What is the function of Abigail Williams in Arthur Miller's The Crucible?

Abigail Williams functions as a main antagonist who drives the play's cataclysmic events forward.  
Initially, Abigail Williams is completely averse to having anybody in the town even whisper about the possibility of witchcraft. She is adamant to Parris that she and the other girls were only dancing in the forest, saying, 

Uncle, we did dance; let you tell them I confessed it—and I'll be whipped if I must be. But they're speakin' of witchcraft. Betty's not witched.

As details about the girls' activities are revealed to the audience, we learn they also drank blood. Many of the girls are very worried, but Abby convinces them to keep quiet about everything. She is determined not to let any rumors of witchcraft survive, threatening,  

And mark this. Let either of you breathe a word, or the edge of a word, about the other things, and I will come to you in the black of some terrible night and I will bring a pointy reckoning that will shudder you. And you know I can do it; I saw Indians smash my dear parents' heads on the pillow next to mine, and I have seen some reddish work done at night, and I can make you wish you had never seen the sun go down!

Had Abigail kept up that kind of attitude, the rest of the play's events would have played out very differently.  
Abigail doesn't keep trying to keep witch rumors away, though. After seeing the attention heaped upon Tituba for naming a supposed witch, Abigail immediately chimes in that she saw other people with the Devil, too.  

Hale: God will bless you for your help.
Abigail rises, staring as though inspired, and cries out.
Abigail: I want to open myself! They turn to her, startled. She is enraptured, as though in a pearly light. I want the light of God, I want the sweet love of Jesus! I danced for the Devil; I saw him; I wrote in his book; I go back to Jesus; I kiss His hand. I saw Sarah Good with the Devil! I saw Goody Osburn with the Devil! I saw Bridget Bishop with the Devil!  

From this point forward, Abigail is the leader of the girls who cry witchcraft, and she accuses whoever she feels like. At first, I believe Abigail enjoys the attention and reverence given to her. Later, Abigail realizes she can use her position of power to have Elizabeth Proctor killed. If Elizabeth is dead, Abigail believes she can resume her affair with John Proctor.  

College Algebra, Chapter 3, 3.7, Section 3.7, Problem 42

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

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


$
\begin{equation}
\begin{aligned}

y =& \frac{x - 2}{x + 2}
&& \text{Apply Cross Multiplication}
\\
\\
y(x + 2) =& x - 2
&& \text{Expand}
\\
\\
xy + 2y =& x - 2
&& \text{Subtract $x$ and $y$}
\\
\\
xy - x =& -2y - 2
&& \text{Factor out $x$ on the left side, add -2 from the right side}
\\
\\
x(y - 1) =& -2(y + 1)
&& \text{Divide both sides by } (y - 1)
\\
\\
x =& \frac{-2 (y + 1)}{y - 1}
&& \text{Interchange $x$ and $y$}
\\
\\
y =& \frac{-2 (x + 1)}{x - 1}
&&

\end{aligned}
\end{equation}
$


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

What details does the author of Reading Lolita in Tehran use to describe Sanaz?

The author describes Sanaz as divided between the two men in her life—her younger brother, a spoiled high schooler who wants to prove he is a man by controlling his sister—and her sweetheart, Ali, who left for England six years before. Sanaz's brother takes to following her, driving her car, listening to her phone conversations, and spying on her. Sanaz has beautiful long hair that she characteristically flicks from side to side, but she hides it beneath her veil, and she wears a scarf over her gold earrings and a robe over the orange shirt and jeans she wears. The author notes Sanaz's pride in her hair to show that Sanaz desires a kind of liberty that her current situation cannot offer her. The author also writes about how she imagines Sanaz goes through the streets of Tehran in a determined way in which she hides her eyes and tries to concentrate on her thoughts rather than on the grim, constricting world around her.

Azar Nafisi, author of Reading Lolita in Tehran, describes the seven young women she has hand-picked for her reading group. She founded this private reading group, devoted to Western literature, after resigning from her university teaching position.
In the first chapter of the book, Nafisi describes all seven women. Sanaz gets less description than many of the others. Nafisi pictures her as a young woman caught between wanting her family's and society's approval and wanting to do her own thing. Her dependence on others shows as she arrives at Nafisi's apartment holding onto the arm of her friend Mitra.
Nafisi says more about her on pages 26 and 27. Here, she describes the double life Sanaz is forced to lead. In Nafisi's apartment she wears an orange shirt and jeans, along with big gold earrings, ordinary Western dress. But to go out on the street, she must cover her head with a scarf and cover her body with a dark Islamic robe. She has to hide who she is from her culture in order to survive.

Why was the Battle of Bunker Hill important?

The Battle of Bunker Hill, though it did not accomplish anything strategically for either the Americans or the British, can be said to have had primarily a kind of psychological importance. Though the British had been defeated two months earlier at Concord, this had been one of those situations (which continued to occur throughout the war) in which they were unprepared for the unorthodox tactics used by the American rebels. The British were not exactly repulsed at Concord Bridge, but during the retreat to Boston, they were repeatedly ambushed by Americans firing at them from farmhouses and concealed positions all along the route. The British believed that if they could confront the rebels in open battle, in a situation more or less replicating European-style set piece battles, they would easily defeat them and quickly bring the rebellion to an end.
At Bunker Hill (actually Breed's Hill), this did not happen. The British had to make multiple charges up the hill, taking a shocking number of casualties, before finally making the American position collapse. This set a pattern, in a way, for much of the warfare over the next six and a half years until the final major confrontation at Yorktown. The British were able to defeat the Americans in open battle, but the cost of doing so was enormous. The British were not prepared to suffer such a high number of casualties or to make the enormous (and expensive, not simply in human terms) effort required to put down the rebellion. This was true especially in view of the fact that much of Parliament, and even many of the British military, were not enthusiastic about prosecuting the war in the first place. The Whig party was sympathetic to the Americans and believed that the rights of the colonists as fellow Englishmen had been violated. Eventually the war dragged on year after year with the rebellion no closer to being put down in 1781 than it had been in 1775.
Bunker Hill, though a British "victory," achieved nothing strategically. It merely inflamed the Americans even more and—given the bombardment that set the town of Charlestown into flames during the battle—demonstrated to them the ruthlessness with which the King and his administration intended to quash the rebellion. Within a year of Bunker Hill, the British were forced to evacuate Boston, with no end to the fighting in sight.

How would you compare "The Ones Who Walk Away from Omelas" and "Harrison Bergeron"? What is the contrast between the two?

Both stories take place in a fantasy society which enforces conformity to soul damaging norms. Both stories are didactic, written to teach the reader cautionary lessons about troubling trends in our own society. But their tones differ radically.
Vonnegut's "Harrison Bergemon" is set precisely in the year 2081. Society has gone to absurd lengths to make sure everyone is "equal" and that nobody stands out. This especially means that people have their intelligence, talents, and good looks suppressed so that nobody else will feel inferior. This norm is enforced through violence: apparently anybody brave or intelligent enough to challenge the system is killed. This is a commentary on moves in our own society to "level playing fields" and give people equal opportunity. This future society, however, is so bad nobody would want to live in it.
LeGuin does not set "The Ones who Walk Away from Omelas" in a specific year. It, too depicts a society that has a troubling core: in this case, everyone else's happiness depends on the extreme abuse and neglect of an innocent child. This alternate society is depicted as appealing except for the child. Through it, LeGuin critiques utilitarian philosophy, which argues that the good life is achieved when a society provides the greatest happiness to the greatest number. Utilitarianism is a rationale used in public policy in our society, which is what LeGuin wants us to ponder.
Vonnegut critiques equalitarianism run amok; LeGuin critiques utilitarianism, even if it has not run amok. The stories are both didactic, but the tones are a study in contrast. Vonnegut's tone is madcap, so exaggerated and comic that one could argue he undermines his message, as it is impossible to envision people putting up with the society he describes. LeGuin's tone is serious and quiet, and her story is perhaps more convincing in urging us to think about how our society, in less stark ways, makes similar decisions to Omelas.

In “The Ones Who Walk Away from Omelas,” the narrator at first describes a utopian community in which all individuals are happy and thriving. In contrast, “Harrison Bergeron” depicts a single couple in their home—one of whom is actively tortured by his handicap in the name of equality. While both texts are dystopian, only “The Ones Who Walk Away from Omelas” describes a utopian existence.

The biggest similarity, of course, is that individuals must suffer in exchange for the happiness of the majority. However, the way in which rebellion is exercised diverges completely.

In “The Ones Who Walk Away from Omelas,” those who cannot accept the suffering of the child simply leave Omelas, traveling to an undisclosed place. The narrator states plainly that the citizens are given the choice to stay or leave, with no dire consequences should they choose the latter. Their silent protest is peaceful and private.

In contrast, the titular Bergeron escapes from the Handicappers and storms onto a live television broadcast, declaring himself a king in front of the viewing public. In response, the Handicapper General herself assassinates both Bergeron and his ballerina “queen” while the broadcast continues. This swift, deadly punishment suggests a totalitarian government in which detractors must choose between silence or death.

Ultimately, while suffering exists in both short stories, and both stories present a moral dilemma, Le Guin asks us to consider what price we might be willing to pay for happiness, while Vonnegut wonders what we might be asked to sacrifice in the name of noble values.

Calculus of a Single Variable, Chapter 2, 2.1, Section 2.1, Problem 33

The given line is :-
2x - y + 1 = 0
or, y = 2x + 1 (the line is represented in slope intercept form)
Thus, the slope of the line = 2
Now, the tangent to the curve f(x) = (x^2) is parallel to the above line
Thus, the slope of the tangent = slope of the line = 2.......(1)
The given function is:-
f(x) = (x^2)
differentiating both sides w.r.t 'x' we get
f'(x) = 2x
Now, slope of the tangent = 2
Thus, 2x = 2
or, x = 1 Putting the value of x =1 in the given equation of curve, we get
f(1) = y = 1
Hence the tangent passes through the point (1,1)
Thus, equation of the tangent at the point (2,4) and having slope = 2 is :-
y - 1 = (2)*(x - 1)
or, y - 1 = 2x - 2
or, y - 2x + 1 = 0 is the equation of the tangent to the given curve at (1,1)

How can I argue that Emily's life has been negatively affected by her search for love and that Emily's (overprotective) father is at the root of her problems?

Emily is very much the product of a strict, loveless upbringing. Her stern father turned away every suitor who showed any kind of interest in his daughter. More than anything, this had the effect of keeping Emily in a state of arrested development, preventing her from growing into an emotionally-mature adult.
Deprived of emotional support for so many years, it's not surprising that Emily came to develop a somewhat warped view of love. For her, love has come to mean possession and control: the kind exerted over her by her father. Just as he wouldn't allow Emily to grow and develop as an adult, so too will Emily not allow the unfortunate Homer Barron to lead any kind of independent life away from her.

Emily Grierson grew up in a home with an overprotective, strict father, who stifled her social development by continually rejecting each one of Emily's male suitors because he thought they were never quite good enough for her. Emily's relationship with her father is best illustrated by the tableau, which depicts Emily's father standing in the foreground holding a horse whip while his daughter timidly stands in the background. Under her father's constant supervision, Emily lived an oppressed life, which dramatically impacted how she viewed love and relationships.
Emily's father's authoritative nature had such an effect on her that she even refused to acknowledge his death for several days after he passed away. One could argue that Emily's father's harsh nature led Emily to believe that love was associated with suffering and oppression, which is one reason she decided to poison Homer Barron and sleep next to his corpse for numerous years after his death. Essentially, Emily inherited her sick and twisted perception of love from her oppressive, authoritative father, who drastically stifled her social development.

How do I start a thorough analysis of the poem "The Good-Morrow" by John Donne?

To write a solid analysis of this poem, you might begin with the significance of the title "The Good-Morrow."  Take this title, which means "good morning," and apply it to the structure and themes of the poem itself. Notice that in the beginning of the poem, the speaker contrasts the lovers' lives before they met each other and after. To emphasize this contrast, he refers to sleeping and waking. Before the lovers met, it was as if they lived in the "Seven Sleepers' den" or a dream world.  
The second stanza takes this contrast a bit further. The title of the poem "The Good-Morrow" is mentioned here as the speaker goes on to show how the lovers are presently. It's as if their souls have awakened to the knowledge that their love is all they need, that their love forms a world which makes them superior to all still searching for fulfillment:

Let sea-discoverers to new worlds have gone,
Let maps to other, worlds on worlds have shown,
Let us possess one world, each hath one, and is one. 

In the last stanza, the speaker describes the physical position of the two lovers, who are now wide awake and looking into each other's eyes. In their eyes, they see a world without coldness or harshness ("sharp north") and without end ("declining west"). Using the metaphor of eyes which reflect the images of each other, Donne writes,

My face in thine eye, thine in mine appears

and then connecting the roundness of the eye to the globe or world, the speaker shows both the perfect union and the eternity of their love. The lovers are saying good morning to each other, the union of their souls, and the everlasting quality of their love.

If our two loves be one, or, thou and I
Love so alike, that none do slacken, none can die.  

Aside from the title and its connection to the contrasts and metaphors within the poem, you might look at how the sounds of the worlds reflect the poet's meanings. For instance, the last three lines of the first stanza contain repetition of the long "e" sound. This assonance creates a gentle and reverent tone as the speaker describes his lover's beauty and her superiority to any other woman he has ever met. The internal rhyme in the last stanza, 

My face in thine eye, thine in mine appears,

brilliantly echoes the idea of unity: "thine" and "mine."  
There are many other facets of this poem that you might explore. I have included some links below that may give you more ideas.  

Why does the narrator call Mr. Chips a legend?

In this particular instance, the narrator calls Mr. Chips a legend because as an air-raid is going on near the school during World War I, Mr. Chips calmly continues his Latin lesson. As the narrator explains, Mr. Chips thinks they are just as safe in the classroom on the schoolhouse's ground floor as anywhere else, even if shrapnel is falling all around them. And while the students are frightened or distracted, Mr. Chips remains unflappable:

So he went on with his Latin, speaking a little louder amid the reverberating crashes of the guns and the shrill whine of anti-aircraft shells. Some of the boys were nervous; few were able to be attentive. He said, gently: "It may possibly seem to you, Robertson—at this particular moment in the world's history—umph—that the affairs of Caesar in Gaul some two thousand years ago—are— umph—of somewhat secondary importance— . . . But believe me—umph—my dear Robertson—that is not really the case."

In part, Mr. Chips is a legend due to this story because the story gets more and more embellished as it is retold, and becomes half fact, half fiction, just as a legend does.
It is also a legend because it exemplifies what Mr. Chips is to the school, a fixture who never changes. At this point he is old, and even a war can't compel him to change his ways. He represents a safe, Victorian world.

Mr. Chips was a master at Brookfield for well over half a century. During that time, the school underwent many profound changes, as indeed did the world outside. Yet throughout it all, one permanent fixture remained: Mr. Chips himself. Chips is a legendary figure because, uniquely, he connects Brookfield's present to its past. As with many legends, all kinds of stories and anecdotes—some of them true, some of them apocryphal—have attached to his name.
Thanks to Chips's kindliness and good humor, he remains deeply popular among both boys and teachers alike throughout his time at the school and beyond. However, the new headmaster Ralston regards him as a bit of a dinosaur, rather a stick in the mud for his unwillingness to embrace the radical changes he's introduced to Brookfield. Yet this is very much a minority opinion. On the whole, the student body and the faculty value Chips enormously for sticking to his guns. In fact, it merely adds to his legendary status as a timeless reminder of what Brookfield's values ought to be.

Write your own parody of the "Double, double, toil and trouble" chant.

When one writes a parody, one is attempting to produce a funny imitation of an author or genre. It is often amusingly hyperbolic, or exaggerated. An audience has to be able to recognize the original text being parodied in order to understand both the similarities and the humor produced.
To begin your parody of this scene, you might want to come up with a scenario in which three women are working on something together. I think that having three females is crucial to ensuring that the original text of the parody is recognizable to your audience. You could choose some kind of stereotypical scenario, such as three mothers wishing that their children would clean up after themselves or that they would listen more, or three wives complaining that their spouses don't do enough around the house. These women could be casting a spell to make their children or spouses listen more or do more. Or you could choose something a bit less expected, like three women chanting about their political concerns or about the challenges of being queer in today's society.
It is also important to retain the way the sisters speak—in rhyming couplets—in order to make the original text clear. Their speech pattern is one of the most obvious stylistic choices that Shakespeare makes for their characters, and this is why it will be important to maintain. In addition to the end rhyme, the witches also speak in a meter called trochaic tetrameter. This means that there are four (tetra-) feet per line, each foot containing two syllables: an accented syllable followed by an unaccented syllable.

Dou ble | Dou ble | toil and | trou ble
Fi re | burn and | caul dron | bub ble

Each of the syllables in bold is accented, and feet are separated by "|." If you can manage to duplicate this meter, I'm sure your teacher would be thrilled! However, if you haven't studied meter, then I think you could probably get away with simply duplicating the end rhyme.
This is a really cool assignment. Good luck!

In Act III, scenes iii and iv of Romeo and Juliet, why is Romeo considered the protagonist?

The protagonist is essentially defined as the main character of a text, typically the character whose life or progress is followed and is presented with some kind of conflict. For this reason, it would be appropriate to define both Romeo and Juliet as the protagonists of this play. In the first scene you cite, 3.iii, it is easy to see Romeo as a protagonist because it shows Romeo in Friar Lawrence's cell, receiving the news that he has been banished from Verona for murdering Juliet's cousin, Tybalt. We see Romeo's response to his punishment as well as his response to the nurse's news of Juliet's grief. The plan is laid for Romeo to journey to Mantua after spending this one night with his beloved. The entirety of the scene really focuses on Romeo's emotional responses and plans for the future.
However, the next scene, 3.iv, doesn't feature Romeo at all. This scene shows Lord and Lady Capulet discussing marriage plans with Count Paris (who still wants to marry Juliet). It's a very short scene in which they make plans for Juliet's upcoming wedding. However, just because neither Romeo nor Juliet show up in person in this scene doesn't mean that they are no longer the protagonists of the play. In this scene, plans are being made which will very seriously impact their hopes for the future and lead to Juliet's faking her own death (and everything that follows). Therefore, they remain the protagonists even though they aren't in the scene themselves.

What was the lasting impact of President Reagan on the United States?

Reagan was one of America's most popular presidents.  The former actor had a real gift for explaining his vision for America so that all could understand.  President Reagan was a leader in ending the Cold War and building positive Russian-American relations. Reagan was also a leader in the War on Drugs and his wife Nancy's campaign of "Just Say No" was quite popular.   
Politically, Reagan did have some problems, however.  Reagan was president during the Iran-Contra scandal and somehow managed to avoid punishment.  Reagan's policies of financial deregulation helped to bring about the Savings and Loan crisis of the late 1980s which hurt the presidency of his successor, George H.W. Bush.  Reagan's increased military spending led to massive deficits that America continues to pay on today.  Today Reagan is considered a hero of the Republican party, but his massive military spending and deficits would make him a liability for fiscal conservatives.  

What are three personality traits of Sir Andrew Aguecheek with quotes to support

Sir Andrew Aguecheek is a comic type still current in comedy today: the super wealthy upperclass twit.
One prominent characteristic of Sir Andrew is that he is a brainless idiot. For example, when Toby Belch tries to introduce him Maria, Toby says to him, "accost," meaning he should woo or court Maria. Aguecheek takes this to be her name and addresses her as follows:

Good Mistress Accost, I desire better acquaintance.

Not surprisingly, Sir Andrew is clueless about what a complete dope he is. Therefore, although he mourns that Olivia will prefer Orsino to him, he is vain enough to be easily flattered (in a backhanded way) by Toby into believing that he has a chance with Olivia. Toby says:

She’ll none o' the count. She’ll not match above her degree, neither in estate, years, nor wit. I have heard her swear ’t. Tut, there’s life in ’t, man.

In other words, she doesn't want a man who is too smart or competent: therefore, Sir Andrew has a chance.
Finally, Sir Andrew shows he is a coward. Urged on by Toby, he challenges Cesario to a duel, but when he hears rumors of what a fierce fighter Cesario is, he quickly backs out of the battle: "I'll not meddle with him," Sir Andrew says, and even offers to appease him by giving him his horse.
Upperclass twits like Sir Andrew are good for comic relief. They are so protected by their money that audiences don't mind laughing at them: theatergoers know these characters' idiocy will do them no real harm.

Sir Andrew Aguecheek from Shakespeare's Twelfth Night is a character primarily intended to be comic relief. Though he is a wealthy man, he is described as a fool, a coward, and a "quarreler," meaning that he is quick to anger and often picks fights. The audience learns all of these facts about Sir Andrew before they ever meet him, from the following exchange between Sir Toby Belch and Maria in act I, scene iii:

SIR TOBY BELCH
Why, he has three thousand ducats a year.
MARIA
Ay, but he'll have but a year in all these ducats:he's a very fool and a prodigal.
SIR TOBY BELCH
Fie, that you'll say so! he plays o' theviol-de-gamboys, and speaks three or four languagesword for word without book, and hath all the goodgifts of nature.
MARIA
He hath indeed, almost natural: for besides thathe's a fool, he's a great quarreller: and but thathe hath the gift of a coward to allay the gust hehath in quarrelling, 'tis thought among the prudenthe would quickly have the gift of a grave.

When Sir Andrew then enters, his reputation preceding him, he is quick to live up to all of these assessments with his own dialogue and actions. He is foolishly lovestruck for the Lady Olivia, who hardly knows he exists. He is quickly infuriated with Malvolio and challenges Cesario to a duel, demonstrating his short fuse and quarrelsome nature. His cowardly nature becomes evident as well when he becomes petrified of fighting Cesario following Sir Toby's (false) reports of Cesario's skill with a sword.
Other traits that you could find textual evidence for in relation to Sir Andrew include the fact that he is self-aggrandizing, easily duped, and a drunkard. Sir Toby Belch and Maria manipulate him throughout the play and often talk negatively about his character.

How is Ismene different from Creon?

Ismene, like Creon, is very much a product of her time and place. Just as Creon acts according to the accepted standards of masculinity, Ismeme embodies the prevailing standards of femininity. She is meek, submissive, and compliant towards Creon, exactly how women in ancient Greece were expected to behave. Creon doesn't remotely contemplate challenging society's rigidly constructed gender roles. He is king, and as such, his word is law. Antigone, as both a subject and a woman, must yield to his will—or else. Ismene, by complying with Creon's express command, is also tacitly accepting the very circumscribed role that society has given her. Antigone's defiance of Creon is as incomprehensible to her as it is deeply insulting to Creon. For good or ill, both Ismeme and Creon have chosen to live and die by society's rules, unlike Antigone, who answers to a higher law than mere social convention.

How do the rationales of therapeutic approaches for treating bipolar and unipolar disorders compare and contrast?

Unipolar disorder, also called unipolar depression or major depressive disorder, is a single mood disorder in which individuals feel abnormally depressed for a period of at least two weeks. In contrast, those who suffer bipolar disorder will feel both highs and lows; they'll shift from feeling depressed to feeling euphoric, energetic, or manic. Both disorders are treated with biomedical therapy, meaning drug therapy, and types of psychotherapy.Since bipolar disorder is both a mood and a behavioral problem, medications are used to help stabilize a patient's mood while psychotherapy can be used to help a patient control his/her behavior and reduce symptoms. Drugs need to be used to control both manic and depressive moods. Lithium and some antipsychotic drugs can be used to treat both manic and bipolar depressive moods, but antidepressants may need to be used as well. The three psychotherapies that are effective for treating bipolar disorder are cognitive-behavioral therapy (CBT), family-focused therapy, and interpersonal rhythm therapy. CBT is used to help a patient change unhealthy thoughts, beliefs, and behavior patterns. Family-focused therapy (FFT) is used to treat the patient's entire family, not just the patient. Improving relationships with family members helps bipolar patients get well and stay well; therefore, FFT is used to help family members better understand the nature of the disorder, understand behaviors that are negatively affecting the patient, and develop problem-solving strategies. Interpersonal and social rhythm therapy is used to help a patient stabilize his or her mood by stabilizing the daily routine and by fixing relationship problems (National Institute of Mental Health, "Intensive Psychotherapy More Effective"; "Psychotherapies").In contrast to bipolar disorder, antidepressants are primarily used in biomedical therapy for unipolar disorder. While cognitive-behavioral therapy can also be used to treat unipolar disorder, other therapies include psychotherapy, interpersonal therapy, and problem-solving therapy. Plus, since depression is caused by a chemical imbalance in the brain, brain stimulation therapies are also used when a patient is not responsive to other therapies. Brain stimulation therapies include electroconvulsive therapy, transcranial magnetic stimulation, and vagus nerve stimulation (National Institute of Mental Health, "Depression").
https://www.nimh.nih.gov/health/topics/depression/index.shtml

What does the fact that Nora pays the porter twice what she owes him suggest about her?

I believe that you're referring to Nora Helmer in A Doll's House. What the incident with the porter shows is that Nora is still somewhat naive in the ways of the world. She doesn't fully understand the value of money and what it entails. Nora has been kept in a state of infantilized ignorance for so long, first by her father, then her husband, that her attitude toward money is that of a child. Although Torvald hasn't taken up his new job, his impending promotion is enough to encourage Nora to start spending his raise before he's actually received it. To Nora, money is a means to an end, a way of making people happy. That's why she over-tips the porter. It's also why she carries out serious financial fraud to pay for Torvald to have some much-needed rest and recuperation.

What is the role of indirect libre writing technique in Madame Bovary?

Free indirect discourse refers to the way the narrator recounts the discourse of a story. Direct discourse typically uses punctuation (such as quotation marks) to clearly mark that the words of the character are being "reported" as they were originally said. Story discourse is "indirect" when the narrator's words are telling what the character said instead of using the character's exact words. This indirect discourse can either be clearly marked as something said by a character, or it can be "free," meaning it is mixed with the narration itself, blurring the line between narrator and character. In Flaubert's work, free indirect discourse is included in the narrative without any markers, removing the distinction between the character's words and the narrator's. Consider the following possible narrative constructions:
Direct discourse
That was a lie. She thought to herself, "No one knows where it is."
Indirect discourse
That was a lie. She thought about how no one knows where it is.
Free indirect discourse
That was a lie. Who knows where it is!
In Madame Bovary, indirect discourse is typically marked by either an exclamation point or a question mark, but it does not have to be explicitly indicated. This is one technique responsible for the effect of an intimately informed narrator who knows Emma's innermost thoughts and feelings.

"Indirect libre" is the French term for "free indirect discourse," which is a narrative technique that developed around the turn of nineteenth century (in English-language literature, its origin is heavily associated with Jane Austen). Free indirect discourse is a kind of middle ground between first and third person narration; it involves a third-person narrator reporting a character's thoughts (or sometimes speech) without explicitly saying that he's doing so. For that reason, free indirect discourse also tends to blur the lines between the narrator and his characters, because our access to the characters' thoughts and feelings depends on the "translation" provided by the narrator.Flaubert used free indirect discourse extensively in his novels, and his work helped popularize the technique. There is no shortage of examples in Madame Bovary, but here is a particularly clear one from chapter 8:

The next day was a long one. She walked about her little garden, up and down the same walks, stopping before the beds, before the espalier, before the plaster curate, looking with amazement at all these things of once-on-a-time that she knew so well. How far off the ball seemed already! What was it that thus set so far asunder the morning of the day before yesterday and the evening of to-day? Her journey to Vaubyessard had made a hole in her life, like one of those great crevices that a storm will sometimes make in one night in mountains. Still she was resigned. She devoutly put away in her drawers her beautiful dress, down to the satin shoes whose soles were yellowed with the slippery wax of the dancing floor. Her heart was like these. In its friction against wealth something had come over it that could not be effaced.

Notice that Flaubert doesn't explicitly say "Emma thought, 'How far off the ball is already!'" but instead uses other cues (e.g., the exclamation mark) to clarify that we are inside Emma's head. Notice also, though, that it's hard to pinpoint exactly when we revert to the narrator's voice: is Flaubert, for instance, simply reporting that Emma "was resigned," or is Emma herself conscious of being "resigned"?

According to "The Lady or the Tiger," "No matter how the affair turned out, the youth would be disposed of." What does this mean? Would justice have been administered fairly?

In Frank Stockton's short story "The Lady or the Tiger," the young lover of the king's daughter is accused of a crime and judged in the king's arena. The man's crime was simply that he dared to be the princess's lover. His appearance in the arena is the king's way of getting rid of the youth because the king believes the man is not good enough to be with the princess. He is a commoner; the princess, royalty. For the king, the arena is the perfect vehicle to dispose of the youth because, after choosing one of the doors, he will either be consumed by the tiger, or promptly married to the lady, "the most suitable to his years and station that his majesty could select among his fair subjects." Regardless of the outcome of the "trial," the princess will no longer be able to see the young man and their love affair will be over.
For the "semi-barbaric" king's way of thinking, the outcome will be perfectly just. The accused's life is in his own hands. Unfortunately, the king's "incorruptible" justice has been corrupted when the princess discovers the secret of the doors and motions to her lover as to which door to choose. It is left in question whether the princess directed him to the lady or the tiger. If she had somehow quenched her passions, she may have chosen the lady, but, if her "semi-barbaric" nature got the best of her, then the young man was certainly doomed. In practical terms, because the young man was only guilty of loving above his status, the only just outcome would be if the lady emerged from behind the door. If he is eaten by the tiger, then the princess should be described as "barbaric," not "semi-barbaric."

Who is the protagonist? What makes the character dynamic, flat, round, or static?

I would argue that the protagonist in "Contents of the Dead Man's Pocket" is Tom Benecke, not least because he's the only real character in the story. But as well as being the protagonist, he's also the antagonist, and this makes him a dynamic character.
When the story begins, Tom's staying at home in his apartment while his wife Clare goes to the movies. Tom feels pretty bad about letting Clare go all by herself, but it's so important for him to get a promotion that he needs to stay home and complete the research he thinks will land him a better-paid position. Initially, then, Tom is fanatically dedicated to his work to the exclusion of pretty much everything else in his life. This explains why he's prepared to risk his life to go fetch his research paper when it blows out of the window and onto the ledge.
But over the course of the story, Tom's attitude changes, and this is what makes him a dynamic character. He comes to realize that work really isn't the most important thing in life after all. It's taken up too much of his time, time that could've been better spent with his wife. Tom now fully appreciates the value of time, something which his workaholic nature prevented him from doing. His whole character has changed, which makes it dynamic.

A block of mass m moves on a horizontal surface with coefficient of friction mu , subject to a constant force F_0 acting vertically downward towards the surface. If the block has initial velocity v , how far does it travel before it stops?

There are 4 forces acting on the block:gravitational force mg downwards,the force F_0 downwards,the reaction force N upwards,the friction force F_f horizontally.
The net force F_(n et), which is their vector sum, gives the block some acceleration a. By Newton's Second law F_(n et) = ma. Because the block moves horizontally, its speed and acceleration are also horizontal. Thus the net force is also horizontal that means all vertical forces are balanced, N = mg + F_0, and F_(n et) = F_f.
It is known that F_f = mu N = mu(mg + F_0). Therefore, the acceleration magnitude is a =mu(mg + F_0)/m =mu(g + F_0/m). Also it is known that friction force is opposite to the direction of movement.
Therefore, the speed of the block is V(t) = v - at and the block stops at time t_1 = v/a (when the speed becomes zero). The distance as a function of time is therefore  D(t) = vt - (at^2)/2, tlt=t_1,  and the farthest distance is
D(t_1) = vt_1 - (at_1^2)/2 = vt_1 - (vt_1)/2 = (vt_1)/2 =v^2/(2mu(g + F_0/m)).
This is the answer.
https://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

Describe how the major trade routes in Europe worked from Italy to Northern Europe. What made trade so expensive?

The answer to this question really depends on what time period you are asking about. Generally speaking though, there are two ways to trade between Italy and Northern Europe: by sea or by land.
Starting in the Bronze Age, limited trade around Europe existed. The Mediterranean region, including Italy, was well connected with trade routes, and goods flowed throughout this region. Some Mediterranean goods such as minerals and spices did make their way to Northern Europe, but the exact routes are not known. As bronze smelting became more widespread, tin from Northern Europe grew in demand in all regions, including Italy. It is likely that trade routes went overland, given the limitations of sea travel at the time. The actual trade routes are unclear, but they likely involved many short legs and passing goods through the hands of many middlemen.
By this period the Amber Road was well established between the Baltic Sea, through what is now Poland, and the Mediterranean. This route, which transported a lot of the precious material amber, thrived all the way through the Medieval Period.
By the Roman period, a single empire connected Italy and Northern Europe. This increased trade, as Rome was fond of goods from all over the empire. The Romans built roads and maintained mountain passes through the Alps. This allowed goods to be traded by land much easier than before. As shipbuilding technology improved, more trading by sea took place. The most common route was to sail around the Iberian Peninsula and out into the Atlantic to reach ports in Northern Europe. This route was quicker than going overland but ran the risk of encountering dangerous storms and currents. The Romans even used rivers to trade. Ships could sail from Italy into the Black Sea, then up the Danube into the interior of Europe. This was a longer route but proved to be much safer. Given the indirectness of trade by ship and the difficulty of mountainous land routes, trading was risky and time-consuming—and therefore expensive. At times the Roman government subsidized merchants trading important or high-demand goods.
In the Middle Ages and Renaissance, Italian merchants were at the center of trade. Many of the old routes from the Roman Empire continued to be used. However, with different kingdoms and city-states along these routes, trade became a little more complicated. Taxes were often charged when passing through different territories by land or stopping in foreign ports. This increased prices along the way. By the Renaissance, Europe was better connected through trade than it had been since the fall of the Roman Empire. Merchants from Northern Italy were becoming some of the wealthiest people on the continent. While trade was still risky and expensive, these merchants were able to make great fortunes by trading valuable goods, particularly silks and spices from Asia, all over Europe.
https://www.sutori.com/story/ruling-an-empire

Read and summarize Martin Luther King's "I have a Dream" speech, and explain its connection to the story Cry, the Beloved Country.

The irony of Martin Luther King Jr.'s "I Have a Dream" speech is that its most famous passage, the part where he relates his "dream," was actually extemporaneous. However, it is the most relevant part of the speech to Cry, the Beloved Country. King dreamed of a day when the United States would embrace the egalitarian rhetoric of the Declaration of Independence. He went on to say that he dreamed of a future in which race would not confer privilege, and, as he put it:

I have a dream that one day the state of Alabama. . . will be transformed into a situation where little black boys and black girls will be able to join hands with little white boys and white girls and walk together as sisters and brothers.

This message of love and reconciliation offered hope that the United States would one day transcend its racist past. In Cry, the Beloved Country, Arthur Jarvis, a white man committed to racial reconciliation and equality in South Africa, is murdered. The killer, ironically, is Absolom Kumalo, a black youth. The book revolves around the relationship between Stephen Kumalo, the boy's father, and James Jarvis, the father of the victim. The two men reach an understanding and a mutual commitment to achieve racial justice. Their relationship has obvious parallels to King's message of equality and redemption. 
https://avalon.law.yale.edu/20th_century/mlk01.asp

Which situations, if any, in contemporary life might cause an American town to be afflicted with general hysteria?

One of the factors that made the witch hunt and the Red Scare so frightening was the fact that one could not simply look at another person and know, without a doubt, that they were either loyal and honest or deceitful and dangerous. It is easy for fear and hysteria to develop when a person feels as though they have no real ability to protect themselves and their loved ones from harm. Miller even once called it a type of guerrilla warfare: waging war on an invisible enemy, one that you cannot pick out from other innocent people. It is then that individuals start to question those they have known for years, second-guessing every statement and interaction, and accusing their neighbors. Any town in which people come to fear a threat they cannot easily identify—perhaps a disease that has no symptoms until it kills its victim or a secret ring of serial murderers (who are hiding in plain sight)—could be susceptible to hysteria.

Given that Arthur Miller wrote The Crucible as an allegory to McCarthyism, one could come up with numerous situations that could mirror the general hysteria illustrated in the play. Hysteria is defined as an exaggerated or uncontrollable emotion or excitement among a group of people. Similar to how McCarthyism targeted communist sympathizers by making unsubstantiated claims toward influential American citizens regarding collusion with the Soviet Union, our current administration could begin targeting United States citizens by accusing them of colluding with Russia or North Korea. Given the current geopolitical environment concerning North Korea's access to nuclear weapons and capabilities, hysteria regarding a nuclear attack could sweep through the nation at any moment. Hysteria regarding the influx of illegal immigrants or the presence of ISIS throughout our nation are other possible instances that could create an atmosphere of hysteria throughout our country or a certain town in America. Even a situation involving mysterious deaths of one or more citizens could result in hysteria throughout a town or nation.
https://www.dictionary.com/browse/hysteria

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 32

min/max
Potential local extrema are found at points where y'=0.
y'=(2-2x)e^(2x-x^2)
(2-2x)e^(2x-x^2)=0
Since e^(2x-x^2)>0 we have
2-2x=0
x=1
To determine whether the function has minimum, maximum or extreme at all at the point x=1 we need to check the sign of derivative before and after that point.
y'(0)=(2-0)e^0=2>0=> function is increasing
y'(2)=(2-4)e^(4-4)=-2e^0=-2<0=> function is decreasing
Therefore, the function has local maximum at x=1. The value of the maximum is y(1)=e^(2-1)=e.
Points of inflection
Points of inflection are found where y''=0.
y''=-2e^(2x-x^2)+(2-2x)^2e^(2x-x^2)=e^(2x-x^2)(4x^2-8x+2)
e^(2x-x^2)(4x^2-8x+2)=0
4x^2-8x+2=0
2x^2-4x+1=0
Now we apply quadratic formula.
x_(1,2)=(4pm sqrt(16-8))/4=(4pm2sqrt2)/4=1pm sqrt2/2
x_1=1-sqrt2/2 x_2=1+sqrt2/2 Asymptotes
Since the domain of the function is set of all real numbers the function has no vertical asymptotes.
Horizontal asymptotes
lim_(x->oo)e^(2x-x^2)=e^(-oo)=0
lim_(x->-oo)e^(2x-x^2)=e^(-oo)=0
Since the function has horizontal asymptote for both -oo and oo it cannot have oblique asymptote.
Sketch of the curve can be seen in the image below.

What is postmodernism? What is post-structuralism?

Postmodernism is, by its very nature, difficult to define since it basically amounts to a rejection of traditional categories of knowledge. Basically, postmodernists call any universal truth, narrative, or point of consensus into question. They argue that our experiences and understandings are subjective because each person comes to these understandings from their own perspective. In history, for example, postmodernists would argue first that modern people cannot really understand the motives and perspectives of historical actors, calling all historical interpretation into question. Second, they claim that there can be no grand narrative of history because there are too many perspectives involved in any historical moment. Basically, postmodernists, whose work has informed almost every academic discipline, question the very assumptions disciplines are based on. 
Post-structuralism also tends to focus on the individual and denies the authority of academic disciplines—especially texts. One of the major ideas associated with post-structuralism is the notion that texts (nonfiction or fiction) cannot have a fixed meaning independent of the reader's interpretation of them. Accordingly, the reader is as important in assigning meaning to texts as the author. In his famous essay "The Death of the Author," Roland Barthes, one of several literary critics closely associated with post-structuralism, claimed provocatively that the "source, [the] voice" of a text "is not to be located. . . this is because the true locus of writing is reading." As a result, he claimed that post-structuralism heralded the "death" of the author because the reader created meaning as much as the author.
Proponents of post-structuralism in particular are notorious for being difficult to read for anyone other than an academic specialist. Despite this, their work, along with that of the postmodernists, has been influential in literary criticism, history, and many other fields. 
https://plato.stanford.edu/entries/postmodernism/

https://www.philosophybasics.com/movements_poststructuralism.html

Post-modernism and post-structuralism are 20th century artistic, literary and philosophical movements that can be understood by differentiating them from the movements they succeeded. 
Modernism reflected the ideas that there are universal truths, and that progress and technology are inherently good. The movement also embodied the notion that art and popular culture were distinct. Post-modernism reflected a more skeptical sense that meanings could be ironic and that art could be taken from mass culture.
Structuralism was based on the idea that human actions can be understood by recognizing there is an overriding "structure", apart from what we see, with which all human activity connects. Post-structuralism rejects the notion of "structure" for the idea that culture and society are great influencers of human actions.
 
 
 
  
 

Why were Montag's colleagues “suddenly fat and odious in their plump fireproof slickers"?

This quote comes from Part 1 of Fahrenheit 451 and follows the disappearance of Clarisse McClellan. Clarisse, Montag’s neighbor, was an unusual girl who did not act like anyone else her age. Clarisse is the catalyst for changing Montag’s view on his life and profession. She asked interesting questions and inspired Montag to wonder about the character of the world he lived in, rather than blindly accepting it. This is evident in the conversation he has in the fire station at the card table, when he asks what happened to the man whose library they burned in the previous week. Beatty answers him:

“They took him screaming off to the asylum.”
“He wasn’t insane.”
Beatty arranged his cards quietly. “Any man’s insane who thinks he can fool the Government and us.”

Montag asks several other questions in the course of this conversation which requires Beatty to remind him of the "history" of firefighting, illustrating Montag's dissatisfaction with what he thought he already knew. Montag’s distraction is further illustrated when he nearly forgets his helmet at their next call, which happens shortly after their game. As they arrive at a woman’s house to burn her library, Montag sees his coworkers as simultaneously ridiculous and dangerous agents, rather than heroic men, fulfilling a duty to their society. He is aware that he looks the same.

In Ray Bradbury’s dystopian novel Fahrenheit 451, protagonist Guy Montag starts to question the way his society operates. A young girl, Clarisse McClellan, asks Montag questions that spark his own line of questioning. Montag’s questioning attitude begins to change the way he sees the world. He wonders about the firemen that used to put out fires and how firemen now burn books. He starts to see that there are things wrong with the way his society works, and this changes his perspective. He no longer sees his fellow firemen as good guys. This is why Beatty, Stoneman, and Black are “suddenly odious and fat in the plump fireproof slickers.” He sees them as despicable and ridiculous in appearance, because it matches how he views their actions.

Choose any one of the fictions and any one of the poems below, exploring in detail one major theme that the works share (i.e., the fiction and the poem). The fictions: "Araby," "Rose for Emily," "Things They Carried," "Hills Like White Elephants," "How to Talk to Girls at Parties," "The Yellow Wallpaper," "Greasy Lake," "The Cathedral," "Everyday Use," "A&P" The poetry: In A Station of the Metro, "The Sky Was," "anyone lived in a pretty how town," "Fire and Ice," "Living in Sin"

The two pieces which stand out for me from these two lists as a good pair for comparison are "Everyday Use" by Alice Walker and "Fire and Ice" by Robert Frost.
Frost's poem weighs up the likelihood of the world ending either in fire or in ice, where he equates "desire" with the former and "hate" with the latter. Both love and hate, Frost determines, "would suffice" to cause destruction, these being equally powerful forces. We can also read "fire" and "ice" as representing two different ways of expressing our feelings towards another person, either through the burning fire of active passion or hatred, or through the "ice" of being cold towards someone, so that "the world" (or a relationship) ends in a freeze, rather than a conflagration.
In "Everyday Use," the focus of the story is on how Dee, Mama, and Maggie all relate differently to their shared history and how they feel about each other. The motif of fire appears in this story too, representative of Dee's destructive hatred, as Mama interprets it, for the world she has inhabited as a child. Mama remembers her two daughters on the night of the burning house very differently, picturing Maggie destroyed by it ("her hair smoking and her dress falling off her"), while Dee wears "a look of concentration on her face": "Why don't you do a dance around the ashes," Mama wanted to ask her. For Maggie, fire is a destructive force; for Dee, there is a sense of cleansing in its destruction, because "she hated that house" so much.
Later, Dee's form of attack upon her old life is different—more akin to Frost's "ice." Instead of attacking it deliberately, she chooses to recreate herself outside of it, giving herself a new name and associating with a man whose hand feels "cold" to Mama. Meanwhile, at the end of the story, Mama's grand gesture of giving the quilts to Maggie, in rejection of Dee's claim that Maggie "couldn't appreciate" them, represents a rebuttal to Dee's thinking that they should "make something of themselves," which withholds things from her, rather than deals out the "fire" of active argument towards her. Passion in this story, as in Frost's poem, can be expressed both through active rage and through cold withdrawal, and each approach is equally effective.

In which direction does John decide to travel in "By the Waters of Babylon" by Stephen Vincent Benét?

In the short story “By the Waters of Babylon,” the protagonist, John, decides to travel east. This decision goes against everything his people believe. 
At the beginning of the story, we are told east is a forbidden direction for John’s people. The first line of the story tells us that

The north and the west and the south are good hunting ground, but it is forbidden to go east.

Later on in the story, this idea is reemphasized. After John has his dream, his father blesses him and then reminds him

It is forbidden to travel east. It is forbidden to cross the river. It is forbidden to go to the Place of the Gods. All these things are forbidden.

Of course, these reminders simply serve to set up what John is about to do. John is going to upend his people’s beliefs. He is going to travel east to the Place of the Gods, and he is going to learn things that will change his society.
After his father blesses him and warns him not to go east, John sees three signs that tell him he must go east. He sees an eagle flying towards the east. He sees three deer, including a white fawn, moving east. A panther tries to kill the white fawn, but John is able to kill it with one arrow through the eye. All these signs tell him something. He says,

Then I knew I was meant to go east—I knew that was my journey.

Why are people afraid of Hannah Tupper in The Witch of Blackbird Pond?

The people of Weathersfield are afraid of Hannah Tupper because they are extremely superstitious people, and Hannah Tupper is different. In general, I think the people are afraid of Hannah Tupper because they do not understand her, and they do not understand her because they make no effort to. Kit makes an effort to befriend the woman, and Kit thinks that Hannah is just fine; however, nobody else bothers to make the effort because they don't see the point.

“But no one in Wethersfield has anything to do with Hannah Tupper.”
“Why on earth not?”
“She is a Quaker.”
“Why is that so dreadful?”
Rachel hesitated. “I can’t tell you exactly. The Quakers are queer stubborn people. They don’t believe in the Sacraments.”
“What difference does that make? She is as kind and good as—as you are, Aunt Rachel. I could swear to it.”

Hannah is a Quaker, and that apparently is so foreign of a way of life that the people of Weathersfield would rather tell scary stories about the old Quaker rather than actually get to know her. For the people of Weathersfield, it is just easier to accept scary stories about Hannah and escalate those stories than it is to try and disprove them. Hannah becomes a self-fulfilling prophecy of sorts, and anything that she does that is "witchlike" just further deepens the people's feelings. Hannah can't even stir a pot without people thinking it might be witchcraft.

Kit looked back at the gray figure bent over a kettle, stirring something with a long stick. Her spine prickled. It might be only soap, of course.

In The Witch of Blackbird Pond, Hannah Tupper is forced to live a life of tremendous isolation, with her cottage located at the edge of the swamp on the outskirts of town.
The people of Wethersfield are afraid of Hannah because she is not like them; Hannah is a Quaker who does not believe in the Sacraments and will not go to the weekly Meetings that the rest of the Puritan community attends.
This fear leads the townspeople to believe Hannah is a witch and ostracize her even more. This tension escalates once a illness begins to afflict the town. Thinking that Hannah's "witchcraft" is the cause of this scourge, a mob burns down Hannah's home in an effort to kill her. She is clearly not a welcome presence in the community.

What do you think was Irving's purpose in writing this story?

Arguably, Irving wrote this story as a warning to his readers that living a life motivated by financial gain will only bring misery. He shows this clearly through the character of Tom Walker. When he makes a deal with the devil, he agrees to become a moneylender in return for the treasure.
Although Tom becomes a "rich and mighty man" in Boston, he begins to feel "anxious" about what will happen when he dies. He starts going to church as a means to save his soul, but his desire for wealth does not fade. He forecloses a mortgage on a poor "land jobber," for example, who begs him for mercy. Instead of helping the man avoid a life of poverty, Tom shows no compassion and goes ahead with the foreclosure. Shortly thereafter, the devil appears at Tom's door and takes him away on a horse. Tom is never seen or heard from again.
Through this ending, Irving argues that people should not live a life dedicated solely to the pursuit of financial gain. If they do, it is certain to bring ruin.

How is the theme of individualism portrayed in Shakespeare's Hamlet and Charlotte Bronte's Jane Eyre (without including quotations)?

Hamlet struggles in the play to express his individuality, or his sense of himself. He is in many ways an intellectual who is devoted to his studies, but he is forced, by dint of events beyond his control, to give up the life of a scholar that he has formerly led and to devote himself to avenging his father's death at the hands of Hamlet's uncle, Claudius. In his famous soliloquy that begins with "to be or not to be," Hamlet struggles with the question of how to live life. In living life, he has to give up a great deal of himself and his individuality and submit himself to the vicissitudes of fortune. In so doing, his individuality is often erased; however, the only other alternative is death, which is the ultimate destroyer of individuality. In Hamlet's quest to live an authentic life and express his individuality, he is often defeated.
Jane Eyre is more successful at expressing her individuality, or her self-worth and her right to live the life she wants. She continually fights for the way she wants to live. For example, she defies Master John Reed when she is just a girl. When he flings a book at her, she fights back with words, and she refuses to be intimidated by a person who is her superior by dint of his gender and class status. Later, she is able to express to Mr. Rochester the type of relationship that she wants; she refuses to accept his proposal of marriage, even though she loves him, because he is still married to Bertha. Jane only accepts Rochester when he is free to marry, and she marries him very much as an equal. Throughout her life, Jane expresses her desires and wants with a sense of her self-worth, even though she lives in a society that demeans her as a woman without means. 

What were the origins of the Old South, and how did slavery fit into this society?

The first Southern settlement was also the first American settlement: Jamestown Colony in Virginia was first established in 1602. Jamestown was beset by many problems, but its settlement did help establish Virginia Colony which, due to its wealth from cash crops, became the wealthiest colony.
The Old South would include Southern states that were a part of the original thirteen colonies: Virginia, North Carolina, South Carolina, and Georgia. All four take their names from British monarchs—Elizabeth, "the Virgin Queen," hence Virginia, Charles II, and King George II. Virginia and North Carolina were tobacco-producing states. Virginia later switched to cotton due to losses from tobacco production and the increased demand for cotton. South Carolina's warm climate allowed for the growth of not only cotton, but also rice, which was its biggest cash crop. Georgia's founder, James Oglethorpe, supposedly did not condone slavery and did not want his colony to allow large landholdings. However, the state's interest in cultivating cotton led it to embrace slavery and a planter class did develop.
The desire to own slaves was purely economic. The cultivation of cash crops was repetitive, and it required hard labor. Cotton was difficult to pick, and one pricked one's fingers while separating it from the plant. To maximize profits and ensure the compliance of the work force (white indentured servants complained and eventually expected their own parcel of land, whereas Native Americans who did not die from disease ran away), it was deemed best to acquire West Africans as slaves.
White Southerners justified their inhumanity with pseudoscience about the supposed inferiority of African people and constructed a gallant myth about themselves as a society built on the classical caste system similar to that of Ancient Rome. The planters saw themselves as patricians; smaller farmers and poor whites, including overseers, were plebeians; and, finally, there were the slaves. Additionally, slave masters often gave their slaves classically significant names, such as "Caesar" or "Cato."
Thus, I would not say that slavery fit into Southern society because not every colony was formed for the purpose of cultivating income for the crown. Virginia was constructed for the purpose of making money, while Georgia was designed with the desire to create a more egalitarian society. Rather, Southern society was designed to fit slavery. Before the 1690s, in Virginia, free blacks were allowed to intermarry. Slaves had relative freedom and could cultivate their own gardens and maintain some livestock. However, the institution of slavery as an economic necessity convinced planters and lawmakers that strictness and cruelty were necessary to keep slaves, as well as laws that restricted their movement due to fears of insurrection.

f(x) = 1/(1-x) ,c=2 Use the definition of Taylor series to find the Taylor series, centered at c for the function.

Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of  f^n(x) centered at  x=c . The general formula for Taylor series is:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...
To apply the definition of Taylor series for the given function f(x) = 1/(1-x) centered at c=2, we list f^n(x) using the  Power rule for differentiation: d/(dx) u^n= n *u^(n-1) *(du)/(dx)  and basic differentiation property: d/(dx) c* f(x)= c * d/(dx) f(x) .
f(x)= 1/(1-x)
Let u=1-x then (du)/(dx)= -1 .
The derivative of f(x) will be:
d/(dx) (1/(1-x)) =d/(dx) (1-x)^(-1)
                  = (-1)*(1-x)^(-1-1)*(-1)
                  =(1-x)^-2 or 1/(1-x)^2
Then, we list the derivatives of f(x) as:
f'(x) = d/(dx) (1/(1-x))
           =(1-x)^-2 or 1/(1-x)^2
f^2(x)= d/(dx) (1-x)^(-2)
            =-2*((1-x)^(-2-1))*(-1)
           =2(1-x)^(-3) or 2/(1-x)^3
f^3(x)= d/(dx) 2(1-x)^(-3)
            =2*d/(dx) (1-x)^(-3)
            =2* (-3*(1-x)^(-3-1))*(-1)
            =6(1-x)^(-4) or 6/(1-x)^4
f^4(x)= d/(dx)6(1-x)^(-4)
            =6*d/(dx) (1-x)^(-4)
            =6* (-4*(1-x)^(-4-1))*(-1)
            =24(1-x)^(-5) or 24/(1-x)^5
Plug-in x=2 , we get:
f(2)=1/(1-2)
        =1/(-1)
        =-1
f'(2)=1/(1-2)^2
          =1/(-1)^2
         =1/1
         =1
f^2(2)=2/(1-2)^3
           =2/(-1)^3
         =2/(-1)
        =-2
f^3(2)=6/(1-2)^4
          =6/(-1)^4
          =6/1
          =6
f^4(2)=24/(1-2)^5
           =24/(-1)^5
          =24/(-1)
          =-24
Plug-in the values on the formula for Taylor series, we get:
1/(1-x) =sum_(n=0)^oo (f^n(2))/(n!) (x-2)^n
=f(2)+f'(2)(x-2) +(f^2(2))/(2!)(x-2)^2 +(f^3(2))/(3!)(x-2)^3 +(f^4(2))/(4!)(x-2)^4 +...
=-1+1*(x-2) + (-2)/(2!)(x-2)^2 +6/(3!)(x-2)^3 + (-24)/(4!)(x-2)^4 +...
=-1+(x-2) -2/2(x-2)^2 +6/6(x-2)^3 -24/24(x-2)^4 +...
=-1+(x-2) -(x-2)^2 + (x-2)^3 -(x-2)^4 +...
The Taylor series for the given function f(x)=1/(1-x) centered at c=2 will be:
1/(1-x)=-1+(x-2) -(x-2)^2 + (x-2)^3 -(x-2)^4 +...
or 
1/(1-x) = sum_(n=0)^oo (-1)^(n+1)(x-2)^n

Compare and contrast Alexander Hamilton and the Federalist Party with Thomas Jefferson and the Democratic Republican Party. What were their philosophies on government? What were their ideas on the economy? What were their biggest fears? Why did the arguments that dominated politics in the 1790s come to an end in the 1810s?

Thomas Jefferson's Democratic-Republican Party differed greatly from Alexander Hamilton's Federalist Party. Jefferson's Democratic-Republican Party thought that the nation would be best off siding with Republican France in terms of foreign policy. They also believed that the nation's economy should be based on agricultural. Jefferson thought of himself as a farmer even though he was a plantation owner, and most of his manual labor was completed by slaves. The Democratic-Republicans believed in a weak central government in which the states had most of the power. This contrasts with Jefferson's actual presidency in which Jefferson passed the Embargo Act of 1807 over the protests of New England, and he completed the Louisiana Purchase. Jefferson's party's biggest fears were too much national debt, a strong military presence, and high national taxes, which would fund the national debt. Under Jefferson and Madison, the national defense budget was cut in favor of state militias, and this would prove disastrous in the War of 1812. The Democratic-Republicans also did not like the idea of a national bank, which they thought would put too much power in the hands of Eastern money interests.
The Federalists under Hamilton were nearly the polar opposites of the Democratic-Republicans. They thought that foreign policy should be favorable to Britain because Britain did not endorse France's Reign of Terror and because Britain was also the United States's best trading partner. The Federalists believed in increasing American industrial output, as this would allow more people to have jobs without having to purchase land. It would also make the United States more self-sufficient in terms of goods. The Federalists believed in a strong central government and a strong US military. They feared what would happen if the states gained too much power. They also believed in a national debt and a national bank because it would tie the states closer to the national government economically.
The foreign policy arguments came to a head during the 1790s and early 1800s because the United States was caught in the middle between the warring powers of Britain and France. Under the Federalist Adams administration, the United States fought an unofficial naval war with France during the Quasi-Wars. After Napoleon signed an agreement to stop harassing American shipping, American animosities turned against Britain and its policies of impressment, which impeded American shipping to the Continent. The Federalists were located in New England, and they feared growing Democratic-Republican popularity in the South and West while these regions grew thanks to cheap land policies and emigration. The Federalists protested the War of 1812, and there was even a push for New England to secede during the Hartford Convention. After word leaked that New England Federalists were contemplating secession, the party soon fell out of favor as American patriotism soared after the successful War of 1812. This would lead to the Era of Good Feelings. There were still political debates, but they were not as turbulent as the fights between the Democratic-Republicans and the Federalists.

The Federalists and the Democratic-Republicans were two political parties that had opposing views on many topics. Alexander Hamilton believed the federal government should be active and involved in many activities. Thomas Jefferson believed the role of the federal government should be limited. He believed that the state governments should have more power. Alexander Hamilton and the Federalists believed the federal government should be actively involved in the economy. Hamilton wanted to combine the state and national debts together and repay them. Hamilton also wanted to create a national banking system. Thomas Jefferson and the Democratic-Republicans opposed the debt and banking plans. They believed the federal government could only do what the Constitution specifically said it could do. Since these ideas weren’t mentioned in the Constitution, the Democratic-Republicans opposed them. They wanted the federal government to have a limited role in the economy.
The Democratic-Republicans were very worried about the federal government having too much power. Many people who eventually became members of the Democratic-Republican Party supported the addition of the Bill of Rights to the Constitution because they feared the federal government would be too strong and abuse its powers. The Federalists were concerned that there would be chaos if the federal government didn’t have enough power. They saw how ineffective the federal government was under the plan of government created by the Articles of Confederation. They were afraid the new government would be less effective and disorder could occur if the federal government didn’t have enough power.
Many of these disagreements came to an end between 1810–1815. The Federalists had become a regional political party and were losing support. When people heard that the Federalists wanted to reduce the power of the federal government, they were viewed as selfish, inconsistent, and unpatriotic. The Federalists also opposed American involvement in the War of 1812. They eventually disappeared as a political party by 1815.
https://law.jrank.org/pages/6058/Democratic-Republican-Party.html

https://www.history.com/topics/early-us/federalist-party

If the color of food coloring is purple, what colors are reflected? What colors are absorbed?

Before answering this question, we need to know what kind of color is in purple food coloring. Is it a purple dye, or is it a mixture of colors like blue and red? Single pigments are normally “brighter,” or have greater color saturation, than mixed pigments. That is why, for example, if you go shopping for acrylic or oil artists’ paints, the tubes have the names of the pigments on them. The colors are not pure red, yellow, green, blue, and so on—the paint company supplies the single pigment so that the artist has maximum control (but also needs to know a great deal about the nature of individual pigments).
We might expect that a purple pigment would make a nice bright purple food colorant. I found a helpful page in the American Chemical Society’s Chem Matters series. It lists dyes approved for use in food. No purple dyes are included. Thus, we conclude that purple food coloring includes a mix of approved red and blue dyes.
The Chem Matters page (link included below) states that blue food coloring absorbs its complementary color of orange most strongly, while red absorbs its complement of green most strongly. It is important to recognize that a dye in a water solution absorbs a range of colors. You do not simply delete one pure hue and keep everything else. Thus, the red dye absorbs some blue along with the green (and some yellow), and the blue dye absorbs some red along with orange and yellow. This is why the result is less saturated than a purple pigment might be.
We would expect the mixed dye, then, to transmit or reflect some blue, violet, and some red, while absorbing most of the green-yellow-orange color range.
https://www.acs.org/content/acs/en/education/resources/highschool/chemmatters/past-issues/2015-2016/october-2015/food-colorings.html

Why did Goethe write Wilhelm Meister's Apprenticeship?

Wilhelm Meister's Apprenticeship is what's called a Bildungsroman. This is a German word given to a story that deals with the moral, intellectual, or spiritual growth of a character. A coming-of-age novel would be an example of this. The eponymous hero of the story yearns to break free from a stultifying bourgeois existence to pursue a life in the theater. This gives us a possible clue as to why Goethe wrote the story. In the late 18th century, many young people—and Goethe was one of them—were becoming intoxicated by new ideas, many of which derived either directly or tangentially from the French Revolution. For a new generation, the old ways seemed so restrictive, so bland and unexciting. That's why many young men and women, like Wilhelm, sought to escape their backgrounds and express their new-found sense of self through artistic endeavors of one sort or another.
Wilhelm Meister's Apprenticeship is a reflection of its age in other respects. It's a novel of ideas. The late 18th century was a time of great intellectual ferment, positively buzzing with new ideas. As well as the ideals of the French Revolution, the makings of what later became Romanticism were also in the air. Goethe was a polymath, a towering intellectual giant with a keen interest in a bewildering array of subjects—art, architecture, drama, science, philosophy, and, of course, literature. In writing his story, Goethe undoubtedly wished to explore through the medium of the novel ideas that he personally found interesting and which would hopefully contribute to the development of European culture, a culture in which Goethe was such a monumental figure.

What happens to Margot while the teacher is out of the classroom?

Margot is considered an outcast in her class on the planet Venus, because she is the only student who genuinely remembers what the sun looks and feels like. Margot is also a shy, timid girl who longs to travel back to Earth, where she grew up. Unlike the other students, Margot was not born on Venus, is severely depressed, and does not participate in games or fun class activities, unless they involve learning or talking about the sun. Margot's parents also plan on returning to Earth because they believe that it is vital to their daughter's health. The other children in Margot's classroom resent her for her future opportunity to leave Venus and do not like her, because she is different. Bradbury writes,

And so, the children hated her for all these reasons of big and little consequence. They hated her pale snow face, her waiting silence, her thinness, and her possible future (2).

Unfortunately, one boy begins to yell at Margot on the one day that the sun briefly shines on the rainy planet for an hour, and the others join in. The children then proceed to shove Margot into a closet and lock her inside. The sun ends up coming out for an hour, and Margot misses out because she is locked in the closet.

Analyze the relationship between psychoanalysis and fantasy literature through the Harry Potter series by J.K. Rowling. What are the main points of fantasy literature ? What is the relationship between fantasy books and psychoanalysis? Is the protagonist in the Harry Potter series schizophrenic? Are all of the events in the book products of Harry Potter's subconscious? How do the events we experience in real life affect our subconscious?

It is arguable that Harry Potter's experiences of Hogwarts and the magical world can be interpreted as the result of mental illness. Some have proposed the theory that Harry is schizophrenic, and it is possible to view the characters and events of the novels as manifestations of Harry's own internal struggles. It is also possible that Harry has invented this world inside his mind in order to escape his situation as a victim of abuse and neglect on the part of his aunt and uncle. As the hero of the story, he is given power, whereas in the real world with Vernon and Petunia he has none. In his new, magical world, good triumphs over evil, which is comforting to a person suffering at the hands of others.

Many of the patterns and themes in the novels can be interpreted from this point of view. For example, Harry is an orphan, living in a home where he is not loved and has no real parental figures. Many of his eventual parental figures, such as Sirius, Lupin, and Dumbledore, eventually die, leaving him again alone to fend for himself. This might represent Harry's fear that he will always be alone. Voldemort, who shares so much with Harry (both are orphaned, both are half-bloods, both possess unique power), could represent Harry's fears about who he may become if his life continues without love. In order to counter these fears and foster his hopes, his mind generates several representations of deep and lasting love through friendships, romance, and family. His mother's love continues to protect him after death, his friends stick by him through all, and he is able to fall in love himself, proving he is not at all like the empty, cruel Voldemort that acts as his foil.

However, this interpretation is likely far off base, especially if one takes into account any of J.K. Rowling's own words on the subject, and the fact that there are several spinoffs of this world that do not involve Harry. A more accurate and meaningful approach would be to view the series, and much of fantasy literature, as an escape and even a poultice for the mental anguish of a reader. Fantasy worlds allow readers to step away from a reality in which they struggle and enter into an enchanting, and often comforting, world. It also allows readers the opportunity to wrestle with deep questions in a safe environment that does not directly affect their own lives. For example, a reader mourning the death of a loved one may feel a certain kinship with Harry when his own loved ones die, and take away lessons on how to deal with death. A lonely reader may find a substitute for friendship in Ron and Hermione and hope that they may eventually find their own true friends. Readers have the opportunity to approach difficult emotions and frightening experiences through the eyes of a fictional character while they are not yet ready to confront them in reality. Wether this is helpful is debatable. For some, fantasy literature may be a bridge to dealing with one's reality. For others, it may be a form of escapism that they never give up.

This series of questions contains a number of topics that are all interconnected, and an understanding of the subconscious is fundamental to a psychoanalytic reading of the Harry Potter novels. The subconscious is the part of the mind that a person is not fully aware of but somehow still has the ability to impact that person's decisions and behaviors. If someone has a subconscious fear of death, that person might avoid doing anything at all that could lead to his or her death, without fully understanding why this avoidance is taking place.
Psychoanalysis is the therapy developed by Sigmund Freud; a psychoanalytic reading applies Freud's therapeutic ideas to the understanding of a literary work. Some Freudian scholars say that fantasy literature is a genre in which a writer can explore unacknowledged fears and unspoken desires as well as other products of the subconscious. The Mirror of Erised at Hogwarts—"desire" spelled backward—is a great example of this kind of exploration. This object shows the person standing in front of the mirror his or her deepest yearning, a yearning of which the person is not likely aware. Somehow, the Mirror of Erised has access to the person's subconscious and is able to reveal a part of the subconscious that was previously unknown.
The question of whether Harry Potter is schizophrenic or not depends whether or not the reader is willing to suspend his or her disbelief in order to "go along" with the fantasy elements of the series. Reading the Harry Potter novels as if they are realist literature may lead a reader to believe that Harry Potter is mentally ill, as he talks to animals and objects, imagines himself riding flying broomsticks, and mixes magical potions. A realistic reading of the events in the book may very well lead to an interesting discussion of Harry Potter's mental health, but debating this point might also lead a reader to miss the whole point of the series, which is to escape into a magical world that does not exist in real life.
Escapist literature gives readers a break from the reality of their lives. The magical existence of Harry Potter and his friends and enemies takes place in a complex world in which a reader can lose him or herself. Freud might say that a reader who enjoys reading about Harry Potter is enjoying the expression of the reader's own subconscious worries, hopes, and dreams as they appear in the pages of the novel. If a reader experiences something frightening, like a fight with someone, the subconscious might absorb the fear so that the reader is not totally aware that fighting is scary; reading about Harry's fights with Draco might be a relief to this reader because he can then see that good guys can win fights, making the reader feel less anxious around fights in the future.
According to Freud, the contents of the subconscious are not readily accessible, and the hidden nature of these fears and desires means that they might sneak out at anytime. Reading about Harry Potter and observing how fears and desires operate in the lives of the characters might enable a reader to feel better prepared for when his or her own subconscious reveals itself.

In Bleak House, why does Dickens use so many nicknames for Esther (Mrs. Durden, Cobweb, Mrs. Shipton, and Little Old Lady)?

Esther is made into the housekeeper of Bleak House almost as soon as she arrives. It is, for her, an awesome responsibility, all the more so because she is only twenty. When she tells Mr. Jarndyce that she hopes she "is clever enough" to do the job, Jarndyce says,

"You are clever enough to be the good little woman of our lives here, my dear," he returned playfully; "the little old woman of the child's (I don't mean Skimpole's) rhyme:

"'Little old woman, and whither so high?' 'To sweep the cobwebs out of the sky.'

"You will sweep them so neatly out of OUR sky in the course of your housekeeping, Esther, that one of these days we shall have to abandon the growlery and nail up the door."

The nicknames fix Esther's identity within the house as "the good little woman." This is meant as a complement, of course, but the effect of these names is to subvert or replace Esther's identity as an individual. As Esther says, 

This was the beginning of my being called Old Woman, and Little Old Woman, and Cobweb, and Mrs. Shipton, and Mother Hubbard, and Dame Durden, and so many names of that sort that my own name soon became quite lost among them.

So, in a way, calling the young Esther names like "old woman" or "Mother Hubbard" is remaking her into those things; her "guardian" Mr. Jarndyce is assigning her a role to play, and Esther hopes she is "clever" enough to play it well. Of course, Esther is more than clever enough to do so, and more clever than Jarndyce give her credit for being; one of the more interesting parts of the book is how Esther, as the narrator, is able to be what Mr. Jardyce expects her to be while at the same time retaining her own independent subjectivity.

What is Rukmani’s family background? Why did she marry Nathan?

Rukmani grew up as the fourth and youngest daughter of a village headman. During her childhood years, her father had been a man of consequence and wealth.
As a result of their father's position, Rukmani's two eldest sisters had managed to make good matches; they married well, with the requisite dowries, jewelries, and lavish wedding ceremonies expected of daughters of a village headman. By the time her third sister married, however, Rukmani discovered that her father's influence had been infinitely diminished. It was now the tax collectors who held all the power and consequence in the villages.
As a result of this change in affairs, Thangam, Rukmani's third sister, only managed to secure a modest wedding and to wed with minimal jewelry on her person. By the time Rukmani was to marry, the family could not afford a dowry at all. Without beauty and without a dowry of any sort, Rukmani was forced to marry an impoverished tenant farmer at the age of twelve. The family's poverty and lack of consequence meant that they could never hope to make a good match for Rukmani, even if they wanted to. This is why Rukmani ended up being married to Nathan.

Why does Flavia marry Rudolf?

Flavia marries King Rudolf because she feels that she has a duty and responsibility to her king and the people of Ruritania. Despite Rassendyll telling her that he will “always love only her” and begging her to leave for England with him, she declines, because she is too honorable to neglect her duty to Ruritania and the king. After King Rudolf gets drunk on coronation day, Rassendyll, his lookalike, takes up his role and is crowned king with the intention of relinquishing power to Rudolf upon waking up. However, that is not the case: Rudolf is seized by Black Michael, forcing Rassendyll to continue acting as the king until the Rudolf is rescued. It is during this period that he meets Flavia and they fall in love. Flavia is engaged to King Rudolf, but all along, she does not realize that Rassendyll is not King Rudolf, because their resemblance is so strong. Once Rudolf is rescued and she is told the truth, Flavia realizes that she still loves Rassendyll. However, she chooses not to leave with him to England and instead marries King Rudolf, as she feels obliged to fulfill her duty to her king and the people of Ruritania.

Flavia marries King Rudolf out of duty; she is, after all, betrothed to him. At one point, she thinks she's fallen in love with Rudolf, but it turns out to be his double, Rassendyll. Despite being his intended, Flavia has never liked Rudolf all that much. That's why she's so surprised to find just how much she enjoys Rudolf's—really Rassendyll's—company all of a sudden.
But her happiness isn't destined to last. When Rassendyll eventually rescues the king from the castle of Zenda, Flavia feels she has no choice but to go ahead with the wedding, even though she loves the English gentleman and not the Ruritanian monarch. Flavia selflessly puts the good of the kingdom ahead of her personal feelings, a decision for which she earns the undying admiration of Rassendyll himself.

What is a brief summary of War Horse? What are the main concerns in the book, and what features has the author used to express these?

In War Horse, Michael Morpurgo explores violence, cruelty, and courage in war through the eyes of a horse, Joey. He's a half-thoroughbred colt purchased by a drunk farmer. The farmer's son, Albert raises Joey and forms a strong bond with the young horse. Albert teaches Joey how to plow, even though the task is difficult for Joey as a half-thoroughbred. Albert's father sells Joey to the army as a war horse. From another horse, Topthorn, Joey learns how to charge into battle. Both horses are captured by the Germans and made to pull ambulances. A local girl named Emilie and her grandfather care for the horses and keep them when the German forces move away. Joey now helps Topthorn learn how to plow fields. Another group of German soldiers take the horses and use them to pull artillery. This work proves too much for Topthorn, who dies. Joey is frightened by a tank into the heart of the battle, where he becomes trapped in barbed wire. Soldiers from both sides stop fighting long enough to free the horse. Recovering from his ordeal, Joey is reunited with Albert, who has enlisted in the army. At the end of the war, Emilie's grandfather helps Albert by outbidding the butcher for Joey. Joey returns to the family farm with Albert. The story details the struggle to adapt and stretch beyond one's perceived limits. This is shown in Joey's adaptation from riding horse to plow horse to war horse. By telling the story from Joey's point of view, Morpurgo emphasizes the waste and trauma experienced on all sides during war.

How does Rousseau justify his arguments about equality?

Rousseau's arguments about equality are framed within his understanding of the Social Contract, the title of one of his best-known works and an idea of society organized around the concept of the "general will." Rousseau differs with Hobbes in his view of human nature, and sees primitive society, the "state of nature," as one where cooperation and harmony are prevalent.
This positive view of humanity challenges Hobbes' darker vision and becomes the foundation for Rousseau's ideas about equality and government. He suggests that inequality comes from existing social arrangements and hierarchy, and that an ideal, egalitarian society would be arranged around a social contract which emerges out of the "general will," in essence the good of the community and the welfare of the whole.
While some might suggest that Rousseau's "general will" runs contrary to individualism, challenging equality, this is no the case. For Rousseau, political power and the role of the sovereign is to secure the freedom and equality of a society's citizens, not limit them. In this respect his vision of government is one which only intervenes to create balance and harmony, not to directly rule. Because of a positive view of human nature, he suggests equality emerges out of the "general will" in a society stripped of previous inequalities.

How is connotation used in "The Lottery"?

Jackson uses words with positive connotations early in the story to help establish a setting that seems idyllic and blithe, slowly building in negatively-connoted words later on; the contrast between the beautiful and happy setting and the events that take place there create irony and interest in the story. Early on, she uses words like "sunny" and "fresh" to describe the summer day. The flowers are "blossoming profusely" and the grass is "richly green." Even the word "lottery" itself typically has a positive connotation. A lottery is something one wins, and there is an element of exclusivity and luckiness within the word's connotation as well.
The major irony of the story is that the idyllic setting hides the horrible tradition maintained by the people of the town. The connotation of the words early in the story as well as the connotation of the word "lottery" mislead the reader, leading us to expect happy summer days where someone wins something wonderful; instead, we get a bloodthirsty mob and a woman's violent death.

Jackson primarily uses a dry, neutral, journalistic style in this short story, telling the tale matter-of-factly. Nevertheless, we get hints that the lottery makes the villagers uneasy and uncomfortable through some of the connotative, or emotionally colored, words she chooses. For example, the black box that hold the lottery tickets had spent "another year underfoot in the post office." The word "underfoot" has the negative connotation of being a bother or encumbrance, something people trip over and resent. Jackson could have used a word like "stored" or "rested," which would have had a much less negative connotation.
We learn that at one time there had been ritual words used at the lottery, which are described as "a perfunctory, tuneless chant." "Perfunctory" and "tuneless" both have negative connotations. "Perfunctory" means going through the motions without caring, and "tuneless," of course, conjures an unpleasant sound. This ritual associated with the lottery was, we can assume, unwelcome.
Mr. Summers, who runs the lottery, wears a "clean white shirt and blue jeans." A clean white shirt carries a connotation of purity, which is at odds with the ritual, while "blue jeans" are a down-to-earth, ordinary piece of clothing.
Jackson describes Mr. Summers and Mr. Adams as "grinn[ing] at one another humorlessly and nervously." Here, the word "grinned" takes on a ghoulish connotation. Normally, smiling or grinning is a pleasant facial expression, but in this context it seems more like the smile we associated with a skull.
One of the most powerful connotations come when Little Dave Hutchinson walks "willingly . . . up to the box." The word "willingly" connotes innocence: Dave comes willingly to draw a piece of paper because he is so young he has no idea it could mean he will soon be stoned.

Connotation is the meaning associated with a word or phrase that goes beyond the literal or denotative meaning. Shirley Jackson uses connotation in several ways in her classic short story.
One of these is ironic. Technically, a lottery is just a random drawing. It could be good or bad. Most often, though, a lottery is held for some kind of prize, and so it carries a positive meaning. In this case, since the "winner" gets stoned, the meaning is very negative.
A second example of connotation is also ironic. Mr. Summers, who runs the lottery, has a name associated with warmth and pleasure. Likewise, the June setting is associated with warmth and pleasure. The lottery, of course, is neither warm or pleasant.
A major non-ironic example of connotation is the box used for the lottery. The box is black, a color associated with death and mourning. This foreshadows the deaths the lottery will bring, and is associated with the black dot on the paper Mrs. Hutchinson opens.
https://www.dictionary.com/browse/connotation

With what topic is the speaker concerned in this sonnet?

"Bright Star" is widely considered to be the last poem John Keats wrote before he died at the age of twenty-five. Scholars believe the "bright star" addressed in the poem to be a representation of Keats's great love, Fanny Brawne. 
The poem is a love poem and describes the speaker's wish to be as steadfast and as constant as a star in the life of his love. That being the case, there are really two main topics with which Keats is concerned: in literal terms, the poem is entirely addressed to a bright star, possibly Polaris, and its "splendour hung aloft the night," "still steadfast, still unchangeable." On a deeper level, however, the sonnet addresses the topic of love: the speaker yearns to stay "pillow'd upon my fair love's ripening breast/To feel forever its soft fall and swell." The bittersweet final lines of the sonnet—"Still, still to hear her tender-taken breath/And so live ever—or else swoon to death"—give an implication of why the speaker so yearns to possess the steadfast and permanent qualities of the star he so admires. The speaker would love to stay forever pressed against his love, but, the wistful tone implies, he may be prevented from doing so by a death that may come too soon.
The star described in the sonnet is portrayed as a "watching" figure, always alert, always at its "priestlike task" of keeping an eye fixed upon its charge, the Earth. We may infer from the poet's wistful tone that he is particularly loath to depart his position upon his love's "ripening breast" because he feels he is responsible for keeping watch over her and does not want to be denied the opportunity to do this forever.
https://www.poetryfoundation.org/poems/44468/bright-star-would-i-were-stedfast-as-thou-art

What was the overall impact the Second Industrial Revolution had on America?

The Second Industrial Revolution impacted the United States in many ways. When the Second Industrial Revolution began, more people began to work in factories. The working conditions in these factories were very poor. Workers were often injured on the job. They worked long hours for low pay. Children often worked in the factories. Eventually, laws were passed to deal with these conditions.
American industrial production increased. New and cheaper methods for making steel were used. This allowed for significant advances in transportation. Steam engines were used to power ships and trains. More miles of train tracks increased the areas to which railroads could travel. Products and people could be transported faster. New roads and canals also improved the transportation system. American products could now also be shipped around the world, opening new markets to American businesses.
Communications also improved. With the invention of the telegraph and later the telephone, it became easier and quicker to communicate. This allowed businesses to receive and process orders more quickly, allowing for these businesses to expand their operations.
The Second Industrial Revolution allowed the American economy to grow and to prosper. While there were some issues connected with the Second Industrial Revolution, the United States benefitted from it in many ways.
http://ushistoryscene.com/article/second-industrial-revolution/

How can I compare the theme of loss in "Out Out" by Robert Frost and "Disabled" by Wilfred Owen?

Both Wilfred Owen's "Disabled" and Robert Frost's "Out, Out--" are poems about the loss of life as it has been. While the boy in Frost's poem completely loses his life, Owen's young man loses his former way of life.
1. Loss of physical ability or death 
When the chainsaw slips in the boy's hand, Frost writes that the saw "seemed to leap" and nearly sever his hand: "He must have given the hand." There is the sense of surrender to the cruelty of chance in the boy's actions, although he seems to hope his hand can be saved when he "saw all." He begs, "Don't let him cut my hand off--" because he fears if he loses his hand, then he can no longer do a man's work as he is accustomed to doing. Of course, the tragic result of this accident is unknown to the boy, whose fate is worse than he fears.This loss of physical ability with the amputation of his legs is also crucial to the soldier in Owens's poem "Disabled." Confined to a wheelchair, the young man who was once a soldier perceives himself as only half a man. With the loss of his legs, he is dependent upon others and "must take whatever pity they may dole." Moreover, he notices how women do not look at him, but "[P]assed from him to the strong men that were whole."
Further, the ex-soldier knows that he will go to a veterans' hospital and just "take whatever pity" is given to him. Much like the boy's fears of losing his hand, a condition which would handicap him, the veteran has fears of his loss of independence. Now he must worry, "Why don't they come/And put him into bed?" because he is no longer independent as he once was "in the old times before he threw away his knees."
2. Loss of family/social contact
When he realizes that his hand is destroyed, the boy of Frost's poem perceives that "all [was] spoiled." At this point the boy only believes that he will no longer be able to use his hand, and, therefore, he will not be able to hold his own in the world of woodsmen, nor will he be able to cut wood for his family. Instead, the others, who "were not the one dead," "turned to their affairs" and go about their work after the boy dies just as they would if he were to live.
In "Disabled," the now handicapped soldier hears the voices of boys that "rang saddening like a hymn," or a song for the dead. He can no longer participate in much of life; instead, he can only listen to the "voices of play and pleasure" in which he once participated.
3. Loss of hope for the future
In the poem "Out, Out--" Frost writes that the boy "saw all spoiled." The boy realizes that even if his hand is not amputated, he will no longer be able to hold the chainsaw or do the other tasks of a man. In his environment of the North Woods, the boy will become alienated from others without being able to participate, and he will have little future because the men all need to work.
Likewise, the veteran who "sat in a wheeled chair waiting for dark and shivered in his ghastly suit of grey" is ruined, too, and is cast aside and "will spend a few sick years in Institutes."
4. Loss of innocence through harsh experience
Both the boy of Frost's poem and the amputee veteran of Owens's poem have lost their innocence as well as their optimistic perspectives on life. Certainly, each has felt that there was much life ahead of him; however, they are both tragically made aware that a person holds onto life with but a gossamer thread.
The boy of Frost's poem has cherished the free time "a boy counts so much when saved from work"; however, once he is severely injured, the boy can no longer play at any game. Similarly, the disabled soldier realizes that he will have no more youth--"Now he is old; his back will never brace"--because he has been aged by becoming disabled and crippled as an old man would be. 
5. Loss of relationship with the natural world
Both the boy and the veteran have lost their relationships with the natural world; no longer can the boy work as a man or play outdoors. Certainly, the young soldier whose legs are gone cannot march or hike or engage in many activities outdoors or even in society. He is only to be pitied because

...half his lifetime lapsed in the hot race,And leap or purple spurted from his thigh...

6. Loss of physical and psychological freedom
Threatened with the loss of his hand, a body part that is so essential, the boy panics, crying out to his sister, "Don't let him, sister!" as he begs her to prevent the doctor from amputating his hand. Surely the boy considers how limited he would be in all aspects of his life without one hand.
Faced with the loss of his legs, the young soldier of Owens's poem recalls how the crowds reacted differently toward him when he returned, and only "a solemn man" thanked him for his sacrifice for him and others in America. "Now he will spend a few sick years in Institutes," and he believes his life will be so much less than it could have been; he will always feel isolated and unfulfilled.
7. The structure of the two poems
There is a singleness to the poem "Out, Out--" because of its one-stanza construction. This single stanza reflects the swiftness of the boy's accident and fate as well as the isolation of the unfortunate incident. Without a rhyme scheme, the verse also moves more quickly than if it were divided into stanzas and had rhyming end words that would separate ideas.
On the other hand, Owens's "Disabled" is divided into six stanzas with alternating lines that rhyme with each other, although this pattern is sometimes broken. The stanzas are not uniform in the number of lines that each has, either. So, the speed is broken as in stanza 5, a short, slow stanza to give the reader time to ponder the tragic effects of the soldier's return as an incomplete man.