In what ways are the perspectives in The Prince and Julius Caesar a response to the fickle nature of mankind?

In The Prince, Machiavelli says that in general, humans are

ungrateful, fickle, false, cowardly, covetous . . .

Therefore, a wise prince must be prepared for the fickle or changeable aspect of human nature. Machiavelli goes on to say that because humans are fickle or untrustworthy

the prince must consider, as has been in part said before, how to avoid those things which will make him hated or contemptible . . .

In Julius Caesar, we see how the very Machiavellian Mark Antony makes mincemeat of Brutus, showing the truth of Machiavelli's observation that people (the "mob") are fickle.
In his speech to the mob following Caesar's death, Mark Antony easily sways the crowd, who, moments before during Brutus's speech, were ready to crown Brutus emperor (even though, ironically, Brutus claimed he killed Caesar to save Rome from that fate).
Mark Antony manages to sway the crowd against Brutus by showing contempt for him. Through repetition, he makes ridiculous Brutus's claim that he is an "honorable" man. By the time Antony is done with the crowd, they are raised to a pitch of anger at Caesar's murder and ready to turn on Brutus and his followers. Civil war ensues.
Julius Caesar illustrates Machiavelli's point that a successful prince must at all costs avoid whatever will make him appear hateful or contemptible. Brutus's sense of honor is his undoing: Antony's ruthless pursuit of power and spot-on manipulation of the crowd, in contrast, serve him well.

Machiavelli's observation, especially in Chapter 18 of The Prince, is that successful leaders have been those able to change their attitudes with the wind, and moreover, to appear to be virtuous, moral, and religious without actually being so. It's clear in Julius Caesar that the conspirators, among them chiefly Brutus, are unable to act this way. Brutus is too honest a man to be an effective ruler, and besides, it's not his ambition to "rule" anyway. The Prince, as its title indicates, and as Machiavelli himself states, deals with how princes, those who rule by hereditary right and hold absolute power in their realms, have most effectively governed and have been successful throughout ancient and modern times. He deals with the quite different situation of republics elsewhere, in the Discorsi. Brutus was a man committed to restoring the Roman Republic which had essentially, though not officially, been brought to an end by Caesar's dictatorship. Brutus is clueless as to how to manipulate the crowd when he goes into the pulpit to address them.
Yet at first, his words seem to have an effect on them, as they cry, "Live, Brutus! We'll make him a king!" The enthusiasm of the crowd for him lasts about five minutes. Though at first they don't wish to hear Antony, as soon as he begins appealing to the emotions of the people and their visceral connection to Caesar, whom they see as having been a great benefactor to them, everything is reversed and there is no sympathy for Brutus and the conspirators. As has occurred throughout history, the emotion of the crowd turns on a dime (or on a denarius, we might say!) and now everyone is out to avenge Caesar's death.
This fickleness of "the people" is precisely what Machiavelli says has been exploited by successful princes, who themselves have cynically shifted their stances and alliances in order to hold onto power. Unfortunately for Brutus and the conspirators, there is no opportunity for them to do so. Events overtake them so quickly that as soon as Antony has completed his speech, he has "let slip the dogs of war," and there is no going back. Shakespeare's depiction of this is telescoped. In actual history, it took at least a week after the assassination for growing resentment and anger against the conspirators to reach the point where they basically had to get out of Rome as fast as they could. But the general point is clear about how easily "the mob" can be manipulated, and how emotion holds sway over reason--phenomena which we see in our own time as well.

What was the cause of the difficulty in uniting Ancient Greece?

Geography always plays a very important role in how humans organize their culture.  This was certainly the case with the Ancient Greeks as geography made it nearly impossible for the early Greeks to unify under a single government. The landscape of Greece is very rugged and mountainous and travel between different areas of the peninsula was very difficult in ancient times.  As a result, regionalism was the reality of those living on the mountainous peninsula.  Each region developed into an independent city-state with elements of government that were unique.  Some city-states, like Athens, evolved into governments that allowed their citizens a greater role in governance.  Other city-states instituted oligarchies or retained monarchs.  With the variety of government types that developed as a result of the rugged geography, uniting Greece under a central government was a challenge that would not be met until the conquests of Alexander of Macedon in the Fourth Century BC. 
http://www.ancientgreece.com/s/Geography/

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 34

Graph the functions $f(x) = - \sqrt{x^3 + x^2}, g(x) = \sqrt{x^3 + x^2}$ and $h(x) = \sqrt{x^3 + x^2}\displaystyle \sin \frac{\pi}{x}$
on the same screen and using squeeze theorem, show that $\lim \limits_{x \to 0} \sqrt{x^3 + x^2} \displaystyle \sin \frac{\pi}{x} = 0$








Proof:



$
\begin{equation}
\begin{aligned}
\lim \limits_{x \to 0} \sqrt{x^3 + x^2}& \frac{\sin \pi}{x} = \lim \limits_{x \to 0} \sqrt{x^3 + x^2} \cdot \lim \limits_{x \to 0} \frac{\sin \pi}{x} \\
\lim \limits_{x \to 0} \sqrt{x^3 + x^2}& \frac{\sin \pi}{x} \text{ does not exist, the function is undefined because the denominator is equal to 0. However, since}\\
\phantom{x}& -1 \leq \sin \frac{\pi}{x} \leq 1\\

\text{We have, }\\

\phantom{x}& - \sqrt{x^3+x^2} \leq \sqrt{x^3+x^2} \sin \frac{\pi}{x} \leq \sqrt{x^3+x^2}\\

\text{We know that, }\\

\phantom{x} & \lim \limits_{x \to 0} \sqrt{x^3 + x^2} = - \sqrt{0^3+0^2} = 0 \text{ and } \lim \limits_{x \to 0} \sqrt{x^3 + x^2}= \sqrt{0^3+0^2} = 0\\

\text{Taking} \\
\phantom{x} & f(x) = -\sqrt{x^3+x^2}, \quad g(x) = \sqrt{x^3+x^2} \sin \frac{\pi}{x}, \quad h(x) = \sqrt{x^3+x^2} \text{ in the squeeze theorem we obtain}\\

\phantom{x} & \lim \limits_{x \to 0} \sqrt{x^3 + x^2} \sin \frac{\pi}{x} = 0
\end{aligned}
\end{equation}
$

In Bad Feminist, how does Roxane Gay tie feminism to popular culture?

In Bad Feminist, Roxane Gay explores many pop culture artifacts through the lens of feminism. One notable example is her essay about the “Prince Charming” figure, in which she examines how popular contemporary novels like Twilight and Fifty Shades of Grey adhere to fairy tale tropes. In the section titled “The Trouble with Prince Charming or He Who Trespassed Against Us,” Gay argues that most fairy tale narratives revolve around a young woman who must pay some kind of price to be with Prince Charming and live her happily ever after; Ariel must give up her voice to be with Prince Eric in The Little Mermaid, and Belle must learn to love a literal beast (who is also her captor) in Beauty and the Beast. Gay argues that the idea that the perfect man is worth a woman’s sacrifice is problematic and might lead women to internalize attitudes that make them okay with toxic or even abusive behavior. For an example of this, Gay looks to the best-selling Fifty Shades of Grey series. Though Gay recognizes that these books are, on one level, simplistic and amusing fantasies, she argues that, given their popularity, the problematic undertones of the series should not be dismissed. Gay argues that—steamy scenes aside—the series essentially chronicles the attempts of Ana, the main character, to change or “fix” her very damaged boyfriend, Christian. Christian is often jealous, overbearing, and emotionally manipulative, but Ana frequently forgives this unhealthy behavior in the hopes of making their relationship work. Gay worries that this narrative reinforces existing unhealthy beliefs about what kinds of toxic behavior women are expected to tolerate in order to find romantic happiness. 

What sort of judgment does the Captain make about the place they are fighting for? How does Hamlet describe it?

In act 4, scene 4, Hamlet is on his way to England. He sees the Norwegian king, Fortinbras, lead his army through Denmark, and is curious to know where they are going. He questions one of the king's captains, who tells him that the Norwegian troops are off to invade Poland. The captain isn't very flattering about the land the Norwegians are planning to invade:

Truly to speak, and with no addition, We go to gain a little patch of ground That hath in it no profit but the name. To pay five ducats, five, I would not farm it. Nor will it yield to Norway or the Pole A ranker rate, should it be sold in fee.

In other words, it's just a small piece of territory, with very little strategic or economic value. It's neither use nor ornament to anyone, Norwegians or Poles. The whole military expedition to seize it is pretty much a waste of time.
The captain's remarks cause Hamlet to muse on the utter futility of Fortinbras's forthcoming military campaign:

Two thousand souls and twenty thousand ducats Will not debate the question of this straw. This is th' impostume of much wealth and peace, That inward breaks and shows no cause without Why the man dies.

Hamlet is even more scathing than the captain about the wisdom of the expedition. He's absolutely certain that, even with such a large invasion force ("Two thousand souls"), even with all that money ("Twenty thousand ducats"), there'll be no speedy resolution to this conflict for the Norwegians.

What are some of the basic principles of the Enlightenment and Scientific Revolution?

Some basic principles of the Enlightenment and Scientific Revolution are the belief in reason over superstition. This belief in reason was behind the changes in political theory and ideas of government during the Enlightenment, as philosophers and political scientists such as Locke and Rousseau believed that governments should respect personal liberty and practice tolerance. These beliefs inspired political theories such as the social contract theory, which stated that the monarch had to follow the will of the people or be removed, and the separation of powers in different branches of government to check the power of the monarch.
In addition, the belief in reason inspired the Scientific Revolution, in which empiricism, or the importance of relying on evidence to corroborate scientific theories, became a guiding principle. This belief was important in laying the evidence-based groundwork for modern science and in ending the belief in superstition or religion to govern one's scientific understanding of the world. 

What are some of the basic principles of the Enlightenment and Scientific Revolution?
Taking its cue from the blossoming Scientific Revolution's of the 16th and 17th centuries, the Age of Enlightenment set out to restructure philosophy, politics, and society on totally new foundations.
The many successes of new scientific inquiries into avenues such as astronomy and cosmology; chemistry; physics; and mathematics by thinkers such as Copernicus, Kepler, Newton, Leibniz, and Descartes had laid the foundation for a radically new and different view of the world than the one passed down from the medieval era and the middle ages.
Starting with Descartes publications of the Discourse on Method (1637) and Meditations on First Philosophy (1641) and continuing roughly through Immanuel Kant's publication of the Critique of Pure Reason (1781, 1787), Enlightenment thinkers set out to explicate these new first principles. These included the quest for scientific certainty and empirical verifiability as the foundations of truth and knowledge. Instead of accepting the arguments of faith or belief handed down to them by the State or the Church, Enlightenment thinkers sought natural explanations for how or why things occurred the way they did. 
Another major principle was the use of scientific reason and experiment as the guiding force of all inquiry; and this reason was universal. All human beings were seen as rational agents capable of achieving enlightenment. These principles did not only apply to science, but to politics and society as well. Because of their belief in universal reason, rights, and the progress of science to make a better world, Enlightenment thinkers challenged the dominant political and social orders. These orders had been based on rigid nobility and inequality which were supposedly bestowed by God (i.e., the divine right of kings), thus ushering in a new era of democratic thinking.
 

The Enlightenment started in the 18th century and was an intellectual movement that questioned old ideas and beliefs. Before the Enlightenment people took for granted what they were told by the Church and by their rulers. With the advent of the printing press and people becoming more educated these ideas were coming into question. Enlightenment thinking stressed reason, natural law, and progress in criticism to the injustices of the day. 
 
Some of the principles that came out of the Enlightenment was natural rights. This is the idea that people are born with certain rights that cannot be taken away. In the American Declaration of Independence these were called unalienable rights; life, liberty, and the pursuit of happiness. John Locke was the Enlightenment philosopher that believed in natural rights along with believing laws must be followed for a productive society. 
 
The Scientific Revolution helped spurn the Enlightenment period.  Scientists such as Galileo, Copernicus, and Newton began to question the science that the Church had been using for centuries. The scientific method started a revolution to examine with what has been taught in the past is correct. The Scientific Revolution used less religious and more secular ways of thinking. New technology and advancements in science helped lead to the Enlightenment era. 

What quotes from Romeo and Juliet show that Romeo and Juliet were trying to escape their present troubles by stating they are in love with each other? For example, Romeo is trying to get over a girl and Juliet is trying to avoid marrying someone her parents want her to marry. What quotes show this?

This is an interesting interpretation. I think it's a mistake to come up with an idea first and then try to retroactively fit the facts to the theory, but it seems you have already spotted elements in the text which you think point towards this reading.
There aren't any quotations which decisively "show" this idea to be true, as such, but I can think of some aspects which might bolster your argument. For example, Benvolio certainly thinks the best way for Romeo to get over his attachment to Rosaline is to latch onto another girl:

Go thither; and, with unattainted eye,Compare her [Rosamund's] face with some that I shall show,And I will make thee think thy swan a crow.

Evidently, Benvolio thinks Romeo is attached to Rosaline without much hope of ever attaining her—and also, he thinks Romeo could do better. Romeo is very certain that he will not get over her: "the all-seeing sun / Ne'er saw her match." He is also, indeed, unhappy with his attachment to Rosaline, believing it to be love and stating that "it pricks like thorn."
I'm not sure that we can argue that Romeo is trying to escape his love for Rosaline by falling in love with Juliet, as such. Certainly that is what his friends hope for him, but as a man who is so disillusioned with love, it's hard to believe he'd want to escape it by rushing headlong into yet another love affair. Rather, perhaps we can argue that Romeo doesn't really love Juliet because he is so fickle—he speaks as if his love for Rosaline is undying one minute, and the next is declaring his love for Juliet:

Did my heart love till now? forswear it, sight!For I ne'er saw true beauty till this night.

One moment, Rosaline is the fairest thing he has ever seen; the next, he is head over heels for a girl he has never even spoken to and declaring that his love for Rosaline was not real love. But is it, then, really love that he feels for Juliet, or is it a case of a young man moving on too speedily and recklessly to the next girl? Even Juliet cautions Romeo against his haste, when he declares that "love's light wings" have helped him into her orchard—"If they do see thee, they will murder thee."
As for Juliet seeking to escape her marriage with Paris, I'm not sure there's evidence that she necessarily dislikes Paris, as such—she does not seem particularly eager to marry at fourteen, but on the other hand, is happy to marry Romeo. When Capulet says that he will "drag [her] on a hurdle" to marry Paris, Juliet resists ("I beseech you on my knees"), not out of personal loathing of Paris, but because she has already declared herself to Romeo. Possibly she simply wants to make her own decisions.
We can also interpret that the young lovers may rush into marriage for another reason—in this time period, they would not have been able to sleep together outside of marriage. So, is it lust that drives Juliet into hasty marriage? Juliet is eager for night to

learn me how to lose a winning match,Play'd for a pair of stainless maidenhoods:Hood my unmann'd blood, bating in my cheeks,With thy black mantle.

I'm sure you can pick out some other elements in the text yourself, but this should offer you a place to start.

Why does Coelho open with the modified myth of Narcissus? How does the new version differ from the original one? How does it change the myth’s meaning? What might the author be suggesting about how we perceive ourselves and the world?

Coelho's opening with a revised version of the Narcissus myth invites us, as the story begins, to be open to seeing the world from a new perspective.
In the original myth, Narcissus is beautiful and proud. One day, he sees himself reflected in a pool of water. He doesn't realize he is seeing an image of himself and falls in love with it, believing it to be somebody else. Eventually, he dies of longing and is turned into the flower called narcissus.
In Coelho's retelling, this judgmental tale of self love punished is turned around. We see Narcissus from the point of view of the pool of water. The pool mourns Narcissus's death because his beauty, reflected in the pond, was a gift to it. The message is that we all have gifts we bestow without even knowing it. In a book that dwells on the positive—discovering and embracing your own Personal Legend—this positive retelling of an old myth sets a tone that asks us to rethink what we think we know and to be open to possibility and the life lessons that surround us.

The original Greek myth about Narcissus tells the story of a beautiful young man who becomes obsessed with his own reflection. In Edith Hamilton's Mythology: Timeless Tales of Gods and Heroes, a chapter about the origin of flower names explains how Nemesis, a goddess of anger, curses Narcissus after he rejects the love of a nymph named Echo. He is cursed to only love his own reflection, and he dies beside the water bank, staring at his own reflection. After his death, the nymphs name the flower that grows on the bank after Narcissus.
The story ends here in classic mythology, but Coelho adds to the story, giving the body of water that Narcissus stares into a personality and agency in the ending. In Coelho's version, the lake is sad about Narcissus dying, and it transforms into a saltwater lake, a lake of tears. When asked why he is sad, he says it is because of Narcissus's death, because by the reflection in Narcissus's eyes, the lake could contemplate its own beauty.
The original myth contains a critical theme about vanity and selfishness, revealing Narcissus to be punishable and cruel for his rejection of Echo. Coelho's myth doesn't mention that Narcissus was cursed at all, only that he loved himself and that the lake loved itself as well because of what it could see of itself in Narcissus. This shifts the message away from criticism and more toward a theme of contemplation. It begs the reader to consider how we learn about ourselves through the eyes of others, or perhaps it asks us to consider our dependence on outside sources to understand ourselves.
As for Coelho's intention for including this preface, considering authorial intent can always help the reader to make an educated guess. Since The Alchemist contains themes of self-discovery and dependence upon the universe to find personal fulfillment, it is reasonable to conclude that Coelho intended to start readers' minds upon the idea that everything is connected in the same way that Narcissus needed the lake and the lake needed Narcissus. Santiago, in his journey toward his treasure, needs many people to find his way and learn his mission. This altered myth suggests that the people Santiago meets along his path need him in much the same way that he needs them.

In Fahrenheit 451, what is the social commentary that is being provided in section 2; The Sieve and The Sand?

Throughout Part Two: "The Sieve and the Sand," Bradbury provides a social commentary on the dystopian society through Montag's conversation with Faber and his experience with Mildred's friends. When Montag allows Faber to look through the Bible, Faber mentions that it is a shame how advertisers and the media have commercialized religion. Montag then begins to explain his unhappiness and Faber mentions that Montag is in search of some of the things that books provide. Faber goes on to explain how the populace desires comfort and does not wish to critique themselves. The majority of citizens have no desire to reflect on their behavior. He says,

"The comfortable people want only wax moon faces, poreless, hairless, expressionless" (Bradbury 79).

Faber also mentions how the society neglects individuality. Society does not value intellectual thought and is content listening to their parlor walls and Seashell radios. Faber also comments on how the citizens do not have any leisure time. They live in a world where everything is immediate and do not have time to think.
Later on, Montag enters his home and listens to a conversation between Mildred and her friends. Mrs. Phelps mentions how she doesn't care about her children and Mrs. Bowles discusses why she decided to vote for President Noble. Bradbury also portrays the dystopian society's affinity for war and lack of compassion. Overall, the citizens refuse to examine their lives and society. They fear being critiqued and prefer to live a superficial life.

How does Annie John relate vanity to her quest of identity ?

For most of her life, Annie's identity has been intimately bound up with the extraordinarily relationship she has with her mother. When she hits puberty and their relationship breaks down, she has to forge a new identity completely from scratch. Throughout the story, Annie is a pretty willful child with a strong sense of her own worth. None of the relationships she develops after the breach with her mom endure in any way. This is not simply because she is looking for something she had with her mom that is now irrevocably lost; it is also because she is fundamentally a vain person, believing herself to be much better than everyone else.
Annie's deep, loving relationship with her mother kept her vanity in check. Although they were more bosom buddies than mother and daughter, there was no doubt who the senior partner in the relationship really was. Annie's mom is very old-school when it comes to parenting. Her word is law, and the house is her domain. As long as Annie does as she is told, all will be well. God help her, though, if she ever steps out of line. Thank goodness, then, that they get on famously.
After Annie hits puberty, all that changes. Mom distances herself because she wants Annie to grow up and start acting like a lady. Annie is shocked and confused. Apart from anything else, she kind of thought that she was almost an equal in the relationship, her mom's "Mini Me," as it were. After all, they used to hang out together, go shopping, and even wear the exact same outfits. (They even have the same name). Annie already felt like a grown-up. Now she realizes that her mom thought of her as a little kid all along, and it hurts like hell.
At the same time, the breakdown of the relationship with her mom gives Annie the opportunity to let her real personality show. Now she can cut the apron strings, emerge from her mom's shadow, and start living like a real individual. However, there is really nothing to show; Annie's life has been so closely linked to her mom's identity that she has no true identity. The separation from her mom has left a gaping void in her soul which Annie somehow has to fill.
She really does not know how to do this. She throws herself into all kinds of adventures, desperately trying to cobble together something approaching an identity. First, Annie befriends Gwen. It is clear that she is looking for a mother substitute, and, initially, it seems that she has found one. This does not last long. The problem is that this is no relationship of equals. Neither was the relationship between the two Annies, but Annie John genuinely thought it was. There is no ambiguity this time, though. Annie is the mom and Gwen is the giggling, immature, little girl in the relationship.
However, we should not be too hard on Gwen. Annie's growing vanity is primarily responsible for their relationship not working out. She think she is a grown-up and wants to be with someone who makes her feel like a grown-up, just like her mom used to do. Gwen cannot do this. On the contrary, she acts as a reminder that Annie is still only twelve years old and just a kid.
This definitely is not a problem with the Red Girl. She has maturity way beyond her years. She shows that if you want to be considered as an adult, you have to act like one. You can gamble, you can steal, you can do whatever you like. After all, that is what adults seem to do all the time. There is no attempt by Annie here to replace her mom's affection. That ship has long since sailed. Now, she sees relationships purely in terms of self-gratification, as an opportunity to display her growing vanity and assuage her elevated sense of who she thinks she is. To hell with the consequences.
No one can ever truly match up to Annie's super fussy standards. She is the most important person in her own world. For a while, she thought her mom was amazing, but that is ancient history. Additionally, Antigua is such a little island, far too small a place to contain Annie's ever-growing ego. She needs a bigger stage to indulge her vainglorious visions. As a result, she leaves for England to work as a nurse. Not only will this allow her to indulge her morbid obsession with dead bodies, it will also give her the chance to be someone, a chance to create an identity in keeping with the superior self-image she has been attempting to develop ever since she fell out with her mother.

In the story of "A Sound of Thunder," what things have changed since the men travelled into the past?

When the men return from the past, Eckels sniffs at the air, noticing a "chemical taint so subtle, so slight, that only a faint cry of his subliminal senses warned him it was there." He notes the colors around him, all normal colors that he is used to, but "there was a feel" of something different, something off. He stands there feeling the "oddness" with the pores all over his body.
He even feels that there is an incredibly high-pitched whistle blowing somewhere, like the kind only dogs can hear but that registers strangely in our brains. It looks like the same man behind the same desk in the office, but he is not the same, somehow. The sign on the office wall is now spelled completely differently, as though there are no rules for spelling words in English, or perhaps that all the rules are radically different from what they used to be.
What is most shocking, I think, is that Keith, the man they were all so glad had won the recent election, was soundly defeated by his opponent, Deutscher, in this reality. The man behind the counter calls Keith a "weakling" and rejoices that they have "an iron man" in charge now, "a man with guts." Before the safari, the man behind the desk had been so glad, had felt so lucky that Keith had won and Deutscher had lost.

When the hunters and tour guides return from the past and arrive back to the office of the Time Safari, both Travis and Eckels notice that something is not quite right. While the same man is sitting at the same desk as he was before they left for the safari, Eckels can tell that there is a faint "chemical taint" to the quality of air. The first visible indication that something has changed is the sign in the office, which is virtually illegible. The sign now reads,

TYME SEFARI INC. SEFARIS TU ANY YEER EN THE PAST. YU NAIM THE ANIMALL. WEE TAEK YU THAIR. YU SHOOT ITT. (Bradbury, 9)

After Eckels discovers that he has trampled and killed a prehistoric butterfly while running off the Path sixty million years in the past, he asks the man sitting at the desk the name of the current president of the United States. The man behind the desk informs Eckels that Deutscher won the election of over Keith and is the current president. Eckels and Travis are both astonished and appalled to discover that the death of a solitary prehistoric butterfly has significantly altered the course of human history, which has resulted in a totalitarian state, where Deutscher is the leader of the United States. Overall, the entire culture and society of the United States has significantly transformed into a dystopia under the rule of an oppressive dictator named Deutscher since Eckels and Travis have returned from the past.

When the men return from the past, a couple of things have changed. Firstly, Eckels notices that the sign he had read earlier is virtually unreadable. The letters are jumbled up, for example, and appear like a foreign language. Secondly, the winner of the presidential election has also changed, from Keith to Deutscher.
These changes have occurred because Eckels killed a butterfly while traveling in the past. Although this was an accident, it has proven the safari guides' assertions correct: that any change made to the past, no matter how small or unimportant it might seem, can have a profound affect on the future. In this case, the death of the butterfly has not only changed the written language of Eckels' society, but also the character of political life.
Eckels is desperate to return to the past to rectify his mistake but there is nothing that he can do. The future is irrevocably changed.

At the beginning of the story, Eckels comments that he is glad a man named Keith has won the election to become the new President of the United States. Eckels is on his way to a time travel safari, where he will be taken back 60 million years to shoot a T-Rex that the travel agency has already determined is about to die. The man behind the desk at the travel agency agrees with Eckels that Keith is a good choice for President, noting that his opponent, Deutscher, would have been a dictator: anti-Christian, anti-human, anti-intellectual and militaristic.
During the safari, Eckels does what is forbidden--he leaves the Path--and accidentally kills a butterfly. When he and his group return to the present, they realize this has changed history. Instead of Keith, the brutal man-of-iron, Deutscher, has won the election.

Discuss your view of and experience with team projects. Do you see team projects in a positive light, or not? Why?

Team projects have various positives and negatives. As a previous student and current educator, I have experienced team projects in multiple ways.
As a teacher, I enjoy giving assessments as team projects so that students learn teamwork, delegation, and cooperation. While working in teams, students are exposed to new viewpoints and get the chance to meet new people. For example, at the beginning of the school year, I created an easy team project for my class to help them get to know each other better on a personal level. It also provides an opportunity to learn how to work with different types of people and collaborate to produce creative projects.
However, there are negatives to working in team projects. In some cases, a couple of people do not do any work throughout the project and still end up getting credit. This is not only stressful but also puts more burden and work on group member's shoulders. For example, many times in my high school career I would stay up until one or two in the morning in order to finish a team project in which one person did not do any work. However, a good solution to this problem is to have the team perform self and peer assessments after the project so everyone gets a grade they deserve. If your team is not able to meet in person throughout the project due to differing schedules, it can also be tough to communicate ideas or instructions over email or online chat.
Overall, I think that team projects are a positive experience for students and coworkers that will help them learn new ways of thinking, learn to collaborate, and learn be creative.

When does the pursuit of individual happiness become destructive or counterproductive?

The pursuit of individual happiness becomes counterproductive when it strays too far from reality. For example, Gatsby's pursuit of happiness lies in his conviction that he can turn back time and erase the past five years. He believes he and Daisy can return to the moment they first fell in love, as if nothing has changed since then. Even when he meets Daisy's daughter, Pammy, he clings to the conviction they can begin anew. Nick tries to tell him you can't turn back time; Gatsby refuses, however, to give up his dream. Of course, the dream is over. Daisy is married and has a child, and too much time has passed for them to rekindle the old romance in the way Gatsby would like.
The pursuit of individual happiness becomes destructive when it is at the expense of other people. For example, when Daisy runs over Myrtle, Daisy only cares about her own happiness in not being bothered by the death. Rather than stop the car and face that she killed someone, she runs away. She and Tom both run away from the mess they have made of other people's lives, leaving others to clean up behind them.

Who controlled the Charlestown Peninsula in 1775?

At that time the British were in control of the Charlestown Peninsula. In that year the famous Battle of Bunker Hill took place on the peninsula, which ended in a Pyrrhic victory for the British—that is, a victory which left them worse off than before. British losses were far greater than those of the American colonists. Although the Americans technically lost the battle, they nonetheless achieved a spectacular moral victory, one that provided a huge boost for the colonists' morale.
However, the Battle of Bunker Hill caused immense damage and destruction, with the town of Breed's Hill, where most of the fighting took place, being almost completely destroyed. Although the British remained in control of the Charlestown Peninsula, their political and military authority had been fatally undermined by the heavy losses they'd sustained at Bunker Hill.

What objection to the proposal does the speaker think readers might raise? How does he answer that objection?

The speaker proposes that “out of the one hundred and twenty thousand children from poor families born annually, twenty thousand should be kept for breed and the remaining one hundred thousand sold as food to persons of quality of fortune, at one year of age.” He does not think that his proposal will raise many concerns among the multitudes, unless if it could be argued that such measures would greatly reduce the population of Ireland. To this singular objection, he accepts that indeed, the proposal aims to reduce the population of people in the kingdom. He further states that all other proposals, previously given, have failed to work. He even lists some of these proposals such as “taxing of absentees at five shillings a pound, promoting the use of local products, love for the country, and fostering of a spirit of patriotism among all people to work towards the general good of the country.” He dismisses all these measures by saying that “let no man talk to me of these and the like expedients until he hath at least some glimpse of hope, that there will ever be some hearty and sincere attempt to put them into practice”. He states that his proposal “offers a wholly new, solid, real, and inexpensive” alternative to the many “visionary” proposals that have failed to take off in the past.
In support of his proposal, the speaker reminds objectors of two points worthy of their consideration. One, how to provide for one hundred thousand poor mouths, and two, the thoughts of poor parents on such a proposal as he has presented—whether they wouldn’t have preferred to themselves be sold for food at one year of age, instead of living to endure “such a perpetual scene of misfortunes.”
The writer makes heavy use of satire to draw the reader’s attention to problems faced by the society of Ireland at the time.

What is the significance of the ending of A Doll’s House (With respect to the author’s choices)?

At the end of the play, Nora Helmer makes a radical decision to leave her husband, Torvald, and her children in order to live independently of society's expectations for women and discover who she really is. She tells her husband,

Our house has been nothing but a play-room. Here I have been your doll-wife, just as at home I used to be papa's doll-child. And the children, in their turn, have been my dolls. I thought it fun when you played with me, just as the children did when I played with them. That has been our marriage, Torvald.

She realizes that she was the plaything of her own father and has since become the plaything of her husband. She is not respected as an individual with personal wants, intentions, and goals. Instead, she is simply expected to fulfill her role, first as a dutiful and obedient daughter and next as a dutiful and obedient wife. Not only is Nora's realization significant, her willingness to strike out on her own in order to discover her sense of self is, in abandoning her family, also quite significant because, at the time, such an action would have been very rare. Nora is essentially giving up her place in society by refusing to follow society's rules for women of her class. She says,

I must stand quite alone if I am ever to know myself and my surroundings; so I cannot stay with you.

Her choice is radical, and it was actually quite controversial at the time of the play's initial performances—one actress actually refused to perform the role as written and insisted on a different ending for a few performances (until she realized the original was better). The radical nature of the choice makes it significant.

“It is a sin to kill a mockingbird”. Connect this metaphor to a current event or event in recent world history.

In order to connect the quote to an event, you have to understand the quote first.  Atticus tells his children that they can shoot at tin cans and bluebirds, but that it's a sin to kill a mockingbird because, as the children learn from Miss Maudie, mockingbirds do but one thing: make music for us to enjoy.  It's then easy to label several characters as mockingbirds in the book, the most obvious being Tom Robinson.
In the case of Tom Robinson, you have a man who is clearly innocent and trying to do the right thing but is now facing death simply because of the color of his skin.  Trayvon Martin could be considered a modern-day black man who was killed due to racial prejudice. In this case, another man felt threatened simply because Trayvon was black and wearing a hoodie. Michael Brown in Ferguson, or Ezell Ford are cases that are also arguably questionable in that both boys were killed by police even though they were unarmed (Ezell also had a potential mental disability).  All of these deaths have resulted in protests against racial profiling or simple racism within our society and, especially, our police force.  Every one of these could be considered modern day "Mockingbirds."

How does the poet describe the world of nature?

“Caged Bird” uses rich nature imagery to evoke the contrast between the caged and free birds. The caged bird can barely sense the natural world outside the cage but retains hope that it will once fly outside in that world. The free bird not only inhabits that world but thinks and feels its possibilities and effects.
The free bird stanzas feature the sky and the earth as the full environment open to the bird. The celestial features of wind and sun are paired with the terrestrial ones of trees, worms, and grass. The sky belongs to the bird: “he names the sky his own.” The wind and breeze, in particular, are shown in several ways: glossed as a stream on which the bird floats, a breeze, and the trade winds making the trees sigh. The worms in the lawn are presented as part of the bird’s thoughts and anticipation.
The caged bird can barely see outside the cage, and it “sings of things unknown but longed for.” The “distant hill” is mentioned twice but not described except as distant. Although dreams are mentioned, they are made concrete only as a “graveyard” –part of the human-made rather than natural world—and contrasted to the “dawn bright lawn” of the free bird’s world.
Thus, Angelou uses imagery of the natural world to convey ideas about hope and its limits.
https://www.poetryfoundation.org/poems/48989/caged-bird

In “Caged Bird” by Maya Angelou, the speaker contrasts a free bird with one that is raised in captivity.
Nature is described in association with the free bird. In the first stanza, the speaker says that the free bird “leaps on the back of the wind” and “dips his wing in the orange sun rays,” daring to “claim the sky.” The buoyant tone of this stanza indicates that the bird is happy and that nature is his to conquer.
Nature is addressed again in the fourth stanza. The description is very similar to the first stanza, insomuch that the free bird “names the sky his own.” The speaker depicts the sky as a boundless expanse in which the bird is the master traveler.
In each of these stanzas, then, nature represents independence, hope, and possibility, in addition to the freedom it allows the bird to experience.

What does Jem reveal to Scout about what happened to his pants?

Jem, Dill, and Scout are curious about Boo Radley. In chapter 6, they decide to sneak onto the Radley property and look in the window to see if they can get a glimpse of Boo. While they are near the house, the children see Mr. Radley's shadow, and they see that he is carrying a shotgun. As they are running away, Jem's pants get caught in the wire of the fence and he has to leave them behind.
The neighbors are gathered outside the Radley front gate as a result of hearing the shotgun. In an effort to avoid being seen as suspicious, Jem, Scout, and Dill join the neighbors. During the conversation, Miss Stephanie notices that Jem is missing his pants. Dill explains that he won Jem's pants in a game of strip poker.
That night, Jem makes plans to get his pants back. Scout fears for Jem's safety, but he returns safely with the pants. In chapter 7, Jem finally discusses his pants with Scout. He explains that his pants were in a tangle when he left them. However, when he went back for them, they were, "folded across the fence . . . like they were expectin' me." They had also been mended but not neatly. Jem then says, "Like somebody was readin' my mind . . . like somebody could tell what I was gonna do."

What clues do you have that people were not kind to the narrator?

The narrator in Rodman Philbrick's novel Freak The Mighty is Maxwell Kane. He is a learning disabled kid who is a gentle giant. He lives with his grandmother and grandfather because his mother is dead and his father is in jail. 
One example that people are not kind to Max is the example of Tony D. and his gang. Also known as "Blade," Tony D. and his gang confront Max and Kevin at the Fourth of July festivities. The gang pursues Max and Kevin to do them harm, and Max puts Kevin on his back in order to run away. This is how they became "Freak the Mighty." 
In the chapter entitled "The Damsel in Distress," Loretta Lee and Iggy are not very kind to Max. Loretta recognizes him as "Killer Kane's" kid. Loretta says, "He's some kinda retard, Ig. He don't even know how big and strong he is, I'll bet." 
In the chapter entitled "Killer Kane, Killer Kane, Had A Kid Who Got No Brain," when Max's teacher Mrs. Donelli asks him to stand and tell the students about his summer, kids in the class begin taunting, saying, "Forget it, Mrs. Donelli! His brain is in his tail!" They also shout, "Ask him to count! He can paw the ground!" and "Maxi Pad, Maxi Pad, ask him quick about his dad!" 
 

(3,0) Write the standard form of the equation of the parabola with the given focus and vertex at (0,0)

We are asked to write the equation of the parabola with focus (3,0) and vertex at the origin.
The formula for a parabola with focus (a,0) and vertex at the origin is y^2=4ax
The equation required is y^2=12x
 

Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 80

Evaluate the equation $|7x + 12| = |x - 8|$.

This equation is satisfied either if $7x + 12$ and $x - 8$ are equal to each other or if $7x + 12$ and $x - 8$ are negatives of each other


$
\begin{equation}
\begin{aligned}

7x + 12 =& x - 8 && \text{or} &&& 7x + 12 =& -(x - 8)
\\
7x - x =& -8-12 && \text{or} &&& 7x + x =& 8-12
\\
6x =& -20 && \text{or} &&& 8x =& -4
\\
x =& - \frac{20}{6} && \text{or} &&& x =& - \frac{4}{8}
\\
\\
x =& - \frac{10}{3} && \text{or} &&& x =& - \frac{1}{2}


\end{aligned}
\end{equation}
$


The solution set is $\displaystyle \left \{ - \frac{10}{3}, - \frac{1}{2} \right \}$.

How do you respond to Curley? Why is he the way he is, and what role does he have in the novel? Where might he fit in within Steinbeck’s view of the "American Dream"?

Curley in Of Mice and Men is the boss's son and is always trying to prove himself and his masculinity to everyone else. Even from the first time he sees George and Lennie, he challenges them and is ready to fight. As he looks them over for the first time "His arms gradually bent at the elbows and his hands closed into fists. He stiffened and went into a slight crouch. His glance was at once calculating and pugnacious" (Steinbeck, 13).
When George asks why Curley is so argumentative, Candy explains that "Curley’s like alot of little guys. He hates big guys. He’s alla time picking scraps with big guys. Kind of like he’s mad at ‘em because he ain’t a big guy" (Steinbeck, 14). Throughout the text, Curley seems nervous that someone else is going to challenge him, and he is always concerned that someone is a threat to his masculinity and especially that someone else might attract the attention of his wife. Curley has been married for two weeks at the start of the story, but his wife has "got the eye" (Steinbeck, 15). In other words, Curley's wife is always flirting with other men, and Candy thinks this is perhaps one reason that "Curley’s pants is full of ants" (Steinbeck, 15).
Overall, Curley is the main opposition to George and Lennie throughout the book. In terms of the vision of the American Dream, Curley is an ordinary person who is intensely aware of the competition aspect of the American Dream and who is always scared that what he has accomplished for himself might be taken away by someone else.

What is the concept of meter and diction according to S.T. Coleridge in his Biographia Literaria?

In chapters 17 and 18 of Biographia Literaria, Coleridge is primarily concerned with either expanding on or, in fact, refuting the principles his friend Wordsworth had laid out in the preface to Lyrical Ballads some years earlier. Wordsworth wished poetry to take a new direction by using the language of ordinary people, especially those who lived in the countryside, for it was this language he regarded as genuinely and more directly expressive of emotion than the diction used by poets of previous ages. He also stated that poetry should be as much like prose as possible, insofar as the poet's word choice should conform essentially to the way people spoke, rejecting affectation and specialized terms which, again, Wordsworth alleged were typically found in poetry.
Coleridge takes issue with the idea that rustic life is especially "real" or that country people speak a more genuine kind of language than others do. He also states that poetry does not, and cannot, be the same as prose, just as written prose is not the same as conversational speech. In Coleridge's view the building-blocks, so to speak, are the same in poetry and prose—he uses an analogy with architecture—but the resulting structure is different.
The most striking passage in Chapter 18 of Biographia Literaria is a critique of Wordsworth's analysis in the Lyrical Ballads preface of Thomas Gray's Sonnet on the Death of Mr. Richard West. Wordsworth had picked apart Gray's sonnet, contending that most of it is worthless as poetry, precisely because it used typically "poetic" diction, rather than the ordinary, prose-like language Wordsworth intended to promote as proper for verse. Coleridge refutes this view. For him, there are combinations of words that are appropriate to poetry and not prose, and vice versa. He points out that most of the lines in Gray's poem that Wordsworth censured are no less poetic than those he accepted. In forging a new path for poetry, Wordsworth seemingly felt it necessary to adopt an extremist view which would have consigned to the rubbish bin not only this particular sonnet of Gray but thousands of other great poems.
Coleridge, in his discussion of meter, gives a more subtle and far-reaching description of the essence of poetry. In some sense, his view is simpler than Wordsworth's, because he regards meter as an element that "tends to increase the vivacity and susceptibility both of the general feelings and of the attention." The metrical construction excites the emotions and causes a more heightened response in the reader than prose would, even if it expressed the same thoughts. But meter, Coleridge makes clear, is by itself just a means to an end, and it is appropriate "only because [the poet uses] a language different from that of prose." This is quite the opposite of Wordsworth's view. Though Coleridge's analysis is lengthy and complex it really boils down to the common-sense view that striking and original diction, combined with meter and rhyme, form the essence of poetry.
It is ironic that although Lyrical Ballads spearheaded the Romantic movement in English verse, not only Coleridge but the poets of the next generation disagreed with Wordsworth's dictum about the ideal poetic language. Wordsworth did succeed in making his own poetry sound like speech, like the way people really talk. Yet there is not necessarily a contradiction between Wordsworth's goals and those of the others. Coleridge's best-known works today, The Rime of the Ancient Mariner and Kublai Khan, are written in language that differs from speech (especially in the former with its deliberate archaisms) but still sounds like natural, unaffected English. The same is true of the younger Romantics: Shelley, Byron and Keats. The corrective to Wordsworth supplied by Coleridge in Biographia Literaria, though it may not have directly influenced these men, conforms to the majority of the poetry written in the Romantic period, and indeed throughout the overall history of English poetry.

What impacts did the Vietnam War have on United States foreign policy?

Before withdrawing from Saigon (the capital of South Vietnam) in 1975, the United States had never lost a war. US involvement in Vietnam really began after World War II. During the war, Japan invaded Vietnam and kicked out the French. The French had colonized Vietnam (it was called Indochina at the time), and after the Japanese were defeated at the end of World War II, the French expected to regain control of their former colony. However, the Vietnamese, led by Ho Chi Minh, fought the French for independence from 1945–1954. The US had supported Ho Chi Minh as he fought the Japanese during World War II, but they were hesitant to back him after the war, as the US was also allied with France. The US therefore attempted to stay out of the conflict, although by 1950 the US government was providing financial aid to the French. When the Vietnamese defeated the French at Dien Bien Phu in 1954, the US helped negotiate the peace talks at the Geneva Conference after. At this conference, Vietnam was temporarily divided at the seventeenth parallel. North Vietnam was Communist, while South Vietnam was anti-communist, and free elections were to be held in 1956. However, the US, fearing that Ho Chi Minh would win these elections, backed South Vietnamese President Diem in his refusal to allow free elections to take place, instead allowing Diem to continue as the leader of South Vietnam. Communist guerrilla forces, called the Viet Minh, then began fighting the South Vietnamese in order to unify the country into one communist nation.
At this point, the US began increasing its role in Vietnam. Initially, the US sent 2,000 military advisors to assist the South Vietnamese. Under President Kennedy, the number of advisors increased to 18,000 by 1963. That same year, Kennedy sanctioned a South Vietnamese coup that overthrew Diem, fearing that he might enter into an agreement with the North Vietnamese to establish a coalition government.
Some of the most drastic changes in US policy toward Vietnam occurred under President Johnson (LBJ), who became president after Kennedy's assassination in 1963. Johnson was reluctant to deepen US involvement in Vietnam. However, he also faced political pressure to not appear "weak" and "lose" a country to Communism. The policy of containment, not allowing Communism to spread, was deeply entrenched in US foreign policy goals by this point, and during Eisenhower's presidency, the "domino theory" became popular. This was the idea that if one country fell to Communism, the surrounding countries (in this case Laos and Cambodia) would also be taken over by communists. This fear greatly shaped US policy and action in Vietnam and other countries seemingly threatened by Communism.
Despite being elected in 1964 on a campaign that included a promise not to commit US troops to Vietnam, the first US troops were sent to Vietnam under LBJ. In 1964, the Gulf of Tonkin incident sparked controversy. US intelligence reported that a US destroyer, the Maddox, had been fired on twice by the North Vietnamese. The Maddox, however, was on a secret intelligence mission in North Vietnamese waters, and it remains unlikely that one of the attacks even occurred. Nevertheless, Congress approved the Gulf of Tonkin Resolution, granting LBJ the power to "take all necessary measures" to fight communist forces. This resolution greatly increased the power of the presidency, essentially allowing the president to send troops without an official declaration of war from Congress.
LBJ responded by sending combat troops to Vietnam and by starting Operation Rolling Thunder, a heavy bombing campaign of North Vietnam. By 1967, there were 549,000 US troops in Vietnam. However, the North Vietnamese and Viet Cong had several advantages. First, they were fighting in their own country and had an extensive knowledge of the terrain and jungles. They also utilized the Ho Chi Minh Trail, a supply line that ran through Laos and Cambodia, to move troops and supplies between North and South Vietnam. The North Vietnamese easily replenished their troops and found some sympathy among South Vietnamese people, further complicating the US war effort—if some of the South Vietnamese supported the North, then why was the US even fighting?
US public support for the war, which was already waning, hit a low in 1968 after the Tet Offensive. Prior to the Tet Offensive, US General Westmoreland claimed that victory was in sight in Vietnam. Then, the North Vietnamese and Viet Cong launched a surprise attack, surrounding the US embassy in Saigon and overrunning cities throughout South Vietnam. Although the North Vietnamese and Viet Cong were eventually driven back, the Tet Offensive was a huge embarrassment for the US and signaled that the US had been misleading the public about the war. The war was looking increasingly unwinnable, and LBJ chose not to seek reelection in 1968. He also called for the beginning of negotiations with North Vietnam.
However, the end of Johnson's presidency and the election of Richard Nixon in 1968 did not signal the end of war. Nixon promised "peace with honor" in Vietnam during his campaign, meaning he would seek a way to end the war while preserving America's integrity as a world power. A big part of Nixon's plan was "Vietnamization"—the gradual withdrawal of US troops and ending of the draft in order to turn the fighting of the war over to the South Vietnamese. At the same time, Nixon invaded Cambodia and then increased secret US bombings of both Cambodia and Laos in order to cut off the Ho Chi Minh Trail. Ultimately these actions had the effect of further angering the American public and destabilizing Cambodia, allowing the oppressive Khmer Rouge to come to power. Finally, in 1973, Nixon agreed to a cease-fire and withdrawal from Vietnam. In 1975, the last US troops left Saigon, and the South Vietnamese soon fell to North Vietnamese forces.
By the end of the war, the US government had spent $176 billion in Vietnam. Over 58,000 Americans died in the war, and the war left a lasting impact on US culture and society. In addition to protests, numerous songs, movies, and novels emerged abut the war. Overall, numerous factors explain the US involvement in Vietnam. The US was perhaps overconfident in its military capabilities after World War II and increasing saw itself as the "policeman" of the world. The Cold War tensions with the Soviet Union increased fears about the spread of Communism and caused the US to see any communist-like government as a pawn of the Soviet Union. Finally, many US policy makers also misunderstood the desires, goals, and commitments of both the North and South Vietnamese.
http://www.digitalhistory.uh.edu/era.cfm?eraID=18&smtID=1

I need some examples of dramatic irony, situational irony, or just irony in general about any of the following Carver short stories: Cathedral, What do you do in San Francisco, What's in Alaska, Neighbors, They're not your husband, Will you please be quiet please, Nobody said anything, or Are you a doctor?

Ray Carver's "Cathedral" contains many examples of irony. The short story is narrated by a man who does little but work at a job he dislikes and stay up late drinking, smoking pot, and watching nothing in particular on television. Perhaps the first irony revealed is that this couch potato is married to a woman who lives on deeper levels: she once felt such despair that she attempted suicide, she writes poetry when an experience moves her, and she's bonded with a blind man named Robert with whom she exchanges audiotapes.
As the narrator describes his discomfort with Robert's upcoming visit, he seems unaware of the unpleasant traits he shows the reader. He admits he "wasn't enthusiastic about his visit. He was no one I knew. And his being blind bothered me." This is the first of many examples of dramatic irony because while the narrator sees nothing wrong with these remarks, the reader is aware that they reveal his close-minded lack of interest in new experiences and his irrational fear of blindness. Upon learning that Robert's wife Beulah has died, his concern is not for the bereaved widower but with the stereotyped belief that Beulah is "a name for a colored woman." He doesn't see that this description is pejorative and reveals his bigotry. He unknowingly shows his sexism and superficiality in his assumption that a blind man would be unable to compliment his wife--as if the only positive attribute a wife could have is her appearance.
While the narrator settles in for another dull night of smoking pot and watching a television show about medieval cathedrals (only because there's nothing else on), Robert experiences these same events in a far more engaged way. He smokes pot for the first time, relishing the new experience, and takes a philosophical interest in cathedrals. "I’m always learning something. Learning never ends," he says. He even gets the narrator to help him "see" the televised cathedrals by convincing him to draw one while he places his hand over the narrator's as he draws. While the narrator finds the blind man's life "pathetic" and worthy of pity, he is unaware of the situational irony: that this blind man lives life to the fullest while his own lack of interest in life makes him the truly pathetic and pitiable man.
In fact, the greatest irony of all comes when the reader considers which of these two men is more handicapped? Which one of them is truly blind?

There is situational irony in Raymond Carver's short story "Cathedral." That is, there is an incongruity between what is expected to happen and what does.
In "Cathedral," the narrator and his wife are somewhat estranged, mainly because the narrator/husband is unsociable and withdrawn. Even with his wife, he does not share his feelings or ask her to share her thoughts and emotions. Consequently, his wife seeks out others such as a blind friend of hers, with whom she develops a close relationship. This makes the husband a little jealous. So, when the wife tells her husband that her friend is coming to stay at their house, he is uncomfortable about the forthcoming visit.
After the blind man named Robert arrives, his warm and outgoing personality diffuses some of the tension between the narrator and his wife. Nevertheless, the narrator is rather taciturn while his wife talks at length to Robert. When she leaves the room, the narrator asks Robert if he wants to smoke some "dope" with him, as is his habit at night. "I'll try some with you," Robert tells him. When the wife returns, she asks her husband with disapproval, "What do I smell?" Nevertheless, she joins them. After a while, though, she grows very tired and falls asleep. It is while they are sitting quietly in the room that Robert asks the narrator what he is watching on the television. "Something about the church and the Middle Ages," the narrator replies because this is all that he can get to come in on his set. When Robert hears the word cathedral repeatedly, he asks the narrator if he can describe one to him. The narrator's attempts at verbal description fail. So Robert suggests that with some paper and a pen they could draw a cathedral together.
The narrator gets a paper shopping bag and returns. When he spreads the bag on a table, Robert moves near him and runs his hands over the bag. With a familiarity, Robert encourages the narrator to draw. Then, he tells the narrator to close his eyes; the narrator does so, observing, "So we kept on with it. His fingers rode my fingers as my hand went over the paper. It was like nothing else in my life up to now."
Ironically, the awkwardness the narrator anticipated with Robert's visit doesn't happen; instead, their interaction is rich and rewarding as Robert touches the narrator in more than just a physical sense. He helps the narrator open his mind and find meaning in sharing with others.

Who are the main characters in Something Rotten by Jasper Fforde?

The primary protagonist of Something Rotten is Thursday Next, who is the main protagonist of the series of the same name. Thursday Next is a "literary detective," solving crimes involving literature and literary heroes. In her world, the border between reality and fiction is much thinner than it is in ours, and Thursday is able to enter stories and interact with the characters in them. For example, Hamlet is also another important character in Something Rotten, although he is absent for much of the book. Thursday's family, including her parents and her young son (Friday Next), also feature heavily in the novel. Additionally, alternate versions of Thursday herself make appearances.
The primary antagonist of Something Rotten is Yorrick Kaine, a previously fictional character who has entered the real world and has high ambitions of leadership. In Something Rotten, he joins forces with an evil megacorporation and plots to become the Prime Minster. Thursday must defeat Yorrick and the Goliath corporation to prevent the ultimate end of the world.

Calculus of a Single Variable, Chapter 3, 3.5, Section 3.5, Problem 20

You need to evaluate the limit, hence, you need to replace oo for x in equation:
lim_(x->-oo) (5/x - x/3) = 5/(-oo) - (-oo)/3 = 0 + oo
Since the result is indeterminate, you need bring the fractions to a common denominator:
lim_(x->-oo)(15 - x^2)/(3x)
You need to factor out x^2 to numerator:
lim_(x->-oo) (x^2(15/(x^2) - 1))/(3x)
Since lim_(x->-oo) 15/(x^2) = 0 , yields:
lim_(x->-oo) (x^(2-1))*(-1/3)= -1/3*lim_(x->-oo) (x^1) = -1/3*(-oo) = oo
Hence, evaluating the given limit yields lim_(x->-oo) (5/x - x/3) = oo.

What is the gift O'Henry refers to in the title and how is it related to the magi in "The Gift of the Magi?"

The real gift is the love that Jim and Della have for each other.
Jim and Della were very poor, but each wanted to surprise the other with a meaningful gift for Christmas.  This was because they believed that they could express their love for each other through material means.  This was a mistake, but it’s the thought that counts.
Jim and Della ironically each tried to get their love something special by giving up the most meaningful possession they had.  In Jim’s case, it was a watch.  In Della’s case, it was her hair.  Jim was shocked to come home to find Della’s short hair, because he had bought a gift for her hair.

"It's sold, I tell you--sold and gone, too. It's Christmas Eve, boy. Be good to me, for it went for you. Maybe the hairs of my head were numbered," she went on with sudden serious sweetness, "but nobody could ever count my love for you. Shall I put the chops on, Jim?"

Ironically, Della sold her hair to buy Jim an especially expensive watch band.  She knew that his watch meant a lot to him, just like he knew how much her hair meant to her.  He didn’t resent her cutting her hair, he was just surprised because it rendered his gift useless.
Useless does not mean meaningless.  O’Henry comments on the beauty of the young couple’s selfless gifts, comparing them to the magi in the Christ story.

The magi, as you know, were wise men--wonderfully wise men--who brought gifts to the Babe in the manger. They invented the art of giving Christmas presents. Being wise, their gifts were no doubt wise ones, possibly bearing the privilege of exchange in case of duplication. 

O’Henry refers to the Dillingham Youngs as “foolish children,” but the focus of the story is the irony of their gifts.  They were as wise as they were foolish.  They did not need to give up what they gave up to show their love, but in doing so, they gave each other a greater gift than anything material.
 

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 48

Find all real solutions of $\displaystyle \sqrt{6} x^2 + 2x - \sqrt{\frac{3}{2}} = 0$.


$
\begin{equation}
\begin{aligned}

\sqrt{6} x^2 + 2x - \sqrt{\frac{3}{2}} =& 0
&& \text{Given}
\\
\\
\sqrt{6} x^2 + 2x =& \sqrt{\frac{3}{2}}
&& \text{Add } \sqrt{\frac{3}{2}}
\\
\\
x^2 + \frac{2}{\sqrt{6}} x =& \frac{\displaystyle \sqrt{\frac{3}{2}}}{\sqrt{6}}
&& \text{Divide both sides of the equation by $\sqrt{6}$ to make the coefficient of $x^2$ equal to 1}
\\
\\
x^2 + \frac{2}{\sqrt{6}} + \frac{1}{6} =& \frac{\displaystyle \sqrt{\frac{3}{2}}}{\sqrt{6}} + \frac{1}{6}
&& \text{Complete the square: add } \left( \frac{\displaystyle \frac{2}{\sqrt{6}}}{2} \right)^2 = \frac{1}{6}
\\
\\
\left( x + \frac{1}{\sqrt{6}} \right)^2 =& \frac{2}{3}
&& \text{Perfect square, simplify the right side of the equation}
\\
\\
x + \frac{1}{\sqrt{6}} =& \pm \sqrt{\frac{2}{3}}
&& \text{Take the square root}
\\
\\
x =& \frac{-1}{\sqrt{6}} \pm \sqrt{\frac{2}{3}}
&& \text{Subtract } \frac{1}{\sqrt{6}}
\\
\\
x =& \frac{-1}{\sqrt{6}} + \sqrt{\frac{2}{3}} \text{ and } x = \frac{-1}{\sqrt{6}} - \sqrt{\frac{2}{3}}
&& \text{Solve for } x
\\
\\
x =& \frac{\sqrt{6}}{6} \text{ and } x = \frac{- \sqrt{6}}{2}
&& \text{Simplify}

\end{aligned}
\end{equation}
$

To what extent can The Old Man and the Sea be considered an epic struggle of man against nature ?

In Hemingway's novella The Old Man and the Sea, the old fisherman Santiago battles for his life after being taken out to sea by a massive marlin that he had intended to catch. The entire work serves as a seminal example of the man-against-nature conflict, for it is the marlin and the sea itself that the man struggles against in order to survive. After nearly catching the marlin, the old man is taken far out to sea, where he finds himself in grave danger of drowning, starving, and freezing. Santiago experiences no conflict with other men, nor with himself. It is the sea—and nature itself—that Santiago must fight against in order to survive.
In one passage, the novella reads:

He looked across the sea and knew how alone he was now. But he could see the prisms in the deep dark water and the line stretching ahead and the strange undulation of the calm. The clouds were building up now for the trade wind and he looked ahead and saw a flight of wild ducks etching themselves against the sky over the water, then blurring, then etching again and he knew no man was ever alone on the sea.

Santiago is made to feel alone amongst the sea and its inhabitants until he notices the ducks. Eventually, Santiago spears the marlin, killing it. When he begins to head home toward the shore, sharks are attracted to the marlin's fresh blood and begin attacking the boat. This serves as another battle that Santiago must fight against nature, for the sharks, some of the sea's natural inhabitants, exist as a part of nature itself. After killing several of the sharks, Santiago arrives ashore safely, having conquered and persevered over nature.

What does Macbeth express in his soliloquy at the end of act 2, scene 1?

There is much that Macbeth expresses through his soliloquy, including guilt, ambitiousness, and the relationship between the ideas of fate and free will. Macbeth, in working himself up to the murder of his king, is filled with hesitancy and doubt. He begins to see a hallucination before his eyes, that of a bloodstained dagger pointing to Duncan's sleeping chambers. Macbeth is immediately aware of the illusory nature of the dagger, calling it a product of his "heat-oppressed brain." However, as Macbeth continues, he recalls the witches and considers fate and the evil things in the world. It is here that it becomes unclear whether the dagger is indeed a result of Macbeth's guilt, or if it is a supernatural vision, sent to push him forward towards his own fate. After all, Macbeth is constantly doubting his ability to kill his own king, and perhaps it is the dagger that finally convinces him that the crime might as well have already been done. Macbeth says at the end of his soliloquy:

Words to the heat of deeds too cold breath gives.

This phrase means that the more he talks about doing the deed, the more he feels his courage to actually do it faltering. However, the phrasing is interesting. Macbeth is forcing the sensible and rational thoughts out of his mind in order to commit a crime that is made entirely of passion with no forethought to the variable future. He may as well be saying that "If I actually think about what I'm about to do, I won't do it." This would lead anyone to do just that, but Macbeth seems to believe that turning back at this point would be impossible even though it could easily be done. This is because Macbeth has already committed in his heart to fate, perhaps his own or perhaps that of the witches' making. From this point on, where free will ends and fate begins, or vice-versa, is hard to discern.

One of many tense and supernatural moments in Shakespeare's Macbeth, Macbeth's speech at the end of Act 2, Scene 1 is his famed dagger soliloquy. In this scene, Macbeth hallucinates that he sees a dagger as he makes his way to Duncan's room to murder him.
Macbeth's speech reveals his hesitation and internal conflict about murdering Duncan. Though he had previously agreed to kill Duncan, his words now show that perhaps he was not as confident in the plan as he had previously led himself to believe.
Throughout the soliloquy, Macbeth appears to speak to the dagger, even acknowledging that he may be hallucinating:
"Art thou not, fatal vision, sensibleTo feeling as to sight? Or art thou butA dagger of the mind, a false creationProceeding from the heat-oppressèd brain?"

As he draws closer to Duncan's room, blood appears on the dagger:
"I see thee still,And on thy blade and dudgeon gouts of blood,Which was not so before."
Blood, a recurring motif throughout the play, symbolizes Macbeth's guilt regarding the murder. At this sight, Macbeth then attempts to convince himself that the dagger is nothing but a hallucination caused by his musings about the murder:
"There’s no such thing.It is the bloody business which informsThus to mine eyes."

Throughout the soliloquy, Macbeth's hesitation, feelings of guilt, and anxiety are expressed. He clearly feels conflicted about having to murder Duncan, but does so anyways.

Macbeth's soliloquy at the end of act 2, scene 1 is the famous "dagger" speech. Fueled by his ambition, Macbeth plans to kill the king in his sleep in order to become the king himself, but in this speech he expresses hesitancy and guilt at the thought of carrying through with his plans.
This guilt manifests in a hallucination of a dagger. Macbeth narrates his actions as he imagines that he sees the fatal instrument in the air in front of him ("Is this a dagger which I see before me?"), yet when he tries to grab the handle he discovers he cannot ("I have thee not, and yet I see thee still"). In response to this vision he draws his own dagger from his belt as a point of comparison. This will be the weapon that he uses to kill King Duncan. In the lines,

Thou marshall'st me the way that I was going;
And such an instrument I was to use.

it becomes clear that Macbeth believes the hallucination to be a portent, guiding him towards the murder he is about to commit. It points his way forward.
As he continues to hallucinate, the "dagger of the mind" begins to drip with blood, a symbol of his guilt. The tone of the monologue is fearful, with Macbeth repeatedly trying to snap out of it, so to speak, and convince himself that he's just seeing things:

There's no such thing:
It is the bloody business which informs
Thus to mine eyes.

Though here Macbeth seems to argue that the hallucination is caused by his impending crime, he then goes on to talk about witches and witchcraft. The fearful tone combined with the violent imagery makes it unclear whether this hallucination is supernatural in origin or indeed just a manifestation of Macbeth's guilty conscience. Both are possible within the world of the play.
Macbeth's musings on the vision and the deed he is about to commit are interrupted by the sound of a bell, a signal from his wife that the king's guards are drugged to sleep and the time for action is now. If the hallucinated dagger was a portent meant to warn Macbeth not to murder the king, he ultimately ignores it, proceeding with his original plan despite any guilt or hesitation he may feel.

I go, and it is done; the bell invites me.Hear it not, Duncan; for it is a knellThat summons thee to heaven or to hell.

What are some Biblical allusions in Waiting for Godot?

Beckett's Waiting For Godot can be analyzed as a fantastic religious, spiritual, and philosophical allegory about man's futile search for a direct connection to God. As the two main characters in the play, Vladimir and Estragon, wait for Godot, some have argued they are essentially waiting for God. They are desperate folks who depend on something greater than themselves to survive and find existential meaning. Having asked for Godot for "a kind of prayer," the two men don't seem to fully understand why they are actually waiting for Godot.
Waiting For Godot is similarly filled with religious images and allusions. The characters frequently discuss components of Christianity, often citing particular passages or stories from the Bible. At one point, Vladimir asks Estragon if he has ever read the bible. Estragon replies, "I must have looked at it" and quickly describes a colored map of the Holy Land, paying particular attention to the Dead Sea. Here, Estragon obviously missed most of the bulk of the Bible, focusing rather on swimming in the Dead Sea and acquiring happiness.
At another point, Vladimir tells Estragon of a story in which four Evangelists disagree as to whether or not a pair of thieves were damned or saved. Only one of the Evangelists suggests the thieves were saved, while two others refrain from mentioning the thieves as a whole.
These references, along with many uses of religious imagery, such as the word "crucify" when talking about Pozzo, appear in addition to much talk about Christ-like suffering.

Godot can be seen as the God of Christianity. In the play, Godot is a figure of redemption and salvation for Vladimir and Estragon.
In act 2, a young messenger’s description of Godot relates to John’s vision in Revelations. His mention of sheep and goats refers to a passage in the Book of Matthew.
Estragon compares himself to Jesus Christ when talking about his own suffering.
Lucky and Pozzo are called Cain and Abel.
The desire to be hung from a tree points to crucifixion. Vladimir also speaks about the two thieves who were crucified with Jesus. One of them was saved by his belief, suggesting that there is hope for the criminal and downtrodden.
Vladimir and Estragon both symbolize the brokenness of man’s relationship with God. The fact that they are tramps further shows that man is helpless and in need of something greater than himself.

Find an object in Murder On The Orient Express that is significant to the main character(s) in the story. Explain clearly why the object you have chosen is of importance to the main character(s) in the story, and draw on your own personal experience if necessary.

This is a fairly open question, which means that you can interpet it in several ways.
What first comes to mind for me is that the question is asking about the personal items identified by Poirot in the story, which serve as clues for him and which help him to solve to the mystery—for example, the embroidered handkerchief which he finds in the murdered man's carriage. The handkerchief is significant to Princess Dragomiroff not only because it belongs to her, but also because it reveals several things about her:
1. In the first place, the behavior of her maid when asked about the handkerchief reveals that the maid is extremely devoted to her mistress, so the handkerchief helps to give some illustration about the relationship between the two women.
2. The fact that the letter on the handkerchief is a "H" rather than a "N," allows her to explain her Russian background and the fact that the embroidered letter is Russian for "N," as in Natalia, her first name. The handkerchief tells us about her first name and background and indicates to the reader how foreign she is in the environment of the story.
3. In explaining the handkerchief, the Princess is also able to demonstrate her internal composure and strength of organization to Poirot. She offers to prove her ownership of the handkerchief by contacting the Parisian manufacturers, showing us that she is wealthy enough to spend time in Paris and make purchases there. Poirot is impressed by her "will."
You could answer this question by taking another of the clues Poirot spots—the pipe or the kimono—and explaining these in connection to one of the main characters. Alternatively, you could interpret the question in a different way and consider a significant object that does not directly relate to the murder. You could make some very interesting observations about Poirot himself, for example, based on his meticulous grooming and what this tells us about his personality. He possesses an enormous pocket watch, and he wears patent leather shoes. Poirot is "exotic" and arguably ridiculous—how does this help him in his career?

What is the mood in "Thank You, M'am"?

The mood of a story consists of the elements the author uses to make us feel a certain way while we are reading. This can include elements like description, setting, metaphors, and similes.
The setting of a story is especially important to establish the mood because it gives you a picture of where the story occurs, and how the characters react to those surroundings. In "Thank you, M'am," the setting is eleven o'clock at night on the street, with very few people around. To show us the setting, the author points out the time, and that the woman is walking alone at night. This gives the story an ominous mood.

It was about eleven o'clock at night, and she was walking alone...

The mood of the conversation between the boy and the woman can be seen by looking at the length of their sentences and the tone of their voices. The woman talks loudly and angrily, while the boy whispers and uses short phrases when he talks. Their interaction is brusque on her end and frightened on his end. The author describes the boy as thin, with shabby clothing. This shows a contrast between the boy and the woman, who is a "large woman." By describing the sweat "popping out" on the boy's face, and his tone of voice during their interactions, the author creates a mood of fear and intense anxiety.
Later, the mood in the story changes. When the woman drags the boy to her house, he realizes that there are other people in the house and that the door is open. This detail shows us that he still feels wary, but he feels safer now because there are other people around. The woman shows caring for the boy by telling him to wait till the water gets warm before washing his face. As the story progresses, the boy (who we now find out is named Roger) relaxes and can sit down and eat dinner with the woman. The mood of the story becomes much more comfortable, relaxed, and friendly. The story ends on a note of gratitude. Roger feels grateful to the woman for how she treated him, but doesn't know how to express it besides for saying, "Thank you, M'am" when she walks him out.

Why doesn't Paul tell his parents about all of the terrible things he has seen Erik do?

It seems like Paul could have avoided a lot of trouble and heartache if he had told his parents about the terrible things Erik did in Edward Bloor's novel, Tangerine, but it's a little more complicated than that.
The main reason he doesn't tell his parents is that he doesn't think they will believe him. In the opening pages of the novel, Paul is having a flashback about Erik speeding in a car and smashing mailboxes with a baseball bat. He tries to tell his parents about it, but they dismiss it.

It was "Erik." I was saying "Erik." Dad finally understood. He looked right into my eyes and asked. "What do you mean by 'Erik'? Erik what, Paul?" I stammered out, "Erik. He tried to kill me." Mom and Dad let go of my shoulders and stepped back. They looked at each other, puzzled. Then Dad raised his arm up and pointed to the right, into the dining room. There was Erik. He was sitting at the dining room table. He was doing his homework. Dad eyeballed me for a few seconds, then went out front to look for my bike. Erik called over, "There he goes. Blaming me again." Mom took me into the kitchen and gave me a glass of water. She ran a finger under the strap of my goggles and slipped them off. "Honey, you know how it is with your eyesight. You know you can't see very well." And that was that. But I can see. I can see everything. I can see things Mom and Dad can't. Or won't.

In the quote from the book above, Paul is remembering how his eyesight was damaged. It was, in fact, Erik's fault, but his parents had never told him the truth about the incident, and since it happened when he was still quite young, he has only fragments of memory that he doesn't put together completely until near the end of the novel. His mother also discredits him in this quote by talking about his poor eyesight. This causes Paul to doubt himself, which is another reason he doesn't tell his parents about the terrible things he has seen Erik do.
The third reason he doesn't tell his parents is that he is afraid of Erik. He has seen Erik commit acts of violence against others, or get one of his henchmen to do them. He has seen Erik plot and scheme against others. He sees the violence and moral turpitude of his brother that his parents are blind to. It isn't until much later in the novel, when Paul finds a group of friends and a place on the team at Tangerine Middle School that he musters enough courage to confront Erik. He also gains courage because Erik instructs his friend to fatally wound a relative of one of Paul's friends, and he sees the pain that it causes them. Between that and the continued flashbacks, Paul has finally had enough by the end of the novel, and because of this, he is instrumental in the demise of the Erik Fisher Football Dream. He also learns the truth of what Erik did to him that caused him to lose his sight.

How do the digestive, circulatory, respiratory and excretory systems provide the body with nutrients and energy?

Every cell in the body needs energy to perform its duties and stay alive. Cells use energy when they have the nutrients they need to perform.
The digestive system converts bulk foods like bread and meat into their components, and absorbs them into the bloodstream through the intestines. The circulatory system moves the nutrients from the intestines to the cells that need them.
The respiratory system provides the oxygen necessary for cells to metabolize, and the circulatory system moves the oxygen around the body and to the cells.
The excretory system and respiratory system both get rid of waste products. The excretory system disposes of all food not absorbed by the body, and any foods that the digestive system couldn't break down. The respiratory system removes carbon dioxide, a waste product of the cell, from the circulatory system.

How did Fogg travel to Allahabad?

Allahabad was between Bombay and Calcutta. Fogg was to take a Great Indian Peninsula Railway train from Bombay to Calcutta; the journey was to take three days by train.

...Leaving Bombay, it passes through Salcette, crossing to the continent opposite Tannah, goes over the chain of the Western Ghauts, runs thence north-east as far as Burhampoor, skirts the nearly independent territory of Bundelcund, ascends to Allahabad, turns thence eastwardly, meeting the Ganges at Benares, then departs from the river a little, and, descending south-eastward by Burdivan and the French town of Chandernagor, has its terminus at Calcutta.

However, Fogg soon discovered himself stranded at the hamlet of Kholby due to there being no tracks for the train to travel on to Calcutta. The hamlet of Kholby was said to be at least fifty miles from Allahabad, where the tracks supposedly picked up again. So, Fogg had to secure passage from Kholby to Allahabad by himself. Meanwhile, Passepartout informed him that he had found an elephant to take them to their destination.
After much haggling, Fogg paid two thousand pounds for the elephant and managed to secure a young Parsee guide for the trip to Allahabad. So, essentially, Fogg traveled from the hamlet of Kholby to Allahabad on the elephant.

According to Aunt Alexandra, Atticus will bring what to the Finch family by defending Tom Robinson?

Aunt Alexandra is the matriarch of the Finch family. As such, she sees herself as the guardian of the family's good name. Alexandra is obsessed with social standing, which is one reason why she is so critical of how Atticus raises his children. The Finches have a reputation to protect and allowing Scout and Jem to run wild doesn't exactly enhance their status in town. Scout really needs to start acting like a lady, thinks Alexandra, instead of being such a tomboy and slumming around in overalls all the time.
Alexandra, then, has a very rigid understanding of social hierarchy and where her family fits into it. It's against this background that we can make sense of her antipathy to Atticus's defense of Tom Robinson. Alexandra, like almost every white adult in Maycomb, shares the prejudices of her time concerning race. Yet social prejudice is much more important to her. She looks upon her brother's acting as Tom's attorney as a threat to the Finch family name and the family's place in the wider society. But family loyalty is also very important to her, so much so that she'll stoutly defend Atticus outside of the family:

I can’t say I approve of everything he does, Maudie, but he’s my brother, and I just want to know when this will ever end.

What is the unstated message in these quotes from the Muriel Spark story "You Should Have Seen the Mess"? 1. "...but he went round like a tramp, lending people money, as I have seen with my own eyes." 2. "He is well spoken, although he has not got a university education behind him."

Muriel Spark's short story "You Should Have Seen the Mess" is about a young woman named Lorna who tends to dismiss anything different from her, or anyone who won't accept her, as messy. She says the first quote about Willy Morley, an artist who the Darbys introduce her to. The unstated message in this quote is that Lorna can't quite understand Willy. He says he wants to paint her, but he never does so. He says she is beautiful, but he never really pushes the relationship beyond that. Lorna dismisses him because he gives away his money, which she doesn't understand; underneath what she says is the reality that Willy confuses her, so she rejects him. 
The second quote is about Mr. Marwood, who is a colleague of Lorna's at Low's Chemical Company. Even though Mr. Marwood looks proper, he isn't college educated. Lorna points this out to dismiss him, as she tends to find a reason to dismiss everyone. The reason she likes Lows's is that there is "special lighting over the desks," and she remains distant from her co-workers. She is defensive because she did not get into grammar school, so she points out other people's educational gaps. The unstated message in this quote is that Lorna tends to dismiss everyone she meets so she can remain untouched and unaffected by them. As she insists on cleanliness in the world, she also insists on keeping her soul antiseptically clean and untouched. 

Analyze the following text in terms of audience, purpose, and context: "Mr. President, Members of the International Olympic Committee. I'm Denise Lewis, Olympic Heptathlon champion from the Sydney Games. I have the pleasure of speaking on behalf of the London Athletes Commission. I was eight when I was inspired by the Moscow Games. I dreamt of emulating the athletes I watched. And my dreams came true when I completed in Atlanta, in Sydney, and in Athens. Like every Olympian, I have unforgettable Olympic memories. And we in London are determined every athlete will leave our city with friendships and memories which last forever. Our Athletes Commission had to answer one fundamental question: how do you give athletes the best possible Olympic experience? We said: give us the best Village in the most convenient location. Everything else follows. Our Village is within walking distance of nine venues. In London, athletes will compete, not commute. The Village is inside the Park to guarante the athletes a special experience. Take it from me: It makes all the difference to be as close to the action as possible. In fact, the whole London plan was conceived with our input. Everything athletes need was designed from day one. Training venues. Security. And, of course, the needs of Paralympians. These are the things athletes want."

The purpose of this speech is to persuade the International Olympic Committee (the audience) that London is the best venue to host the 2012 summer Olympics. Because the speaker is Denise Long, an Olympic gold medal champion, she has credibility: she knows what it is like to stay in an Olympic village and compete as an athlete in the games. 
Long's context is that she can speak as an insider with persuasive knowledge of what athletes need and how the London location meets those needs. She uses facts about the London location to show that it will be a good place for athletes, primarily because the Olympic Village is close to where the athletes will compete, so they will not have a long commute. She also notes that athletes had input into designing the London plan from the beginning, so it accounts for their needs for safety, security, and training.
Coming from an athlete speaking to a commission made up of people who are not necessarily athletes, this speech makes a persuasive case for the London location.   

To analyze the audience, purpose, and context of this speech, we actually need a bit more background information. We can find this speech both published and analyzed in Jon Steel's book Perfect Pitch: The Art of Selling Ideas and Winning New Business.
Through some basic research, we can discover both the context and purpose of this speech. Olympic champion Denise Lewis gave this speech as part of a lobbying effort to win the bid to host the 2012 Summer Olympic Games in London. In terms of more specific context, the speech was given at the Raffle City Convention Centre in Singapore on July 6, 2005. Lewis was chosen to seek in order to establish "ethos" (or credibility) for London's bid, as she had participated (as she states) in the Games in Atlanta, Sydney, and Athens and knows what athletes want. Lewis uses her time in the spotlight to discuss London's plan for giving future Olympic athletes the best possible experience by centralizing the location of the Olympic Village. This establishes London as a great geographic candidate for hosting. 
We can note that Lewis identifies her audience right at the beginning of the speech by directly addressing the President and Members of the International Olympic Committee (IOC), who was responsible for voting on who would host the 2012 Olympics. 
Finally, the good news is that this was obviously an effective speech! The IOC did indeed choose London to host the 2012 Summer Olympic Games. 

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 20

We have to evaluate the integral:\int \frac{x-2}{(x+1)^2+4}dx
Let x+1=u
So, dx=du
Hence we have,
\int \frac{x-2}{(x+1)^2+4}dx=\int \frac{u-3}{u^2+4}du
=\int \frac{u}{u^2+2^2}du-\int\frac{3}{u^2+2^2}du

First we will evaluate \int \frac{u}{u^2+4}du
Let u^2+4=t
So, 2udu=dt
Therefore we can write,
\int \frac{u}{u^2+4}du=\int \frac{dt}{2t}
=\frac{1}{2}ln(t)
=\frac{1}{2}ln(u^2+4)

Now we will evaluate, \int \frac{3}{u^2+4}du
\int \frac{3}{u^2+2^2}du=\frac{3}{2}tan^{-1}(\frac{u}{2})

Therefore we have,
\int \frac{x-2}{(x+1)^2+4}dx=\frac{1}{2}ln(u^2+4)-\frac{3}{2}tan^{-1}(\frac{u}{2})+C
=\frac{1}{2}ln((x+1)^2+4)-\frac{3}{2}tan^{-1}(\frac{x+1}{2})+C
=\frac{1}{2}ln(x^2+2x+5)-\frac{3}{2}tan^{-1}(\frac{x+1}{2})+C

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 74

Find the area of the region above the hyperbola $\displaystyle y = \frac{2}{x-2}$.

By using vertical strips,


$
\begin{equation}
\begin{aligned}

A &= \int^{-1}_{-4} \left( y_{\text{upper}} - y_{\text{lower}} \right)
\\
\\
A &= \int^{-1}_{-4} \left(0 - \left( \frac{2}{x-2} \right) \right) dx
\\
\\
A &= \int^{-1}_{-4} \frac{-2}{x-2} dx
\\
\\
\text{Let } u =& x - 2
\\
\\
du =& dx

\end{aligned}
\end{equation}
$


Make sure that the upper and lower units are in terms of $u$.


$
\begin{equation}
\begin{aligned}


A &= -2 \int^{-1-2}_{-4-2} \left( \frac{1}{u} \right) du\\
\\
A &= - 2 \int^{-3}_{-6} \frac{du}{u}\\
\\
A &= -2 [\ln u]^{-3}_{-6}\\
\\
A &= -2 [\ln(-3)-\ln(-6)]


\end{aligned}
\end{equation}
$



We can't evaluate the area since $\ln$ of negative number doesn't exist. However, since the function is reflected about $x = 2$ its area is equal to the region bounded by the curve, $x$-axis and the lines $x = 5$ and $x = 8$. $A = 1.3863$ square units.

Why is Trump president?

Regardless of varying personal opinions about Donald Trump, he is the legitimate forty-fifth president of the United States. He won the 2016 presidential election by capturing 306 electoral votes (270 or more are needed to win), even though he lost the popular vote by almost three million votes.
It is important to understand how the United States voting system works to completely understand how one candidate can lose the popular vote but win the presidency. Donald Trump is not alone in losing the popular vote but winning the presidency. John Quincy Adams (1824), Rutherford Hayes (1876), Benjamin Harrison (1888), and George W. Bush (2000) all lost the popular vote but won the electoral vote and thus the presidency.
You may ask yourself, “How can someone lose the popular vote and win the presidency in a democracy?” The answer is that the United States is not a direct democracy—the United States is a democratic republic. As a democratic republic, United States citizens both directly and indirectly choose elected officials. When voting for city council members, state senators and house members, governors, and federal-level senators and house members, United States citizens directly vote, meaning the candidate that wins the popular vote wins the seat. This is not the case for the presidential and vice presidential election. The electoral college determines the winning candidates of the presidential and vice presidential election.
What is the electoral college? The founding fathers established the electoral college in the constitution. It is made up of 538 electors with varying numbers of electors representing each state and the District of Columbia. The electors represent the president and vice presidential candidates. When citizens vote for a presidential and vice presidential candidate, they are actually voting for that candidate’s electors in their state. Those electors then cast their vote for their candidate. All states but Nebraska and Maine are “winner-takes-all” states in that whoever wins the popular vote in that state wins all electoral votes for that state. Nebraska and Maine use proportional representation, which means that electors are divvied up by the percent of the popular vote each candidate receives in that state.
The original purpose of the electoral college is two-fold. First, the founding fathers believed that the electors would more aptly choose a qualified president and guard the citizens against exploitation. They also believed that the public was not necessarily able to make the right choice and that by having the electoral college meet only once in determining the winner of the election, they would be less likely to be corrupted by any one candidate. Second, the electoral college was one of the compromises made at the Constitutional Convention to create equal representation in the government for the small states.
After the 2016 election, many people are calling for the abolishment of the electoral college.  Those calling for its abolishment say that the electoral college creates a system where the person with the least amount of votes could still win the presidency, it is complicated and discourages individuals from voting, and it gives small states and swing states more influence in the election. Those who support the electoral college say that it helps protect the interests of states with smaller populations, supports the two-party system (which they say helps create stability in the political system), and gives more power to the states.
Donald Trump successfully won the majority of electoral college votes by relying on the states he knew he could win (traditionally red states) and appealing to the disenfranchised voters in blue and purple states, effectively winning the popular vote in those states (even by a slim margin) and taking those electoral votes. Political pundits say that his win was a surprise because those on the left were using traditional political tactics and past successes while the Trump campaign tapped into the disenfranchised voters in traditionally blue states—most especially, working, middle-class white men. Election polls that have accurately predicted the winner failed to do so in this election. The 2016 presidential election was a turning point in American politics that has sparked entrance of new and fresh blood in politics and review of what some believe are antiquated aspects of the electoral system (like the electoral college). The 2020 presidential election shall be interesting to witness.
https://www.archives.gov/electoral-college/about

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 70

Find all solutions of equation

$
\begin{equation}
\begin{aligned}
&\text{(a)} 2x + 4i = 1\\
\\
&\text{(b)} x^2 - ix = 0\\
\\
&\text{(c)} x^2 + 2ix - 1 = 0\\
\\
&\text{(d)} ix^2 - 2x + i = 0
\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}
\text{a.) } 2x + 4i &=1 \\
\\
2x &= 1 - 4i && \text{Subtract } 4i\\
\\
x &= \frac{1-4i}{2} && \text{Divide by 2}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{b.) } x^2 - i x &= 0\\
\\
x(x-i) &=0 && \text{Factor out } x\\
\\
x &= 0 \text{ and } x - i = 0 && \text{Zero product property}\\
\\
x &= 0 \text{ and } x = i && \text{Solve for } x
\end{aligned}
\end{equation}
$


c.) To find the solution for $x^2 + 2ix - 1 = 0$, we use quadratic formula

$
\begin{equation}
\begin{aligned}
x &= \frac{-2i \pm \sqrt{(2i)^2 - 4(1)(-1)}}{2(1)}\\
\\
&= \frac{-2i \pm \sqrt{4i^2 + 4}}{2}\\
\\
&= \frac{-2i \pm \sqrt{-4 + 4}}{2}\\
\\
&= \frac{-2i}{2} = -i
\end{aligned}
\end{equation}
$

Thus, the solution is $x = -i$

d.) To find the solution for $ix^2 - 2x + i = 0$, we use quadratic formula

$
\begin{equation}
\begin{aligned}
x &= \frac{-(-2) \pm \sqrt{(-2)^2 - 4(i)(i)}}{2i} \\
\\
&= \frac{2\pm \sqrt{4-4i^2}}{2i}\\
\\
&= \frac{2 \pm \sqrt{4+4}}{2i}\\
\\
&= \frac{2 \pm 2 \sqrt{2}}{2i}\\
\\
&= \frac{1\pm\sqrt{2}}{i}
\end{aligned}
\end{equation}
$

By multiplying the complex conjugate

$
\begin{equation}
\begin{aligned}
x &= \frac{1 \pm \sqrt{2}}{i} \left( \frac{-i}{-i} \right) \\
\\
&= \frac{(1 \pm \sqrt{2})(-i)}{-i^2}\\
\\
&= \frac{(1 \pm \sqrt{2})(-i)}{1} \\
\\
&= (1 \pm \sqrt{2})(-i)
\end{aligned}
\end{equation}
$

Thus, the complex solutions are $ x = (1 + \sqrt{2})(-i)$ and $x = ( 1 - \sqrt{2})(-i)$