College Algebra, Chapter 9, 9.3, Section 9.3, Problem 76

A certain drug is administered once a day. The concentration of the drug in the patient's bloodstream increases rapidly at first, but each successive does has less effect than the preceeding one. The total amount of the drug (in mg) in the bloodstream after the $n$th dose is given by

$\displaystyle \sum_{k = 1}^n 50 \left( \frac{1}{2} \right)^{k-1}$

a.) Find the amount of the drug in the bloodstream after $n = 10$ days.

b.) If the drug is taken on a long-term basis, the amount in the bloodstream is approximated by the infinite series $\displaystyle \sum^{\infty}_{k = 1} 50 \left( \frac{1}{2} \right)^{k-1}$. Find the sum of this series.

a.) After $n = 10$ days, the amount of drug in the bloodstream is


$
\begin{equation}
\begin{aligned}

\sum^{10}_{k = 1} 50 \left(\frac{1}{2} \right)^{k-1} =& 50 \left( \frac{1}{2} \right)^{1-1} + 50 \left( \frac{1}{2} \right)^{2-1} + 50 \left( \frac{1}{2} \right)^{3-1} + 50 \left( \frac{1}{2} \right)^{4 - 1} + 50 \left( \frac{1}{2} \right)^{5-1}+ 50 \left( \frac{1}{2} \right)^{6-1} + 50 \left( \frac{1}{2} \right)^{7-1} + 50 \left( \frac{1}{2} \right)^{8-1} + 50 \left( \frac{1}{2} \right)^{9-1} + 50 \left( \frac{1}{2} \right)^{10-1}
\\
\\
=& 99.90 \text{ mg}

\end{aligned}
\end{equation}
$


b.) Recall that the formula for the infinite geometric series is

$\displaystyle S = \frac{a}{1 - r}$

Notice that $a = 50$ and $\displaystyle r = \frac{1}{2}$. So,

$\displaystyle S = \frac{50}{\displaystyle 1 - \frac{1}{2}} = \frac{50}{\displaystyle \frac{1}{2}} = 100$

Therefore, the total amount of drug in the bloodstream after infinite days is 100 mg.

Why does her mother oppose Lily's ideals of being a Birthmother?

In chapter 3, Jonas's father brings Gabriel home for the first time, and Lily is excited to meet the newborn baby. Lily comments on his pale eyes and mentions that Gabe looks cute. Lily then says that she would enjoy being assigned as a Birthmother and her mother immediately chastises her. Lily's mother tells her that there is no honor in being assigned as a Birthmother. Lily then responds by telling her mother that she heard Birthmothers live luxurious, easy lives and are pampered all day long. Jonas's mother corrects Lily by informing her that Birthmothers enjoy three years of living carefree lives before spending their remaining days as Laborers. Lily's mother wants her daughter to have a valuable occupation and does not want her to engage in hard labor for the remainder of her life. Lily's father then interjects and mentions that Birthmothers do not get to see their babies and that Nurturers actually care for the infant children in the community.

Is being in an anger management program an example of a subculture? Explain. Which theoretical perspective in sociology (functionalism, conflict theory, etc.) can be used to explain the example (being a member of the anger management program)?

Yes, in some ways, an anger management program constitutes a subculture. A subculture has different norms and values than the culture as a whole, and our culture can seem to celebrate anger and reward acting out in anger. Anger management programs advise people to deal with anger not by acting out but by learning skills to recognize their anger and deal with it in constructive ways, such as communicating their needs effectively, not using verbal or physical violence, and engaging in problem solving. These norms and values—of using logic and communication skills to diffuse one's anger and express one's emotions more calmly and effectively—are not always part of the larger culture, so therefore an anger management program can be said to represent a subculture.
The theoretical perspective that might apply to an anger management course is functionalism, as this theory posits that each part of society contributes to the greater well-being of the society as a whole. If people express their anger effectively by using the communication and problem-solving skills they learn in an anger management course, they are contributing to the greater well-being of the society and the social consensus that holds together society.

How is As You Like It a subversive play? Consider Shakespeare's use of dramatic methods as well as the context of the play.

In terms of context, at the time that Shakespeare wrote this play, women were not allowed to perform on stage. Therefore, Shakespeare would directly acknowledge the fact that male actors were playing female characters with a number of dramatic conceits that allowed the men playing women to wear men's clothing and pretend to be men in order to fool their fellow characters for various reasons.
In this play, Rosalind must briefly go into exile from the court in the Forest of Arden, and because she is "more than common tall" she decides to dress as a man and calls herself Ganymede. Ganymede is an androgynous figure from mythology, a cupbearer who is also associated with the astrological sign Aquarius, and this mythology contributes to the portrayal of both genders that this character embodies.
Rosalind is in love with Orlando, but when Orlando meets Ganymede in the forest, he doesn't realize it is really Rosalind. Therefore, Rosalind is able to cajole Orlando into telling him all about his difficulties in love. There is also a situation where the shepherdess Phebe falls in love with Ganymede, not knowing that Ganymede is really Rosalind in disguise.
There are different ways in which these situations taken together could be seen as subversive. On one level, Rosalind/Ganymede is effectively portrayed as being bisexual because she must embody male and female characteristics at different times, and must also convincingly fool others when she is in disguise as Ganymede. Although she is not in love with Phebe, she is at first unable to reveal the true reason why she is not available or likely to be attracted to the insistent shepherdess. Phebe's pursuit of Ganymede is somewhat subversive also, in that she immediately turns her attentions from her previous lover Silvius. And Ganymede's attempts to get Orlando to talk about all the ways in which he is in love with Rosalind is somewhat subversive because it is manipulative and dishonest. This also allows for a playful conceit in which the two "men" become friendly and share a bond of affection, which in some productions is played up to allow for an undercurrent of homoeroticism.
The climactic scene of the play which Rosalind admits that, dressed as she is in a way that does not represent her true nature, she cannot satisfy anyone's expectations of her. But when she appears in women's clothing as Rosalind, Orlando realizes who she has been all along, and Phebe realizes her crush is misplaced.

I need help with a postgraduate essay. I want to compare two novels from the Gothic era, Wuthering Heights by Emily Bronte and The Brownie of Bodsbeck by James Hogg. The point I want to focus on is their negative perspective about women. First of all, Catherine Earnshaw is described as a materialistic woman who sacrifices her love for material gain. From Heathcliff's perspective, Catherine is mean. Second of all, Katherine in The Brownie is depicted as horrible and possessed by an evil spirit. How can I compare and contrast the novels? How should I construct the essay so the ideas can be clearly expressed?

The first thing you will need to do to create work on the postgraduate level is to sort out some factual details.
The Gothic period was the late eighteenth century. Wuthering Heights, although borrowing some of the literary conventions of the Gothic, was written in 1845, considerably later than the classic works of Gothic fiction such as The Castle of Otranto or The Mysteries of Udolpho. The Brownie of Bodsbeck (1818) is somewhat closer to the traditional Gothic in period, and in its historical Scottish setting resembles The Bride of Lammermoor (1819), blending a Gothic atmosphere with Scottish regionalism. Thus one issue you need to mention is the 27 years between the composition of the two novels and the difference in situations of the authors (Hogg was a Scottish man, Brontë an English woman).
Next, you should note that Katherine is not, in fact, "horrible" nor is she actually possessed by an evil spirit. The "Brownie" turns out to be John Brown, a man fighting for religious freedom. As for Catherine Earnshaw, she is an ambivalent character, but one should note that as Heathcliff is violent, vindictive, cruel, prone to unpredictable emotional outbursts, and abusive, Linton would be a far more sensible choice for far more than just monetary reasons; he would also be a better father as Heathcliff engages in what we now would consider child abuse.
Both novels have a wide range of female characters. Interestingly, the characters portrayed as having the most knowledge, and often holding information unknown to the protagonists are female domestic servants, Nanny in Hogg's novel and Nelly Dean in Wuthering Heights. This suggests an interesting way to organize a paper by thinking about how class and gender intersect. In both cases, lower class women bear some form of true knowledge and sustain local traditions and memories, often almost subversively, keeping secrets from the upper classes and men, and having a power rooted in observation and empathy. 
For a postgraduate paper, you want to avoid such terms as "horrible" and attempts to judge literary characters as though they are actual people. Instead, you want to think about the construction of female characters in the novels as reflecting historical or ideological contexts. You might look at how the women of The Brownie of Bodsbeck operate within traditional feminized spaces, and end up achieving the closure of happy endings in their role as nurturing and supportive, while the women of Wuthering Heights are far more conflicted in their roles. 
In writing an essay, you might want to narrow your focus. You could look at the difference between Hogg's concern with nationalism and religion and Brontë's purely psychological fiction or think about what the two authors consider the ideal of womanhood for women of different classes. Another possibility would be to look at the language used to describe women in both novels or the way the viewpoints and narrators affect how we see the women of the novels.

In To Kill a Mockingbird, why did Jem have such a difficult time accepting how the trial ended?

The primary reason Jem struggles to accept the guilty verdict given to Tom is because he is unwilling to accept the fact that in his society, justice does not always win out.
Throughout the novel Lee builds events in the story in a way in which Scout and Jem (and therefore the read) have to learn tough lessons about kindness and mercy and justice. What's more, these lessons were learned for characters who are considered "lower" in society. Scout learns to be kind and merciful to her schoolmate who is poor. Scout and Jem learn to respect and defend Boo Radley. Atticus even sends the message of mercy when he puts down the rabid dog. The author instills this message throughout the novel and builds an expectation of justice and fairness.
When Tom receives a guilty verdict, despite sound evidence and a moving speech from Atticus, Jem is not able to reconcile what he knows and expects about justice with the reality of justice in his time. Jem also experiences a pang of resentment towards his father, who has expected kindness and mercy and justice from his own children, but was unable to execute it himself.

Jem is idealistic and naïve to the prejudices and unfairness of the world and how these biases will impact the jurors. It's his idealism that causes him to feel overly confident and optimistic that his father will produce an acquittal for Tom Robinson based on the testimony heard throughout the trial.
As Reverend Sykes predicted, Tom Robinson is found guilty and Jem witnesses for the first time the reality of the injustices of the judicial system when it pertains to colored people. The strong beliefs he once held in the goodness of people is now false. The realization that there is true evil within their society shakes Jem to the core and he is unable to accept the jury’s unfair conviction. He must now reevaluate his understanding of human nature and come to terms with the disappointing realities of inequality and racism. As Atticus once told Jem that the courtroom was a place where everyone is seen as equal, Jem now knows that his father was wrong.

Throughout the trial, Jem carefully listens as his father presents moving, logical arguments proving Tom Robinson's innocence. However, Jem is a naive child and does not take into consideration the significant impact that the jurors' prejudice will have on the verdict. Jem takes note of the Ewells' conflicting testimonies, witnesses his father prove that Bob Ewell was motivated to assault his daughter, considers the fact that Tom Robinson is handicapped, and understands the importance of Bob being left-handed, which corresponds to the location of Mayella's injuries. In Jem's mind, Atticus clearly proves Tom's innocence and he firmly believes that Tom will be acquitted. Before Judge Taylor reads the verdict, Jem even tells Reverend Sykes in confidence that Atticus will win the case.
Unfortunately, Tom is wrongly convicted of assaulting and raping Mayella, which destroys Jem's childhood innocence and upsets him. Before Judge Taylor read the verdict, Jem believed that he lived in a just, fair society. After witnessing profound racial injustice for the first time, Jem's naive belief in the justice system and Maycomb's "Christian" ideals is destroyed. He immediately begins to cry and continually tells Atticus that the verdict was not fair. Jem ends up becoming a jaded individual, who can no longer trust his fellow citizens after witnessing Tom's wrongful conviction.

The wave function for an electron that is confined to x >= 0 nm See the image below. a) What must be the value of b? I don't know if this is correct but is this simply 1/sqrt(L/2) =.559 mm^-1/2 b) What is the probability of finding the electron in a 0.010 nm-wide region centered at x = 1.0 nm? Is this simply .00228630*100 = .23% c) What is the probability of finding the electron in the interval 1.15 nm

Hello!
Psi is the standard symbol for a wave function. Its square is the probability density pd(x). By the definition of probability density, the probability of being between c and d is  int_c^d pd(x) dx. In our case for positive c and d it is
b^2 int_c^d e^(-(2x)/L) dx = b^2*L/2*(e^(-(2c)/L) - e^(-(2d)/L)).
a) the value of b must be such that the total probability, int_(-oo)^(+oo) pd(x) dx, = 1. In our case it is  int_0^(+oo) b^2 e^(-(2x)/L) dx = b^2*L/2 = 1.
So yes, b=sqrt(2/L) and for L=6.4 it is about  0.559 ((nm)^(-1/2)).
And the formula for a probability becomes 
for positive c and d. If c is negative, c must be replaced with zero.
b) use this formula for c=1-0.005 and d=1+0.005.
c) use this formula for c=1.15 and d=1.84.
(there is an error at the picture, must be "for x>=0 nm", not "for x>=nm")
 
 

What are the differences that could keep Mr. Darcy and Elizabeth and Mr. Bingley and Jane apart?

Darcy and Bingley are from a different class than Elizabeth and Jane. Darcy is from the landed gentry, and Bingley is from the successful business class. Elizabeth and Jane, on the other hand, are from the middle class, and their family does not have a great deal of money. In Regency England, when the book takes place, wealthy men (particularly men from a higher class such as Darcy) were expected to marry women within their class. These marriages were seen as the proper way for people to pair off, and they were also ways to keep money flowing into the upper classes.
In addition, the Bennett family does not seem like the appropriate kind of family for a man like Darcy to marry into. In today's terms, Mrs. Bennet seems tacky and ill mannered, and Elizabeth's and Jane's sisters, such as Kitty and Lydia, flirt with soldiers in a most unrefined way. When Lydia runs off with Wickham without being married to him, her act has the potential to bring shame to the entire Bennet family until Darcy arranges the marriage between Lydia and Wickham. Darcy is better suited to Caroline Bingley than to Elizabeth, as Caroline has money and has been raised to be upper class, but in the end, Darcy marries Elizabeth for love. Bingley also marries Jane for romantic reasons. 

How do the differences in mood in Berlin and Auschwitz affect Bruno's character in Boyne's The Boy in the Striped Pajamas?

At the time of the setting, the capital of Germany, Berlin, is an old, heavily populated, cultured metropolitan city. Auschwitz is a location in southern Poland, near Oświęcim, an industrial town. This location, which had over forty parallel railroad tracks, was annexed by Germany at the beginning of World War II.
Clearly, then, there are marked differences between these two locations. For the young Bruno, even without his knowing what his father's position is and why they now live in Auschwitz, his new home is a desolate place. Theirs is the only house around; there is no neighborhood or anything like there would be in an established city.
Beyond one of the windows, Bruno and Gretel see a garden, but after this garden there is barren land, and then tall fences and wooden telegraph poles with wire bales. Even farther away, there are small huts and small buildings with smoke stacks. The children also notice that there are hundreds of people who appear very dirty. Bruno and Gretel decide that it is an "awful landscape" despite the forestland in another direction.  
On the other hand, Berlin is a charming city that has a history where families have lived for generations; there is a culture of music, art, drama, food, and customs with holidays, etc. Beautiful homes and buildings and many shops are in Berlin. 
Bruno has his family and friends in Berlin; in Auschwitz he has no friends until he meets Schmuel. In Berlin his grandparents play an active role in his life, especially his grandmother, who was on the stage when she was young. She would dramatize sometimes for the family, and Christmastime was always enjoyable.
So, in Berlin Bruno had his friends and family and always something to do and to anticipate with eagerness. Now, in Poland, he is disheartened and unhappy in a house that is not nearly as pretty as his Berlin home.

What impact does Walker's use of point of view have on the reader's understanding of the plot in "Everyday Use"?

The use of the first-person narrative by the story's Mrs. Johnson is especially important to the plot's development because her voice represents the past, and the respect and dignity that it should be afforded, most particularly as it applies to the sacrifices and challenges faced by previous generations that have allowed Dee to move out successfully into the world.
Mrs. Johnson and her daughter Maggie live in a house that is not much better than a shack.

It is three rooms, just like the one that burned, except the roof is tin; they don't make shingle roofs any more. There are no real windows, just some holes cut in the sides, like the portholes in a ship, but not round and not square, with rawhide holding the shutters up on the outside. 

Maggie is shy of the world—especially new people—because of scars she suffered as a child when the previous house burned. 

How long ago was it that the other house burned? Ten, twelve years? Sometimes I can still hear the flames and feel Maggie's arms sticking to me, her hair smoking and her dress falling off her in little black papery flakes.

Maggie also bears scars that cannot be seen, and her behavior bears this out:

She has been like this, chin on chest, eyes on ground, feet in shuffle, ever since the fire that burned the other house to the ground.

Maggie demands nothing of the world. Maggie's sister, Dee, is very different in several key ways.

Dee is lighter than Maggie, with nicer hair and a fuller figure. 

Dee had been outside watching the fire burn the house, without offering help or showing concern. Mrs. Johnson saw her and expected Dee to celebrate the event:

Why don't you do a dance around the ashes? I'd wanted to ask her. She had hated the house that much.

Her mother says Maggie "is not bright. Like good looks and money, quickness passes her by."
Early on, Dee is her own person. She wanted a better life and better things for herself. We can infer she was hateful toward her sister, until Mrs. Johnson and the church raised money to send Dee away to school. At graduation, Dee had to have a "yellow organdy dress." She understood style when no one else around her knew of such a thing. And she "was determined to stare down any disaster." Life has changed considerably for Dee. When she left, she never looked back. On this particular day, she is returning with the man in her life, "Hakim.a.barber."
Dee and her man arrive, and as one might expect, she is beautiful. Her mother says she has lovely feet that look like God fashioned them himself. Dee is wearing bright and very long native African clothing. She has real gold jewelry on her ears and wrists. Looking at their visitors, Maggie makes a sound in her throat like you would "when you see the wriggling end of a snake just in front of your foot on the road."
Dee has obviously left her past behind. Not only is she grandly dressed, but she also has renamed herself "Wangero Leewanika Kemanjo," refusing to bear, as she says, the name given to her by her people's white oppressors. Mrs. Johnson explains that it is a name given to her in honor of her aunt, but like much of what Mrs. Johnson has to say, Dee is barely listening. Even though her mother is right there, missing nothing, Dee is rude enough to make meaningful eye contact with Hakim.a.barber over Mrs. Johnson's head.
Mrs. Johnson describes her daughters and Dee's man. In describing herself, we find little resemblance to the others—in this woman who whittled out a quiet—though rough—life, surviving as a single mother in her ramshackle home.

In real life I am a large, big boned woman with rough, man working hands. . . I can kill and clean a hog as mercilessly as a man. . . I can eat pork liver cooked over the open fire minutes after it comes steaming from the hog.

Mrs. Johnson has no illusions about life. She has unrealistic dreams in her sleep sometimes, but when she wakes she knows who see is, what her life is like, and how it is likely to remain. She has lived during difficult times and fended for herself and her family. She does not have a need for frivolousness and fancy behavior. She is, however, amiable enough to try to please Dee in accepting the changes in her daughter's life.
The reason it is so important to the plot that the story is told by Mrs. Johnson is expressly because she knows who she is and where she belongs in this world. She understands the importance of those who have come before her to make her life possible. She remembers those in her past. She recalls being a part of a long line of strong, hardworking women.
Dee, on the other hand, has made it her business to reinvent the world according to what she wants. While it appears she has done well for herself, she is seemingly oblivious to how she might help her mother's meager existence.
As Dee makes her way around the house, she begins to ask her mother if she can have some things that catch her attention, the churn top and the dasher. She then goes into her mother's trunk in her bedroom. It contains quilts, one of which Dee very much wants. Grandma Dee pieced it together; Big Dee and Mrs. Johnson quilted it. There were pieces in the quilt with Great Grandpa Ezra's Civil War uniform. This quilt is almost a living thing, carrying a history with it that Dee cannot and will not ever appreciate. As is always the case with Dee, she believes if she wants something, she should have it. She has no nostalgic ties to any of the items; she sees only how everything would look gracing her home.
Maggie, on the other hand, loves this quilt because of its history. In this way, she is much like her mother. For Maggie, the quilt would not be hung on a wall, but used as it was intended and, with an appreciation for the time and hands that created it, used everyday.

Dee lacks understanding of her heritage.

Maggie does not. Mrs. Johnson understands this truth and the importance of it. Ironically, Dee believes she is becoming more connected with her ancestors by changing her name and manner of dress. In truth, the connections she should strive to establish are with those who came before her: the women who were treaty badly and/ or enslaved. Those women managed to survive, something that ultimately allowed Dee to be born and improve her circumstances beyond her humble beginnings.
Giving the quilt to Dee would be like cutting off a part of the Johnson women's identity. In truth, none of the women are in any way connected to their forbearers in Africa, but there is a steely connection that lies between these women and their heritage—something Dee cannot conceptualize.
Mrs. Johnson drives the plot by allowing the reader to see things from Dee and Maggie's eyes, but she also provides the reader with an understanding that where and who you come from is more important than what you own or where you live. Mrs. Johnson is not a dreamer; she has been a warrior her entire life. She understands the value of the women who have come before them, and recognizes there is no better way to pay homage to these women than Maggie's "everyday use" of the quilt.

How would you analyze the section of Dutchman that is marked in purple in the attached image?

The highlighted passage involves Lula's attempt to seduce Clay and to tempt him to indiscretions with her sensual dance.
Yet, even as Lula beckons Clay to join her, he remains resolute in his decision to reject her advances. Notice how Lula tries to goad Clay into displaying his rage by insulting him: "And that's how the blues was born. Ten little niggers sitting on a limb, but none of them ever looked like him. [Points to CLAY, returns toward the seat, with her hands extended for him to rise and dance with her." Her actions epitomize the racist belief that black men lack self-control and can be easily provoked to feral or brutish behavior.
Lula is the antithesis of Senta in Wagner's The Flying Dutchman. In The Fying Dutchman, it is supposedly Senta's purity and loyalty that saves the Dutchman from eternal sojourn on the seas. In his play, Leroi Jones turns this on its head: Lula exemplifies the worst of human nature. She personifies the racist colonial attitude that will doom someone like Clay to obscurity and degradation. Although Lula portrays herself as a savior of sorts, she is really a predator: "As she sings she rises from her seat, still throwing things out of her bag into the aisle, beginning a rhythmical shudder and twistlike wiggle, which she continues up and down the aisle, bumping into many of the standing people and tripping over the feet of those sitting. Each time she runs into a person she lets out a very vicious piece of profanity, wiggling and stepping all the time."
Lula manages to hide her intent for a time, but her true purposes are exposed towards the end of the play. Notice that Lula abuses every passenger along her path; she is equally dismissive of both the white and black passengers on the train. Her actions signify her intent to destroy anyone who refuses to bend to her will; Lula is a faux savior and is not to be trusted. She aims to goad Clay into displaying reckless behavior because her true objective is to destroy him. In the passage, her contempt for Clay is evident. Leroi Jones seems to be making the point that black men like Clay must look to themselves if they hope to achieve a measure of success in their lives.

Single Variable Calculus, Chapter 7, 7.3-1, Section 7.3-1, Problem 50

Determine the limit $\displaystyle \lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)]$

$
\begin{equation}
\begin{aligned}
\lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)] &= \lim_{x \to \infty} \ln \left( \frac{2+x}{1+x} \right)\\
\\
\lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)] &= \lim_{x \to \infty} \ln \left( \frac{\frac{2}{x}+ \frac{x}{x}}{\frac{1}{x}+\frac{x}{x}} \right)\\
\\
\lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)] &= \lim_{x \to \infty} \ln \left( \frac{\frac{2}{x}+1}{\frac{1}{x}+1} \right)\\
\\
\lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)] &= \ln \left( \frac{0+1}{0+1}\right)\\
\\
\lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)] &= \ln \left( \frac{1}{1}\right)\\
\\
\lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)] &= \ln 1\\
\\
\lim_{x \to \infty} [\ln (2 + x) - \ln (1 + x)] &= 0
\end{aligned}
\end{equation}
$

Why does Macbeth kill the body guards?

Before Macbeth enters King Duncan's chamber to assassinate him, Lady Macbeth drugs his chamberlains so that they will not interfere with the crime. Both Macbeth and his wife plan on blaming Duncan's murder on both of his chamberlains, who would be completely unaware of their actions when they awake from their drug-induced sleep. However, Macbeth ends up stabbing and killing both of the chamberlains after he assassinates King Duncan.
In act two, scene two, Macbeth informs his wife that one of Duncan's chamberlains yelled "Murder!" while he was in the king's chamber and the other servant cried out "God bless us!". One could assume Macbeth feared that Duncan's chamberlains would wake up and witness him in the king's chamber, which is why he murdered them. If the chamberlains would have awakened to find Macbeth in Duncan's chamber, they would have surely blame the murder on him and ruined the couple's plan to usurp the Scottish throne.
After killing King Duncan and his two chamberlains, Macbeth carries the bloody daggers out of the room. Macbeth then refuses to return to Duncan's chamber and is immediately overwhelmed with guilt. Lady Macbeth then takes matters into her own hands by placing the bloody daggers back into the room and smearing Duncan's blood all over the servants. When the Scottish lords arrive to discover that Duncan and his two chamberlains have been murdered, Macbeth confesses to killing the chamberlains in a fit of rage to conceal his role in the king's death.

Just a short time earlier, Macbeth killed the king while the king was actually asleep in the same room as his chamberlains, who were quite intoxicated (Lady Macbeth added liquor to their drinks so as to get them so drunk that they would pass out and have no memory of the night). However, Macbeth tells her that, while he was in the king's room, committing the murder

One cried "God bless us" and "Amen" the other,As they had seen me with these hangman's hands,List'ning their fear. (2.2.37-39)

In other words, then, the chamberlains were not completely passed out and seem to have had some awareness of Macbeth's actions in the room. Why else would they suddenly ask for God's blessing in the middle of the night? It seems to imply some fear on their part. Therefore, it is not terribly surprising that Macbeth would kill them because they likely witnessed at least a portion of the murder. Macbeth tells the others that he killed them out of "fury" and implies that a truly loyal servant of the king could hardly be "reason[able]" when faced with the king's murderers (2.3.124, 130). He says that his "violent love" for Duncan made it impossible for him to remain calm in the moment (2.3.129). Of course, this is a convenient excuse for him to have killed them! Lady Macbeth helps to draw attention away from Macbeth by pretending to faint. It is also of note that Macbeth does not consult his wife in this— they never discussed killing the chamberlains—and he already begins to act on his own.

In act 2, scene 3, Macbeth tells Macduff that he killed Duncan's bodyguards because he saw them covered in blood, realized that they had murdered Duncan, and could not stop himself. In other words, he says that he was so overcome with grief over Duncan's death that he felt it necessary to kill the guards as an act of revenge:

For ruin’s wasteful entrance; there, the murderers,
Steeped in the colors of their trade, their daggers
Unmannerly breeched with gore. Who could refrain,
That had a heart to love, and in that heart
Courage to make ’s love known?


Macbeth claims, therefore, that this crime was one of passion. It was borne out of love for Duncan and that anyone who feels love would have done the same.
However, this is not the real reason for killing the guards. As the reader knows, it is Macbeth who killed Duncan. Killing the guards is, therefore, a necessary step in covering up his crime. Macbeth could not risk having any witnesses to this murder because it would ruin his chances of becoming king.

What were the consequences of European expansion on global politics?

European colonization and expansion meant that wars could truly become global events now.  Nationalistic rivalry between Britain and France led to over 150 years of nearly non-stop war between 1650 and 1815.  Not only did the wars involve people who lived in the two nations, but it also involved native groups allied with those countries and colonial subjects.  These large-scale wars were not cheap to fight, so Britain and France had to improve their abilities to tax their subjects.  Britain lost its American colonies due to its inability to tax them fairly and the French monarchy was deposed due to its unfair tax burden on the peasantry.  
European colonization would also play a role in both world wars of the twentieth century as well.  Economic and nationalistic rivalries in Europe stemming from colonization helped to drive the tensions that created WWI.  In WWII Japan sought to end European colonization in Asia by making themselves the major regional power in Asia--this was one of the driving factors of WWII.  After WWII colonies in Asia and Africa sought their independence from their parent countries.  In many cases these newly formed countries such as North and South Vietnam would ally with one of the world's leading superpowers, the United States or the Soviet Union.  This would be part of the Cold War as America and the Soviet Union fought proxy wars in the developing world.  All of this was a continued legacy of European colonization.  

How is Mathilde from "The Necklace" vain? Thanks.

From early on in "The Necklace," Maupassant defines Mathilde Loisel's personality in terms of her vanity. She is is a person who cares deeply about appearances, about wealth, status, and glamour. There's a tension between her own exalted self image (the kind of life, Maupassant tells us, that Mathilde believes she has been born for) and the actual reality of her current condition, and this results in great distress and even shame.
She exhibits this fixation on appearances throughout the events of "The Necklace." When her husband first tells her about the party, her reaction is actually to refuse attending, on account of not having a suitable dress, and after her husband buys her a dress (one which cost 400 francs, which is established by the narrative as a quite significant sum), she next complains about the lack of jewels. Take careful note of some of her complaints here and the focus she places on appearances (specifically the appearance of wealth) and the perception of others. At the thought of not having jewels, she complains, "I shall look poverty-stricken. I would almost rather not go at all." She further states that "there's nothing more humiliating than to look poor among other women who are rich." This vanity, then, is not only established through way of the story's narration (Maupassant's description of Loissel) but also by Mathilde's own statements and actions within the story.

Mathilde is vain because she thinks she is better than she really is. Although she leads a pretty normal, lower-middle class life, Mathilde genuinely believes herself to be of noble descent. When her husband receives an invitation to the Education Ministry ball, she sees an opportunity to show everyone just how special she thinks she is. This leads her to borrow what she falsely believes is Madame Forestier's valuable diamond necklace for the night.
At the ball, Mathilde is the center of attention; all the men want to dance with her, and the women comment on her incredible beauty. Mathilde is in her element. At long last, she feels truly at home in what she sees as her natural habitat: a high society gathering attended by the social elite. Mathilde loves showing off the necklace to all, which feeds her already enormous vanity. Unfortunately, the necklace, like her vanity, has no substance.

Why does Scout quiz Atticus about his visit to the Radley house?

Early in the story, Scout shares that inside the Radley home lives a "malevolent phantom." She describes the home as being darkened from its original white and green to a gray color. The shingles are rotted and the yard is unkempt. The creepy appearance of the home adds to the superstitions and misconceptions regarding Boo Radley. After hearing news of Mrs. Radley's death, Atticus visits the Radley home to pay his respects to the family. At the time of her death, the children are still under the impression that the terrifying tales of Boo shared by neighbors are true. Scout and Jem are convinced that Boo must have killed his mother. When Atticus returns from the Radley house, the children are disappointed to learn that her death is a result of natural causes. Scout asks Atticus, "Did you see Mr. Arthur?" She quizzes him because the children are curious about Boo. Atticus's stern reply and sharp look when he answers, "I did not," put an end to Scout's questions.

At the beginning of Chapter 8, Mrs. Radley dies, and Atticus visits her home to express his condolences. When Atticus returns home, Jem and Scout are anxiously waiting to ask him questions concerning Boo's existence. Jem and Scout are still under the impression that Boo is a malevolent creature and believe that Boo finally murdered his mother. Much to their dismay, Atticus informs the children that Mrs. Radley died of natural causes. However, Jem and Scout are still anxious to learn more about their reclusive neighbor, and Scout finally asks her father if he saw Mr. Arthur. Atticus directly replies, "I did not" before he begins to read the newspaper (Lee, 65). Following their short conversation with Atticus, Jem tells his sister that Atticus is still "touchous" about their fascination with the Radleys.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 31

a.) Find an equation of the tangent line to the curve $y^2 = 5x^4 - x^2$ which is also called Kampyle of Eudoxus, at the point $(1, 2)$.

Solving for the slope $(m)$


$
\begin{equation}
\begin{aligned}

\frac{d}{dx} (y^2) =& 5 \frac{d}{dx} (x^4) - \frac{d}{dx} (x^2)
\\
\\
2y \frac{dy}{dx} =& (5)(4x^3) - 2x
\\
\\
2yy' =& 20x^3 - 2x
\\
\\
\frac{\cancel{2y} y'}{\cancel{2y}} =& \frac{20x^3 - 2x}{2y}
\\
\\
y' =& \frac{20x^3 - 2x}{2y}
\\
\\
y' =& \frac{\cancel{2} (10x^3 - x)}{\cancel{2}y}
\\
\\
y' =& \frac{10x^3 - x}{y}

\end{aligned}
\end{equation}
$


For $x = 1$ and $y = 2$, we obtain


$
\begin{equation}
\begin{aligned}

y' =& \frac{10(1)^3 - 1}{2}
\\
\\
y' =& \frac{10 - 1}{2}
\\
\\
y' =& \frac{9}{2} \text{ or } m = \frac{9}{2}

\end{aligned}
\end{equation}
$


Using Point Slope Form


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
\\
\\
y - 2 =& \frac{9}{2} (x - 1)
\\
\\
y =& \frac{9x - 9}{2} + 2
\\
\\
y =& \frac{9x - 9 + 4}{2}
\\
\\
y =& \frac{9x - 5}{2} \qquad \text{Equation of the tangent line at $(1,2)$}

\end{aligned}
\end{equation}
$


b.) Graph the curve and the tangent line on a common screen

What does Nettie not like about the Senegalese?

When she first sets foot on Senegalese soil, Nettie is highly enthusiastic. She feels a real sense of homecoming. At long last, she can openly express her racial identity as a black woman without fear. Soon, however, she becomes somewhat disillusioned by what she sees in this French colony. Although deeply impressed by the sheer blackness of the Senegalese skin color, she does not think much of the local people she sees in the marketplace. All they seem to care about is selling their produce. If you are not interested in buying anything they have to offer, then they look right through you in just the same way that they would if they were dealing with white French colonialists.
This unpleasant experience challenges Nettie's somewhat romanticized notion of racial solidarity. Skin color is one thing, but the traders in the Dakar marketplace still have to make a living; they are not about to treat Nettie with courtesy and respect simply because she is the same race.

What is the tone of the story?

There is a scary and menacing tone to the story “The Most Dangerous Game.” At the very beginning of the story, Rainsford’s friend, Whitney, talks of a mysterious island called Ship-Trap that fills most sailors with dread.
When Rainsford falls off the yacht and swims his way to Ship-Trap Island, he learns firsthand why the island has such a bad reputation among seafarers. The island, Ship-Trap, belongs to a Cossack, General Zaroff, who hunts human beings for the thrill of it. Zaroff is highly skilled at his sport. When humans land on his island, he offers them two options: to be hunted by him or to be knouted by Ivan, the giant servant. Both options present dreadful eventualities to the victims, who are essentially trapped with no escape. Rainsford is also faced with these two options and chooses to be hunted by Zaroff.
Though a hunter himself, Rainsford has to contend with Zaroff’s excellent hunting skills, experience, and the fact that this hunter is well acquainted with the hunting grounds. Throughout the chase, the reader can feel the danger and the tension in the air. Rainsford is terrified when he realizes that Zaroff is “playing with him” like “a cat plays with a mouse before finally killing it.” The gravity of his situation sinks in, and he realizes that he has to “play” for his life: either he lives or he dies.

What is it like to live under a monarchy?

It all depends on what kind of monarchy one lives under. If you live under an absolute monarchy, for instance, you are a subject, but one totally without rights. You only enjoy, if that's the right word, privileges granted to you by the king or queen. As the monarch is absolute he or she exercises absolute power. As such, you have no say whatsoever in the government or the future direction of your country. Laws are little more than royal edicts, made purely and solely in the interests of the king or queen. If you don't like these laws, then tough; you have no right to complain or protest. And if you dare to try, then you'll be punished for treason or sedition. As the monarch is absolute, such punishment can take many different forms, some of them positively blood-curdling. Torture can also be used to extract confessions from those suspected of crimes against the state. An absolute monarchy is a rule of men and women, not of laws.
A constitutional monarchy is a different ball game entirely. The monarch has a role to play but it's usually no more than formal; the king or queen is essentially a figurehead, representing a sense of historical continuity. The idea is that a notionally impartial figure at the head of state provides an element of stability amidst the turmoil of ever-changing governments.
The monarch formally approves laws, but plays no part in drafting them. In the United Kingdom, for example, laws passed by Parliament are given what's called the Royal Assent before they reach the statute book. The government is formally known as "Her Majesty's Government," but again, this is purely formal. In substance, the government is conventionally formed from the largest party in the democratically-elected House of Commons. The leader of this party must formally obtain permission from the Queen to form a government, but the request is never denied. The Queen is there to provide a measure of continuity after the cut-and-thrust of a contentious General Election campaign.
On the whole, life under a constitutional monarchy is infinitely more agreeable than that under the absolute variety. For one thing, you have a say in government. And that government operates under the rule of law, not the mere whim of a monarch and his or her advisers. Under a constitutional monarchy you're still technically a subject, rather than a citizen, but you do have formal legal rights, though they differ depending on which particular country you're talking about. In any case, you normally have the perfect right to criticise the institution of monarchy itself and can actively argue and campaign for its abolition. You can also voice the opinion that it might be more modern, more democratic, and considerably less costly to have an elected President instead of a king or queen as head of state.

How are the themes of warfare, search for identity, and jealousy used in A Separate Peace by John Knowles?

When the action of the book starts, Gene is a high school student faced with an identity crisis, and he is filled with fear. He writes of that time, "We were in shaky transit that summer from the groveling status of Lower Middlers to the near-respectability of Upper Middlers." Even Gene's status in the school, caught between the youngest kids and the oldest, is unclear. Gene, an intellectual, is unsure of his identity, and he befriends Finny, a popular boy, in part to cover up for his own insecurities and to feel less afraid. 
Part of Gene's fear has to do with the war, as the book's action starts in 1942, during World War II. He says:




"The class above, seniors, draft-bait, practically soldiers, rushed ahead of us toward the war. They were caught up in accelerated courses and first-aid programs and a physical hardening regimen."

While Gene and his classmates are still "numbly reading Virgil," students just a bit older than them are preparing to enter the war and to leap into the unknown, worsening Gene's fears. 



While Gene admires Finny, he is also jealous of his friend's ability to get away with behavior none of the other boys would dare exhibit. For example, when Finny wears a bright pink shirt, the teachers only find it funny, not punishable. Gene thinks:

"I was beginning to see that Phineas could get away with anything. I couldn’t help envying him that a little, which was perfectly normal. There was no harm in envying even your best friend a little."

Gene's insecurity and confused identity, worsened by the coming war, makes him more and more jealous of Finny until he decides to deliberately shake the branch of the tree on which Finny is climbing. 

Why do you believe the Great Depression lasted so long? How did the New Deal transform the relationship between the federal government and American citizens?

A critical factor in explaining the length of the Great Depression was that the economic downturn was global. When the Wall Street crahsh took place in October 1929, it had an immediate impact not just on the United States, but also Britain and the rest of Europe. Global trade and economic output collapsed, causing millions to be thrown out of work. For example, in Germany, which had relied heavily on American loans to rebuild its economy during the 1920s, unemployment skyrocketed and a process of political radicalization began that culminated in the coming to power of Hitler in 1933. The response of many governments only made things worse. Protectionist trade measures were adopted which increased tariff barriers between countries, and accelerated the division of the world economy into trade blocs. The most important example of this was the Smoot-Hawley Tariff Act, signed by President Hoover, which hiked tariffs to an average of 50 percent. This created additional barriers to economic recovery and laid the basis for the conflicts that would later erupt in world War II. The tariff barriers also led to countries around the world abandoning the gold standard and devaluing their currencies, moves which played havoc with the exchange system. Some saw the fundamental cause of the crisis in the nature of the capitalist system, which had created unsustainable levels of social inequality and poverty. During the 1920s, many American banks were poorly regulated and over-extended their operations, while wages failed to keep pace with corporate profits. This led many intellectuals and workers to turn to Marxism or more socially-oriented economic models. It is a matter of one’s own political views whether their arguments should be accepted. But they would have presented the persistence of the Great Depression as capitalism’s failure. Roosevelt’s new deal, largely implemented during his first 100 days in office, not only gave government a much larger role in providing aid to the unemployed and elderly through programs like Social Security. Huge public works programs, like the Tennessee Valley Authority, created jobs for the unemployed, and new regulations increased the power of the federal government in trade and finance. If you compare this to the actions of successive governments, at least prior to Hoover, the difference is stark. Their reaction was generally to reduce spending Further reading: https://www.britannica.com/event/Great-Depression/Political-movements-and-social-change https://www.britannica.com/place/United-States/The-Great-Depression#ref613060

There were several reasons why the Great Depression lasted so long. One reason was the collapse of the stock market, along with the collapse of the banking system. So many people and businesses lost everything when they were unable to get their money from their bank accounts and when their investments became worthless as businesses closed.
Another factor is that there were government regulations that interfered with free market forces. The National Industrial Recovery Act allowed businesses to set codes of production. Minimum wages were set along with a maximum number of hours a person could work. Minimum price levels for products were also established. The price fixing that occurred was generally at higher levels than the free market would have allowed. This reduced the amount of wealth that could be generated. When free market forces aren’t allowed to determine the price of products, fewer goods are produced and sold when prices are above free-market levels.
A third factor was that some of the government programs to deal with Great Depression seemed to be of limited value. The Works Progress Administration created some important jobs, such as infrastructures jobs building roads and bridges, but some jobs went toward building swimming pools and playgrounds. Additionally, the Agricultural Adjustment Act led to higher food prices, which created difficulties for people who already had very little money.
The New Deal altered the relationship between the government and the American people. The American people began to believe that the government should serve as a safety net during times when people are in great distress. People have come to rely on the government for social programs as a result of the Great Depression. One such program created during the Great Depression and that still exists today is the Social Security program. This program is very important to those people who have reached the retirement age at which benefits from Social Security become available.
https://www.forbes.com/2009/04/30/1930s-labor-wages-business-ohanian.html

In what chapter does Angus Tuck prove that he is immortal?

In chapter 7 of Tuck Everlasting, Winnie learns the story of the Tuck family and how they all found out that they are immortal.
Winnie meets Jesse Tuck when she sees him drink from a spring. He tells her not to drink from the spring because it would be bad for her. Winnie is insistent about drinking from the spring, but more of the Tuck family stumble upon the two and carry Winnie off to explain the situation to her.
Mae, Miles, and Jesse explain to Winnie that they came to Treegap 87 years before, and they stumbled on the same spring that Winnie saw Jesse drink from. They noticed that the water tasted strange, but they did not think too much of it until strange things started to happen to the family. Jesse fell out of a tree and ate poisoned mushrooms, Mae cut herself, Pa got a snakebite, yet all of them survived. They also noticed that year after year, they never seemed to age.
Finally, they suspected that the spring water had made them immortal, and Angus Tuck set out to prove it. Mae explains:

"He said he had to be sure, once and for all. He took his shotgun and he pointed it at hisself the best way he could, and before we could stop him, he pulled the trigger." There was a long pause. Mae's fingers, laced together in her lap, twisted with the tension of remembering. At last she said, "The shot knocked him down. Went into his heart. It had to, the way he aimed. And right on through him. It scarcely even left a mark. Just like—you know—like you shot a bullet through water. And he was just the same as if he'd never done it" (Babbitt 40).

What is "the other?"

Totality and Infinity is a philosophy treatise written by Emmanuel Levinas in 1961. It takes up the question of the ultimate fate of mankind, as well as questions of ethics, theology, and history. According to Levinas, "the other" is any person (or more broadly, any phenomenon) identified as outside of one's own subjective ego. For Levinas, "the other" is a representation of what we cannot grasp through our own limited ego. "The other" represents infinity, eternity, and God. It also represents theological concepts such as boundless love, charity, and an encounter with the Divine.
"I will say this quite plainly," says Levinas, "what truly human is—and don't be afraid of this word—love." For Levinas, it is only through encounters with "the other" that we are able to express and embody love: "To approach the Other in conversation is a teaching [in love]," he says. Approaching the other allows us "to have the idea of infinity," and to experience "the very epiphany [of religion]." For Levinas, encountering "the other" is the only mechanism we have for reaching outside of our limited ego to experience something greater, namely, the mystery of God.

How does Darzee's wife affect the plot of "Rikki-Tikki-Tavi"?

Darzee's wife, a tailorbird, is integral to the plot of "Rikki-Tikki Tavi." Her actions are important in the inciting incident, rising action, and climax. First, the conflict of the story starts when Rikki wanders into the garden and hears Darzee and his wife crying about the baby bird they lost to Nag. Their sad state is Rikki's first introduction to Nag. As Rikki is talking to them to find out why they are crying, the antagonist, Nag, appears for the first time.
During the rising action portion of the plot, Darzee's wife steps in to help Rikki when Darzee is too bird-brained to do so. Darzee's wife acts as a decoy to lure Nagaina away from the melon-bed where the young cobras are about to hatch so that Rikki can destroy most of the eggs. She volunteers to help, even though doing so puts her own life at risk. She also warns Rikki that Nagaina has gone to the veranda with the intent of killing the boy, Teddy. 
Finally, during the climactic battle between Rikki and Nagaina, Darzee's wife intervenes again, fluttering in front of the fleeing Nagaina just enough to slow her down. This allows Rikki to catch up to the snake and grab onto her tail with his teeth just as the cobra "plunged into the rat hole."
Thus, Darzee's wife plays an important role in three parts of the plot: the inciting incident, the rising action, and the climax.

From Richard Connell's "The Most Dangerous Game," is Rainsford responsible for Zaroff's death?

In Richard Connell's "The Most Dangerous Game," whether Rainsford is responsible for Zaroff's death or not can be argued two ways. First, one could argue that Rainsford is responsible for Zaroff's death simply because he wins the final battle. Two men, seemingly of equal strength and wits, face each other to the death in Zaroff's room. The fight, therefore, is fair, and Rainsford wins by killing Zaroff. As a result, yes, Rainsford is responsible for Zaroff's death. Zaroff even accepts the terms of this fight and freely participates when he says the following:

"I see. . . Splendid! One of us is to furnish a repast for the hounds. The other will sleep in this very excellent bed. On guard, Rainsford."

On the other hand, one could argue that Rainsford is not responsible for killing Zaroff because he virtually turns into a beast that simply fights for its life. Therefore, the argument could be that Rainsford is so far past rational human thinking at the end of the story that he reacts like a beast. In fact, Rainsford claims the following:

"I am still a beast at bay. . . Get ready, General Zaroff."

When Rainsford speaks metaphorically about being a beast at bay, he might also be speaking from a psychologically literal sense. For example, Zaroff forces Rainsford to act like a hunted beast for three days and nights in a jungle. Due to the mental trauma inflicted upon him over the course of these days, Rainsford starts to think and behave like a beast in order to survive. A "beast at bay" means that it has been cornered and must turn and fight to survive. Therefore, one could argue that Rainsford is not responsible for his actions when he kills Zaroff because he has been driven to the point of irrational thinking--thinking like a beast at bay and not as a human. One might also say that Rainsford could probably plead insanity for killing Zaroff and not be held responsible for his actions. 

Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 36

Differentiate $\displaystyle F(z) = \log_{10} (1 + z^2)$


$
\begin{equation}
\begin{aligned}

F'(z) =& \frac{d}{dz} [\log_{10} (1 + z^2)]
\\
\\
F'(z) =& \frac{1}{(1 + z^2) \ln 10} \cdot \frac{d}{dz} (1 + z^2)
\\
\\
F'(z) =& \frac{1}{(1 + z^2) \ln 10} \cdot 2z
\\
\\
F'(z) =& \frac{2z}{(1 + z^2) \ln 10}


\end{aligned}
\end{equation}
$

How can we compare the moral and ethical issues in Kazuo Ishiguro's Never Let Me Go with our current society?

This question is a broad one, so I will address one specific moral and ethical issue in detail. By writing Never Let Me Go, Ishiguro insists that the reader confront the tension that exists around the normalization of artificiality in today's society. This is a moral and ethical issue for many people, as things that are artificial are being mistaken for real, which causes problems of trust and reliability.
Artificial is a synonym for fake, or created, or contrived, and it is the opposite of words like authentic, real, and natural. The artificiality of the clones and their creation for the purpose of harvesting organs to save humans are a reminder to readers of all the artificiality we have come to rely on in our own world.
Any teenager can identify any number of day-to-day artificial experiences, ranging from "friends" and relationships on Facebook that only exist on the screen but somehow hold emotional power, to so-called "fake news" that misleads society and rattles faith in journalism, or to artificial depictions of life supported by social media that mislead viewers to believe they are true. Though Facebook, the news, and social media all have positive qualities to offer society, the artificial side of these important social influences can be dangerous, much like the cloning of humans for human benefit is morally dangerous.

Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 8

Determine the general indefinite integral $\displaystyle \int \left( y^3 + 1.8y^2 - 2.4y \right) dy$

$
\begin{equation}
\begin{aligned}
\int \left( y^3 + 1.8y^2 - 2.4y \right) dy &= \int y^3 dy + \int 1.8 y^2 dy - \int 2.4 y dy\\
\\
\int \left( y^3 + 1.8y^2 - 2.4y \right) dy &= \int y^3 dy + 1.8 \int y^2 dy - 2.4 \int y dy\\
\\
\int \left( y^3 + 1.8y^2 - 2.4y \right) dy &= \frac{y{3+1}}{3+1} + 1.8 \left( \frac{y^{2+1}}{2+1} \right) - 2.4 \left( \frac{y^{1+1}}{1+1} \right) + C\\
\\
\int \left( y^3 + 1.8y^2 - 2.4y \right) dy &= \frac{y^4}{4} + 1.8 \left( \frac{y^3}{3} \right) - 2.4 \left( \frac{y^2}{2} \right) + C\\
\\
\int \left( y^3 + 1.8y^2 - 2.4y \right) dy &= \frac{y^4}{4} + 0.6 y^3 - 1.2 y^2 + C
\end{aligned}
\end{equation}
$

y = x^3 , x = 0 , y = 8 Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

We can use a shell method when a bounded region represented by rectangular strip is parallel to the axis of revolution. It forms of infinite number of thin hollow pipes or “representative cylinders”.
 In this method, we follow the formula: V = int_a^b (length * height * thickness)
or V = int_a^b 2pi* radius*height*thickness
For the bounded region, as shown on the attached image, the rectangular strip is parallel to x-axis (axis of rotation). We can let:
r=y
h =f(x) or h=x_2 - x_1
The x_1 will be based from the boundary line x=0.
The x_2 will be base on the equation y =x^3 rearranged into x= root(3)(y)
h = root(3)(y)-0
h=root(3)(y)
For boundary values, we have y_1=0 to y_2=8 (based from the boundary line).
Plug-in the values on
 V = int_a^b 2pi *radius*height*thickness, , we get:
V =int_0^8 2pi y*root(3)y*dy
Apply basic integration property: intc*f(x) dx = c int f(x) dx.
V = 2pi int_0^8 y* root(3)(y)dy
Apply Law of Exponent: root(n)(y^m)=y^(m/n) then root(n)(y)= y^(1/3)and y^n*y^m = y^(n+m)
V = 2pi int_0^8 y y^(1/3)dy
V = 2pi int_0^8  y^(1/3+1)dy
V = 2pi int_0^8  y^(4/3)dy
Apply power rule for integration: int y^n dy= y^(n+1)/(n+1).
V = 2pi y^(4/3+1)/(4/3+1) |_0^8
V = 2pi y^(7/3)/(7/3) |_0^8
V = 2pi y^(7/3)*(3/7) |_0^8
V = (6pi y^(7/3))/7 |_0^8
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a).
V = (6pi (8)^(7/3))/7 -(6pi (0)^(4/3))/7
V =(768pi)/7-0
V =(768pi)/7  or 344.68 (approximated value).

Who are the protagonists?

Tessie Hutchinson is the story's protagonist, though this does not become clear until the story's conclusion. The reader first notices her as a housewife who is late to the gathering for the drawing. It is clear that she will become important because so many people take note of her arrival and because of the exchange she has with Mrs. Delacroix, whom she bids farewell with a tap on the arm as she moves to join her family.
When the Hutchinson family's name is drawn, they become the focus of the village's attention and could be considered, as a group, the story's protagonists. Tessie's panic is immediate, and she begins to try to negotiate, asking that her married daughter's family be included and protesting that her husband was hurried as he drew for them. She is reminded of the rules, and Mr. Hutchinson accepts that someone in their family will be the chosen one.
Tessie is set upon by the villagers at the end, and as the lottery's victim, she becomes the main figure of the story at its conclusion.

Calculus of a Single Variable, Chapter 9, 9.9, Section 9.9, Problem 13

f(x)=(4x)/(x^2+2x-3), c=0
Let's first factorize the denominator of the function,
x^2+2x-3=x^2+3x-x-3
=x(x+3)-1(x+3)
=(x+3)(x-1)
Now let, (4x)/(x^2+2x-3)=A/(x+3)+B/(x-1)
4x=A(x-1)+B(x+3)
4x=Ax-A+Bx+3B
4x=(A+B)x-A+3B
equating the coefficients of the like terms,
A+B=4 ----------------(1)
-A+3B=0 ------------(2)
From equation 2,
A=3B
Substitute A in equation 1,
3B+B=4
4B=4
B=1
Plug in the value of B in equation 2,
-A+3(1)=0
A=3
The partial fraction decomposition is thus,
(4x)/(x^2+2x-3)=3/(x+3)+1/(x-1)
=3/(3(1+x/3))+1/(-1(1-x))
=1/(1-(-x/3))+(-1)/(1-x)
Since both fractions are in the form of a/(1-r)
Power series is a geometric series,
=sum_(n=0)^oo(-x/3)^n+sum_(n=0)^oo(-1)x^n
=sum_(n=0)^oox^n/(-3)^n+sum_(n=0)^oo(-1)x^n
=sum_(n=0)^oo(1/(-3)^n-1)x^n
Interval of convergence |-x/3|<1,|x|<1
|x/3|<1 and |x|<1
-3Interval of convergence is the smaller of the intervals of convergence of the two individual fractions,
So, Interval of convergence is (-1,1)

In the book The Witch of Blackbird Pond, how does Kit Tyler change over time?

Kit Tyler changes quite a bit over the course of this story. When readers are first introduced to Kit, she is a rich and spoiled girl. She is used to having fine clothes and servants. She is really out of her element when she comes to the Puritan colony in Connecticut, and she is shocked to find out how difficult manual labor actually is. Additionally, she comes to the colonies as a fairly strong supporter of the crown, so it is very surprising for her to hear such open talk about defying the King. Kit tries to fit in, but she does not do a great job of it. A big roadblock for her is her friendship with Hannah Tupper, but Kit does eventually prove to the community that she is working to do right by their values. By the end of the book, Kit has really come to appreciate the hardworking Wood family. In fact, she decides to not return to Barbados and become a governess for a wealthy family. Instead, she chooses a life that allows her to be close to Nat, Hannah, and all of the people that she has grown to love.

She did not dare to look up at him. "Can I see her, Nat?" she asked instead. "Will you take me on board?"
"No, not yet." His voice was full of decision. "I want to see your uncle first. Kit—" his words came in an unpremeditated rush. "Will he think it is enough—the new ketch? There'll be a house someday, in Saybrook, or here in Wethersfield if you like. I've thought of nothing else all winter. In November we'll sail south, to the Indies. In the summer—"
"In the summer, Hannah and I will have a garden!"

What does Macbeth mean when he says, "There is none but he/ Whose being I do fear"?

As his paranoia increases, Macbeth becomes very anxious about Banquo, as the witches told him his sons will become kings.
In the beginning of Act III, at Forres, the castle that was King Duncan's and is now Macbeth's, Banquo, who is a guest, realizes Macbeth has all that "the weird women" promised him. Also, he fears Macbeth had a hand in his own fortune: "Thou play'dst most foully for 't" (Act III, Scene 1, line 3). Then, because of the turn of events, Banquo wonders if the witches' prophecy about himself will come true.
Later, Banquo informs Macbeth that he and his son Fleance plan to ride for an hour; Macbeth extends good wishes for an enjoyable ride and urges Banquo to return for the banquet that evening.
After Banquo and his son's departure, Macbeth expresses his fear of Banquo, who heard the prophesy about him and received prophesies of his own.

To be thus is nothing, but to be safely thus—Our fears in Banquo stick deep.And in his royalty of nature reigns that Which would be feared. . . He hath a wisdom that doth guide his valorTo act in safety (Act III, Scene 1, lines 50-56).

When Macbeth says he fears Banquo's "being," he means he is worried that since the predictions of the witches have come true for him—even though he helped cause some of this reality—those predictions about Banquo's becoming the father of kings may also become real. Since Macbeth has no heirs, he fears he may have sold his soul to the Devil in order to make Banquo's sons kings as the witches have foretold. 

Only for them, and mine eternal jewel [his soul]Given to the common enemy of man [the Devil to whom he has sold his soul],To make them kings, the seeds of Banquo kings! (Act III, Scene 1, lines 71-73)

In addition, he worries Banquo may take some actions himself for his "safety." Macbeth hires two murderers and sends them to kill Banquo and his son.

How is the society in 1984 similar to and different from contemporary America?

The type of society depicted in 1984 bears a number of similarities and differences to contemporary America. One of the most striking differences is the nature of political power. In Oceania, the Party came to power in a violent Revolution. In the modern United States, the government is democratically elected.
Moreover, the citizens of the modern US have a number of rights and freedoms which are protected by legislation, like the Constitution, and cannot be denied by the government. In contrast, in Oceania, Party members live a very restricted life of which every aspect is controlled by the Party. They cannot date who they like, for example, or complain about their poor standard of living. Proles are the only exception to this rule; they live as they please, but only because the Party does not view them as a political threat.
Both the Party and the United States use surveillance to monitor their citizens. In 1984, the Party installed telescreens in the homes of Party members and in the public places they frequent. These devices constantly monitor the conversations and actions of every Party member. While surveillance in modern America is not as invasive, it has steadily increased since the 1980s, driven in part by the modern threat of terrorism (see the first reference link). 
Please also see the second reference link provided for more information.
https://www.bbc.co.uk/news/magazine-22274770

College Algebra, Chapter 8, 8.1, Section 8.1, Problem 54

Suppose that a reflector for a satellite dish has cross section in parabolic form, with a receiver at focus $F$. The reflector is $1$ ft deep and $20$ ft wide from rim to rim. How far is the receiver from the vertex of the parabolic reflector.

"Please see figure"

If we let the vertex of the parabola lies on the origin and midway between $20$ ft span then its equation is $x^2 = 4py$ where the focus is located at $(0, p)$ and endpoints at $(10,1)$ and $(-10, 1)$. Hence, the endpoints are the solution of the equation, so


$
\begin{equation}
\begin{aligned}

x^2 =& 4py
\\
\\
(10)^2 =& 4p(1)
\\
\\
100 =& 4p
\\
\\
p =& 25

\end{aligned}
\end{equation}
$


Therefore, the receiver is $25$ ft from the vertex of the parabolic reflector.

Find the equation of the line which passes through (-4,1) and is at an angle of 135° with the positive direction of the x axis.

The angle essentially gives the slope.  If you consider, slope is a measure of the steepness of a line, a lot like a hill, which will go up at a certain angle.  To use it for the slope, we need to take tangent function (from trigonometry) of the angle:tan135 = -1
So, in the equation for the line, slope = m = -1
So, we have m = -1 with a point on the line (-4,1).
Various ways to get the equation from there.  We could put this information into the equationy=mx+b:1 = -1*-4 + bSo, we can solve that for b:
1 = 4 + b
b = -3
So, then, we have m and b.  So, we can write the equation for the line:y = -x - 3

Examine the growth of worldwide trade from 1500 to 1800. Discuss the rise and implications of a global trading system. (Keep in mind implications to: political, social, economic, cultural, environmental, etc.)

The Age of Exploration began around 1500, led mostly by Spain and Portugal, which had the wealth to fund explorers, their ships, and tools of navigation. The goal was to find faster routes to Asia in the interest of bringing sought-after spices back to Europe. Of course, an error in navigation resulted in finding continents that Europe had not known existed: what are now North and South America.
In the Americas, new foods, such as tomatoes and corn, were discovered and integrated into European diets. Without this exchange, the Western culinary traditions that we know today would not have developed.
However, there were also negative effects. The first slaves were brought to Hispaniola, the island that now comprises Haiti and the Dominican Republic, in 1502, ten years after Columbus's fateful voyage which landed him on the Caribbean island of Dominica. Not long after the "discovery" of new lands, Europeans began to colonize them. Indigenous peoples who were not slaughtered died from European diseases, such as yellow fever, smallpox, and influenza. Africans were then kidnapped from West Africa and brought to the Americas, particularly Brazil and the Caribbean, to work on plantations growing sugarcane, rice, tobacco, and, later, cotton.
Cotton was key to the Industrial Revolution, which began around 1750. Textile mills in New England and Great Britain depended greatly on cotton from the American South, which was separated from seeds more quickly and easily after Eli Whitney's invention of the cotton gin in 1793.
Industrialism led to overcrowding and pollution in cities that were hubs for manufacturing, particularly London. Though factory workers were not slaves, they worked very long hours, had no safety protections at work, and lived in crowded and dirty tenements. Children were also employed. The environmental effects of industrialism, including air and water pollution, persisted for centuries and have only recently been addressed in some countries. The effects of climate change, a warming phenomenon caused by the release of excessive carbon dioxide in the atmosphere which diminishes the atmosphere, remain an urgent concern today.

What is the central conflict in "Where Are You Going, Where Have You Been?" by Joyce Carol Oates? When, where, and how does it develop or become more complicated as the story unfolds? How is it resolved at the end of the story? Why and how is that resolution satisfying?

I am not allowed to write an essay for you, but I believe that I can get you on the right track by answering several of the questions in the prompt.  
There are several conflicts in "Where Are You Going, Where Have You Been?" It's going to be up to you to decide which one you think is most "central."  There is a conflict between Connie and her parents.  She desires to be more independent, and she also sees them as too traditional.  There is also a conflict that exists between Connie and her sister, June.  It's not a huge conflict, and I'm not certain that June is even aware of it.  The conflict is that Connie has a problem with how "plain and steady" June is.  Connie doesn't understand how June doesn't desire to be more flirty and cool.  I don't believe that either of those conflicts are the central conflict.  For the central conflict, I would definitely write about the conflict that develops between Connie and Arnold Friend. 
The question asks about the nature of the conflict and how it changes.  I believe that those two questions come together.  When Connie first sees Friend, there's very little conflict to speak of.  He creepily says "Gonna get you, baby," but Connie just keeps walking.  The encounter seems to be over and done with. 
It's not until a few days later that the conflict between Connie and Friend becomes extremely serious.  Readers are told that Friend shows up at Connie's house near midday on a Sunday.  Connie opens the door to see who it is, and Friend immediately begins trying to convince her to get in his car and go for a ride. 

"You wanta come for a ride?" he said.
Connie smirked and let her hair fall loose over one shoulder.
"Don'tcha like my car? New paint job," he said. "Hey."
"What?"
"You're cute."

At first, Friend's tactics resemble confident flirting; however, as Connie continues to fend off his advances, Friend becomes threatening.  His threats are a combination of psychological and physical manipulation.  He knows things about Connie and her family that he just shouldn't know.  He knows exactly where her family is and how long they are likely to be gone.  

"But my father's coming back. He's coming to get me. I had to wash my hair first—'' She spoke in a dry, rapid voice, hardly raising it for him to hear.
"No, your daddy is not coming and yes, you had to wash your hair and you washed it for me."

Eventually, it becomes clear to Connie that Friend is really bad news.  He threatens to physically come in the house after her if she attempts to call the police.  By this point, Connie is so scared that she decides to risk rushing for the phone.  Friend comes in the house as he threatened to do, and he stabs her "again and again with no tenderness."  She's not being stabbed with a knife or anything like that, and critics have various opinions on what is actually happening to Connie; however, the result is still the same.  Connie leaves the house with Friend, and she is unable to fight any longer.  She's a complete shell either because she's so scared or because she has given up.  
The final part of your question asks about the conflict's resolution.  The conflict is resolved when Friend wins.  Connie leaves her house thinking that she will never see her family again.  

She thought, I'm not going to see my mother again. She thought, I'm not going to sleep in my bed again.

This story is one of those rare times that the "bad guy" wins.  In my opinion, the resolution is not satisfying.  Perhaps it is more realistic than the ever-present happy ending conflict resolution, but happy endings are satisfying to me.  I love teaching this story to classes because students are upset at the ending.  They are not happy that the story doesn't have a clean, happy, and satisfying conflict resolution.  

Metaphors-Would you say the speaker has a positive, negative, or neutral attitude toward her pregnancy? Which metaphors give you this impression?

I would say that the speaker of this poem has a negative attitude toward her pregnancy.  Typically, a woman who calls herself, or is called, an "elephant" or is said to be as big as a "house" is not receiving a compliment.  Further, and perhaps more tellingly, the speaker says that "Money's new-minted in this fat purse."  In this metaphor, the baby is the thing of value, the money, and she is simply the "fat purse" that contains the valuable item.  Again, "fat" is also not a word that has a positive connotation: in this situation, used to describe a full purse,  "fat" takes on a bit of positivity, but only in relation to the fact that the purse is fat because it contains so much of something so valuable.  It is the money that it important, not the purse.
Also, we might describe something as "a means to an end," and the end is the important thing.  However, here, the speaker is simply the "means," and we can assume that the baby is the end.  The baby is, thus, the important thing; the mother, less so.  Finally, the inevitability of the final metaphor which compares pregnancy to a train which one cannot get off makes it seem as though, if the speaker had a choice, she would choose to get off that train.  All this appears to confirm the speaker's negative attitude toward her pregnancy.

In the book First They Killed My Father, who are the main characters and what is their importance to the story?

First They Killed My Father is a true story about the Cambodian Holocaust initiated by the Khmer Rough.  The main character is the author herself:  Loung Ung.  Considering that Loung Ung is fifth in a line of seven children, the other main characters in the story are members of her family.  The family’s true hell begins in 1975 when the Khmer Rouge evacuates Phnom Phenh.  The Ung family is part of the evacuation because they are considered “middle class” which means they are “unclean.”  In a situation that sounds similar to the Nazi holocaust, the captured members of the middle class are forced into crowded trucks and transported to rural areas where inhumane treatment and genocide begin. 
Through the Ung family’s struggle, we learn about the individual members of the family as important characters.  An additional character is Loung’s father:  Seng Im Ung.  Seng Im Ung becomes associated with the government of Lon Nol; therefore, Seng Im Ung is kidnapped.  He is never seen again.  Two other characters are Meng Ung and Khouy Ung:  two of Loung’s brothers.  They are forced to leave the family and work in labor camps.   Another important character is Ay Choung Ung, Loung’s mother.  Ay Choung Ung is a mom who makes a great sacrifice.  Knowing that she has already lost many of her children and her husband, she sends Loung and her brother out on their own so that they can survive.  Ay Choung Ung knows that any child who stays with her will surely die.   Only Geak (who is only three and, therefore, a minor character) remains with Ay Choung. 
Throughout the hell of the Cambodian holocaust, the characters of First They Killed My Father (who are all members of the Ung family) exhibit the admirable qualities of faith, compassion, and integrity.

Who was hurt by Reconstruction in 1865 and why?

It is important to know that Reconstruction was a project that was never completed.
The purpose of Reconstruction, which was started in 1865 and was discontinued after Rutherford B. Hayes signed the Compromise of 1877, was not only to rebuild, or reconstruct, the South, but also to provide black people with political agency and property. The promise of "forty acres and a mule" was made during Reconstruction, but was never fulfilled.
Southern whites' resentment of the federal government and of the North may have intensified during this period. Firstly, there was the matter of black people becoming members of Congress. Secondly, federal troops continued to occupy the South. Thirdly, opportunistic northerners, frequently called "carpetbaggers," went south to profit off of the South's diminished status.
Given the historical record, in my view Southern blacks were hurt most -- not by Reconstruction, but by its unfulfilled promise. Hayes's compromise with Southern legislators resulted in the disfranchisement of black people, and in the creation of a new system of bondage: sharecropping. 
In this system, white planters hired black workers to pick cotton or other crops on their land. For a season of work, the workers would receive shelter, a parcel of land on which they could have their own gardens, and a share of the profits from that season's crops. However, very frequently, planters would cheat workers out of their fair share of profits.
In addition, lynchings became very common soon after Reconstruction, as a means of controlling and terrorizing black populations and diminishing their potential political and economic power.

What does Paul's choice of sport and Erik's choice of sport say about each one of them?

While Paul chooses soccer, Erik chooses football. I’d argue that the popularity ratings of both sports show differing aspects of the brothers’ personalities.
As of right now, in the United States at least, soccer is not as popular of a sport as American football. In 2013, Gallup reported that 39% of American adults rated football as their favorite sport to watch. Only 4% chose soccer. Though soccer’s popularity is rapidly increasing and many children play on recreational teams, it still does not draw the same enthusiastic crowds in the USA as American football does, especially for major events like the college football playoffs and the Super Bowl. Also, it’s important to remember that Tangerine was written in 1997, a time when soccer’s popularity was even more meager compared to football’s widespread appeal. I think the sports’ wildly different ratings relate to the brothers’ personalities because Erik seeks acclaim. He never acts in a kind or mature way unless his parents are watching, and he enjoys the attention of his crowd of lackeys. It makes sense that he would choose a sport that offers more opportunities to be highlighted and celebrated. In contrast, Paul often does good deeds without asking for any rewards. It makes sense that he would feel happy to play the sport that he loves, not the one that wins him the most glory.
I’d also argue that football allows Erik to have many moments of individual glory. As a placekicker, he doesn’t have to rely on his teammates or display any teamwork and cooperation. He kicks alone and takes the glory for himself. In contrast, soccer doesn’t offer many opportunities for individual glory, since at all times, the players are working together for a common goal. This shows that Paul has a greater sense of community, collaboration, and teamwork than Erik does.
https://news.gallup.com/poll/4735/sports.aspx

Why is the novel, American Sniper (Chris Kyle) relevant today and what can you gain from reading it?

American Sniper offers an inside perspective on U.S. Special Forces, the nature of war, and the problem of mental health. By reading it, a person can gain knowledge about topics that would otherwise be closed to them, from a point-of-view that they may not have considered before.
Chris Kyle's experiences in the military and as a Navy SEAL, in particular, are the center of the novel. He explains how he became the kind of person who doesn't attach a feeling to killing enemy combatants. Rather, he aims, shoots, kills, and then gets ready to aim again. The lack of feeling for the people he shoots is of particular interest to a reader who likely has not experienced that type of situation. Moving through Kyle's life and experiences in the war, it becomes clearer why he's able to be so emotionally removed. When at first he hesitates to shoot, eventually that hesitation disappears. The reader follows him on that journey and his reasons for it.
The book also sheds light on the nature of war in the modern era. One thing that's discussed by Kyle's wife is that he's forced to fight people with rules that don't govern them. It makes the reader wonder what the better option is—because surely US soldiers shouldn't fight like terrorists. At the same time, though, endangering soldiers isn't a good option either. There are no good answers to the questions of war. Kyle makes it clear that from his perspective, might is what wins wars. The might of the United States (the soldiers who fight for the country) are what allowed them to win engagements and take back cities.
The mental health and relationships of soldiers are other things that make the book relevant. The relationships that Kyle has with his family, friends, wife, and children are all affected by his job. His wife notes that she believed he loved being a SEAL more than her. Kyle had a lot of problems adjusting when he came home from the war because he was haunted by some of his experiences there. This sheds light on the plight of veterans who may not have the resources or support they need to heal from their experiences.

In "The Rocking-Horse Winner," why do the father and the mother in the story have too little money?

In D.H. Lawrence's short story, "The Rocking Horse Winner," the problem is not really that the parents have too little money, it's that they perceive that they have too little money. It's a problem of greed. If you don't live within your means, it doesn't matter how much money you make, it won't be enough. We've all seen stories of celebrities and millionaires who file for bankruptcy. It wasn't that they didn't have enough money---they had more than most people would see in a lifetime. The problem was that they spent more than they had. Consider this quote from the story: 

"They lived in a pleasant house, with a garden, and they had discreet servants, and felt themselves superior to anyone in the neighborhood. Although they lived in style, they always felt an anxiety in the house. There was never enough money. The mother had a small income, and the father had a small income, but not nearly enough for the social position they had to keep up." 

Readers see that the family lives quite comfortably in this passage. They have a nice home and even employ some servants. Both parents are bringing in an income, which seems more than enough to meet the needs of the family, but it's not enough to meet the wants of the parents. The parents want more money to continue to maintain their superiority, to send their children to elite schools, and to satisfy their expensive tastes. 
In the opening line of the story, the woman is described as having married for love, but then the love turned to dust. The woman is described as having a cold heart devoid of love for her children. The father is described as someone who always had prospects, but they never amounted to anything. Throughout the story, the house is seen repeating the phrase  "there must be more money, there must be more money."  It is as though the parents believe that money is the answer to all their problems. Money, it is thought, would heal their hearts of stone and make their lives fulfilling. 
When Paul asks his mother why they don't have a car, she answers that it's because his father has no luck. When Paul begins to predict the horse races and gives his winnings to his mother, even those ever-increasing amounts of money are not enough to make her happy. 

What do you think would happen if Earth's tectonic plates ever stopped moving? Why?

The tectonic plates stopping per se would not be catastrophic. It would reduce the formation of new crust on volcanic vents and stop the formation of mountains. Eventually, the Earth would erode until almost all land was at the same level, meaning everything would be underwater. Life could definitely still survive that, though; indeed, most of the world's life lives underwater. Moreover, it would take millions of years to do this, so land-dwellers would have a lot of time to prepare. In the meantime, there would be no more earthquakes to deal with!The real catastrophe would come from why the tectonic plates stopped moving. The only really plausible way this could happen would be if the Earth's core cooled and solidified, meaning there was no longer hot magma being fed upward into and through the mantle. If that ever happened, it would be catastrophic, though it would take a long time.While the flow of the core—and the resulting magnetic field of the Earth—has changed direction and strength over thousands of years, it has never completely stopped. If it did, solar radiation reaching the surface would increase dramatically. This would have a direct effect of killing many organisms on the surface (it would be like the whole world was sitting in the Van Allen Belt), but the now-freed solar wind stripping away the Earth's atmosphere would be even more problematic. It would take a few billion years to strip away completely, and life might be able to adapt, but we're pretty sure this is what happened on Mars and that's why no life has been discovered there.
https://www.nasa.gov/topics/earth/features/2012-poleReversal.html

According to the poet,what should our attitude be to the past to the future?

In this poem, Longfellow promotes the attitude that "the soul is dead that slumbers" and that we must not see life as a "funeral march" toward the grave, but as something "real" and "earnest," an opportunity for our souls to grow. As such, the poet recommends that we "let the dead Past bury its dead" and "act in the living Present." We should not dwell on what has passed, but strive to "make our lives sublime," making a mark that will endure after us and even inspire others to strive similarly to better themselves. We should "trust no future, howe'er pleasant," which does not help us ensure that "each to-morrow" will "find us farther than to-day."
Longfellow's attitude in this poem is that we should never simply plod on like "cattle" in mindless expectation that the future will be whatever it will be. On the contrary, he suggests we put the past behind us and embrace the future, with the ideology that we can always be "achieving" and "pursuing" throughout life, such that we make "footprints" of our own on our futures.

What is the history of laws against cruel and unusual punishment?

In addition to prohibiting excessive bail or fines, the Eighth Amendment to the US Constitution prohibits cruel and unusual punishment. It was ratified in 1791, but the idea of prohibiting unjust consequences can be traced all the way back to 1689 to the English Bill of Rights, which also forbade cruel and unusual punishment. George Mason included a similar law in Virginia's Declaration of Rights in 1776 as well.
What, exactly, "cruel and unusual" means is based on the amount of pain, suffering, and/or humiliation that the recipient might be subjected to. In 1972, the United States Supreme Court case Furman v. Georgia refined that definition further, establishing a set of principles that can be used to discern whether a proposed consequence is "cruel and unusual." According to these guidelines, a punishment cannot:
Degrade one's humanity
Be arbitrary
Be something that is clearly rejected by society's sense of justice
Be less effective than a less severe form of punishment
Clearly, there's overlap between these principles, and that is intentional. The underlying goal set forth by Justice William Brennan in his Furman v. Georgia opinion was to set a precedent for punishment that preserves human dignity. To that end, he made it clear that he expected individual states to not create laws that violate these four principles.
https://constitutioncenter.org/interactive-constitution/amendment/amendment-viii

Caribbean Poetry Discuss the thematic and stylistic characteristics of Grace Nichols's poetry (focusing on her poems "Waterpot," "Without Song," and "Old Magic"), and compare these to the thematic and stylistic characteristics of Kamau Brathwaite (focusing on his poem "Starvation and Blues").

Grace Nichols's and Kamau Brathwaite's poetry is about claiming a distinct Caribbean identity separate from that of Western Europe and the United States. To this end, the poets use local vernacular and speak about the experience of Afro-Caribbean people.
Nichols's poetry attempts to reclaim African folk heritage and the dignity of slave women to provide a rich history of the African diaspora. For example, in "Waterpot," Nichols writes about the experience of slavery. She writes, "The daily going out/and coming in/always being hurried along/like like...cattle." She uses a simile, comparing slaves to cattle, to describe the way in which they are constantly asked to tend fields without rest. The slave woman described in the poem holds herself erect "like royal cane." This is another simile in which the woman is compared to what she harvests--sugar cane. She holds herself with pride and makes an attempt to express her pride in the only way she can, but the overseer sneers at her "pathetic display of dignity." Nicholas uses local objects, such as sugar cane, to express the woman's self-determination. In "Without Song," Nicholas writes of children who are so stricken that "They have fallen/into exile/moving without song/or prayer." In these short, staccato lines, she describes children, perhaps slaves, perhaps poor and starving, who are suffering so much that they don't have a song, as most children do. The song and prayer stand, in a metaphorical way, for the joy and hope of children who have good lives. The exile she writes about is an allusion to the exile of slaves from Africa in the New World, in addition to the exile of the Jews in the Bible. In "Old Magic," a nameless African woman speaks about the experience of slavery.
Like Nichols, Brathwaite uses vernacular but does not concentrate on the experience of women. Brathwaite's "Starvation and Blues" uses a form of Caribbean vernacular to reinvent English literary tradition. For example, the poem begins, "This is no white man's lan'," which echoes the first line of Yeats's "Sailing to Byzantium" ("That is no country for old men"). His poem uses the rhythm of blues in lines such as "this place is empty bottles/this place is a woman satisfied." The poem uses the rhythm of the blues and images from the Caribbean to express the experience of living in the Caribbean and having a culture that has been transported from Europe and America but that has been remade and re-imagined in the Caribbean. 

What are the themes of Act II, Scene 2 in The Merchant of Venice?

Most of the themes in this scene are also themes in the larger play. Let us take the themes in the order they appear:
In lines 1 - 29, the clown Launcelot is wrestling with himself about whether he should run away from Shylock, whom he works for as a servant. Launcelot feels his conscience is telling him to stay with Shylock, but "the devil" is telling him to run away. Though he uses funny, convoluted language, Launcelot is expressing the theme of being torn between duty and self-preservation, which will become a problem for Antonio later.
For both Launcelot and Antonio, this conflict is caused directly by the fact that they have dealings with Shylock, who tends to use the rules to make other people's duties hateful to them.  So another theme in this scene and in the play is the harshness of Shylock and of Jews in general (with the exception of Jessica). This seems awfully anti-Semitic (and perhaps it is), but it is less-objectionable if we see Shylock as standing for a strict legalism under which no one can live. 
In lines 30 - 88, Launcelot encounters his father Gobbo. Gobbo is partially blind ("sand blind"), and apparently has not seen Launcelot for some time (a few years?). Launcelot pretends to be someone else and tells his father that Launcelot is dead. He doesn't keep up the joke for very long, but once he does try to reveal his true identity to his father, the old man remains confused and does not believe it's really Launcelot until Launcelot mentions his mother's name. This is a comic variation on the theme of the difference between appearance and reality, which we will also see in the subplot with Portia and the caskets, and again when Portia dresses up a young lawyer. 
In the same part of the scene (lines 69 - 71), Launcelot makes an ironic and insightful comment: "Nay, indeed [even] if you had your eyes you might fail of the knowing me; it is a wise father that knows his own child." This idea of parents not knowing their own children is also a minor theme in the play. Shylock does not realize how much Jessica hates living with him, and he is shocked when she runs away. Portia's father, with the way he set up the casket test in his will, seems to have handed her a frustrating limitation, although he had her best interests at heart. 
Comic confusion is a theme throughout the whole scene. Launcelot and his father are there to provide comic relief. It starts with Launcelot's tongue-twisting monologue, continues when Gobbo doesn't know his own son, and goes further when the two of them try to talk to Bassanio, interrupting each other with one malapropism after another (line 115: “he hath a great infection to serve" and line 123: “as my father, being I hope an old man, shall fruitfy unto you“).
The scene becomes a little more serious at the end, when Gratiano shows up asking Bassanio if he may go with him to Belmont. (Bassanio is going to Belmont to try to win Portia's hand. We will find out later that Gratiano hopes to go because he is interested in Portia's maid, Nerissa.) Bassanio quickly agrees, but warns Gratiano to restrain his usual tendencies to be "too wild, too rude, too bold of voice" while they are in Belmont.  Bassanio says he personally doesn't mind these things about Gratiano, but if Gratiano behaves that way in Belmont, it may hurt Bassanio's chances with Portia. In short, Bassanio fears he will be exposed to loss and trouble by the character flaws of a good friend. This is exactly what happens to Antonio, when Bassanio's need for money causes him to fall into the hands of Shylock.

What racial differences did Lincoln perceive?

Abraham Lincoln is often called “The Great Emancipator” and hailed as a heroic opponent of slavery. However, just because he played a pivotal role in ending slavery in the United States doesn’t mean that he believed all races to be inherently equal.
When he ran for Senate against Stephen Douglas in 1958, Lincoln stated clearly in the debates that while he thought African American people should be entitled to live as freely as whites, he did not accept them as intellectual or moral equals. He didn’t want to give them the right to vote or hold office, and he was against intermarriage. He definitely thought that the white people should still be in charge of everything.

“There must be the position of superior and inferior, and I, as much as any other man, am in favor of having the superior position assigned to the white race. I say upon this occasion I do not perceive that because the white man is to have the superior position the negro should be denied everything.”—Abraham Lincoln, in the Lincoln-Douglas Debates

As racist as that opinion sounds to us today, Lincoln's view that African Americans should at least be able to live freely was a revolutionary (and unpopular) idea for the time. Lincoln lost the Senate race but won the presidency in 1860. A few months later, the Southern states (whose economy depended on slavery) seceded, and the Civil War began.
https://www.minnpost.com/eric-black-ink/2013/05/facing-facts-about-lincoln-and-his-views-slavery/

In Warriors Don't Cry by Beals, how is Melba able to survive her year at Central High School?

In addition to seeing herself as a warrior, Melba was also able to survive because she created a support system for herself. While other students left—voluntarily or forcibly—Melba stuck it out because of the support she received from others. Melba developed a close friendship with Link, a white high school boy, who helped her (for example, by letting her borrow his car) as she helped him better understand racial issues.
She also became close with fellow Little Rock Nine members, who looked to one another for encouragement and solidarity. Furthermore, she looked to the local black newspaper publisher, Daisy Bates, as a mentor and source of strength. Every time Melba felt like giving up in the text, she sought the advice of her friends, mentor, and tight-knit family.
With their support and her self-determination to persevere regardless of the abuses she suffered, Melba survived her year at Central High.

Melba is able to survive her year at Central High School, when she was one of the Little Rock Nine desegregating the school, by remembering what Danny, a soldier from the 101st Airborne Division who was sent to the school to protect the African-American students for a while, told her. He said to her, "Warriors survive" (page 163), and she faced the segregationists as a warrior would face his or her opponents. Even when the 101st Airborne was sent back to Kentucky and the segregationists thought they could force the African-American students to leave Central High School, Melba says, "the warrior growing inside me squared my shoulders and put my mind on alert to do whatever was necessary to survive" (page 182). She dealt with everything that happened to her like a solider would. When her locker and its contents were sprayed with ink, she quickly asked for a new locker and books without brooding about it. When she was kicked in the shins, she did everything she could to stay mobile. It was not a mode that was necessarily comfortable for her, but it allowed her to survive in a very hostile climate for the school year.