Organisms have evolved physiologically and anatomically to adapt. How have their systems evolved to maximize their purpose of maintaining homeostasis and equilibrium? Explain.

I'm unsure whether "how have their systems evolved" is asking for a likely method of evolution or is asking about what specific things an organism does to maintain homeostasis and equilibrium.  If it is the second option, the question is also confusing because it doesn't mention which organism is being examined.  Not all creatures are capable of maintaining equilibrium and homeostasis the way that humans/mammals do.  
If the question is asking about a method of evolution, then Darwin's explanation using adaptation and fitness levels is probably the most appropriate. Because of sexual reproduction, new genetic combinations are always occurring within any given species.  Those changes in the genetic code will cause an organism to be better or worse adapted to a particular environment.  An organism that is better adapted is said to be more "fit."  Fit organisms tend to survive (survival of the fittest).  Because they are surviving, they are more likely to pass on their particular adaptation. Generations will go by and eventually the entire species will have that adaptation.  In other other words, nature selects which adaptations a species will evolve with.  Applied to the original question, that means that at some point in history, an organism developed some kind of adaptation that allowed him/her/it to more effectively maintain homeostasis.  That in turn somehow allowed that creature to better survive in that particular environment.  Its progeny then inherited that adaptation until that adaptation eventually spread through the entire population. 
https://www.ndsu.edu/pubweb/~mcclean/plsc431/popgen/popgen5.htm

What did the Spanish do in response of La Salle's activities in Texas?

When the Spanish authorities received information about La Salle’s from a French deserter and from Native Americans, they were very concerned that the creation of a French settlement on the coast of Texas might become a launching point for attacks on Spanish outposts and silver mines.
Spain sent several expeditions to try to locate the French settlement. When they finally succeeded in April, 1689, they found the fort was empty and destroyed. By this time, La Salle himself had died. Native Americans of the Karankawa nation had attacked the fort a few months previously and killed the remaining adult settlers; they spared only four children. The Spanish destroyed all traces of the French settlement and buried the French cannons. They continued to feel threatened by the possibility of more French explorations, and so increased the tempo of their own explorations and settlement in Texas.

Mike buys an old airplane with the intention of repairing, restoring, and selling it. He anticipates that it will cost him $275,000 to purchase, repair, and restore the plane, and that he can sell the finished plane for $310,000. When he has spent a total of $275,000 on the project, he discovers that he needs to replace the engine. It will cost Mike $95,000 to replace the engine. He can sell the plane without the new engine for $180,000. What should he do? Explain. How much money does Mike make? In your answer, refer to the marginal benefits and marginal costs of each option.

If we are looking at this issue purely from an economic point of view, Mike should buy the engine and then resell the airplane. This would give him a greater marginal benefit (relative to marginal cost) from this point forward.
Economists say a person should not let their decisions be affected by money they have paid out in the past. In other words, Mike should not pay any attention to how much he has already spent or what he had thought would happen when he bought the plane. The money that he has already spent is called a “sunk cost.” It should have no effect on what he does going forward. All he should think about is what will make him the most money (or lose him the least) starting right now.
So, we have to think about this as if Mike were starting from zero right now. He has two choices. He can sell the plane as is for $180,000 without incurring any further costs. His “profit” from here on out would therefore be $180,000. His other choice would be to buy the engine for $95,000, at which point he could sell the plane for $310,000. When you subtract $95,000 from $310,000, you get a figure of $215,000. That means that Mike’s “profit” from here on out would be $215,000 if he were to buy the new engine, fix the plane, and resell it.
From this, it is clear that Mike should buy the engine, finish restoring the plane, and sell it. He will still lose money overall, but this is the best choice given that he cannot go back and refrain from buying the plane in the first place. Mike needs to forget his sunk cost and just look forward. If he does this, he will see his marginal benefit from buying the new engine and then selling the plane will exceed the marginal benefit of just selling the plane as is.

Do you think Shakespeare's main message in Othello is "Don't trust outward appearances"?

In Othello and other plays by Shakespeare, it is difficult to isolate any single theme or idea as the main message. Most readers and audiences will agree that it is a good thing not to trust appearances without doing some investigation and that the plot of Othello demonstrates this fact. Othello is easily tricked by Iago's appearance of friendship and loyalty to him and by the appearance of things Iago has manipulated, such as the missing handkerchief. (In this case it is more of a disappearance.) But these things are more the result of other factors that represent the deeper themes of the play.
Iago's acts of deception are effective because Othello is too virtuous to even consider that a trusted friend would lie to him. In general, those who are honest and decent toward others have difficulty believing that there are people who tells lies just for the sake of lying and that there are people who have no qualms about doing evil things, even when there is evidence of it. To me, this is more thematically important to the play than the idea of not trusting appearances, though one could say that the two ideas are related.
Though many commentators have downplayed this aspect of the play because it is a sensitive issue, Othello's status as "the other," an outsider in the European culture, is also a major theme. Iago exploits Othello's sensitivity based on that status, and the catastrophe that concludes the play is a result of Iago's own racial hatred, as well as Othello's insecurity. Again, "not trusting appearances" is a good idea, but the meaning of Shakespeare's play goes much deeper than this.

I tend to agree with this statement, as the tragedy in Shakespeare's Othello relies upon deceptive appearances and exploited assumptions about these appearances. After all, Iago is able to dupe Othello (and pretty much everyone else) so effectively because he successfully makes himself seem like a loyal and trusted advisor. Similarly, Iago is able to manipulate and warp the appearances of other characters, most notably Cassio and Desdemona, in order to make them seem like scheming traitors. As such, the play's tragic ending is a result of mistakenly assuming that one's appearance is an accurate translation of one's character. Since Iago is the mastermind behind these deceptive appearances, his quote in Act III, Scene 3 is especially ironic: 

Men should be what they seem;
Or those that be not, would they might seem none (130-31).

In this passage, Iago is essentially saying people should be what they appear to be. In light of the hidden, villainous nature of Iago's character, this assertion becomes one of the play's most disturbing (and fascinating) quotations.

Analyze three characters in the novel, indicating how they portray the theme of fighting for individualism.

Many of the themes in The Outsiders revolve around ideas of individualism vs. collectivism. In many ways, the entire story is about learning to see individuals instead of the collective, because all of the characters in the novel have been characterized by a collective stereotype. Whether they are Socs or Greasers, the stereotype of that gang follows each character, and people assume that they know that character because of his or her association with each group. Several of the characters fight this by getting to know each other on a personal level and seeing other people as individuals instead of just as a group label.
Ponyboy and Cherry are two characters that fight for individualism in their relationship with each other. Ponyboy feels that he can talk to Cherry and tell her personal things, even though she's a Soc and they've only just met (Hinton, 34). Cherry sees past the Greaser stereotype with Ponyboy and imagines that he reads books and watches sunsets (Hinton, 35). Ponyboy admits that he likes both and asks her about whether or not she likes sunsets too. As Ponyboy thinks this over, he tells the reader:

I pictured that, or tried to. Maybe Cherry stood still and watched the sun set while she was supposed to be taking the garbage out. Stood there and watched and forgot everything else until her big brother screamed at her to hurry up. I shook my head. It seemed funny to me that the sunset she saw from her patio and the one I saw from the back steps was the same one. Maybe the two different worlds we lived in weren't so different. We saw the same sunset (Hinton, 35).

Both of these characters see beyond the stereotype, and the fact that they are "supposed" to be enemies, to the person underneath.
Johnny also stands out from the gang. Ponyboy describes him by saying:

Johnny Cade was last and least. If you can picture a little dark puppy that has been kicked too many times and is lost in a crowd of strangers, you'll have Johnny. He was the youngest, next to me, smaller than the rest, with a slight build (Hinton, 11).

Johnny is the boy that all the other Greasers want to protect, and although he is depicted as meek and scared for most of the novel, he also demonstrates his individualism by seeing it in others and by sticking up for what he believes is personally right. He is the one who, at the end of the novel, seems to most clearly understand Ponyboy. He writes him a personal letter about the meaning of the poem that he and Ponyboy shared. He is also the one who sticks up for Cherry at the movies, despite the fact that she is in a different gang.

Can you provide a character sketch of Macbeth?

When Shakespeare's Macbeth begins, Macbeth is a noble and courageous military leader. He's defeated the King of Norway and the treacherous Macdonwald in a decisive battle, and for his efforts he is fated to earn King Duncan's approval and admiration. Based on the way the play opens, it's easy to view Macbeth as an honorable man, one who could be potentially destined for greatness.
The way that Macbeth's character unravels is what makes him a tragic figure. With the Weird Sisters' prophetic promises ringing in his ears, Macbeth increasingly allows his ambition to get the better of him. At first, though he is clearly tempted by the chance to kill Duncan and steal the crown, Macbeth seems reluctant to follow through with his schemes. However, once Macbeth actually does murder Duncan, he truly begins to change. He becomes increasingly paranoid and resorts to ruthlessness to satisfy his craving for security. Indeed he even goes so far as to murder one of his closest companions, Banquo, and all of Macduff's family. By the end of the play, Macbeth has become a true tyrant, and, when Macduff kills him, Macbeth seems to have recognized the uselessness of his hunger for power and to have embraced despair. For an example of Macbeth's despair, take a look at his famous soliloquy responding to Lady Macbeth's death in Act 5, Scene 5:

Tomorrow, and tomorrow, and tomorrowCreeps in this petty pace from day to dayTo the last syllable of recorded time;And all our yesterdays have lighted foolsThe way to dusty death. Out, out, brief candle!Life's but a walking shadow, a poor playerThat struts and frets his hour upon the stageAnd then is heard no more. It is a taleTold by an idiot, full of sound and fury,Signifying nothing. (21-30)

This soliloquy is a meditation on the apparent uselessness of life, at least according to Macbeth's perspective. Thus, we can see that Macbeth begins the play as a courageous, even heroic figure, but through the course of the narrative he transforms into a paranoid and despairing tyrant. This transformation is truly tragic, and it's impossible to avoid wondering what kind of man Macbeth might have been if he hadn't heard the Weird Sisters' prophecy. 

Why is Bob's nickname "Silky" Bob in "After Twenty Years" by O. Henry?

Even Bob's first name is not mentioned until near the end of the story, and the nickname "Silky" Bob is mentioned only once. This is when the plainclothes detective tells him, 

You've been under arrest for ten minutes, ‘Silky’ Bob.

Bob's last name is never mentioned in the story. O. Henry has some reason for not wanting to identify Bob by his name. This is undoubtedly because Bob is continually on the lam and probably uses many different names. Jimmy Wells, of course, would know Bob's last name, but he cannot call him by his first name, last name, or nickname when he is talking to him in front of the hardware store because he has quickly decided not to reveal who he is or that he knows who Bob is. Jimmy makes this decision when Bob lights his cigar and Jimmy sees that his old friend is the man who is wanted by the Chicago police. From that point on, there is no exchange of names. Bob speaks of Jimmy Wells, but he does not know he is talking to Jimmy Wells. Bob is called "the man" and "the other," and at one point he is called "the man from the West," but he is not called Bob until the arresting officer arrives on the scene and calls out:

“Is that you, Bob?” he asked, doubtfully.

The plainclothes detective only knows the name because Jimmy Wells has told it to him. O. Henry could not have had Jimmy addressing Bob by name because Jimmy was pretending he didn't know him. Bob would have had no reason to introduce himself by name to a strange cop unless asked to show some form of identification. Both Jimmy Wells and Bob's identities are unknown to the reader until near the end of the story, which is O. Henry's intention because he wants a surprise ending.
Bob probably got the nickname 'Silky' Bob for two reasons. One is because he is apparently a smooth talker, as he demonstrates when he encounters the cop while he is standing in the hardware-store doorway. Bob is slick. He is like silk. Another reason is that Bob has a taste for luxuries, as demonstrated by the diamond scarf-pin he is wearing and his diamond- studded pocket watch. He probably also favors silk clothing. This would easily get him the nickname 'Silky' Bob in underworld circles. Crooks generally go only by their first names or a nickname to avoid being caught.
The word 'Silky' appears only once. The plainclothes detective has to show that he knows the man he is arresting. He has to make a positive I.D. This is why O. Henry has him say,

You've been under arrest for ten minutes, "Silky" Bob.

It may be that the Chicago police do not even know Bob's last name but have identified Bob in their telegram as "Silky" Bob. This would be sufficient for the New York detective to arrest Bob, although Jimmy Wells could supply Bob's last name when booking him. Bob might have many reasons for wanting his last name to be unknown, and Jimmy could cause him a lot of trouble all over the Midwest when he reveals what it is. If Bob is wanted by the Chicago police, he may very well be wanted by the police in a lot of other towns.

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 7

int (x^2+2x)cosx dx
To evaluate, apply integration by parts int udv = uv - int vdu .
So let
u = x^2+2x
and
dv = cosx dx
Then, differentiate u and integrate dv.
du = (2x + 2)dx
and
v = int cosx dx = sinx
Plug-in them to the formula of integration by parts. So the integral becomes:
int (x^2+2x)cosx dx
= (x^2+2x)sinx - int sinx * (2x + 2)dx
= (x^2 + 2x)sinx - int (2x + 2)sinx dx
To take the integral of (2x + 2sinx)dx, apply integration by parts again.
So let
u_2 = 2x + 2
and
dv_2 = sinx dx
Differentiate u_2 and integrate dv_2.
du_2 = 2dx
and
v_2 = -cosx
So the integral becomes:
= (x^2+2x)sinx - [ (2x + 2)*(-cosx) - int -cosx * 2dx]
=(x^2+2x)sinx - [-(2x + 2)cosx + 2int cosx dx]
=(x^2+2x)sinx - [-(2x + 2)cosx + 2sinx]

= (x^2+2x)sinx +(2x +2)cosx -2sinx
= (x^2+2x - 2)sinx + (2x + 2)cosx
Since the given is indefinite integral, add C.
= (x^2+2x - 2)sinx + (2x + 2)cosx + C

Therefore, int (x^2+2x)cosx dx = (x^2+2x-2)sinx= (x^2+2x - 2)sinx + (2x + 2)cosx + C .

Do you think Mourad is "crazy" in "The Summer of the Beautiful White Horse"? Why or why not?

When we are first introduced to Mourad, we are told by his cousin that he was "considered crazy by everybody who knew him except me." We are then told, immediately after, of the time when Mourad, astride "a beautiful white horse," woke his cousin at four in the morning by tapping on the window of his room. This would certainly suggest that Mourad is at least eccentric.
Mourad's cousin, Aram, says that "Mourad enjoyed being alive, more than anybody else who had ever fallen into the world by mistake." This implies a hedonistic approach to life which may partially explain why everyone else considered Mourad to be "crazy." We then find out that Mourad had stolen the horse, which we might consider "crazy" if we think about the possible repercussions for Mourad and, more significantly, for the reputation of his family. This seemingly cavalier attitude towards the possible consequences of his actions might also be a characteristic of one thought of as "crazy."
When we usually think of people who might be deemed "crazy," we might think of people who are over-excitable and who perhaps find it difficult to control their emotions. Mourad certainly doesn't qualify as "crazy" in this sense. Indeed, when Aram asked him what they should do after the horse ran away and it was too late to return it to its owner, Mourad calmly replied, "Well . . . we'll either take him back or hide him until tomorrow morning." And toward the end of the story, when the horse's owner, John Byro, found the boys with his horse, Mourad was again calmness personified.
Overall, I don't think Mourad qualifies as "crazy" in any really meaningful sense of the word. In the story, he seems to be in full possession of his intellectual faculties—but is perhaps rather impulsive and a little reckless. The fact that he is rather impulsive and a little reckless, however, is possibly far more satisfactorily explained by the fact that he also happens to be a thirteen-year-old boy.

In this story, the narrator's cousin, Mourad, has the reputation of inheriting the crazy streak in the family. However, when we look at the way he is characterized, we get a different impression of his "craziness." Firstly, Mourad is considered crazy because he roars and sings when he is riding the horse. Arguably, though, this is not a sign of being crazy; rather, it is a sign of his happiness. Knowing how much Mourad loves horses, this is not a surprising or crazy reaction to riding one.
Similarly, regarding the theft of the horse, we cannot call Mourad crazy for doing this. Given how much he wanted a horse of his own, we can empathize with his reasons for the theft. It is more apt to describe the theft as reckless than it is to say it is crazy. 
Moreover, at the end of the story, Mourad returns the horse to its rightful owner, a sign that he understands that this was the right and ethical thing to do.
So, while Mourad's actions and behavior might be considered reckless, it is not a sign that he is crazy. Instead, it is a sign of his passion for fun and his love of horses.

(x+1)/(x+6)+1/x=(2x+1)/(x+6) Solve the equation by using the LCD. Check for extraneous solutions.

(x+1)/(x+6)+1/x=(2x+1)/(x+6)
LCD is x(x+6)
Multiply all the terms of the equation by LCD and simplify,
x(x+6)((x+1)/(x+6))+x(x+6)(1/x)=x(x+6)((2x+1)/(x+6))
x(x+1)+(x+6)=x(2x+1)
x^2+x+x+6=2x^2+x
x^2+2x+6=2x^2+x
x^2+2x+6-2x^2-x=0
-x^2+x+6=0
Factorize the above equation,
-1(x^2-x-6)=0
(x^2+2x-3x-6)=0
(x(x+2)-3(x+2))=0
(x+2)(x-3)=0
use the zero product property,
x+2=0  or x-3=0
x=-2   or x=3
Let's check the solutions by plugging them in the original equation,
For x=-2,
(-2+1)/(-2+6)+1/(-2)=((2(-2)+1))/(-2+6)
(-1)/4-1/2=(-3)/4
-3/4=-3/4
It's true.
For x=3,
(3+1)/(3+6)+1/3=(2(3)+1)/(3+6)
4/9+1/3=7/9
7/9=7/9
It's true.
So, the solutions of the equation are 3 and -2.

What is a monastery? Why does Portia want to stay there?

A monastery is a building or group of buildings in which monks or nuns live, work, and pray after taking religious vows. In act 3, scene 4 of The Merchant of Venice, Portia instructs Lorenzo to take charge of her household, claiming that she and Nerissa are planning to stay in solitude at a nearby monastery in order to have a restful time of prayer and contemplation. She does not actually plan to go to the monastery but has selected the setting for an alibi, knowing that she will be allowed an unquestioned respite from her household while there. Portia concocts the monastery story to ensure that no one will realize she and Nerissa are traveling to Venice to impersonate lawyers at Antonio's trial with the goal of freeing him from Shylock's trap.

why do they take soma in Brave New World?

It's important to understand that Soma, the drug that has "All the advantages of Christianity and alcohol; (and) none of their defects" is not just taken in the future world that Huxley created; it is given by the state as a combination of sacrament, aphrodisiac, and consciousness-altering substance. It's a world where government and religion have merged into a single entity, and the only real foe of such a state is dissension generated by unhappiness.
Any kind of negative emotion, be it anger, fear or sadness, would be instantly wiped out and replaced with "the warm, the richly coloured, the infinitely friendly world of Soma-holiday" where "Eyes shone, cheeks were flushed, the inner light of universal benevolence broke out on every face in happy, friendly smiles."
Every aspect of their lives is infantilized. Sex, rather than being an intimate act, is turned into a series of ritualized orgies. Instead of physical contact creating strong emotions, it served to numb intense feelings and prevent emotional connections. Taking Soma is institutionalized, and it doesn't just make people happy, it makes them "never want what they can't get." Not only do the people have no freedom, they willingly give it away. They want a dependable, easy uncomplicated pleasure that takes away all the messy and character-defining moments of being human, in part because that's all they've ever known.
Soma can be interpreted literally or as a metaphor for any number of things, including alcohol, religion, a sports team or any activity that serves as a distraction from not just the miseries of daily life, but also from the small joys that a full range of feelings can provide.

Soma is a drug that makes people feel better by altering their consciousness to a more dreamlike state. People take soma when they start to have bad feelings. It helps to take the edge off their psychic pain, and it also helps to improve pleasurable experiences. It is an important part of a world that has been engineering to reduce human suffering to a bare minimum.
We learn, more specifically, that soma helps people take a "holiday" from "malice" and "bad-temper." The drug also helps people get in the mood for the orgies that are part of the religious practice in the World State. Soma is part of the ritual preparation for the orgy.
When Bernard wants to be alone with Lenina hovering over the water in the helicopter, no other people around, Lenina, is distressed at the idea. She proposes soma as a solution:

. . .why you don’t take soma when you have these dreadful ideas of yours. You’d forget all about them. And instead of feeling miserable, you’d be jolly.

Linda, while on the Indian Reservation, uses peyote, which she likens to soma.
We can see from these examples that soma helps people feel better, helps numb people so that they don't have to think, and helps people achieve an altered state of consciousness so they can better enjoy rituals like orgies.

Single Variable Calculus, Chapter 7, 7.3-2, Section 7.3-2, Problem 12

Evaluate $\ln (2x + 1) = 2 - \ln x$.



$
\begin{equation}
\begin{aligned}

& \ln (2x + 1) + \ln x = 2
\\
\\
& \ln x (2x + 1) = 2
\\
\\
& e^{\ln x (2x + 1)} = e^2
\\
\\
& x (2x + 1) = e^2
\\
\\
& 2x^2 + x = e^2
\\
\\
& 2x^2 + x - e^2 = 0


\end{aligned}
\end{equation}
$


Using Quadratic Formula


$
\begin{equation}
\begin{aligned}

x =& \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\
\\
x =& \frac{-1}{ \pm \sqrt{(1)^2 - 4(2) (-e^2)}}
\\
\\
x =& \frac{-1 \pm \sqrt{1 + 8e^2}}{4}


\end{aligned}
\end{equation}
$


Since, $\displaystyle x = \frac{-1 - \sqrt{1 + 8e^2}}{4}$ will not satisfy the original equation because $\displaystyle \ln \frac{-1 - \sqrt{1 + 8e^2}}{4}$ is undefined.

Therefore, $\displaystyle x = \frac{-1 + \sqrt{1 + 8e^2}}{4}$

Hello, I'm looking for a topic for a documentary project, but I didn't come up with anything good. Any idea will work! Thanks in advice!!

Let’s begin by defining what a “documentary project” is.  A documentary is a nonfiction research product in which a researcher gathers facts into a coherent, organized presentation designed to clarify a topic for its readership or audience.  So the first step for a student is to examine your interests and areas of expertise, since you will be dealing with the topic in depth for a considerable length of time.  You might want to list the documentaries that have impressed or influenced you in the past – perhaps on a science TV channel or in a book on a documentary subject.  Next, look at your sources of information; do you have any special access to information, beyond mere googling.  For example, you might have access to a museum or art collection because of some special connection with a staff member.  Finally, choose a topic that works well with the medium your final product will assume: for example, if you choose music as your topic, it works well if your project presentation is a recording, but if it is visual, an art or photography topic may work better.  If your final presentation is a written essay or speech, you might want to choose a language or literature project.  So, to sum up, first, think of a topic that will hold your interest for a long time; second, choose a topic that allows you to make use of otherwise inaccessible sources; finally, select a topic that is compatible with the mode of final presentation.

What does Polonius want Reynaldo to do when he gets to France in act 2?

Polonius has hired Reynaldo to spy on Laertes while he's studying in Paris. Polonius has already given his son lots of fatherly advice ("Neither a borrower nor a lender be . . .") but it's clear that he doesn't quite trust Laertes to behave himself, surrounded as he'll be by all the temptations of youth. Polonius is worried that Laertes will behave in a way that will bring shame and dishonor to the family name, so he instructs Reynaldo to put about false stories of Laertes's alleged debauchery as a means of finding out from his friends and acquaintances what he's really been up to.
This whole unedifying episode illustrates once again Polonius's penchant for devious manipulation. Not content with sending one of his lackeys to spy on Laertes, later on in the play he embroils his own daughter, Ophelia, in a sordid plot to discover the reasons behind Hamlet's apparent madness.

We can find the answer to this question in act 2, scene 1, which opens with Polonius briefing Reynaldo on his mission in Paris. Polonius tells Reynaldo to "inquire me first what Danskers are in Paris" and what company they keep, knowing that Reynaldo will soon discover through these inquiries that "they know [his] son," Laertes. Having ascertained this, Reynaldo is tasked to then claim "some distant knowledge" of Laertes, such as that Reynaldo is a friend of the family but not close to Laertes personally.
Polonius then wants Reynaldo to "put on [Laertes] what forgeries" he pleases—that is, to tell those he meets in Paris that Laertes is given to "wild and unusual slips," not sufficient statements to completely ruin his reputation but enough to suggest that he is a "wild" youth. Polonius gives some suggestions of what to cite, such as "drinking, fencing, swearing, quarrelling." These would all be completely untrue rumors, but having spread them, Polonius feels the people who know Laertes in Paris would be more inclined to tell their own stories in return about what Laertes is actually doing there.

How do you define the concept of social classes?

Social classes are the divisions of human beings in a hierarchal structure based on economic, cultural and political elements. This concept is often divided into the high, middle, and low classes. While there are many uses for social classes, such as those in sociology, I believe that they are primarily socio-economic. Those who enjoy large amounts of wealth are in the higher class. The middle and lower classes possess smaller amounts of wealth and are often considered poor. Another element to these classes that helps make some distinctions is education. For instance, the middle class is largely more educated than the lower class. This distinguishes the educated middle class from the working lower class. Finally, social classes can also be political in nature. Socialism aims to provide a classless society because of the economic undertones and disadvantages in the capitalist view of social classes.

Social classes refer to divisions in society. They are usually based on economic or social status. There are many ways that different societies divide people into different social classes. More prestige and political influence typically accompany people of the upper classes. In most societies, the population of lower classes outnumbers that of the upper classes.
Most commonly social class is based mainly on economic wealth. The wealthiest people in a society occupy the upper class and the poorest make up the lower class. There can also be a middle class which consists of educated workers.
Sometimes education and occupation are used to separate the classes. This is the case when we see terms such as "working class" or "professional class."
Family and birth determine class in some societies. In these societies, some people are born into upper, or noble classes, while others occupy the peasantry. Clearly, the upper classes enjoy more privileges than the lower classes. In these types of societies, there tends to be very little mobility between classes.
http://udel.edu/~cmarks/What%20is%20social%20class.htm

Explain how far you think shakespeare presents lord capulet as a good farther

What constitutes a good father is notoriously difficult to pin down with any degree of accuracy. Furthermore, in examining this question, we need to acknowledge the huge cultural differences between Shakespeare's day and ours. The best procedure is to set out how Shakespeare presents the character of Lord Capulet and then make up our own minds as to whether he can reasonably be described as a good father.
At the start of the play, Lord Capulet appears to be quite a sympathetic character. In Act I Scene II he's talking with Count Paris, one of Juliet's suitors. Paris has requested Juliet's hand in marriage, but initially, her father dissuades him. Juliet's too young:

"But saying o'er what I have said before:My child is yet a stranger in the world,She hath not seen the change of fourteen years;Let two more summers wither in their prideEre we may think her ripe to be a bride."

So far, so good. It seems that Lord Capulet is genuinely looking out for Juliet and has her best interests at heart. But before long, Capulet relents and agrees to marry off Juliet to Paris. In keeping with the conventions of the time, the proposed match is a power marriage, the cementing of a political alliance between two prominent aristocratic families. Like other women of her time and class, Juliet is little more than a bargaining chip in a formal business arrangement.
Juliet is dead set against her arranged marriage to Paris. And as the nuptials approach, she becomes ever more indignant that she won't go through with the ceremony. She's head over heels in love with Romeo and simply cannot imagine being apart from him:

"Now by Saint Peter's Church, and Peter too,He shall not make me there a joyful bride.I wonder at this haste; that I must wedEre he that should be husband comes to woo.I pray you, tell my lord and father, madam,I will not marry yet; and when I do, I swearIt shall be Romeo, whom you know I hate,Rather than Paris:--these are news indeed!" (Act III Scene V).

But Capulet, the paterfamilias, won't hear of it:

"Hang thee, young baggage! disobedient wretch!I tell thee what,--get thee to church o' Thursday,Or never after look me in the face:Speak not, reply not, do not answer me;" (Act III Scene V).

How dare Juliet defy her father! How dare she be so ungrateful! If Juliet refuses to marry Count Paris, then Capulet will personally drag her to the church himself. His "fingers itch," clearly implying that he wants to beat some sense into his wayward daughter. The mask of benevolence appears to have slipped. Lord Capulet is absolutely furious at his paternal authority being so wilfully undermined. At the same time, we have to make a judgement as to whether Capulet is acting in character, or simply doing what's expected of him as the head of an aristocratic household, protecting his daughter's honor and his family's good name.
There's little doubt, though, that Capulet is genuinely crestfallen when he learns of what he thinks is Juliet's death on the eve of her wedding. There is nothing remotely conventional about his heartbroken response this time:

"Death, that hath ta'en her hence to make me wail,Ties up my tongue and will not let me speak." (Act IV Scene V).

We need to bear in mind that Juliet is actually still alive at this moment. This adds a touch of authenticity to her father's grief. Capulet, then, is a more complex character than we might think. While on the one hand he loves his daughter, he still retains an unthinking adherence to the prevailing social standards of the day. Realistically, he has no other choice. Verona at that time had a rigidly hierarchical society, one in which everyone was expected to perform certain functions conducive to the city's overall stability. In that sense, Lord Capulet is as much a victim of his time as Juliet. Whether this makes him a good father or not, is a matter largely for conjecture. But Shakespeare has been skilfull enough to present us with a suitably ambiguous picture, one that allows us to draw our own conclusions.
 
 

Explain how tone, actions, and words were used by the characters to display racism in To Kill a Mockingbird?

Mrs. Dubose's words demonstrate racism in To Kill a Mockingbird. One day Scout and Jem are walking into town. Jem, who recently celebrated his birthday, agrees to buy Scout a baton. Mrs. Dubose begins to interrogate the children with questions about where they are going and what they are doing. She insists that the children are up to no good, and she proposes that Scout will never be able to accomplish anything more than "waiting for tables at the O.K. cafe" if she does not change her behavior. Jem and Scout maintain their composure despite Mrs. Dubose's verbal attacks toward them.
However, Mrs. Dubose directs her next attack at Atticus Finch, their father. This upsets Jem far more (and leads him to take his anger out on Mrs. Dubose's flower garden a bit later). Mrs. Dubose says to the children,

"Not only a Finch waiting on tables but one in the courthouse lawing for niggers! . . . Yes indeed, what has this world come to when a Finch goes against his raising? I'll tell you! . . . Your father's no better than the niggers and trash he works for!" (ch. 11)

While this scene expresses Mrs. Dubose's disapproval of Atticus Finch's choices, it also reveals her immense racism. She believes that it is morally wrong for Atticus to defend an African American man. She says that this behavior is "against [Atticus's] raising." Additionally, she equates dark-skinned people with trash and suggests that Atticus must also be trash for defending Tom Robinson.
A significant action in the book that reveals racism is seen in chapter 15 when Heck Tate and several other men come to see Atticus after hearing rumors of possible trouble when moving Tom Robinson to the county jail. When the men arrive, Jem asks Heck Tate and his companions if they want to come inside. They refuse his offer but want Atticus to go outside to talk to them. This refusal shows the distance between Atticus and these men. The men do not want to be closely associated with Atticus and his family at this moment. Soon later, Mr. Link Deas, another visitor, explains his thoughts:

"—don't see why you touched it [the court case] in the first place. . . . You've got everything to lose from this, Atticus. I mean everything" (ch. 11).

Mr. Tate, Mr. Deas, and the other men do not understand Atticus's decision to support an African American man at court. They insinuate through their words and actions that a black person's life is worth less than a white person's life. They can't understand why he would risk the comfort and well-being of his family for Tom Robinson. Atticus contradicts this idea in his response:

"Link, that boy might go to the chair, but he's not going till the truth's told. . . . And you know what the truth is." (ch. 11)

Atticus is determined to defend Tom Robinson because he believes that Tom is telling the truth. He does not defend people because of their skin color; he seeks to promote justice, alone.

Are Hallows and Horcruxes connected to Celtic mythology?

Author J.K. Rowling has openly stated that parts of the Harry Potter books are based upon Celtic and British mythology, as well as Greek myth and the Bible. Hallowed items are very common parts of the folklore and mythology of the British Isles, with variances on the tale from place to place. The Irish-Celtic tradition tells a story of an ancient race of people who brought Four Treasures from the Otherworld to the island of Ireland. Among these Four Treasures are two items which have counterparts in the Deathly Hallows myth—the stone and the wand. The Stone of Destiny is supposed to "cry out" whenever the true King of Ireland is nearby, and the Spear of Lugh is an unbeatable weapon. The Resurrection Stone, of the Harry Potter series, does not have the same abilities as the Stone of Destiny, but it is quite probable that Rowling liked the idea of a magical stone and incorporated it into her work. The Elder Wand is plainly drawn from the Spear of Lugh, and variations on the myth describe the spear alternately as a staff or wand. 
The third Hallow, the Cloak of Invisibility, is drawn from a later mainland British mythology—the Arthurian legends. In this tradition, there are Thirteen Treasures of Britiain, including a mantle (also called a hood or cloak) which gave Arthur the power to be invisible. 
As for the Horcruxes, the idea of using a physical object to store a part of one's soul for safekeeping in the event of bodily death is most likely drawn from Slavic mythology—as opposed to British or Celtic—and the tale of Koscei the Deathless. Koscei is a character of Slavic mythology who is known for hiding his soul in various animal or object vessels. In one telling, he hides his soul in a needle inside of an egg inside of a duck inside of a rabbit inside of a locked chest! Only by destroying this vessel can Koscei really be killed. This myth might've made its way to the British Isles in one of the many waves of Northern European migration, or Rowling might've come across it in her own studies. 
The items Voldemort chose for his Horcruxes and their respective powers or special qualities may also be drawn from myth. Let's start with one which is reminiscent of the Koscei narrative—Nagini. Voldemort hid a portion of his soul in his magical pet snake, who could fight off or run from attackers. Again, this is a parallel to Slavic mythology, but snakes are such an important creature to Voldemort and the Harry Potter series that there's no better choice for an animal vessel.
As for the other six Horcruxes, several are highly reminiscent of British mythology. The Sword of Godric Gryffindor is special because it can only be summoned by a true Gryffindor and someone who is loyal to Albus Dumbledore. Swords are numerous in British mythology, and Gryffindor's sword has some parallels to the mythic Exaclibur or Caledfwlch. Only the true King of Britian could (variably) use, lift, or summon this sword.
Ravenclaw's Diadem, Slytherin's Locket, and Marvolo Gaunt's Ring do not have any precise parallels in British mythology, but these sorts of valuable items with special powers are a theme in many myths. Similarly, Hufflepuff's Cup does not have a precise parallel, but it does resemble many a mythic cauldron of British myth. Food and its multiplication are major themes in British myths, with several stories telling of magical cauldrons that multiply and/ or improve the flavor of any food put inside it. Hufflepuff's Cup does not multiply what is inside, but the copies of the cup from Gringotts Wizarding Bank's Vault multiply themselves when touched.
The diary and Harry do not have any parallels I am aware of in British mythology.
Just for fun, let's consider one more part of the Harry Potter series drawn from British mythology—wizard's chess! In the Harry Potter universe, witches and wizards enjoy passing the time by playing chess with figures who move themselves across the board as commanded. In British myth, Gwenddolyn (also spelled Gwenddolau) was a king and friend of Merlin who owned a golden chessboard with silver pieces who would move about it as instructed!
https://harrypotter.fandom.com/wiki/Deathly_Hallows

https://harrypotter.fandom.com/wiki/Horcrux

https://valeriefrankel.wordpress.com/2012/05/15/the-real-deathly-hallows-in-welsh-mythology/

Why does Melinda refer to herself as a ''wounded zebra''?

It's Melinda's first day at high school. One thing we already know about her is how incredibly isolated and lonely she is. On her way to school, she was the only one on the bus who sat alone. This pretty much sets the scene for how she'll behave when she gets to school. Along with all the other ninth-graders she's herded into the auditorium for student orientation. Melinda looks around, making note of all the various high school clans. She doesn't fit into any of them.
Rachel, her ex-best friend, mouths the words "I hate you." Melinda tries to deal with the insult by biting her lip until it bleeds. Then:

I stand in the center aisle of the auditorium, a wounded zebra in a National Geographical special.

Melinda uses this metaphor to highlight just how lonely and vulnerable she feels at that specific moment. If you've ever seen a National Geographic wildlife special, you'll know that zebras often become separated from the herd by lions and other predators, which then makes it easier for them to attack and kill. Melinda doesn't have a herd to belong to, and she's surrounded on all sides by predators. One of these is Mr. Neck, a teacher, who rudely tells her to sit down.
After she does as she's told, Melinda notices another "wounded zebra" smiling at her. She introduces herself as Heather from Ohio. But there's no time for a chat. The lights go down and it's time for student orientation, or as Melinda calls it "The First Ten Lies They Tell You In High School." 

How does the assignment of Receiver differs from other assignments?

The assignment of being the community's Receiver of Memory is dramatically different from the other assigned occupations Jonas's peers are given during the Ceremony of Twelve. The Receiver of Memory is selected by the Committee of Elders and not assigned like the other occupations. The Receiver of Memory has the important assignment of preserving the community's memories of the past. In Jonas's highly structured, organized society, ideas and memories of the past are kept by the Receiver of Memory in order to protect the community from physical and emotional pain, starvation, and civil strife.
Unlike the other assignments, Jonas has a special set of rules that allow him certain privileges and restrict him from engaging in typical behaviors. Jonas is exempt from rules governing rudeness, is allowed to ask any questions, and is also permitted to lie. Jonas is forbidden from dream-telling, cannot discuss his training with anyone, cannot take medication for any pain or injury related to his training, and cannot apply for release. Along with Jonas's special rules and guidelines, his assignment as Receiver of Memory is extremely painful and enlightening. Each day Jonas has an opportunity to experience something new and gains perspective on what life was like before Sameness.

Why is Curley's wife so lonely on the ranch in Of Mice and Men?

The primary reason why Curley's wife is so lonely is due to the fact that she is the only female on the ranch; she has no one to identify with, does not have a sympathetic husband, and lacks social interaction. Unlike the workers, who are all male and relatively enjoy each other's company in the bunk house, Curley's wife lives an isolated life and struggles to have social interactions with the men. The majority of workers on the ranch view her as a threat and think that she is a "tart" because she is constantly flirting with them.
When one views Curley's wife's behavior from her perspective, she may simply be attempting to have a conversation with the workers because she lacks opportunities to socially interact with others. In addition to her isolated position as the only female on the ranch, Curley's wife is also lonely because her authoritative husband forbids her from interacting with anyone else. Curley is an extremely insecure man, who does not trust his wife and is an abrasive, callous individual. Curley's refusal to sympathize with his wife and allow her to socialize with the workers also contributes to his wife's loneliness.

Curley's wife is lonely because there are no other women around to whom she can relate, and the ranch hands avoid any entanglement with her because she is the wife of the boss's son. She also isolates herself by cruel remarks to others.
Isolated on the large ranch, Curley's wife--who is but a genitive of her husband in this novella as she is given no name--hungers for attention and communication with others, although she often seeks this attention in the wrong manner. For, knowing that she is the only woman and that she is attractive, Curley's wife positions herself in a seductive manner:

A girl was standing there looking in. She had full, rouged lips and wide spaced eyes, heavily made up....She put her hands behind her back and leaned against the door frame so that her body was thrown forward. (Ch. 2)

But, even though she physically entices the men, they are afraid of tangling with Curley, who is very pugnacious, and can get them fired. Consequently, they do not respond to her seductive looks, nor do they engage in conversation with his wife. To her dismay, they instead leave her alone.
Curley's wife is also lonely because, although she desires company, she has the tendency to exploit the weaknesses of men with whom she has contact. For instance, she exploits the vulnerability of Crooks as she reminds him that he is a social inferior and outcast, rather than being friendly to him. So he retreats and will speak to her no more. 

What is the speaker implying about his feeling in lines 23-24?

James Whitcomb Riley's poem "When the Frost is on the Punkin" expresses the speaker's love of autumn. He describes the features of the season as well as his joy at welcoming it each year.
Lines 23 and 24 close out the third of four stanzas. The speaker exclaims,

O, it sets my hart a-clickin’ like the tickin’ of a clock,
When the frost is on the punkin and the fodder’s in the shock!

Line 23 describes the speaker's feelings: his heart is beating quickly with excitement. This implies that he feels a sense of joy when the autumn season begins. The reference to the clock could also indicates that he feels this way each year when fall begins. His enthusiasm is reliable and regular at this time of year. Line 24 repeats the same line that closes each stanza of the poem, which could again support the point that the speaker feels the same way each fall.
Other lines of the poem support the speaker's excitement, as well. In the first stanza he describes fall as a time "a feller is a-feelin’ at his best" (5). The second stanza describes the pleasant weather and the beautiful scenery. The speaker says, "Is a pictur’ that no painter has the colorin’ to mock" (15), meaning an artist cannot recreate the beauty of the season. Further, the use of exclamation points at the end of each stanza after the repeated line evoke the speaker's joy and enthusiasm for autumn.

Why was the colonization of Africa a bad thing?

This is not a question that can be fully answered here. Colonialism was born out of racist ideologies and the idea that the people of Africa were not entitled to keep either the land in which they were born or the natural resources that land contained. European countries warred with each other to conquer, divide, and mine Africa for its resources, without considering the long-term effects on native Africans. These effects can still be seen in Africa today and have left it a continent disconnected from its own history, divided by borders drawn on a map by Europeans, which separated tribes from each other and overrode the boundaries which had previously existed for centuries.
Today, Africa has a significant amount of impoverished and war-torn areas. Its natural resources have been stripped away, and its native cultures have been worn down by centuries of foreign values. Because the European colonizers sought to control their colonized peoples, they propagated an idea of African culture as inferior and even nonexistent, such that many Africans today still labor under the false impression that Africa—which has had its own great civilizations, including Ancient Egypt—has contributed nothing to the world. Africans can sometimes suffer from a loss of identity. In South Africa, Apartheid was an overt demonstration of the racism that drove colonial expansion, with black Africans demeaned, diminished politically, and stripped of their lands in favor of whites.
During the colonizing years, thousands upon thousands of Africans were massacred by European colonizers. This may no longer be happening, but the damaging effects of colonialism—the imposition of foreign ideologies, which held that black people were inferior and that they must adhere to a social structure not their own—are still strongly felt in Africa today.

How do women are act immorally in The Decameron?

In many of the stories in The Decameron, women are more sinned against than sinning, but in the third story on the third day, a woman does plot to cheat on her husband--and uses an unwitting friar to make this happen.
This woman has been married against her will to a rich merchant. She's not too happy about this, especially as she had hoped to be married to an aristocrat. She decides to have an affair and picks out the man she desires. 
To communicate her wishes to the young man, she tells the local friar that this man has been flirting with her. She asks the friar to tell him to stop. The man at first protests his innocence when the friar speaks to him, but then realizes that the woman is communicating to him that she wants a flirtation. He stops by her house and flirts with her. Later, the woman tells the friar that the young man peeped into  her window and saw her naked. The friar tells the young man he shouldn't do that.  The young man shows up at her window, and the two make love. They also make fun of the woman's husband and the friar. 
The stories in The Decameron are often bawdy, for the travelers escaping the plague wanted to entertain themselves as they journeyed. 

int tan^6(3x) dx Find the indefinite integral

To evaluate the integral int tan^6(3x) dx , we apply u-substitution by letting:
u =3x then  du = 3 dx or  (du)/3 = dx .
Plug-in the values, we get:
int tan^6(3x) dx =int tan^6(u) * (du)/3
 Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int tan^6(u) * (du)/3= 1/3int tan^6(u) du
Apply integration formula for tangent function: int tan^n(x)dx = (tan^(n-1)(x))/(n-1)- int tan^(n-2)(x)dx .
1/3int tan^6(u) du =1/3 *[(tan^(6-1)(u))/(6-1)- int tan^(6-2)(u)du]
                             =1/3*[(tan^(5)(u))/(5)- int tan^(4)(u)du]
Apply another set integration formula for tangent function on int tan^(4)(u)du .
int tan^(4)(u)du =(tan^(4-1)(u))/(4-1)- int tan^(4-2)(u)du
                          =(tan^(3)(u))/(3)- int tan^(2)(u)du
For the integral of int tan^(2)(u)du , we may apply integration formula: int tan^2(x) dx = tan(x)-x+C .
int tan^(2)(u)du =tan(u)-u +C
 
Applying int tan^(2)(u)du =tan(u)-u +C , we get:
int tan^(4)(u)du =(tan^(3)(u))/(3)- int tan^(2)(u)du
                         =(tan^(3)(u))/(3)- [tan(u)-u] +C
                          =(tan^(3)(u))/(3)- tan(u)+u +C
Applying  int tan^(4)(u)du=(tan^(3)(u))/(3)- tan(u)+u +C . we get:
1/3int tan^6(u) du=1/3*[(tan^(5)(u))/(5)- int tan^(4)(u)du]
                              =1/3*[(tan^(5)(u))/(5)- [(tan^(3)(u))/(3)- tan(u)+u]] +C
                             =1/3*[(tan^(5)(u))/(5)- (tan^(3)(u))/(3)+ tan(u)-u] +C
                             = (tan^(5)(u))/15- (tan^(3)(u))/9+ tan(u)/3-u/3 +C
Plug-in u = 3x on (tan^(5)(u))/15- (tan^(3)(u))/9+ tan(u)/3-u/3 +C ,we get the indefinite integral as:
int tan^6(3x) dx=(tan^(5)(3x))/15-( tan^(3)(3x))/9+ tan(3x)/3-(3x)/3 +C
                          =(tan^(5)(3x))/15-( tan^(3)(3x))/9+ tan(3x)/3-x +C
 

Where is the "boxed in" motif in Death of a Salesman? How is this theme important throughout the play?

The idea of being “boxed in” is first mentioned in a line of Willy’s in Act I, but the apartment buildings are included previously in the stage directions.
Willy, complaining of the room being stiff, asks Linda to open a window, not noticing that they are already open. He then states:

The way they boxed us in here. Bricks and windows, windows and bricks.

After Linda comments that they should have bought the lot next door to them, he continues:

The street is lined with cars. There’s not a breath of fresh air in the neighborhood. The grass don’t grow any more, you can’t raise a carrot in the back yard. They should’ve had a law against apartment houses.

The stage directions refer to the house’s placement among the surrounding apartment buildings.

Before us is the Salesman’s house. We are aware of towering, angular shapes behind it, surrounding it on all sides.… As more light appears, we see a solid vault of apartment houses around the small, fragile-seeming home.

Thus, Arthur Miller tells the reader that as the Salesman’s home seems “fragile” among the “solid” apartment houses, so Willy’s existence is fragile. His desire for open windows and fresh air indicates his internal anxiety.
Throughout the play, there are further references to the back yard and Willy’s stated desire to grow vegetables there, including his stating he is going to buy seeds—which he actually does not do. Willy remains enclosed rather than extend himself outside the psychological box that confines him. When he does finally plant the seeds, it is because he has lost his grasp of reality, as he does so in the middle of the night; this serves as an indication of the tragedy to come, of losing his life.
Willy’s feeling of being confined and his inability to move beyond those confines are emblematic of his personality and his failures in his career. Willy lacks many of the necessary qualities of the successful salesman, and he has never moved up the ladder as he wished to do. Yet he retains belief in the American dream, even though the world of commercial hype has let him down. Willy is boxed in by his own attitudes, not just by the system’s restrictions. It is also appropriate that, when he finally ends his life, it is out on the road rather than inside his home, a kind of escape from the “bricks and windows.”
https://genius.com/Arthur-miller-death-of-a-salesman-act-1-annotated

The "boxed in" motif is part of the feeling of being trapped and unable to escape that pervades the play. This is represented in the play by Willy Loman, who becomes trapped by his failures as well as his lies. The world has moved on without him, as it no longer needs door-to-door salesmen, and the only client Willy can still keep is the one that he is having an affair with. He wants to keep his family happy as well as have them love and respect him. If they find out about his failing career or the affair, he fears that he will lose that love and respect that he has tried so hard to keep. When this happens, he feels he has only one option, to kill himself in an automobile accident so that his family can make it through with his life insurance. Some movie adaptations of the play visually place Willy in a box, and the actor visually shows that he is worn out and trapped.

y = 1-x^2/4 , 0

To find the area of this surface, we rotate the function y = 1 - x^2/4 about the y-axis (not the x-axis!) and this way create a surface of revolution. It is a finite area, since we are looking only at a section of the x-axis and hence y-axis.
The range of the x-axis we are interested in is  0 <= x <=2   and hence the range of the y-axis we are interested in is 0 <=y <=1
It is easiest to swap the roles of x and y , essentially turning the page so that we can use the standard formulae that are usually written in terms of x (ie, that usually refer to the x-axis).
The formula for a surface of revolution A is given by (interchanging the roles of x and y)
  A = int_a^b (2pi x) sqrt(1 + (frac(dx)(dy))^2) dy
Evidently, we need the function y = 1 - x^2/4 written as x in terms of y rather than y in terms of x . So we have
x = pm2sqrt(1 - y)
This describes a parabola, which is two mirror image sqrt curves when considered in terms of the y-axis. But we need only one half, the positive or the negative, to rotate the graph about the y-axis because the other half will be part of the resulting roatated object anyway. Without loss of generality (wlog for short) we can take the function to rotate about the y-axis as
x = 2sqrt(1-y)
To obtain the area required by integration, we are effectively adding together tiny rings (of circumference 2pi x at a point y on the y-axis) where each ring takes up length dy on the y-axis. The distance from the circular edge to circular edge of each ring is sqrt(1 + (frac(dx)(dy))^2) dy
This is the arc length of the function x = f(y) in a segment of the y-axis dy in length, which is the hypotenuse of a tiny triangle with width dy and height dx . These distances from edge to edge of the tiny rings are then multiplied by the circumference of the surface at that point, 2pi x , to give the surface area of each ring. The tiny sloped rings are added up to give the full sloped surface area of revolution.
We have for this function, x = 2sqrt(1-y) , that
frac(dx)(dy) = -1/sqrt(1-y)
and since the range (in y ) over which to take the integral is [0,1] we have a=0 and b=1 .
Therefore, the area required, A, is given by
A = int_0^1 4pi sqrt(1-y)sqrt(1 + 1/((1-y))) dy
This can be simplified to give
A = 4pi int_0^1 sqrt((1-y) + 1) \quad dy
= 4pi int_0^1 sqrt(2-y) \quad dy = - frac(8)(3) pi (2-y)^(3/2)|_0^1 
So that the surface area of rotation A is given by
A = -8/3 pi (1 - 2sqrt(2))
http://mathworld.wolfram.com/SurfaceofRevolution.html

what happens in chapter 6 of percy jackson

Chapter 6 of Percy Jackson and the Lightning Thief shows Percy exploring Camp Half-Blood and dealing with a troublesome student.
Percy is still coming to terms with his heritage as Chiron takes him around the camp, showing him the various features and people that live there. People are whispering about Percy and discussing how he killed the Minotaur; he's already famous at the camp.
He shows him the cabins where people live. Each one is dedicated to a particular god and the students related to that god live there. Since they aren't sure who Percy is related to, though, he can't be assigned to the cabin of his relation.
Annabeth relieves Chiron and shows Percy to Cabin 11, which belongs to Hermes. Anyone who doesn't know their heritage is welcome to stay there, because Hermes is the god of travelers and thieves. Percy is still having trouble accepting that he's related to god, but Annabeth tells him that if he wasn't, the food and drink they used to heal him would have killed him.
Clarisse, the daughter of Ares, comes and bullies Percy. She rips his hair out as she drags him to the bathroom to put his head in the toilet. When she tries, though, the water sprays out, misses Percy, and hits Clarisse. The force of it knocks her out of the bathroom. When it happens, Percy feels a tug in the pit of his stomach.
When he leaves the bathroom, Clarisse threatens him but Percy tells her that she can end up with a mouth full of toilet water again if she continues. She leaves and Annabeth reconsiders Percy, saying she wants him on her team for capture the flag.

In chapter 6 of Percy Jackson and the Olympians: The Lightning Thief, Percy is being led around Camp Half-Blood by his centaur tour guide, Chiron. As he's wandering around the camp, Percy begins to notice that he's attracting quite a few stares and glances from the campers.
Chiron shows Percy that there are twelve different cabins that the campers live in—each cabin is associated with a particular god, and the relatives of each god live in the appropriate cabin. Cabin eleven is the cabin of Hermes—who happens to be the god of travelers—and, because Percy has no other home yet, he is put in this cabin.
Percy continues to wonder how he could be related to a god, but his friend Annabeth suggests that he surely must be, since he was able to kill a minotaur.
Percy soon meets a mean young woman named Clarisse who attempts to haze Percy by giving him a swirly. Oddly enough, water spouts out of the toilet and onto Clarisse and her rude friends, all while Percy stays bone-dry.

How did an escaped slave live in the north?

When slaves escaped to the North, they had, in theory, their freedom. After the passage of the Fugitive Slave Act in 1850, slaves had to be more guarded about how they lived if they stayed in the North.
Prior to the passage of the Fugitive Slave Act, escaped slaves still had to be careful about how they lived their lives. There was a provision in the Constitution that said that slaves who ran away would not be free. This was known as the Fugitive Slave Clause. The Fugitive Slave Act of 1793 stated that slave owners could search for any slave that had run away from his or her owner. This law was not widely supported in the North. Vigilance committees would offer protection to the runaway slaves. These groups also assisted escaped slaves in trying to find work and find a place to live. However, runaway slaves still had to be careful if they continued to live in the North.
Once the Fugitive Slave Act was passed in 1850, slaves needed to be even more careful. Northerners were required by law to capture and return runaway slaves to their owners in the South. Federal commissioners would handle cases dealing with runaway slaves. These commissioners were paid more if they returned a runaway slave than if they freed a runaway slave. As a result, many runaway slaves went to Canada, where they would be completely free. The runaway slaves who stayed in the North had to live a low profile lifestyle in order to avoid being recaptured.
https://docsouth.unc.edu/neh/grimes25/summary.html

https://history.howstuffworks.com/historical-events/underground-railroad3.htm

https://www.history.com/topics/black-history/fugitive-slave-acts

Describe how Mr. Chips has a peaceful life with no worries at Mrs. Wickett's.

After he retires from many years of teaching at Brookfield, a boarding school for boys in England, Mr. Chips moves to Mrs. Wickett's house near the school. He is peaceful and happy here, because, despite the sadness of losing his wife after a brief marriage, he can look back on a happy and fulfilling life spent as a beloved teacher.
Second, he is a man of few and simple wants. A cup of tea, a warm fire, and a detective novel are enough to keep him happy and content. He enjoys remembering the old days at Brookfield, a school he liked from the beginning when he first arrived on a sunny June day.
Finally, Chips carries a sense of humor with him into old age. He even sees the humor in aging, and often when Mrs. Wickett comes in with his tea, she finds him crying tears that are mixture of remembering humorous incidences and experiencing a sweet sadness over days gone by.
Overall, because he has lived a good, quiet, and honorable life, Mr. Chips has a peaceful old age, looked in on and cared for by those who cherish him.

After returning from Germany for medical treatment, the retired Mr. Chips stays in a rented room at Mrs. Wickett's house near the school. Here he leads a very cozy, comfortable life, drinking endless cups of tea by the fire, marking the occasional exam paper and contributing articles to the old boys' magazine. Mrs. Wickett is a kindly old lady who used to be in charge of the linen room at Brookfield, so she knows Mr. Chips very well indeed. She also understands just how much Chips misses his late wife Katherine and how important it is for him to live in an environment in which he can experience the comforts of home.
Though retired from teaching at Brookfield, Chips still organizes his daily life according to the rhythms of the school day. For example, before retiring to bed for the night, he always winds up his clock after the last bell at Brookfield has rung. It would seem that you can take the master out of the school but you cannot take the school out of the master.

In Two Kinds, what advantages are offered to the child? What disadvantages? How typical is Tan’s story of the mother-daughter conflict? Explain.

In the story, the mother offers her daughter the advantage of learning to play the piano. In the mother's opinion, she is also offering her daughter the advantage of living in America, a country she feels rewards hard work and resourcefulness. The mother is convinced that her child has an advantage by having a parent who will make sacrifices for her well-being and future success.
As for disadvantages, it can be argued that the mother is putting too much pressure on her child to succeed. She harbors the conviction that her child can be a prodigy in some way, so she works tirelessly to make this dream a reality. In her zeal to make a prodigy out of her daughter, she fails to take several things into account. First, she fails to account for the possibility of her daughter experiencing burnout. She is adamant that every daughter must obey her mother implicitly. Second, she is determined to compete against other Chinese-American parents who have talented children. She fails to consider how her own inclinations and stressors will affect her child. So the child is disadvantaged by having a mother who is indifferent to her input regarding her future. 
As for how typical Tan's story of the mother-daughter conflict is, one can argue that mother-daughter conflicts have existed since the dawn of time. In some families, however, the animosity between the mother and daughter is so palpable that the relationship descends to one of dysfunction. In such a relationship, the mother can be so domineering that she destroys her daughter's sense of self. In "Two Kinds," Amy Tan profiles a typical relationship between an ambitious Chinese-American mother and her beleaguered daughter. The daughter struggles to forge her own identity in the face of daily pressure from her mother to conform to a narrow definition of success.
Tan's story is typical in the sense that it is a humorous and poignant story about how parental ambition can destroy an intimate connection between a mother and her daughter. It is also typical in the sense that many mothers (whether Chinese-American or of other nationalities) feel compelled to secure their children's futures, either because of a sense of competitiveness or a desire to protect their children from future want and suffering.
 

Ho claims that Vietnam's independence is consistent with the philosophical principles which the Allies claimed were paramount during World War II. What principles was Ho referring to, and does he make references to occasions where those principles were reasserted?

Ho Chi Minh is highlighting specific principles that were established in the Atlantic Charter of August 14th, 1941.  The Atlantic Charter was a post-war plan that was to be enacted at the conclusion of World War II.  Some of the more pertinent points in the charter are as follows: 

“First, their countries seek no aggrandizement, territorial or other;
Second, they desire to see no territorial changes that do not accord with the freely expressed wishes of the peoples concerned;
Third, they respect the right of all peoples to choose the form of government under which they will live; and they wish to see sovereign rights and self government restored to those who have been forcibly deprived of them
Fourth, they will endeavor, with due respect for their existing obligations, to further the enjoyment by all States, great or small, victor or vanquished, of access, on equal terms, to the trade and to the raw materials of the world which are needed for their economic prosperity;
Fifth, they desire to bring about the fullest collaboration between all nations in the economic field with the object of securing, for all, improved labor standards, economic advancement and social security.” (Source)

By analyzing these statements, one can see how Ho Chi Minh can apply them to the notion of independence from France.
France during World War II was completely overrun and controlled by Germany in what appears to be a similar fashion to how the French colonized Vietnam through economic imperialism.  The French were getting a taste of what the Vietnamese had felt under the yoke and rule of the French.
Ho Chi Minh reasserts these ideas in the Vietnamese Declaration of Independence by referencing not only the American Declaration of Independence but also the French Declaration of the Rights of Man and of the Citizen.

"All men are created equal. They are endowed by their Creator with certain inalienable rights, among these are Life, Liberty, and the pursuit of Happiness" This immortal statement was made in the Declaration of Independence of the United States of America m 1776. In a broader sense, this means: All the peoples on the earth are equal from birth, all the peoples have a right to live, to be happy and free. The Declaration of the French Revolution made in 1791 on the Rights of Man and the Citizen also states: "All men are born free and with equal rights, and must always remain free and have equal rights." Those are undeniable truths. Nevertheless, for more than eighty years, the French imperialists, abusing the standard of Liberty, Equality, and Fraternity, have violated our Fatherland and oppressed our fellow-citizens. They have acted contrary to the ideals of humanity and justice. In the field of politics, they have deprived our people of every democratic liberty.”

Source - New China News Agency, April 6, 1951.
As you can see, it was an effective tactic to make a profound point using the very words of their oppressors against them.
Ho Chi Minh highlights the ideas that all men are created equal and that freedom must be guaranteed to the people.  By pointing out that the French imperialists have abused the ideals of liberty and equality, he justifies independence by the same means the French did during the French Revolution as well as the Americans during the American Revolution.  The French would have a hard time justifying their economic control over Vietnam after what they recently experienced with Hitler's brutal takeover of France.
So by examining the declarations of independence as well as the Atlantic Charter, you can see where Ho Chi Minh's claims are not only appealing but logical as well.
https://avalon.law.yale.edu/wwii/atlantic.asp

Was the Gilded Age a facade?

To answer this question, one must first define the "Gilded Age" as well as "facade." The Gilded Age ran from around 1870 to 1900 in the United States and is characterized by population growth, technological advancements, and social progress. A facade is a false front meant to hide problems within a structure.
The Gilded Age was a facade because many historians attempt to highlight the advancements of the time, overlooking the many problems in the United States.
Population growth saw millions of "new immigrants" arrive from southern and eastern Europe. However, when these people arrived in the United States, they faced racism at the hands of the "old immigrants" from northern and western Europe. The West Coast of the United States saw an influx of Asian immigrants, who likewise were met with racist attitudes.
While technological advancements were important to the growth of America, they came at a cost. Working on the railroad was difficult and dangerous work, typically reserved for the new immigrants. Even working conditions in the urban factories were demanding. Employees were forced to work in dangerous conditions for extended shifts, and tired workers tended to make mistakes.
While some social progress occurred during the Gilded Age, a myriad of social issues remained. Many women worked toward voting rights and equal employment opportunities, but both of these were still decades away. Labor unions fought for workers' rights but were often crushed at the hands of the company. Politics were dominated by corruption, and several cities were completely owned by political machines.

In "The Tell-Tale Heart," why does the narrator have a "light heart"?

Toward the end of the story, after the narrator has killed, dismembered, and hidden the body of the old man in order to rid himself of the "vulture eye," he hears a knocking at his door. Though it is only four o'clock in the morning, the narrator says, "I went down to open it with a light heart, -- for what had I now to fear?" The implication, then, is that the narrator has a light heart because he has no fear of being caught. He has already taken "wise precautions" to be sure that the body will not be discovered and that no blood was left to stain the floors (he'd thought to use a tub to catch it all when he took the old man's body apart). He feels that he has no reason to fear anyone who might be knocking at his door at this hour because he has been so careful, so meticulous, and that he has committed the perfect crime.

Single Variable Calculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 17

State whether the function is even, odd or neither even nor odd.



$
\begin{equation}
\begin{aligned}

\text{ a)} f(x) =& 2x^5 - 3x^2 + 2\\
f(-x) =& 2 (-x)^5 - 3 (-x)^2 + 2\\
f(-x) =& -2x^5 - 3x^2 + 2\\
\end{aligned}
\end{equation}
$


.: The function is neither odd nor even


$
\begin{equation}
\begin{aligned}

\text{b) } f(x) =& x^3 - x^7\\
f(-x) =& (-x)^3 - (-x)^7\\
f(-x) =& -x^3 + x^7\\
f(-x) =& -(x^3 - x^7)

\end{aligned}
\end{equation}
$


.: The function is odd


$
\begin{equation}
\begin{aligned}

\text{c)} f(x) =& \cos (x^2)\\
f(-x) =& \cos ((-x)^2)\\
f(-x) =& \cos (x^2)

\end{aligned}
\end{equation}
$


.: The function is even


$
\begin{equation}
\begin{aligned}

\text{d)} f(x) =& 1 + \sin x\\
f(-x) =& 1 + \sin (-x)\\
f(-x) =& 1 - \sin x

\end{aligned}
\end{equation}
$


.: The function is neither odd nor even

What is the significance of the symbols and images in Seamus Heaney's poetry, with examples from his poem "After a Killing"?

Seamus Heaney's "After a Killing" is a poem about the Irish Troubles. Heaney uses symbols and imagery to emphasize not only the struggles of the people, but the inevitability of trouble returning to Ireland. The poem begins with the stark image of two men with rifles, and the suggestion that this image is not new—instead, they were "as if our memory had hatched them, / As if the unquiet founders walked again." This allusion brings to mind the idea of a collective racial memory ("our memory") and summons the image of the founders of Ireland, not at rest ("unquiet") but walking again among the hills. In contrast with the men with rifles, this is incongruous and unsettling.
The landscapes of Ireland are depicted through the use of images little elaborated upon and the use of enumeratio: "rain and scoured light and wind-dried stones / Basalt, blood, water, headstones, leeches." Each of these images summons a host of associations in itself: the first line speaks to the Irish weather, while "blood, water" evokes the Biblical "Blood is thicker than water," and "headstones, leeches" speaks to a history of death and illness.
The "stone house" in the poet's memory once caused the heart to "lift," but the contrast to the girl in the modern day is again unsettling—the food she carries seems plentiful, but "the mould fresh upon them" reminds the reader of the continuing rot and disorder in the state of Ireland, never eradicated.

Why does social stratification persist generation after generation?

Social stratification is a means of organizing (and limiting) access to power, prestige, and privilege in society by assigning an arbitrary value to certain attributes. Some forms of social stratification, like India's traditional caste system, are closed in that they have rigid rules which limit mobility. In the United States, socioeconomic class is a little more mobile and changes in a person's wealth or social power can affect their SES status. That being said, seemingly mobile, open, or fluid class status often comes with some hang-ups based on the present structure of stratification.
One of the features of human culture is that it is constantly undergoing transformation while retaining an element of continuity. The best way to understand this is through language. If you have grown up speaking the same language as your grandparents, consider some of the ways in which your particularities of speech differ. Do you always use the same terms and phrases? Do you know slang words that they don't? Probably! However, the general rules of your spoken language have most likely remained the same.
Social stratification persists because of the "general rules" of society that we have learned to function in, under, and through. Change in social stratification and the justification thereof does happen, but it can take a lot longer than just one or two generations to really be visible. Below I have attached a diagram which lists some of the ways social stratification and injustice may be perpetuated in society. Remember those "arbitrary values" I mentioned before? In most stratified societies, it has been determined that certain genders, biological sexes, races, ethnic identities, languages, religions, health status, and ancestries are preferable to others. The devaluation of certain identities is performed and experienced through the acts listed in the diagram below, and cyclically justified based upon those arbitrary values.
In order for social stratification to persist, these arbitrary values have to be taught and believed by the uppermost portions of a stratified society. It takes active un-learning of these arbitrary values for a society to really take action to remedy stratification. Without devaluation of one or more identities, social stratification cannot be justified.

How did railroads shape the development and settlement of the nation?

The rise of railroads in the decades following the Civil War (around 1865-1900) helped spur the growth of the industrial economy in America and also led to new settlement and commercial patterns as the country was tied together by faster, more efficient transportation. During the Civil War, Congress passed the Pacific Railway Act (1862), approving the building of a transcontinental railroad that would link railroads in the eastern states to the Pacific. Rather than one railroad, the transcontinental railroad was actually a system of several railroads that were funded by the federal government. In addition, the government provided land grants to these railroad companies. The railroad companies then leased or sold this land to settlers at cheap prices, attracting farmers and immigrants and promoting further westward settlement.
The growth of railroads also stimulated western settlement by providing economic opportunities. Many Chinese and Irish immigrants helped build the railroad, and the railroads created new economic markets. Farmers in the West now had faster, more reliable ways to ship their goods across the country. In addition, the West provided new markets for goods from the eastern states as more and more people moved West, and railroads facilitated faster and cheaper ways of connecting these regions. Not only could people travel further and faster, but so could goods. In 1888 Sears Roebuck used the first print catalog to advertise goods from watches to clothing and furniture, allowing consumers to order from the catalog and have goods shipped to them. By 1883, coordinating railroad schedules had become so important that the country was divided into four time zones.
Railroads also shaped the development of the economy by driving up demand for iron, coal, lumber, and steel, leading to the rise of new industries. Men like Andrew Carnegie (Carnegie Steel) amassed vast fortunes by creating monopolies in these industries. Railroads not only bought and used these commodities, but they also distributed them across the country. Steel produced in Pittsburgh could be used to build bridges in San Francisco; coal mined in West Virginia could be used to heat homes in Oregon.
Unfortunately, there were negative effects of the growth of the railroad industry. While railroad companies became important employers of much of the nation's workforce, these large corporations came to dominate, allowing them to charge high rates for shipping and passengers. When workers went on strike, which occurred numerous times in the railroad industry (most notably in 1877), the entire country could be affected when railroads could no longer run on schedule. Finally, the rise of railroads also meant the further decline of Native Americans' rights and the rise in conflicts with Native Americans over land. Aside from the defeat of General Custer at Little Big Horn in 1876, Native Americans suffered heavy losses to both federal troops and settlers. Tribes such as the Lakota Sioux and the Nez Perce were forced to move to reservations or assimilate into "American" society.

This story is often seen a partial allegory. What concepts do each of the three characters stand for?

The narrator tells us that Aylmer, Georgiana's husband, "had devoted himself . . . too unreservedly to scientific studies ever to be weaned from them by any second passion." He represents human pride and men of science: Aylmer's confidence in his own scientific abilities convinces him that he can remove the birthmark that Nature (or God) bestowed on his wife. He tells her, "'I feel myself fully competent to render this dear cheek as faultless as its fellow; and then, most beloved, what will be my triumph when I shall have corrected what Nature left imperfect in her fairest work!'" Aylmer feels that he can perfect Nature, that he can improve on something Nature, and by extension God, created. He suffers from severe hubris, a terrible pride that claims his wife.
Aylmer tells Georgiana, "'you came so nearly perfect from the hand of Nature that this slightest possible defect, which we hesitate whether to term a defect or a beauty, shocks me, as being the visible mark of earthly imperfection.'" Georgiana, then, represents human imperfection. Her red, hand-shaped birthmark prevents her from being "one living specimen of ideal loveliness without the semblance of the flaw." Such a thing, however—a perfect and flawless human being—is not possible. Natural things are marked by imperfection; our mortality might be termed an imperfection—we grow old, wither, and eventually die and decay. Perfection can only be achieved by the divine, and so when Aylmer successfully removes Georgiana's birthmark, he overreaches and tampers with Nature, and his wife must perish because human beings simply cannot be perfect. It is not our nature. The birthmark "was the fatal flaw of humanity which Nature, in one shape or another, stamps ineffaceably on all her productions . . ."
Aminadab, Aylmer's laboratory assistant, seems to represent faith or men of faith. He is named for a Biblical high priest, and he feels that "'If [Georgiana] were [his] wife, [he'd] never part with that birthmark.'" He seems to understand that it is her birthmark, a symbol in itself, that makes her human. When the draught prepared by Aylmer begins to work on his wife's face, the assistant breaks into a "gross, hoarse chuckle . . . Aminadab's expression of delight." It is true that Aylmer's science succeeds in removing the birthmark, but Aylmer's pride outstripped his moral sense, and his wife's life is forfeit. Aminadab seems to understand what Aylmer cannot: that humankind is not a more perfect creator than Nature, or God.

Write a research problem that would be best studied using a non-probability sample.

Non-probability sampling does not use a random sample, and, therefore, researchers can not assume that the sample represents the population as a whole. Non-probability sampling is often conducted on purpose when it is not feasible or economical to carry out a probability sample (which uses random selection). Sometimes, non-probabilty sampling is done by accident, when researchers, for example, only use college students in their studies (as such subjects are easily available to researchers in universities).
An example of when a researcher might want to use a non-probability sample is the study of what medical experts in the cardiology field think about a procedure such as a new method for heart surgery. This study will not involve large numbers of subjects but instead will choose from the small population of doctors who work in cardiology and will ask these doctors' opinions. Using such a sample is useful in this case because the researcher is not interested in what a wider sample thinks of the procedure, and the researcher knows that the doctors' opinions do not represent a random sample and therefore can not be generalized to larger populations--such as doctors as a whole or to larger populations. 

How does James Joyce criticize Father Flynn in his story "The Sisters"?

Joyce's depiction of Father Flynn in "The Sisters" is marked by hints, innuendoes, and vague suggestions. As such, we never get a full picture of who this man really was or what made him tick. The only portrait we have of him comes to us through the eyes of others, such as the narrator and the old priest's sisters. This means, inevitably, that what little information we are given about Father Flynn is partial, incomplete, and potentially unreliable.
Nevertheless, the allusive quality of Joyce's descriptions of Father Flynn does suggest a certain critical stance on the part of the author, both toward Flynn as a priest and as a man. To some extent, Father Flynn's paralysis is symbolic of the general cultural malaise that Joyce believed had hung over Ireland for centuries. Joyce also believed that one of the main components of this malaise was the malign cultural influence exercised by the Catholic Church over Irish society. Paralysis is a common theme throughout Joyce's stories, and it is clear from "The Sisters" where much of the blame ultimately lies for the cultural and intellectual stasis at the heart of Irish life.
At a number of points in the story, Joyce vaguely suggests that the relationship between Father Flynn and the young boy was potentially inappropriate:

Old Cotter looked at me for a while. I felt that his little beady black eyes were examining me but I would not satisfy him by looking up from my plate. He returned to his pipe and finally spat rudely into the grate."I wouldn't like children of mine," he said, "to have too much to say to a man like that.""How do you mean, Mr. Cotter?" asked my aunt."What I mean is," said old Cotter, "it's bad for children. My idea is: let a young lad run about and play with young lads of his own age and not be . . . Am I right, Jack?""

The use of ellipses after the words "not be" is suggestive. According to Old Cotter, there is something unhealthy and rather troubling about a young lad spending so much time in the company of an adult.
Later on, we discover that Father Flynn confessed to the boy that he was a simoniac. This is someone who has committed the sin of simony—the buying and selling of church privileges. At the very least, this would suggest greed and moral corruption on the part of the old priest.
Nevertheless, as Joyce's portrayal of Father Flynn is suitably ambiguous, we should proceed with caution before ascribing any definitive character evaluations to the author, negative or otherwise. Most, if not all, references to the priest in the story can be interpreted in a number of different ways. Consider this passage, for example:

Sometimes he used to put me through the responses of the Mass which he had made me learn by heart; and, as I pattered, he used to smile pensively and nod his head, now and then pushing huge pinches of snuff up each nostril alternately. When he smiled he used to uncover his big discoloured teeth and let his tongue lie upon his lower lip—a habit which had made me feel uneasy in the beginning of our acquaintance before I knew him well.

There are two ways in which we can examine this excerpt. On one hand, we could say that this shows Father Flynn to be rather sadistic: he smiles devilishly at a naive young boy as he struggles to recite the responses of the Mass. On the other hand, Father Flynn's smile could be one of recognition: his mind could be returning to the time in his own childhood when he had to go through the exact same ordeal. In fact, we know through his sisters that Father Flynn was of a nervous disposition himself, so it is perfectly plausible that his smiling at the young boy was perfectly harmless, even if it induced a profound sense of unease at the time.
Father Flynn's nervousness was the start of his paralysis—or so his sisters believe. One day he broke the chalice, a sacred vessel designed to hold the body and blood of Christ. There was nothing in the chalice when Father Flynn broke it, but the sisters remained convinced that this was the beginning of the end. It is the same in life, as in death: Father Flynn, lying in his coffin, has only a very loose grasp of the sacred Eucharist chalice.
Again, Joyce forces us to choose between two different but related interpretations. We could see Father Flynn as a symbol of the Catholic Church in Ireland, casting a pall of social and cultural paralysis over all who come into contact with it. Alternatively, we could see him as one of the Church's victims, his life stunted and ruined by a thankless devotion. Irrespective of whichever explanation we think is best, there can be little doubt that the main thrust of Joyce's criticism is firmly directed toward the Church itself. The question that remains is whether Father Flynn is somehow a victim of the Church or whether he is actively complicit in the spread of its malign influence upon his native land.

How are the poets Walt Whitman and T.S. Eliot similar and different in their writing styles?

Whitman and Eliot are similar in that their works, such as Whitman's "Song of Myself" and Eliot's "The Wasteland," are accounts of the way the individual reckons with reality. Whitman's poetry describes the idiosyncratic way in which one individual perceives reality, including the reality that comes from the senses, and makes sense of it. He writes in "Song of Myself":

"Houses and rooms are full of perfumes, the shelves are crowded with perfumes, /I breathe the fragrance myself and know it and like it, /The distillation would intoxicate me also, but I shall not let it."

From the perception of perfumes, Whitman thinks about how reality will affect his consciousness and how he will interpret it. 
Similarly, Eliot writes of sensory perception in "The Wasteland:"

"'You gave me hyacinths first a year ago; / 'They called me the hyacinth girl.'— / Yet when we came back, late, from the Hyacinth garden, / Your arms full, and your hair wet, I could not/Speak, and my eyes failed, I was neither Living nor dead, and I knew nothing."

Both poets use incoming sensory information and filter this information to make a decision about the ways in which their consciousness will interpret this information and make sense of it.
However, Whitman's perceptions of the world around him lead him to develop an essentially hopeful and cohesive view of the world around him. He writes, for example,

"The delight alone or in the rush of the streets, or along the fields and hill-sides, / The feeling of health, the full-noon trill, the song of me rising from bed and meeting the sun."

In his vision of the cosmos, people and nature are one, and he feels unified with the physical reality around him. His vision is also a very American one. He feels at home in the world and with "the grass I love," and he experiences spiritual regeneration from his interaction with the world.
Eliot's perceptions of the world around him, on the other hand, lead him to have a fractured and uncomfortable view of the world. He writes, for example, of "A heap of broken images, where the sun beats, / And the dead tree gives no shelter, the cricket no relief." While Whitman finds comfort in nature, Eliot feels only discomfort and a sense of alienation. While Whitman's view is distinctly American, Eliot's vision is rooted in the destroyed Old World. He writes of London that it is an "unreal City, / Under the brown fog of a winter dawn." Eliot's world is one of unreality and spiritual deadness, while Whitman's world is one in which he enjoys solidarity and spiritual renewal.

Beginning Algebra With Applications, Chapter 8, 8.1, Section 8.1, Problem 122

a. Which of the following expressions are equivalent to $x^2 - 5x + 6$?

I. $x^2 - 15x + 10x + 6$

II. $x^2 - x - 4x + 6$

III. $x^2 - 2x - 3x + 6$

All of the expressions are equivalent to $x^2 - 5x + 6$. Simplifying all the middle terms of each expression will give $x^2 - 5x + 6$.

b. Which expression in part a can be factored by grouping?

The expression $x^2 - 2x - 3x + 6$ can be factored by grouping. We have


$
\begin{equation}
\begin{aligned}

x^2 - 2x - 3x + 6 =& (x^2 - 2x) - (3x-6)
\\
=& x(x-2) - 3(x-2)
\\
=& (x-3)(x-2)

\end{aligned}
\end{equation}
$

What is the role of setting in "The Open Window"?

There are a few different aspects to the setting in this story. The first point to note is that the residence that the protagonist, Framton, arrives at, is described as a "rural retreat" and a "restful country spot." This seemingly idyllic setting lures the reader, and Framton, into a false sense of security. Accordingly, the macabre story that the niece relates seems all the more sinister because it seems so out of place.
Within the niece's story, we also have the settings of the moor and the marshes. Moors and marshes are settings often used in ghost stories (The Woman in Black, Wuthering Heights) and evoke a sense of isolation and eerie, untamed wildness.
Finally, the time of day at which Framton sees the three ghost-like figures walking towards the open window is also significant. Saki sets this moment in "the deepening twilight." Twilight in literature is often used to evoke an ominous atmosphere, because it is the time of the day when light is fading and darkness is taking over. Therefore, twilight is the perfect time (from a writer's perspective) to have the three ghostly figures return. It suggests that they are figures of the night, and of the darkness.

The setting of "The Open Window" is absolutely crucial in conveying Saki's ironic intent. The story takes place in a large, comfortable, Edwardian middle-class house in the depths of the English countryside. This is not a place where we'd expect anything especially horrific or terrifying to take place. That is, unless you happen to be Framton Nuttel, of course. He's staying in the countryside on doctor's orders, hoping to find a rest cure for his nervous disorder.
On the face of it, it would seem that a visit to the Sappleton residence could be just what the doctor ordered. And when Framton is introduced to a rather normal, ordinary-looking young lady, there doesn't appear to be anything about this social visit that might remotely damage his poor, frayed nerves. The apparently calm, tranquil, thoroughly respectable setting of "The Open Window" lulls both Framton and the reader into a false sense of security which makes Vera's gruesome shaggy dog story all the more effective.

Why does Charles Dickens draw a parallel between Paris and London in A Tale of Two Cities? How are the French characters depicted in the novel compared to the British characters?

I am going to answer your second question first. Charles Dickens did create a huge contrast between his French characters and the English, depicting most of his French characters as much more volatile and violent than their English counterparts. Compare Charles Darnay with his uncle, the Marquis St. Evrémonde. Evrémonde is haughty, arrogant, and heartless, the perfect example of French aristocracy. Darnay's blood is no less aristocratic, but his character is far more noble, kind, socially conscious, and concerned with justice. These are traits he shares with several of his English compatriots. Even the irredeemable Sydney Carton possesses more empathy and chivalry than the "noble" Evrémonde. This dichotomy presents in several character pairs: Miss Pross and Mme Defarge, Mr. Lorry and M. Defarge, Jerry Cruncher and John Barsad, and so on.
Now the question is why. Why juxtapose French volatility so glaringly against English stability?
Meltem Kiran-Raw, a Lecturer in English, Department of American Literature and Culture at Baskent University, explains:

In the eighteen-fifties, Charles Dickens was concerned that social problems in England, particularly those relating to the condition of the poor, might provoke a mass reaction on the scale of the French Revolution. In a letter written in 1855, for example, he refers to the unrest of the time as follows:
I believe the discontent to be so much the worse for smouldering, instead of blazing openly, that it is extremely like the general mind of France before the breaking out of the first Revolution, and is in danger of being turned . . . into such a devil of a conflagration as never has been beheld since. (Collins, Irene. "Charles Dickens and the French Revolution." Literature and History 1.1 [1990]. Page 42)

Kiran-Raw suggests that A Tale of Two Cities was further social commentary on Dickens's concern. Even in the novel, she maintains, he editorializes on his present-day England:

"The period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only" (1; bk. 1, ch. 1).

Other researchers at Stanford write that Dickens researched carefully for his novel and wrote a highly accurate summary of revolutionary France (dickens.stanford.edu), possibly to highlight that history was in real danger of repeating itself. However, by presenting his English characters in such an admirable light, I believe Dickens also gave his readers hope and encouragement that their society could rise above the social concerns of the day.
http://dickens.stanford.edu/tale/historical_context.html

http://www.victorianweb.org/authors/dickens/2cities/turlit12.html

what are some allusions in the odyssey?

In the first book, the gods discuss Orestes, the son of Agamemnon, alluding to a story that we are not told outright in this particular epic. Essentially, Agamemnon had been away, fighting in the Trojan War with Odysseus (among others), and, while he was gone, his treacherous wife, Clytemnestra, and her lover, Aegisthus, plotted his murder. When Agamemnon returned from the war, hoping to be greeted by a loyal and adoring wife, he was murdered by his disloyal wife's new lover instead. Orestes, Agamemnon's son, then grows up and kills his mother, Clytemnestra, as well as Aegisthus, proving himself to be a good and loyal son for avenging his father's death. At various points in the narration, Telemachus is compared to Orestes because he, too, is proving himself to be loyal to his own long-absent father, Odysseus.