Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is important because avoiding a nuclear war is of paramount importance.
In Clancy’s story, the Americans are put in the awkward position of having to help Captain Marko Ramius in his efforts to defect to the United States with his nuclear-powered ballistic missile submarine and having to help the Soviet Union to “find” the highly-secret submarine—in order to avoid a panicked reaction against the United States. The Hunt for Red October was written during a period of intense and extraordinarily dangerous relations between the United States and the Soviet Union. The early-1980s were characterized by a large build-up in American military capabilities after a period of degradation. Modernization of American nuclear forces was a very prominent component of that build-up. In addition, both sides were adept at carrying out sophisticated naval operations intended to both collect intelligence on the other side while enabling ship and submarine crews to prepare for an actual war—a war that thankfully never materialized. Submarines and anti-submarine warfare were among the most secretive elements of the military competition between the two superpowers, and Clancy’s novel accurately captured the technological intricacies and political machinations that played out daily in the world’s oceans and seas.
The United States, under the circumstances depicted in The Hunt for Red October, helped Captain Ramius because the Navy and intelligence community desperately wanted to know as much as possible about Soviet submarine design and construction: the Red October represented the pinnacle of Soviet engineering. In addition to the intelligence that could be gleaned from examining the submarine firsthand, enormously valuable information could be conveyed by Captain Ramius after his arrival in the United States. As Admiral Greer points out at one point regarding the Soviet naval officer, "He's about the best sub driver they have, a real charger.” Captain Ramius could provide the West with invaluable insights into the thought processes of the Soviet Navy, as well as information on Soviet naval tactics. In short, the Americans had powerful incentives to help the defecting Soviet officers aboard the Red October.
The more important question regards the decision to help the Soviet government track its missing submarine. Here is where Cold War machinations and intelligence-gathering methodologies come into play. Until Ryan can convince his superiors, all the way up to the presidency, that Captain Ramius is a genuine defector, the United States must cooperate with the Soviet Union in locating the Red October so that it can be captured or destroyed before it is able to launch an attack on the United States. It is, in short, in both sides’ interests that the submarine be located and neutralized.  As Ryan notes in his meeting with the president,

The SS-N-20 has a range of six thousand miles. That means he could have hit any target in the Northern Hemisphere from the moment he left the dock. He's had six days to do that, but he has not fired. Moreover, if he had threatened to launch his birds, he would have to consider the possibility that the Soviets would enlist our assistance to locate and sink him.

Once the American government becomes convinced, however, courtesy of Ryan’s persuasiveness, that Captain Ramius is defecting and is not a rogue officer intent on starting a war, the United States still must be seen cooperating with the Soviet Union to enable the surreptitious capture of the submarine and its commanding officers without the Soviets knowing it has succeeded. This requires a deft touch; the Navy has to be perceived as helping the Soviet Union while simultaneously conspiring against it.
American assistance to the Soviet Union is significant because it is considered mutually advantageous and because it is part of a ruse to secure possession of the submarine without the Soviets knowing it.

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 8

Evaluate $\displaystyle \int x^2 \cos mx dx$ by using Integration by parts.
If we let $u = x^2$ and $dv = \cos mx dx$, then
$du = 2x dx$ and $\displaystyle v = \int \cos mx dx = \frac{1}{m} \sin mx$

So,

$
\begin{equation}
\begin{aligned}
\int x^2 \cos mx dx = uv - \int vdu &= \frac{x^2}{m} \sin (mx) - \int \left( \frac{1}{m} \sin mx \right) (2x dx)\\
\\
&= \frac{x^2}{m} \sin (mx) - \frac{2}{m} \int x \sin (mx) dx
\end{aligned}
\end{equation}
$


To evaluate $\displaystyle \int x \sin (mx) dx$, we must use integration by parts once more, so...
If we let $u_1 = x$ and $dv_1 = \sin (mx) dx$, then
$ du_1 = dx$ and $\displaystyle v_1 = \int \sin (mx) dx = \frac{1}{m} \left(-\cos (mx) \right)$

Thus,

$
\begin{equation}
\begin{aligned}
\int x \sin (mx) dx &= u_1 v_1 - \int v_1 du_1 = \frac{-x}{m} \cos (mx) - \int \frac{-\cos (mx) dx}{m}\\
\\
&= \frac{-x \cos (mx)}{m} + \frac{\sin(mx)}{m^2} + c
\end{aligned}
\end{equation}
$


Therefore,



$
\begin{equation}
\begin{aligned}
\int x^2 \cos mx dx &= \frac{x^2}{m} \sin (mx) - \frac{2}{m} \left[ \frac{-x \cos (mx)}{m} + \frac{\sin (mx)}{m^2} + c\right]\\
\\
&= \frac{x^2 \sin (mx)}{m} + \frac{2x \cos (mx)}{m^2} - \frac{2 \sin (mx)}{m^3} + c
\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 92

Prove that $\displaystyle f''(x) = \lim_{h \to 0 } \frac{f(x+1)-2f(x) + f(x-h)}{h^2}$ suppose that $f''(x)$ is continuous.

By applying L'Hospital's Rule
$\displaystyle f''(x) = \lim_{h \to 0 } \frac{f(x+1)-2f(x) + f(x-h)}{h^2} = \lim_{h \to 0} \frac{f'(x+h)(1)+f'(x-h)(-1)}{2h}$

Again, we must apply L'Hospital's Rule since the limit is an indeterminate form

$
\begin{equation}
\begin{aligned}
\lim_{h \to 0} \frac{f'(x+h)(1)+f'(x-h)(-1)}{2h} &= \lim_{h \to 0} \frac{f''(x+h) - f''(x-h)(-1)}{2}\\
\\
&= \lim_{h \to 0} \frac{2f''(x+h)}{2}\\
\\
&= \lim_{h \to 0} f''(x+h)\\
\\
&= f''(x+0)\\
\\
&= f''(x)
\end{aligned}
\end{equation}
$

What is a theme of Touching Spirit Bear and textual evidence that explains the theme?

Touching Spirit Bear by Ben Mikaelsen is a coming-of-age story about a young man named Cole who undergoes a healing treatment on a deserted island as punishment for violently attacking another boy. Cole is taken under the wings of two men: 
Garvey—Cole’s parole officer who got him into the rehabilitation program called Circle Justice.
Edwin—He is one of the Native Americans in charge of Circle Justice.
It’s not surprise that isolation would become a central theme to the book since Cole is put on an island alone to work out his problems. The ideal goal for Cole is to reflect on his actions and reenter society as a changed person. Isolation is explored in several ways—mostly through Cole’s experiences.
 First, Cole feels social isolation from the community. For example, Cole believes that people in his community try to help him be a better person only because they want to get rid of him. Mikaelsen writes, “He hated their fake concern. They didn't really care what happened to him. They were gutless—he could see it in their eyes. They were afraid, glad to be rid of him. They pretended to help only because they didn't know what else to do.” Do you see how Cole is isolated from society? He does it to himself, but his community also pushes him away too.
Second, Cole experiences physical isolation. He is physically placed on an island alone. The separation from others really gets to him. Mikaelsen says, “Some nights he cried himself to sleep from loneliness. He couldn't help it. The silence became overpowering, and he longed to hear another human voice.” It’s not that Cole even wants to interact with others; he just wants to hear them to know that he isn’t alone. 
Isolation persists throughout the book until the end when Cole returns to society. From there, he must use his new skills to reenter his community.

While the "circle" theme (or, "karma") is a great and prominent theme in Mikaelsen's Touching Spirit Bear (as outlined above), there are also a myriad of other themes Mikaelsen weaves through his narrative that are worthy of exploration.
Healing is a major theme of the novel. The urge and necessity to "heal" spans across dimensions, both physical and spiritual. Some textual examples are:

Cole's initial assault on Peter. This attack is a necessary step towards healing, and is a physical and spiritual endurance on both characters thereafter.

When the Spirit Bear attacks Cole. This instance explores Cole's pain and path to healing that parallels his initial assault on Peter.

Edwin and Gavey's atonement for their past sins. This highlights a prominent struggle towards peace that promotes healing.

Cole's Mother, and her broken heart. In "letting go" of her troubled marriage, Cole's Mother embarks on a very tenuous path to healing.
Along with healing, comes forgiveness. This is another theme Mikaelsen explores, and almost works hand-in-hand with "healing". Each of the examples above insight pain, healing, and forgiveness as the ultimate goal. A vital asset in healing is forgiveness, and each character is on their own path towards enlightenment.
In choosing a theme above (or creating your own) I'd advise you to consider which theme speaks to you, and investigate your own reasoning into why the author uses this theme. This will help you create a strong thesis statement and argument.

There are several wonderful themes in Ben Mikaelsen's novel. Touching Spirit Bear. 
One dominate symbol and theme in the novel is the circle and traveling in circles. In literature, circles can mean wholeness or healing.  Cole Matthew's life moves in a full circle as he is sent to the Alaskan island as a 15-year old juvenile delinquent who assaulted a boy for telling on him and later returning to the island and living with Peter Driscal, the boy he assaulted.
Some additional textual evidence of circles as a theme are:
Cole keeps getting himself in trouble and his parents and their high-priced lawyers usually rescue him.
Cole burns down the hut and later rebuilds it.
Cole continuously tries to swim off the island, running from his problems, only to return to the island to complete his healing.
Through flashbacks, Mikaelsen shows events that led Cole to being on the island and how his parents' actions contributed.  Later during physical therapy he reconciles with his mother.
Cole blames everyone for his anger and later learns to forgive.
Peter beats up on Cole in anger and later heals
Cole and Peter carve a circle symbol as the last symbol on the totem pole symbolizing their healing.

Edna Pontellier could not have told why, wishing to go to the beach with Robert, she should in the first place have declined, and in the second place have followed in obedience to one of the two contradictory impulses which impelled her. A certain light was beginning to dawn dimly within her—the light which, showing the way, forbids it. At that early period it served but to bewilder her. It moved her to dreams, to thoughtfulness, to the shadowy anguish which had overcome her the midnight when she had abandoned herself to tears. In short, Mrs. Pontellier was beginning to realize her position in the universe as a human being, and to recognize her relations as an individual to the world within and about her.This may seem like a ponderous weight of wisdom to descend upon the soul of a young woman of twenty-eight-- perhaps more wisdom than the Holy Ghost is usually pleased to vouchsafe to any woman. But the beginning of things, of a world especially, is necessarily vague, tangled, chaotic, and exceedingly disturbing. How few of us ever emerge from such beginning!How many souls perish in its tumult! The voice of the sea is seductive; never ceasing, whispering, clamoring, murmuring, inviting the soul to wander for a spell in abysses of solitude; to lose itself in mazes of inward contemplation. The voice of the sea speaks to the soul. The touch of the sea is sensuous, enfolding the body in its soft, close embrace. 1. The “it” in line 9 refers to: a) “ the two contradictory impluses” b)“a certain light...beginning to dawn” c) “the way” d) ”the shadowy anguish” 2. In line 23,”vouchsafe” can be best replaced by: a) bestow b) inform c) refuse d) deign 3. The final paragraph of the passage(lines 34-36) foreshadow a) Edna’s affair with Arobin b) Robert’s shipwreck on his way to Mexico c) the sucide at the end of the novel d) doctor Mandalet’s disapperance 4. Which of the following lines best describes Edna’s journey from this point to the end of the novel? a) “the voice of the sea speaks to the soul.” b)”this may seem like a ponderous weight of wisdom” c)”it moved her to dreams, to thoughtfullness, to shadowy anguish...” d)”of a world especially,is necessarily vague, tangled, chaotic and exceedingly disturbing.” 5. Line 30 contains an example of which literacy device? a) polysyndeton b)asyndeton c)anthropomorphism D) metonymy 6.the final two paragraphs depict a sea that is: a) anthropomorphised b) didactic c) personified d) dynamic 7.which of the following best describes edna’s characterization in the passage: 1. She is firm in her resolve to do as she pleases. 2. She is confused and lost regarding who she is and what she wants. 3. She is young and a bit naive. a) 2 only b) 1 and 3 c) 2 and 3 d) 1,2, and 3 8. The shift in perspective in the sentence beginning on line 26 and ending on line 27 does all of the following except a) give the reader a direct connection to the emotions Edna is feeling. b) imply that the situation is not uncommon c) give the narrator the opportunity to insert her commentary and experiences d) describe a situation for Edna to be a part of something greater than she. 9. The ”anguish in line 12,most likely refers to a) Edna’s distress over the creole culture and her lack of understanding with it. b)the heartbreak Edna felt when she listened to Madame Ratignolle reveal the intimate details of her delivery, knowing she would never be a “mother-women” c) the torment of knowing that is on the beach with Robert and the moment,though beautiful to her, would have repercussions. d) the sadness Edna felt when she realized, after being scolded by Leonce and checking on Raoul, that she is trapped. 10. The tone of the passage the best be described as a) sardonic b)reverent c) didactic d)solemn What is a literacy foil? Which characters serve as foils in The Awakening and how does their relationship illuminate the text? Protagonist Edna Pontellier is said to possess “that outward existence which conforms, the inward life that questions.” Identify a character who outwardly conforms while questioning inwardly. Analyze how this tension between outward conformity and inward questioning contributes to the meaning of the work. Avoid mere plot summary.

You ask what a literary foil is, which characters serve as foils in the text, and what their relationships with Edna might illuminate.  To begin, a foil is a character who possesses traits that contrast the traits of another character, often the protagonist, in order to illuminate the qualities possessed by that other character.  We might consider both Adele Ratignolle as well as Mademoiselle Reisz foils to Edna, each accomplishing something different. 
The contrast with Adele shows us how short Edna falls when it comes to doing her duty to her husband, Leonce, and behaving in accordance with her Creole community's mores.  Adele is quite feminine, a "sensuous Madonna," and a "mother-woman," who spends her time ministering to her children and performing her wifely duties as though they were a divine calling.  She keeps up her music to beautify her home and to bring joy to her husband.  She would do nothing that might embarrass him or subject him to ridicule by his peers.  
Mademoiselle Reisz, on the other hand, shows us how very far short Edna falls when it comes to becoming an artist and giving up the need to be accepted by society.  Reisz is invited to parties in order to be the entertainment, not because she is accepted as an equal.  However, Edna is unwilling to give up ties to society completely, and she still craves acceptance and praise, especially from Adele.  Reisz says Edna must have strong wings to soar above the plain of tradition, but Edna is not strong enough to do so alone.  
Both of these characters illuminate Edna's inability to choose a role.  Initially, she chooses to be a Creole wife and mother, but she finds that unfulfilling.  Then, she wishes to be an artist. She dabbles without any real, serious talent, but she finds that unfulfilling as well.  She must be willing to give something up in order to have each one, but neither option is, in the end, sufficient to satisfy her.  
To address your next open-ended question, the tension between Edna's outward conformity and inward questioning illuminates the theme that the individual is almost always at odds with society in some way.  Further, the tension conveys the idea that the price of total freedom from society's rules is alienation from that society.  Edna cannot break the rules of society and still be accepted by that society.  No person can.

Is the Commander sterile in The Handmaid's Tale?

The short answer is yes, probably, the Commander is sterile. When Offred goes for her routine appointment at the gynecologist, he says as much to her and offers to get her pregnant himself. She is horrified by the doctor's suggestion and is sure that he could be an Eye (a spy for the government) or that he might report her as disloyal and disobedient if she declines his offer—but the fact is that Offred has had a child before, and so we know it is most likely possible for her to become pregnant again. However, the Commander has never fathered a child, and, because of his age, it is extremely likely that he cannot do so. The doctor implies that this is the case himself.

The reader is never explicitly told whether or not the Commander is sterile, but it can be inferred that he is. The Commander is an older officer of the “Sons of Jacob,” so because he is in a respectable position in this dystopian society, it is forbidden to even insinuate that he is sterile. Actually, it is forbidden to insinuate that any man in power is sterile, even though it is a fact that most of the civilization has become sterile from toxicity in the environment. Sterility is publicly blamed only on the women because of the patriarchal nature of Gilead.
The handmaids, then, are a group of women that are forced to reproduce by these men in power because they have been proven to have healthy reproductive systems, which is difficult to find. Childbirth has become so rare that any single healthy child is revered and celebrated while the handmaids continue to live a life of reproductive slavery. In this society, however, even being in this position is a “blessing” because there are many other worse positions to be in, such as cleaning up toxic waste until eventual death.
Offred, having not produced a child for the Commander yet, is in grave danger of being sent to the toxic wastelands because the handmaids have a “deadline” that they must produce a child within. The reader can assume that the Commander’s wife, Serena Joy, is aware that her husband is most likely sterile. It is difficult for her to watch the monthly “ritual” between the Commander and Offred (essentially a ritual of rape), so she arranges for Offred to sleep with her husband’s chauffeur, Nick, in secret. This is a risky move that could get all three of them in trouble, but both Nick and Offred are afraid of what Serena Joy may do should they not follow her instructions so they oblige.

While we never know for sure, the text strongly suggests that the Commander is sterile. The reason handmaids exist at all is that pollution has rendered much of the population sterile. The Commander is an older man who has never fathered a child. Given the high levels of infertility in the culture, the Commander's age, and his lack of other children, the odds are very high that he can't procreate.
However, in this dystopia, a fundamentalist Christian world, a man can never be considered sterile. The myth that protects the men is that it is always the woman's fault if a pregnancy doesn't occur. If a handmaid doesn't eventually get pregnant, she is blamed, even if every likelihood is that the problem is with the man.
Serena and Offred both know this. Serena, a pragmatist, understands that her husband is most likely sterile. (Her thoughts on the subject help convince us that he is sterile.) Therefore, she arranges for Offred to have sex with the younger, very possibly fertile Nick. Although this is a risky move, Offred agrees to it, knowing that if she doesn't get pregnant, she will be sent to die cleaning up toxic waste.

In what ways are the current problems facing the United States similar to and/or different from the problems identified during the founding ?

The founders of the American constitution were challenged with an immensely bold undertaking: to address the problems faced by the colonies but do so in such a way that their solutions would pave the path for "a more perfect union" for centuries to come. Therefore they had to build a rigid but flexible structure, able to handle both the crises of the day and those of the future. In many ways they created a framework that has done just that—in other ways, at best, there were obstacles no one could have foreseen.
The largest of the discrepancies have stemmed from three main things: technology, political norms, and geography. Technology may be the largest unforeseeable factor: today our communication, governance, social glue, journalism, news reporting, and, therefore, democracy are all fundamentally changed by technology. New questions about the second amendment and gun rights are raised by entirely new forms of weapons in civilian hands. The internet has brought us self-publishing, which has shaken trust in established central news outlets, and instantaneous transmission, whereas communication in late-18th century America was done via horseback or stagecoach. Drones, missiles, and AI are changing our warfare and national security. The existence of smart phones and big data affect our privacy and central intelligence. When drafting both the protections of individuals under the Bill of Rights and the powers of the three branches of government, we have seen how simple wording in the Constitution can have profound consequences. Take, by example, how the wording "right to assemble" can be interpreted in an online context or how "a well regulated Militia" can be understood in the context of assault weapons, bombs, and gases designed to kill crowds. Granted, the Bill of Rights followed the founding of America in 1791, but the examples still stand as disparities in problems faced across time.
The second difference, political norms, is one that has changed in part because of the US constitution. The founders were responding to the central power of a king, whereas today we have presidents, prime ministers, and congresses whose powers are more distributed than monarchs of old. The difference, more broadly, is due to a general shift in regional powers from colonialism to tighter nation states and the constraining realities of nuclear power, economic warfare, cyber warfare, and global alliances such as the UN, EU, and NATO that shape global hegemonies.
The third major difference is a simple matter of geography. Some argue it was easier for Americans to fight for independence as colonial entities in America because they were separated from their oppressors by an ocean and had at their disposal a wealth of resources and land (after they had committed terrible genocide against the many indigenous populations existing before them). Any separatists and secessionists of today's America will find it much harder, as the South discovered in the mid-19th century.
I chose to end with the similarities between the problems the founders faced and those that exist now because I find them far more compelling. Of the similarities of great significance are the troubles imposed by a tyranny of the majority, the danger of factions to democracy, the power of money to corrupt, the threats misinformation and alienation of news sources bring to the people's right to free press and sharing of information, the damage to national security caused by degradation of trust in intelligence agencies, and the conflicts of interest held by a governing entity having lasting consequences. Many of the beliefs held by the founding fathers were to thwart these various threats against democracy and to create institutions that could withstand them. By drafting checks and balances between the executive, judicial, and legislative branches of government and by preserving freedom of speech and the press as a fourth check on the government, the founders hoped that the nation would continue to build on its good assets while fortifying against the corruption that has so often toppled former regimes. They also hoped to eventually purge the country's inherited habits of oppression, as was the case with institutionalized slavery (a slow process). The current dilemmas we face today that we share with the colonies are more important than ever.

What are some quotations from A Separate Peace that show peace and conflict in the scene where Gene visits Finny in the infirmary?

In chapter 5, the closest quotes that show peace and conflict during Gene's visit to Finny are below:

"I don't know; I must have just lost my balance. It must have been that. I did have this idea, this feeling that when you were standing there beside me, y—I don't know. I had a kind of feeling. But you can't say anything for sure from just feelings. And this feeling doesn't make any sense. It was a crazy idea. I must have been delirious. So I just have to forget it. I just fell . . . that's all . . . I'm sorry about that feeling I had."
He was never going to accuse me. It was only a feeling he had, and at this moment, he must have been formulating a new commandment in his personal decalogue: never accuse a friend of a crime if you only have a feeling he did it. And I thought we were competitors. It was so ludicrous I wanted to cry.

In the first quote, Finny hints that he had suspicions about Gene's involvement in his accident. However, since he only has his feelings to go by, he refuses to make accusations. 
In the second quote, Gene comes to the grim realization that he's been mistaken about Finny, and he becomes ashamed of the way he's treated him.The conflict first originated in Gene's mind. However, the tension between the two is clear in the two quotes above.
Gene visits Finny again later in the book, and we find them reconciled in chapter 12. Here, your best bet for quotes about peace and conflict are:

. . . I've gotten awfully mad sometimes and almost forgotten what I was doing. I think I believe you . . . Something just seized you. It wasn't anything you really felt against me, it wasn't some kind of hate you've felt all along. It wasn't anything personal.
. . . Tell me how to show you. It was just some ignorance inside me,some crazy thing inside me, something blind, that's all it was.
. . . I believe you. It's okay because I understand and I believe you. You've already shown me and I believe you.

In Americanah by Chimamanda Ngozi Adichie, who are Curt and Blaine?

Curt and Blaine are both past lovers of the main character Ifemelu.Curt becomes Ifemelu’s boyfriend for a couple years when Ifemelu is living in the United States. In her blogs, Ifemelu refers to Curt as the “Hot White Ex.” Curt and Ifemelu meet through Curt’s cousin Kimberly. Kimberly hires Ifemelu to be a babysitter in her home. While Curt is compassionate and kind to Ifemelu, he is also a Caucasian male who comes from a wealthy family and he doesn’t completely understand the racism and culture shock that Ifemelu regularly endures. Blaine is an African American professor at Yale University who later becomes Ifemelu’s boyfriend after she has been in the United States for several years. Ifemelu was immediately able to conclude that Blaine was African American, not African. Blaine is highly intelligent and intellectual, but he can also come across as snobbish and close-minded. For these reasons, Ifemelu becomes dissatisfied with the relationship.

In Chimamanda Ngozi Adichie's Americanah, a deeply exploratory and engaging novel on race and identity Curt and Blaine are minor characters. The reader is introduced to Curt who becomes Ifemelu's (main character) first boyfriend since she came to America for work and study. Ifemelu meets Curt while babysitting for his cousin Kimberly. A rich, handsome white man, Curt is enchanted and immediately drawn to Ifemelu and they soon start dating. Curt is a happy go lucky, optimistic and spontaneous man and everything always seems to fall into place for him. Despite their relationship appearing to be happy and solid on the surface, they are unable to have any serious conversations pertaining to race. This culminates to the disintegration of their relationship when Ifemelu cheats on Curt. Following their breakup, Ifemelu starts a blog called Raceteenth or Various Observations About American Blacks (Those Formerly Known as Negroes) by a Non-American Black.
Though not chronologically her first boyfriend, the reader is first introduced to Blaine before Curt. Ifemelu meets Blaine on a train and she is immediately drawn to his sharp wit and charm. An African-American professor at Yale and a fellow blogger, their shared interests in race and it's role in America heralds the beginning of a romance. However over time it becomes clear that Ifemelu doesn't quite fit in with Blaine, his friends, their intellectual discussions and political correctness. This puts a strain on their relationship and eventually Ifemelu decides to move back home to Nigeria.

Curt and Blaine are American men with whom the main character, Ifemelu, has significant relationships in Chimamanda Ngozi Adichie’s novel Americanah. Curt is the well-to-do cousin of Ifemelu’s boss, Kimberly. In Part II of Americanah, Ifemelu and Curt start dating, and he helps her find a job. At the beginning of Part IV, Ifemelu has just broken up with him. Although Curt—who is white—loved Ifemelu, he never really understood her experiences as a Nigerian woman dealing with racism in the US, nor did he realize that he could sometimes be subtly racist himself. After their breakup, Ifemelu starts a blog called Raceteenth or Various Observations About American Blacks (Those Formerly Known as Negroes) by a Non-American Black. When she blogs about Curt, she refers to him as “The Hot White Ex.”
Blaine, who is African American, is a fellow blogger and teaches at Yale. He and Ifemelu met years ago on a train and reconnect at one of the lectures Ifemelu is invited to give after the unexpected success of Raceteenth. Ifemelu moves to New Haven to be with him. While Blaine is supportive of Ifemelu’s writing, he sometimes disagrees with her on political issues. After Ifemelu doesn’t come to a demonstration Blaine organizes, he refuses to speak to her, and Ifemelu goes to stay with her Aunty Uju until Blaine arrives to make amends. Reunited, the two of them look for an apartment in Princeton, where Ifemelu has received a fellowship at the university. She and Blaine grow closer when she decides to join him in supporting Barack Obama as a presidential candidate, but before long Ifemelu grows unhappy and decides to move back to Nigeria.

What is the writer telling us about human nature and the world?

Yukio Mishima's retelling of Takeyama's suicide gives the reader a glimpse into the lengths that people will go to for the sake of preserving traditional values. In Mishima's eyes, Japan's growing materialism was a cause for concern. It seemed like Japan was focusing more on economic success instead of maintaining the values of the past. Takeyama's desire for transcendence outweighs any temporal reward he would gain if he complied with Japan's interest for profit during the 1960s.
Takeyama's decision to commit suicide calls back to a feudal tradition in which the losing hero would kill himself as an act of bravery. Once all other options are exhausted and he is put in a predicament where he can't win, Takeyama chooses to hold on to his honor. While most readers may be put off by Mishima's inclusion of the preparation prior to the suicide, it shows a level of admiration for a culture that he grew up in.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 36

Determine the derivative of the function $\displaystyle f(t) = \sqrt{\frac{t}{t^2+4}}$


$
\begin{equation}
\begin{aligned}
f'(t) &= \frac{d}{dt} \left(\frac{t}{t^2+4} \right)^{\frac{1}{2}}\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \frac{d}{dt} \left(\frac{t}{t^2+4} \right)\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{(t^2+4)\frac{d}{dt} (t) - (t) \frac{d}{dt} (t^2+4)}{(t^2+4)^2}\right]\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{(t^2+4)(1) - (t)(2t)}{(t^2+4)^2} \right]\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{t^2 + 4 - 2t^2}{(t^2+4)^2} \right]\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{-t^2+4}{(t^2+4)^2} \right]\\
\\
f'(t) &= \frac{1}{2} \frac{(t)^{\frac{-1}{2}}(4-t^2)}{(t^2+4)^{\frac{-1}{2}}(t^2+4)^2}\\
\\
f'(t) &= \frac{4-t^2}{2(t)^{\frac{1}{2}}(t^2+4)^{\frac{3}{2}}}
\end{aligned}
\end{equation}
$

What is Edward Bloom's vision of success and greatness from Big Fish by Daniel Wallace?

Edward Bloom's vision of greatness takes one form when he is younger and changes over time into another vision when he matures and becomes a father. According to William, Edward's son, Edward the child and young man, sees successful accomplishment of many different goals and challenges as a vision of greatness, but later in life, he wants to be remembered as a great man who did great things.
Daniel Wallace, the author of Big Fish, uses many mythological allusions to emphasize Edward's greatness when he encounters challenges as a child and a young man. Hyperbole works with these allusions to emphasize Edward's larger-than-life ability and personality; for example, when Edward is bedridden, he reads to pass the time, and over several months, he reads a thousand books. The weather changes dramatically in response to Edward's birth and milestones. Later in life, Edward somehow avoids being attacked by a particularly aggressive dog when he tries to walk through a town, suggesting he has a unique power over animals. Edward's powers of observation and persuasion are prodigious, powers that better suit a young god , rather than a mere mortal. In his own eyes, Edward sees himself as great thanks to his ability to take on difficult tasks successfully.
Of course, the reader learns about these stories through William, Edward's son, and William heard them all from Edward, his father. Through William's telling, the reader can gather that Edward wants to be remembered as a great man of many successes. The emotional depth and the significance of Edward's desire, later in life, to be remembered well is poignant when it is understood within the context of the family problems that afflict the Blooms. Edward turns out to be a cheating husband, which calls into question his other promises and claims, and by the end of the novel, Edward's vision of success is tempered. If, after all the hurt and disappointment, he can be remembered by his son as a great man, perhaps that will be enough.

When does Atticus show courage in the book To Kill a Mockingbird?

After the death of Mrs. Dubose and Atticus's disclosure that she died free of any drugs by withdrawing from morphine, Atticus defines courage for his son: 

It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do (Ch.11).

This definition serves Atticus when he is asked by Judge Taylor to be the defense attorney for Tom Robinson, a black man who has been accused of the crime of rape. Before the trial begins, the town of Maycomb is filled with tense, hostile, and excited public feeling. On the day of the trial, there is a virtual parade of people from both the county and the town who cram the courtroom. Certainly, Atticus is aware that Tom Robinson has only the truth on his side. He is a black man accused of raping a white woman, Jim Crow laws are in existence, and the jury is made of twelve white men from the area. (True to his definition, Atticus "begins anyway.")
Even in spite of the fact that there is no medical evidence proving that any rape occurred, that Bob Ewell is a known reprobate, and that there are contradictions in the testimonies of the Ewells, Atticus does not count out any evidence in support of the defense. He very wisely disproves that Tom could have choked and struck Mayella: she testifies that she was injured on both sides of her neck and struck on the right side of her face—all indications that a left-handed man inflicted her injuries. Tom Robinson has a useless left arm, which was injured years ago.
In other instances, Atticus has the courage to follow his code of ethics, morals, and child-rearing. He holds to his convictions by not engaging in gossip about Boo Radley and by insisting that the children "leave that man alone." On the night of the pageant when his children are attacked, Atticus bravely accepts that Jem may have killed Bob Ewell. He refuses to lie to protect Jem from the consequences. (Later, Sheriff Tate informs Atticus that his son was not the one who killed Ewell; Boo Radley saved both Scout and Jem.)

In Gulliver's Travels by Jonathan Swift, what makes Gulliver leave his house?

Gulliver leaves his childhood home in Nottinghamshire in order to acquire an education.  He attends a school in Cambridge called Emanuel College from age fourteen to seventeen.  After this, as the third of five sons, he is sent to be an apprentice to a doctor in London.  He studies as much as possible, but he eventually leaves this home in order to continue his formal education in medicine at Leyden.  When he returns to London, he leaves home again, at the suggestion of the man he had formerly apprenticed, in order to be the doctor on board the Swallow, a ship on which Gulliver travels for over three years. 
Later, after Gulliver marries and sees his medical practice fail, he leaves home to go to sea again and travels for six years more.  At this time, he determines to remain at home, but when he cannot make another business work, he goes, again, to sea, and thus begins his journey to Lilliput.

Based on the myth "The Wrath of Achilles," what are four reasons why the Greeks won the war against the Trojans?

The student's question does not specify any particular text, although one could logically presume that Homer's The Iliad provides the basis of the inquiry. The classic text tells the story of the ten-year war between a coalition of Greek kingdoms and the Kingdom of Troy, lead by King Priam. Priam's son, Paris, of course, takes Helen, the beautiful wife of King Menalaus, for himself. The Greeks retaliate by attacking and laying siege to Troy. During the course of the ten-year conflict, many well-known figures from Greek mythology appear and play prominent roles, including mortals and immortals alike. The Iliad, alone, however, may be insufficient to provide a full response on the Greek victory over Troy. Other sources of Greek mythology must also be consulted.
The question asks for four reasons the Greeks prevailed over Troy. The most direct answer as to why, or how the Greeks prevailed is the successful use of deception involving a giant wooden horse. As students of the Trojan war know, the Greeks, despite their long siege of Troy, had been unable to penetrate the king's fortress walls. The giant wooden horse was the brainchild of Odysseus (the hero of Homer's other well-known classic The Odyssey) and was constructed with the aid of Athena and Epeius, a respected carpenter. It was hollow inside, allowing for the concealment of a number of Greek soldiers. The horse was inscribed to the Trojans as a monument to Athena and is presented as a gift. Despite the misgivings of some Trojans, the wooden horse was wheeled inside the fortress walls. The Greek soldiers sneak out of the horse in the darkness of night and proceed to slaughter and/or rape all those within the fortress walls.
The "Trojan Horse," in effect, is the main reason for the Greek victory. It does not, however, answer the student's question. That answer, perhaps, can best be formulated by drawing on the recommendations of Helenus, brother of Paris and a seer who Odysseus and other Greeks interrogated in an effort at attaining valuable intelligence on the Trojan enemy. The lessons taken away from this interrogation are that, in order to defeat Troy, the Greeks must meet several conditions: they must enlist the son of Achilles, Neoptolemus, in their fight; they must retrieve and transport to Troy the bones of Pelops, whose grandson, Agamemnon, was among the most powerful of the Greek leaders; they need to bring into the battle Philoctetes, a master archer who would use the the weapons of Hercules in the battle against the Trojans and who had been abandoned by the rest of the Greeks on the island of Lemnos; and the Greeks would have to capture the Palladium, a wooden statue crafted by Athena in the image of Pallus, the god of war. 
The four tasks prophesied by Helenus were executed by Odysseus and Diomedes. It was the wooden horse, however, that sealed Troy's fate while revolting all those upset by the vengeful slaughter carried out by the Greek soldiers who had been hidden in the hollow structure.
https://ryanfb.github.io/loebolus-data/L170N.pdf

What ghost has the best effect on Scrooge?

No single ghost has a "best" effect on Scrooge.  In fact, the messages of all of the spirits, including Marley's ghost, are essential in helping Scrooge become a better person.  Looking at what Scrooge gains from each of them will help illuminate their joint effect.Marley's ghost not only shocks Scrooge, he also gives him a direct warning regarding his chains and the connection to the chains that Scrooge is forming in life.  By starting with Marley's ghost, Scrooge is given a touchstone and a level of familiarity with the ensuing events in his journey.  While the spirits do wish to shock him, their entire goal is to help him change.  As terrible as his afterlife is, Marley's  afterlife is significantly better than the afterlife that awaits Scrooge if he does not change.The Ghost of Christmas Past is essential to reminding Scrooge of where he came from and of the kindness that Scrooge experienced earlier in his life.  Through a glimpse of Scrooge's childhood at the boarding school, the spirit reminds Scrooge of what it is like to be lonely and abandoned. However, the spirit also shows Scrooge what it is like to feel love through Scrooge's sister.  This scene also reminds Scrooge to love Fred, the only family he has left.  Through Fezziwig, the spirit shows Scrooge how a boss should act.  Through Scrooge's breakup with Belle and the view into her life on the eve of Marley's death, the spirit shows Scrooge what he could have had.The Ghost of Christmas Present shows Scrooge a number of important scenes that help him to change.  By showing Scrooge Cratchit's meager home and Fred's dinner party, the spirit shows Scrooge the kindness, love, and forgiveness of the holiday season.  Though Scrooge has mistreated all of them, they all toast him and wish him the best.  Further, the spirit also introduces Scrooge to Ignorance and Want, the manifestation of humankind's worst traits.  Finally, the spirit also throws Scrooge's own words in his face to show him how calloused Scrooge has become.Finally, the Ghost of Christmas Yet to Come reveals the future that lies ahead if Scrooge fails to change.  Rather than hint at Scrooge's afterlife, as Marley did, the spirit shows Scrooge the world without him.  Tiny Tim dies, and Scrooge dies cold and alone; his possessions are stripped from him and pawned off.  The only good that comes from his death is the relief of those who owe him money.Each spirit is essential to Scrooge's movement from greedy to giving.  Without the combination of past, present, and future, Scrooge would not have been able to change.  This reflects Dickens's own belief in the importance of experience.  Experience is important;  it comprises who we are and who we will become.

How does Jack London use the literary element of flashbacks to impact his audience in "A Piece of Steak"?

Jack London uses flashbacks in "A Piece of Steak" to help the reader see exactly where Tom King had once been in his life. The flashbacks simply help the reader compare and contrast Tom King's former status with his current one.
As Tom King is making his way to his next fight, on foot, he remembers what it was like when he was considered the best in the world.

Big money--sharp, glorious fights--periods of rest and loafing in between--a following of eager flatterers, the slaps on the back, the shakes of the hand, the toffs glad to buy him a drink for the privilege of five minutes' talk--and the glory of it, the yelling houses, the whirlwind finish, the referee's "King wins!" and his name in the sporting columns next day.

This lets the audience know that Tom King was, at one point, used to glory and fame and all of the privileges that came along with it. The flashback shows Tom King once had people fawning over him, buying him food, and practically throwing money at him. When compared to what Tom King is going through currently in the story, it's a sharp contrast. 

The secretary of the Gayety Club had advanced him three pounds--the loser's end of the purse--and beyond that had refused to go. Now and again he had managed to borrow a few shillings from old pals, who would have lent more only that it was a drought year and they were hard put themselves.

This quote shows Tom King's current status in life: penniless and borrowing money from any source he could. Tom King fell from grace, and he had to learn how to reconcile that fact within himself. 

How, in Animal Farm, does Napoleon's use of of obedience tactics help the farm?

In a general sense, Napoleon's tactics lead to greater productivity on the farm. His insistence that the animals follow instructions and remain loyal guarantees that the animals remain committed and unquestioning. In such a system, more focused and productive labor ensures greater returns and bigger profits. Furthermore, the tactic guarantees a servile attitude and minimizes the risk of recalcitrance and rebellion.
Napoleon ensures that the animals remain obedient not only through propaganda, misinformation, and deceit, but also brutally enforces control by slaughtering those who dare rebel against him. The best example of this occurs in chapter seven, when the three hens who resisted his instruction to sacrifice their eggs are executed by his dogs. Animals who supposedly plotted against him also suffer the same fate. In this manner, Napoleon establishes a merciless tyranny. He becomes supreme leader and his authority cannot not be questioned.
The success of this strategy is proven by the successful completion of the windmill after it had been destroyed, the lack of wastage on the farm, and the general air of commitment, although enforced, that exists. This is best encapsulated by Boxer's two maxims: "I will work harder" and "Napoleon is always right." These statements reflect the overall sentiment on the farm, with the exclusion, to a certain extent, of Benjamin. Although he is quite cynical and recalcitrant, Benjamin does what is asked of him.
Although Napoleon's strategy leads to the successful running of the farm, it is, sadly and ironically, only the pigs and Napoleon's dogs who truly benefit. They live lives of luxury whilst the other animals are always tired, hungry, cold, and miserable.
The greatest irony lies in the fact that the gullible general animal populace believe they have achieved utopia when, in fact, their dream has resulted in a dystopian reality that is worse than the one they experienced under Jones's rule.

How is Pip rescued from Orlick?

In chapter 53 of Charles Dickens's Great Expectations (1861), Philip Pirrip (nickname: Pip) is lured by an anonymous letter to a sluice house. Once he arrives, he is ambushed by Dolge Orlick. A noose is put around Pip's neck, and he is tied to a ladder.
Orlick was first introduced in chapter 15 and resents Pip for a variety of reasons. At this time, he reveals some of them to Pip. He believes Pip is the reason that Biddy did not fall in love with him, and he hates that Pip was preferred over him as an apprentice. On this occasion, Orlick also confesses to the attack on Mrs. Joe.
Just as Orlick grabs a hammer to kill Pip, the latter is rescued by Herbert, Startop and Trabb's lad. Herbert later reveals that they managed to arrive just in time because he had found the anonymous letter at Pip's apartment and—worried for his safety—had decided to chase after him. The three men attack Orlick (who escapes) and then take Pip away to the town.

In the chapter titled "Signlight and Moonlight" there is this paragraph: “I want some gum-drops,” she said, humorously apologetic; “you can’t guess what for this time. It’s just that I want to bite my finger-nails, and I will if I don’t get some gum-drops.” She sighed, and resumed as they stepped into the empty elevator: “I’ve been biting ‘em all day. A bit nervous, you see. Excuse the pun." I am not a native English speaker and I do not understand the pun in here. In Chapter II (Symposium) what's the meaning of "unpleasantly undergraduate" in the phrase "the best of the men not unpleasantly undergraduate"? Further on when Maury speaks of himself he says "I read Smith, who laughed at charity and insisted that the sneer was the highest form of self-expression–but Smith himself replaced charity as an obscurer of the light." What exactly does the author mean by obscurer of the light?

In terms of the pun in the first quotation, I cannot be entirely certain without seeing the full context, but I would interpret this to be a joke on the part of the author—that is, there is not actually a pun at all. A phrase like "Excuse the pun" might be dropped into conversation by a nervous person almost as a figure of speech, without this person having actually made a pun. The joke is therefore that, whatever pun the speaker is thinking of, it was not evident to the listener. It is entirely possible that the pun could be on "gum-drops" and nail-biting—with "gum" here referring both to the gums in the mouth and the gum that the drops themselves are made of—but this is extremely tenuous and not truly a pun.
"Unpleasantly undergraduate" is an interesting one; "undergraduate" is here being used as an adjective, but it is typically used as a noun. If someone is "unpleasantly undergraduate" that means that they are behaving unpleasantly like an undergraduate (a student who has not yet graduated from university). As a result, an "unpleasantly undergraduate" person is immature in the manner of someone aged between 18 and 21 and probably has some mannerisms particular to a college student (pretentiousness, an inflated sense of self, and so on).
In the third example, "obscurer of the light" would literally mean someone who gets in the way of the light. In this case, it is probably being used metaphorically: an "obscurer of the light" is someone who makes it difficult to see or understand things clearly, or, alternatively, it could refer to someone who makes it difficult for goodness to shine through.

How are political parties and interest groups similar and different?

Political parties and interest groups are similar in one important way. That is that they both attempt to get political candidates elected. Political parties choose candidates for office through a primary voting process in which members vote for the one they support. This is true at almost every level of government. Once the party chooses its candidates, it supports them with money, provides exposure, and provides the legitimacy that party candidacy entails. The fact that it is so difficult for third party or independent candidates to get elected in the United States demonstrates how effective they are in this process. Interest groups, on the other hand, usually represent a certain issue, or "interest." They support candidates who take acceptable positions on whatever issue or group they are organized around. Like political parties, they provide financial support through donations but especially through advertising for candidates they back. One major difference between special interest groups and political parties is that parties are best described as coalitions of many different groups of people. While parties generally share an ideological perspective, they take positions on a number of issues, called a platform. On the other hand, interest groups generally represent a single group (such as retired people or gun owners) or a single issue (like abortion rights). Interest groups, while extraordinarily powerful, do not have the kind of structural influence over American politics that parties do.

Beginning Algebra With Applications, Chapter 5, 5.5, Section 5.5, Problem 62

Depreciation is the declining value of an asset. For instance, a company purchases a truck for $\$ 20,000$. The truck is an asset worth $\$ 20,000$. In 5 years, however, the value of the truck will have declined, and it may be worth only $\$ 4000$. An equation that represents this decline is $V = 20,000 - 3200x$, where $V$ is the value, in dollars, of the truck after $x$ years.

a. Write the equation in functional notation.

The equation $V = 20,000 - 3200x$ can be written in functional notation as $f(x) = 20,000 - 3200x$

b. Use the coordinate axes to graph the equation for values of $x$ between 0 and 5.

Using the equation in part a. Substitute values of $x = \{ 0,1,2,3,4,5 \}$


$
\begin{equation}
\begin{aligned}

f(0) =& 20,000 - 3,200(0) = 20,000
\\
f(1) =& 20,000 - 3,200(1) = 16,800
\\
f(2) =& 20,000 - 3,200(2) = 13,600
\\
f(3) =& 20,000 - 3,200(3) = 10,400
\\
f(4) =& 20,000 - 3,200(4) = 7,200
\\
f(5) =& 20,000 - 3,200(5) = 4,000

\end{aligned}
\end{equation}
$



The ordered pairs are $(0,20000), (1,16800), (2,13600), (3,10400), (4,7200)$ and $(5,4000)$







c. The point $(4,7200)$ is on the graph. Write a sentence that explains the meaning of this ordered pair.

The point $(4,7200)$ means that in four years the value of the truck will be worth $\$ 7,200$.

I am still struggling with my compare and contrast essay on Larkin's "This Be The Verse" and Ibsen's A Doll's House. I need help with the thesis and some points of comparison with sub-points. (What is a sub-point?)

Ibsen's A Doll's House and Larkin's "This Be the Verse" are both about the unhappiness in families. This might be a point of comparison that you can make between both works. However, A Doll's House is about the deceit and misunderstanding between a husband and wife, while Larkin's poem is about the ways in which parents are flawed because their parents were flawed too.
In writing your thesis, you want to include both a comparison between the works (for example, that they both treat familial problems) and a contrast between the works (for example, that Ibsen concentrates on marriage, while Larkin concentrates both on marriage and parental relationships). Sub-points include minor points that you will discuss in your body paragraphs. These points might include how, for example, Ibsen portrays the flaws in marriage. In his play, Nora is the "doll"; her husband patronizes and treats like a child, while she, for her part, tries to deceive her husband about the money she has borrowed. Your other sub-points might include what Larkin expresses in his poem. Take apart each line and think about what he is saying about parents' relationships with their children. For example, he writes, "They fill you with the faults they had / And add some extra, just for you." What is he saying about the ways in which parents unwittingly pass along their flaws to their children? What does the metaphor "It deepens like a coastal shelf" mean in reference to families' misery? By answering these questions, you can develop sub-points in your body paragraphs.

Precalculus, Chapter 3, 3.4, Section 3.4, Problem 21

Add 9 to both sides
e^x=28
Take the ln of both sides and bring down the exponent
xlne=ln28
x=ln28/lne
x=3.332

What is Bottom's view of love?

Bottom's love story in A Midsummer Night's Dream is a side-plot, mainly intended for comic relief. He is given the head of a donkey by the mischievous fairy Puck, who then enchants Titania, the queen of the fairies, to be infatuated with him. Bottom never seems particularly taken with her, though he appreciates the luxuries of her court. When he first meets her, he tries to get away, more concerned with getting back to his theater troupe than starting a romance with the supernatural beauty. Eventually, both enchantments are lifted, and the pair part ways without heartache on either side.
Bottom's response when Titania first sees him and tells him that she loves him in act 3, scene 1 is as follows:

"Methinks, mistress, you should have little reasonfor that: and yet, to say the truth, reason andlove keep little company together now-a-days."

This is the most explicit statement we see from Bottom regarding his view on love in general. It is clear in this statement about reason and love that Bottom believes love to be ungoverned and ungovernable by logic or sense. This view allows him to accept Titania's sudden proclamation of affection, illogical and unfounded as it may seem.

Dante clearly revered Virgil as an influence and teacher of sorts. I need help with understanding the legacy of Dante in Western literature with regard to Homer and Virgil. How does Dante measure up to his predecessors from a twenty-first century perspective?

Many authors in western literature have been influenced by all three of these figures, with Homer probably the most popular. Among the most famous recent adaptations of Homer is Nobel prize–winner Derek Walcott's "Omeros," which places Homer in a Caribbean setting. Margaret Atwood's "Siren Song" restates an episode of The Odyssey from the viewpoint of the Sirens. These two examples are typical in that they reflect identity politics, looking at the western tradition from the stance of the "other."
Dante's Inferno was a 2010 action-adventure video game based on Dante. Several of Virgil's works have recently been re-translated, and his Georgics still influence nature poetry. Orality-literary theory remains important for studying Homer, while The Aeneid has attracted interest as a work concerning colonialism. 

The main issues you will need to address here are what you mean by "measure up" and "a twenty-first century perspective."
There are over seven billion people in the world. The two most populous countries in the world are China and India. The most important writers in China might include Li Po, Tu Fu, and Bai Juyi. Similar in importance to Homer and Virgil in the west in India would be such traditional epics as the Ramayana, Mahabharata and Bhagavad Gita. In general, the importance of the western European literary tradition is greatest in western Europe and those parts of the world colonized by Europe (the Americas, Australia, etc.) Even within Europe, there are differences. Homer is overwhelming influential in Greece while both Dante and Virgil have strong associations with Italy. 
Comparing their legacy is a part of literary studies know as reception theory. The fields of "classical tradition" and "medievalism" focus on the respective receptions of Graeco-Roman and medieval works. All of these approaches tend to argue against thinking about how works "measure up" in some absolute manner and simply emphasize studying how the ways people think of given works change over time. 
Because Homer influenced Virgil and Virgil and Homer influenced Dante, when their works are taught in translation they are normally taught in chronological order, with treatments of later works referring back to earlier ones. In language pedagogy, though, students traditionally study Latin (and thus Virgil) before Classical Greek (and thus Homer) because of its slightly less complex syntax, making reading Virgil in Latin more common than reading Homer in Greek in schools. Far more students at the secondary level study Latin than Greek in most countries although in Greece and Slavic countries reception history is different. You might look at A Handbook to Classical Reception in Eastern and Central Europe in your university library for more details. 
One way to examine the relative influence of these authors is to search for how often their names and works are mentioned using the Google Ngram viewer which searches a huge literary corpus and reports word usage frequency. It can be found at: 
https://books.google.com/ngrams/
One problem with word counts though is that you must be careful to use author/title combinations as names such as Dante or Homer can refer to contemporary popular culture figures as well as earlier authors. 
Another possibility is looking at new editions and translations of the works. You can search a British university library union catalog quite easily at:
http://www.copac.ac.uk
A quick search will reveal Homer as twice as popular as Virgil and Dante slightly behind Virgil. This does, I think, represent a general consensus in which all three are regarded as significant poets, with Homer having the slightly greater universal appeal or influence, Virgil following Homer, and Dante being most influential in Roman Catholic educational tradition, but slightly less frequently studied than the other two elsewhere.  
 

how does gerda use her imagination to survive the war

All But My Life is the incredible true story of how Gerda Weissmann Klein survived the Holocaust. One of the ways that she was able to achieve this was to focus, not on the horrors that were happening in front of her, but on the past and on the future. She imagined good things that had happened in her past, such as remembering her old house and spending time in her garden. She also looked forward to a future in which she could get married and have children and live a normal life. She even thought about what color dress she would wear to parties to keep her mind occupied.
She often imagined and hoped that somehow, on the next stop of the trains she rode on, she would see her family members again. Although imagining these things didn't lessen the dire nature of her situation, they did help her to stay mentally focused on life instead of death. In a quote from Teaching Tolerance magazine, Klein says "I was fortunate not to be a realist, because I saw far too many realists in the camps who did not survive."
https://www.tolerance.org/magazine/fall-2005/here-to-tell-my-story

What does the title mean in "May Day" by F. Scott Fitzgerald?

May Day, or May 1, is celebrated worldwide as International Workers Day. It is in remembrance of the Haymarket bombing in Chicago in 1886. The bombing killed eleven people, including seven police, at a peaceful demonstration for workers rights and the official eight-hour work day.
Though no one proved who carried out the bombing, eight anarchists were falsely accused. Four of them were hanged and one committed suicide before the rest had their sentences commuted by Illinois Governor Richard Ogleby after public protests. Six years later, the next governor pardoned them all. The Haymarket bombing played a central role in the struggle for an eight-hour work day.
In nearly all nations worldwide, May 1 is an officially recognized national holiday. In the US, it is not. In fact, in 1947, the Veterans of Foreign Wars declared May 1 to be Loyalty Day, with demands for loyalty oaths. The American Bar Association later declared May 1 to be Law Day, with mock trials presented to the public. The holiday in the US continues to be marked by unofficial demonstrations by unions, socialists, occasionally anarchists or communists, immigrants rights groups, and the Occupy movement.

In this long short story, part of Fitzgerald's 1922 anthology Tales of the Jazz Age, May Day refers both to a private dance held by privileged people on May 1, 1919 and the protests held by socialists and those who came back from World War I to face poverty. It spills over into May 2 and focuses on the aftermath of the May Day activities at both ends of the economic spectrum.
The wealthy revelers are celebrating May Day at Delmonico’s, an expensive restaurant in New York City, where the alcohol flows freely despite Prohibition at the Gamma Psi dance. These people of privilege enjoy a May Day far different and more decadent (if angst ridden) than that of the earnest street protesters hoping to initiate social change.
One socialite, Edith, leaves to find her socialist brother Henry. He says to her:

There’ve been riots all over the city to-night. It’s May Day, you see.

Fitzgerald, always sensitive to class difference in America, shows the contrast between May Day as a careless party time for the rich and a day of political struggle to the poor. May Day, historically, has been both a time of pagan fertility rites and celebrations and a time when international communist and socialist groups marched for change.
It's tempting to think that May Day also means a cry of distress, for Gordon Sterrett kills himself at the end of the story, but "May Day" as a distress signal was not coined until 1923, after the book came out.

In many countries, May Day is a traditional public holiday, one commemorated since the 19th century by different political groups. It's also celebrated in many cultures as an ancient fertility rite involving dancing round the maypole. F. Scott Fitzgerald's "May Day" manages to combine both of these cultural elements. The story revolves around a dance attended by privileged members of the upper-classes, well-heeled graduates from Yale, and takes place against the backdrop of the May Day riots of 1919. These disturbances broke out in a number of cities across the United States after a parade held by socialists and other relatively radical groups in support of Eugene V. Debs, the imprisoned leader of the Socialist Party of America, degenerated into violence amongst widespread political disagreement.
The charmed life of the fashionable crowd depicted by Fitzgerald stands as a stark contrast to the desperate plight of the workers protesting outside. Those attending the dance might as well live on a different planet to the massed ranks marching through the streets. To the Yalies, the noise outside has nothing to do with them, and certainly isn't about to spoil their fun. The drunken carousing of this well-heeled crowd is paralleled by the chaos and disorder in the streets outside. But the riotous partying of the over-privileged is of a completely different order to the desperate political struggles being fought out on the blood-soaked streets of New York, Cleveland and elsewhere.

Why did Edmund lie about Narnia?

Lucy first comes back from Narnia at the beginning of chapter 3.  She is wonderfully excited about her recent adventure, and she assures her siblings that she is just fine.  They wonder what she is talking about, and Lucy tells them that she has been gone for hours and hours.  The siblings don't believe her.  It has been hours in Narnian time, but it has only been a few moments in real time.  Already at this point, Edmund is giving Lucy a hard time about her wardrobe experience. 

"But I've been away for hours and hours," said Lucy.
The others all stared at one another.
"Batty!" said Edmund, tapping his head. "Quite batty."

Edmund continues to antagonize Lucy for the next few days.  

The others who thought she was telling a lie, and a silly lie too, made her very unhappy. The two elder ones did this without meaning to do it, but Edmund could be spiteful, and on this occasion he was spiteful. He sneered and jeered at Lucy and kept on asking her if she'd found any other new countries in other cupboards all over the house.

Edmund will eventually end up in Narnia himself during this same chapter.  He will meet the White Witch and strike his evil deal with her.  Lucy eventually discovers that Edmund is in Narnia, and the two siblings return together.  Lucy is ecstatic that Edmund can corroborate her story, but he lies about it instead.  

And Edmund gave a very superior look as if he were far older than Lucy (there was really only a year's difference) and then a little snigger and said, "Oh, yes, Lucy and I have been playing - pretending that all her story about a country in the wardrobe is true. just for fun, of course. There's nothing there really."

I think that Edmund lies about his time in Narnia for a few reasons.  First, he wants to seem older and more mature than Lucy.  Admitting to something so unbelievable will make Peter and Susan think he's just as childish as Lucy.  Second, Edmund was so awful to Lucy about Narnia that he's now having a hard time admitting that he was completely wrong.  Third, Edmund doesn't want to admit much about his time there, because he might be forced to reveal his time with the White Witch.  

What is the moral lesson of the myth about Persephone?

As with most of the Greek myths, the overriding moral is not to defy the gods. The gods are presented not as moral exemplars but as capricious and amoral tyrants, shamelessly using mortals to get what they want, whenever they want it. Yet however badly the gods behave, the divine will must always be obeyed, otherwise there will be serious consequences.
In the myth of Persephone, Demeter does what any normal mother would do in a similar circumstance and searches high and low for her abducted daughter. But Demeter is also a goddess, and as such she has no hesitation in wreaking revenge upon the mortal world, which she holds responsible for Persephone's disappearance.
Unknown to Demeter, however, her daughter has been abducted by Hades and spirited away to his underworld domain. Not only that, but this was all part of a plan cooked up between the god of the underworld and the mighty Zeus himself. As the father of the gods has so decreed that Persephone must yield to Hades, there is nothing that Demeter can do about it. Persephone has learned the hard way that the will of Zeus must always be obeyed, irrespective of the terrible consequences that sometimes follow. Bearing in mind also that Zeus is Persephone's father, we might also see the myth as reinforcing existing gender relations in ancient Greek society, where men were expected to exercise complete control over their wives and daughters.

Persephone is the daughter of Zeus and the harvest god Demeter. In the classic mythological story, she is following along with her mother Demeter one day and is abducted by Hades, the god of the underworld. Demeter is furious and by withholding her life-giving powers to bring vegetation to the earth, she forces Zeus to confront Hades and secure Persephone's return. Hades tricks Persephone by giving her pomegranate seeds to eat, and because of this, she is forced thereafter to spend a portion of every year down in the underworld with him.
This myth becomes an sort of moral story or explanation for the change of seasons. When Persephone and her mother Demeter are reunited, the earth springs forth with life. But when she is forced to return to the underworld for a time every year, the earth once again becomes more lifeless and barren.
The myth is repeated in many different contexts and is adopted by the Roman tradition as well, with Demeter being replaced by Ceres, Zeus by Jupiter and Hades by Pluto.
https://www.theguardian.com/books/2008/jan/12/greekmyths.greekmythsfeatures3

How does Yusef Komunyakaa use style and structure to convey the speaker's attitude toward the game of basketball in the poem "Slam, Dunk, and Hook"?

Komunyakaa employs a lot of playful, joyful structural (formal) and stylistic choices in this poem to express the speaker's joy in basketball.
Regarding the poem's style, Komunyakaa uses bright, playful, and movement-heavy language: "bad angels," "a high note hung there for a long second," "muscles were a bright motor," "swish of strings like silk," "a lyric slipknot of joy." Komunyakaa also uses a lot of body and animal imagery to describe the raw physicality of this game: "storybook sea monsters," "glide like a sparrow hawk," "glistening with sweat," and "swivels of bone and faith." The playful, movement-heavy language and the animal imagery tell us that the speaker finds uninhibited freedom and joy in the movement and the raw physicality of basketball. 
Also regarding style, Komunyakaa uses a lot of alliteration and assonance to create a musical, rhythmic quality to the poem. This musical rhythm helps drive the poem forward and also gives the speaker a sense of joy: "swish of strings like silk," "a high note hung," "dribble, drive to the inside & glide," "bodies spun on swivels," etc.
Regarding the structure, or form, the poem has relatively short lines, which help the poem move faster down the page, much like how a basketball player moves quickly across the court. Komunyakaa also uses a lot of very concise sentence fragments, or caesurae, in the middle of his poetic lines to create a lurching, staccato, stop-and-go kind of rhythm, especially in the poem's opening line: "Fast break. Lay ups." These midline caesurae once again mirror the way a basketball player might move across the court—dribbling the ball, turning, moving forward, stopping, doubling back—and convey the joy, freedom, and powerful self-expression the speaker finds in basketball.

What goal did Franklin D. Roosevelt have with regards to territorial expansion?

Franklin D. Roosevelt was not a proponent of American colonialism or the notion of the United States controlling other nations. In fact, he was a vocal critic of the actions of European countries in acquiring colonies. Roosevelt did, however, realize that acquiring important islands in the Caribbean and Pacific was vital to allow the United States to grow militarily. The goal of territorial expansion under Roosevelt was to secure naval bases in the waters that surround the United States.  Roosevelt realized that air and sea power were the future of warfare and in order to continuously defend the continent, the United States would need to be a leader in these areas. Roosevelt understood the strategic value of acquiring islands that could be used for naval and air bases and as refueling stations. This was of special importance with the emergence of Japan as an economic and imperial power in the Pacific.
http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6563.1973.tb01177.x/abstract
 

How would Stockton's "The Lady, or the Tiger?" be different if readers learn what is behind the door indicated by the princess?

The whole magic behind Stockton's story "The Lady, or the Tiger?" is that the ending doesn't tell the reader which fate the princess's lover receives. The story thrives on the ambiguity left in the wake of a compelling tale. If readers discover if a lady or a tiger emerges from the door indicated by the princess, then nothing would be left for readers to decide after reading it. The narrator leaves readers with the following:

"The question of her decision is one not to be lightly considered, and it is not for me to presume to set myself up as the one person able to answer it. And so I leave it with all of you: Which came out of the opened door—the lady, or the tiger?" 

The narrator says in the above passage that since the lover's fate should not be taken lightly, the narrator shouldn't be the one to reveal the princess's decision. As a result, the author/ narrator hands over the decision to readers, which empowers them to decide the ending of the story.
On the other hand, if Stockton just allows the narrator to give up the ending, then readers would not enjoy the internal debate that can exist in their minds afterward. Furthermore, readers would know for sure if the princess would rather see her boyfriend married off to someone else or die a horrible death by a tiger. The character of the princess would be decided, and no other discussion about the story would take place. Either the princess would be crowned a selfish girl by allowing her boyfriend to be eaten by a tiger, or she would be considered a loyal lover who would rather see her beloved happy in another's arms than with her if it meant that he lives.
The story lingers in readers' minds long after reading it because of the ambiguous ending. This is the magic of the story. The fact that readers are empowered to decide the ending gives it an original quality rarely found in other stories.

College Algebra, Chapter 9, 9.2, Section 9.2, Problem 66

When an object is allowed to fall freely near the surface of the earth, the gravitational pull is such that the object falls 16 ft in the first second, 48 ft in the next second, 80 ft in the next second, and so on.

a.) Find the total distance a ball falls in 6 s.

b.) Find a formula for the total distance a ball falls in $n$ seconds.

a.) If we let $D_T$ be the total distance of the ball after 6 s, then


$
\begin{equation}
\begin{aligned}

D_T =& 16 + 48 + 80 + 112 + 144 + 176
\\
\\
D_T =& 576 \text{ ft}

\end{aligned}
\end{equation}
$


b.) If $a = 16$ and $a_2 = 48$, then their common difference $d = 32$. Therefore, the total distance the ball fell in $n$ seconds is represented as..


$
\begin{equation}
\begin{aligned}

D_n =& \frac{n}{2} [2(16) + (n-1)(32)]
\\
\\
D_n =& \frac{n}{2} [32 + 32(n-1)]
\\
\\
D_n =& \left( \frac{n}{2} \right) (32) [1 + (n-1)]
\\
\\
D_n =& 16n [n]
\\
\\
D_n =& 16n^2

\end{aligned}
\end{equation}
$

Who is Becky in Chains, and what perspective does she have on the war?

Becky is the head servant to the Locktons in New York. She's mainly in charge of the cooking, but she also decides which work is to be done by which slave or servant.  
Explaining exactly how Becky feels about the war is a much more difficult answer. Becky understands that she works for awful people; however, Becky also knows she works for a very wealthy and influential family. She doesn't want to do anything to jeopardize her standing in the Lockton household. Because of that motivation, Becky tries not to let her feelings about the war show.  
Chapter seven contains a small exchange between Becky and Isabel that somewhat shows how Becky feels about the war. Becky is explaining to Isabel how to do some of the work around the house. Three Patriot soldiers walk past, and Becky says the following:

"I wish they'd all go home. . . Soldiers is a nuisance."  

Isabel thinks Becky is a Loyalist because of the comment, and asks for further clarification. Becky quietly explains that the Locktons are Loyalists. As a servant of Loyalists, Becky says she is a Loyalist in public as well. 

"Listen to me good. Them that feeds us" — she pointed upstairs — "they're Loyalists, Tories. That means we're Tories, too, understand?"  

Based on that comment, I think Becky secretly supports the Patriots, but she isn't willing to risk her station in order to publicly support her feelings.

How does Bruno's father's office compare with the rest of the house in The Boy in the Striped Pajamas by John Boyne?

Bruno's father's office is unlike the rest of the house (except for the large bathroom near his parents' room) because it isn't a place where the children are allowed; it's not meant for family life. Instead, it's a place that's purely for work. Because of this, it intrigues Bruno in a way the rest of the house doesn't.
The office faces the dining room and the door is usually closed. When Bruno first mentions the office, he capitalizes his description of it, saying it is "Out Of Bounds At All Times." This means that his father's rule to not enter the office was given and reinforced very seriously.
The rest of the house is a place for fun. Bruno thinks of sliding down the banister from the top floor. His parents's room is on the floor below the top floor, and he thinks that he isn't supposed to be in their bathroom. The next floor is his room, Gretel's room, and the smaller bathroom. His favorite thing about the house is the banister.
The office in their old house had the same restrictions as the office in the new house. He thinks the rule about not going into his father's office is one of the most important rules he's ever learned.
Bruno's father spends a lot of the time he isn't in the camp in his office.

Father's office is quite an intriguing place for Bruno in The Boy in the Striped Pajamas.  In addition to the numerous soldiers always going in and out of Father's office for meetings, the best description of Father's office would be “Out Of Bounds At All Times And No Exceptions.”  This description, provided in all capital letters from the book, adds to its intrigue.  Bruno is not allowed in Father's office on his own at any time.  Father's office compares to the rest of the house in that most of the other rooms are free to explore for Bruno and his sister, Gretel.  It is a rare moment when Bruno is actually called into this mystical room and, when that rare moment happens, Bruno is far more worried about what Father will say than what Father's office looks like.  This description is a perfect example of Bruno's innocence.  Bruno only knows what he sees: numerous women with typewriters, soldiers in uniforms, and many other "important" people who bustle in and out of Father's office.  It shows Bruno that Father is a very important member of the Nazi regime. 

I need a detailed note on the Greek creation myths: Pelasgian creation, Orphic creation, Olympian creation, two philosophical creations, and the castration of Uranus.

There are many different stories the Greeks told about the creation of the cosmos and the early history of mankind. These stories are found in several different works and traditions and, as Paul Veyne has argued, many were not meant as scientific accounts of human or cosmic history, but rather as allegories of how the Greeks understood the world in which they lived.
One of the best known accounts of the creation of both humanity and the cosmos can be found in Hesiod's Theogony, which discusses the origin of the world and the generations of the gods. In the beginning, the universe was a formless Chaos from which arose primal deities, Gaia (Earth), Eros (Desire), Tartarus (Underworld), Erebus (Darkness), and Nyx (Night). Gaia was the mother of Ouranos (the sky) and Ouranos mated with Gaia to produce the generation of the twelve Titans, including Oceanos, Hyperion, Iapetos, Rhea, Themis, Mnemosyne, and Kronos. Kronos castrated his father Ouranos. Where the blood land on earth, it engendered the Furies and the Giants. Ouranos tossed the testicles into the sea, where they gave birth to Aphrodite, goddess of love. Kronos married his sister Rhea, and the offspring of this marriage were the Olympian gods.
The Titan Prometheus created man out of mud with the help of Athena. Zeus created the first woman, Pandora, in part as a punishment for humans, in response to Prometheus giving man fire. In Hesiod's account, there were five ages of man, beginning with a golden age and gradually declining into the present iron age.
Orphism was a mystery religion and many of its details were known only to initiates, limiting what we actually know of Orphic beliefs, although, the discovery of the Derveni papyrus has added significantly to our knowledge. In this text, which has only been partially deciphered due to its poor state of preservation, Night gives birth to Ouranos who is the father of Kronos, the father of Zeus. Dionysus figures far more significantly in this work than in non-Orphic mythology; also, among the Orphics, the human soul was immortal and transmigrated after death of the body.
In ancient Greece, the term Pelasgians refers to people who lived in Greece before the Mycenaeans and spoke a different language. Their identity is unclear. Strabo claims that they included an ancient kingdom in Thessaly, and Herodotus also mentions them as ancient non-Greek speaking peoples living in remote areas in Greece.
For philosophical accounts of creation, you might want to look at Plato's Timaeus in which a Demiurge imposes a rational order on chaos (undifferentiated matter) to form an ordered kosmos. Aristotle, in his Metaphysics, argues that the world must be eternal, as it is impossible to create something out of nothing.

College Algebra, Chapter 3, 3.7, Section 3.7, Problem 46

Find the inverse of $\displaystyle f(x) = x^2 + x; x \geq - \frac{1}{2}$

To find the inverse of $f(x)$, we write $y = f(x)$


$
\begin{equation}
\begin{aligned}

y =& x^2 + x
&& \text{Solve for $x$ by completing the square: add } \left( \frac{1}{2} \right)^2 = \frac{1}{4}
\\
\\
y + \frac{1}{4} =& x^2 + x + \frac{1}{4}
&& \text{Perfect Square}
\\
\\
y + \frac{1}{4} =& \left( x + \frac{1}{2} \right)^2
&& \text{Take the square root}
\\
\\
\pm \sqrt{y + \frac{1}{4}} =& x + \frac{1}{2}
&& \text{Subtract } \frac{1}{2}
\\
\\
x =& \frac{-1}{2} \pm \sqrt{y + \frac{1}{4}}
&& \text{Interchange $x$ and $y$}
\\
\\
y =& \frac{-1}{2} \pm \sqrt{x + \frac{1}{4}}
&& \text{Apply restrictions } x \geq \frac{-1}{2}
\\
\\
y =& \frac{-1}{2} + \sqrt{x + \frac{1}{4}}
&&

\end{aligned}
\end{equation}
$


Thus, the inverse of $f(x) = x^2 + x$ is $\displaystyle f^{-1} (x) = \sqrt{x + \frac{1}{4}}$.

What impact does King say that the Emancipation Proclamation had on the American people?

King spoke often about the Emancipation Proclamation. He famously sent a telegram to newly inaugurated President John F. Kennedy in 1961 petitioning the President for a "second Emancipation Proclamation" in the form of federal civil rights legislation. On another occasion, speaking in New York City in a speech commemorating the Proclamation, he cited its importance in establishing justice:

The Emancipation Proclamation shattered in one blow the slave system, undermining the foundations of the economy of the rebellious South; and guaranteed that no slave-holding class, if permitted to exist in defeat, could prepare a new and deadlier war after resuscitation.

While he acknowledged the incomplete nature of the Emancipation--i.e. that it did not actually bring about an end to slavery in regions under federal control, and it failed to bring about any other rights for African-Americans--it began a process by which slavery could be destroyed, and ensured that slavery would end with the destruction of the Confederacy. 
King also referred to the Emancipation Proclamation in his famous "I Have a Dream Speech," where he opened by invoking the memory of the document, issued of course by Abraham Lincoln, whose monument overlooked the proceedings. King said the Proclamation was a "great beacon of light" for millions of enslaved people. But in this speech, as he did in many other mentions of the Emancipation Proclamation, King emphasized the limitations of the freedoms it conferred on Black Americans:

But one hundred years later, the Negro still is not free. One hundred years later, the life of the Negro is still sadly crippled by the manacles of segregation and the chains of discrimination. One hundred years later, the Negro lives on a lonely island of poverty in the midst of a vast ocean of material prosperity. One hundred years later, the Negro is still languishing in the corners of American society and finds himself an exile in his own land. So we have come here today to dramatize a shameful condition.

Like the Declaration of Independence, the US Constitution, and other sources of American liberties, the Emancipation Proclamation was a promissory note to the American people, one which had yet to be called in. King framed the Civil Rights Movement as an attempt to make good on that promise.

College Algebra, Chapter 2, 2.3, Section 2.3, Problem 28

Graph the circle $(y-1)^2 + x^2 =1$ by solving for $y$ and graphing two equations involved.

$
\begin{equation}
\begin{aligned}
(y-1)^2 + x^2 &= 1 && \text{Model}\\
\\
(y-1)^2 &= 1-x^2 && \text{Subtract } x^2\\
\\
y - 1 &= \pm \sqrt{1-x^2} && \text{Take the square root}\\
\\
y &= 1 \pm \sqrt{1-x^2} && \text{Add } 1\\
\\
y &= 1 + \sqrt{1 - x^2} \text{ and } y = 1- \sqrt{1-x^2} && \text{Solve for }y
\end{aligned}
\end{equation}
$

Thus, the circle is descended by the graphs of the equations
$y =1 + \sqrt{1+x^2}$ and $y = 1 - \sqrt{1 - x^2}$

The first equation represents the top half of the circle because $y \geq 0$ while the second represents the bottom half. If we graph the first equation in the viewing rectangle $[-1,1]$ by $[-2,2]$ then we get...


The graph of the second equation is....



Graphing the semicircles together on the same viewing screen, we get the full circle...

College Algebra, Chapter 1, 1.6, Section 1.6, Problem 12

Solve the linear inequality $-4x \geq 10$. Express the solution using interval notation and graph the solution set.


$
\begin{equation}
\begin{aligned}

& -4x \geq 10
&& \text{Given}
\\
\\
& x \leq \frac{-10}{4}
&& \text{Divide both sides by } -4
\\
\\
& x \leq \frac{-5}{2}
&& \text{Simplify}


\end{aligned}
\end{equation}
$

What literary devices are used in Thomas Love Peacock's poem "Maria's Return"?

One literary device Peacock uses in this poem is a rhyme scheme. Each stanza is six lines long, consisting of rhyming couplets in the first two lines and in lines four and five. Lines three and six also rhyme. For example, in the first stanza, the words "ground" and "bound" rhyme in the first two lines, while line three's "falling" rhymes with line six's "appalling."
The poem also employs images, which are descriptions that use the five senses. In the first stanza, for example, the poet uses sight images, to conjure the picture of the falling snow, and sound images, to convey the sound of wind whistling: "snow is swiftly falling," the speaker says, and "coldly blows the northern breeze, / And whistles through the leafless trees."
In the lines quotes above, the poem also uses alliteration, which is starting words in the same line with the same consonant, in order to create a sense of rhythm. "Snow" and "swiftly" begin with the letter "s," while "blows" and "breeze" begin with "b."
The narrator, a young woman jilted by her lover, Henry, speaks in a way that personifies death as if it were a human. She refers to "Death's icy dart" as if Death were a person throwing a weapon at her to kill her.
Finally, the bleak wintry imagery of snow and cold becomes a symbol of the desolation and coldness the narrator experiences because of her rejection by her lover. Her heart is like the barren landscape. She writes, "My very heart-blood freezes!"

How was Turtle Wexler able to profit from the storm?

Turtle Wexler is able to profit from the storm by selling handmade candles at an exorbitant price.
After the storm wipes out the electricity, Turtle goes door to door to sell her handmade candles. Although the candles are crooked, she tells everyone that they are actually quite practical and romantic. Of course, Turtle is merely using a marketing ploy to get everyone to buy her candles.
She tells the other "heirs" that the stripes on each candle are unique because they tell time. For example, each stripe is supposed to burn for half-an-hour. Since there are approximately twelve stripes on each candle, Turtle concludes that each candle will burn for six hours.
She sells the candles for five dollars each. Of course, the heirs do not appreciate her avaricious ways. However, they have little choice but to purchase her candles. The reason is that they must race against time to discover Sam Westing's killer in order to be eligible for the Westing fortune.

I believe that this question is asking about the beginning of chapter 8. The residents of Sunset Towers awake to find that the snow flurries from earlier have increased to a full-blown blizzard. The residents are snowed in and "imprisoned by fifteen-foot snowdrifts." To make matters worse, the building's power and telephones have been knocked out by the storm. Ever the intelligent and crafty entrepreneur, Turtle Wexler decides that she can take advantage of the situation by selling the other residents the candles that she made at summer camp. She places herself in a location where the residents will see her and her product, and she sweetens the deal with a great sales pitch.

“These handmade candles are both practical and romantic."

The residents know that they need light in order to work on their clues. Turtle Wexler knows this as well, so she doesn't sell the candles cheap.

“How much?”
“Not wishing to take advantage of this emergency, I’ve reduced the price to only five dollars each.”
Outrageous. Even more so when the electricity came on two hours after her last sale. “Sorry, no refunds,” Turtle said.

Create a comprehensive timeline of To Kill a Mockingbird.

In Harper Lee's To Kill a Mockingbird, a timeline follows the major events that shape the plot development of this timeless novel.
The author first introduces the small, dusty town of Maycomb as seen through the eyes of young Scout (Jean Louise) Finch. The introduction prepares the reader for not only observations of a child still unfamiliar with the vagaries of her community in such a brutal era, but also the pain and resentments of the South, where the loss of the Civil War is still keenly felt. The changes Scout relates to the reader express issues that also face the rest of the country in one way or another.
A great deal of the story deals with the relationships of the characters. Atticus is a widower that does his best to instill in his children knowledge of right and wrong, based upon his own morality and integrity. In chapter three, the author describes Atticus' belief that one should always try to understand another by looking to that person's experiences and perceptions. He tells his children:

You never really understand a person until you consider things from his point of view. . . until you climb into his skin and walk around in it.

Scout is still naive enough to have little regard for her father's career, believing that what he does is not in the least exciting:

Our father didn't do anything. He worked in an office, not in a drugstore. Atticus did not drive a dump-truck for the county, he was not the sheriff, he did not farm, work in a garage, or do anything that could possibly arouse the admiration of anyone (57).

Calpurnia is a surrogate mother to the children, an unusual circumstance because she is black and raising white children in this strongly segregated community.
Additionally, the introduction of Dill as the children's new friend allows for circumstances that shape the plot's movement. Most prominent is the children's growing knowledge of, and interest in, the mysterious Boo Radley. (Unbeknownst to them, Boo is as captivated by them as they are of him.)
When Atticus agrees to defend Tom Robinson, a good and decent husband, father and member of the community, difficulties immediately arise because Tom is black. At that time, the word of a black man was always trumped by the word of a white person, even though the facts glaringly supported the claims of innocence by Tom Robinson, the accused. The truth does not matter in the courtroom of white men, even though the highly regarded Atticus Finch defends Tom.
When Tom is found guilty, Atticus is certain that if he can appeal the decision, they might have a chance to win an acquittal. However, Tom Robinson has no faith in the court system. In the prison yard, he attempts to climb the fence and escape. Being shot so many times in the back seems to support Tom's lack of faith in receiving justice.
Jem is devastated by the verdict against Tom Robinson. He talks to Atticus about the unfairness of Tom's death sentence verdict:

Tom Robinson's a colored man, Jem.  No jury in this part of the world's going to say "We think you're guilty, but not very" on a charge like that.  It was either a straight acquittal or nothing. (219)

The truth of the community's ugliness opens Jem's eyes to realities of which he was never aware. As for Scout, she does not understand the ramifications of the trial's outcome, and the reader can see how she is still unaware of, or protected from, the ugly truth.
Bob Ewell, Mayella's father, is not satisfied with Tom's conviction, and he is also angry about Atticus's portrayal in court of himself. He menaces Atticus, but Atticus chooses to ignore his threats.
The seasons change, and Dill returns home at the end of the summer. The children go back to school, and on a fateful autumn evening they walk home after the fall festival. Scout is in her costume with limited vision and movement. Someone Scout cannot see attacks her and Jem. Her brother fights back but is overpowered. The attacker turns to kill Scout with a knife that her costume successfully deflects. Suddenly, there is a scuffle between the attacker and an unknown challenger. 
When the fighting stops, Scout sees someone carrying her unconscious brother home. The doctor and police are called, and Bob Ewell's dead body is found. Conjecture abounds as to what happened, and Atticus and Chief Heck Tate strongly disagree about how the situation is to be handled. Scout notices a quiet man hidden in the shadows of Jem's room. It is Boo Radley. As Atticus realizes the truth of what has happened, Scout walks Boo home. She agrees with Heck Tate's assessment as to how the news of the attack should be relayed to the community:

Well, it'd be sort of like shootin' a mockingbird, wouldn't it? (169)

This directly reflects Atticus's warning that Jem and Scout should never harm a mockingbird, a creature that does no harm but sings its heart out to the pleasure of those who hear it.
While evil seems to trounce good with regard to Tom Robinson, love overcomes evil at the story's end, perhaps the most satisfying theme of this amazing and classic novel.

Who is the cab driver?

Although the ending of “The Demon Lover” is somewhat ambiguous, the driver’s identity is linked to Kathleen Drover’s ex-fiancé. Twenty-five years after he was presumed dead, Kathleen discovers a note that reminds her of a promise that she made to him to meet him on a certain day at an hour that she can no longer remember. In fact, Kathleen realizes that she can remember very little about him and cannot even recall what his face looked like.
As the story progresses, Kathleen becomes increasingly anxious and decides to flee her house and seek safety with a taxi. Her decision is ultimately ironic. When she enters into the taxi, she realizes that the driver starts leaving even before she provides a destination. Moments later, the cab stops, and the story ends with her face-to-face with the driver:

Mrs. Drover’s mouth hung open for some seconds before she could issue her first scream. After that she continued to scream freely and to beat with her gloved hands on the glass all round as the taxi, accelerating without mercy, made off with her into the hinterland of deserted streets.

Scholars disagree about who exactly the cab driver is, and it is certainly left to some interpretation. The title suggests that he might be some demonic form of her ex-lover, and some scholars have argued that he is a wartime hallucination brought on by the stress around her. Regardless of how you choose to interpret his identity, it is important to note that his return is historically symbolic: the lover was presumed dead after fighting in World War I, and he—or at least the idea of him—reappears during World War II. Her ex-lover is less of a person than a historical occurrence, and their time together was not romantic so much as it was transactional and lacking detail. In this way, the cab driver—whether it is her ex-lover or a hallucination—is about the return of the horrors of a world war.

What are some similes and metaphors in "The Lottery" by Shirley Jackson?

The only example of simile in "The Lottery"—and a particularly weak one at that—is when Mrs. Hutchinson taps Mrs. Delacroix on the arm "as a farewell." This could reasonably be interpreted as a simile in that two dissimilar things are being compared using the word "as."
In terms of metaphor, the black box used to draw the "winning" names represents death. Again, death and a black box are two completely dissimilar things, yet in the overall context of the story, the box is a metaphor for death because the unfortunate individuals whose names are chosen from it will be sacrificed as part of this annual pagan ritual.
Old Man Warner can be seen as a metaphor for unthinking devotion to tradition. At no point has he ever stopped to consider the sheer, unadulterated barbarism of the ritual in which he's been such an enthusiastic participant over the years. In fact, Old Man Warner has become so deeply attached to the lottery tradition that he thinks it outrageous that the younger generation in neighboring villages have started giving up the old ways.

There are no obvious similes in the story, and there are no particularly obvious metaphors either. There are, however, some implicit comparisons which can be deemed similes and some figures of speech which might be considered metaphorical.
For example, commenting on how frequently the lottery seems to come around each year, Mrs. Delacroix says, "Seems like we got through with the last one only last week," and Mrs. Graves replies, "Time sure goes fast." The words "seems like" indicates that Mrs. Delacroix is comparing her impression that time has gone quickly with the time frame of one week. This simile helps us to understand just how short the year since the previous lottery seems to have been for those who have to participate in it.
Early in the story, Jackson writes that on the morning of the lottery, "the feeling of liberty sat uneasily on most," referring to the school children who had only recently finished school for the summer. They were not yet used to their freedom or liberty, and thus the "feeling of liberty" is said to have "sat uneasily" upon them. This feeling, of course, did not literally sit upon the children, but using this metaphorical language helps to convey the sense of weight and discomfort that the children felt. They had become so accustomed to the school routine that anything different felt at first unusual and uncomfortable, like a weight that's awkward to hold.

A metaphor is a comparison that does not use the words "like" or "as."
The shabby and splintered box that holds the lottery tickets is a metaphor for the increasingly worn and outdated lottery ritual. The black color of the box can be compared to the darkness of the lottery, which ends in the death of a community member at the hands of his or her neighbors. The refusal to repair the box can be likened to the denial the village residents seem to be in about the lottery. Like the box, they are caught in a limbo between wanting to hold onto an outmoded tradition and knowing down deep they need to change.
Old Man Warner likens giving up the tradition of the lottery, which to his mind promotes social stability and prosperity, to living in caves, implying that the loss of the lottery would lead to barbarism.

Shirley Jackson's writing style in "The Lottery" does not utilize much figurative language; there are no similes. However, there are a couple of metaphors in the protests of Old Man Warner.
Old Man Warner defends the existence of the annual lottery, disdainfully remarking "they'll be wanting to go back to living in caves" with regard to its critics. His exaggeration is a metaphor; he does not literally mean that the community will regress to that extent, but he clearly has strong feelings about retaining the tradition of the lottery.
Warner follows up his disdainful remark with another: "first thing you know, we'd all be eating stewed chickweed and acorns." Chickweed is, as the name suggests, a weed, or an uncultivated plant generally not consumed as food. Acorns are eaten by undomesticated animals, and this comment follows up on his idea that discontinuing the lottery will have a negative influence on the civilization of the community.

College Algebra, Chapter 3, 3.6, Section 3.6, Problem 34

Determine the functions $f \circ g, \quad g \circ f, \quad f \circ f$ and $g \circ g$ and their domains if $f(x) = 6x - 5$ and $\displaystyle g(x) = \frac{x}{2}$
For $f \circ g$

$
\begin{equation}
\begin{aligned}
f \circ g &= f(g(x)) && \text{Definition of } f \circ g\\
\\
f \circ g &= 6 \left( \frac{x}{2} \right) - 5 && \text{Definition of } g\\
\\
f \circ g &= 3x - 5 && \text{Definition of } f
\end{aligned}
\end{equation}
$

The domain of the function is $(-\infty, \infty)$

For $g \circ f$

$
\begin{equation}
\begin{aligned}
g \circ f &= g(f(x)) && \text{Definition of } g \circ f\\
\\
g \circ f &= \frac{6x-5}{2} && \text{Definition of } g\\
\\
g \circ f &= 3x - \frac{5}{2} && \text{Definition of } f
\end{aligned}
\end{equation}
$

The domain of the function is $(-\infty,\infty)$

For $f \circ f$

$
\begin{equation}
\begin{aligned}
f \circ f &= f(f(x)) && \text{Definition of } f \circ f\\
\\
f \circ f &= 6(6x-5)- 5 && \text{Definition of } f\\
\\
f \circ f &= 36x - 30 - 5 && \text{Simplify}\\
\\
f \circ f &= 36x - 35 && \text{Definition of } f
\end{aligned}
\end{equation}
$

The domain of the function is $(-\infty,\infty)$

For $g \circ g$

$
\begin{equation}
\begin{aligned}
g \circ g &= g(g(x)) && \text{Definition of } g \circ g\\
\\
g \circ g &= \frac{\frac{x}{2}}{2} && \text{Definition of } g\\
\\
g \circ g &= \frac{x}{4} && \text{Definition of } g
\end{aligned}
\end{equation}
$

The domain of the function is $(-\infty,\infty)$