Why does Utopia make the idea of family something unacceptable and unsavory?

Mustapha Mond, controller of the World State, explains more than once what is wrong with traditional families, a form of social organization he seems to particularly abhor. He states,

What suffocating intimacies, what dangerous, insane, obscene relationships between the members of the family group!

Mond also notes the following:

Our Freud had been the first to reveal the appalling dangers of family life. The world was full of fathers—was therefore full of misery; full of mothers—therefore of every kind of perversion from sadism to chastity; full of brothers, sisters, uncles, aunts—full of madness and suicide.

As the above quotes show, the World State believes family life breeds dysfunction and misery because family members are too closely involved with each other. The state has decided people are more emotionally healthy if they are raised in a communal, dormitory-type setting rather than in a nuclear family. This way, people can be conditioned to accept and appreciate their lot in life and grow up as well-socialized members of the larger community.
To prevent the formation of nuclear families, eggs are harvested from women and artificially inseminated with sperm, then divided into as many identical twins as possible—the lower the caste is, the more embryos are produced. Bearing a child is considered disgusting and obscene.
In this society, the emphasis is on social harmony. This is best achieved through fleeting, superficial relationships between people, rather than strong attachments. It is easier for the society to enact its motto that everyone belongs to everyone else if all people are raised as part of a mass, not in family units.
Huxley, of course, satirizes this form of mass social organization.

In Brave New World, the idea of family is unacceptable and unsavory because it goes against this society's key philosophies. For a start, a family (the traditional unit for the procreation of children) goes against this society's program of artificial reproduction. A family would negate the need for the Hatcheries and the Conditioning Centers where children are molded into particular types of people.
Secondly, a family is also seen as unsavory because it contravenes the sexual liberation of this society. As we see through characters like Lenina, this society also values sexual promiscuity. Moreover, women have ready access to drugs that can prevent cases of pregnancy.
Because the society of Brave New World believes that it has created a utopia, the idea of reinstating the family unit would, in theory, destroy this creation. By allowing people to form loyalties and attachments to one another and to allow couples to procreate, this society as its inhabitants know it would be completely destroyed.

Precalculus, Chapter 4, 4.5, Section 4.5, Problem 10

In both Glaspell's short story and her play of the same name, remarks are made by the men about how women focus upon insignificant things, and nothing in the kitchen can be of any consequence in finding evidence to solve the murder of Mr. Wright. Ironically, however, this thinking of the men foreshadows the failure of the sheriff's investigation to uncover the "trifles" that provides the motive for Wright's murder.

"Well, can you beat the women! Held for murder, and worrying about her preserves!"

This is the portentous remark that Sheriff Peters makes when his wife notices that the glass jars of Mrs. Wright have broken from the freezing temperature. In the play of the same name, Mr. Hale, a neighbor to the Wright's makes a similar comment, "Well, women are used to worrying over trifles."
With such an attitude, the men decide that there is nothing in the kitchen which would be instrumental in solving the crime. So, they leave the women there and go upstairs to the bedroom where Mr. Wright was killed and search for evidence. While the two women wait in the kitchen, the neighbor of the wife accused woman, Mrs. Hale, talks to the sheriff's wife, relating how the former Minnie Foster was in the choir at church and loved music and being around other people, but here on the farm she has been isolated for years without even a phone. Further Mrs. Hale realizes by noting the dirty towel, and other details of the kitchen that Mrs. Wright was probably depressed and no longer interested in cleaning and such. Then, the women notice a quilt that Mrs. Wright had been working on that has some erratic stitching in sharp contrast to the neat stitches that are prevalent throughout the rest of the quilt. Finally, Mrs. Hale opens a cupboard and discovers a fancy box that contains a dead canary with its neck wrung. The two women look at each other with immediate comprehension of why Mr. Wright was strangled. These trifles of the erratic stitching (She may have been quilting when she heard the commotion upstairs as he husband opened the bird cage and strangled the canary) and the dead bird found in the insignificant room of the kitchen are clearly motives. But, the women hide this evidence from the men when they come downstairs because of their sympathy for Mrs. Wright and partly because the men have insulted them, thus profoundly affecting the outcome of the sheriff's investigation.

In "Rules of the Game" by Amy Tan, how does Waverly first view the game of chess?

Waverly is interested in chess because her brothers are so excited about the new chess set.
When the family gets a used chess set for Christmas, their mother tells them to throw it away.  She does not think it has any value because it is just an old chess set with missing pieces.  The boys are thrilled however, and can’t wait to play.  Seeing their enthusiasm, Waverly is interested in chess too.

And my brothers wore such serious faces that I was sure something was at stake that was greater than avoiding the tradesmen's door to Hong Sing's.
"Let me! Let me!" I begged between games when one brother or the other would sit back with a deep sigh of relief and victory, the other annoyed, unable to let go of the outcome.

Waverly bribes her brother with candy pieces to replace the missing ones, and he agrees to let her join them.  The winner gets to eat the Life Savers!  Vincent explains the rules and Waverly immediately begins asking questions.  Their mother becomes curious and reads the rule book.  She tells them to learn the American rules, so they can beat Americans and not be tricked.

"This American rules," she concluded at last. "Every time people come out from foreign country, must know rules. …” 

Eventually, Waverly is the one who becomes good at chess.  She becomes so good that she starts playing strangers in the park, who teach her chess etiquette and more moves.  In time, she enters tournaments and gets better and better.  She doesn’t have to do chores, and her brothers pick up the slack.  Waverly’s life becomes about chess. 
Waverly’s mother still gives advice, even when Waverly becomes incredibly successful.  Waverly gets frustrated that she focuses on not losing pieces, rather than winning the game.  She doesn't think her mother gets it, but her mother points out she is still winning.  Waverly loves chess, and she is good at it, but she doesn't like the pressure her mother puts on her.

Are Didion's subjects able to obtain the "California Dream"?

In looking at the book as a whole, and not necessarily just at one essay, the ultimate answer to whether or not Didion's subjects obtain the California Dream is that several did for a moment in time, but the dream was often ultimately spoiled for them.
Many of the essays in the book present California as an ideal frontier where people come to live out their wildest dreams, dreams they cannot possibly accomplish elsewhere. However, these same people often find that their fantasy of California and their reality are very different from one another. In essence, the California Dream is more like a gold-leaf-covered rock than a real gold nugget.
Although some of Didion's subjects are happy for a while, or successful for a while, there always seems to be some tinge of sadness, disappointment, or tragedy for them. For example, in "John Wayne: A Love Song," Didion recounts meeting the actor at the end of his life when he was dying of cancer. He was no longer the overtly strong and masculine cowboy that had once dominated Western films and found such wild success in Hollywood.
Similarly, she recounts the strangely ironic stories of Lucille Miller and Howard Hughes. Again, these are both people who did have success in California, but at some point it became sadly tarnished.
Because of the focus of multiple essays, the ways the people in them are characterized, and the fact that most of these essays do not emphasize happiness, it could be argued that although some of the people Didion writes about enjoyed the California Dream for short periods of time, the dream was ultimately spoiled for them.

Describe the atmosphere in which the laugher usually works.

"The Laugher" is narrated by a man that is a professional laugher.  Over the course of the short story, he informs readers about his job.  The narrator spends some time early in the story telling readers that his laughter repertoire is quite diverse.   

I laugh like a Roman emperor, or like a sensitive schoolboy, I am as much at home in the laughter of the seventeenth century as in that of the nineteenth, and when occasion demands I laugh my way through all the centuries, all classes of society, all categories of age.

Because of his skills, the narrator admits that he is in high demand.  He works on all kinds of various media types, and directors and producers feel that the narrator is "indispensable."  Therefore, the atmosphere that the narrator works in is an atmosphere of respect.  The directors don't treat him like a novelty.  They need him to perform a particular task in order to get a particular effect.  That also makes the work environment direct, straightforward, and demanding.  The narrator has to hit his marks and queues like any other actor.  

I have become indispensable; I laugh on records, I laugh on tape, and television directors treat me with respect. I laugh mournfully, moderately, hysterically; I laugh like a streetcar conductor or like a helper in the grocery business; laughter in the morning, laughter in the evening, nocturnal laughter and the laughter of twilight. In short: wherever and however laughter is required—I do it. 

The demanding work atmosphere is made more clear to readers when the narrator explains how his laughing skills are in demand from mediocre comedians.  He is frequently hired to make sure that audiences laugh at the correct moment.  He must time his outbursts so that they are both natural sounding and infectious at the same time.  That demanding kind of atmosphere is tiring to the narrator.  

It need hardly be pointed out that a profession of this kind is tiring, especially as I have also—this is my specialty—mastered the art of infectious laughter; this has also made me indispensable to third- and fourth-rate comedians, who are scared—and with good reason—that their audiences will miss their punch lines, so I spend most evenings in night clubs as a kind of discreet claque, my job being to laugh infectiously during the weaker parts of the program. It has to be carefully timed: my hearty, boisterous laughter must not come too soon, but neither must it come too late, it must come just at the right spot: at the pre-arranged moment I burst out laughing, the whole audience roars with me, and the joke is saved.   

If the original question is meant to ask about the overall mood/atmosphere of the story as a whole, then I think "calm" effectively describes the atmosphere created by the story's narration.  The narrator describes events in a very straightforward, factual manner.  He's calm throughout most of the piece.  The atmosphere of the story does change near the end of it though.  As the narrator explains that he doesn't laugh outside of work anymore, the atmosphere is much more melancholic.  The narrator admits that he's happy with his marriage, but he also admits that laughter is not a part of that marriage.  

So our marriage is a quiet, peaceful one, because my wife has also forgotten how to laugh: now and again I catch her smiling, and I smile too.

The story ends with the narrator admitting that despite the fact that his job is laughing, he doesn't believe that he has ever actually heard his real, natural laugh.  

So I laugh in many different ways, but my own laughter I have never heard.

That's bordering on creating a depressed atmosphere for readers.  
 
 

Which passage from Frankenstein best illustrates the theme of the destructive power of revenge?

By the end of the novel, both Victor Frankenstein and his creature have been destroyed by their desire for revenge.  Victor has sought to avenge the deaths of all his loved ones -- William, Justine, Henry, Elizabeth, and Clerval -- and it has completely and utterly wasted him, physically.  On his deathbed, he asks Captain Walton to swear that he will not let the monster live, "'that [Walton] will [...] satisfy [Victor's] vengeance in [the monster's] death.'"  He begs Walton not to listen to the creature but to "'call on the manes of William, Justine, Clerval, Elizabeth, [Victor's] father, and the wretched Victor, and thrust [his] sword into [the monster's] heart.'"  Victor declares that he will "'hover near" and help to aim Walton's sword.  His desire for revenge surpasses even his desire to remain alive; Victor has given up on his own life and only cares about his revenge now: such is the destructive power of revenge.
Confronted by Captain Walton over the dead body of his creator, the creature says, "'[...] I was the slave, not the master of an impulse, which I detested, yet could not disobey [....].  Evil thenceforth became my good.'"  His desire for revenge changed him, made him a thrall so that he seems to have no agency of his own; he could only seek to satisfy his need for vengeance.  It has consumed him, and now there is no reason left for him to live.  He vows to end his life.  His need for revenge has destroyed him.

Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 48

Determine whether the equation $y = |x|$ defines $y$ as a function of $x$. Give the domain in each case. Identify any linear functions.


By using the property of Absolute value, we have

$
y = |x| \Longrightarrow y =
\begin{array}{c}
x & \text{for} & x > 0 \\
\\
-x & \text{for} & x < 0
\end{array}
$


The graph of this function is obtained by the union of the line $y = x$ and $y = -x$.
And because those lines are not vertical lines, we can say that the given relation defines
a function because there is only one corresponding value of $y$ for every value of $x$.
However, the factor is defined for every values of $x$ except for . Therefore, the domain
is $(-\infty, 0) \bigcup (0, \infty)$. This equation is not an example of a linear equation
because the slope is not constant all throughout the graph.

Which section of the Declaration of Independence outlines the general beliefs about government that justifies a rebellion?

In the link that I am providing, check out the second paragraph.  It states that all men are "endowed with unalienable rights, that among these are life, liberty, and the pursuit of happiness."  This is probably the most famous phrase from the document.  Jefferson borrowed it from John Locke and substituted "the pursuit of happiness" for Locke's "property."  Jefferson goes on to say that government gets its power from the consent of the governed. This gives the people the right to rebel or even to overthrow a government that does not preserve these natural laws.  Jefferson then goes on to encourage citizens to be "prudent"; this means that the people should not rebel in the event of a first offense. Rather, they should seek other opportunities to correct the government.  Jefferson himself was a fan of revolution that brought government back to these original principles.  This made him quite a few enemies among conservatives who did not believe that the people were capable of self-governance.  
https://www.ushistory.org/declaration/document/

How does Twain use parallel scenes in the first 15 chapters of Huckleberry Finn?

Basically, Twain uses parallel scenes in the first 15 chapters of Huckleberry Finn to lay the foundation for Jim and Huck's developing friendship. This friendship is an important one, as it is of central relevance to the plot.
In Chapter 7, Huck makes his escape from his father's cabin. He fakes his murder by spreading pig blood all over the floor. For good measure, he smashes the door with an ax to give the impression that he was ambushed by thieves. Then, Huck hides in the canoe. When night falls, he makes his way down the river, barely missing his father (who has just returned). Huck ends up on Jackson Island.
While all this is happening, Jim is making his own escape. In Chapter 8, we learn why Jim ran away: he had overheard Miss Watson discussing the terms for his sale. Deciding that he would rather run away than be sold to a slave trader for eight hundred dollars, Jim ends up on Jackson Island, where Huck is staying. In Chapter 9, Jim warns Huck that the rains are on their way, so the two camp out in a vast cavern on higher ground.
A few nights later, the two friends discover a frame house floating down the river. There is a dead man's body in the house, but Jim covers it up with old rags. The man appears to have been shot in the back. The reality is that the dead man is Huck's father, and Jim wanted to spare Huck the pain of knowing this. This chapter is an important one, as it highlights the affection Jim feels for Huck.
In Chapter 10, Huck reveals that he is beginning to care about Jim's welfare as well. So, when Huck's prank goes wrong and Jim is bitten by a rattlesnake's mate, Huck tries to hide the evidence of his guilt. He doesn't want to hurt Jim, who he is beginning to care about. While all this is going on, a group of people are looking for Huck's supposed murderer. Unfortunately for Jim, everyone thinks that he's the killer. This new development poses a great threat to the two new friends, so they must stay together and remain focused on their main objective.
By Chapters 14 and 15, the two have plotted to head north together, to the free states. So, Twain effectively uses parallel scenes (with concurrent events involving different characters) to lay the foundation for a friendship that is central to the novel's plot. It is Huck and Jim's partnership that drives much of the action in the rest of the novel. So, the use of parallel scenes is an important literary device.

Should we as consumers think of buying "American made" first in our buying decisions?

The answer to this question is a matter of personal opinion.  Different people could legitimately have different views.  I will provide an argument on each side of the issue.
On the one hand, we can say that people should make it their first priority to “buy American.”  If we can buy a product that was made in America, we should do it even if there are better, cheaper products made in foreign countries.  There are two main arguments for this view.  First, we can say that we should do this for patriotic reasons.  We should want to support people in our own country, not foreigners.  We should want to make America our first priority rather than thinking of our own convenience.  Second, we could argue that buying American is good for us as well.  If we buy American, that will increase the demand for products that are made here.  When demand for these products rises, there will be more jobs for American workers.  This will boost our economy, which will presumably make it more likely that we and our children will get good jobs.
On the other hand, we can say that we should look first at price and quality when buying.  For one thing, this is the capitalist, non-socialist way of doing things.  If we just blindly buy American even if the goods are inferior, we are rewarding American companies who do a bad job, simply because they are American.  This is like homeschooling your child and giving them good grades because you love them even when they do bad work.  We do not want to reward people who do not deserve it.  Secondly, it is not at all clear that buying American is the best thing for our economy.  If we only buy American goods, we will put more Americans to work.  However, what happens when we drive out foreign competition, making the goods that we buy more expensive and of poorer quality?  Don’t we hurt our country just as much by reducing our standard of living in this way?  By buying the best products, regardless of where they are from, we keep prices low and quality high, allowing Americans to have the best possible products.
Which of these arguments makes more sense to you?
https://www.forbes.com/sites/davidmarotta/2013/04/28/is-there-a-moral-case-for-buy-american/

Ben, a police officer, accidentally stumbles onto several joints of marijuana at his friend Jim's house. Assume that the possession of any quantity of marijuana is illegal in the municipality in which this event takes place. Using a utilitarian calculus, what would be the right thing for Ben to do in this circumstance?

A utilitarian calculator, first developed by Mill and revised by Bentham, measures the amount of pleasure or pain that will result from an action; an action is morally right if it produces more pleasure than pain. Bentham added the following dimensions to the calculator: 
Intensity: how intense is the pleasure or pain?
Duration: how long will the pleasure or pain last?
Certainty: how certain is the pain or pleasure to take place?
Propinquity or nearness: how close or far in the future is the pleasure or pain?
Fecundity: how likely is it that the pleasure will lead to other pleasurable things?
Purity: how likely is it that the pain will lead to other pain?
Extent: how many people are affected by the pleasure?
Using this calculator makes Ben's dilemma quite difficult. If he turns in Jim to the police and Jim has legal problems, it will result in pain for Jim and Ben, as well as for both of their wives. The pain for Jim will be intense, long, and certain, and it will occur soon, as Jim will potentially face jail time or other consequences. In addition, the extent of the pain will be great, as Jim and his wife will face painful consequences. Ben and his wife could also face painful consquences, as Jim and Sandy will likely not be their friends anymore. 
If Ben does not report Jim, Ben will likely experience intense, long, and possibly certain pleasure by enjoying Jim's friendship. Jim will also experience this type of pleasure. However, it is difficult to determine the nearness of the pleasure or how likely it is that Jim and Ben will experience pleasure in the future (as they just began their friendship). In addition, it will also be difficult to determine the extent of the pleasure, as the course of their future friendship is difficult to know. However, there is no doubt that Jim will experience greater pleasure if Ben doesn't report him. Therefore, the calculus in this scenario is complicated and difficult to calculate. 

How could you use fabric architecture and its principles to design interiors that conserve natural resources? Use as an example a business, such as an Apple store or Target, and describe what you would do and how it would be "greener" than what is in existence now.

Fabric architecture includes the use of fabrics in tensile membrane structures, as well as fabric shades and sculptures. Fabric architectural pieces can be made of PVC coated polyester, which is very durable, flexible, and long lasting (with a life of up to 15-20 years). This type of fabric is often used for canopies for entrances to businesses and public spaces, and it could be used at the entrance to this store to provide additional shade and conserve energy. 
To make a retail space such as an Apple store greener, or more sustainable, you could concentrate on using windows and doors that maximize energy efficiency. In addition, materials such as wood flooring could come from local or recycled sources to save shipping costs and conserve energy and trees. The tables in the store on which the products are displayed could be made from local or recycled natural products rather than from synthetics shipped from long distances. This practice conserves resources and reduces the use of fuel needed for shipping. The fabrics can also be made from durable local materials or be recycled from other sources. Display structures in the store could also be built using fabric architecture, structures made out of fabric. These structures are energy efficient and durable. The lighting can be generated from energy-efficient sources such as LED or compact fluorescent bulbs. Rather than having a windowless roof, the store can feature skylights to make the most of natural sunlight, and the skylights could be covered or shaded using fabric architecture. In addition, many stores such as Apple and Target are quite large. Making these spaces smaller makes them more energy efficient. 

Explain how the title “Revelation” could actually apply to ALL of O’Connor's stories.

In all—or almost all—of O'Connor's stories, one of her characters has a moment of revelation or illumination, when the grace of God breaks into this person's life and shows a glimpse of God's love or God's mercy or, conversely, a character obtains a glimpse of true evil beneath a "good" facade. Almost always, the characters O'Connor creates are grotesques, people with deep flaws, either inside or out (or both), who have not confronted the deepest levels of either grace or darkness in their lives.
In "A Good Man is Hard to Find," for example, a difficult, manipulative, and racist older woman who has caused her family to be murdered sees the Misfit, the man who has just ordered the death of her family and is about to kill her, through the eyes of love. Through the grace of God, she is able to connect with him for a for an instant before he kills her. That is a moment of revelation for her. Likewise, in "The Artificial Nigger," an ignorant, racist old man named Mr. Head goes to Atlanta with his grandson Nelson and then, out of fear, denies knowing Nelson when Nelson accidentally causes a commotion. Nelson's anger, rejection, and coldness is a form of hell to Head, who experiences a revelation of God's deep mercy when Nelson forgives him. In "Good Country People," Hulga, an educated woman, meets Pointer, a traveling Bible salesman and is unable to see his evil until he tells her he believes in nothing and steals her artificial leg out of spite. At that point, Hulga has a revelation in which she learns that for all her education, she has not before understood pure evil.   

Which allusions and references to other literary works are used in Shakespeare's Hamlet?

A good place to start looking for allusions is in Hamlet's soliloquies.  Since Hamlet is characterized as a scholarly young man, his language reflects his education. In his first soliloquy, for instance, in Act 1, Hamlet refers to his deceased father as "Hyperion"--an allusion to the Greek sun god.  He compares Gertrude to Niobe, a mother from another Greek myth.  At the end of Act 3, Hamlet refers to Nero, the cruel Roman tyrant who killed his own mother:  

Let not ever
The soul of Nero enter this firm bosom.

In this case Hamlet is reminding himself not to hurt his mother, not to be like Nero who murdered his.
We can also find allusions in Hamlet's dialogue with other characters.  In Act 2, he demonstrates his knowledge of Roman mythology by asking the Player to recite lines from the Aeneid.  Major players in the Trojan war are mentioned: Hecuba, Pyrrhus, and Priam. When talking with Polonius, Hamlet mentions Jephthah, an allusion to a story in the Old Testament, in which a father sacrifices his daughter for a military victory.  
Ophelia also uses allusions. In Act 4, Ophelia's mad songs and phrases are derived from well known English folk songs.  
These are just a few to get you started.  An interesting analysis of these allusions might involve looking at what is revealed about the characters through the allusions they use--Hamlet's references to history, literary works, and the bible, or Ophelia's references to folk songs and tales, for instance. 

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 23

Find the derivative of $\displaystyle g(x) = \sqrt{1 + 2x}$ using the definition and the domain of its derivative.

Using the definition of derivative


$
\begin{equation}
\begin{aligned}

\qquad f'(x) &= \lim_{h \to 0} \frac{g(x + h) - g(x)}{h}
&&
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{\sqrt{1 + 2(x + h)} - \sqrt{1 + 2x}}{h}
&& \text{Substitute $g(x + h)$ and $g(x)$}
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{\sqrt{1 + 2x + 2h} - \sqrt{1 + 2x}}{h} \cdot \frac{\sqrt{1 + 2x + 2h} + \sqrt{1 + 2x}}{\sqrt{1 + 2x + 2h} + \sqrt{1 + 2x}}
&& \text{Multiply both numerator and denominator by $\sqrt{1 + 2x + 2h} + \sqrt{1 + 2x}$}
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{\cancel{1} + \cancel{2x} + 2h - \cancel{1} - \cancel{2x}}{(h)(\sqrt{1 + 2x + 2h} + \sqrt{1 + 2x})}
&& \text{Combine like terms}
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{2\cancel{h}}{\cancel{(h)}(\sqrt{1 + 2x + 2h} + \sqrt{1 + 2x})}
&& \text{Cancel out like terms}
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{2}{(\sqrt{1 + 2x + 2h} + \sqrt{1 + 2x})} = \frac{2}{(\sqrt{1 + 2x + 2(0)} + \sqrt{1 + 2x})}
&& \text{Evaluate the limit}
\\
\\
\qquad f'(x) &= \lim_{h \to 0} \frac{\cancel{2}}{\cancel{2} \sqrt{1 + 2x}}
&& \text{Cancel out like terms}
\\
\\
\end{aligned}
\end{equation}
$


$\qquad \fbox{$f'(x) = \displaystyle \frac{1}{\sqrt{1 + 2x}}$}$

Both functions involves square root that are continuous for $1 + 2x \geq 0$.

$\displaystyle \begin{array}{cc}
1 + 2x & \geq 0 \\
x & \geq \frac{-1}{2}
\end{array} $

However, $\sqrt{1 + 2x}$ is placed in the denominator of $g'(x)$ that's why $\displaystyle \frac{-1}{2}$ is not included in its domain. Therefore,

The domain of $g(x) = \sqrt{1 + 2x}$ is $\displaystyle \left[ \frac{-1}{2}, \infty \right)$

The domain of $g'(x) = \displaystyle \frac{1}{\sqrt{1 + 2x}}$ is $\displaystyle \left( \frac{-1}{2}, \infty \right)$

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 81

a.) Prove that if $f$, $g$, and $h$ are differentiable, then $(fgh)' = f'gh+fg'h+fgh'$ by using product rule

$
\begin{equation}
\begin{aligned}
(fgh)' & = [f(gh)]'
&& \text{Group the three functions and assume that we only have two factors}\\
\\
(fgh)' & = f(gh)' + f'(gh)
&& \text{Apply Product rule}\\
\\
(fgh)' & = f(gh'+g'h)+f'gh
&& \text{Apply product rule again in } (gh)'
\end{aligned}
\end{equation}
$


Therefore, $(fgh)' = fgh'+fg'h+f'gh$

b.) Prove that $\displaystyle \frac{d}{dx}[f(x)]^3 = 3[f(x)]^2f'(x)$ by taking $f =g = h$ in part(a)
Let $f^3 = (fgh)$, so we have
$(f^3)' = (fff)'$

Applying Product rule twice we get


$
\begin{equation}
\begin{aligned}
(f^3)' & = f'ff+f(ff)'\\
\\
(f^3)' & = f'ff+f(f'f+f'f)\\
\\
(f^3)' & =f^2f'+f^2f'+f^2f'\\
\\
(f^3)' & = 3f^2f'
\end{aligned}
\end{equation}
$


In other words, $\displaystyle \frac{d}{dx} [f(x)]^3 = 3 [f(x)]^2 f'(x)$

c.) Differentiate $y = (x^4+3x^3+17x+82)^3$ using part(b)
Let $f(x) = x^4 + 3x^3 + 17x + 82$

Using $\displaystyle \frac{d}{dx}[f(x)]^3 = 3[f(x)]^2f'(x)$


$
\begin{equation}
\begin{aligned}
\frac{d}{dx} [f(x)]^3 & = 3(x^4+3x^3+17x+82)^2 \left[ \frac{d}{dx}(x^4)+3\frac{d}{dx}(x^3)+17\frac{d}{dx}(x)+\frac{d}{dx}(82)\right]\\
\\
\frac{d}{dx} [f(x)]^3 & = 3(x^4+3x^3+17x+82)^2 [4x^3+(3)(3x^2)+(17)(1)+0]\\
\\
\frac{d}{dx} [f(x)]^3 & = 3(x^4+3x^3+17x+82)^2 (4x^3+9x^2+17)
\end{aligned}
\end{equation}
$

sum_(n=1)^oo n^(k-1)/(n^k+1) , k>=2 Use the Limit Comparison Test to determine the convergence or divergence of the series.

Limit comparison test is applicable when suma_n and sumb_n are series with positive terms. If lim_(n->oo)a_n/b_n=L where L is a finite number and L>0 , then either both series converge or both diverge.
Given series is sum_(n=1)^oon^(k-1)/(n^k+1),k>=2
Let the comparison series be sum_(n=1)^oo1/n
The comparison series sum_(n=1)^oo1/n is a p-series with p=1.
As per the p-series test,sum_(n=1)^oo1/n^p is convergent if p>1 and divergent if 0So, the comparison series is a divergent series.
Now let's use the limit comparison test with: a_n=n^(k-1)/(n^k+1)
b_n=1/n
a_n/b_n=(n^(k-1)/(n^k+1))/(1/n)
a_n/b_n=(n(n^(k-1)))/(n^k+1)
a_n/b_n=n^k/(n^k+1)
a_n/b_n=n^k/(n^k(1+1/n^k))
a_n/b_n=1/(1+1/n^k)
lim_(n->oo)a_n/b_n=lim_(n->oo)1/(1+1/n^k)
=1>0
Since the comparison series sum_(n=1)^oo1/n diverges, the series sum_(n=1)^oon^(k-1)/(n^k+1) as well, diverges as per the limit comparison test.

Single Variable Calculus, Chapter 2, 2.4, Section 2.4, Problem 23

Show that the statement $\displaystyle\lim\limits_{x \to a} x=a$ is correct using the $\varepsilon$, $\delta$ definition of limit.

Based from the defintion,


$
\begin{equation}
\begin{aligned}

\phantom{x} \text{if } & 0 < |x - a| < \delta
\qquad \text{ then } \qquad
|f(x) - L| < \varepsilon\\

\phantom{x} \text{if } & 0 < |x-a| < \delta
\qquad \text{ then } \qquad
|x-a| < \varepsilon\\

\end{aligned}
\end{equation}
$


The statement suggests that we should choose $\displaystyle \delta = \varepsilon$

By proving that the assumed value of $\delta$ will fit the definition...



$
\begin{equation}
\begin{aligned}
\text{if } 0 < |x-a| < \delta \text{ then, }\\
& \phantom{x}
|x-a| < \delta = \varepsilon
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

& \text{Thus, }\\
& \phantom{x} \quad\text{if } 0 < |x-a| < \delta \qquad \text{ then } \qquad |x-a| < \varepsilon\\
& \text{Therefore, by the definition of a limit}\\
& \phantom{x} \qquad \lim\limits_{x \to a} x=a


\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 86

If $f''(x) = x^{-2}$, $x > 0$, $f(1) = 0$ and $f(2) = 0$, find $f$
If $f''(x) = x^{-2}$, then by applying integration...

$
\begin{equation}
\begin{aligned}
f'(x) &= \int x^{-2} dx\\
\\
&= \frac{x^{-1}}{-1} + c_1\\
\\
&= -\frac{1}{x} + c_1
\end{aligned}
\end{equation}
$

Again, by applying integration...

$
\begin{equation}
\begin{aligned}
f(x) &= \int \left( -\frac{1}{x} + c_1 \right) dx\\
\\
f(x) &= - \ln x + c_1 x + c_2
\end{aligned}
\end{equation}
$


If $f(1) = 0$, then

$
\begin{equation}
\begin{aligned}
0 &= - \ln (1) + c_1(1)+c_2\\
\\
0 &= c_1 + c_2\\
\\
c_1 &= -c_2 \qquad \Longleftarrow \text{(Equation 1)}
\end{aligned}
\end{equation}
$

Also, if $f(2) = 0$, then

$
\begin{equation}
\begin{aligned}
0 &= -\ln(2) + c_1(2)+c_2\\
\\
\ln(2) &= 2c_1 + c_2 \qquad \Longleftarrow \text{(Equation 2)}
\end{aligned}
\end{equation}
$

By using Equations 1 and 2 simultaneously...

$
\begin{equation}
\begin{aligned}
\ln (2) &= 2c_1 - c_1\\
\\
c_1 &= \ln 2
\end{aligned}
\end{equation}
$

Thus, $c_2 = - \ln 2$
Therefore,
$f(x) = -\ln x + x \ln (2) - \ln (2)$

How do polar bears behave in Antarctica?

Actually, polar bears are Arctic animals, not Antarctic. The largest carnivores on the Antarctic continent are seals and penguins. These animals feed on fish and are quite approachable since there is almost nothing in Antarctica that would want to eat them. Antarctica is located at the South Pole; the polar bears you mention are at the North Pole. This is the Arctic Circle of Northern Alaska and Canada.
If your question was about polar bear behavior in the Arctic, it would be different. Polar bears hunt seals over breathing holes in ice. They also take advantage of seal breeding grounds as well as migratory fish. Polar bears enjoy carrion when they can get it. Polar bears can swim for miles in search of new hunting areas. If polar bears were transplanted to the Antarctic, they would be at the top of the food chain until they had eaten all of the penguins and seals. After this, the polar bear population on the continent would collapse without a food source.

How had Abigail been previously employed in The Crucible?

Abigail Williams was formerly employed by John and Elizabeth Proctor as a sort of helper around the house: she would assist Elizabeth with taking care of the children, doing the cooking and chores, and so forth. The Reverend Parris asks Abigail about her dismissal from the Proctors' employment as well as her reputation in town. He asks this because it has been "seven month[s]" since she was "discharged from [their] service," and no one else has inquired about hiring her for the same kind of role.
Although Abigail protests her own innocence, blaming Elizabeth's personality for their parting, we learn from the conversation between her and John in act 1 that Elizabeth fired Abigail because she was having an affair with John. Abigail says to him, "It's she put me out, you cannot pretend it were you. I saw your face when she put me out, and you loved me then and you do now!" John admits their affair, and he expresses regret.  And though he may "think of [Abigail] softly from time to time," he is committed to his marriage and says that he would cut off his own hand before he ever reaches for her again.

What are the direct and indirect changes that occur in Achebe’s Things Fall Apart after the arrival of the missionaries?

The direct changes to the village of Umuofia after the arrival of the white missionaries involve the establishment of European trading outposts, stores, schools, and churches in the region. When the European missionaries arrive, they initially decide to take a passive approach to colonization by establishing trading posts, stores, and schools, which benefit the villagers and earn their trust. The Igbo villagers are attracted to the benefits of trade, new marketplaces for their crops and services, and the opportunity to gain a valuable education. The stores, trading posts, and schools open the villagers up to foreign European culture, which allows the missionaries to introduce the Christian religion to the villagers in a favorable manner. They initially recruit the outcasts of Umuofia, and the church gains popularity among the pariahs of the village until respected individuals begin converting to Christianity. Subsequently, many villagers convert to Christianity, which creates disparity and dissension among the citizens of Umuofia.
The indirect effects of the arrival of European missionaries involve the gradual destruction of traditional Igbo culture. As the Christian religion and European influence gain popularity throughout the village and region, traditional Igbo culture and customs lose their favor and are slowly replaced by European culture. Achebe illustrates how European colonists purposely undermine traditional Igbo culture and religion by introducing schools, stores, and churches to the villagers, which allows them to establish a bureaucracy in the region and completely colonize the African territory.

Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 90

dy/dx = (1-2x) / (4x-x^2)
This differential equation is separable since it can be written in the form

N(y)dy =M(x)dx
Bringing together same variables on one side, the equation becomes
dy=(1-2x)/(4x-x^2)dx
Taking the integral of both sides, it turns into
int dy = int(1-2x)/(4x-x^2)dx
y+C_1 = int(1-2x)/(4x-x^2)dx
y+C_1= int (1-2x)/(x(4-x))dx
To take the integral of right side, apply partial fraction decomposition.
(1-2x)/(x(4-x)) = A/x + B/(4-x)

1-2x = A(4-x)+Bx

Let x=0.


1-2(0) = A(4-0)+B(0)
1=4A
1/4=A
Let x=4.
1-2(4)=A(4-4)+B(4)
-7=4B
-7/4=B

1/(2x-x^2) = (1/4)/x + (-7/4)/(4-x)

1/(2x-x^2) = 1/(4x) + (-7)/(4(4-x))

1/(2x-x^2) = 1/(4x) + (-7)/(-4(x-4))

1/(2x-x^2) = 1/(4x) + (7)/(4(x-4))
So the integrand at the right side decomposes to
y + C_1 = int (1/(4x) + 7/(4(x-4)))dx
Then, apply the formula int 1/u du = ln|u| + C .
y + C_1 = 1/4ln|x| + 7/4ln|x-4|+C_2
Isolating the y, the equation becomes
y= 1/4ln|x| + 7/4ln|x-4|+C_2-C_1
Since C1 and C2 represent any number, it can be expressed as a single constant C.
y = 1/4ln|x| + 7/4ln|x-4|+C

Therefore, the general solution of the given differential equation is y = 1/4ln|x| + 7/4ln|x-4|+C .

Single Variable Calculus, Chapter 4, 4.5, Section 4.5, Problem 4

Use the guidelines of curve sketching to sketch the curve. $y =8x^2 - x^4$

The guidelines of Curve Sketching

A. Domain.
We know that $f(x)$ is a polynomial having a domain of $(-\infty, \infty)$

B. Intercepts.
Solving for $y$-intercept, when $x = 0$.
$y = 8 (0)^2 - (0)^4 = 0$
Solving for $x$-intercept, when $y=0$,

$
\begin{equation}
\begin{aligned}
0 &= 8x^2 - x^4\\
\\
0 &= x^2(8-x^2)
\end{aligned}
\end{equation}
$


we have, $x = 0 $ and $x^2 - 8 =0$
So the $x$-intercept are $x = 0$, $x = 2.8284$ and $x = -2.8284$


C. Symmetry.
$f(-x) = f(x)$, therefore the function is symmetric to $y$-axis.

D. Asymptotes.
None.

E. Intervals of Increase or Decrease.
If we take the derivative of $f(x)$, we have $f'(x) = 16x - 4x^3$

$
\begin{equation}
\begin{aligned}
\text{when } f'(x) &= 0\\
\\
0 &= 16x-4x^3\\
\\
0 &= 4x(4-x^2)\\
\\
\\
\\
\text{we have, }\\
\\
x &= 0 \text{ and } x^2 - 4 = 0\\
\\
\text{The critical numbers are, } \\
\\
x &= 0 \text{ and } x = \pm 2

\end{aligned}
\end{equation}
$

So, the intervals of increase or decrease are...

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f''(x) & \text{Concavity}\\
\hline\\
x < - 2 & + & \text{increasing on } (-\infty, -2)\\
\hline\\
-2 < x < 0 & - & \text{decreasing on } (-2,0)\\
\hline\\
0 < x < 2 & + & \text{increasing on } (0,2)\\
\hline\\
x > 2 & - & \text{decreasing on } (2, \infty)\\
\hline
\end{array}
$



F. Local Maximum and Minimum Values.
Since $f'(x)$ changes from positive to negative at $x = 2$ and $x = -2$, then $f(2) = 16$ and $f(-2) = 16$ are local maximum. On the other hand, since $f'(x)$ changes from negative to positive at $x = 0$, then $f(0) = 0$ is local minimum.


G. Concavity and Points of Inflection.

$
\begin{equation}
\begin{aligned}
\text{if } f'(x) &= 16x - 4x^3, \text{ then }\\
\\
f''(x) &= 16 - 12x^2\\
\\
\\
\\
\text{when } f''(x) &= 0,\\
\\
0 & = 16 - 12x^2
\end{aligned}
\end{equation}
$

Thus, the concavity can be determined by dividing the interval to...

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f''(x) & \text{Concavity}\\
\hline\\
x < -1.1547 & - & \text{Downward}\\
\hline\\
-1.1547 < x < 1.1547 & + & \text{Upward}\\
\hline\\
x > 1.1547 & - & \text{Downward}\\
\hline
\end{array}
$


H. Sketch the Graph

College Algebra, Chapter 3, 3.6, Section 3.6, Problem 44

Determine the functions $f \circ g, \quad g \circ f, \quad f \circ f$ and $g \circ g$ and their domains if $\displaystyle f(x) = \frac{2}{x}$ and $\displaystyle g(x) = \frac{x}{x+2}$
For $f \circ g$,

$
\begin{equation}
\begin{aligned}
(f \circ g)(x) &= f(g(x)) && \text{Definition of } f \circ g\\
\\
(f \circ g)(x) &= f \left( \frac{x}{x + 2} \right) && \text{Definition of } g\\
\\
(f \circ g)(x) &= \frac{2}{\frac{x}{x+2}} && \text{Simplify}\\
\\
(f \circ g)(x) &= \frac{2(x+2)}{x} && \text{Definition of } f
\end{aligned}
\end{equation}
$

The function can't have a denominator equal to zero.
So the domain of $f \circ g$ is $(-\infty, 0) \bigcup (0,\infty)$

For $g \circ f$

$
\begin{equation}
\begin{aligned}
(g \circ f)(x) &= g(f(x)) && \text{Definition of } g \circ f\\
\\
(g \circ f)(x) &= g \left( \frac{2}{x} \right) && \text{Definition of } f\\
\\
(g \circ f)(x) &= \frac{\frac{2}{x}}{\frac{2}{x}+2} && \text{Simplify}\\
\\
(g \circ f)(x) &= \frac{2x}{2x(1 + x)} && \text{Simplify}\\
\\
(g \circ f)(x) &= \frac{1}{1+x} && \text{Definition of } g
\end{aligned}
\end{equation}
$

The denominator is not defined when $x = y$. So the domain of $g \circ f$ is $(-\infty, -1) \bigcup (-1, \infty)$

For $f \circ f$,

$
\begin{equation}
\begin{aligned}
(f \circ f)(x) &= f (f (x) ) && \text{Definition of } f \circ f\\
\\
(f \circ f)(x) &= f \left( \frac{2}{x} \right) && \text{Definition of } f\\
\\
(f \circ f)(x) &= \frac{\frac{2}{2}}{x} && \text{Simplify}\\
\\
(f \circ f)(x) &= x && \text{Definition of } f
\end{aligned}
\end{equation}
$

The function is define for all values of $x$, so the domain of $f \circ f$ is $(-\infty, \infty)$

For $g \circ g$,

$
\begin{equation}
\begin{aligned}
(g \circ g)(x) &= g(g(x)) && \text{Definition of } g \circ g\\
\\
(g \circ g)(x) &= g \left( \frac{x}{x+2} \right) && \text{Definition of } g\\
\\
(g \circ g)(x) &= \frac{\frac{x}{x+2}}{\frac{x}{x+2}+2} && \text{Simplify}\\
\\
(g \circ g)(x) &= \frac{\frac{x}{\cancel{x+2}}}{\frac{x+2x+4}{\cancel{x+2}}} && \text{Simplify}\\
\\
(g \circ g)(x) &= \frac{x}{3x+4} && \text{Definition of } g
\end{aligned}
\end{equation}
$

The denominator is not define when $\displaystyle x = -\frac{4}{3}$. So the domain of $g \circ g$ is $\displaystyle \left( -\infty, \frac{-4}{3} \right) \bigcup \left( \frac{-4}{3}, \infty \right)$

What do the parts about King George in the Constitution mean?

King George III is not mentioned in the Constitution. The Constitution of the United States was written in 1787, more than a decade after the colonies had declared their independence from Great Britain, and four years after independence was formally established by the Treaty of Paris. So King George was not relevant to the Constitution, though its prohibitions against religious tests, noble titles, writs of assistance, and other clauses certainly were a tacit reaction to the actions of the King and Parliament. 
It is likely, however, that this question is referring to the Declaration of Independence, which levies many accusations against King George. These accusations ranged from claims that he refused to approve laws that were good for the colonies, to his approval of unjust taxes, to allegations that he urged enslaved people and Native Americans to rise up against the Americans during the early days of the Revolution. Of course, most of these actions, to the extent they actually occurred, were not really undertaken by the King. In fact, it was Parliament that levied taxes, and the king's ministers who formulated imperial policy. For many years, the colonists had actually protested to the King, who they claimed was the protector of their liberties against the corrupt members of Parliament. By levying these accusations against the King, then, they sent a clear message that they were striking out on their own. They were moving from claiming rights as British subjects to rejecting British rule outright.

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 5

At what rate is the height of the water increasing?

Given: $\displaystyle r = 5m, \frac{dv}{dt} = 3m^3/min$

Required: $\displaystyle \frac{dh}{dt}$

Solution: Let $V = \pi r^2h$ be the volume of the cylinder

where $r$ = radius

$\qquad h$ = height

It is also stated in the problem that $r$ is a constant so,


$
\begin{equation}
\begin{aligned}

\frac{dv}{dt} =& \frac{dv}{dh} \left( \frac{dh}{dt} \right) = \pi r^2 \left( \frac{dh}{dt} \right)
\\
\\
\frac{dv}{dt} =& \pi r^2 \left( \frac{dh}{dt} \right)
\\
\\
\frac{dh}{dt} =& \frac{1}{\pi r^2} \left( \frac{dv}{dt} \right)
\\
\\
\frac{dh}{dt} =& \frac{1}{\pi (5)^2} (3)
\\
\\

\end{aligned}
\end{equation}
$


$\fbox{$\large \frac{dh}{dt} = \frac{3}{25 \pi} m/min $}$

What was William Tecumseh Sherman's role in the war?

I am going to answer this question based on the assumption that you mean William Tecumseh Sherman, Union general during the Civil War.  Sherman was one of the most prominent generals of the Western Theater of the Civil War, having worked closely with Grant in the taking of Vicksburg, the final link the Confederates still possessed on the Mississippi River in 1863.  In 1864 Sherman was given a major campaign and his army marched from southern Tennessee to South Carolina, tearing railroads, telegraph lines, and anything else that the Confederacy might have of value.  His soldiers lived off the land and brought the misery of war home to the Deep South. Sherman's "March to the Sea" was one of the major factors that led to the end of the war.  Sherman's capture of Atlanta was a welcome piece of victory for the North at the time of Lincoln's re-election campaign in 1864.  After reaching the sea in South Carolina, Sherman then marched North, continuing to destroy vital supplies and infrastructure.  Sherman was going to link his army with Grant's before the final push to Richmond, but Lee surrendered to Grant at Appomattox Court House soon after Richmond fell to Union forces.  Sherman took the final surrender of the Army of Tennessee in North Carolina soon after Richmond.

The Piligrims established a tradition of more or less peaceful coexistence with the Native Americans that lasted over fifty years. Why did that tradition collapse in the 1670s and what might have been done to prevent it?

The Pilgrims established peace with the Wampanoags around Cape Cod after they arrived in 1620. Their migration was followed by other migrations that brought increased English settlement to New England. For example, 20,000 Puritans came to the area during the Great Migration of 1620-1640 to escape religious persecution in England. They settled along the Connecticut River and the coast and were beginning to settle at points in between, causing increased pressures on the Native Americans in the region to give up their lands. In addition, the later settlers were not part of the original peace settlement that the Pilgrims had established with Native Americans.
In 1675, King Philip's War broke out between the English settlers and Native Americans, who were led by Metacom (also called King Philip), the son of Massasoit (who had lived peacefully alongside the Pilgrims). This war led to the horrific defeat of the Wampanoags and Narragansett tribes. As a result, the flow of English settlement over Native American lands in most of New England was unrestricted. The war might have been prevented if the English settlers had respected Native American claims to the land, but the English did not. 

What type of substance is always made up of a single type of atom?

All matter is composed of atoms. If a substance is made of only a single type of atom, then the substance is an element. Conveniently, all of the known elements are listed on the periodic table of elements. Substances like gold, silver, oxygen, carbon, hydrogen, and helium are all elements. This means that gold is made of gold atoms, and oxygen is made of oxygen atoms. Additionally, because elements are made up of a single atom, they cannot be broken down into simpler substances; they are pure.
A substance that is made of at least two different elements that are chemically bonded together is a compound. Water is a common example. It is made of hydrogen and oxygen. If the two elements are not bonded together, then the substance is a mixture. Air is a good example of a mixture.
https://www.pobschools.org/cms/lib/NY01001456/Centricity/Domain/517/Copy%20of%20elements-compounds-mixtures020714hw.pdf

How do you know that the children in the poem do not like the work they do?

Blake's "The Chimney Sweeper" shows in various ways that the children do not like the work they do. First, the little boy telling the story mixes up the word "sweep," which the chimney sweepers are supposed to shout in the street to get jobs, with the word "weep," suggesting (although this also is meant to show the little ones lisp) he associates the job with tears and crying.
Then, Tom Dacre does cry when his head is shaved, and he has to be comforted by the narrator. Sadness seems to permeate this job.
Third, the narrator dreams of being released from his "coffin," which is an unhappy image for a bed or a chimney, and being allowed to play outside in the sun and green grass, splashing and getting clean in a river. That this ordinary outdoor activity is dream that is out of reach of the chimney sweeps shows how harsh their young lives are.
At the end of the poem, innocent Tom is happy despite the cold and dark because of his dream: it is not anything to do with his job or real existence that brings him joy, but a fantasy world that is entirely different from his reality.

There are several reasons that we know that the children do not enjoy their work in "The Chimney Sweeper: When my mother died I was very young" by William Blake. 
First, the original audience of the poem and most educated readers would assume that working as in indentured servant, living in dire poverty, and spending one's life crawling up and cleaning narrow filthy chimneys is not enjoyable.
Next, in the first stanza the narrator describes the death of his mother and his being sold by his father as a child so young he could barely speak. The narrator describes Tom Dacre crying. The vision that keeps Tom happy despite the cold and miserable environment in which he works is one of dying, being placed in a coffin, and then going to heaven. What this tells us is that the children are so miserable in their work that they think of dying as preferable.

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 30

a.) Suppose that $f(t) = t^2 - \sqrt{t}$, find $f'(t)$.

Using the definition of derivative




$
\begin{equation}
\begin{aligned}

\qquad f'(t) =& \lim_{h \to 0} \frac{f(t + h) - f(t)}{h}
&&
\\
\\
\qquad f'(t) =& \lim_{h \to 0} \frac{(t + h)^2 - \sqrt{t + h} - (t^2 -
\sqrt{t})}{h}
&& \text{Substitute $f(t + h)$ and $f(t)$}
\\
\\
\qquad f'(t) =& \lim_{h \to 0} \frac{\cancel{t^2} + 2th + h^2 - \sqrt{t + h} - \cancel{t^2} + \sqrt{t}}{h}
&& \text{Expand the equation and combine like terms}
\\
\\
\qquad f'(t) =& \lim_{h \to 0} \frac{2th +h^2 - \sqrt{t + h} + \sqrt{t}}{h}
&& \text{Isolate the terms that has square root and multiply it by its conjugate}
\\
\\
\qquad f'(t) =& \lim_{h \to 0} \frac{2th + h^2}{h} + \frac{\sqrt{t} - \sqrt{t + h}}{h} \cdot \frac{\sqrt{t} + \sqrt{t + h}}{\sqrt{t} + \sqrt{t + h}}
&& \text{Get the factor of the first term and multiply both numerator and denominator of the second term by $(\sqrt{t} + \sqrt{t + h} )$}
\\
\\
\qquad f'(t) =& \lim_{h \to 0} \frac{\cancel{h}(2t + h)}{\cancel{h}} + \frac{t - \cancel{\sqrt{t(t + h)}} + \cancel{\sqrt{t (t + h)}} - (t + h)}{h(\sqrt{t} + \sqrt{t + h})}
&& \text{Cancel out and combine like terms}
\\
\\
\qquad f'(t) =& \lim_{h \to 0} 2t + h + \frac{\cancel{t} - \cancel{t} - h}{h(\sqrt{t} + \sqrt{t + h})}
&& \text{Combine like terms in the second term}
&&
\\
\\
\qquad f'(t) =& \lim_{h \to 0} 2t + h - \frac{\cancel{h}}{\cancel{h}(\sqrt{t} + \sqrt{t + h})}
&& \text{Cancel out like terms in the second term}
\\
\\
\qquad f'(t) =& \lim_{h \to 0} \left( 2t + h - \frac{1}{\sqrt{t} + \sqrt{t + h}} \right) = 2t + 0 - \frac{1}{\sqrt{t} + \sqrt{t + 0}} = 2t- \frac{1}{\sqrt{t} + \sqrt{t}}
&& \text{Evaluate the limit}
\\
\\
f'(t) =& 2t - \frac{1}{2 \sqrt{t}}
&&

\end{aligned}
\end{equation}
$


b.) Compare the graphs of $f$ and $f'$ and check whether your answer in part (a) is reasonable.

In The Communist Manifesto, what do Marx and Engels have to say about people in pain and who experiences pain under capitalism?

In The Communist Manifesto, Marx and Engels suggest that the way capitalism exploits labor for profit is painful for the working class.  
The Communist Manifesto is quite direct in attributing exploitation for profit as the reason that people suffer. Marx and Engels argue that capitalism is predicated on manipulation.  The wealthiest of people generate their profit at the cost of workers.  For example, the owner of the factory is able to make more money when the worker is paid less for their efforts.  The less the worker receives, the more profit the owner makes.  Marx and Engels believe this helps to explain why capitalism is synonymous with suffering and pain for the working class:  "These labourers, who must sell themselves piecemeal, are a commodity, like every other article of commerce, and are consequently exposed to all the vicissitudes of competition, to all the fluctuations of the market."  Marx and Engels feel the wealthy have no qualms about increasing the suffering of the working class in order to meet the demands of the marketplace.
Marx and Engels are emphatic in suggesting that capitalism's success is dependent on the workers' pain. Suffering is unavoidable.  Marx and Engels describe how "masses of labourers, crowded into the factory, are organized like soldiers" and exist "under the command of a perfect hierarchy of officers and sergeants."  Such control makes workers "slaves of the bourgeois class, and of the bourgeois State."  In order for capitalism to thrive, Marx and Engels believe that the laborer is "daily and hourly enslaved by the machine, by the overlooker, and, above all, by the individual bourgeois manufacturer himself."  Suffering is inevitable when capitalism reduces workers to slaves.  When the drive for economic profit makes workers a mere "commodity," the end result is the workers' pain.  As a result of its objectification of the working class, Marx and Engels blame capitalism for the suffering it causes. 

Does Zeffirelli's Hamlet film (1990) lack any elements of a Shakespearean Tragedy? For example, a tragic hero (Hamlet) and supernatural elements (Ghost) are evident as Zeffirelli maintains the general story line of the original play. However, he removes Fortinbras, the conflict with Norway, and reduces Hamlet's interactions with Horatio. So, do Zeffirelli's cuts/edits change the Hamlet story line enough for it to not fulfill some of the elements of a Shakespearean Tragedy? Thank you for your help!

In my view, the film doesn't change the story line enough to disqualify it as a Shakespearean tragedy. Even with its omission of the Fortinbras subplot and Hamlet's abbreviated interactions with Horatio, the film still contains all of the elements of a Shakespearean tragedy: a tragic hero, a struggle between good and evil, a fatal character flaw of the tragic hero, the tragic destruction of the good along with the bad, plenty of both external and internal conflicts, supernatural elements, a lack of poetic justice, and some comic relief. While the irony of Young Fortinbras's ultimate taking of the Danish throne is missing entirely, the tragic elements inherent in the play remain intact in this adaptation (despite its many flaws as a film).
https://owlcation.com/humanities/Shakespearean-Tragedy-Definition-and-Characteristics-of-Shakespearean-Tragedy

How does Lynda Barry's text One Hundred Demons (pages 98–106) employ media and/or modes? What do you find particularly challenging? What tensions, ambiguities, or uncertainties may an intermediality or modality scholar encounter when dealing with the text? How does the literary text test the limits of theories of intermediality and/or multimodality? Lynda Barry, One Hundred Demons (2002), pp. 98-106

This section of the text deals with the themes of transformation, betrayal, and memory. Barry’s art has always seemed like a mask to me: her stylized, intentionally inelegant and ugly drawings of herself seem as much an attempt to hide behind the drawing as an attempt at honest representation. In One Hundred Demons, Barry is coming as close as she can to autobiography. She is doing her best, I think, to tell the “truth,” although what the “truth” might be behind how she feels about Ev is difficult to explain.
This is why the inclusion of the snapshot of the real Barry and Ev, as children, is so important. In terms of intermediality, it represents a moment when Barry steps out from behind the mask of her art and and asserts the reality of her experience. In this chapter, Barry remembers the summer she spent watching her younger brothers while her parents both had affairs and the moment the ”magic” of childhood disappeared. That passage into adolescence is what separates Barry from Ev; the empathetic bond that Ev and Barry shared is replaced by listening to moody pop music in dark rooms. At the time, Barry did not fully understand what was going on inside her or why it was suddenly inappropriate to have an eleven-year-old friend. The photo, on the other hand, makes things very clear: there is Ev in the foreground, hamming it up, and behind her, with a guilty smile, is Barry. It explains their relationship in a way the drawings cannot. It also represents a tremendous personal risk for Barry, in that it is a window into her real life unmediated by her art.

In the novel Monster by Walter Dean Myers, how is Steve treated like he is less than human?

Steve Harmon is the protagonist of Walter Dean Myers's Monster. He has been accused of participating in the murder of a shopkeeper by acting in the role of lookout. Throughout the novel, Steve is ever the voiceless observer. Myers uses the other characters to create the narrative of the crime, the arrest, and the trial, but we're never given Steve's version of events. Myers never confirms or denies Steve's involvement. He isn't given the opportunity to defend or even stand up for himself.
Steve is young, black, and poor. This combination causes him to be persecuted and forgotten. The prosecution presents Steve and co-defendant James King as "monsters." Even Steve's attorney, Kathy O'Brien, is disinterested in his guilt or innocence. Her job is to defend him, and she does work hard to win the case. Steve suspects that she thinks he's guilty, and they never build a rapport. At the end of the case, after they win, Steve moves to hug her and she gathers her papers and walks away.
Throughout the novel, Steve tries to make sense of who he believes himself to be, juxtaposed against the interpretations of those around him. He is surrounded by people who think he is guilty, call him a monster, and express that he is less than they are. In his heart, Steve believes he's a good kid, but he's constantly second-guessing it. Notably, those judging him throughout the novel do not know much about him at all. Since he hangs around "the wrong crowd," is a minority, and doesn't have much money, he is dismissed by them and categorized as nothing.

Throughout the novel, Myers examines how the judicial system treats young minorities as subhuman beings instead of unique individuals. At the beginning of the novel, the prosecuting attorney, Sandra Petrocelli, labels Steve Harmon a "monster." From the start of the trial Steve is viewed as less than human. Throughout the majority of the trial, Steve is voiceless and unaware of what is going on. He is essentially treated as an absent participant whose fate lays in the hands of the attorneys and jurors. Whenever Steve is not in the courtroom, he is locked behind bars inside a jail. Steve describes his violent, dangerous environment as a place where inmates continually attempt to harm one another at all hours of the day. Steve fears for his life and is forced to act like he is a callous, threatening individual in order to survive. Steve's experience in prison also makes him feel like he is less than human.

What was the purpose of writing the novel?

According to Louis Lowry herself, the idea for this novel was inspired by the history of Nazi-occupied Denmark as it was narrated to Lowry by her Danish friend, Annelise. Annelise had been a child when the events happened. Lowry admits that the story is set in a time and culture that is different than her own, but the idea is to show the value of humanity and the role that humans play in moments of adversity.
Essentially, Lowry wanted to inform and entertain at the same time. She tells a historical fiction story based on true events that happened to her friend, as well as to other characters who are immortalized in the novel. However, rather than dwelling entirely on the historical nature of the novel, she extrapolates the value of human agency, emphasizing on what happens when people see others in danger.
Moreover, she further expands upon the topics of empathy, human connection, mercy, and industry. Notice that, in this novel, people who would not have to worry about the Nazis persecuting them still put their lives in peril to help those who are in danger of being captured by the Nazis. Those who empathize with the persecuted plan, execute, initiate, and hope, all on behalf of the Jewish people, and not themselves. This is quite powerful!
Notice also that some feelings, such as empathy, sympathy, and industry are felt differently from person to person. Number the Stars, however,shows how, when people get together for a common cause, those feelings become stronger and focused on a purpose. The purpose is to help others battle the injustice of an evil regime. Telling this from the point of view of a child shows these emotions from an even more powerful, innocent, and unbiased perspective.
https://www.scholastic.com/teachers/articles/teaching-content/number-stars-authors-note/

Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 13

You need to first find derivative of the function using the product rule:
f'(x)= (x^3 + 4x)'*(3x^2+2x-5)+(x^3 + 4x)*(3x^2+2x-5)'
f'(x)= (3x^2 + 4)*(3x^2+2x-5)+(x^3 + 4x)*(6x+2)
f'(x)= 9x^4 + 6x^3 - 15x^2 + 12x^2 + 8x - 20 + 6x^4 + 2x^3 + 24x^2 +8x
Combining like terms yields:
f'(x)=15x^4 + 8x^3 + 21x^2 + 16x - 20
Hence, evaluating the derivative of the function, yields f'(x)=15x^4 + 8x^3 + 21x^2 + 16x - 20.
You need to evaluate f'(c) at c = 0, hence, you need to replace 0 for x in equation of f'(x).
f'(0)=15*0^4 + 8*0^3 + 21*0^2 + 16*0 - 20
f'(0)=-20
Hence, evaluating the derivative of the function, yields f'(x)=15x^4 + 8x^3 + 21x^2 + 16x - 20 and evaluating f'(c) at c = 0, yields f'(0)= -20.

How would you describe Liem from The Refugees by Viet Thanh Nguyen?

Liem is the main character of “The Other Man” from The Refugees. He is eighteen years old and grew up in Long Xuyen, Vietnam. When he was seventeen, his family sent him to work in Saigon. While he was there, Liem learned a bit of English and realized that he needed to flee the communist regime should Saigon fall to the People’s Army of Vietnam (the fall of Saigon was preceded by a mass evacuation of American troops as well as an exodus of Vietnamese citizens who feared being seen as supporters of the southern Vietnamese government). Liem boards a barge and travels to Camp Pendleton in San Diego. He is eventually sponsored by a Parrish, a wealthy San Franciscan man, and moves into Parrish’s comfortable home. Liem finds work at a liquor store and is generally happy with his new life in the United States. Though he is grateful to Parrish, Liem finds himself attracted to Parrish’s lover, Marcus, and they have an affair while Parrish is out of town. Through his affair with Marcus, Liem learns more about his sexuality and begins to think more deeply about how he can shape his own identity.

What is the author's main point in Black Boy?

The author's main point in Black Boy is the redemptive power of art. For example, when a schoolteacher is boarding with Richard's family and reads him Bluebeard (a novel), Richard's world is forever changed. Wright writes:

"I ceased to see the porch, the sunshine, her face, everything. As her words fell upon my new ears, I endowed them with a reality that welled up somewhere within me.... As she spoke, reality changed, the look of things altered, and the world become peopled with magical presences" (page 44).

Literature causes Richard's world to change forever, and it is almost as if he is reborn when the schoolteacher reads aloud to him. Richard's childhood world is scarred by poverty, racism, hunger, and misunderstanding. Only the world of art and literature can feed his desire for a better world--a world he doesn't find in the racist South or the communist groups of the North. Even as a child, Richard knows that when he gets older, "I would buy all the novels there were and read them to feed that thirst for violence that was in me, for intrigue, for plotting, for secrecy, for bloody murders" (page 45). Only literature can sate Richard's desire to know more of the world and to experience more of the world than what he can experience as a poor African American child in the South.
Early in the story, Richard, as a four-year-old, is obsessed with fire, "fascinated with the quivering coals" (page 4). Richard is fixated by the fire, which is symbolic of the great life and vitality inside of him that cause him dissatisfaction in the South, where he must contend with racism, poverty, and his family's sense of religiosity (which he does not share). In the North, he is not satisfied by a life of routine labor or by the promises of the communist party. 
In the end, Richard believes that for white people to understand his life, it "would have meant nothing short of a revolution in theirs" (page 310). He seeks to provide white people with "the inclusion in their personalities of knowledge of lives such as I lived and suffered" (page 310). It is through writing that Richard seeks to provide this revolution and to provide redemption and satisfaction for himself.

Junior gets an email from his sister. Where and how was she doing?

In chapter 13, Junior gets an email from his sister, Mary, dated November 16, 2006. The letter provides a point of view shift as Mary is able to speak for herself and add a different layer of legitimacy to the "absolutely true" portion of The Absolutely True Diary of a Part-Time Indian.
In her email, Mary explains that she is currently living in Montana with her husband. Her email is an overly optimistic one as she explains to her brother that dreams can come true and details how happy her life is. She gushes over her love for her husband, their new town, and her brother. She admits to having some trouble looking for a job and gives hints to homesickness as she describes the traditional Indian frybread on her honeymoon at Flathead Lake as being nearly as good as their grandmother's. Mary explains that the reservation (the Flathead reservation) is very large, as it is comprised of six or seven towns in Montana that are different in that they seem to have more white people than Indians.
Mary's short letter is extremely happy, but as the reader knows her fate, it can be read as one that masks her pain.

What was the attitude of President Johnson toward the Reconstruction of the South?

Like Lincoln, Johnson wanted the former Confederate states brought back into the Union as quick as possible. Johnson did not insist on the Radicals "Ironclad Oath" which prohibited anyone who willingly helped the Confederacy from taking an active role in government.  Johnson realized that this would not only prohibit former Confederate bureaucrats from holding office, but it would also stop former soldiers of the Confederacy from playing an active role in Reconstruction.  Johnson, a resident of East Tennessee before the war and military governor of the state during the conflict, did not like the planter class because he felt as though they dragged the majority of Southerners into the Civil War.  Johnson also believed that the former slaves would be for the planters' interests because of the security provided under the slave system.  Johnson, while desiring free enterprise in the South, wanted to see a system where blacks would continue to work the former plantations for wages.  He saw black suffrage as a hindrance to Reconstruction because it would only cause whites in the South to hinder the Reconstruction process.  Johnson wanted the Reconstruction South to be ably maintained, even if this meant giving government positions to the planter class that he personally despised.  Johnson personally pardoned many former Confederate officials, much to the consternation of the Radicals in his own Cabinet and Congress.   

Single Variable Calculus, Chapter 6, 6.3, Section 6.3, Problem 30

$\displaystyle 2 \pi \int^2_0 \frac{y}{1 + y^2} dy$ represents a volume of a solid. Describe the solid.

We can see from the equation that shell method was used with horizontal strips. The distance of these strips from a line that it will be revolved in is $y$. If you revolve this length about such line, you'll get a circumference of $C = 2 \pi y$. By these data, we assume that the line we are talking is $x$-axis. Also, the height of these strips resembles the height of the cylinder by $\displaystyle H = x_{\text{right}} - x_{\text{left}} = \frac{1}{1 + y^2} - 0$. Thus,


$
\begin{equation}
\begin{aligned}

V =& \int^2_0 C(y) H(y) dy
\\
\\
V =& \int^2_0 (2 \pi y) \left( \frac{1}{1 + y^2} \right) dy
\\
\\
V =& 2 \pi \int^2_0 \frac{y}{1 + y^2}

\end{aligned}
\end{equation}
$


In short, this expression is obtained by rotating the region bounded by $\displaystyle x = \frac{1}{1 + y^2}$ and $x = 0$ about $x$-axis using shell method.

What is your response to James Joyce's "Araby"? What do you agree and disagree with in this piece? What does the author get right or wrong?

One way to think about these questions about Joyce's short story "Araby" (published in 1914 in his book Dubliners) is to consider what Joyce is trying to represent in this piece and whether or not he succeeds. The story is told in first-person from the perspective of a boy who goes to school, plays with his friends in the streets, and has a crush on a girl who is never given a name but who is known as Mangan's sister. All he wants to do is go to the bazaar, which takes place on the weekend, to buy something for the girl. After he promises this to her, the boy describes how, during the course of the next week as he waited for his chance to go to the bazaar, everything else in his life became drab. He explains,




What innumerable follies laid waste my waking and sleeping thoughts after that evening! I wished to annihilate the tedious intervening days. I chafed against the work of school. . . . I answered few questions in class. I watched my master's face pass from amiability to sternness; he hoped I was not beginning to idle. I could not call my wandering thoughts together. I had hardly any patience with the serious work of life which, now that it stood between me and my desire, seemed to me child's play, ugly monotonous child's play.







Everything he normally did and all the people with whom he normally associated became essentially meaningless or childlike to him as he waited, with great apprehension and anxiety, for the bazaar.
Joyce focuses in on the boy's feelings as he waits for Saturday evening to arrive. You might consider whether you think he does this effectively and, as you do so, think about how he describes the way the boy felt before his conversation with the girl, as he waited for the bazaar, and then, finally, what he was thinking and feeling at the bazaar itself. Are there certain words Joyce uses? Does the tone he use or the setting he builds throughout the story add anything of value to our understanding of the boy's experience?
Another aspect of the story to think about is how the relationships between the boys and the adults in their world, as well as between the boys and the girls in their neighborhood, are represented. Do you think that Joyce does a good job of describing these relationships? Can you relate to how the boy thinks about his uncle, his aunt, Mrs. Mercer, and so on? What about with how he relates to the girl? At what period in your life might you have felt similarly to how the boy was feeling, or might have related to girls (or boys) and adults in this way?
You might say that the boy was crushed by the reality of the bazaar, which turned out not to be all that he made it in his mind, and that this realization also demystified the girl for him, "bursting his bubble," as it were. What are your reactions to this ending? Could you see something similar happening in your own life?

Where and when was Gandhi born?

Mohandas Karamchand Gandhi was born in Porbandar on October 2, 1869, a city on the west coast of Kathiawar peninsula in British India (now the Indian state of Gujarat). He was the youngest of four children born to Karamchand and Putlibai Gandhi; Karamchand also had two daughters from a previous marriage. His family on his father’s side had lived in the house where he was born since the 17th century. The males in the family, including Gandhi’s father, served as the chief ministers of the principality of Porbandar. His mother was descended from a family of wealthy local merchants. Talented and religious, she influenced her son greatly, despite his rebellious attitude as a youth, interested in going to England for his university education; such a choice violated the strict ritual prohibitions associated with his caste. His ancestral house is now part of Mahatma Gandhi’s national memorial, Kirti Mandir, which honors six religions in its architecture, incorporating Hindu, Buddhist, Jain, Parsi, Christian, and Muslim features.
 

A chain of mass M and length L is suspended vertically with its lower end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length x of the chain has fallen? Neglect the size of the individual links.

There are two quantities which effect the reading on the scale. The weight of the chain that has accumulated on the scale after falling a distance x and the impulse per unit time imparted by the chain colliding with the scale. The total force is the sum of these two contributions.
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html

What do you think Saki is trying to show about the nature of children and adults in Lumber Room?

Your question is asking you to form an opinion based on the text of the story. In “The Lumber Room” by Saki, the author is trying to demonstrate how adults often believe they are wiser than children based solely upon their age, not their intellect.
Saki creates a witty, cunning, intellectual character as she develops the protagonist, Nicholas. Even as a child, he has the ability to outsmart the adults in his family.
While sitting at the breakfast table, Nicholas claims there is a frog in his milk and bread. The adults assure him this is an impossibility until he produces the frog, which he placed there himself. Saki is demonstrating how adults often refuse to listen to children when something seems implausible.
One of the adults attempts to impose her authoritarian ways upon Nicholas but he is able to outsmart her a number of times. He is also able to prove that she does not listen when the other children are talking. He explains why the beach trip he is being excluded from will be a disaster based on what the other children said. Unfortunately, the aunt was so caught up in her anger and intent to punish Nicholas that she did not hear what they said.
In general, Saki is demonstrating the nature of adults to feel superior and wiser than children. They consider themselves to be authority figures. It is the nature of children to test their limits with authority figures, and many of them have valid reasons for doing so.

Compare the business models and areas of strength of Apple, Google, and Microsoft.

Alphabet (the parent company of Google), Apple, and Microsoft as of 2017 were the three top companies in the world by market value. All three are technology companies with a strong focus on innovative software, but otherwise Google is quite different from the other two in its business model and the era in which it was founded. In some ways, though, all three companies are converging.
The oldest of the three companies is Microsoft, officially founded in 1975, which started by offering a programming language (Basic) and then an operating system (MS DOS, which later evolved into Windows) and eventually business and productivity software, with well-known products such as Word and Excel. Although Microsoft has made limited forays into hardware, its greatest success has been in dominating a software market for open architecture hardware. In other words, Windows runs on computers of similar architecture from multiple manufacturers. It only gradually moved into the hardware market with products such as the Xbox gaming system, Microsoft phones, and the Surface computer. Microsoft also is active in the server business and attempts to diversify by buying promising technology start-ups as well as innovating internally.
In contrast to Microsoft's reliance on open architecture, Apple remains a tightly closed shop, selling premium-priced computers, music players, and smartphones that consistently integrate an Apple user interface across multiple product lines. The closed nature of the Apple ecosystem has made Apple enormously profitable, as once one has invested in an Apple device, one is committed to making additional Apple purchases. Like Microsoft, Apple started early in the personal computer era, but it began with a greater focus on hardware, graphical interfaces, and upscale design rather than systems emphasizing functionality and raw computing power at a given price point. Apple's greatest financial success came with its early entry into the mobile market, with the iPod, iPad, and iPhone each dominating their initial markets and remaining premium products locking users into Apple ecosystems.
Google was founded in 1998 and began as a search engine company in the era of the internet. Thus, it differs from the other two in having started as an internet company. The bulk of its search revenue comes from advertising, and it pioneered the concept of enticing users to give away free information about themselves (which Google could then repackage and sell to advertisers). Its business model in a sense is one which trades use of a search engine for data about the people searching, and its most profitable product is the data it holds on users. Google, like the other two firms, has gradually been diversifying, offering tablets, small portable computers, smartphones, a popular smartphone operating system (Android), a search engine (Chrome), mapping software, email (Gmail), and other software. It is also competing in new areas such as self-driving cars and augmented reality, which merge hardware and software.

What did Prospero do with his magical books and wand?

Most of the magic that is referenced in Shakespeare's The Tempest is good magic, or "white magic," which is ultimately used to promote good rather than to harm. Prospero, the Duke of Milan, uses magic throughout the play. He uses magical books and a wand to employ his powers.
In act V, scene I, Prospero and Ariel enter; Duke Prospero is wearing his magic robes. Prospero tells Ariel that everything is going according to plan. Ariel explains that all of the people affected by Prospero's magic are very upset and in great turmoil:

"They cannot budge till your release. The king,His brother, and yours, abide all three distracted,And the remainder mourning over them,Brimful of sorrow and dismay . . .Your charm so strongly works 'emThat if you now beheld them,your affections would become tender" (lines 11–18).

Prospero responds that he will soon take pity on the people he's used magic on, even though they committed many wrongs. He will still show them mercy; he will stop the spells he cast on them:

"Go release them Ariel.My charms I'll break, their senses I'll restore,And they shall be themselves" (lines 31–33).

After he tells Ariel that he will end his magic, he explains his future plans for his staff and books:

"I'll break my staff,Bury it certain fathoms in the earth,And deeper than did ever plummet soundI'll drown my book" (lines 56–59).

Prospero plans to break his staff and bury it underground. He plans to send his books (of magic spells) to the deepest depths of the ocean. Prospero no longer plans to make use of these magical tools.
http://shakespeare.mit.edu/tempest/full.html

Compare and contrast the poems “Ozymandias” by Percy Shelley and “Ulysses” by Alfred, Lord Tennyson. What are these poems’ views of life achievements? What similarities exist between Ulysses and Ozymandias? How do their attitudes differ in regards to their eventual goals? How do these similarities and differences contribute to the overall tones and interpretations of the poems?

Percy Shelley's “Ozymandias” was written about the statue of an ancient Egyptian pharaoh, a real historical person. Tennyson's “Ulysses” is about a Greek mythological hero, more commonly known in modern schools as Odysseus, from Homer's epic The Odyssey.
The similarities between the two poems lie in their treatment of power and fame as fleeting. Although Ozymandias wanted to ensure his immortality by building a great statue, Shelley's poem shows us this is ultimately impossible—this is what the statue looks like now, according to the poem's speaker:

Two vast and trunkless legs of stone 
Stand in the desert. . . Near them, on the sand, 
Half sunk a shattered visage lies

With time, everything fades, even powerful rulers and their impressive memorials. Ulysses feels the same kind of thing is happening to him while he still lives. He has been a great adventurer, and warrior, and although he is now the king of Ithaca, he already sees the end coming.
Ulysses expresses this idea in this way:

How dull it is to pause, to make an end,
To rust unburnish'd, not to shine in use!
As tho' to breathe were life! Life piled on life
Were all too little, and of one to me
Little remains

Ulysses is still living, but he doesn't feel very alive. He feels almost like Ozymandias's statue; he is crumbling, he has lost his sense of grandeur.
Ozymandias and Ulysses are different in terms of their desire to rule. Ozymandias loves the power that comes from governing a kingdom. We see this in the words he had transcribed at the base of his statue:

My name is Ozymandias, King of Kings;
Look on my Works, ye Mighty, and despair! 

Ulysses, however, doesn't want to rule anymore. He wants to return to the life he led as a younger man:

Death closes all: but something ere the end, 
Some work of noble note, may yet be done, 
Not unbecoming men that strove with Gods. 

He knows he is getting closer to death, and he wants one more shot at what he considers glory: striving with the Gods.
The tone of the two poems differs because of the self-awareness, or lack thereof, of the poems' human subjects. Ozymandias makes a bold but ultimately foolish declaration. He seems oblivious to the transitory nature of life and power. He is not a sympathetically tragic character because he does not perceive his own weakness and his own eventual destruction.
Ulysses, on the other hand, is driven by a self-awareness of his desire to live fully while he still can, although he knows it will be brief and will probably end tragically. He says,

I cannot rest from travel: I will drink 
Life to the lees.

This means Ulysses will live life to its fullest. The lees are the sediments at the bottom of a wine barrel. Although this sediment is not particularly good, Ulysses means he will experience all of life, the good and the bad.
The reader empathizes with Ulysses's desire to avoid a quiet resignation about finishing out his days doing something he doesn't want to do.

College Algebra, Chapter 7, 7.1, Section 7.1, Problem 42

Find the complete solution of the system

$
\left\{
\begin{equation}
\begin{aligned}

-4x - y + 36z =& 24
\\
x - 2y + 9z =& 3
\\
-2x + y + 6z =& 6

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


We first write the augmented matrix of the system and using Gauss-Jordan Elimination.

$\left[ \begin{array}{cccc}
-4 & -1 & 36 & 24 \\
1 & -2 & 9 & 3 \\
-2 & 1 & 6 & 6
\end{array} \right]$

$\displaystyle \frac{-1}{4} R_1$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{4} & -9 & -6 \\
1 & -2 & 9 & 3 \\
-2 & 1 & 6 & 6
\end{array} \right]$

$\displaystyle R_3 + 2 R_1 \to R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{4} & -9 & -6 \\
1 & -2 & 9 & 3 \\
0 & \displaystyle \frac{3}{2} & -12 & -6
\end{array} \right]$

$\displaystyle \frac{2}{3} R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{4} & -9 & -6 \\
1 & -2 & 9 & 3 \\
0 & 1 & -8 & -4
\end{array} \right]$

$\displaystyle R_2 - R_1 \to R_2$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{4} & -9 & -6 \\
0 & \displaystyle \frac{-9}{4} & 18 & 9 \\
0 & 1 & -8 & -4
\end{array} \right]$

$\displaystyle \frac{-4}{9} R_2$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{4} & -9 & -6 \\
0 & 1 & -8 & -4 \\
0 & 1 & -8 & -4
\end{array} \right]$

$\displaystyle R_3 - R_2 \to R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{4} & -9 & -6 \\
0 & 1 & -8 & -4 \\
0 & 0 & 0 & 0
\end{array} \right]$

$\displaystyle R_1 - \frac{1}{4} R_2 \to R_1$

$\left[ \begin{array}{cccc}
1 & 0 & -7 & -5 \\
0 & 1 & -8 & -4 \\
0 & 0 & 0 & 0
\end{array} \right]$


This is in reduced row-echelon form since the last row represents the equation $0 = 0$, we may discard it. So the last matrix corresponds to the system


$
\left\{
\begin{array}{ccccc}
x & & - 7z & = & -5 \\
& y & - 8z & = & -4
\end{array}
\right.
$


To obtain the complete solution, we solve for the leading variables $x$ and $y$ in terms of the nonleading variable $z$ and we let $z$ be any real numbers. Thus, the complete solution is


$
\begin{equation}
\begin{aligned}

x =& 7t - 5
\\
y =& 8t - 4
\\
z =& t

\end{aligned}
\end{equation}
$


where $t$ is any real number.

How is morality explored in Will's dream vision? His pilgrimage is a quest for salvation and the justness of society, but how exactly are these elements of morality explored in the text (with particular references to the prologue)? The allusions to the tower and dungeon as representations of Heaven and Hell are clearly a first indicator of his concern with right and wrong, however, I'm not sure in what other ways his visions are concerned with morality. Could you please clarify the ways in which Piers Plowman relates to morality, and are there any concrete examples within the text? Thank you.

Great question! It is true that the beginning of the prologue uses the tower and the dungeon as representations of Heaven and Hell. On an even deeper level, the tower represents God's Truth and the dungeon is filled with prisoners who represent the damned souls that occupy Hell. The prologue further expounds upon the ways in which Will's dream are connected to his quest for morality and justification.
The world between the tower and the dungeon represents mortal life, which determines where all living souls will end up. Will is urged by a woman who goes by the name of Holy Church to obtain the Truth found in the tower, but he faces many obstacles in pursuit of this moral goal. Holy Church warns him that his soul's salvation rests on following Truth and that the dungeon is full of all Wrong in the world. The dungeon is also associated in the text with Satan. After this initial warning, Will witnesses a marriage arrangement between Lady Mede, who represents Reward, and False. This setup is a representation of the false reward that comes with choosing Wrong. Instead, the king of London suggests that Lady Mede should marry Conscience. This sparks a moral debate on whether Reward is a matter of falsehood or good conscience.
Lady Mede is the primary source of conflict between Theology and Holy Church as well, and this conflict is the catalyst for Will's journey. Later in the text, the moral themes presented in the prologue gain more depth. As Will receives a second vision or dream, he preaches to others in an effort to compel them to repent of their sins. On another level, the prologue explores the nature of morality as it relates to the different social classes. In the beginning of Will's vision, he sees beggars, noblemen, clergy, and workers all engaged in their normal duties. While their lives are different, the moral conflicts they face all lead to the same eternal consequences. All major aspects of Will's visions are connected to morality in similar ways. The different people he meets represent either aspects of humankind (the king of London, for example) or a moral dilemma (the marriage conundrum between Lady Mede, Conscience and False.)

In "Inchcape Rock," why and how did Sir Ralph's ship sink?

"Inchcape Rock" by Robert Southey is a short narrative poem based on a Scottish tradition. According to the poem, the Abbot of Aberbrothok had placed a bell on Inchape Rock, a reef that could be covered by the high tide and which thus constituted a major hazard for ships. The bell would alert mariners to the proximity of this hazard, allowing them to avoid it.
Sir Ralph the Rover was a pirate who profited by scavenging the wreckage from ships that ran aground in storms. He removed the bell from Inchape Rock in order to lure unsuspecting mariners to wreck their ships on the rock so that he could steal their cargoes.
During one storm, after Sir Ralph had removed the bell, his ship was sailing looking for potential wrecks he could plunder. In the darkness and the absence of the bell as a navigational aid, Sir Ralph's ship struck Inchcape Rock and the waves rushed in through the damaged hull causing the ship to sink.

Sir Ralph's ship sank because it crashed onto the Inchcape Rock. As the ship filled with water, it sank.
Every ship floats because the buoyancy force (the force that pushes up the ship) is greater than the gravity force (the force that weighs the ship down). In Sir Ralph's case, as the ship filled up with water, the extra weight increased its gravity force relative to its buoyancy force. That's why it sank.
In the poem, the Abbot of Aberbrothok had put a bell on a buoy to warn sailors about the "perilous" Inchcape Rock. However, Sir Ralph had effectively "cut the bell from the Inchcape Float" so that "“The next who comes to the Rock,/ Won’t bless the Abbot of Aberbrothok.” Sir Ralph had been intent upon causing others harm, but he himself later fell prey to his own machinations.

Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 122

a. Prove that the equation $y+3 = 2(x+4)$ is a linear equation by writing it in the form $y = mx + b$.


$
\begin{equation}
\begin{aligned}

y+3 =& 2(x + 4)
&& \text{Given equation}
\\
y+3 =& 2x + 8
&& \text{Apply Distributive Property}
\\
y + 3 - 3 =& 2x+8 - 3
&& \text{Subtract } 3
\\
y =& 2x+5
&&

\end{aligned}
\end{equation}
$


b. Determine the ordered-pair solution that corresponds to $x = -4$.

Using the equation in part a.


$
\begin{equation}
\begin{aligned}

y =& 2(-4)+5
&& \text{Substitute } x = -4
\\
y =& -8+5
&& \text{Simplify}
\\
y =& -3
&&

\end{aligned}
\end{equation}
$


The ordered-pair is $(-4,-3)$.

How many moons does Mercury have?

This would appear to be something of a trick question. Unlike Earth, Mercury has no moons at all. Mercury is, of course, the nearest planet to the Sun. And because of this close proximity to the Sun and its gravitational field, Mercury simply wouldn't be able to hold on to a moon of its own in the way that Earth does. Just imagine for a moment what would happen if Mercury actually did have a moon. Due to its proximity to the sun any moon that it had would more than likely crash right into that gigantic ball of fire. Even if such a moon could orbit the Sun for a while, it would get sucked in eventually, succumbing to the Sun's extraordinarily powerful gravitational pull.
https://spaceplace.nasa.gov/how-many-moons/en/

Why was Winston's concern for her a "curious emotion"?

At the beginning of part 2, chapter 1, Winston is walking towards the men's restroom when the mysterious dark-haired girl wearing a sling stumbles in front of him. As Winston goes to help the girl up, he notices an appealing look in her eyes that resembles fear instead of pain. Orwell writes, "A curious emotion stirred in Winston’s heart" (133). The curious emotion that Orwell refers to is Winston's sexual attraction and animosity towards the dark-haired girl. Winston initially believes that the dark-haired girl is a government spy who is an agent of the Thought Police. Despite Winston's malicious feelings towards the dark-haired girl, he is sexually attracted to her. Winston goes out of his way to avoid her but comes in contact with her for the first time when she purposely stumbles in front of him. As Winston watches her compose herself, he struggles to decide whether to view her as an enemy or a human being in pain. Instinct takes over, and Winston helps the girl up. Following their brief interaction, Winston notices that she had purposely slipped him a small note saying, "I LOVE YOU."

How would you compare and contrast the relationship of Oliver and Orlando with that of Rosalind and Celia?

The most obvious contrast is Oliver's hatred of Orlando compared to Celia's loyalty to Rosalind at the beginning of the play.  Despite being brothers, Oliver hates Orlando, in part because Orlando is better loved than he is.  In explaining his hatred in 1.1, Oliver says Orlando is "so much in the heart of the world and especially of my own people, who best know him, that I am altogether misprized."  Celia and Rosalind, on the other hand, are as close as sisters, even though they are only cousins.  Duke Frederick even says that Celia is made to seem less important as long as Rosalind is in the court (1.3 "She robs thee of thy name, / And thou wilt show more bright and seem more virtuous / When she is gone."), but that does not move Celia, who is so devoted to Rosalind that when Rosalind is banished, Celia considers herself banished as well.  While Rosalind, Celia, and Orlando take refuge in the forest of Arden, Oliver remains at the court and is coerced by Duke Frederick to pursue Orlando.  When Orlando saves his life, Oliver has a change of heart.  While he is no longer actively working against Orlando, Oliver never expresses the sort of affection for his brother that Celia holds for Rosalind.  In the only onstage moment where the brothers talk together after their reconciliation (5.2), the topic of conversation is Oliver's relationship with "Aliena," not their feelings for each other.  Much of Celia's character, on the other hand, revolves around her love for and loyalty to Rosalind.  While Oliver has other priorities and concerns--his estate, his status, even his love for Aliena--Celia is always centered on Rosalind.

Why is effective school management important in the classroom?

School management is a big topic because it covers a huge range of subjects.  School management topics include things like attendance, student behavior, dress code, curriculum, enrollment, recruiting, retention, scheduling, hiring, firing, budgeting, pay scales, teacher evaluations, professional development requirements, etc.  
With all of the possible responsibilities for school management, I'm glad that the question specifically asks about school management's impact on daily classroom teaching and learning.  Many of the above items do affect the classroom.  I'd like to expand on three of them. 
Let's start with the hiring of new faculty members.  I have served on several committees that have made the final recommendation to the school board about which teaching candidate to offer a contract to.  A central concern is always "What can this teacher do for us in the classroom?"  Along with that question is the question of teaching experience.  Are we hiring a first year teacher or a master teacher?  A master teacher likely has solid classroom management procedures in place, and that will allow that teacher to effectively focus on student learning rather than student behavior.  A classroom that is focused on student learning is a better classroom.  Effective school management tries to always hire the most effective teacher in order to have effective classrooms. 
Next, let's look at how school management's budgeting can impact classroom learning.  I teach science, and as a consequence, I feel that I am very aware of my budget.  I am currently fortunate enough that I have been able to supply every lab investigation with funding from my school budget.  That directly impacts student learning because labs allow students to collaboratively work in groups, problem solve, and practice content skills.  Those are all linked to student achievement. Without school management recognizing the value in funding school labs and effectively running a budget, science labs in schools would end to the detriment of classroom teachers and student learners.  
Curriculum is next.  Effective school managers are involved with school curriculum.  They need to ensure that the curriculum is in line with government education policies.  Additionally, effective school management regarding curriculum involves making sure that the curriculum is broad and balanced.  The curriculum should also spiral in its scope and sequence across grade levels.   Finally, effective school management will determine what the curriculum review process will entail.  Without these procedures in place, the overall direction of classroom student learning runs the risk of not having enough guidance.  I like the analogy of driving and directions.  Teachers might be great drivers, but without directions, 10 teachers might drive in 10 different directions.  School management gives the directions and the end goals.  Teachers drive students toward that goal.  Effective school management doesn't guarantee effective classrooms, but it does help a lot. 
https://www.edb.gov.hk/attachment/en/sch-admin/sbm/sbm-forms-references/tips%20for%20school%20managers_eng.pdf