
0 =& x^2 - 2x + 1
&& \text{Factor}
\\
\\
0 =& (x - 1)^2
&& \text{Take the square root of both sides}
\\
\\
0 =& x - 1
&& \text{Add } 1
\\
\\
x =& 1
&&

\end{aligned}
\end{equation}
$

Why did the American ambassador Mr. Otis purchase the Canterville Castle, although people told him it was haunted?

Mr. Otis, because he is American, simply does not believe in ghosts. He also is not afraid of ghosts, even if they do exist. Being a can-do American, he believes he will quickly have any ghost subdued and mastered. Therefore, he has no fear of Canterville Castle. As he tells Lord Canterville:

I reckon that if there were such a thing as a ghost in Europe, we'd have it at home in a very short time in one of our public museums, or on the road as a show.

Lord Canterville, nevertheless, insists that the ghost of Canterville Hall is quite real. He says the ghost has been haunting the family for three centuries, since 1584. Mr. Otis remains skeptical. He informs Lord Canterville that even the British aristocracy can't suspend the laws of nature, a concept Lord Canterville comically can't comprehend.
Thus, from the start, the story sets up a comic opposition between the British, with their respect for the past and faith in tradition, and the very pragmatic Americans, who have to see a ghost to believe it. The Otises do end up accepting the reality of the Canterville ghost, but they never let it intimidate them.

Mr. Otis, an American ambassador, purchases Canterville Castle, even though everyone tells him that it is haunted. His reasoning is that the United States has everything that money can buy, and if there really were ghosts in Europe, there would surely be one in a museum in America. The family takes a very commonsensical approach to the presence of a ghost. When Mrs. Otis finds a blood stain in her living room, the housekeeper tells her it's the blood of Lady Eleanore de Canterville, whose husband, Sir Simon de Canterville, killed his wife in 1575. The eldest son, Washington, immediately applies stain remover to the spot, but when the blood stain disappears, there is a flash of lightning and a clap of thunder. The next night, Mr. Otis sees the ghost and offers it some lubricator to make its chains less noisy.

Discuss the Protestant Reformation. What were the major issues involved? What were the reasons for success, and what were the effects on the New World?

The major issues involved in the Reformation were the corruption of the Catholic Church and the desire of some Christians to establish a closer relationship to God and the Scriptures. When Martin Luther nailed his 95 Theses to the wall of the Church of Wittenburg, he sought to address the buying of indulgences, the practice of buying one's way out of sins, and simony, the buying or selling of ecclesiastical favors or church offices.
There was widespread discontent with these church practices, which is part of the reason for the Reformation's success. Pilgrims and Puritans, religious groups who had a major cultural impact on the early American colonies, were also Protestants. Though the Anglican Church, a Protestant Church that had been established in England, existed largely as an excuse for King Henry VIII to marry whom he pleased without interference from the Catholic Church, Pilgrims and Puritans could not realize religious freedom in England. The Pilgrims went first to the Netherlands, which was a freer society, but continued on to Plymouth Colony to establish their own society founded on their religious principles. The Puritans, who sought a "pure" approach to Scripture, had the same goal.
It is important to note that both Protestants and Catholics populated the New World. Florida, for example, was initially a Spanish territory. The area sold during the Louisiana Purchase in 1803, as well as parts of the Midwest, were populated by the French. The British Caribbean islands, including the sugar-rich island of Barbados, was part of the Anglican tradition, while those colonized by Spain, such as Cuba, were Catholic.

To what does Martin Luther King Jr. make allusions in his "I Have a Dream” speech?

King's "I Have a Dream" speech is full of literary and historical allusions. One of the most famous ones which pervades the speech is to the Declaration of Independence and the Constitution, which King describes as a "promissory note" on which the nation has "defaulted as far as her citizens of color are concerned." King tells his vast audience in Washington that they are in Washington to "cash this check." He goes on to allude to a line from Shakespeare's Richard III by describing the "sweltering summer of the Negro's discontent" (Shakespeare coined the phrase "winter of our discontent"). He alludes to the famous patriotic hymn "My Country 'tis of Thee," and to the old spiritual "Free at Last" in his stirring conclusion to the speech. Overall, the entire speech alludes to the promise of American democracy, and to the hope that the blessings of democracy will be extended to all Americans regardless of race. King also alludes to many of the struggles experienced by civil rights activists, stating that he understands many may have come from the "narrow cells" of Alabama and Mississippi to attend the march. 
https://kinginstitute.stanford.edu/king-papers/documents/i-have-dream-address-delivered-march-washington-jobs-and-freedom

How is The Strange Case of Dr. Jekyll and Mr. Hyde thematically similar to gothic literature and how does it differ? In what ways is it more Victorian rather than Gothic?

First, it's not really useful to think of "Victorian" and "Gothic" as two competing elements in this work. "Gothic" is a genre; "Victorian" is not a genre, but an umbrella term describing works of all genres produced during a certain period of time. As such, there are characteristics of Victorian literature which we can find in Gothic literature of the time—and in romantic literature, drama, and so on, without making the text any less of its own genre. Dr Jekyll and Mr Hyde is a Victorian Gothic work. This puts it in a specific genre of its own which reframes Gothic elements in a Victorian context. We can track the similarity between Victorian, or fin-de-siecle, Gothic works (such as Dorian Gray, Dracula, The Island of Dr. Moreau) and first wave Gothic works (The Castle of Otranto, The Monk, Frankenstein), while also observing how elements of the Victorian have changed what Gothic means.
Strong Gothic elements in Dr Jekyll and Mr Hyde include:

Mystery and the supernatural. Perhaps the key component of Gothic literature, this is also key to this story. The mystery of the connection between Jekyll and Hyde maintains tension throughout the story, while Hyde's misdeeds are presented in a suspenseful way. Meanwhile, there's obviously a supernatural element in Jekyll's transformation (or is there? More on that below).


Isolation. Dr. Jekyll works primarily alone, which is why he is able to achieve what he does, away from the prying eyes of society.


The setting as character. While the setting in this novel, Victorian London, is dissimilar to the moor and castle settings of early Gothic novels, it is described equally as if it is an important part of the plot and theme of the novels, and used to create atmosphere.

Meanwhile, Victorian preoccupations which have made their way into the text include:

Class. Victorian literature often explored questions of class and society; in Dr. Jekyll and Mr. Hyde, the tension between the well-to-do professional classes and the dubious lower classes is encapsulated in one person and his two halves. The "bad" part, Mr. Hyde, symbolizes the part of us we try to repress, or the part of society the upper classes like to pretend is not there.


The tension between science and religion or the"when does a scientist become a man playing God"? See point 1 above—at what point does science, sufficiently advanced, become something supernatural, and something with which mankind should not meddle? Dr. Jekyll meddles in affairs beyond his understanding, to his detriment. Note, however, that this science/religion question is not unique to Victorian literature, but had already been evolving—and seen as something to be explored in Gothic texts—since Mary Shelley wrote Frankenstein in 1816.

Now, as stated, "Victorian Gothic" is understood to be its own genre. As such, it has its own particular defining features which show the influence of both Gothic literature and Victorian preoccupations and which we can find in this text, such as:

Duality. The duality of man, and of society, is absolutely key to Victorian Gothic and can be found in all the major texts. While a man is seen to be respectable, on the one hand, some part of him is actually prowling the underworld of Victorian London. This betrays Victorian concerns about the hypocrisy of London, which, on the one hand, was a very class-focused, genteel society and, on the other, played host to Jack the Ripper and child prostitution. We also find duality explored in other Victorian texts—think The Importance of Being Earnest—but it's a defining feature of Victorian Gothic.

So, rather than asking what parts of this text are Gothic and which are Victorian, it's easier to explore how it represents the revival of the Gothic genre within a Victorian context.

In "The Adventure of the Speckled Band," why does Holmes think the mystery is particularly intriguing?

Helen Stoner tells Sherlock Holmes that she is at present unable to pay him for his services. Yet he takes on her case for at least two reasons. One is that he feels sympathetic for a young woman who is so frightened and helpless. The other is that he finds one aspect of the mystery especially intriguing. Dr. Watson frequently mentions in his Sherlock Holmes tales that the great detective is mainly motivated by mental challenges, since he has been successful enough in his investigations to have no further cares about money. What intrigues Holmes is that the case presents what is commonly called a "Locked Room Murder Mystery." As Holmes explains to Dr. Watson:

“Yet if the lady is correct in saying that the flooring and walls are sound, and that the door, window, and chimney are impassable, then her sister must have been undoubtedly alone when she met her mysterious end.”

Holmes senses that if he could unravel the mystery of how Helen's sister Julia came to be killed while sleeping in such a room, he could also solve Helen's problem of believing that her life is in danger from the same source. This is what happens in the denouement of the story. 
The prototype of the "Locked Room Murder Mystery" is probably Edgar Allan Poe's famous tale "The Murders in the Rue Morgue." Two women were horribly murdered in a room which appeared to be completely inaccessible from the outside. The protagonist in that story is an amateur detective named C. Auguste Dupin, who has many of the characteristics of Arthur Conan Doyle's Sherlock Holmes.

What does Emerson mean when he writes the aphorism “envy is ignorance, imitation is suicide”?

The lines quoted from Ralph W. Emerson's "Self-Reliance" are part of a passage about maturity and identity. Emerson is saying that each person comes into a mature sense of self or full adult status when they accept who they are and do not make the mistake of envying another person. We live in ignorance of what is going on inside the other person so it would be an error to be jealous of what we think they have. Each person has unique value and must embrace their uniqueness; "he must take himself for better, for worse, as his portion...."
If we turn our efforts toward trying to be someone we are not, we will sacrifice our identity. Because we have the autonomy to blaze our own trail, failure to do so would also be our responsibility. Thus he uses the heavily weighted term suicide, not just death. Emerson goes on to emphasize uniqueness:

The power which resides in him is new in nature, and none but he knows what that is which he can do, nor does he know until he has tried.

"Envy is ignorance, imitation is suicide," is a quote from Ralph Waldo Emerson's essay, "Self-Reliance, which was published in 1841.
This means that you should be your own person, be yourself, and be noteworthy. Know your own strengths and weaknesses, which make you unique and original and use these to become interesting, remarkable, and significant.
Do not look at other people and what they have. More importantly, do not compare yourself with other people, because that's when envy sets in. When you are envious of other people, of what they are, what they have, and what they have accomplished, you are revealing your ignorance of yourself, your strengths, and your uniqueness.
When you try to imitate other persons, you are denying and dismissing your own identity and your own person. The more you imitate others, the more your own person and uniqueness disappears, until you are unable to know who you really are anymore.
Instead, build up on your own unique traits and talents, build up on your strengths and chart your own path. There are no limits to what you can achieve. They are only limited by your own fears, hesitation, and self-doubt. Do not pay attention to what other people say about you. Choose who you want to be and do it.
 

Emerson, who wrote this in his essay "Self-reliance," is simply saying the following: be yourself. Don't worry about what other people are doing. Don't conform. Do what is right for you.
When he says "envy is ignorance," he means that it is a mistake to be jealous of what another person has or is doing. If you envy another person, it means you are ignorant or unaware of the deepest longings of your own soul. What another person has, or is, has nothing to do with what is right for you. Look inside yourself.
Emerson means the same thing when he writes, "imitation is suicide." When you imitate the life another person is leading, you may not being killing your body, but you are killing your soul. Emerson says that every individual is born with his own unique destiny planted in him by a divine power. Figure out what that destiny is. Follow it, no matter what other people say or do. 

y = 3x , 0

The quantity to be calculated is the area of what is called a surface of revolution. The function y = 3x is rotated about the x-axis and the surface that is created in this way is a surface of revolution. The area to be calculated is definite, since we consider only the region of the x-axis x in [0,3] , that is, x between 0 and 3.
The formula for a surface of revolution (which is an area, A) is given by
A = int_a^b (2pi y) sqrt(1 + (frac(dy)(dx))^2) dx

The circumference of the surface at each point along the x-axis is 2pi y and this is added up (integrated) along the x-axis by cutting the function into tiny lengths of sqrt(1 + (frac(dy)(dx))^2) dx 
ie, the arc length of the function in a segment of the x-axis dx in length, which is the hypotenuse of a tiny triangle with width dx and height dy .  These lengths are then multiplied by the circumference of the surface at that point 2 pi y to give the surface area of rings around the x-axis that have tiny width dx yet have edges that slope towards or away from the x-axis. The tiny sloped rings are added up to give the full sloped surface area of revolution.  
In this case,  frac(dy)(dx) = 3 and since the range over which to take the arc length is [0,3] we have a = 0 and b = 3 . Therefore, the area required, A, is given by
A = int_0^3 6 pi x sqrt(10) dx = 3sqrt(10) pi x^2 | _0^3 = 27sqrt(10)pi
 

Is Shakespeare the greatest English playwright?

I would argue he is. Shakespeare's plays have endured hundreds of years, and audiences still pay to see them performed, either in period costumes or with modern settings and interpretations. Despite the enormous difference in the way Shakespeare's use of English sounds compared to modern English, his use of language is so artful, poetic, and powerful that we accept the challenge to make sense of it. Those producing and performing his plays must work to make the language accessible to modern audiences. In addition to the impressive use of language, Shakespeare also created many memorable characters and stories that are still relevant to contemporary culture. His plays are taught in schools and performed by theatre companies (such as the annual Shakespeare in the Park performances in New York every summer, or the many Shakespeare plays performed in Stratford-on-Avon, Shakespeare's hometown). Romeo and Juliet is often called the greatest love story ever written, and was remade into a contemporary musical called West Side Story, and a contemporary film by Baz Luhrmann starring Leonardo DiCaprio and Claire Danes. Hamlet is seen as an outstanding example of a young man struggling with his own depression and ambition. The Merchant of Venice and Othello have much to teach modern audiences about the nature of ethnic and racial prejudice. So much of Shakespeare's work is central to our experience of language and the arts that it is impossible to imagine the worlds of theatre or literature without it.

Calculus of a Single Variable, Chapter 9, 9.6, Section 9.6, Problem 47

To apply Root test on a series sum a_n , we determine the limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
In order to apply Root Test in determining the convergence or divergence of the series sum_(n=1)^oo (1/n -1/n^2)^n , we let: a_n =(1/n -1/n^2)^n.
We set-up the limit as:
lim_(n-gtoo) |(1/n -1/n^2)^n|^(1/n) =lim_(n-gtoo) ((1/n -1/n^2)^n)^(1/n)
Apply the Law of Exponents:(x^n)^m= x^(n*m) .
lim_(n-gtoo) ((1/n -1/n^2)^n)^(1/n) =lim_(n-gtoo) (1/n -1/n^2)^(n*1/n)
=lim_(n-gtoo) (1/n -1/n^2)^(n/n)
=lim_(n-gtoo) (1/n -1/n^2)^1
=lim_(n-gtoo) (1/n -1/n^2)
Evaluate the limit by applying the limit property: lim_(x-gta)[(f(x))-(g(x))] =lim_(x-gta) f(x) -lim_(x-gta) g(x) .
lim_(n-gtoo) (1/n -1/n^2)=lim_(n-gtoo) 1/n -lim_(n-gtoo) 1/n^2
= 1/oo - 1/oo^2
= 1/oo - 1/oo
= 0 -0
= 0
The limit value L=0 satisfies the condition: L lt1 since 0lt1 .
Conclusion: The series sum_(n=1)^oo (1/n -1/n^2)^n is absolutely convergent.

What gesture of friendship cements Miss Maudie and Scout's relationship?

As Scout, Dill, and Jem continue to grow up, they also begin to change. One of the most evident changes is that Dill and Jem start to bond more as boys, leaving Scout behind in their games. As a result, Scout ends up spending more time with her neighbor, Miss Maudie, who likes to garden and has a very amiable way of treating children. Scout was not too familiar with Miss Maudie as a child, but, as part of her own growth into young womanhood, she is now warming up to the dynamics of female friendships. After all, why not be friends with Miss Maudie? She makes the best cakes in town!
As time went on and Scout spent more time with Miss Maudie, she was able to get more insight about the lives of the Radleys. She finds a lot of information that serves as a way for her to understand that there is much more to the rumors and myths surrounding the family. Scout learns a lot from Miss Maudie. However, the ultimate act that cements their friendship is when Miss Maudie opens up and shows Scout a little secret: her dentures.

[When] she grinned she revealed two minute gold prongs clipped to her eyeteeth. When I admired them and hoped I would have some eventually, she said, “Look here.” With a click of her tongue she thrust out her bridgework, a gesture of cordiality that cemented our friendship. 

Notice that Scout says that it was an honor to see the bridgework. It is a gesture that indicates that there are no secrets between them and that they are friends. It is clear that this was an important moment in Scout's life: she remembers it as a symbol of a long-lasting friendship. 

How does Bill's plea to Sam not to leave him alone with the boy add suspense to "The Ransom of Red Chief"?

In O. Henry's "The Ransom of Red Chief," Bill's plea to his partner Sam not to leave him alone with Ebenezer Dorset's red-haired boy creates suspense because Bill is afraid what might happen to him if he is left alone with the rambunctious boy.
After the two men go into the town of Summit, Alabama, and kidnap the son of the town's wealthy banker Dorset, they eagerly anticipate their gains when they receive the ransom money. However, the young redhead proves to be more trouble than they have expected. The young Dorset "put(s) up a fight like a welter-weight cinnamon bear" as they take him up to the cave. After dark, Bill drives the rented buggy, which they have used for the kidnapping, back to the town of Summit.  He then walks back to the cave. By the time Sam arrives, Bill is pasting "court-plaster" over the scratches and bruises on his face. 
Red Chief has the time of his life at Bill's expense. At daybreak, he plans to scalp Bill, whom he has renamed Old Hank, the Trapper. The boy talks incessantly and excitedly.  Now and then he lets out a war-whoop that causes Old Hank the Trapper, to shiver. "That boy had Bill terrorized from the start." Sam comments. He sleeps fitfully that night and wakes to the sounds of Bill's screaming because Red Chief has a knife and is ready to scalp the terrorized man. After this incident, neither Bill nor Sam sleep for fear of being scalped and burned at the stake.
The next day Bill goes into the town to hear any rumors that are circulating. There is nothing said about the Dorset boy. The kidnappers wonder why the town is so calm. In the meantime, they live in fear. After Bill is ridden like a horse for hours by Red Chief, the man attempts to return the boy to town. But the intimidating boy hikes back to the cave. Desperate to be rid of this maniacal boy who finds his kidnapping an adventure, the men agree to pay the father two hundred and fifty dollars to take back the boy.
 

Calculus of a Single Variable, Chapter 8, 8.7, Section 8.7, Problem 24

Given to solve,
lim_(x->oo) ((5x+3)/(x^3-6x+2))
as x->oo then the ((5x+3)/(x^3-6x+2)) =oo/oo form
so upon applying the L 'Hopital rule we get the solution as follows,
as for the general equation it is as follows
lim_(x->a) f(x)/g(x) is = 0/0 or (+-oo)/(+-oo) then by using the L'Hopital Rule we get the solution with the below form.
lim_(x->a) (f'(x))/(g'(x))

so , now evaluating
lim_(x->oo)((5x+3)/(x^3-6x+2))
= lim_(x->oo) ((5x+3)')/((x^3-6x+2)')
= lim_(x->oo) (5)/(3x^2-6)
by plugging the value x=oo , we get
= (5)/(3(oo)^2-6)
= 5/oo
= 0

Glencoe Algebra 2, Chapter 2, 2.6, Section 2.6, Problem 37

f(x) = |x+(1/2)| , the the domain and range is given as follows
(i)Domain definition:
The domain of a function is the set of the input or argument values for which the function is real and defined.
In this function, The function has no undefined points, so the domain is
-oo (ii)Range definition
It is the set of values of the dependent variable for which a function is defined.
For this function the interval has a minimum point at x= -1/2 with value f(x) = 0
so the range of |x+(1/2)| is f(x) >= 0
It can also be observed from the graph below:

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 64

Find the volume obtained by rotating the region bounded by $y = \sec x$ and $y = \cos x$ from $\displaystyle 0 \leq x \leq \frac{\pi}{3}$ about $x$-axis.



By using vertical strips, notice that if you slice the figure, you'll get a cross section of a washer with outer radius $r_o = 1 + \sec x$ and inner radius $r_i = 1 + \cos x$. So, the cross sectional area is computed by subracting the outer circle to the inner circle. A washer = $A_{\text{outer}} - A_{\text{inner}} = \pi (1 + \sec x)^2 - \pi (1 + \cos x)^2$. Thus, the volume is...


$
\begin{equation}
\begin{aligned}
V = \int^b_a A (x) dx &= \int^{\pi/3}_0 \left[ \pi (1 + \sec x)^2 - \pi (1 + \cos x)^2 \right] dx\\
\\
&= \int^{\pi/3}_0 \left( 1 + 2 \sec x + \sec ^2 x - 1 - 2 \cos x - \cos^2 x \right) dx\\
\\
&= \int^{\pi/3}_0 \left( \sec^2 x + 2 \sec x - \cos^2 x - 2 \cos x\right) dx && \text{ recall that } \cos^2x = \frac{1+ \cos(2x)}{2}\\
\\
&= \int^{\pi/3}_0 \left(\sec^2 x + 2\sec x + \left[ \frac{1}{2} + \frac{\cos(2x)}{2} \right] - 2 \cos x \right) dx\\
\\
&= \pi \left[ \tan x + 2 \ln |\sec x + \tan x| - \frac{1}{2} x - \frac{1}{2} \left( \frac{1}{2} \right) \sin (2x) - 2 \sin x\right]^{\pi/3}_0\\
\\
&= 5.95 \text{ cubic units}
\end{aligned}
\end{equation}
$

In "Gathering Blue," who wants to create a song for Kira?

The answer to your question lies in Chapter 18. There, we discover that Jo wants to write a new song for Kira.
In the story, Jo has been assigned to prepare for her eventual role of Singer. She is an orphan and is described as "hardly more than a toddler." However, her exceptionally beautiful voice has led to her being chosen as the next Singer. Like previous new "artists," Jo is locked in her room at night; as a Singer-in-training, she is forced to learn new songs every day. In Chapter 15, we discover that Thomas has carved a key that will unlock any door in the Edifice; this is the key he and Kira use to unlock Jo's door when they slip in to see her at night.
In Chapter 18, during a visit, Jo offers to make a new song for Kira. In reply, Kira cautions that they must be quiet on their visits so as not to alert the authorities to their nightly get-togethers. Jo understands this and maintains that, one day, when she gets the chance to, she will sing her new song for Kira "horrid loud." They both discuss the upcoming Gathering, and Jo proudly proclaims that she will be right up front during the event. The exchange ends with Jo asserting that, when she is Singer, she will be able to make her own songs again.
 

When writing an outline for an informative speech topic that involves stages or a process such as "how to fix a flat tire,"is there any other organization pattern to use besides chronological? It just seems to me that topical, cause/effect, spatial, or others just won't fit the topic.

That is a good question. On first glance, it would appear you're right. Since most processes are chronological, a chronological order would be the most common organizational structure.
It is not the only organizational structure possible, though. One of the easiest alternative structures to apply, and one that can make a stage or process speech more interesting, is a narrative. You can tell a story that illustrates the stages or processes by vividly recounting actual stories of people going through those stages. Rather than just explaining the steps to become a doctor, you'd tell stories about medical school and residency.
A cause-and-effect structure could also apply. If you used this structure, you'd give the causes for following a specific process, and the effects of doing so (and, if you have time, the effects of not doing so). This can be useful for processes with a number of options, like how to plant a garden.
A spatial structure is useful if the process has spatial implications or details. You can see this clearly in discussions of how to organize your life. You have to organize different spaces (such as your car, bedside, and wallet), and these different spaces might require different processes.

How is Eric Birling presented in An Inspector Calls?

Eric Birling is first presented as the ne'er-do-well son of the wealthy and hardheaded businessman Arthur Birling, but later he proves his worth as an honest man.
Eric is an alcoholic, whose behavior has been dissolute and irresponsible, but his mother pretends that there is nothing wrong with her son. In the end, unlike his parents, Eric, along with his sister, demonstrates that he does possess a moral compass and a worthy conscience, by not excusing his guilt in the death of a poor young woman.
While the Birling family enjoys a celebratory dinner for their daughter Sheila and her fiance Gerald Croft, a police inspector arrives to question the family about a young woman named Eva Smith, who later calls herself Daisy Renton, who has committed suicide. The inspector shows each person separately a photograph, and he describes the poor girl's history.
At first, he talks to Mr. Birling and Gerald. However, as the drama develops, it is demonstrated all of the Birlings are involved in the tragic events that lead poor Eva to taking her life. The inspector also reveals that both Gerald and Eric have been romantically involved with Eva after her firing at the Birling factory and another job.
When Eva, who calls herself Mrs. Birling, appears before Mrs. Sybil Birling's charity group to appeal for financial help, the outraged Mrs. Birling prevents Eva from obtaining anything. She insists, ironically, that the father of the child must be held responsible. Eva tells her that this young man has given her some money, but she suspects that it has been stolen, so she cannot accept anything from him. (The young man, of course, is Eric and his impregnating Eva is why she has called herself Mrs. Birling.)
After all the inspector's revelations, Eric and his sister Sheila, who caused Eva's firing from a dress shop, admit their guilt. Further, Eric confesses to his father that he did, in fact, steal fifty dollars which he gave to Eva. Arthur Birling's first reaction is how to cover up the loss of the fifty dollars so no one will know. He tells his children that "a man has to mind his own business and look after himself and his own."
Further, Birling says there is reason to excuse his and his wife's behavior, but he is ashamed of Eric. On the other hand, Eric replies that he is ashamed of them, as well, as his father began her misfortunes and his mother directly caused her and his child to die. Nevertheless, in the end, the parents justify their actions because the inspector has performed a ruse and is not a real policeman. Only Eric and his sister accept their social responsibilities.

Who is Old Bryson in "One Thousand Dollars" by O. Henri?

Old Bryson is the rather brusque and vinegary member of the men's club that young Gillian frequents.
Old Bryson is really not old; at forty years of age, he is simply one of those anti-social men who join social clubs so that they can sequester themselves in dark corners and be exasperated by others. While they pretend to be absorbed in their reading, they listen to a great deal, and know about many of the members.After the death of his guardian, who leaves him one thousand dollars, Gillian comes to his club to ask Old Bryson what he should do with this inconvenient amount of money.

"I thought," said Old Bryson, showing as much interest as a bee shows in a vinegar crust, "that the late Septimus Gillian was worth something like half a million." ("One Thousand Dollars")

Demonstrating that he is not unlike Bryson in his cynicism, Gillian "assents joyously" to Old Bryson's remark. "...and that's where the joke comes in." He tells Bryson that his uncle has left most of his money to science for the invention of a bacillus and the rest to "establish a hospital for doing away with it again" ("One Thousand Dollars"). The butler and the housekeeper get a seal ring and $10 each, and he gets $1000.00.
No longer disinterested, Bryson reflects that Gillian has always had copious amounts of money to spend. Gillian concurs, "Uncle was the fairy godmother as far as an allowance was concerned" ("One Thousand Dollars"). And, when Bryson asks if there are any other heirs besides Gillian, the young man replies, "None." He tells Bryson about a ward of his uncle, a Miss Hayden, who lives in the house. But, she also has only received $10 and a ring. Finally, Old Bryson rubs his glasses and smiles, and Gillian knows that he will be more offensive than usual.
Bryson finally suggests that Gillian spend the lump sum on a Miss Lotta Luriere, who works at the Columbine Theatre. Then, he tells Gillian, he can "inflict" his presence on a  sheep ranch in Idaho. "I advise a sheep ranch as I have a particular dislike for sheep," says Bryson ("One Thousand Dollars"). Gillian rises, thanks Bryson and heads to the theatre, resolving to rid himself of his inheritance.

Why does Amir feel distant from Soraya in The Kite Runner?

The Kite Runner deals primarily with the themes of guilt and redemption. In many ways, both those things are defined by the harsh Afghan culture and the society that dictates how people's lives should be run. Amir, the novel's protagonist, has a particularly hard time separating his own truths from those of the people around him. This ends up being the cause of the guilt that pains him for years, until he finally decides to try and redeem himself.
His wife, Soraya, on the other hand, never struggles with that particular problem. Being born a woman, she was always in a more difficult situation than Amir, but she ended up a much stronger person. Despite the patriarchal society she lives in, Soraya grew up to be both rebellious and good. She was able to critically determine exactly which parts of her culture she agreed with and which she didn't want to adhere to. Her decision to run away with an Afghan man, to whom she wasn't married, cost her a lot and put her in a difficult position, but Soraya's problems are all external, while Amir's are internal. She is criticized by the refugee community for her actions, but Soraya herself is not a conflicted person. She is aware that the community is being unfair to her. Amir, on the other hand, knows he's in the wrong and does nothing about it, being eaten up inside by his own conscience. Amir envies Soraya; that is the reason why he feels a bit distant from his wife. He loves her a lot, but he also feels inferior to her.
Unlike Amir, who can't bring himself to confess what happened to Hassan, Soraya is able to be honest about her past. This means that Amir is keenly aware of how far ahead of him Soraya is. She owns up to her "mistakes"—which are only mistakes according to their oppressive community—while he hasn't been able to deal with much worse things that are definitely his fault. Like with Hassan many years before, Amir starts to feel distant from a person he loves who makes him feel quite small with their example. This time, however, that feeling leads to Amir finally taking steps to atone for his sins and ends up bringing him closer to Soraya as well.

In the story, Amir briefly felt distant from Soraya when she told him the truth about her past, while he was unable to share his past. Soraya told Amir about how in the past she ran away with a man. She was rebellious, and the man was into drugs. Members of her community talked about it, and the situation brought shame to her family. Eventually, her father found her, and she went back home.
Amir, on the other hand, thought of telling Soraya about his past, but he couldn’t talk about it and decided to keep it a secret. Amir wanted to tell Soraya of how he betrayed Hassan, how he framed him for theft, which led to the end of a forty-year relationship between his father and Ali. According to Amir, Soraya was better than him because she had the courage to tell him the truth.

What did Neil Gaiman mean when he stated that “death is the great democracy”?

He simply means that death is the great leveler; despite the differences there may be between us in life in terms of wealth, race, social status, and so on, we're all equal in death. The graveyard itself is not a democracy, as Gaiman makes clear. This is because some of the dead have more elaborate gravestones than others, or are more fondly remembered. But those gravestones are part of the living world they've left behind, and so have no impact on the voices of the dead, all of which are equal in this post-mortem democracy. And so all the spirits in the graveyard get to have their say in whether or not Bod, the living child, should be allowed to stay.

The text tells us that all of the dead at the cemetery make their voices heard in the decision to keep or banish Bod.
According to Neil Gaiman, "death is the great democracy." This means that all humans must eventually die, no matter who they are. In that sense, all humans are considered equal in the face of death. So, in terms of deciding whether to keep Bod at the graveyard, none of the dead can claim precedence in terms of wisdom or position. In the story, all the inhabitants of the graveyard are dead and so, must have equal voice in the decision.
Of course, the decision is not an easy one. Josiah Worthington rightly argues that the graveyard is no place for a living, human baby. Yet, because of the danger Bod is in, the inhabitants of the graveyard must do everything they can to protect the child. In the end, three hundred voices are raised in reference to the matter. Each one of the dead clamors to be heard; yet a conclusive decision is not reached until the Lady on the Grey appears on her horse. Her words, "The dead should have charity" decides the course of action the graveyard inhabitants will take.
This is how Bod comes to spend his formative years at the graveyard. Mr. and Mrs. Owen volunteer to be Bod's parents, while Silas offers to be Bod's guardian. Between them and the rest of the dead, they do an admirable job in preparing Bod to meet his nemesis in battle.

f(x)=1/(1+x)^2 Use the binomial series to find the Maclaurin series for the function.

Recall binomial series  that is convergent when |x|lt1 follows: 
(1+x)^k=sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!)x^n 
  or         (1+x)^k= 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4- ...
 For given function f(x) =1/(1+x)^2 , we may  apply Law of Exponents: 1/x^n = x^(-n) to rewrite it as:
f(x) = (1+x)^(-2)
This now resembles (1+x)^k for binomial series.  
By comparing "(1+x)^k " with "(1+x)^(-2) ", we have the corresponding values:
x=x and k = -2 .
 Plug-in the values  on the formula for binomial series, we get:
(1+x)^(-2)=sum_(n=0)^oo (-2(-2-1)(-2-2)...(-2-n+1))/(n!)x^n
               = 1 + (-2)x + (-2(-2-1))/(2!) x^2 + (-2(-2-1)(-2-2))/(3!)x^3 +(-2(-2-1)(-2-2)(-2-3))/(4!) x^4- ...
             = 1 -2x + 6/(2!) x^2 -24/(3!)x^3 +120/(4!)x^4- ...
              = 1- 2x +3x^2 -4x^3 +5x^4- ...
              or  sum_(n=0)^oo (-1)^n (n+1)x^n
Therefore, the Maclaurin series  for  the function f(x) =1/(1+x)^2 can be expressed as:
1/(1+x)^2 =sum_(n=0)^oo (-1)^n (n+1)x^n
or 
1/(1+x)^2 =1- 2x +3x^2 -4x^3 +5x^4- ...

What are some analogies in "If I Forget Thee, Oh Earth"?

In Arthur C. Clarke's short story "If I Forget Thee, Oh Earth," we meet Marvin, whose father is taking him on a trip to "the Outside" for the first time. The story begins with lots of imagery and description before we get into analogies in the form of similes and metaphors. Analogies make comparisons; in the form of a simile, the writer compares two unlike things using "like" or "as."
At almost the halfway point of the story as Marvin's father speeds across this land that has as yet been unknown to Marvin, the narrator says, "Father was driving with a reckless and exhilarating skill as if—it was a strange thought to come into a child's mind—he were trying to escape from something." Marvin imagines that his father is driving recklessly as if trying to evade some unknown force. In the same paragraph following more imagery describing the landscape, the narrator writes, "The crests of the mountains, catching the low sun, burned like islands of fire in a sea of darkness: and above them the stars still shone as steadfastly as ever." The effect of the sun shining on the mountains is compared to burning "islands of fire." This simile allows us to picture the radiant light and to understand how extreme the view is to Marvin.
Eventually, we become aware that Marvin is viewing Earth from a distance, totally in awe of the sight. He wonders why he and his father cannot live there:

Why could they not return? It seemed so peaceful beneath those lines of marching cloud. Then Marvin, his eyes no longer blinded by the glare, saw that the portion of the disk that should have been in darkness was gleaming faintly with an evil phosphorescence: and he remembered. He was looking upon the funeral pyre of a world— upon the radioactive aftermath of Armageddon.

The narrator relates that Earth is now uninhabitable: a "funeral pyre of a world." This metaphor compares the planet to the way some cultures put their dead to rest: by burning their bodies on a pile of flammable materials. This is a vivid analogy that conveys the utter hopelessness of living on Earth again. On the contrary, their current abode, known as the Colony, is a "little oasis of life." Again this analogy in the form of a metaphor shows that the Colony provides relief in a world that is mostly marked by destruction and death.
Ultimately, we leave Marvin with some sense of hope that he or his children will one day return to Earth, but he also imagines he will continue to pass this story on as his father has passed it to him. The ambiguous ending leaves us wondering how much hope really is left and how long it can be kept alive.

When Agamemnon calls an assembly of the army and says they should leave Troy, who does he blame?

Because Achilles sulks in his tent, his Achaean comrades suffer in their epic conflict with Troy. No matter how many times the Achaeans try to persuade Achilles to join the battle, he pointedly refuses to emerge from his tent. It is a desperate situation, and Agamemnon has made an important decision. He calls together an assembly of the Achaeans. The mood is somber, and morale is low as Agamemnon begins to speak. The grief-stricken king tells the assembled throng that the Achaeans should return home. Having been driven back to their ships by the rejuvenated Trojans, it is clear that the Achaeans are not favored by the gods. If the gods are against them, then there is nothing to do but head home. In particular, Agamemnon says that Zeus, the father of the gods, has turned against them.

What is the characterization like in "Porphyria's Lover" by Robert Browning?

This poem is one of Browning's great dramatic monologue. The dramatic monologue is a specific type of poem in which the speaker reveals to an implied audience some relevant piece of information. In doing so, the diction and style the speaker uses eventually reflects more about his or her own mental or moral character than is initially intended. As others have mentioned, this is a form of direct characterization, such that the reader must piece together the true from the false.
This speaker has committed a horrific crime by strangling his beloved so that he can keep her with him forever without change in the relationship. The poetic lines move quickly and smoothly along, masking the morbid events described.
Some readers note that the first half of the poem involves the beloved's molding the speaker to her preferences, while the second half involves him molding her. These mutual shapings create a disturbing center marked by death. The fact that the speaker does not break his tone or pacing at this moment seems to enhance the macabre tone, which is further punctuated by the end in which the speaker seems to be waiting for a divine retribution that does not come.

In the Browning poem "Porphyria's Lover," the characterization of the narrator is direct, as the reader hears his voice. Browning establishes the characterization of the narrator slowly. At first, the reader only sees Porphyria, as she comes in from the stormy night and stokes the fire; then, she puts the narrator's arm around her waist, bares her shoulder, and lets her yellow hair fall about her. The narrator takes no action throughout this part of the poem, so the characterization builds slowly. It is only once Porphyria declares her love for the narrator, and he knows that this love will not last, that he strangles her with her beautiful hair. Browning establishes the narrator's character from this one horrible act, as the lover then opens her eyes, unwinds her hair from her neck, and props her head on her shoulders. The entire characterization of the narrator is based on this act of violence, followed by a few tender gestures. We never know anything else about him, save his desire to preserve Porphyria's love forever. 

What does Ponyboy think it is better to see Socs as “just guys”? What do you think he means by this?

In chapter 7, the Greasers discover that Johnny has a broken back and a slim chance of survival. The next day after visiting, Johnny, Ponyboy and Two-Bit stop at the Tasty Freeze to buy some sodas and Randy Adderson pulls up in a blue Mustang. Randy asks to speak with Ponyboy and commends him for saving the children trapped in the building. Randy proceeds to lament about Bob Sheldon's unfortunate death and gives Ponyboy insight into his background. Randy then says that he is sick of all the violence and will not participate in the upcoming rumble between the gangs. Randy is depicted as a sensitive, confused adolescent, and Ponyboy tells Randy that he would help him if he could. After Randy leaves, Two-Bit refers to Randy as "Mr. Super-Soc," and Ponyboy responds by telling Two-Bit that Randy is "just a guy." Pony then thinks to himself,

Socs were just guys after all. Things were rough all over, but it was better that way. That way you could tell the other guy was human too (Curtis, 100).

Pony is one of the most insightful, perceptive characters throughout the novel and is beginning to realize that Socs and Greasers have many similarities and both experience struggle throughout their lives. For Ponyboy, it is easier to view Randy and his gang members as "just guys" instead of Socs because it humanizes them, making it easier for Ponyboy to sympathize with their situations.

Which line from "The Leap" foreshadows what happens during the storm?

In "The Leap," the following quote foreshadows the storm:

"There came a rumble of electrical energy, drowned out by the sudden roll of drums."

This foreshadows the lightning that strikes the tent when Anna and Harry are performing. Specifically, this bolt of lightning hits the main pole as Harry is poised to catch Anna, causing him to topple forward and fall to the ground. Meanwhile, Anna realises that something is wrong and removes her blindfold so that she can see what is going on. She then changes the direction of her body and "twisted" towards a wire from which she is able to descend to the ground. Despite receiving burns to her hands, Anna saves her own life, though, tragically, she is unable to save the life of her unborn daughter.
In addition, the following line also foreshadows the storm:

"Winds generate instantaneously behind a hill and crash upon you without warning."

Through reference to the "crash," this line can be read as hinting both at the storm and the toppling of the tent as well as at the broken arm which Anna receives as the result of an over-zealous rescuer.

What is the difference between compound, element, and mixture?

An element is the simplest substance, one which cannot be broken down into smaller parts through typical physical or chemical approaches. Elements can be found in the periodic table, which organizes and lists them out according to their properties, such as mass. Elements consist only of atoms or molecules (in other words, two or more atoms of the same or different elements that have been bound together chemically) of identical chemical properties. 
Compounds are atoms of two or more different elements which have bonded together and which can be broken down into elements via chemical means.
Mixtures are a combination of different elements and/or compounds. For example, when we add salt to water, we are making a mixture; new molecules are not produced as a result of this. Instead, they mix together while keeping their own identities intact. 

Which lines from "The Love Song of J. Alfred Prufrock" provide an example of stream of consciousness?

As Eliot's speaker offers a dramatic monologue about his indecisiveness and reticence to take social risks, he at times interrupts himself to sink into a deeper subjectivity and morose self-evaluation.
 
Prufrock's affecting lack of self-worth and self-confidence are expressed when he rehearses some lines that he imagines could make him sound deep and poetic at a social gathering ("Shall I say, I have gone at dusk through narrow streets. . ."), and then breaks off to edit himself with the stream of consciousness line "I should have been a pair of ragged claws / Scuttling across the floors of silent seas."  Prufrock apparently finds himself so pathetic and stilted in his thoughts that he believes he is undeserving of his very humanity.
 
Immediately following a stanza in which he compares himself to a bit player in Hamlet, the speaker further denigrates himself with the stream of consciousness line "I grow old . . . I grow old . . . I shall wear the bottoms of my trousers rolled" as if his corporeal self is shrinking and withering away.
 
Just before the final stanza in which Prufrock offers a sensual image of mermaids riding the waves, he expresses his belief, in a last line of stream of consciousness, that in contemplating these beautiful creatures he "[does] not think that they will sing to" him. 

 
 
 
https://www.poetryfoundation.org/poetrymagazine/poems/44212/the-love-song-of-j-alfred-prufrock

Most of this great poem is a dramatic monologue, in which the narrator delivers an extended reflection on a topic. At some points, though, it slips into stream of consciousness.
In stream of consciousness writing, writers try to portray the way thoughts move through a person's mind. These thoughts tumble one after another, and the mind sometimes jumps from topic to topic in ways that are normal within the mind but uncommon in daily conversation.
In "Prufrock," you can see several examples of stream of consciousness.
Consider this brief stanza:

"In the room the women come and go
Talking of Michelangelo."

The first time it occurs in the poem, it is possible the narrator actually saw women walking in and out, and that's what they were talking about. However, when the same lines recur later, it is more likely they are bits of memory that drift in, as the narrator is reminded of something.
After the second time that couplet occurs, you'll find these lines:

"And indeed there will be time
To wonder, “Do I dare?” and, “Do I dare?”
Time to turn back and descend the stair,
With a bald spot in the middle of my hair —
(They will say: “How his hair is growing thin!”)"

That sudden moment of self-consciousness, and that image of hair going thin, is the same kind of self-conscious intrusion that is a common element in stream of consciousness.

Think about the characteristics of Elizabeth and Darcy at the beginning of the novel and at the end. How do they change throughout the course of the novel? What do you think the author is saying through the development of these characters?

Both Elizabeth and Darcy change over the course of the novel as they experience more of one another. These positive changes allow them to become fit life companions.
Elizabeth's great flaw is her prejudice. She makes snap judgments about people based on her first impressions of them. (The novel, in fact, was originally titled First Impressions.) Her tendency to leap to judgment doesn't give her time to really get to know a person before she has decided what he is like, which leads her to false assumptions. Because Darcy makes a terrible first impression on her by saying she is not pretty enough for him to dance with, she is predisposed to hate him and believe Wickham's stories about being cheated and mistreated by him. She is likewise charmed by her first impression of Wickham's looks and personality, and this prejudices her too much in his favor.
Darcy's great flaw is his pride. After all, it's very arrogant to decide a young woman is not pretty enough for you to dance just one dance with! His pride makes him act like a jerk, a characteristic which comes into play with disastrous results when he proposes marriage to Elizabeth. He assumes that she would never, ever turn down him and manages to insult her and her family by saying he deigns, in all his greatness, to marry her despite all the deficits she brings. Not surprisingly, this approach only serves to make him the last man on the planet she would ever consider marrying.
Elizabeth has to get over her prejudices or snap judgments about people and situations, and Darcy has to get over his pride before the two can get together and marry. Luckily, both characters are able to learn and grow.

Both Elizabeth and Mr. Darcy undergo profound change throughout the novel. Initially, Lizzie is extremely hostile toward Darcy, and it's not hard to see why. He comes across as aloof, cold, arrogant, and rude. He appears to be possessed with an exaggerated sense of self-importance, an over-inflated pride based on his wealth and high social standing.
Lizzie's initially unfavorable estimation of Darcy is compounded further when he actively interferes with Mr. Bingley's courtship of Jane. His crashing snobbery simply won't allow him to accept that Bingley should be involved with someone Darcy regards as a social inferior. Darcy even lets his pride get in the way of his feelings for Lizzie. He's falling for her in a big way, but just can't get over his innate snobbery. She's of a lower social class, and that's all there is to it.
For her part, Lizzie harbors a considerable degree of prejudice toward Darcy; she's simply not prepared to see that there might be something beneath that brooding, intimidating exterior of his. Yet she comes to see a different side to Darcy when she reads his letter regarding the true nature of the superficially charming Mr. Wickham. Lizzie had trusted Wickham implicitly and, due to her prejudice, was ready to believe the false stories he told her about Darcy. But Darcy's letter sets the record straight, showing Wickham to be nothing but an ingrate and an opportunist who shamefully abused his family's care and hospitality to try and get his greedy claws on the inheritance of Darcy's sister.
The letter is important because it makes Lizzie see Darcy in a different light. She hasn't completely overcome all her prejudices toward him, however; but then that's because he hasn't completely overcome his pride, either. He still insists that he did the right thing in breaking up Bingley and Jane's relationship. But the seeds of a future reconciliation between the couple have been sown. Both Lizzie and Darcy transcend their respective faults and listen to their hearts. Love conquers all, even what seems like deeply ingrained pride and prejudice.

Both Elizabeth and Mr. Darcy change quite a bit over the course of the novel.  Darcy realizes that his pride in his dealings with Mr. Wickham after Wickham tried to elope with Darcy's sister, Georgiana, actually enabled Wickham to take advantage of another girl: Lydia Bennet.  Had Darcy exposed what kind of man Wickham really was, Wickham likely would not have been able to do this.  Further, he realizes that he ought not to have gotten in between Bingley and Jane.  He also understands how unspeakably rude he had been and that he had "been a selfish being all [his] life."  By the time Elizabeth went to Pemberley, however, Darcy says that he wanted to "obtain [her] forgiveness, to lessen [her] ill opinion, by letting [her] see that [her] reproofs had been attended to."  He stops seeing himself as superior to her and begins to think of how he might please her.
Elizabeth also realizes that she has judged Darcy too harshly.  He virtually saved her family from ruin by forcing Wickham to marry Lydia, paying him in lieu of any dowry from the Bennets.  She realizes that, instead of finding him the last man on earth that she could ever want to marry (as she had months before), she feels a great deal of "gratitude" for Darcy's generosity, propriety, and discretion.  
It seems that Austen is pointing out the faults of both.  We see how excessive pride and willing prejudice can prevent, or at least delay, a realization of how well-suited two people might be for one another.  Elizabeth and Darcy, we might assume, will have an equal marriage based on mutual love and respect.  It would be sad, indeed, if their mistakes had prevented their happiness.