Functional behavioral assessment (FBA) is a popular topic in special education literature. What is FBA and how does it assist with behavioral challenges?

The Individuals with Disabilities Education Act (IDEA) states that a Functional Behavioral Assessment may be required for a child with a disability that has been out of placement for more than 10 days and displays behaviors that interfere with the learning environment. An FBA may be requested for a student as a proactive measure to address a pattern of interfering behaviors. While the procedures and timelines may vary by school district, typically a Special Education Counselor or an LSSP, Licensed Specialist in School Psychology, will begin the process by gathering data. Sources of data may include interviews with parents, administrators, and teachers, school discipline and attendance records, and report cards. A student’s FIE, or Full Individual Evaluation, may also be consulted to look for information that may be relevant to problem behaviors.
The purpose of the FBA would be to consider the possible causes for the behavior and to offer replacement behaviors. When the cause of an interfering behavior can be determined, steps can be taken to prevent the behavior. It is also important to consider whether the behavior occurs in a structured or unstructured setting. Preparing the student for more unstructured settings or transitions may decrease problem behaviors.

What does the word "phony" mean in the context of the book The Catcher in the Rye?

Holden Caulfield is depicted as an extremely cynical, hypercritical teenager who has a traumatic past and desperately wishes to avoid transitioning into adulthood. As a neurotic adolescent, Holden feels that the majority of adults and nearly every individual in the entertainment industry is a "phony." According to Holden, anyone who is the slightest bit insincere or fake is a phony, which includes seemingly genuine individuals like Mr. Spencer. Despite being a sympathetic, concerned adult, Holden considers Mr. Spencer a phony for laughing at the headmaster's lame jokes while he is being evaluated.
Holden's cynicism towards others and intolerance towards insincerity reflect his fear of entering the competitive world of adults. By labeling people phony, Holden is indicating that they are selfish, dishonest people who are primarily concerned with attaining wealth, improving their reputation, or advancing their social status. Overall, anyone who is insincere, is fake, or has ulterior motives is a phony in Holden's opinion.

"Phony" is one of Holden Caulfield's favorite words. He uses it quite a few times throughout The Catcher in the Rye. According to the standard meaning of the word a phony is someone who is fake. But Holden expands the meaning of the word to include just about everyone he comes into contact with. He still retains part of the word's original meaning in that he applies it to those who are not one hundred percent genuine. But in Holden's vocabulary, the word "phony" comes to be used indiscriminately to describe anyone he doesn't like. And there are plenty of such people in the world.
Holden is at a difficult age. He's trying desperately to find a place in the world, to assert his developing sense of individuality. This makes him rebel instinctively against anything that smacks of convention or outward conformity to rules and standards. Fellow students, teachers, actors, the people he sees at the cinema—none of them are true individuals in Holden's eyes; they've all been defined by other people's rules, standards, and expectations. Thus they are complete phonies, all of them. Holden doesn't see himself that way, though of course he does ironically enough behave like a phony himself when he spins a web of outrageous lies to Mrs. Morrow on the train in the guise of Rudolf Schmidt, the school janitor. But Holden is too immature, too lacking in self-awareness, to realize the irony in all of this.

What attitudes of the British Empire are expressed through "The White Man's Burden"?

Rudyard Kipling's poem "The White Man's Burden" expresses the idea that the British, Americans, and other colonizers from the West are doing native peoples a great favor when they come and take over their countries. Whites are pictured as members of a superior, Eurocentric culture that nobly sends its best young men to sacrifice themselves to bring the gift of civilization to people who Kipling calls "half devil and half child."
The poem also strongly implies that the "sullen" natives should be more grateful for the gift of white presence they are being offered, but also that, nevertheless, the whites should solider on patiently as they bear the "thankless" burden of colonizing. This includes being blamed and hated by the inferior people they are trying to help:

The blame of those ye better
The hate of those ye guard

To Kipling, the colonizers' purpose is:

To seek another’s profit
And work another’s gain

The poem never asks whether the natives want the white men bestowing the blessings of their "civilization" on them or if colonies operate primarily for the benefits of the white overlords. The attitudes expressed are the racist views of conquering peoples who can't understand why those whose country they've taken over might be resentful.

What are the similarities between a unitary and federal government system?

Federal governments, like that of the United States, have state-governments that operate between the national and the municipal level. The states themselves enjoy a certain degree of independence from the highest level of government. State laws are technically subservient to laws passed at the national level, but it is usually up to the national government to choose whether or not to enforce this. Usually, the lower levels of government are free to make any laws that are not already enumerated or that do not conflict with the laws of higher levels of government. Federal systems allow for a higher degree of civic engagement. It is often easier to engage with smaller municipal and state governments than with the larger national government. This allows citizens to have more of an ability to participate in and influence their local government. This also leads to more transparency in government, as there is usually more citizen oversight at local levels.
Contrast this to a unitary government that does not have lower levels of lawmaking bodies at the state level. All the political power is concentrated in a single body that governs the entire country. Cities and towns may have some local control, but their ability to make and pass local laws is severely limited and almost always must conform with the laws of the central government. Laws that are passed by the central government apply to the entire country and, therefore, may sometimes overlook the local needs of a particular place. Unitary governments tend to be more efficient than federal ones. They are free from the many bureaucratic levels that exist between the different levels of government. Therefore, unitary governments can more quickly pass laws.

Both unitary and federal government systems can be defined by the relationship between the national government, representing the nation as a whole, and any subnational governments, representing subnational divisions like states or provinces. For example, within the United States of America, the national government is on the level of the nation itself, while each state maintains its own subnational or state-level government. 
Within unitary systems, such as the United Kingdom, the national government is supreme, and the majority of power is centralized within it. The national government delegates powers down to the subnational governments, which then exercise these delegated powers and implement policy decisions that originate within the national government. 
Federal systems, such as the United States, tend to have a weaker national government, with powers distributed among the national and subnational levels. This can sometimes lead to conflicts among jurisdictions. Consider the status of medicinal or recreational marijuana in the United States: it is legalized or decriminalized in a number of states while still remaining illegal on a federal level. 
In both systems, there is a great degree of variability in exactly how power is distributed. The United States was originally designed to have a weaker national government with more autonomous states, but, over the course of its history, the national government has consolidated more power. 
All that said, both systems are quite different in how they distribute power and execute matters of policy and law. In terms of similarity, it may only be possible to say that both systems are ways to administer a nation. Ultimately, the unitary/federal split is chiefly concerned with how power is distributed. How the government is formed, how laws are made, how administrations change—all of this is largely removed from the simple question of how power is distributed among administrative divisions. 
https://www.britannica.com/topic/unitary-state

A unitary system of governance features a strong central authority that controls the power in a country. A federal system of governance is based on the division of power between the national and local governments.
Similarities between the two systems of government include the following:
Both the unitary and federal systems of government consider elections as an important aspect of their existence. The two systems extend the opportunity to the citizens and/or different institutions to choose the leaders.
The unitary and federal forms of government are both systems of national administration. The administrative responsibility creates a sense of order and direction for the country.
The unitary and federal systems of government are both responsible for resource management in line with national administrative obligations.
The two systems of government are also responsible for policy formulation and implementation. The policies are important in achieving the set goals and objectives at the national and local levels.
The two systems are responsible for representing the peoples’ will and wishes in government.
The unitary and federal systems of government are responsible for representing the country in regional and international discussions and agreements.
http://guides.skylinecollege.edu/c.php?g=279117

There are not necessarily any similarities at all between these two systems other than the fact that both have governments.  These two systems can be quite different.
In a federal system, power is shared (by law) between a national government and local governments (often called state or provincial governments).  Neither level of government can legally take power away from the other level.  In a unitary system, things are different.  The national government is the only government that has the right to exist.  The national government can create local governments and give them powers, but it can always take those powers away.  The national government, in this system, is all-powerful and the local governments (if they exist) only have whatever powers the national government decides that they should have.
From this, we can see that these two have little in common.  Both systems can have national and local governments, but they do not have to.  Both systems can be democratic, but they do not have to be.  The only thing that they have to have in common is that they both have to have a national government of some sort.

Using only the reading provided, argue against some point the author makes about lying that you disagree with. Be sure to use quotes from the reading to support your answer. https://lesbianhistorygroup.files.wordpress.com/2016/10/adrienne-rich-women-and-honor.pdf (Some examples for assignment clarification purposes: Perhaps the author makes a distinction between this and this, what does she mean by this? She keeps using it for this, it’s X and not Y. Why is this important? Focus on one point and expound on it)

In this reading, the author argues that women are forced continually into lying because of their powerless state. The author writes, "We have been depicted as generically whimsical, deceitful, subtle, vacillating. And we have been rewarded for lying." In other words, women are not rewarded for being strong and honest in our society, but instead must practice deceit and lying to follow societal norms.

You may decide to disagree with a part of the author's writing. I chose the quote below:

"And she may also tell herself a lie: that she is concerned with the other's feelings, not with her own. But the liar is concerned with her own feelings."

The author is arguing that, although women are asked by society to concern themselves with other people's feelings and not their own, women, like everyone else, actually are concerned with their own feelings. I believe that this is true sometimes but not all the time. A healthy person balances concern for herself with concern for others. A woman can be concerned with others without neglecting herself; in fact, concern for others can enlarge one's concern for oneself. By caring about others, one becomes better and more powerful in her own mind and heart.
The following excerpt also gives a lot of food for thought:




"We have been expected to lie with our bodies: to bleach, redden, unkink or curl our hair, pluck eyebrows, shave armpits, wear padding in various places or lace ourselves, take little steps, glaze finger and toe nails, wear clothes that emphasised [sic] our helplessness."

The author equates the clothing and beauty regimens that women follow with a form of lying. There is some truth in this statement for some people. However, for others, these beauty regimens help them emphasize what they like about themselves. Curling one's hair, for example, may simply be a way to feel good about oneself rather than a form of lying. Clothes can enhance our sense of ourselves and our confidence rather than represent a form of deceit.

How are the lives of the three female characters in Alice Walker's "Everyday Use" symbolic, and how are they significant to the theme of the story?

Alice Walker's short story "Everyday Use" examines the lives of black women in rural America in the 1960s. The story addresses the pivotal moment the African-American community was facing as it re-evaluated its identity amidst changing times. There are three female characters in the story: a mother and two daughters, Dee and Maggie. Each woman in the story represents a facet of the choice African American women faced at that moment in history.MaggieMaggie is the younger daughter who still lives at home with her mother. She is soon to be married and partakes in familial traditions, such as sewing quilts. Maggie represents a woman who has chosen to keep African-American traditions alive and close as she moves into adulthood. Dee/WangeroDee is the daughter who has moved out of the house and is with a Muslim man. She is in the process of redefining her identity. Instead of embracing her rural heritage, she is distancing herself from it. She instead chooses to identify with African tribal heritage in a movement known as Cultural Nationalism. She has changed her name from Dee to Wangero. At birth, she was named after her Grandma Dee. The fact that she is deciding to no longer identify with that familial name illustrates the way she is distancing herself from her roots. Dee represents the choice to distance the past rather than keep it close.MotherThe mother serves as the entity which can observe these two daughters and two choices at once, then make a decision between them. Walker's choice to use first person narration creates a vehicle to invite the reader into the decision between the daughters. Walker ends the story with the mother deciding to give the quilts to Maggie. With this ending, Walker shows that the better path for African-American women is to keep tradition close, rather than put it at a distance.

Do you think Belgium’s compensation structure for employee sick leave is too generous? If so, what could better compensation involve?

In Belgium, the sick day is very loosely regulated, and it is permissible for employees to take practically unlimited leave and retain their position. Studies have shown that the average sick leave taken in Belgium is just shy of twenty days a year, roughly twice the European average and some four times the American average. The policies are most likely at least somewhat exploited, but there is also a legitimate depression epidemic that is gripping that nation.
There are many proposed solutions, but a comprehensive approach will likely help the most. Counseling and clinical services should be offered on site and should be recommended for individuals taking above-average amounts of sick leave. Additionally, government and corporate caretakers could be used to check on the ill to help rehabilitate and reintroduce them into the workplace. The proposed solution is typically not to remove permissive sick day policies like Belgium's, but to help cure the underlying issues that cause people to use a large number of sick days.

Belgium's employee sick leave program allows workers to take a great deal of sick leave, or even unlimited sick leave. One study, reported in "Belgians Take Lots of Sick Leave, And Why Not, They're Depressed" in the Wall Street Journal on January 9, 2009, showed that Belgian government employees in some departments had an average of 35 sick days per year (the national rate was half that). The U.S. average of sick days per year is 4.5, and the European average is 11.3 days. Sick days in Europe cause a loss of 1.3% to GDP (Gross Domestic Product). In Belgium, employers pay for sick leave for 30 days, and then, generally, government insurance pays for as long as the employees need it. While people pay for these benefits through very high taxes, it could be argued that mandated paid sick leave can leave workers less-than-motivated. 
Some of the reforms mentioned in the Wall Street Journal article include having government workers check on sick employees at home to see how they are. In this way, they can encourage workers who are functional to return to work, or they can encourage people with mental health issues to get the help they need. However, given Belgium's generous sick leave policies, it is likely that high rates of absenteeism will remain a problem unless workers are subject to more rigorous medical exams or unless their pay starts to decline a great deal after a period in which they don't work. 

Do I need a tourist card to visit the Dominican Republic?

I entered without one? they never asked me for one..

If you are an American citizen, you can visit the Dominican Republic with either a passport and visa or a passport and tourist card. You must have (with your passport) either a visa or a tourist card. If you have a visa, you will not need a tourist card.
According to the Embassy of the Dominican Republic in the United States:
 

1) Does an American citizen require a Visa to enter the Dominican Republic as a tourist?
No, American citizens do not require a visa to enter the Dominican Republic as tourists. You just need to purchase a tourist card (Fee US$10.00) online... or at your port of entry in the Dominican Republic.
 
2) Is a visa required for non US citizens to enter the Dominican Republic as a tourist?
Any person who can legally travel or reside in the United States, Canada and the European Union (including Great Britain) does not need a Visa to visit the Dominican Republic for tourist purposes and can enter the Dominican Republic with a Tourist Card and a valid passport.

 
According to the United States Department of State, under Entry, Exit, and Visa Requirements, "Visitors who do not obtain a Dominican visa must purchase a tourist card at the airport for 10 USD upon entry or online prior to travel." So, you will only need to purchase a tourist card (which allows you to stay up to 30 days) if you have not obtained a visa.
Please refer to the links below, which also includes phone numbers for the United States embassy in Santo Domingo, Dominican Republic.
http://www.domrep.org/faqconsular.html

https://travel.state.gov/content/travel/en/international-travel/International-Travel-Country-Information-Pages/DominicanRepublic.html

What major incident happened to Melinda in Speak?

Speak begins with a central mystery: what happened to Melinda? She is ostracized from her high school community for calling the police to bust a party over the summer, and she feels like she can't tell anyone what's happened. Even when people insult and confront her about ruining the party, Melinda doesn't fight back or even acknowledge what really happened. She slips into a long period of silence, literally and metaphorically.
Only in the third marking period—much later in the novel—does Melinda relive that night at the party. It was her first high school party, and no one's parents knew where she and her friends really were. After drinking too much too quickly from nerves, she goes outside and encounters Andy Evans, a handsome senior boy who looks like a "Greek God." He recognizes that she's drunk as she leans against him, and he reaches down to grab her butt, then kisses her twice, hard. Because she's drunk, she doesn't quite realize what's happening, but then they're on the ground, and he rapes her; as she struggles and tries to scream, he covers her mouth. Once it's over, she calls the police for help, sealing her fate as a social outcast. Because everyone judges her and bullies her for calling the police, she doesn't feel like she can speak out about what happened to her.
From page 135 of Speak:

We were on the ground. When did that happen? "No." No I did not like this. I was on the ground and he was on top of me. My lips mumble something about leaving, about a friend who needs me, about my parents worrying. I can hear myself—I'm mumbling like a deranged drunk. His lips lock on mine and I can't say anything. I twist my head away. He is so heavy. There is a boulder on me. I open my mouth to breathe, to scream, and his hand covers it. In my head, my voice is as clear as a bell: 'NO I DON'T WANT TO!' But I can't spit it out. I'm trying to remember how we got on the ground and where the moon went and wham! shirt up, shorts down, and the ground smells wet and dark and NO!—I'm not really here, I'm definitely back at Rachel's, crimping my hair and gluing on fake nails, and he smells like beer and mean and he hurts me hurts me hurts me and gets up
and zips his jeans
and smiles.

The major incident that happened to Melinda was that she was raped.  
That particular incident happens before the events of the book begin.  In the summer before beginning her freshman year of high school, Melinda went to a party for high school students attending Merryweather High School.  The party had students of all ages there, and alcohol was present as well.  Melinda had been drinking too, but she did not give sexual consent to Andy Evans.  Andy Evans raped Melinda.  Melinda called the police from the party, and consequently all of the students at Merryweather High School treat her very poorly.  Over the course of the novel, Andy antagonizes Melinda to no end and tries to rape her a second time.  His actions are discovered, and people now realize what actually happened to Melinda at the party. 

What evidence can you find to support the interpretation that A Doll's House is not only about the Helmers’ marriage, but also about the institution of marriage itself?

In the very opening scenes of Ibsen's play, there is little to indicate clearly that the marriage of Nora and Torvald is dysfunctional. They appear devoted to each other and, at least in a nineteenth-century context, all seems normal. But this is precisely the point Ibsen is making about marriage in general, not just that of the Helmers. There is an inherent power dynamic we see in Torvald's cute epithets for Nora, his "mild" criticisms about her eating sweets (interestingly, not because she'll gain weight but because she'll ruin her teeth), and the coquettish way she thanks him for money. From our standpoint 140 years later, all of this seems a bit much, and Ibsen as well, despite his time's conventions, recognizes the absurdity of it, which eventually becomes explicit as the plot progresses.
Nora, of course, is in the typical (and, therefore, characteristic of marriages of the time, not just her specific marriage) housewife position of being totally dependent on Torvald. Significantly, the one act of independence for which she is in trouble—taking out a loan under false pretenses by forging her father's signature—has been done for Torvald's benefit, to obtain money for the treatment of his illness years earlier. Her inability to tell Torvald about this is a symptom of the typical power dynamic and lack of equality in traditional marriage overall.
Also typical are Torvald's constant though seemingly good-natured criticisms of Nora over stupid little things. "She's forgotten everything I taught her!" he exclaims to Dr. Rank, when Nora does not dance according to his expectations. As most of the usual, arrogant husbands of the time, Torvald thinks himself an expert on everything, including dance. He goes ballistic upon reading the blackmail letter from Krogstad, pouring out a stream of abuse at Nora in the typical way of blaming the wife for everything. Though the situations in A Doll's House are unusual, given the fact of Nora's being blackmailed by Krogstad, the interactions between husband and wife are emblematic of "traditional" marriage in general, of Ibsen's time and later.

In "Trifles," Mrs. Hale notices that, while most of Mrs. Wright’s sewing is very neat, her most recent stitching is “all over the place.” Why does Mrs. Hale pull out the messy stitches?

In the one-act play Trifles by Susan Glaspell, a group of people come to a remote farmhouse to investigate the murder of John Wright, the owner of the farm. His wife, Mrs. Wright, is being held as a suspect. While Sheriff Peters, the county attorney, and Mr. Hale (who discovered the murder) walk around looking for clues, Mrs. Peters and Mrs. Hale wait in the kitchen. They talk about Mrs. Wright's loneliness and the deterioration of her joyful spirit after she married her husband.
While they wait, the women begin to find little clues suggesting not only Mrs. Wright's unhappiness but also possible abuse on the part of her husband. They come across pieces of quilt Mrs. Wright was sewing and notice that though most of the stitches in the quilt are "nice and even," the sewing on the last block is "all over the place." Perhaps Mrs. Wright was anxious and wasn't concentrating on what she was doing.
The women look at each other, as if suddenly aware that this could be an important indication of Mrs. Wright's state of mind. Mrs. Hale then begins to correct the sewing by pulling out the messy stitches and replacing them with neat ones. She says that bad sewing makes her fidgety, but the implication is that she is doing this to cover up Mrs. Wright's possible guilt. Although messy sewing would not at first seem a viable clue to the men, the women are able to use it to read Mrs. Wright's motivation for possibly committing the murder.
Later, the women notice the damaged bird cage and the dead canary in the box. They cover up this evidence as well. In their opinion, although Mrs. Wright may have killed her husband, it's possible that she was justified in doing so because of the way he had treated her. That's the real reason why Mrs. Hale pulls out and corrects the sewing, and also why Mrs. Peters hides the dead bird and does not show it to the men.

When Mrs. Peters asks Mrs. Hale why she is pulling out Mrs. Wright's hasty, messy stitching, Mrs. Hales says,

Bad sewing always made me fidgety.

Of course, that's not the real reason Mrs. Hale removes the stitches. It's clear that she knows that poor stitching is a sign that Mrs. Wright was nervous about something—possibly about having murdered her husband.
Mrs. Peters tells Mrs. Hale she shouldn't tamper with evidence. Mrs. Hale responds by saying she will simply fix the sewing. She then asks what Mrs. Peters thinks Minnie Wright was nervous about. Mrs. Peters suggests that perhaps Mrs. Wright wasn't nervous at all, but tired. Mrs. Peters say she sometimes sews "awful queer" when she is tired.
Both women clearly know that the detail of Mrs. Wright's sloppy sewing reveals a good deal about her state of mind and might even implicate her as guilty of murder. They try to cover up for her. While they can read the signs of what was going on and reconstruct the crime, the men dismiss and overlook these sorts of details as worthless "trifles."

Mrs. Hale takes the stitches out of the quilt because their hasty stitching shows Mrs. Wright was preoccupied and possibly indicates her guilt.
To the women, the quilt provides insight into Mrs. Wright’s mind. The men would not notice this, but women would. To the men, all the little domestic indicators are meaningless trifles. The women realize their true meaning. They understand Mrs. Wright was miserable.
When Mrs. Hale sees the quilt Mrs. Wright was working on, she notices the stitching is off.

MRS HALE: (examining another block) Mrs Peters, look at this one. Here, this is the one she was working on, and look at the sewing! All the rest of it has been so nice and even. And look at this! It's all over the place! Why, it looks as if she didn't know what she was about!

Again, the men would not notice this at first. Upon closer examination, however, it would be evidence showing Mrs. Wright’s state of mind. Her husband was dead and her stitches were crazy. Even a man could figure out this meant Mrs. Wright was not entirely well and likely killed her husband.
Mrs. Hale feels sorry for Mrs. Wright. The whole situation is becoming apparent to her, from how Mr. Wright treated his wife to the circumstances of his death. She pulls out the stitches.

MRS PETERS: Oh, what are you doing, Mrs. Hale?
MRS HALE: (mildly) Just pulling out a stitch or two that's not sewed very good. (threading a needle) Bad sewing always made me fidgety.

No one noticed Minnie Wright withdraw from society and stop being her sunny self after she married. The women realize they didn't see the signs and intervene. There is a certain sense of guilt there, but also some womanly camaraderie in their instinct to protect Mrs. Wright by hiding evidence.

Single Variable Calculus, Chapter 4, 4.4, Section 4.4, Problem 34

Determine the horizontal and vertical asymptotes of the curve $\displaystyle y = \frac{x^2 + 1}{2x^2 - 3x -2}$

Solving for the vertical asymptotes

We set the denominator equal to zero


$
\begin{equation}
\begin{aligned}

2x^2 - 3x - 2 =& 0
\\
\\
(2x + 1)(x - 2) =& 0
\\
\\
2x + 1 =& 0
& x - 2 = 0
\\
\\
2x =& -1
& x = 2
\\
\\
\frac{\cancel{2}x}{\cancel{2}} =& \frac{-1}{2}
\\
\\
x =& \frac{-1}{2}

\end{aligned}
\end{equation}
$


So the horizontal asymptotes are $\displaystyle x = \frac{-1}{2}$ and $x = 2$

Solving for the horizontal asymptotes

In the equation $\displaystyle y = \frac{x^2 + 1}{2x^2 - 3x - 2}$ we remove everything except the biggest exponents of $x$ found in the numerator an denominator.

So we have


$
\begin{equation}
\begin{aligned}

y =& \frac{\cancel{x^2}}{2\cancel{x^2}}
\\
\\
y =& \frac{1}{2}

\end{aligned}
\end{equation}
$



Thus, the horizontal asymptote is $\displaystyle y = \frac{1}{2}$

Therefore,

the vertical asymptotes are $\displaystyle x = \frac{-1}{2}$ and $x = 2$ and the horizontal asymptote is $\displaystyle y = \frac{1}{2}$

f(x) = 1/(x+1) , n=5 Find the n'th Maclaurin polynomial for the function.

Maclaurin series is a special case of Taylor series that is centered at x=0 . The expansion of the function f(x) about 0 follows the formula:
f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n
 or
f(x)= f(0)+(f'(0))/(1!)x+(f^2(0))/(2!)x^2
+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +(f^5(0))/(5!)x^5+...
To determine the Maclaurin polynomial of degree n=5 from the given function f(x)=1/(x+1) , we may apply Law of Exponent: 1/x^n = x^(-n) . The function becomes:
f(x) = (x+1)^(-1)
Apply Power rule for differentiation: d/(dx) u^n = n * u^(n-1)* (du)/(dx) to list the derivative of f(x) .
Let u =1+x then (du)/(dx) = 1 for each derivatives.
f'(x) = d/(dx)(x+1)^(-1)
       = (-1) *(x+1)^(-1-1)*1
       = -(x+1)^(-2) or -1/(x+1)^2
f^2(x)= d/(dx) -(x+1)^(-2)
            =-1*(-2 *(x+1)^(-2-1))*1
            =2(x+1)^(-3) or 2/(x+1)^3
f^3(x)= d/(dx) 2(x+1)^(-3)
            =2*d/(dx) (x+1)^(-3)
             =2* (-3*(x+1)^(-3-1))*1
             =-6(x+1)^(-4) or -6/(x+1)^4
f^4(x)= d/(dx) -6(x+1)^(-4)
            =-6*d/(dx) (x+1)^(-4)
             =-6* (-4*(x+1)^(-4-1))*1
            =24(x+1)^(-5) or 24/(x+1)^5
f^5(x)= d/(dx) 24(x+1)^(-5)
            =24*d/(dx) (x+1)^(-5)
             =24* (-5*(x+1)^(-5-1))*1
            =-120(x+1)^(-6) or -120/(x+1)^6
Plug-in x=0 , we get:
f(0) = 1/(0+1)
         =1/1
          =1
f'(0) = -1/(0+1)^2
            =-1/1^2
             =-1
 f^2(0) =2/(0+1)^3
            =2/1^3
             =2
f^3(0) =-6/(0+1)^4
           =-6/1^4
            =-6
f^4(0) =24/(0+1)^5
           =24/1^5
            =24
f^5(0) =-120/(0+1)^6
           =-120/1^6
            =-120
Plug-in the values on the formula for Maclaurin series. 
sum_(n=0)^5 (f^n(0))/(n!) x^n
    = 1+(-1)/(1!)x+2/(2!)x^2+(-6)/(3!)x^3+24/(4!)x^4+ (-120)/(5!)x^5
     = 1-1/1x+2/2x^2-6/6x^3+24/24x^4-120/120x^5
     = 1-x+x^2-x^3+x^4-x^5
The Maclaurin polynomial of degree  n=5 for the given function f(x)= 1/(x+1) will be:
P_5(x)=1-x+x^2-x^3+x^4-x^5

In The Kite Runner, why did Khaled Hosseini have Amir Sohrab and Assef come together the way they did in their encounter?

You originally posed this question asking why these characters came together "in the same way," which is a bit unclear. I am basing my response on the understanding that you are asking why this encounter toward the end of the book parallels in some ways the encounters of Amir, Hassan, and Assef earlier in the novel. 
This is a novel about wrongdoing and redemption. Hosseini has created a character, Amir, who makes regrettable choices and another character, Hassan, who shows Amir how people should behave. Hassan is a true friend to Amir, saving both of them from Assef and his friends with a slingshot. Amir cowardly fails to save Hassan from Assef raping him. He says,

I had one last chance to make a decision. . . I could stand up for Hassan—the way he'd stood up for me all those times in the past. . . In the end, I ran. I ran because I was a coward (Hosseini 77).

While this is not Amir's only wrongdoing toward his friend, it is the most striking and significant, setting the stage for the banishment of Hassan and his father Ali from Baba's household, which results in Hassan and Ali being left behind to die after Baba and Amir flee to America. 
When Amir is offered a chance "to be good again" (2) and returns to Afghanistan to save Hassan's son, Sohrab, he is on his way to redemption in a scene that is a kind of combined reenactment of the two crucial encounters with Assef, the first being the slingshot encounter, the second being the rape of Hassan. In this encounter, Sohrab is a kind of "stand-in" for Hassan, who is dead, but whose son is still alive. Amir rescues Sohrab from the evil Assef, who clearly has been molesting Sohrab since he took him. Sohrab rescues Amir by slaying Assef with a slingshot, just as his father did before him. This is almost like a do-over for Amir, a way for him to be make the choice to be brave and rescue Sohrab. Khaled Hosseini creates a kind of symmetry to the book by setting up this situation to contrast Amir the immature, cowardly child with the mature, brave man he becomes.

What was going on in the Ford Madox Ford chapter and what is his significance in the book?

In A Moveable Feast: The Restored Edition there are actually two sections dealing with the English writer and editor Ford Madox Ford. One of these sections, "The Acrid Smell of Lies," was added in the restored edition by Hemingway's grandson Sean. Both vignettes are extremely unflattering to Ford. In the chapter called "Ford Madox Ford and the Devil's Disciple" Hemingway details an encounter with Ford in a Paris cafe. He describes Ford derisively "as an ambulatory well clothed up-ended hogshead." Hemingway goes on to insult Ford throughout the piece, suggesting that Ford had a bad odor and that Hemingway needed to hold his breath when he was near the man. In the introduction to the restored edition Sean Hemingway admits that his grandfather's dislike for Ford has "puzzled" biographers, especially because Ford often praised Hemingway's writings and was one of the first publishers, in his Transatlantic Review, to print Hemingway's stories. Hemingway's disdain of Ford, however, is quite in line with the insulting treatment (although a bit harsher) he gives other literary luminaries who were his friends, including F. Scott Fitzgerald, Gertrude Stein and Sherwood Anderson (in Torrents of Spring).
The main insult in "Ford Madox and the Devil's Disciple" is to suggest that Ford could not even recognize the famous French writer and historian Hilaire Belloc (and thus was probably unable to recognize true genius). Ford claims that he has "cut" Belloc when he refuses to acknowledge the writer's presence when Belloc looks toward the table where he and Hemingway are seated. At the end of the sketch after Ford has left, Hemingway discovers that the man who Ford thought was Belloc was actually Aleister Crowley, an occultist who was often accused of worshipping Satan. This portrait of Ford tends to be ironic since Ford was well-known for recognizing great writing and promoting the careers of men such as Joseph Conrad, H. G. Wells, Thomas Hardy and Hemingway himself. As with many of Hemingway's relationships, there seems to be a good deal of jealousy on Hemingway's part. Another explanation of the poor treatment of Ford is posited by Sean Hemingway and is explicitly revealed in "The Acrid Smell of Lies" where Hemingway writes, "He [Ford] lied about money and about things that were important in daily living that he would give you his word on." Therefore, Hemingway's dislike may have originated because of a deal involving money. Years later, then, when he was writing A Moveable Feast, Hemingway couldn't help but harangue Ford in the worst of ways.

What does "The Rape of the Lock" reveal about the 17th century?

"The Rape of the Lock" was actually written in the 18th century (in March of 1714, to be more specific) by Alexander Pope. In the form of a mock heroic epic, this poem dramatizes a minor theft within an aristocratic family: the Baron, who lusts after Belinda cuts off a lock of the woman's hair without her consent, creating an enormous melodrama. This crime gets escalated to the status of the gods, with comparisons of the theft being made to the kidnapping of Helen of Troy and the other silly events of the day (a card game, Belinda waking up in the morning, coffee drinking) all being described in theatrically and mythologically large ways. 
So while Pope riffed off of 17th century literature (namely, taking his parodied "sylphs" from Nicolas-Pierre-Henri de Montfaucon de Villars' novel Comte de Gabalis), he was actually providing commentary about the 18th century and the shallowness and wastefulness of the newly formed English aristocratic class. By depicting the protagonists' vanity with such grossly overblown attention to detail, Pope makes it clear that he is criticizing the rich, their obsession with triviality, and their ignorance of the world outside their carefully curated and sheltered lives.
Pope points out that many of the relationships and interactions that occur within this realm of wealth are merely formalities or matters of convenience--the result of superficiality. The events of the poem were actually based on a real-life incident in which a certain Lord Petre, an acquaintance of Pope, cut off a lock of Arabella Fermor's hair, creating a huge rift between their respective families. The penning of the poem was meant to create a sense of reconciliation between the two, but ending up becoming one of the best known examples of satirical verse from this time period. 

How old was Thomas Paine when he published Common Sense?

Thomas Paine was born on February 9, 1737. He died on June 8, 1809. Common Sense was published on January 9, 1776. He was 38 years old when Common Sense was published. Common Sense was a pamphlet that explained the reasons why the colonists should become independent from Great Britain. Many colonists were not sure if they should declare independence from Great Britain. They knew they had issues regarding how the British were treating them. They were concerned about the tax laws that had been passed without their consent. They also were concerned about the blood that had been shed. This pamphlet changed many minds in the colonies. Many colonists who were unsure if they should declare independence from Great Britain believed they should declare their independence after reading Thomas Paine’s pamphlet.
https://www.history.com/this-day-in-history/thomas-paine-publishes-common-sense

What words does the author use to avoid repeating "the road"?

One thing that Robert Frost does to avoid using the word "road" over and over again throughout this poem is to use pronouns instead of "road." For example, line five is as follows:

To where it bent in the undergrowth

"It" refers to one of the two roads. This pronoun is used again in line eight. In line ten, the narrator uses "them" instead of "roads."
For much of the rest of the poem, Frost substitutes various other words to stand-in for "road." The stand-in word is more often than not meant to be followed by the word "road," but Frost simply avoids using the word "road" and lets readers assume that the road is what he is talking about. For example, let's look at lines two and four:  

And sorry I could not travel both [roads]
And be one traveler, long I stood
And looked down one [road] as far as I could

Frost does this dropping of "road" a few more times in the poem. Lines six, eleven, and thirteen do the same thing.  
 
Finally, in line nineteen, the narrator substitutes "road" for the word "one."

I took the one less traveled by

Who is Storm in The Swiss Family Robinson?

Storm is the family's buffalo. He is tied to the harpoon rope in Chapter 9 so that Fritz can bring ashore an enormous sturgeon that is eight feet long. In this chapter, the family sets up a fishing operation, and they use a harpoon and bow and arrow to kill large fish. However, they can not drag the largest fish to shore, so Storm is very useful to them. The family often relies on Storm as they would rely on a horse. Later, Storm is used, along with the bull named Grumble, to carry the mother of the family in a basket that is slung between the two animals. Storm is also used, with Grumble, to carry off the deadly serpent that kills their ass, and he is later employed in carrying the basket with Grumble when the family is gathering corn. Storm is a reliable work animal for the Robinson family. 

How did they build their first home?

The family's means of building their first house depends on a sound understanding of nature. First, the family choose a big tree with branches at a great height, so that a rope ladder could be strung from the branches. For temporary shelter, a sailcloth is slung over this tree to make a sort of tent, but this is only the first step. The family intends to find wood to build a house with, and possibly some rod to build a ladder with. Ernest finds some bamboo in the sand, and the family cut these to lengths of five feet and bring them back to the tree.
Using geometric calculations, they determine that they should build their house thirty feet up in the tree. They build a ladder and fix it to the ground with stakes. Then they fashion a pulley so that materials can be brought up into the tree.
Later, more wood is collected from the beach for building, and these planks are pulled up into the tree to be arranged as a "smooth solid floor." The sailcloth is then brought up to be slung over the highest branches in the tree and nailed down to the platform of planks. This makes a sort of treehouse or "nest" high up in the tree, enclosed on three sides by the sailcloth and the tree trunk, with the front left open to allow access down the ladder and to allow the sea breeze to blow in.

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 41

The mean value theorem is applicable to the given function, since it is a polynomial function. All polynomial functions are continuous and differentiable on R, hence, the given function is continuous and differentiable on interval.
The mean value theorem states:
f(b) - f(a) = f'(c)(b-a)
Replacing 1 for b and 0 for a, yields:
f(1) - f(0) = f'(c)(1-0)
Evaluating f(1) and f(0) yields:
f(1) = 1^(2/3) => f(1) =1
f(0) = 0
You need to evaluate f'(c):
f'(c) = (c^(2/3))' => f'(c) = (2/3)c^(2/3 - 1) => f'(c) = (2/3)*(c^(-1/3)) => f'(c) = 2/(3 root(3) c)
Replacing the found values in equation f(1) - f(0) = f'(c)(1-0):
1 - 0 = (2/(3 root(3) c))(1-0) => 1 = 2/(3 root(3) c) =>3 root(3) c = 2 => root(3) c = 2/3 => c = (2/3)^3 => c = 8/27 in [0,1]
Hence, in this case, the mean value theorem can be applied and the value of c is c = 8/27 .

In "When I Am An Old Woman," how does Jenny Joseph present her feelings of growing old?

How does Shelagh Delaney present the character of Geoff as an outsider In A Taste Of Honey?

In the poem, the narrator presents her feelings about growing old in a humorous and upbeat manner.
She portrays the idea of growing old as a period of great freedom. During her sunset years, she will no longer need to adhere to societal expectations for accepted behavior. As she presumably will have little responsibility for anyone but herself, Joseph maintains that she will be able to engage in activities that were previously considered socially unacceptable.
For example, the narrator looks forward to wearing clothes that don't match, just for the fun of it. She looks forward to spending her pension on frivolous items and later complaining about having no money to buy nourishing food. She maintains that it is the province of the elderly to do outrageous things, especially if they were responsible figures in their younger years.
The narrator looks forward to making up for the "sobriety" of her youth, learning how to spit, putting on weight, eating whatever she pleases, and learning rude manners. She revels in the idea of being able to sit down wherever she is, if she happens to be tired. For now, though, she believes she has to act respectably; after all, she must "set a good example for the children."
Despite wanting to set a good example, Joseph muses that she should probably start to "practice a little" these odd new ways she will take up in her elderly years; otherwise, people may be shocked when she is old and suddenly begins acting contrary to her present behavior. In all, the narrator presents her feelings of growing old in a lighthearted and upbeat manner.

Intermediate Algebra, Chapter 4, 4.2, Section 4.2, Problem 18

Solve the system of equations $
\begin{equation}
\begin{aligned}

6.2x - 1.4 y + 2.4z =& -1.80 \\
3.1x + 2.8y - 0.2z =& 5.68 \\
9.3x - 8.4y - 4.8z =& -34.20

\end{aligned}
\end{equation}
$.


$
\begin{equation}
\begin{aligned}

6.2x - 1.4y + 2.4z =& -1.80
&& \text{Equation 1}
\\
37.2x + 33.6y - 2.4z =& 68.16
&& 12 \times \text{ Equation 2}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

43.4x + 32.2y \phantom{-2.4z} =& 66.36
&& \text{Add}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

12.4x - 2.8y + 4.8z =& -3.60
&& 2 \times \text{ Equation 1}
\\
9.3x - 8.4y - 4.8z =& -34.20
&& \text{Equation 3}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

21.7x - 11.2y \phantom{-4.8z} =& -37.80
&& \text{Add}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

43.4x + 32.2y =& 66.36
&& \text{Equation 4}
\\
21.7x - 11.2y =& -37.80
&& \text{Equation 5}

\end{aligned}
\end{equation}
$


We write the equations in two variables as a system


$
\begin{equation}
\begin{aligned}

43.4x + 32.2y =& 66.36
&& \text{Equation 4}
\\
62.3875x - 32.2y =& -108.675
&& 2.875 \times \text{ Equation 5}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

105.7875x \phantom{-32.2y} =& -42.315
&& \text{Add}
\\
x =& -0.4
&& \text{Divide each side by $105.7875$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

43.4(-0.4) + 32.2y =& 66.36
&& \text{Substitute } x = -0.4 \text{ in Equation 4}
\\
-17.36 + 32.2y =& 66.36
&& \text{Multiply}
\\
32.2y =& 83.72
&& \text{Add each side by $17.36$}
\\
y =& 2.6
&& \text{Divide each side by $32.2$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

6.2(-0.4) - 1.4(2.6) + 2.4z =& -1.8
&& \text{Substitute } x = -0.4 \text{ and } y = 2.6 \text{ in Equation 1}
\\
-2.48 - 3.64 + 2.4z =& -1.8
&& \text{Multiply}
\\
-6.12 + 2.4z =& -1.8
&& \text{Combine like terms}
\\
2.4z =& 4.32
&& \text{Add each side by $6.12$}
\\
z =& 1.8
&& \text{Divide each side by $2.4$}

\end{aligned}
\end{equation}
$



The ordered triple is $\displaystyle \left( -0.4,2.6,1.8 \right)$.

Why does Iago want Desdemona, Cassio, and Roderigo to be killed?

Iago wants Desdemona dead because getting rid of her will help him to destroy her husband, Othello. Desdemona is a threat to Iago because she doesn't trust him. So, long as she's around, she can act as what Iago regards as a dangerous influence on her husband, and Iago can't stomach such a prospect. So he sets about convincing Othello that Desdemona's been cheating on him, poisoning the man's jealous mind with lies, innuendos, and snide insinuations. Othello comes to be obsessed with Desdemona's alleged infidelity, and Iago's only too happy to fan the flames of his unhinged jealousy by helpfully uncovering "evidence" such as the handkerchief.
Iago has put it in into Othello's head that Michael Cassio is Desdemona's lover. Again, this is a total lie, but like the most effective lies, it has an air of plausibility about it. After all, Desdemona did intercede with her husband on Cassio's behalf in the wake of Cassio's public disgrace. She's only doing it out of kindness, of course, the kindness of an old and faithful friend—but that's not how Othello sees it. As far as he's concerned, Cassio is making a cuckold out of him and must forfeit his life as punishment.
For his part, Iago hates Cassio for being promoted over him. As a seasoned military veteran, he deeply resents the entitled young aristocrat from getting what he believes is rightfully his. So what better way to get Cassio out of the way than to goad an insanely jealous Othello into killing him?
The hapless Roderigo is a rich, handsome, but criminally stupid, young man. He also happens to be head over heels in love with Desdemona. Iago cynically plays upon his all-consuming lovesickness and tries to convince him that, with his help, he can win over Desdemona. But Roderigo is just the latest in a long line of gullible fools easily manipulated by the evil Iago to do his bidding. When Roderigo finally uncovers the truth about Iago's deception, Iago wastes no time in finishing him off, completing the job started by Cassio in his brief skirmish with the young rake. Roderigo knows too much, and if news of Iago's base treachery and deceit should ever get out, then Iago will be finished. So he murders Roderigo to keep him quiet, for dead men tell no tales.

Describe the history of jazz music.

Though the United States purchased the state of Louisiana from Napoleon in 1803, the city of New Orleans never quite went the way of the busy, industrious cities of New England to the north, nor did it fully conform to the influence of the leisurely, stiff-necked cities of King Cotton to the south.
Instead, New Orleans at once became a city where all cultures ran together like watercolor paint, even while still retaining the dignified Old World charm of its European sister cities. Though conservatism would still dominate culturally for another century and a half, the city's wide, cobblestone streets seethed with activity late into the night while the tinkling of piano keys floated tantalizingly down from the open windows of lively street-front saloons and brothels. The city's cuisine, as well, was unlike any other in America—spicy, zesty, featuring full flavored gumbos and fresh fish grilled in oiled paper and limes. Even the local dialects proudly evaded utter surrender to the polite southern drawl of the city's near southern neighbors, and instead the pleasant lilt of both French and Spanish languages clung to the tongues of those who flocked into the bustling city of New Orleans.
But for all its many rich cultural influences, there is one aspect of New Orleans culture that is truly second-to-none on a global scale, and that is its music scene. Powerful enough to define a nation and appealing enough to transcend international borders, the music of New Orleans has breathed life into the proud city for centuries.
The city's signature sound was, in fact, purely an African American invention, with roots going down into West Africa. The song-and-dance rituals of West African tribes were carried across the ocean on slave ships, surviving apartheid in the American south and giving birth to a new kind of music known as jazz. And what better birthing place than the city of New Orleans.
Jazz is noteworthy in American history not only for blending traditional African sounds with the more modern soulfulness of church gospel, but also for being lyrically centered in the daily aspect of hard work.
Though jazz served as a bridge of sorts between black and white cultures, segregation and racial violence prompted many of Louisiana's earliest jazz musicians to flee the state for places like Chicago and New York City. By the mid-twentieth century, the smooth, rich, bluesy flavor of jazz music could be heard across the nation's radio waves, and though it was soon being tempered to suit the tastes of white, middle-class listeners, jazz continued its legendary ascent, and indeed it continues to influence virtually all genres of American music today.
https://archive.nytimes.com/www.nytimes.com/books/first/g/gioia-jazz.html?mcubz=1

https://www.kent.edu/musicedonline

Jazz traces its origins to New Orleans, Louisiana, in the late 1800s and early 1900s, reaching the height of its popularity in the 1920s. Jazz originated in African-American communities, drawing its influence from both blues and ragtime. Both of these musical genres blended African musical traditions with European folk music and instruments. Africans brought to the Americas during the slave trade brought with them West African musical traditions, which then spawned the rise of slave spirituals and hymns. Slaves often used whatever makeshift instruments they could find—washboards, barrels, boxes, sticks, and jugs—in order to make music. Many African Americans also started learning how to play European instruments such as violins, especially after the abolition of slavery in 1865.
The diversity of New Orleans helped lead to the rise of jazz music in this area. In addition to large populations of African Americans, there were also French, Caribbean, Italian, Mexican, and German influences that influenced the music and culture in New Orleans. Instruments such as the trombone, piano, saxophone, and trumpet combined with the rhythms, dances, and chants of slave spirituals to create unique sounds that were often improvised. Louis Armstrong became one of the most famous examples of improvisation in jazz music, known for his ability to play his trumpet in unique and expressive ways.
During and after the Great Migration, which started around WWI as African Americans moved North to find more opportunity and jobs, jazz spread to other areas of the countries, becoming particularly popular in cities like New York and Chicago. In New York in the 1920s, the Cotton Club became famous for its jazz music and featured some of the most famous and influential black jazz musicians, including Louis Armstrong and Duke Ellington. Unfortunately, the Cotton Club enforced a strict "whites only" policy, so while African Americans were able to enter the club as entertainers and musicians, they were barred from attending the club as part of the audience. Jazz also helped give rise to the Harlem Renaissance, an explosion of African American literature, art and culture during the 1920s. Jazz music became nationally and then internationally popular and continues to influence musical traditions.
http://www.frenchquarter.com/jazzmasters/

How are themes of language developed within Anthony Burgess's A Clockwork Orange?

Burgess's A Clockwork Orange extends and amplifies the theme of language in a dystopian society, dealt with earlier in Huxley's Brave New World and Orwell's 1984.
Unlike those two earlier novels, written in ordinary language in the third person, Burgess has his central character Alex narrate the story in a strange futuristic English in which, significantly given that the novel was written in 1962 at the height of the Cold War, there are many words borrowed from Russian. The Russian-derived words often have an inverted-meaning implication. For instance, the word khorosho which means "good," becomes "horrorshow" in this new English. Droog (friend) sounds like the English word "goon"—an apt description of Alex and his buddies. Apart from the Russian-isms, there is a strange, dreamlike quality to Alex's language. In a way that seems astonishingly prophetic, this scaled-down and rambling English anticipates the informal and abbreviated language of text messages, and of social media in general, of our time.
The weirdness of Alex's English emphasizes the distance between his generation and the older people, the survivors from the Establishment of the previous age who are depicted still doing such things as watching TV and writing books. The man Alex encounters doing the latter is writing a manuscript actually titled "A Clockwork Orange." This phrase in itself presents a linguistic riddle that is at the heart of the novel's theme. Most Americans, and possibly even most British people, have (or had, before Burgess himself explained it) no idea that these words are evidently Cockney slang, used in the phrase "queerer than a clockwork orange." Though Burgess and others have advanced additional meanings, it would be almost as valid to regard "a clockwork orange" as a deliberately nonsensical phrase, symbolizing the meaninglessness of the chaotic future world of the novel.
In Brave New World, though the characters speak normal English, their language is also dominated by catchphrases and sloganeering, altered from past expressions and reflective of their dystopia, such as "Ford's in his flivver, all's right with the world." In 1984, the Party, in creating "Newspeak," is undertaking a massive reduction in the English vocabulary, in order to limit thought and essentially turn people into automatons. In A Clockwork Orange, Burgess takes these literary techniques a step further by writing the narrative itself in a futuristic form of English that is emblematic of a dysfunctional world, in which the new normal is the violence and psychosis of his main character, Alex.

int_0^(0.2) sqrt(1+x^2) dx Use a power series to approximate the value of the integral with an error of less than 0.0001.

From the table of power series, we have:
(1+x)^k = 1 +kx+ (k(k-1))/2! x^2 +(k(k-1)(k-2))/3!x^3 + ...
 To apply this on the given integral int_0^0.2 sqrt(1+x^2)dx , we let:
sqrt(1+x^2) =(1+x^2)^(1/2)
 Using the aforementioned power series, we may replace the "x " with "x^2 " and "k " with "1/2 or 0.5 ".
(1+x^2)^(1/2) =1 +0.5x^2+ (0.5(0.5-1))/2! (x^2)^2 +...
              = 1 +0.5x^2 -0.25/2! x^4 +...
             = 1 +x^2/2-x^4/8 +...
The integral becomes:
int_0^0.2 sqrt(1+x^2)dx = int_0^0.2[1 +x^2/2-x^4/8 +...]dx
To determine the indefinite integral, we integrate each term using Power Rule for integration: int x^ndx =x^(n+1)/(n+1) .
int_0^0.2[1 +x^2/2-x^4/8 +...]dx = [x +x^3/(2*3) -x^5/(8*5) +...]|_0^0.2
                = [x +x^3/6 -x^5/40+...]|_0^0.2
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
F(0.2)=0.2 +0.2^3/6 -0.2^5/40+ ...
             =0.2+1.3333x10^(-3)-8x10^(-6)+ ...
F(0) =0+0^3/6-0^5/40+ ...
          = 0+0-0+...
All the terms are 0 then F(0)= 0.
We can stop at 3rd term (8x10^(-6) or 0.000008) since we only need an error less than 0.0001 .
Then,
F(0.2)-F(0) = [0.2+1.3333x10^(-3)-8x10^(-6)] -[0]
                         = 0.2013253
Thus, the approximated integral value is:
int_0^0.2 sqrt(1+x^2)dx ~~0.2013

What is the theme of the poem "The people of Tao-Chou" by Po-Chü?

This poem describes an annual presentation that used to be made to the Emperor of China by a number of dwarf slaves from Tao-Chou, where people only grew to be three feet tall. These offerings were made until Yang Chen became governor, at which point he declared to the Emperor, "among all the things that live in Tao Chou, I only find dwarfish people, not dwarfish slaves." The poet concurs with this assessment, saying that the dwarfs could not be a "natural product," as this is dehumanizing and does not take into account the fact that these were people being separated from their families and lives. The Emperor, moved by Yang's declaration, prohibited further shipments of dwarfish people as slaves, and the poet goes on to explain that children born in Tao-Chou were sometimes given the name Yang in memory of this event. 
The primary theme of this poem, then, is that of slavery and how it relates to personhood, but we also find elements of the importance of ancestry, and of memorializing history, possibly to guard against repeating it unnecessarily. The people of Tao-Chou "still enjoy this gift," and the poet seems to suggest that we should all appreciate the struggles of our ancestors in helping us achieve a position in life where our personhood is respected. 

int x^2/sqrt(36-x^2) dx Find the indefinite integral

Given
int x^2/sqrt(36-x^2) dx
This can be solved by using the Trigonometric substitutions  (Trig substitutions)
when the integral contains sqrt(a-bx^2) then we have to take
x=sqrt(a/b) sin(t) in order to solve the integral easily
 
so here , For
int x^2/sqrt(36-x^2) dx
x is given as
x= sqrt(36/1) sin(t) = 6sin(t)
=> dx = 6 cos(t) dt
so ,
int x^2/sqrt(36-x^2) dx
=int (6sin(t))^2/sqrt(36-(6sin(t))^2) (6 cos(t) dt)
= int 36(sin(t))^2/sqrt(36-(6sin(t))^2) (6 cos(t) dt)
= int ((36)*(6)(sin(t))^2 *cos(t)) /sqrt(36-(6sin(t))^2) dt
=int (216(sin(t))^2 *cos(t)) /sqrt(36-36(sin(t))^2) dt
= int (216(sin(t))^2 *cos(t)) /sqrt(36(1-(sin(t))^2)) dt
=int (216(sin(t))^2 *cos(t)) /sqrt(36(cos(t))^2) dt
=int (216(sin(t))^2 *cos(t)) /(6(cos(t))) dt
= int (216/6) sin^2(t) dt
= int 36 sin^2(t) dt
= 36 int sin^2(t) dt
= 36 int (1-cos(2t))/2 dt
= (36/2) int (1-cos(2t)) dt
= 18 [int 1 dt - int cos(2t) dt]+c
= 18[t- (1/2)sin(2t)]+c
but we know that
x= 6sin(t)
=> x/6 = sin (t)
=> t= sin^(-1) (x/6) or arcsin(x/6)
so,
18[t- (1/2)sin(2t)]+c
= 18[(arcsin(x/6))- (1/2)sin(2(arcsin(x/6)))]+c
so,
int x^2/sqrt(36-x^2) dx
=18arcsin(x/6)- 9sin(2(arcsin(x/6)))+c

Why does the Handicapper General require different people to wear different kinds of handicaps?

To figure out why the Handicapper General requires different people to wear different kinds of handicaps, you need to remember her role of ensuring that no one is "smarter," "better looking," "stronger," or "quicker" than anyone else (paragraph 1).
With this in mind, you should review the reason why George, who has above average intelligence, must keep a "mental handicap radio" in his ear. You should compare this reason to the purpose for having the pretty, graceful ballerinas wear masks, sash weights, and bags of bird shot. You may also want to reread the description of Harrison Bergeron's police photograph and identify the "equalizing" function of each handicap Harrison wears (e.g., scrap metal to cancel out his superior strength, black caps to hide his attractive teeth).
Matching each handicap in the story with the mental or physical advantage it offsets may help you understand why different people wear different handicaps.
https://www.christenseninstitute.org/blog/the-united-states-handicapper-general/

How do people make magnesium?

Well, we don't exactly "make" it because it's an element which can only be created in the cores of stars. (Maybe we could create a very small amount in particle accelerators, but it would be far too expensive to be practical.) Rather, we extract it from natural sources.Magnesium can be extracted from a variety of minerals, most commonly magnesite, dolomite, brucite, bishoviete, carnallite, and olivine. It is generally extracted either by thermal reduction, which involves heating the mineral to extremely high temperatures until its chemical bonds separate and magnesium vapor is released (which can then be condensed into usable magnesium), or electrolysis, which uses electrical current to break the chemical bonds directly and separate the mineral into its constituent elements. Electrolysis is much more efficient, but it is also much more expensive due to the need for more capital investment and higher technology. As a result, rich countries like the US generally use electrolysis, while poor countries like China generally use thermal reduction.

What effect does the structure of the text create on the story itself?

Ray Bradbury's "There Will Come Soft Rains" is structured in a way that it slowly peels away the facade of the technological improvements made by society to reveal the devastation some advancements can cause. Bradbury structures this story by turning something quaint into something terrifying.
The actions in the story, absent of any human presence, suggest this family that lived in the Allendale, California house led a fulfilled life. They celebrated birthdays, played together, ate as a family, and even listened to poetry.
While all of this seemingly pleasant life is occurring in the narration, Bradbury reveals the terrible thing that had happened. At 10 o'clock, the house was the only one standing amid "rubble and ashes" and a "radioactive glow" could be seen for miles. Not only this, but the fate of the family is even more devastating:

The entire west face of the house was black, save for five places. Here the silhouette in paint of a man mowing a lawn. Here, as in a photograph, a woman bent to pick flowers. Still farther over, their images burned on wood in one titanic instant, a small boy, hands flung into the air; higher up, the image of a thrown ball, and opposite him a girl, hands raised to catch a ball which never came down.

After this reveal, Bradbury returns to the activity of the house going on about its business. The house dealt cards, served dinner, and cleaned up. The nursery walls performed for no audience. But, in contrast to the pleasant opening of the story, the house now seems to be a haunting reminder of the meaninglessness of this type of activity. Other technology—particularly nuclear weapons—would make every object useless.
In a story without any human action and no traditional characters, Bradbury effectively relies on his story's structure to create an emotional response in readers.

Where are Nag and Nagaina killed?

Nag and Nagaina are two cobras featured in Rudyard Kipling's short story "Rikki-Tikki-Tavi," which was part of the author's work called The Jungle Book.
In this story, the title character is a mongoose who saves the family from the cobras. Nag is the male cobra, and Rikki-Tikki-Tavi attacks him when in the bathroom after Nag and Nagaina have plotted a sneak attack against the family. Rikki-Tikki-Tavi finds Nag in the bathroom sluice. A sluice is an open channel for water to go through. Rikki-Tikki-Tavi bites Nag on the head and is thrashed about by the snake until the "Big Man" in the house shoots the snake. Below is the description of where Nag was before Rikki-Tikki-Tavi attacked him:

He stole off to Teddy's bath-room, but there was nothing there, and then to Teddy's mother's bath-room. At the bottom of the smooth plaster wall there was a brick pulled out to make a sluice for the bath water, and as Rikki-tikki stole in by the masonry curb where the bath is put, he heard Nag and Nagaina whispering together outside in the moonlight.

Nagaina engages in a fight with Rikki-Tikki-Tavi on the veranda of the bungalow where the family lives. She is seeking revenge for Nag's death and targeting Teddy, the child in the family.

Teddy and his mother and father were there at early breakfast, but Rikki-tikki saw that they were not eating anything. They sat stone-still, and their faces were white. Nagaina was coiled up on the matting by Teddy's chair, within easy striking distance of Teddy's bare leg, and she was swaying to and fro, singing a song of triumph.

She takes the fight to a hole underground in the garden, and it is there that she dies.

What is the theme of "Goe, and Catche a Falling Starre"?

"Goe, and Catche a Falling Starre" is a rather cynical poem expressing the view that all beautiful women are unfaithful and false. This is of course a misogynistic, bitter, and irrational complaint, likely motivated by the poet's own misfortunes with women.
The speaker says that one could wander for "ten thousand daies and nights" and never find "a woman true, and faire." In fact he says that such a treasure would be as impossible to find as it would be impossible to "catche a falling starre," or "heare Mermaides singing." One might wonder, at this point, about the speaker's implication that there is a direct, causal link between a woman's beauty, or how "faire" she might be, and how faithful or unfaithful she is. Perhaps he thinks that plain, less beautiful women are capable of the faithfulness which evades their more beautiful counterparts.
In the third stanza, the speaker says that if one were to find a woman that seemed true, she would inevitably prove "False, ere I come, to two, or three." This false, unfaithful nature of beautiful women constitutes the primary, ostensible theme of the poem. One might also say, however, that the implied rejection, or rejections, and the consequent bitterness and cynicism of the speaker, constitute the implicit and far more interesting theme of the poem.

The theme of John Donne's poem "Goe, and catche a falling starre" is bitterness at a love betrayed. The speaker invites the reader to try doing impossible things, saying that even if the reader succeeds, there is one impossible thing they will never do: meet a faithful woman. Even a woman who appears faithful will show herself to be false, given enough time.
To catch a falling star, or hear the singing of mermaids, is as unlikely to the speaker as "keep[ing] off envies stinging" or discovering the means to "advance an honest mind." The speaker feels he has been poorly treated, despite being "honest," and not even someone gifted with psychic powers could give him proof that his bitterness is unwarranted:

If thou beest borne to strange sights,Things invisible to see,Ride ten thousand daies and nights . . .Thou . . . wilt sweareNo whereLoves a woman true, and faire.

A faithful woman is more mythical than the powers of the mandrake root. Should the reader succeed in finding one, the speaker would not go to meet her, for all women are only faithful for a time, before giving their love to others.

What is an analysis of Dorine's character in the play Tartuffe?

Dorine is very much a stock character: the "wise servant." In this role, she acts almost as a Greek chorus, supplying the audience with a running commentary on events. She highlights certain negative character traits of the foolish members of the upper-classes, with which she's surrounded. There's a substantial element of social satire here as Molière presents us with a far from flattering portrayal of the French social elite.
Right from the start, Dorine sees right through Tartuffe, while her alleged social betters are beguiled by the warm words and overpowering charisma of this irredeemable charlatan. Amidst all the hypocrisy and delusion, she is a voice of sanity; her openness and honesty provides the audience with some much-needed relief from the vapidity and mendacity that the other characters exhibit.

Dorine in “Tartuffe” is a very independent minded character.  As a servant, she should fade into the background and speak only when addressed.  However, Dorine is far different from the typical servant (or woman) of her day.  Mme. Pernell is the first one to point this out when she says, “Girl you talk too much and I’m afraid/You’re far too saucy for a lady’s maid” (1.1). Dorine is not afraid to express herself to any member of the family, and when she speaks, she sees through the heart of the matter to the truth.  For example, when Dorine hears Orgon telling Mariane she should marry Tartuffe, she is not afraid to step in and have her say: “There’s lately been a rumor going about--/Based on some hunch or chance remark, no doubt/That you mean Mariane to wed Tartuffe/I’ve laughed it off, of course, as just a spoof.” (2.2).  Unlike most of the women of her time, Dorine is not afraid to speak up against her employer.  Dorine is not afraid to speak out against the tradition of arranged marriages.  She is an independent, strong woman in a time when such a woman was an anomaly.

Before the Cold War many argue the US and the Soviet Union were natural enemies over ideology but one might argue then we should have had and still have a cold war with China. Why do you think we did with the Soviet Union and did not really with China?

The United States did not trust the Soviet Union ever since Russia backed out of WWI despite receiving American aid to stay in the war.  During the 1920s American leaders were on high alert to prevent a Bolshevist takeover or an anarchist uprising and many people of Russian descent or sympathies were deported.  It was not until the Franklin Roosevelt administration that America finally recognized the Soviet government that had been in place for over a decade.  After WWII the United States criticized the totalitarian  puppet states which sprang up in Eastern Europe in the wake of the advancing Soviet armies.  The United States thought that all Communist regimes were taking orders from Moscow and that the next world war would take place between the U.S. and the Soviet Union.  It did not help when the Soviets clandestinely exploded an atomic bomb.  
America initially did not trust the new Communist regime in China that ousted its WWII ally Chiang Kai Shek.  China fell to Communist forces during the Truman administration, and it was not until the Nixon administration that American-Chinese relations normalized.  Nixon saw an opportunity to drive a wedge between China and the Soviets and he took advantage of this.  Nixon turned a blind eye to China's human rights' abuses and even built trade relationships with the nation that still exist today.  America needs Chinese trade more than that of the former Soviet Union, and that partially explains why the U.S. has better relations with China than with the Soviet Union.  

What makes Nnaemeka in the short story "Marriage is a Private Affair" by Chinua Achebe a complex character?

A complex character has many different traits and is often referred to as a dynamic character. This kind of character undergoes a change within the story and has multiple traits that he or she has learned by experience. Nnaemeka, through his experience of love for Nene, realizes the new and immediate family he will create with Nene is more important than Ibo tribe tradition. Nnaemeka first worries about telling his father, considers Nene's request for a written explanation, and then decides to tell his father in person. Even though Okeke completely objects to the marriage, Nnaemeka chooses love over tradition and marries Nene. They have two beautiful sons together as a result. It is precisely Nnaemeka's devotion to family that allows him to agree to the meeting of Okeke and his grandsons at the end of the story. This decision proves Nnaemeka is a mature character who is able to forgive his father.

Calculus of a Single Variable, Chapter 3, 3.3, Section 3.3, Problem 10

You need to find the open intervals on which the function is increasing or decreasing, hence, you need to find where the derivative is positive or negative, so, you need to evaluate the first derivative of the function, such that:
f'(x) = (12x - x^3)' => f'(x) = 12 - 3x^2
You need to solve for x the equation f'(x) = 0:
12 - 3x^2 = 0
-3x^2 = -12 => x^2 = (-12)/(-3) => x^2 = 4 => x_1 = 2; x_2 = -2
You need to notice that f'(x)<0 on intervals (-oo,-2) U (2, +oo) and f'(x)> on (-2,2).
Hence, the function increases for x in (-2,2) and the function decreases for x in (-oo,-2) U (2, +oo).

How was everyone equal in the year 2081 in Kurt Vonnegut's "Harrison Bergeron"?

In Kurt Vonnegut's "Harrison Bergeron," everyone is equal because the United States government has instituted several amendments to the Constitution that prohibits anyone from being better than anyone else. It has created a lowest common denominator that those who have greater abilities must bring themselves to in order to participate in society.
Equality in this society is characterized by Hazel Bergeron, the title character's mother. She is not required to wear any handicaps—devices that prevent a person from thinking, showing his or her athletic ability, or masking his or her beauty—because she is already perfectly average. Meanwhile, her husband, George, is required to wear both mental and physical handicaps. George, whose "his intelligence was way above normal," has to wear a mental handicap that "would send out some sharp noise to keep people like George from taking unfair advantage of their brains."
Another example is the beautiful ballerina who read the news that Harrison escaped had to wear a "hideous" mask and then had to change her "warm, luminous, timeless" voice to make is "absolutely uncompetitive." In addition, the narrator says, "It was easy to see that she was the strongest and most graceful of all the dancers, for her handicap bags were as big as those worn by two-hundred pound men."
George, Hazel and the ballerina are the best examples for how equality works in this society. Harrison, meanwhile, never really succumbs to these restrictions placed on him by the government.

what determines an object's temperature?

Every substance is comprised of molecules, atoms, and/or other subatomic particles of that substance. These particles are in constant motion, colliding with each other and perpetually moving. These particles each have their own unique velocity at which they are in motion. Therefore, each of these particles has its own unique kinetic energy of motion. The temperature of a substance is a way of measuring the average kinetic energy of all the particles comprising that substance. 
For example, water is made up of H2O molecules that are in constant motion. Each molecule is constantly moving, with its own velocity and kinetic energy. When this water is heated in a pot on a stove, the heat that is transferred as thermal energy from the stove to the pot and then to the water excites the water molecules in the water, increasing the average speed and therefore kinetic energy of the water molecules in the pot. As these particles increase their rate of collision with each other and the pot, they get even faster and faster. Hence, the temperature of the water increases, as the average kinetic energy of the H2O molecules that make up the water goes up as the molecules speed up.
https://en.wikipedia.org/wiki/Kinetic_theory_of_gases

Why does the monster argue that Frankenstein has shirked his responsibility as father/creator and that he should pay for this rejection in Mary Shelley's Frankenstein?

A dominant theme in Mary Shelley's Frankenstein is responsibility for one's actions, especially responsibility for what one creates. The creature sees that Frankenstein has behaved recklessly by bringing him to life and carelessly by rejecting and abandoning him, actions that have caused him to suffer immensely. Because of his suffering, the creature feels Frankenstein has a moral obligation to take responsibility for the creature's suffering and to ease his suffering, just a little, by creating him a mate.In chapter 11, the creature begins relaying to Frankenstein his story of suffering. He starts by explaining he had developed his own education by observing the De Laceys in their cottage. While living in the De Laceys' shed, he discovered a leather trunk full of clothes and books, and he began reading the books. One of the books he read was Milton's Paradise Lost. From the book, the creature learned about how God created Adam to be a "perfect creature, happy and prosperous" (Ch. 15). The creature further learned that God protected Adam and educated him through conversation. The creature sees that Frankenstein has behaved in the exact opposite way as God. Instead of creating something that is beautiful and in Frankenstein's own image, just as Frankenstein and all mankind are in God's image, Frankenstein has instead created something so hideous all of mankind is revolted by the creature, terrified of the creature, and desiring to kill the creature. Also contrary to God, Frankenstein himself was so revolted by his own creation that Frankenstein ran from his creation then forgot all about him, leaving him to suffer and fend for himself all on his own. The creature explains that because he was abandoned, misjudged, and hurt so frequently, he was filled with rage and a desire for revenge, a desire that led him to murder Frankenstein's young brother William and frame Justine for the murder. Though the creature has committed murder, he sees himself as ultimately innocent because he sees Frankenstein as being to blame for the rage in his heart, rage that has stemmed from immense suffering. We see the creature's view of his own innocence when, while imploring Frankenstein to have compassion for him and hear his story, the creature says of himself, "Frankenstein, I was benevolent; my soul glowed with love and humanity; but am I not alone, miserably alone?" (Ch. 10). We further see Frankenstein's view of his own innocence when he compares himself to Satan, the fallen angel from Paradise Lost, when he should have been like Adam to Frankenstein:

I ought to be thy Adam, but I am rather the fallen angel, whom thou drivest from joy for no misdeed. (Ch. 10)

When the creature speaks the phrase "no misdeed," we see that he is declaring his innocence. Since the creature sees Frankenstein as to blame for the creature's loss of benevolence towards mankind, the creature feels it is only right that Frankenstein make him a companion so that he might, for once, "feel gratitude toward [Frankenstein] for one benefit!" (Ch. 17). Frankenstein is at first repulsed by the idea of a second creature, yet he feels compassion for his creature and agrees that, as the creator, it is his responsibility to provide for the creature as much as possible, just as God provided for Adam in Paradise Lost.

What characteristic best describes Phillip Enright? Name two incidents or events occurred that show Phillip is this characteristic.

This is a tough question because Phillip changes so much over the course of the novel.  I'm also not sure if the characteristic in question has to apply to Phillip over the course of the entire novel, or if it can be any characteristic with supporting evidence.  I'm going to go with the latter.  
In the beginning of the novel, Phillip is a complete jerk.  He's rude, antagonistic to just about everybody, a racist, and believes that he is superior to most people.  For example, Henrik is one of Phillip's friends, but Phillip doesn't exactly talk about Henrik in positive terms.  Phillip flat out tells the reader that he finds Henrik annoying.  

. . . Henrik had an irritating way of sounding official . . .

Phillip follows that thought up by describing what Henrik looks like.  

His face was round and chubby. His hair was straw-colored and his cheeks were always red.

That's not exactly a glowing description of a friend.
Phillip doesn't hold back from his mother either.  He's equally rude and insensitive to her.

Then I became angry and accused her of being a coward. She told me to go off to school.  I said I hated her.

The above thoughts are all from people that Phillip at least supposedly respects.  Here's what Phillip has to say about Timothy.  

"You ugly black man! I won't do it! You're stupid, you can't even spell."

From the early parts of the novel, if I had to pick a single way to describe Phillip's personality, I would say that he is an insensitive jerk.    

Why did the Renaissance start from Italy? Discuss the cause.

The Renaissance was destined to start in Italy. Italy had Rome and access to Roman philosophers. The Italian states of Venice and Florence were also valuable trading centers who had ready access to ports in Greece and Constantinople. Even after the fall of Constantinople to the Ottoman Turks, these city-states continued to trade with the Ottoman Empire and ultimately gained access to rich Asian spices through Middle Eastern traders. This brought the cities the wealth needed to fund artistic works by great artists such as Michelangelo. The Medici family of Florence funded many great works of art in order to demonstrate their prestige. The Vatican was also a center of wealth, thanks to pilgrimages, and the popes commissioned works of art as well. After the fall of Constantinople, many Greek scholars came to Italy, and they brought with them knowledge of ancient Greek thinkers. This led to renewed interest in ancient philosophy and thought. The Italian city-states had often been at war with one another, and many looked to antiquity for a golden age that could be attained through education. This desire to bring about more prosperity and peace led to the Italian city-states being the birthplace of the Renaissance.

Which character in Hamlet (the play) could be a foil to Macbeth (the character)?

Actually, Hamlet, the tragic figure of Hamlet, one of Shakespeare's tragedies, could serve as a foil for Macbeth, the tragic figure of Macbeth, another of Shakespeare's tragedies.
Remember that a foil doesn't have to present the ideal way of handling a situation in contrast to the tragic hero's way of handling a situation. A foil just presents a different way. Laertes, for instance, handles his situation, which is of course similar to Hamlet's, with impetuous and hot-headed anger; he's quick to violent action. Hamlet, in contrast, is contemplative and logical and investigative. Whether he is guilty of a "delay" or not can be argued, but whatever the reason, his vengeance takes the entire course of the play to be enacted and never involves reckless passion like Laertes's does.
To connect the two plays you ask about, remember that Hamlet's revenge against Claudius would result in Hamlet's ascension to the throne if Hamlet were to survive. Ascension to the throne is what Macbeth is all about in the play bearing his name. Both Hamlet and Macbeth are one assassination of a king away from being kings themselves at or near the beginning of their respective dramas. Yet, I say remember when referring to Hamlet, because Hamlet does not dwell on this aspect of the situation. His concern is with knowing the truth about his father's death. His reaction is to "put an antic disposition on" (Act I.v.171)—to pretend to be mad or insane like a court jester—in order to determine the authenticity of the Ghost and the truth of its version of events. You see, Hamlet wants to avenge the assassination of a king.
Macbeth, on the other hand, wants to assassinate a king so he can become one. He is guilty of the heinous act that Hamlet wants to avenge. Hamlet's thoughts are far removed from the fact that killing Claudius would make him king, while Macbeth asks himself:

Why do I yield to that suggestion
Whose horrid image doth unfix my hair,
And make my seated heart knock at my ribs
Against the use of nature? (Act I.iii.137–140)

The unnatural suggestion that creates the image that Macbeth yields to and that makes his hair stand up and his heart pound is the thought of his assassinating King Duncan so he can become king himself.
Both Hamlet and Macbeth encounter opportunities that could lead to their being crowned king. Hamlet thinks only of his father. Macbeth thinks only of himself.

How does Locke believe knowledge is possible? Explain two different ways we know this based on his basic model.

John Locke provides his definition of knowledge in An Essay Concerning Human Understanding, written in the late seventeenth century.  Locke believed knowledge is obtained the moment you perceive that you agree or disagree with an idea.  He described three types of knowledge.  Intuitive knowledge is not based on any immediate facts but is instead something we just know to be true.  For example, you may know that someone loves you.  You may have a direct and immediate recognition of this knowledge even though you may not be able to trace the knowledge back to one specific event.  
Demonstrative knowledge is defined by Locke as knowledge obtained through a series of thoughts or chain of reasoning.  For example, you may know that Jimmy likes everything that Sally likes.  If you also know that Sally likes dogs, you can conclude through demonstrative knowledge that Jimmy will also like dogs. 
Locke’s third type of knowledge is defined as sensitive knowledge.  This is when you become aware of knowledge from a sensation outside of yourself.  We may know that someone is entering a room because we smell their perfume.  We may not even recognize the role of smell in our thought process, but our senses give us additional knowledge.  There has been much debate over sensitive knowledge and whether it truly exists or if it is just another form of intuitive and demonstrative knowledge. 

How does racism affect the life experiences of characters in the novel To Kill a Mockingbird?

Racism plays a strong role in To Kill a Mockingbird by Harper Lee.
Tom Robinson, an African American male, is wrongly accused of raping Mayella Violet Ewell. In the novel, Mayella makes romantic advances towards Tom. When Robert Ewell, Mayella's father, witnesses these advances, he beats Mayella. He then accuses Tom of raping and beating her. Since racism plays a large role in their hometown of Maycomb, Robert Ewell knows that people will believe that Tom Robinson is guilty, despite not having any evidence. Mayella Ewell, despite knowing that Tom is innocent, says "That nigger yonder took advantage of me..." (167, Lee), using racism to her advantage.
Atticus Finch, a Maycomb lawyer, takes on Tom Robinson's case. Finch sets out to prove that Robinson is innocent. During the trial, people in Maycomb turn their backs on Finch and his family because he is representing an African American male, which is frowned upon for a white citizen. Despite clearly proving Tom's innocence in the trial, Finch loses simply because Robinson is African American. Even after the trial, Atticus and his family are looked down upon.
Scout, Atticus's daughter, observes how people treat her dad and the rest of her family during and after the trial. In chapter 11 of To Kill a Mockingbird, Scout asks her father, "Atticus...what exactly is a nigger-lover?" (144, Lee)
After Atticus asks her if anyone had called her that, Scout goes on to say, "No sir, Mrs. Dubose calls you that. She warms up every afternoon calling you that. Francis called me that last Christmas, that's where I first heard it" (144, Lee).
The town of Maycomb is stuck in a time when racism plays a prevalent role in society. Tom Robinson is wrongly accused of rape because of racism. Mayella and Robert Ewell wrongly accuse a man of a crime he didn't commit because of racism. Atticus Finch's reputation is tainted because of racism. Scout Finch experiences her family being treated poorly due to racism. Unfortunately, racism affects many events that happen in To Kill a Mockingbird.

What is the main idea of paragraph 13?

The thirteenth paragraph of W.W. Jacob's classic short story "The Monkey's Paw" reads,

At the third glass his eyes got brighter, and he began to talk, the little family circle regarding with eager interest this visitor from distant parts, as he squared his broad shoulders in the chair and spoke of strange scenes and doughty deeds; of wars and plagues and strange peoples. (2)

The thirteenth paragraph is part of the exposition of the story, which reminds Mr. White to question Sergeant-Major Morris about the magic monkey's paw. The main idea of the paragraph is that Sergeant-Major Morris is an experienced traveler, who entertains the White family with his elaborate, fascinating stories from distant parts of the world, which will eventually introduce the story of the magic monkey's paw. After his alcoholic beverage loosens him up, Morris proceeds to tell the eager White family intriguing stories, which serve as the catalyst for Mr. White to bring up the story Morris once told him about acquiring a magic monkey's paw in India. Overall, the thirteenth paragraph serves as a bridge for Mr. White to bring up the topic of the magic monkey's paw that Morris previously spoke about. As their conversation continues, Morris reluctantly speaks about the monkey's paw, and the reader becomes aware that the talisman may be ominous and wicked.

Paragraph thirteen of "The Monkey's Paw" is:

After the third glass his eyes got brighter and he began to talk. The little family circle listened with growing interest to this visitor from distant parts, as he squared his broad shoulders in the chair and spoke of wild scenes and brave acts; of wars and strange peoples.

The main idea in this paragraph is that it provides exposition; the monkey's paw will become the catalyst for much of the story's action, and this paragraph sets up the introduction of the monkey's paw. The Sergeant-Major loosens up after a few glasses of whiskey and begins to describe his exploits, and Mr. and Mrs. White and their son are enthralled as he transports them away from their rural, uneventful existence to exotic India, where he obtained the magical monkey's paw. This paragraph is preceded by one in which readers learn that the Sergeant-Major has recently suffered a loss, so his animation in telling his story captivates the reader along with the Whites. It is clear that this is more than a war story or travelogue.

What did Mr. Auld forbid Mrs. Auld to do? Why?

Mr. Auld forbids his wife from teaching Frederick Douglass how to read. Mrs. Auld is a very kind, considerate woman. She doesn't like it when Frederick adopts a posture of cringing servility towards her, but it's all he knows. Mrs. Auld has never owned a slave before, so she has no experience of how most owners treat their slaves. For Frederick and Mrs. Auld, this is a whole new experience for both of them.
When Mr. Auld catches his wife teaching Frederick the alphabet, he's absolutely furious. Teaching a slave to read isn't just wrong; it's against the law. If slaves are taught how to read they'll start getting ideas above their station. Then they're liable to become resentful about their condition as slaves. Mr. Auld genuinely believes that teaching slaves to read will seriously undermine the foundations of society.
Mr. Auld's intervention backfires terribly. It simply makes Frederick all the more determined to learn how to read, as he now realizes that lack of education is used by white people to keep slaves in a state of ignorance and subjection.

How does Shaw employ literary devices within the text to showcase Eliza's frustration with the situation she landed in?

Shaw uses several devices to communicate Eliza's frustration with her situation. Shaw primarily wants to reveal her annoyance at the insensitive Mr. Higgins, who treats her as less than human.
Shaw causes Eliza to expostulate or make noises of disagreement that express her frustration. Shaw's script repeatedly has Eliza saying, "Ah—ah—ah—ah—ow—ow—oooo!!!" Those sounds have no meaning except to convey  frustration in her situation.
Shaw underscores Eliza's Cockney background by having her respond physically to Higgins's rudeness. Shaw uses stage directions to indicate Eliza's frustration. For example, towards the end of the play, he directs that she start 

snatching up the slippers, and hurling them at him one after the other with all her force.

The slipper throwing uses the image of flying slippers striking Higgins to communicate, without words, Eliza's welling frustration and anger.
Shaw also uses dialogue. Eliza, when she can find the right words, is forceful in expressing her frustration. For example, after throwing the slippers at Higgins, she cries out:

There are your slippers. And there. Take your slippers; and may you never have a day's luck with them!

Shaw uses the exclamatory stage direction shown below to indicate Eliza's frustrated mood. The direction is exclamatory because it ends with two exclamation points, communicating Eliza's strong feelings. We read that she

gives a suffocated scream of fury, and instinctively darts her nails at his face!!

Shaw doesn't leave the audience or reader in the dark as to Eliza's emotions.

Why don’t Johnny and Ponyboy cry?

It's understandable that Johnny and Ponyboy should vent their emotions after everything that's happened. But there comes a time when the tears must stop flowing, and that's when the two young men have finally adapted to their new surroundings. The harsh reality of their situation has hit them hard and they must handle it as best they can. Crying was the boys' way of dealing with the sudden shock of being holed up in the church as a couple of fugitives. For all their youthful bravado they're still emotionally immature. But even at such a young age the instinct for self-preservation is ever present. And once that instinct kicks in the tears dry up and the boys start to think seriously about their next move.

In Chapter 5, Ponyboy wakes up in the abandoned church, and Johnny returns from the store with supplies. The two boys then cut and dye their hair, which is extremely traumatic for Ponyboy. The two boys then begin thinking about their unfortunate situation and burst into tears. Ponyboy and Johnny are young, homesick boys, who have committed a series of crimes and begin to feel overwhelmed, which is why they start crying. Pony mentions that he cried himself to sleep and wakes up later that night with a different attitude. When Ponyboy gets up, he wakes Johnny and tells him that they aren't going to cry anymore. Johnny replies by saying that they are all "cried out" and have to accept the reality of their difficult situation. Essentially, Ponyboy and Johnny decide not to cry anymore and stop feeling sorry for themselves. They are determined to face their adversity without crying and begin to occupy their time by reading the novel Gone With the Wind.

In "Where Are You Going & Where Have You Been" by Oates is the central conflict internal or external, and what would be considered the two opposing conflicts in the story?

This is an interesting question, and one could easily argue that there are really two central conflicts: the internal ones that rage within Connie herself, and the one between Connie and Arnold when he shows up at her house. These are the opposing conflicts in Oates's story.
Connie's internal conflicts are centered on her desire to be noticed and valued for her beauty, even when that means breaking rules, defying her parents, and exemplifying the opposite of her sister June who is "plain and steady." The narrator describes Connie as having a dual, conflicting nature: "Everything about her had two sides to it, one for home and one for anywhere that was not home."  While she is at first flattered by Arnold Friend's attention, his interest in her becomes a serious problem.
While Connie's internal conflict is not at all unusual or potentially catastrophic in a fifteen-year-old girl, the conflict in which she becomes enmeshed with Arnold Friend is quite dangerous.  He is a predatory adult male with naive, vain Connie in his sights.  She is no match for his determination to have her, and at the moment he strikes, no one is available to help her. Ultimately, she is unable to help herself.  Readers are left to assume that the conflict ends badly for Connie. 

Attached are a question and the matlab code. The code gives the total surface area as 639.4828, but the figure is not showing up. Also, the question says to use surface integral to calculate the surface area, not matlab. Please help me on this. Thanks.

i, j, k are unit vectors.
r(u,v)=(b+a*cos(u))*cos(v) i + (b+a*cos(u))*sin(v) j + a*sin(u) k
0<=u,v<=2pi and a=1/4 and b=1
 
The surface area is:
A=double integral of magnitude of (r_u x r_v) dA
r_u is the partial derivative of r(u,v) with respect to u and r_v with respect to v:
r_u(u,v)= -a*sin(u)*cos(v) i -a*sin(u)*sin(v) j +a*cos(u) k
r_v(u,v)= -(b+a*cos(u))*sin(v) i +(b+a*cos(u))*cos(v) j
 
Compute the cross product:
r_u x r_v = -a*cos(u)*(b+a*cos(u))*cos(v) i - a*cos(u)*(b+a*cos(u))*sin(v) j - a*(b+a*cos(u))*sin(u) k
 
Compute the magnitude:
magnitude(r_u x r_v)= sqrt(a^4*(cos(u))^2+2*a^3*b*cos(u)+a^2*b^2)= a*(b+a*cos(u))
 
Lastly, evaluate the integral:
integral(integral(a*(b+a*cos(u)),v,0,2*pi),u,0,2*pi) = 4*pi^2 * a * b
With a=1/4 and b=1 the surface area is pi^2.
 
The Matlab code for the plot is:
clear allsyms u va=1/4; b=1;x=(b+a*cos(u))*cos(v);y=(b+a*cos(u))*sin(v);z=a*sin(u);ezsurf(x,y,z,[0,2*pi,0,2*pi])