Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 32

Determine an equation for the line that is shown below:


a.) Write the equation in slope intercept form.
b.) Write the equation in standard form


a.) The line passes through the points $(2, 0)$ and $(0,2)$. Then by using two point form, we have

$
\begin{equation}
\begin{aligned}
y - y_1 &= \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)\\
\\
y - 0 &= \frac{2 - 0}{0 - 2} (x - 2)\\
\\
y &= \frac{2}{-2} (x - 2)\\
\\
y &= -(x - 2)
\end{aligned}
\end{equation}
$

So, the equation in slope intercept form is
$y = -x + 2$

b.) Thus, the equation of the line in general form $Ax + By = C$, we get
$x +y = 2$

Where does it talk about drugs in the book Always Running?

Always Running is the memoir of Luis J. Rodriguez about his life among gang members in Los Angeles. Because of the topic material, drugs are a frequent topic throughout the book. There are a few specific places where they're mentioned that are interesting.
Rodriguez explains that "my teen years were ones of drugs, shootings and beatings, and arrests" because that explains to the reader what the book will be about. It's clear that he had lots of exposure to drugs; people around him both used drugs and sold drugs. This had major consequences on their lives. As he says, "By the time I turned years old, 25 of my friends had been killed by rival gangs, police, drugs, car crashes, and suicides."
Later he explains why so many people turned to drugs. He talks about the experience of a 10-year-old boy in Humboldt Park where it was possible to make up to $100 per day by acting as a lookout for drug dealers. Even when people aren't doing drugs, they're still part of the drug industry. As he says, "The drug trade is business. It's capitalism."
This business is something that colors a great deal of Rodriguez's time in East Los Angeles.

Drugs play a prominent role in the memoir Always Running by Luis Rodriguez. Many of the people described in the memoir use, sell, and are often surrounded by hardcore junkies. The author is exposed to drugs from a very young age. He sniffs aerosol sprays and glue and later uses marijuana, pills, and heroin. Rodriguez addresses the drug trade early in his memoir, explaining that selling drugs is a form of underground economy that emerges in poorer neighborhoods, one which recruits even children to participate as paid lookouts. Rodriguez describes almost dying from a drug overdose, as so many of the friends he had growing up did. Rodriguez shows how drugs also function as a form of escapism, allowing many young people to escape the boredom or poverty of their environments.

Who is the antagonist in "Soldier's Home"?

The protagonist and antagonist of a novel are the opposing forces that drive the plot along. The protagonist is the main character, typically the "hero" of the story, as the plot is centered around them. However, they don't have to be a morally upright or heroic person; many novels deal with bad characters receiving their comeuppance through the events of the story. Harold Krebs, a man recovering from the trauma of war, is the protagonist.
The main force which prevents him from achieving his goals—such as reintegrating into society, having relationships, and living a peaceful, normal life—is his Post-Traumatic Stress Disorder or "shell shock," as it's referred to in the novel and the language of the day. This force acts to keep him from achieving his goals and being happy—which is the definition of antagonist, since it doesn't need to be a person.

The antagonist of the story is Krebs's mother, who comes to represent everything that her son has rejected. That's not to say that she's a particularly wicked or unpleasant character, as many antagonists are. It's simply that in her desire to get her shell-shocked son to move on with his life, she's ranging herself against him.
The truth, however, is that Krebs can't move on, even if he wanted to. As well as being traumatized by his experiences of war, he no longer shares the same values as his mother. This is graphically illustrated by his inability to join with her in prayer. He no longer believes in God, just as he no longer believes in his mother. Incapable of giving love or receiving it, Krebs is unavoidably antagonistic towards his mother, despite the fact that she remains a generally sympathetic character.

The protagonist is the main character of a literary work whose conflict sets the plot in motion. The antagonist is the character or force which struggles against or blocks the protagonist. In Hemingway's short story "Soldier's Home" the main character and protagonist is Harold Krebs. Krebs has recently returned from service as a Marine fighting in World War I. Judging by what the third person narrator tells the reader it could be said that Krebs suffers from what was then called "shell shock" and is now diagnosed as Post Traumatic Stress Disorder. The narrator admits that during the war, Krebs "had been badly, sickeningly frightened." Back home, Krebs is depressed and somewhat anti-social. His idea is to avoid complications, consequences and for "life to go smoothly." For a time he is able to do this. Eventually, however, the antagonist, in the form of his parents, especially his father who never actually appears in the story, look to force Krebs out of his apathy by insisting he go out into the world and get a job and maybe a girlfriend. His mother tells him,

"You know we love you and I want to tell you for your own good how matters stand. Your father does not want to hamper your freedom. He thinks you should be allowed to drive the car. If you want to take some of the nice girls out riding with you, we are only too pleased. We want you to enjoy yourself. But you are going to have to settle down to work, Harold. Your father doesn't care what you start in at. All work is honorable as he says. But you've got to make a start at something."

Krebs initially rebels at his mother's suggestions but she soon shames him, crying when he claims he doesn't love her. At the end of the story he concedes that he must go to Kansas City to find a job and get on with his life. Although he would rather continue a life without consequences he must heed his parents' wishes.

Was conscription morally justified during World War I?

The answer to your very interesting question will depend upon your perspective regarding war. First, you will have to decide whether the war was justified.
Was World War I fought to defend the innocent, assist invaded allied nations, or stop human rights violations? This would be consistent with what we call the just war theory. The Allied Powers of World War I (mainly consisting of Britain, France, Russia, Italy, and the United States) would have argued that the war was a just war. Meanwhile, the Central Powers (consisting of Germany, Bulgaria, the Ottoman empire, and the Austrian-Hungarian empire) would have made a similar argument.
Ostensibly, the immediate cause for World War I was the assassination of Archduke Ferdinand, the heir to the Austro-Hungarian empire. However, the real reason for the war was that certain major powers of Europe were angling for dominance of the continent. In the end, alliances solidified, leading the British, French, and Russians to form the Triple Entente, while Italy, Germany, and Austria-Hungary formed the Triple Alliance. 
Germany nursed hegemonic ambitions, and many historians believe that the country was the main aggressor during World War I.
To get back to your question, we must decide whether Germany's ambitions were valid and whether the Allied powers were right to defend their countries from attack. We must remember that both the Triple Entente and Triple Alliance members conscripted soldiers to fight during the war. The Bulgarians and Italians conscripted 55% of males from 18-50 to fight, Austria-Hungary conscripted 78%, and France and Germany conscripted 81%.
At the same time, Britain and the United States also instituted a draft during the war. In addition to those drafted, there were a few million men who volunteered to fight for both armies. If the just war theory holds, then war was justified on the side of the Allied powers. 
As for conscription, we must decide whether individual rights supersede the responsibility to defend one's country in the event of an attack. This is the crux of the issue.
http://www.bbc.co.uk/ethics/war/just/cause_1.shtml

https://www.bl.uk/world-war-one/articles/recruitment-conscripts-and-volunteers

Near the end of Chapter 5, what was decided during the selection about Eliezer's father? What happened to him after the decision was made?

In Chapter 5, Eliezer and his father are forced to go through the first selection process. Eliezer takes off his clothes and sprints in front of the SS guards. Eliezer passes the selection process and is ecstatic to see that his father also passed the selection. A few days pass and their block leader eventually informs the prisoners that there will be a second selection process. Unfortunately, Eliezer's father was chosen to go through the selection process for the second time. Before the selection begins, Eliezer shares an emotional moment with his father. Eliezer's father gives his son his knife and spoon in case he is chosen. Eliezer is extremely depressed and worried that his father will not pass the second selection. Fortunately, when Eliezer returns from work his father is waiting for him. Eliezer's father was deemed healthy enough to continue working at the camp. Eliezer then gives his father back his knife and spoon. Later on in the chapter, Eliezer and his father are forced to evacuate the concentration camp because the Russian forces are closing in.

What is the role played by Eastern religion and philosophy in Ursula K. Le Guin's The Lathe of Heaven?

Le Guin's novel is heavily influenced by Taoism, an Eastern religion characterized in the West by "go with the flow." It is based on a philosophy of "non-action" that believes in living in harmony with nature and the chi, or energy of the universe. In essence, speaking metaphorically, you let the water of the universe's energy carry you where you need to go, rather than try to swim against the tide.
Le Guin uses Taoist quotes by ancient Taoist Chuang Tse as chapter heads, such as those that start chapters II and XXIII:

Confucius and you are both dreams, and I who say you are dreams am myself a dream. This is a paradox. (II)

and

Those whom heaven helps we call the sons of heaven. They do not learn by learning. They do not work by working. They do not reason by using reason. To let understanding stop at what cannot be understood is a high attainment. Those who cannot do it will be destroyed upon the Lathe of Heaven. (XIII)

Chuang Tse is also famous for saying he dreamed he was a butterfly, and when he awoke, wasn't sure if he were a man who had dreamed of being a butterfly a butterfly who dreamed of being a man.
This questioning of what is dream and what is reality is at the heart of Le Guin's novel. Main character George Orr, who represents the Taoist worldview, has the power to dream new realities into existence. For instance, he rids the world of racism by dreaming everyone to the same pale gray skin. However, as the novel progresses, we become increasingly unsure what is a dream and what is reality as dreams and realities multiply—and much goes awry.
Unfortunately, this is because Orr dreams dreams, at the behest of Dr. Haber, that attempt to fix the world. Dr. Haber represents Western rationalism and the principle of making everything "better." All his attempts to engineer "improvements" through Orr's dreams, however, bring unintended consequences that make things worse.
Le Guin thus uses Eastern religion and philosophy to question Western notions of reality and "improvement." The novel suggests that the Tao "Way" of non-action and going with the flow of the universe, rather than Western rationalism and utilitarianism, which is the idea of the greatest good for the greatest number, is the better way to live.

Why is Renzo the protagonist instead of Lucia?

In this book, both Renzo and Lucia are the protagonists. They are equally important and have the same goal. Renzo is perhaps talked of more in the book, having more of an active role in the movement of the plot. Lucia, however, plays just as vital a role.
Although this book is told as a love story, it is also viewed as a veiled attack on the Austrian Empire, which controlled the region of Northern Italy when the novel was written. It is also favourably viewed by historians for its extraordinary description of the plague that broke out in Milan at the time.
Most interesting in relation to your question is the inclusion of Lucia as an active protagonist. At the time very few books included much about women, even as main characters. However, Lucia is given a very active role and a detailed description. She is, like many depictions of women in that time period, a kind and pious young woman, but she is not all good. She can also be cruel and self-centered. Another interesting inclusion is the character of La Monica di Monza (or the Nun of Monza), who is depicted as a bitter, frustrated, and somewhat ambiguous woman with a dark past, who befriends Lucia. This character was based on an actual woman, Marianna de Leyva.
The author, Alessandro Manzoni, was beyond a doubt ahead of his time with his depictions of real and honest characters and his inclusion of women of all types and backgrounds in his novel. It is little wonder that this book has been called the most widely read novel in the Italian language.

I do not know exactly what the public's role is in congressional decision-making in the modern House of Representatives. Does the public's role means the role of interest groups or the role of private citizens?

The role of the public in decision-making in the House of Representatives is generally meant to mean individuals, but certainly people in special interest groups are members of the public, too, so it would be accurate to say they are part of the "public." 
Individuals are at least superficially encouraged to get in touch with their representatives, all of whom must maintain a local presence in their respective districts with staff to respond to their constituents.  Often in high school civics classes, students will be assigned to find out who their representatives are and to write letters about a problem of general concern in their district. It is the wise representative who writes back! When there are campaigns on various issues, the campaigners will almost always advise people to write to their senators and representatives to express their opinions on the matter, for matters such as environmental concerns or funding Planned Parenthood.  Most representatives get in touch with their constituents routinely, with mailings or emails to inform them of their latest efforts, and to encourage a dialogue.  And representatives do pay attention to what their constituents think, even though they don't always vote the way some want them to.  They also take polls on various issues and sometimes will vote on a bill in accordance with what the majority of their districts wants.  I don't think anyone should ever hesitate to get in touch with his or her representative on any matter that representative is going to be voting on.  It is part of their job description to listen to their public.  
Special interest groups are usually represented to interact with Congress by one person or a few people, whom we call lobbyists.  Nevertheless, they comprise individual members of the public.  These members of the public have banded together for some common cause, and the fact that they have banded together should by no means take away their right to try to influence what their representatives will do. People are troubled by lobbying, particularly when it is very wealthy interest groups who are trying to exert influence, but I don't think you can have a democracy in which some members of the public can try to exert influence while others cannot because they have more money and have joined together.  It is not reasonable for us to be able to pick and choose this way. 
So, individual members of the public can and do affect the decision-making in the House of Representatives.  But special interest groups do, too, and they are part of the public. 
https://www.thoughtco.com/house-of-representatives-3322270

What is the importance of studying history?

The “importance" of anything is dependent on the circumstance – the “importance” of sugar depends on whether you are baking cookies or Zweiback; the “importance” of auto brakes depends on whether you are stopping or parked, etc.  So the “importance" of history is that the events of the past, large and small, have formed the present.  In order to use the present to shape the future (as far as we are capable of influencing the shape of the future), we need to see the forms, the structure, the actions that are universal in human nature and in the laws of physics/mathematics, and that are available to us to give a favorable substance to the future.  Studying history brings those forms and actions to our awareness, and they can then act as tools to give the future its shape.  For example, Athenian democracy and its actions that caused the Athenians to survive the Persian attacks serve as examples and models for subsequent democracy experiments, such as in the United States and in France.  Communism in Russia served to give shape to Communism in China.  The studying of history does not confine itself to memorizing dates, but to discerning patterns, following the logical consequences of actions, and weighing the elements of past events -- Leaders? Geography?  Technology? etc. – to predict, or at least influence, future outcomes.  Studying wars, for example, may not be as important as studying the failure of Peace Treaties.  What happened to the League of Nations, for example, and how can the United Nations avoid a similar fate?  If the colonies could form the United States, and Europe could form the European Union, what forces would bring the South American nations together?  Studying history, the past, is the act of learning how to deal with the present to shape a desirable Future.

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 58

Find an equation of the circle with center $(-1,5)$ and passes through $(-4,-6)$


Recall that the general equation for the circle with center at $(h,k)$ and
radius $r$ is..


$
\begin{equation}
\begin{aligned}

(x - h)^2 + (y - k)^2 =& r^2
&& \text{Model}
\\
\\
(x - (-1))^2 + (y - 5)^2 =& r^2
&& \text{Substitute the given}
\\
\\
(x + 1)^2 + (y - 5)^2 =& r^2
&& \text{Simplify}
\\
\\
(-4 + 1)^2 + (-6 - 5)^2 =& r^2
&& \text{Substitute the point $(-4, -6)$ to $x$ and $y$ respectively and solve for $r$}
\\
\\
(-3)^2 + (-11)^2 =& r^2
&&
\\
\\
9 + 121 =& r^2
&&
\\
\\
r^2 =& 130
&&

\end{aligned}
\end{equation}
$


Thus, the equation of the circle is..

$(x + 1)^2 + (y - 5)^2 = 130$

Compare and contrast "The Use of Force" (by William Carlos Williams) and "The Giraffe" (by Mauro Senesi).

The two stories we are comparing here are not, at first glance, an obvious pairing. The first story was written in the nineteenth century and is about a doctor who finds himself engaged in a battle of wills with a young girl who will not let him examine her. Eventually, he forces her mouth open with the use of a spoon, finally exerting his power over her and forcing her to reveal the "secret" of her diseased tonsils. The second story is a twentieth-century tale written from the point of view of a young boy not yet old enough to need a razor, who comes into possession of a giraffe after its owner abruptly dies. The boy and his friends try to shelter the giraffe, keeping it in the church until the townspeople elect to kill it, whereupon the giraffe and the boys fly from the town. The giraffe ultimately dies, refusing to allow the boys to feed it hay. The narrator interprets the giraffe's death as a symbol that in this town, "giraffes can't live, because there's room only for the things that are already here." This is normally interpreted as a comment on the closed-minded attitude of the town and its unwillingness to accept anything foreign or unfamiliar, which does not seem to "fit."
Certainly, we can make some initial comparisons between the two stories in terms of format, narration, and so on. Both pieces are short stories written in the first person. Both stories also contain significant amounts of conversation between people aimed at solving a problem. In the first story, this concerns the daughter who is unwilling to submit to the doctor; in the second story, the problem is what to do with the giraffe. It is notable that the stylistic omission of quotation marks, which is a characteristic of William Carlos Williams' story, is not echoed in Senesi's story.
In terms of theme, while Senesi's story is more frequently considered in terms of what it says about the townspeople and their reluctance to accept change, we might compare it to Williams's story by looking at it from a different perspective—that of the giraffe.
The giraffe, like the little girl in Williams's story, is resistant to being compelled. At the end of the story, the giraffe "stood still, its head piercing the sky" while the boys use physical force to try to convince it to open its mouth to be fed—language like "punched" conveys the visceral force—but the giraffe resists. It "folded its legs . . . before flowing to the ground," and, the boy notes, it "died by itself . . . there was no need for them to kill it." The giraffe's resistance, however, is passive. It does not respond to the boys' physical coercion. Ultimately, however, its stubbornness ends with its own death, and this is the outcome the townspeople wished for, although the giraffe has arrived at it through its own methods. The giraffe passively resists force in order to preserve its dignity and agency.
In "The Use of Force," we see the dynamics of power play out differently. The little girl, whose fire the doctor initially finds "attractive," resists the doctor's attempts to examine her with stubborn force. "The battle [then] began." Her stubbornness encourages the doctor's physical use of force: as she "f[ights], with clenched teeth, desperately," the doctor becomes "furious" and forces a wooden spatula into her mouth until she reduces it "to splinters." The child's mouth is now a scene of devastation, "her tongue . . . cut," and the child "scream[s] hysterical shrieks." As the battle rages, the doctor begins to feel that "it [is] a pleasure to attack her," using the justification that she must be "protected against her own idiocy," but he knows that "blind fury" is actually driving him. Eventually, the doctor forces the child into submission, and as he uncovers the "secret" of the membrane on her tonsils, the child is overpowered by "defeat."
Here, then, we can see that the child is seemingly, like the giraffe, resisting what is in its best interests. However, while the giraffe resists passively—and dies—the child resists with matched force. Eventually she is overpowered by the doctor's so-called good intentions, but she feels "defeated" by the battle of wills. What is interesting is that the doctor's feelings toward the child seem to change from admiration for her to an increasing sense of "fury" as he overpowers her. Meanwhile, the giraffe remains a stately, elegant thing in the eyes of the boys as it resists passively, determined to die according to its own wishes. The two stories, then, both represent attempts to use force to "help" another creature, but in each story, the attempt is received differently. Consequently, each story ends differently. We can consider, then, what each author is saying about the nature of resistance, agency, and what happens to our feelings for each other when we respond to force with force and, thus, escalate tension.
We can also consider the way the two stories portray what "society" forces us to do. The townsfolk in "The Giraffe" want to evict the giraffe because it does not fit into their understanding of what town life should be. The doctor in "The Use of Force" justifies his forceful treatment of the daughter by saying that it is "a social necessity" and that "others must be protected against her." In both cases, the recipient of the force is somebody or something who is disturbing the order of society and must be subdued.

What praises do Hero and Ursula use on Benedick, and how do they make him seem pitiful?

I think you are referring to the conversation between Hero and Ursula in act 3, scene 1, of the play, when the two women discuss Benedick's feelings for Beatrice in Leonato's garden.
Hero declares that when Beatrice arrives, "our talk must only be of Benedick," and they must "praise him more than ever man did merit." At this juncture, Beatrice enters, and Hero and Ursula move closer to her so that she will be able to hear all the "false sweet bait" they intend to offer her.
Ursula declares that Benedick "deserve[s] as full as fortunate a bed / As ever Beatrice shall couch upon," and Hero agrees that he deserves "as much as may be yielded to a man." However, Hero also says that Beatrice "cannot love." Ursula agrees with this and says that she is glad Beatrice does not know of Benedick's feelings for fear that she might "make sport at it." Naturally, this makes Benedick appear pitiful: the women are suggesting that they feel protective of him because of his feelings, and they are suggesting that they do not wish Benedick's feelings to be hurt by the "self-endeared" Beatrice.
The two discuss how Beatrice tends to criticize even seemingly perfect men, and they determine that Benedick should be allowed to "consume away in sighs, waste inwardly," as this would still be better than for him to "die with mocks." Hero then determines that she shall go to Benedick and "counsel him to fight against his passion." The two women agree that Benedick is a "rare" gentleman; indeed, he is "the only man of Italy," and a man who "for shape, for bearing, argument and valor" is peerless. He also has "an excellent good name." Altogether, the two create a picture of Benedick as a wonderful man, much wronged by Beatrice, who is forced to conceal a great passion for her out of fear of being unfairly mocked.
Their machinations ultimately succeed; Beatrice is moved by the "bait" and declares that she will "requite" Benedick if he does indeed still love her.

How does Napoleon trick the humans into thinking that Animal Farm is still successful and thriving?

Having expelled the hated human oppressor Mr. Jones from the farm, the animals are now firmly in charge. Manor Farm has become Animal Farm; the ideology of Animalism has triumphed at long last, finally realizing Old Major's dream. This is a good start, but it's not enough. Not only does Animalism need to be established, it must also be maintained. The animals need to show human beings that they can make it on their own, that they can establish a successful, thriving farm without any help or assistance from their erstwhile oppressors.
As winter sets in, however, things aren't going so well. The animals are working harder than ever, but thanks to Napoleon's incompetence, there's a chronic shortage of food. Just to make matters worse, the jerry-built windmill's now broken and so the animals will have to rebuild it, with all the crippling effort that that will entail. But Napoleon must keep up appearances at all costs; he must show the humans that Animalism is a living, breathing ideology that can inspire the animals to do better than humans.
On the domestic front, this means a massive increase in propaganda, with the ever-loyal Squealer giving long-winded speeches on the importance of heroic sacrifice. More ominously, the level of terror steps up. Snowball is being blamed for everything bad that happens on the farm. In this toxic environment of paranoia and delusion, animals are forced to make public confessions of assisting Snowball in acts of sabotage. They are then brutally executed for their alleged crimes.
In relation to foreign affairs (i.e., relations with humans) Napoleon enlists the help of a lawyer by the name of Whymper to act as an intermediary between himself and the outside world. When Whymper pays his weekly visits to the farm, Napoleon is anxious to make sure that everything seems on the up and up. Neither Whymper, nor anyone else from the outside world, must ever suspect that the Animalist utopia isn't working as well as it should.
Napoleon has betrayed the values of Animalism by agreeing to supply four hundred eggs a week to Whymper; and this at a time of chronic food shortages. But again, the facade of normality must be maintained at all costs. So a number of selected animals—mainly sheep—are instructed to remark casually within Mr. Whymper's earshot that their rations have increased, which of course is the exact opposite of what's really happened. Napoleon also gives an order that the empty bins in the storage shed must be filled with sand and then covered up with what little grain is left to make it look like there's a plentiful supply. Once again, this is a completely false picture of reality on the farm; there's actually a chronic shortage of grain, and the animals are staring starvation right in the face.

In the poem "Breaking Out" by Marge Piercy please explain the lines "Nasty stork king of the hobnobbing doors was a wooden yardstick dusty...there were things I should learn to break."

This poem is a personal exploration in which  the poet reflects upon a repressive abusive childhood when she was disciplined with corporal punishment. Corporal punishment is a less common method used in child rearing now, and many people of previous generations, including writers and artists, describe related experiences in their work based upon how their own formative years were affected by it. Pierce was obviously deeply affected by these experiences and the poem is generally reflective of the theme of female empowerment.
This stanza introduces the object used by her parents to discipline her: a yardstick (made of lightweight wood and used for measuring):

Nasty stork of the hobnobbingdoors was a wooden yardstick dustywith chalk marks from hem’s rise and fall.

The "nasty stork" describes how Piercy's young mind saw the stick standing in the corner. "Hobnobbing" is a word that means socializing or fraternizing, as with other social circles, perhaps doors that separated servants from the family. The yardstick is "dusty with chalk marks" that show its use for hemming garments as someone stood on a chair. The idea that an object used for a mundane purpose such as hemming a skirt, and also for beating, underscores the daily stress and fear Piercy lived with as a child, constantly reminded of the potential for corporal punishment by this object she saw frequently. She tells us in the next stanza "that stick was the tool of punishment."
In the next stanza she describes her parents different levels of intensity using the stick, and how she would inspect her bruises afterwards, seeing them as "red and blue mountain ranges" and visualizing the veins as a map that would guide her eventual escape from this abusive upbringing. She then describes taking the ruler (yardstick) at age eleven and smashing it to "kindling" (an image that conjures burning, a powerful metaphor for transformation).
She becomes "an adolescent not a child" when she owns her power and destroys this implement of pain. Her comparison to herself as Sisyphus, the Greek character from mythology who is condemned to roll a boulder uphill again and again, is meant to emphasize her escape from torture, and her empowering act of breaking through her pain and oppression.
 
 

What is the primary conflict the headmaster faced in the story "Dead Men's Path"?

The man versus society conflict is most easily identified in Achebe's short story, "Dead Men's Path." The headmaster, Michael Obi, faces extreme tension with the people of the village. Due to his closing of the footpath through school grounds, the villagers become infuriated because they see the footpath as the route of arriving babies and of departing elders. When a mother dies in childbirth in the village, the villagers are so outraged that they destroy many things at the school. So, we have a man and his wife at odds with the entire village in which they live and work.
However, on a deeper level, Obi is merely a representation of progress and modernization in stark contrast to the traditionalist village. Therefore, the seemingly unresolvable conflict can also be understood as one of ideas rather than man versus another force. As is true with many of Achebe's stories, he makes the motif of convention and change a central idea of the story. This motif is clearly demonstrated through Obi's conversation with the priest. Although the priest advises him to "let the hawk perch and let the eagle perch," Obi cannot bring himself to compromise any of the modern beliefs that he holds so dearly, nor can the villagers abandon the ways of their ancestors. Thus, the reader is presented with an illustration of the unavoidable conflict between ideas that occurs with tradition and progress.

The primary conflict that Michael Obi faces in Achebe's short story "Dead Man's Path" is a Man vs. Society conflict regarding the issue of whether to reopen the ancestral footpath that runs through his school's compound or keep it closed and risk upsetting the villagers. Michael Obi is depicted as a proud man, who is a staunch proponent of modernity and opposes traditional African culture and beliefs. Michael Obi is compelled to close the villagers' ancestral footpath that leads through the school's compound because he feels that it is a distraction and opposes his stance on modernity and contemporary values. The conflict arises after Obi closes the path and refuses to compromise with the village priest. It is considered a Man vs. Society conflict because Michael Obi opposes the entire village, which is in favor of opening the footpath. After a woman dies during childbirth, the villagers destroy the school's grounds and Michael Obi is fired from his position as headmaster.

This is primarily a man versus society conflict. In the story, the protagonist is Michael Obi; his main conflict is with the villagers of Ndume.
While the villagers cherish their time-tested and revered religious traditions, Michael views these beliefs as antithetical to modernization and progress. As the new principal, Michael hopes to restructure the academic programs and to revolutionize teaching methods at Ndume Central School.
Michael is enthusiastic about Ndume's future, but he fails to take into account the deep respect for tradition among the village people. In a conversation with a teacher, he laments the use of an unsightly footpath that crosses the school grounds. The teacher relates that the footpath joins the village shrine to a traditional burial place, but Michael ignores the import of what the teacher tells him. He commissions heavy sticks to be deposited at the entrance and exit sections of the footpath, and he orders both sections to be reinforced with barbed wire.
Meanwhile, the village priest begs Michael to reconsider his unforgiving stance. He tells Michael that the dead walk the path to the afterlife by it and that revered ancestors visit the living by it. He also reiterates that newborn children enter the world through the foot path. Michael scoffs at what he considers backward superstitions that have no place in a modern world.
The priest ominously proclaims that both should agree to "let the hawk perch and let the eagle perch." However, Michael is resolute in his stance; he refuses to compromise on the situation.
The impasse is resolved the next morning when Michael wakes up to find the school grounds vandalized, the flower beds destroyed, and one of the school buildings torn down. So, Michael's modernization efforts fail because he neglects to show respect for the entrenched beliefs of the villagers.

In chapter 12 of On Democracy, Dahl says that democracy requires a relatively homogenous society in which cultural conflicts, if they exist, are “weak.” Does American society meet this requirement? What type of cultural conflict, in your opinion, poses the greatest threat to American democracy? And what method (see Dahl’s discussion) offers the best hope for keeping that conflict in check?

On Democracy was written by Robert A. Dahl, a prominent expert on writing about democratic political institutions. The book can be read as a text that explains the cultural and economic underpinnings which tend to hold democracies together, and the pitfalls that tend to unravel democracies. Dahl's text is a highly informative book for those who want to understand why democracies work, why democracies sometimes fail, and how we can all preserve democratic political institutions in a time period when these institutions are under a high level of scrutiny and pressure. Most people who already understand politics but who do not know which forces work for democracy and against it would probably benefit most from reading the book.
American society essentially consists of people who believe in freedom and democracy. Although there is a mosaic of cultures, backgrounds, and religions, people in America expect their will to be carried out and respected, and this belief unites most people on some common ground. According to Dahl, that is a good starting point for preserving democracy, and I think most people would agree. But there is a high level of ideological conflict that is pervasive in American culture.
Intense partisanship and ideas about whether communist, socialist, or capitalist systems work best are being debated constantly nowadays, and this conflict seems to pose the biggest threat to American democracy, since those who subscribe to each respective system's ideas are unavoidably in opposition to each other. This division can create hostility and resentment toward groups in American society. Conflicts which concern income inequality, in particular, can foment incredible levels of turmoil, since those who believe in capitalism do not really see income inequality as a social problem. Those who believe in socialism do see it as a social problem.
Dahl makes the argument that a democratic society's preservation is tied to a healthy, functional free market economy, and that the stability of a democracy relies on limiting or resolving economic tensions that could exacerbate cultural conflict. If true, this lends support to the notion that conflicts about which system—communist, socialist, or capitalist—is best for the people in society seem to present the biggest challenge, and keeping those conflicts in check would offer the best hope for preserving democracy. At the end of the day, economic disparities and resentment are a cause for great concern, and keeping those in check offers the best hope. A method for controlling that conflict through open discussion, governmental policies, and reforms offers a good solution.

Robert A Dahl's "On Democracy," published in 1998, sets forth the assertion that democratic political institutions are more likely to develop, remain stable, and even flourish in societies that are culturally homogenous and lack the sort of sub-cultural conflicts that could weaken the society at large. These conflicts could be the result of language, politics, race and religion (among other areas). However, he does not say this is an absolute.
While many sociologists acknowledge competing and conflicting sub-cultures as an ever-present facet of American life, Dahl specifically notes that a handful of countries (the US, Canada, Switzerland, Belgium, and the Netherlands in particular) are exceptions to this notion, with democratic institutions surviving and even thriving due to a handful of interdependent processes such as forced assimilation, the shared idea of consensus, the establishment of non-partisan electoral systems, and the fear of separation for those who don't assimilate.
Dahl references the fact that most American settlers and immigrants in the early twentieth century assimilated despite vast differences in socio-economic and cultural backgrounds either voluntarily or as a result of social mechanisms like "shaming," causing them to cast off the identities of their home cultures while embracing Americanism. He notes blacks and Native Americans required greater levels of coercion to assimilate and were excluded or ostracized if they didn't comply.
According to Dahl, the greatest threat to undermining America's democratic institutions are large-scale political, economic, ideological, military, or international crises that could foment conflict between subcultures. He also notes that the principles of a democratic society are closely linked to a functional free market economy, and that the stability of a democracy relies on mitigating economic tensions that could exacerbate cultural conflict.

According to the essay "Supernatural and Shakespeare," during Shakespeare's time "witches were a convenient way to explain all the terrible maladies and misfortunes that occurred, seemingly without cause, on a daily basis." Explain how the witches in Macbeth support this idea and remove blame from Macbeth himself. Be sure to use key details from the play to support your ideas.

If the Weird Sisters truly know the future and are not simply manipulating Macbeth into thinking that they do, then everything that happens in the play is the result of fate, or destiny, and not effects of Macbeth's corruption.  In other words, if the future is knowable, then it must be fated, and if it is fated, then no one can be blamed for their role in bringing it about; Macbeth is exonerated from responsibility for his deeds.  For example, the witches tell Banquo, "Thou shalt get kings, though thou be none" (1.3.68).  In other words, Banquo's line of descendants will produce kings.  This is true.  The king on the throne when Macbeth is first performed is King James I (James VI of Scotland), and he can trace his lineage back to Banquo. 
Further, when the Weird Sisters call up the apparitions in Act 4, scene 1, the first is an "armed head" (a disembodied head, wearing a helmet) which says that Macbeth must "Beware Macduff" (4.1.73).  It turns out that Macbeth should fear Macduff because it will be Macduff who kills him by cutting off his head after Macbeth has donned his armor.  Therefore, the apparition -- created and conjured by the Weird Sisters -- not only knows the future but takes the shape of something to occur in the future as well.  Likewise, the second apparition appears as a "bloody child" who says, "Laugh to scorn / The power of man, for none of woman born / Shall harm Macbeth" (4.1.81-83).  Macduff was not technically born, as he tells us later, he was from his "mother's womb / Untimely ripped," i.e. he was born via Caesarean section  (5.8.15-16).   So, the apparition appears as a bloody child because a child born by C-section would be bloody since the mother's been cut, and it knows the future: that Macbeth will be killed by someone not "born."  Finally, the last apparition, "a child crowned, with a tree in his hand," says that "Macbeth shall never vanquished be until / Great Birnam Wood to high Dunsinane Hill / Shall come against him" (4.1.96-98).  The child's appearance gives a clue as to how this will happen: a rightful king (Malcolm, child of Duncan) will march on Dunsinane with his army, each soldier holding up a bough of a tree in order to shield his army's numbers from Macbeth's lookouts.  Again, the apparition (produced by the witches) knows the future.
Ultimately, then, Macduff isn't in control of his fate: he is destined to kill Macbeth.  Malcolm isn't in control of his fate: he is destined to lead an army against Macbeth.  This means that Macbeth cannot be in control of his fate either: he must perform the actions that lead him into this place at this time, and thus we cannot fault him for killing Duncan because that action was only the one to set this destiny into motion.  It was fated too.  If we accept that the Weird Sisters know the future, then that means the future is knowable, and if the future is knowable then we do not possess the free will to change it; we are only pawns of fate and thus not responsible for our actions.

What process prevents water from forming runoff?

Runoff can be thought of as the water that flows over the surface of Earth after a precipitation event or after excessive water application to an area (say, through irrigation). The water present on the surface of Earth after a precipitation and/or irrigation event has two pathways: it can either flow over the surface of Earth, forming runoff, or infiltrate below the earth's surface (where it may ultimately reach the groundwater, depending on a number of factors).
Thus, it is infiltration that may prevent water from forming runoff. If soil is saturated, then excess water will form runoff; otherwise, water is likely to infiltrate the soil until the surface becomes completely saturated. Soil has empty spaces, known as pores, between its particles. These pores can get filled with water, and once they are saturated, the excess water has nowhere to go but form runoff.
Hope this helps.

“The lady protests too much, methinks.” Explain why this is an example of dramatic irony.

Although we never learn exactly what changes Hamlet asked The Players to make in their script, it is almost certain that the changes included the dumbshow portion that presents the Fellow pouring poison into the King’s ear as well as the lines about fidelity and widowhood. One aspect of the irony is that Hamlet requested the changes so he could watch Claudius’s reaction: to “catch the conscience of a king.” He later tells his step-father that the play’s title is The Mouse-Trap, but his mother’s reaction is initially stronger.
The irony concerning his mother’s remarks relates to the degree of her involvement in the regicide. Hamlet probably meant to similarly trick her into revealing her involvement, or at least shame her into reacting. However, it is never certain whether her reaction incriminates or exonerates her; Gertrude’s reaction can be interpreted as reflecting either her guilty conscience or her lack of insight into the murder plot. While there is some doubt that she was complicit in her husband’s murder, the fact remains that she did marry his brother sooner than was customary, and could not be unaware of public opinion of that impropriety.
Proclaiming her unswerving love for her husband, the Player Queen calls down a curse on herself if she were to remarry if he died: “In second husband let me be accurst!” Before leaving to go to bed, she continues, “. . . never come mischance between us twain!” referring to herself and the Player King. Upon her exit, Hamlet asks his mother how she likes the play, and she utters the line about protesting.
While Gertrude may be complaining about the overacting, the most common interpretation is that she is acknowledging the inverse parallel to her own behavior.
http://shakespeare.mit.edu/hamlet/hamlet.3.2.html

Dramatic irony is a literary device whereby we, the audience, know something that a character in the story doesn't. The line in the question comes from act 3, scene 2 of Hamlet. Hamlet is staging a play called The Murder of Gonzago, which is meant to reflect the murder of his own father by Claudius. The Player Queen, obviously meant to be Gertrude, declares somewhat overdramatically that she will never remarry in the event of her husband's death.
Hamlet is keen to gauge his mother's reaction to her representation on stage. It's then that she utters those immortal words: "The lady doth protest too much, methinks." The dramatic irony lies in the fact that the Player Queen behaves in exactly the same way that Gertrude did in real life, but Gertrude herself is so singularly lacking in self-awareness that she cannot see this. Or if she has caught on, she is not showing it.

Single Variable Calculus, Chapter 2, 2.4, Section 2.4, Problem 13

(a) Determine a number $\delta$ such that if $| x - 2 | < \delta$ then $| 4x - 8 | < \varepsilon$, where $\varepsilon = 0.1$

Based from the definition,

$
\begin{equation}
\begin{aligned}

\begin{array}{c}
\text{ if } |x -a| < \delta \text{ then } |f(x) - L| < \varepsilon\\
\text{ if } |x -2| < \delta \text{ then } |4x - 8| < 0.1

\end{array}

\end{aligned}
\end{equation}
$


To satisfy inequatlity $| x - 2 | < \delta $

We want,

$
\begin{equation}
\begin{aligned}
& | 4x - 8 | < 0 . 1
&& \phantom{x}\\

& | 4(x - 2) | < 0.1
&& \text{ Factor}\\

& \frac{4 | x - 2 |}{4} < \frac{0.1}{4}
&& \text{ Divide both sides by 4}\\

& | x- 2| < 0.025
&&

\end{aligned}
\end{equation}
$


Hence,
$\quad \delta < 0.025$

(b) Repeat part (a), where $\varepsilon = 0.01$

Using the definition,

$
\begin{equation}
\begin{aligned}

& | 4x - 8 | < 0.01
&& \\
& 4| x - 2 | < 0.001
&& \text{ Factor }\\

& \frac{4| x-2|}{4} < \frac{0.01}{4}
&& \text{ Divide both sides by 4}\\

& |x-2| < 0.0025
&& \\


\end{aligned}
\end{equation}
$

Hence,
$\quad \delta < 0.0025$

This means that by keeping $x$ within $0.0025$ of $2$, we are able to keep $f(x)$ within $0.1$ of $8$.

Although we chose $\delta = 0.0025$, any smaller positive value of $\delta$ would also have work.

What social, political, and economic characteristics differed from both sides during World War 2? Need a Venn diagram.

For this question, I will address both the Allied and Axis powers.
During World War 2, the most powerful Allied members were the United States, China, the Soviet Union, and England. For the Axis members, we have Japan, Italy, and Germany.
In a seemingly curious alliance, the Soviets stood with the United States and England, countries that had free societies. Both the United States and England accorded their citizens political, social, and economic rights that Soviet citizens could only dream of.
Now, back to the Soviets and Germans. The Soviets, of course, were Stalinists and staunchly Communist. On the other hand, Nazi Germany was anti-communist. Although the two countries shared similar ideals, especially in the importance of utopian biopolitics, they differed in other respects.
Now, I will address the subject of utopian biopolitics. Both the Soviets and Germans believed that the state had every right to decide reproductive policy for its citizens. Stalin and Hitler maintained that the citizenry must be managed through a centralized health-care system. These two leaders were obsessed with the national birthrates in their respective countries. They championed the importance of motherhood, as a service to the state, of course; it was the duty of the mother to birth future soldiers.
Where the Soviets and Germans differed was in their focus: The Germans, under Hitler, wanted an Aryan nation, a racially-pure society. Hitler espoused institutional racism. Non-Aryans were Untermenschen (inferior peoples), while Aryans were Ubermenschen (the master race). Both Hitler and Stalin believed in the Darwinist "survival of the fittest" ideology, but Hitler went a step further. He maintained that only Aryans deserved the glory of being the "fittest." Thus, all German state reproductive policies were focused on racial purity.
Hitler believed that it was his duty to cull his country and the world of genetically impure peoples. This rationalization for an "optimal" racial pedigree led to the Holocaust. For his part, Stalin also leveraged state power to foist his reproductive policies on his people. However, he and Hitler differed in another regard. While Hitler endeavored to cleanse his society of the Untermenschen, Stalin targeted the Chechens and Ingush minorities because they occupied strategically important regions of the Soviet Union.
The Soviets were just focused on propagating Stalinist socialism throughout the world and were prepared to use violence to fulfill this objective. However, the Germans focused on being violent at the reproductive level in order to fulfill their racial objectives. They sterilized and eliminated homosexuals, the disabled, Untermenschens, and the mentally ill, conducting mass murder in the name of eugenic science and racial purity. As for the Soviets, they eventually rejected eugenics as a "fascist" science. For more differences between Germany and the Soviet Union during World War 2, please refer to the links and sources below.
Now, I would like to discuss the other members of the Allied and Axis powers: China and Japan. During World War 2, China sided with the Allied powers, while Japan formed part of the Axis powers. Politically, the Japanese favored a nationalist-militarist ideology. The Japanese government saw itself as a liberating force, especially among Asian countries. It widely promoted what was called the Amau Doctrine, the idea that Japan was privileged to act as a unilateral peacekeeper in Asia.
It can be argued that the Amau Doctrine was not wholly altruistic in nature. After all, China had the raw materials Japan needed for its manufacturing industry. So, it is no surprise that Japan became obsessed with China. Historians have documented Japanese atrocities in China during World War 2, so I will not get into that here. However, I want to stress an important difference between China and Japan during World War 2; while the Japanese were obsessed with the idea of dominance over other Asian cultures, the Chinese did not share this ideology. This is the main reason China lent its support to the Allied powers during World War 2.
Based on these differences, you may be able to draw your own Venn diagram showing the differences between the Allied and Axis countries in political, economic, and social terms.
Sources:
1) Beyond Totalitarianism: Stalinism and Nazism Compared by Michael Geyer and Sheila Fitzpatrick.
2) Stalinism and Nazism: Dictatorships in Comparison by Ian Kershaw and Moshe Lewin.
3) Power across the Pacific: A Diplomatic History of American Relations with Japan by W. Nester.
http://afe.easia.columbia.edu/special/japan_1900_power.htm

What are some examples of foreshadowing in the story?

Foreshadowing is a literary technique whereby the author drops subtle hints of what is going to happen later in the story. There are many examples of this in The Great Gatsby, but here are just a few of them:

[Gatsby] stretched out his arms towards the dark water in a curious way... I glanced seaward and distinguished nothing except a green light... that might have been the end of a dock. When I looked once more for Gatsby he had vanished, and I was alone again in the unquiet darkness.

Nick is the narrator of these events, of course. The green light can be said to symbolize Daisy, and Gatsby stretches out his arms towards the light in the hope of being with her. Yet when the green light disappears, so does Gatsby. This indicates that they will never be reconciled, an impression confirmed by another piece of foreshadowing later on:

 The day agreed upon was pouring rain.

Gatsby and Daisy agree to meet up; but on the day of their meeting it is raining. It seems that the weather reflects something about their relationship. It is not surprising that it wouldn't work out between them, especially when Daisy's feelings for Gatsby are so superficial:

"They're such beautiful shirts," she sobbed. "It makes me sad because I've never seen such—such beautiful shirts before."

Isn't Daisy so incredibly shallow? Yet this is the fullest extent of her feelings towards Gatsby. If two people in a relationship have such a different understanding of love, then there is no future between them.
Gatsby's death is foreshadowed in a number of places too:

I couldn't sleep all night; a fog-horn was groaning incessantly on the Sound, and I tossed half sick between reality and savage frightening dreams. Toward dawn I heard a taxi go up Gatsby's drive and I immediately jumped out of bed and began to dress—I felt that I had something to tell him, something to warn him about and morning would be too late.

Nick has had a terrible nightmare. What could it have been about? We don't know, but it certainly points towards an unhappy ending for Jay.

[Life] starts all over again when it gets crisp in the fall.

These are the words of Jordan Baker. Gatsby decides to take his fateful last swim in the pool on the first day of fall, a time of death and rebirth. Gatsby will die, but all the shallow, superficial rich folk of the two Eggs will start over as if nothing has happened. The fact that so few of them have the decency to attend Jay's funeral confirms this.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 78

For what point does the normal line to the parabola $y = x-x^2$ at the
point $(1,0)$ intersect the parabola a second time. Illustrate with a sketch.
Given: $y = x -x^2 \quad$ $P(1,0)$

Solving for the slope of the tangent line

$
\begin{equation}
\begin{aligned}
y & = x - x^2\\
\\
y' & = \frac{d}{dx}(x) - \frac{d}{dx}(x^2)\\
\\
y' & = 1 - 2x
\end{aligned}
\end{equation}
$


Let $y' = $ slope$(m_T)$ of the tangent line

$
\begin{equation}
\begin{aligned}
y' = m_T &= 1 - 2x
&& \text{Substitute value of } x\\
\\
m_T &= 1-2(1)
&& \text{Simplify the equation}\\
\\
m_T &= -1
\end{aligned}
\end{equation}
$


Solving for the slope of the normal line

$
\begin{equation}
\begin{aligned}
m_N &= \frac{-1}{m_T} && \text{Substitute value of the slope of the tangent line}\\
\\
& = \frac{-1}{-1}\\
\\
m_N &= 1
\end{aligned}
\end{equation}
$

Solving for the equation of the normal line

$
\begin{equation}
\begin{aligned}
y - y_1 & = m_N(x-x_1)
&& \text{Substitute the value of }x,y \text{ and slope}(m_N)\\
\\
y - 0 & = 1(x-1)
&& \text{Simplify the equation}\\
\\
y & = x -1
\end{aligned}
\end{equation}
$

Equating the normal line and the parabola to find the point of intersection

$
\begin{equation}
\begin{aligned}
\text{Normal line } \qquad y &= x - 1\\
\\
\text{Parabola} \qquad y& = x-x^2
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
x - x^2 &= x -1
&& \text{Add } -x \text{ to each sides}\\
\\
x - x - x^2 &= x - x - 1
&& \text{Comine like terms}\\
\\
-x^2 &= -1
&& \text{Multiply -1 to each sides}\\
\\
x^2 &= 1
&& \text{Take the square root of each sides}\\
\\
x =1, \quad x = -1
\end{aligned}
\end{equation}
$

Finding for the second point of intersection

$
\begin{equation}
\begin{aligned}
y &= x - x^2\\
y &= -1 - (-1)^2\\
y &= -2
\end{aligned}
\end{equation}
$


Thus, the point where the normal line intersects the parabola for the second time is at the point $(-1,-2,)$

Where is Rainy Mountain and why does Momaday return there?

In the prologue, we learn the reason why Momaday returns to Rainy Mountain:


I returned to Rainy Mountain in July. My grandmother had died in the spring, and I wanted to be at her grave. She had lived to be very old and at last infirm.

Momaday also tells us that Rainy Mountain rises out of the plain in Oklahoma, northwest of the Wichita Range. Rainy Mountain represents an old landmark for the Kiowa people, from whom he is descended. Rainy Mountain is described as an inhospitable place with difficult weather. However, Rainy Mountain represents an important link between him, his grandmother, and the Kiowa culture in general.
In fact, although Momaday does not speak Kiowa and has a scarce understanding of his identity, he returns home precisely to honor and explore his Kiowa origins. Most of what he knows of Kiowa culture was passed on to him through his grandmother; she was the one who told him about the history of the Kiowas and their legends. 
Momaday's journey is a pilgrimage of sorts, which allows him both to honor his grandmother's memory and to pay tribute to his Kiowa heritage. After this, Momaday returns to his own life with a stronger understanding of Kiowa culture and of his own identity.

Scott Momaday describes the location of Rainy Mountain quite precisely in his book The Way to Rainy Mountain. He says that:

A single knoll rises out of the plain in Oklahoma, north and west of the Wichita Range. For my people, the Kiowas, it is an old landmark, and they gave it the name Rainy Mountain.

The Wichita mountain range is a mountain range located in southwestern Oklahoma. It consists of igneous rocks that were uplifted 330 to 290 million years ago and have since gradually been worn down by erosion. The peaks average approximately 2,000 feet above sea level. Rainy Mountain is slightly to the northwest of the rest of the range. It is located in Kiowa County, Oklahoma, and served as a landmark and spiritually significant site for the Kiowa people. 
The narrator returns to the mountain to visit the grave of his grandmother after her death. It is part of his physical and spiritual journey to reconnect with his people and their origins. 
https://www.okhistory.org/publications/enc/entry.php?entry=WI002

Rainy Mountain is located northwest of the Witchita range in Kiowa County, Oklahoma. The narrator returns there to visit his grandmother's grave.
Rainy Mountain was a landmark for the Kiowa people, from whom the narrator is descended. He says that it had some of the harshest weather in the world, including blizzards and heat. Momaday says the Kiowa are people who prefer the summer and deal with the winter. 
Momaday has a lot of love for his grandmother, who died after a long life. After his grandmother dies, Momaday first goes to her house where there is nothing but quiet. The next day, he goes to Rainy Mountain to see her grave. He writes:

The next morning I awoke at dawn and went out on the dirt road to Rainy Mountain. It was already hot, and the grasshoppers began to fill the air. Still, it was early in the morning, and the birds sang out of the shadows. The long yellow grass on the mountain shone in the bright light, and a scissortail hied above the land. There, where it ought to be, at the end of a long and legendary way, was my grandmother's grave. Here and there on the dark stones were ancestral names. Looking back once, I saw the mountain and came away.

To view Rainy Mountain's location, click on the Google Maps reference link.
https://www.google.com/maps/place/Rainy+Mountain/@35.0245804,-99.0233533,10.25z/data=!4m5!3m4!1s0x87ac67437053b9c1:0x163fe1dc0260ac88!8m2!3d34.997003!4d-98.8495131?dg=dbrw&newdg=1

Momaday tells us this in the first two paragraphs of his Introduction. Rainy Mountain is a special place to the Kiowa people, the author’s Native American ancestors. It is a rounded hill that stands alone but near the Wichita Mountains in southwestern Oklahoma. Below is a link to the nearby national wildlife refuge. Rainy Mountain is not part of this protected land; yet looking at the photographs on this site will give you an idea of the terrain.
The author goes back to Rainy Mountain one July, after his grandmother has passed away. She was his last living link to the traditional ways of the Kiowa. He wanted to honor and remember her as well as the many others who had gone on before. The cemetery is located near the mountain. Momaday’s return was part of his longer personal journey of tracing the historic migration of the Kiowa from the headwaters of the Yellowstone River in western Wyoming and Montana, east and south through the Black Hills and plains to Oklahoma.
https://www.fws.gov/refuge/wichita_mountains/

Calculus of a Single Variable, Chapter 5, 5.5, Section 5.5, Problem 34

To simplify the logarithmic equation: log_5(sqrt(x-4))=3.2 , recall the logarithm property: a^((log_(a)(x))) = x .
When a logarithm function is raised by the same base, the log cancels out which is what we need to do on the left side of the equation.
As a rule we apply same change on both sides of the equation.
Raising both sides by base of 5:
5^(log_5(sqrt(x-4)))= 5^(3.2)
sqrt(x-4) = 5^(3.2)
To cancel out the radical sign, square both sides:
(sqrt(x-4))^2 = (5^(3.2)) ^2
x-4 =5^(6.4)
x= 5^(6.4)+4
x~~29748.593 (rounded off to three decimal places)
To check, plug-in x=29748.593 in log_5(sqrt(x-4)) :
log_5(sqrt(29748.593-4))
log_5(sqrt(29744.593))
log_5(172.4662083)=3.2 which is what we want

So, x=29748.593 is the real solution.
Note: (x^m)^n= x^((m*n ))

Find the potential a distance z above the center of a uniform line of charge with charge density lambda and length 2L .

For a continuous potential to equation is
V=int (k*dq)/r
Where k=1/(4pi epsilon_0) , dq is an infinitesimal piece of charge, and r is the distance away dq is from the point we are measuring.
We know the charge per unit length lambda=(dq)/(dl) where dl is an infinitesimal chuck of the wire. If we let the wire lay along the x-axis then dl=dx . Therefore,
dq=lambda dx
Now, looking at the picture we have a right triangle. So we know r=sqrt(x^2+z^2) . Then the integral becomes,
V=int_(-L)^L (k*lambda dx)/sqrt(x^2+z^2)=k*lambda int_(-L)^L dx/sqrt(x^2+z^2)
From a table of integrals we can find that
V=k lambda ln(x+sqrt(x^2+z^2))|_(-L)^L
V=lambda/(4pi epsilon_0) ln((L+sqrt(L^2+z^2))/(-L+sqrt(L^2+z^2)))
To simplify multiply the numerator and denominator by L+sqrt(L^2+z^2)
V=lambda/(4pi epsilon_0)ln[(L+sqrt(L^2+z^2))^2/(-L^2+L^2+z^2)]
V=2*lambda/(4pi epsilon_0)ln[(L+sqrt(L^2+z^2))/z]
V=lambda/(2pi epsilon_0)ln[(L+sqrt(L^2+z^2))/z]
This is the answer.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potlin.html

How did Americans respond to the challenges to the social order presented by their doctrine of equality?

This is a broad question, but over the course of their history, Americans with power (i.e., whites) have responded to the conflict between the equality promised in foundational documents of the United States, such as the Declaration of Independence and the Constitution, and the existence of an unequal social order, especially in the South, by reaffirming pre-existing racial and gender categories. In other words, instead of promoting widespread equality across the board at the beginning of the republic, elites made sure "equality" became the exclusive domain of white males. Groups such as black slaves, Native Americans, and women were excluded from notions of equality.
Native Americans, for example, were to be allowed sovereignty over their reservations only after they had given up their "primitive" ways and adopted white cultural norms. Until then, they were under rigid supervision by white government superintendents.
Black slavery was first upheld. Then, even after emancipation, segregation, which denied blacks equal access and equal opportunity, was normalized for a century. United States history has been characterized by a long struggle by people considered non-white or non-Nordic, such as Eastern or Southern European immigrants, blacks, Asians, and Native Americans, for legal equality. Women, too, have had to struggle for full legal personhood and the franchise.

Should states continue to allow ballot initiatives and other forms of direct democracy?

This is largely a matter of opinion, and it is important to examine both sides of the argument carefully. Speaking personally, I would argue against ballot initiatives and other forms of direct democracy for a number of reasons. First of all, it goes against the long-established principles of American democracy. When the Founding Fathers established the Republic, they instituted a system called representative democracy. This means that we elect people—Senators, members of Congress, state legislators—to make decisions on our behalf. Even when the population of the United States was fairly small, this was felt to be a more efficient way of expressing the people's will.
The Founding Fathers were very suspicious of direct democracy because they feared that it would lead to the establishment of mob rule; people would act on the spur of the moment in making crucial political decisions. They would act on their emotions instead of taking the time to examine the issues carefully before reaching a decision. Although we may regard the Founding Fathers' innate suspicion of direct democracy as somewhat overstated, we can still sympathize with their anxiety to avoid the consequences of a lack of deliberation and reasoned reflection in the process of formulating legislation.
This leads me on to the next criticism of direct democracy. Decisions made in plebiscites, referenda, ballot initiatives, and so forth provide nothing more than a snapshot of how people are feeling at any particular time. One could argue, however, that meaningful democracy is a process that develops over time. It involves a constant interaction between the voters and their elected representatives. The whole process transcends those single moments of history captured when democratic decisions are made in popular initiatives. This means, among other things, that representative democracy is better able to respond to changes in public opinion. With direct democracy, once a policy has been adopted, there is little that can be done to change it no matter how disastrous the consequences.
There are all kinds of other objections to direct democracy, such as the notoriously low turnouts it often encourages and the frankly ludicrous, trivial proposals that somehow manage to find their way onto the ballot. (In 1993, voters in San Francisco were asked if a police officer should be allowed to walk his beat with a ventriloquist's dummy.) But the final objection I want to raise is a simple one. If we have direct democracy initiatives, then what is the point of having elected representatives? Representatives are precisely that: those who represent us. They are not delegates; they are not there simply to carry out the voter's instructions to the letter. They must be given some leeway in the use of their judgement. If we do not like how they use their judgement, this is not a problem; we can always vote them out of office during the next election.
We cannot do this with direct democracy, so there is a disturbing lack of political accountability. If I do not like how an elected official behaves, then I can always reject them come election time. In other words, like all other voters, I am able to hold elected representatives accountable for the decisions they have made in office. But if those decisions are made by the voters themselves in a direct ballot initiative, then who carries the blame when things go wrong? How can the voters ever possibly hold themselves accountable? The very notion is absurd.
In the meantime, I would submit that our representatives must be allowed to get on with the job for which they are being paid and for which they have been authorized to perform by the United States Constitution. They represent; we are represented. That is how it works, and that is how it should continue to work.

What is Malala's relationship with her brothers like?

Although Malala has a good relationship with her brothers, she admits that she still quarrels with them. In the book, Malala details how she played and fought happily with Khushal and Atal during their childhood days. Malala shares a strong bond with her brothers, and she harbors great affection for them. In return, despite their nonchalance, they deeply cherish and respect their sister. After Malala was shot, her brothers showed great concern for her welfare. They cried and worried, frightened that she would not survive her ordeal.
After she was admitted to the Armed Forces Institute of Cardiology, Khushal was sad that Malala was absent from the family dining table. The brothers were then happy to be reunited with their sister at the Queen Elizabeth Hospital in Birmingham. Both Khushal and Atal even admitted to missing Malala. Despite the warm reunion, however, Malala remembers that she commenced quarreling with Khushal almost immediately. Despite their squabbles, Malala credits her brothers with keeping her grounded. By treating her normally, Khushal and Atal allowed Malala to retain much of her innocence during the most dangerous days of their childhood years.

In Night, what is a quote that shows how cultural understanding is essential to the growth of an individual within a community?

In Night, cultural understanding in the form of religion is essential to Eliezer's growth within the Jewish community.
Night highlights the important role that religion plays in the Jewish community's culture.  The narrative's opening shows this through Eliezer's relationship with Moshe the Beadle. Moshe serves as Eliezer's spiritual teacher.  He guides Eliezer to understanding the importance of religion in the Jewish culture:

There are a thousand and one gates allowing entry into the orchard of mystical truth. Every human being has his own gate. He must not err and wish to enter the orchard through a gate other than his own. That would present a danger not only for the one entering but also for those who are already inside.

These words have a profound impact on Eliezer:

And Moishe the Beadle, the poorest of the poor of Sighet, spoke to me for hours on end about the Kabbalah's revelations and its mysteries. Thus began my initiation. Together we would read, over and over again, the same page of the Zohar. Not to learn it by heart but to discover within the very essence of divinity.

Religion defines Eliezer's culture in Night.  They help to carve out Eliezer's place in the community.  While people like his father embrace commerce and less spiritual notions of the good, Eliezer is content with the place that religious worship affords him in the culture of the Jewish community of Sighet.   Eliezer's growth is based on religious understanding.  At thirteen years old, Eliezer sought to better understand how "question and answer would become one."  Religion was the cultural lens through which Eliezer's growth in the community took place. 
The force of religion on Eliezer's growth can be seen as he endures the Holocaust.  His experiences in the camp compel him to change his view of religion. He begins to ask questions to God, demanding to know where he is as Eliezer and his community suffer. Eliezer is unwilling to see questions and answers as one. He is not able to embrace the divine's mystical complexities.  Instead, he wants answers about the pain he and his community experience in the Holocaust: 

What are You, my God? I thought angrily... why would I bless Him? Every fiber in me rebelled. Because He caused thousands of children to burn in His mass graves? Because He kept six crematoria working day and night, including Sabbath and the Holy Days? Because in His great might, He had created Auschwitz, Birkenau, Buna, and so many other factories of death? How could I say to Him: Blessed be Thou, Almighty, Master of the Universe, who chose us among all nations to be tortured day and night, to watch as our fathers, our mothers, our brothers end up in the furnaces? Praised be Thy Holy Name, for having chosen us to be slaughtered on Thine altar?

Eliezer's cultural understanding through religion plays a critical part in his transformation.  Initially, he embraces a profoundly personal view of spirituality.  He is content with his place that religion affords him in the culture of the Sighet community.  Through Moshe's guidance, he believes that individuals must find their path to universal truth through the "orchard of mystical truth." However, as a result of his experiences in the Holocaust, his view of religion changes. He becomes angry and insists on answers.  He is unable to reconcile the cultural view of God as merciful with what he sees in places like Auschwitz, Birkenau, and Buna.  He is no longer able to participate in community services such as Rosh Hashanah and Passover fasting.  These quotes show the role that cultural understanding in the form of religion plays in Eliezer's development within the community.  They show how he changes from one who is an active participant in the cultural lifeline of the community to one who is estranged from it.

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 8

Determine whether each function is continuous or discontinuous at the following scenarios and explain why.

(a) The temperature as a function of time at a specific area.
The function is continuous since the temperature changes with respect to time proportionally.

(b) The temperature as a function of time due west from Oklahoma City at a specific time.
The function is continuous since the temperature changes with respect to distance proportionally.

(c) The altitude above sea level as a function of distance due west from Oklahoma City.
The function is discontinuous since the altitude may increase abruptly up to a certain height with respect to the distance.

(d) The fare on a taxi as the function of the distance traveled.
The function is discontinuous since the cost of a taxi ride inccrements on a certain value with respect to the distance.

(e) The Light's current in the circuit as a function of time.
The function is discontinuous because when you turn the light on, the current jumps on a certain value but when you turn it off, the current return to its initial value .

Looking at both Tables 4 and 5, do lesbians or gay males have higher average victimization scores? Article name—Button, D. M., & Worthen, M. G. (2014). General Strain Theory for LGBQ and SSB Youth The Importance of Intersectionality in the Future of Feminist Criminology. Feminist Criminology, 9(4), 270-297.

Table 4 in this study presents the results of an ANOVA analysis looking at only females. This table compares the differences in victimization scores and negative outcomes (including poor academic performance, substance abuse, and suicidality) for lesbian, bisexual, questioning, and SSB (same-sex behavior) groups among females. Table 5 presents the ANOVA analysis of the same variables for male-only groups of gay, bisexual, questioning, and same-sex behavior groups (SSB). On page 284, the authors report that all LGBQ and SSB youth are equally likely to report suicidality, substance abuse, and poor academic performance. With regard to victimization, lesbians have higher average victimization scores (M=5.40) than gay males (M=4.07). However, bisexual, questioning, and same-sex behavior females have lower victimization scores than their comparable male groups. 
Regarding the data in Table 2, the authors report that victimization is greater among males (M=4.46) compared to females (M=2.39), but there are no other differences among males and females. That is, males are more likely to report victimization, but males and females are equally likely to report poor academic performance, substance abuse, and suicidality in the study.

How does waiting for services affect the poor?

Many Americans face the problems outlined in Evicted and struggle to meet the basic needs of food, shelter, and employment. An increase in rent, a personal emergency, or unexpected expenses can quickly become a crisis. Evicted tackles issues like the feminization of poverty, cyclical issues of poverty, and social advocacy.
It is no secret that many women in America will face or have faced a socioeconomic crisis, especially because they continue to receive unequal pay compared to their male counterparts. Therefore, it is more likely that women will be faced with the burden of waiting for social services in the event of a crisis like eviction. Additionally, this issue is often compounded by the need to find daycare for their children. Therefore, women often have to seek social services such as TANF, Section 8, Food Stamps, or WIC, which may be quickly taken away if they reach an income level that is slightly over the requirements of these services. If this happens, they will need to find alternative means to meet their basic housing needs.
Low-income individuals who are waiting for social services in the aftermath of an eviction may be faced with the dangerous realities of living in a shelter, living on the streets, or even squatting. Many face compounding issues such as substance abuse disorders, career crises, or even mental health issues. Many of these issues may go unnoticed by typical social services programs, even as they cause repeated problems. As a result, the cyclical nature of poverty not only traps people in personal poverty but also creates a continuous burden on the American economy.
In light of the fieldwork presented in Evicted, it's more important than ever that mental health counselors, social workers, and rehabilitation programs provide social advocacy services for these individuals and their families. Although second-chance housing is possible in some areas of the US, it is more than likely that these individuals will face social and familial crises while they wait for social services. As a consequence, social advocacy is needed not only on an individual scale but on a national level.
https://ui.uncc.edu/sites/default/files/pdf/LATEST.Evicted%20Book%20Club%20CLT%20Study%20Guide.pdf

Waiting for services affect the poor in different ways. Emotionally, it can cause depression, anxiety, or anger. A low self esteem can arise with the span of time waiting for services and not being able to make decisions due to lack of meeting the necessities of life. For example, loss of job can lead to not being able to pay rent and buy food for the family. The children will not be able to go to school because of not having a home to live in, moving from one place to another. Waiting for services can also lead to abuse of different sorts such as verbal abuse or physical abuse because of frustration and insecurity of not knowing if life will be the same tomorrow. Waiting for services can also cause health issues because some people are not able to take the consequences of not having a home or food to eat. Sometimes the poor are placed in services that are suppose to help them but it serves more damage than good and this creates more instability and insecurity for the poor.

Evicted provides a firsthand look into the compounding factors that make escaping poverty difficult and highlights how greatly eviction and the affordable housing crisis affect those living in poverty. In your scenario of waiting for services, factors that might have an impact are:
Lack of a permanent or long-term address. Tenants with a record of past evictions have difficulty securing affordable housing, and tenants spending a large portion of income on housing are more likely to grow behind on rent. This cycle ensures that evicted renters remain at a high risk for eviction, which impedes access to services requiring contact by mail or confirmation of address.
Inflexible work schedule. Eviction is directly connected to job loss. Since a person fired from a past job will have more difficulty finding a new job, and since a person living in poverty greatly depends on each paycheck, someone in this situation may not be able to miss work to attend to other business. If procuring services requires an appointment during a set time period, a poor person with an inflexible work schedule may not have the option of attending.
Lack of reliable transportation and lack of reliable childcare may also be obstacles.

Waiting for social services perpetuates cyclical poverty, and this passing of time creates greater need. When people can't get the help they need when they need it, their problems become compounded while they wait. The cyclical nature of these setbacks (i.e., that waiting for aid begets greater need for that aid), ultimately puts more pressure on the individual, as well as the society they live in.

Describe the general appearance of Eliza before she was changed by Professor Higgins in Pygmalion.

Eliza, prior to her transformation at the hands of Professor Higgins, was essentially a beggar—impoverished and working on the street. She was the exact opposite of well-dressed and dignified, with nothing about her appearance or bearing that would suggest high social standing. Professor Higgins was seeking someone who could illustrate the ultimate transformation, and he did well by finding Eliza.
Eliza is described as covered in dirt with ragged clothes that were wrinkled and ripped and old. She also attempted to improve her looks by wearing ostentatious ostrich feathers in her hair which, in reality, did nothing to help the situation. Professor Higgins takes her in and cleans her up. With a wash, she instantly looks better, and he is able to dress her in nice clothes to make her look wealthy and refined.

Eliza comes into Mr. Henry Higgins's laboratory looking like a poor young flower-selling woman that she is. She tries to look nice by wearing a hat decorated with ostrich feathers in the colors red, sky-blue, and orange. Her apron is not quite clean, and she has on a shabby coat that "has been tidied a little." She is putting her best foot forward but nevertheless is unmistakably a lower class person out of place in a well-to-do home. As Higgins says of her:

She's so deliciously low—so horribly dirty—

Higgins sends her off immediately to be bathed, and we learn she has never had a full bath in her life. Eliza's appearance shows how wide the class divide was in the England of a hundred years ago. Today, a poor working person like Eliza would probably be able to wear clean clothes and bathe. Eliza's circumstances force her to be dirty and shabby.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 11

You need to use mathematical induction to prove the formula for every positive integer n, hence, you need to perform the two steps of the method, such that:
Step 1: Basis: Show that the statement P(n) hold for n = 1, such that:
2 = 1(1+1) => 2 = 1*2 => 2=2
Step 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds:
P(k): 2 + 4 + .. + 2k = k(k+1) holds
P(k+1): 2 + 4 + .. + 2k + 2(k+1) = (k+1)(k+2)
You need to use induction hypothesis that P(k) holds, hence, you need to re-write the left side, such that:
k(k+1) + 2(k+1) = (k+1)(k+2)
You need to notice that you can factor out k+1 to the left side, such that:
(k+1)(k+2) = (k+1)(k+2)
Notice that P(k+1) holds.
Hence, since both the basis and the inductive step have been verified, by mathematical induction, the statement P(n): 2 + 4 + 6 + ... + 2n = n(n+1) holds for all positive integers n.

Why does Miss Merle slap Janey, and how does this make you feel after reading the chapter narrated by Merle in A Gathering of Old Men?

In A Gathering of Old Men, although slapping Janey is rather cruel, Miss Merle realizes that the servant is hysterical and she needs answers from Janey immediately.
In the beginning of Gaines's novel, the conflict is established early on as the Cajun farmer Beau Boutan lies dead, having been shot by Mathau. This situation is dire because the Boutan family has a history of violence and Beau is white and Mathau is black. Candy Marshall is white and from the family that once owned the former plantation; nevertheless, she claims she has shot Beau in order to protect Mathau, who has been like a father to her.
In Chapter Three, Myrtle Bouchard (also called Miss Merle) has a pie made so she can take it to the Marshall's house where the Major resides. After she arrives at the Marshall home, she observes that the servant Janey has been crying. When Janey tells her about the murder, Miss Merle tries to awaken the drunken Major on the porch, but he is passed out. As a result, she drives alone to where the black people of the community live -- in the former slave quarters. There she observes Mathau, Johnny Paul, and Rufe sitting on the porch holding shotguns. She sees the bloodied body of Beau Boutan, and Candy Marshall tells Miss Merle that she has shot Beau. Miss Merle does not believe her, yet Candy insists that she committed the murder, adding that the three men have also confessed to the crime. Candy asks Miss Merle to ask Janey to get the names of as many men as she can that do not like Fix, the father of Beau, and have them come with shotguns. 
Miss Merle returns to the Marshall house. She asks Janey who does not like Fix. The terrified Janey says that she does not know anyone who does like Fix. Then, Miss Merle asks her if these men will stand up to Fix. Janey cries, "I don' know what you talking about." Miss Merle explains that Candy is going to protect Mathau by having as many men as she can come with shotguns and have them all claim to have shot Beau. Their guns will have one barrel empty, so she needs used 12 gauge shotgun shells as proof of this. 
"Get them on that phone!" Miss Merle orders her, but Janey begs her, "Please don't make me do nothin' like that." Miss Merle slaps Janey and orders her to get on the phone. She admits that she took her frustrations out on poor Janey, but narrates that if she has to slap her to make her understand that she must get involved, she will. The situation is dire, and Janey is the only one who can contact these men. Unfortunately, Miss Merle feels she has to slap Janey to get her to think sensibly so she will obey her. Sometimes when people are hysterical, it does become necessary to give them a little shock back into reality. Often someone will shake a person; however, Miss Merle perceives Janey as a servant and is crueler than she should be.

In Golden Boy by Abigail Tarttelin, consider the depiction of gender, sexuality, and violence. How normalized are such representations? What do they imply about gender, sexuality and power? Does the book make any social commentary?

Golden Boy is a compelling story by author Abigail Tarttelin that tackles a variety of complex themes, including gender, sexuality, violence and power. Each of these themes is explored in relation to the others as well.
Gender, Sexuality and Violence
Throughout Golden Boy, the themes of sexuality and gender are explored in depth. The main character, Max Walker, is intersex. His parents have tried hard to keep his condition a secret, but as Max grows up, his mother's control begins to wane. When his father stands for election to Parliament, Max suddenly finds himself thrust into the national spotlight along with the rest of his family. As an adolescent, he goes through many typical struggles to understand his sexuality and gender, even if his condition makes the process a bit more complicated. Max also faces the threat of violence that is often leveled at anyone who is different from what society deems acceptable and is forced to come to terms with the fact that some people will not accept him simply because he is different. Tarttelin does a compelling job of showcasing Max's unique problems on one hand while normalizing his family life on the other. Secrets abound in the Walker family, but at their core, they are just like any other family struggling to love each other through chaos.
Power Dynamics Throughout the Story
Power is a major theme throughout Golden Boy, and both Max's father and mother hold power to some degree. Max's mother, Karen, is one of the most powerful criminal lawyers in the nation and his father is a prominent politician. These power dynamics cause conflict in their relationship as Karen often resents her husband's decision to put his family in the spotlight, despite their closely guarded secrets. In this sense, power is explored through the lens of the roles of husband and wife in a modern family.
Power is also explored as a theme through Max's childhood friend Hunter, who makes a sudden and controversial reappearance in his life. Hunter has known from an early age that Max is intersex. At one point in the book, Karen discusses how she confided in Hunter's mother about the family secret. "Leah was the first person I confided in about Max’s condition, and Hunter has known since he was four. He was young when he found out, sharing a bath with Max before bedtime, but he seemed to understand as much as a child could. We just told him Max is different. Max is special."
While the relationship between Max and Hunter begins as one of childhood friendship and innocence, it eventually escalates into a major source of conflict for the Walker family. Hunter uses his knowledge of Max's condition against him, creating an imbalance of power in the friendship.
Social Commentary
While the story is told through the personal perspectives of its main characters, there is significant social commentary as well. Max is seen as perfect, but his physical condition threatens this perception not only in the eyes of his family but the world around him. There is also significant commentary on the nature of privacy in politics. Max's father struggles to keep his family's home life private, but the media proves to be demanding and sometimes ruthless. The story also challenges the concept of gender norms through both Karen and Max's experiences.
http://www.abigailtarttelin.com/golden-boy/

https://www.simonandschuster.com/books/Golden-Boy/Abigail-Tarttelin/9781476705811

Carbon-14 dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true, the amount of absorbed by a tree that grew several centuries ago should be the same as the amount of absorbed by a tree growing today. A piece of ancient charcoal contains only 15% as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? (The half-life of Carbon-14 is 5715 years.)

It is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any instant in time. Therefore, given a sample of a particular radioisotope, the number of decay events −dN expected to occur in a small interval of time dt is proportional to the number of atoms present N, i.e.
-(dN)/(dt)propto N
For different atoms different decay constants apply.
-(dN)/(dt)=\lambda N
The above differential equation is easily solved by separation of variables.
N=N_0e^(-lambda t)  
where N_0 is the number of undecayed atoms at time t=0.
We can now calculate decay constant lambda for carbon-14 using the given half-life.
N_0/2=N_0e^(-lambda 5715)
e^(-5715lambda)=1/2
-5715lambda=ln(1/2)
lambda=-(ln(1/2))/5715
lambda=1.21 times 10^-4
Note that the above constant is usually measured in seconds rather than years.
Now we can return to the problem at hand. Since the charcoal contains only 15% (0.15N_0 ) of the original carbon-14, we have
0.15N_0=N_0e^(-1.21times10^-4t)
Now we solve for t.
e^(-1.21times10^-4t=0.15)
1.21times10^-4=-ln 0.15
t=-(ln0.15)/(1.21times10^-4)
t=15678.68
According to our calculation the tree was burned approximately 15679 years ago.                                                                                                    
https://en.wikipedia.org/wiki/Radioactive_decay

https://en.wikipedia.org/wiki/Separation_of_variables

What are some similes found in "The Celebrated Jumping Frog of Calaveras Country"?

Mark Twain's use of similes in the text heightens the humor found in the piece as well as adds to the Local Color aspects of the story. For instance, when describing Jim Smiley's dog, Andrew Jackson, Twain writes that when the betting was getting serious, the dog's "underjaw'd begin to stick out like the fo'castle of a steamboat." Twain, who takes his name from steamboat and boating terminology, uses a simile that places this story with the adventurers of the Mississippi and West. The "forecastle" of a steamboat is the portion of the boat that sticks out in the front and was used for storage of things like the anchor or stage planks. Twain uses another simile in the same sentence describing Andrew Jackson that also relates to steamboat terminology: "his teeth would uncover, and shine savage like the furnaces." The furnaces were used to boil the water that created the steam.
Another way Twain uses similes is to create humorous imagery. The second of Smiley's animals that Twain describes in detail is Dan'l (Daniel) Webster. When describing the "jumping frog of Calaveras County," he writes, "you'd see that frog whirling in the air like a doughnut—see him turn one summerset, or may be a couple, if he got a good start, and come down flat-footed and all right, like a cat." When one thinks about a frog jumping, he or she imagines a simple jump up and down, but Twain's similes create a more humorous image of that frog. All of Smiley's betting animals did not look or act as one would think, like the mare that had asthma, but the fact that they all could win bets for Smiley adds to the disbelief created in this story, thus adding to the humor.

How is the trailer park similar to and different from the North Side of Milwaukee?

Class oppression and capitalist exploitation are the common realities that exist for people living in both the trailer park and the North Side of Milwaukee. In both living situations, the land lord is able to exploit the tenants and profit off their poverty. The less money and power a person has, the more a landlord can exploit the person through refusing to make repairs, charging ridiculous late fees, arbitrarily fining and penalizing people, and enacting arbitrary and often illegal evictions. Without the ability to hire a lawyer, tenants are often unable to effectively fight back against the powerful landlords. These conditions and realities exist for both the tenants in the trailer park and the houses of the North Side.
Capitalism and state oppression is also incredibly racialized, and as such, Evicted speaks to how black folks must endure both class oppression and racialized oppression by the state and capitalist exploiters such as landlords. On the North Side, tenants must endure more heavy policing/police presence in their neighborhoods and more forceful and brutal police evictions. Additionally, evictions can result more readily and easily in long-term consequences such as houselessness due to racism and the racism of potential employers. As such, the book explores the commonalities of classism and the intersections of classism and racism.

Matthew Desmond's Evicted is a critical look at extreme poverty in the United States, particularly in the city of Milwaukee, Wisconsin. It paints a stark picture of those affected by the severe lack of affordable housing. Desmond himself was originally inspired to study the correlation between poverty and the housing market after his lower middle-class family lost their home during his studies. Two areas that he studies quite closely are the College Mobile Home Park, owned by negligent Tobin Charney, and the north side of Milwalkee, specifically a group of properties owned and operated by the ambitious Sherrena Tarver.The most glaring difference between the the two areas is the racial population. The trailer park houses predominantly white tenants while Sherrena's properties rent to mostly black tenants. Another difference is that when members of the trailer park community are evicted, they have a much easier time finding replacement housing due to their race. Tenants of Sherrena, however, are one step away from the homeless shelter at all times. Other than the inherent differences that come with race, much of these two living situations present the same issues. Both landlords, while not entirely unkind, are equally exploitative. Sherrena markets exclusively to the impoverished black population simply because she can earn more for less by taking advantage of black tenants with criminal records, as they are desperate for housing. Similarly, Charney neglects the trailer park to the point that the tenants are living in filth and squalor, insisting that they clean up toxic messes around the park.

Evicted: Poverty and Profit in the American City is a nonfiction book written in 2016 by American author Matthew Desmond. The account explores issues of poverty, affordable housing, and economic exploits at the hands of the underprivileged through an examination of eight families who live in various areas of Milwaukee, Wisconsin during the 2008 financial recession.
The two key areas detailed are the north side, which has neighborhoods primarily consisting of African Americans, and the trailer park on the south of the city, which primarily consists of white residents. These racial disparities are the first and most visible indicator of the differences between the areas.
These areas have a fair amount in common though, specifically the fact that regardless of skin color, families struggle to make rent payments to their landlords. The families struggle to get by financially and the difficulty they experience in making ends meet, specifically with regard to rent payments, is universal. Both areas are exploited by landlords who take advantage of their tenants. The profits of the landlords exist in stark contrast to the extreme poverty they exploit.
Throughout the account, another important difference comes to light. The eviction rates of the black community are significantly higher than the eviction rates of the white community, which uncovers and epitomizes the inherent racism with regard to the affordable housing market.

Evicted shows us, among other things, that Milwaukee is one of the most racially segregated cities in the United States. The north side of town consists largely of impoverished neighborhoods, with an overwhelmingly African American population. Just south of the Menomonee river there's a trailer park where most of the residents are white.
But aside from the obvious racial differences, these communities have quite a lot in common. For one thing, they are both continually exploited by a system that makes huge profits out of the poor housing in which these people are forced to live. On the North Side, Sherrena makes hundreds of thousands of dollars a year from renting out low-quality properties in some of the worst ghetto neighborhoods. Meanwhile, farther south, Tobin Charney makes nearly half a million dollars from trailer park rents.
Nevertheless, Matthew Desmond presents us with evidence of a so-called racial dividend in relation to evictions as with much else in Milwaukee. Eviction rates among white tenants, though rising, are still considerably lower than those of African Americans. This feeds into a sense of white privilege among the residents of the run-down trailer park in Evicted despite the appalling conditions in which they live.
A system that exploits poor people of color nonetheless serves to maintain and reinforce feelings of white supremacy. The white tenants who live in Tobin Charney's trailer park may have little or nothing, but as far as most of them are concerned things could be a whole lot worse; they could be forced out, possibility having to move to the black ghettos of the North Side. So the system marches inexorably on, exploiting deep-seated racial hostility and obscuring the common class interests that should unite the North Side with the white trailer parks in a campaign for real economic and political change.