Does Macbeth determine what happens to him?

Macbeth is certainly the one who determines the course his life takes. The moment he decides to murder king Duncan is the moment he accepts evil. Once he does that, he cannot go back to the point when he was considered to be a loyal and good warrior, ready to support his king and others.
Macbeth's ambition consumes him, and although he is motivated by the witches' prophecy and pressured by his manipulative wife, he does have free will to decide who he wants to become. He decides that he wants to pursue his ambition even though it entails resorting to the most unlawful means.
Once he gets rid of king Duncan, he cannot stop. He begins to murder many other innocent characters, such as Banquo and Macduff's family, because of his obsessive desire for security. He does not want to allow his power to slip away from him by letting others stop him from being the leader of the country:

I am in blood Stepp'd in so far that, should I wade no more, Returning were as tedious as go o'er:

He states that going back to the point when his conscience was clear would be as tedious as going forward. He believes he should continue being ruthless and evil because he cannot erase the crimes that have already accumulated.
Macbeth's desire to get rid of anyone who stands in his way eventually leads him to his imminent downfall. So, he is the one to blame for his death.

How does Zlata try to keep her life normal?

In the midst of war, Zlata struggles to maintain a sense of normalcy by not giving in to despair. Prior to the conflict, Zlata enjoyed going on vacations and practicing the piano, and she was about to attend the fifth grade. Although there are hints of a coming war, Zlata believes that it won't affect her peaceful life. This is proven to be false once violence and gunshots arrive in her native Sarajevo.
With casualties and deprivation surrounding her, Zlata wrote down her thoughts and feelings in her diary. She expresses her frustrations about war and questions if it will ever end. But what keeps Zlata grounded is her family. Even though the war caused some of her friends to either flee or die, it's her closeness to her family that kept hope alive for her.

Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 2

Identify each function whether it is a power function, root function, polynomial(state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

$
\begin{equation}
\begin{aligned}
(a.) \displaystyle y = \frac{x - 6}{x + 6}
\end{aligned}
\end{equation}
$



$\boxed {\text{The given function is a rational function}}$



(b.) $\displaystyle y = x + \frac{x^2}{\sqrt{x - 1}} $



$\boxed {\text{The given function is an algebraic function}} $


(c.) $\displaystyle y = 10^x $



$\boxed {\text{The given function is an exponential function}} $



(d.) $\displaystyle y = x^{10}$

$\boxed {\text{The given function is a power function}} $



(e.) $\displaystyle y = 2t^6 + t^4 - \pi$


$\boxed {\text{The given function is a polynomial function with the degree of 6} }$


(f.) $\displaystyle y = \cos \theta + \sin \theta $



$\boxed {\text{The given function is a trigonometric function}} $

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 38

3/(x^4+x)
Let's factorize the denominator,
x^4+x=x(x^3+1)
=x(x+1)(x^2-x+1)
Let 3/(x^4+x)=A/x+B/(x+1)+(Cx+D)/(x^2-x+1)
3/(x^4+x)=(A(x+1)(x^2-x+1)+B(x)(x^2-x+1)+(Cx+D)(x)(x+1))/(x(x+1)(x^2-x+1))
3/(x^4+x)=(A(x^3-x^2+x+x^2-x+1)+B(x^3-x^2+x)+(Cx+D)(x^2+x))/(x(x+1)(x^2-x+1))
3/(x^4+x)=(A(x^3+1)+B(x^3-x^2+x)+Cx^3+Cx^2+Dx^2+Dx)/(x(x+1)(x^2-x+1))
3/(x^4+x)=(x^3(A+B+C)+x^2(-B+C+D)+x(B+D)+A)/(x(x+1)(x^2-x+1))
:.3=x^3(A+B+C)+x^2(-B+C+D)+x(B+D)+A
equating the coefficients of the like terms,
A+B+C=0 - equation 1
-B+C+D=0 - equation 2
B+D=0 - equation 3
A=3
Plug the value of A in equation 1,
3+B+C=0
B+C=-3
C=-3-B
Substitute the above expression of C in equation 2,
-B+(-3-B)+D=0
-B-3-B+D=0
-2B+D=3 - equation 4
Now solve equations 3 and 4 to get the solutions of B and D,
Subtract equation 3 from equation 4,
(-2B+D)-(B+D)=3-0
-3B=3
B=-1
Plug the value of B in equation 3,
-1+D=0
D=1
Plug the value of A and B in equation 1,
3+(-1)+C=0
2+C=0
C=-2
:.3/(x^4+x)=3/x-1/(x+1)+(-2x+1)/(x^2-x+1)

Are there any puns in stave 3 of A Christmas Carol?

Yes, here is an example of a pun in stave 3. While Scrooge is with the Ghost of Christmas Present, the ghost takes takes him to the home of his poor clerk, Bob, and his clerk's family, the Cratchits. The spirit smiles when they reach the house, and he sprinkles his special torch on the family's dwelling. Just then, the narrator says:

Think of that! Bob had but fifteen "Bob" a-week himself; he pocketed on Saturdays but fifteen copies of his Christian name; and yet the Ghost of Christmas Present blessed his four-roomed house!

Thus, the narrator (ironically) marvels that this lowly person who makes such a little amount of money is lucky enough to be blessed by the spirit. Bob is Mr. Cratchit's first name, but a bob is also another name for a shilling. So, we learn that Bob makes fifteen shillings a week. The sentence includes a pun made of these two words. A pun is a comedic device that exploits a word with two different meanings (like this one: Bob is a name and bob is another name for a shilling) or two words that sound similar and have very different meanings.

In "The Revolt of Mother," the mother takes over the new barn as her new house. She also stands up to the minister when he questions her about it. In these scenes, how does Freeman reveal Mother's character through destruction and figurative language?

Sarah Penn is a patient woman who has finally had enough. She has been waiting 40 years to move from her family's small farmhouse to a larger one. As she watches her husband build yet another barn, she decides enough is enough. When Adoniram leaves home to purchase a horse, Sarah takes his absence as a sign that she and her children should move into the new barn and make it a home.  Freeman describes this move as equal to "Wolfe's storming of the Heights of Abraham," an allusion to General James Wolfe's successful siege against the French army during the French and Indian War.  To compare Mrs. Penn to a general strategizing against her husband reveals the patience and tenacity of Mrs. Penn. While she admits that she had not written her bother, who was selling the horse, the opportunity presented itself to Mrs. Penn when her husband left town. As a good general would do, Mrs. Penn struck and struck quickly.
With Mrs. Penn's encounter with the Rev. Mr. Hersey, another allusion is used to reveal her devotion to her cause: a reference to the Pilgrims at Plymouth Rock:

“I think it's right jest as much as I think it was right for our forefathers to come over from the old country 'cause they didn't have what belonged to 'em,” said Mrs. Penn. She arose. The barn threshold might have been Plymouth Rock from her bearing.

Mrs. Penn's choice to move into the barn was one of urgency and justice, just like the Pilgrims' decision to move to the New World. She feels righteous, and this new side of Sarah frightens her husband. The end of the story shows Adoniram weeping, and the last simile of the story is used to circle back to the reference to war: "Adoniram was like a fortress whose walls had no active resistance, and went down the instant the right besieging tools were used."

Calculus: Early Transcendentals, Chapter 4, 4.1, Section 4.1, Problem 54

Given: f(x)=x/(x^2-x+1), [0,3].
Find the critical values by setting the first derivative equal to zero and solving for the x values. Find the derivative using the quotient rule.
f'(x)=[(x^2-x+1)(1)-x(2x-1)]/(x^2-x+1)^2=0
x^2-x+1-2x^2+x=0
-x^2+1=0
x^2=1
x=+-sqrt(1)
x=+-1
The critical values are x=1 and x=-1. Substitute the critical values and the endpoints of the interval [0, 3] in to the original f(x) function. Do NOT substitute in the x=-1 because it is not in the given interval [0, 3].
f(0)=0
f(1)=1
f(3)=3/7
Evaluate the f(x) values to determine the absolute maximum and absolute minimum.
The absolute maximum occurs at the coordinate (1, 1).
The absolute minimum occurs at the coordinate (0, 0).

What are some examples of antithesis in Martin Luther King Jr's "Letter from Birmingham Jail"?

Antithesis, literally meaning "opposite," is the juxtaposition of two contrasting ideas within a parallel grammatical structure. Indeed, literally, to use antithesis is to posit two theses (ideas) that seem to oppose each other: anti-theses. When used as a rhetorical device, antithesis employs similar grammatical structures to draw attention to, and thus amplify, the contrast between the two theses.
In King's letter, written during his incarceration in Birmingham Jail at the time of the 1963 Birmingham Campaign, antithesis is used to express King's key concern that there is one rule in America for whites, and another for blacks, with King's peaceful protest being met with harsh rebukes. Indeed, because King felt that treatment of blacks ran antithetical to that of whites, the rhetorical device suits his purpose well. For example: "freedom is never voluntarily given by the oppressor; it must be demanded by the oppressed." The antithesis here is very much marked, with "given" opposing "demanded," while "oppressor" counteracts "oppressed."
Another example in the same vein is "justice too long delayed is justice denied." The antithesis here serves to underline the hypocrisy inherent in the system: in King's view, to "delay" justice is no better than to deny it outright, as delaying justice is an injustice in itself.
We can also see some examples of extended parallelism in this letter, utilising anaphora (repetition of the same word or phrase at the beginning of several sentences or clauses within sentences) to amplify the antithetical effect. For example,

So I, along with several members of my staff, am here because I was invited here. I am here because I have organizational ties here.
But more basically, I am in Birmingham because injustice is here.

Here, the paragraph break serves as a caesura or dramatic pause, hugely amplifying the effect of the antithesis as it illuminates how the "basic" reason seems to contrast to the other, more mundane ones that precede it.

Antithesis is the opposition or contrast of ideas or words in parallel structure.  Parallelism occurs when structures within sentences or parts of a sentence take the same form.  Parallelism is a grammatical repetition.
One of King's most quoted lines is an example of antithesis: "Injustice anywhere is a threat to justice everywhere."  First, one must understand how this sentence is in parallel form.  If one were to break the sentence down to its parts of speech, it would follow this structure: noun, adverb, verb, adjective, noun, preposition, noun, adverb.  The two parts that are underlined show the two structures that are repeated, so one knows this is an example of parallelism.  Looking at those two parts in the sentence ("Injustice anywhere" and "justice everywhere"), one can see that the phrases are opposites of one another.
So what is the reason for antithesis?  King wants to show his audience (particularly the eight clergymen who sent him the letter to which he is responding) that his purpose in being in Birmingham is greater than Birmingham; it is about rooting out injustices across the country to protect and elevate justice for all.  It is not a Black or White issue; it is the country's issue.
Some other examples of antithesis (with the parallelism underlined):
"Whatever affects one directly, affects all indirectly." (para. 5)
"...the kind of tension in society that will help men rise from the dark depths of prejudice and racism to the majestic heights of understanding and brotherhood." (para. 10)
"We know through painful experience that freedom is never voluntarily given by the oppressor; it must be demanded by the oppressed." (para. 13)
"One has not only a legal but a moral responsibility to obey just laws. Conversely, one has a moral responsibility to disobey unjust laws." (para. 15)
"Any law that uplifts human personality is just. Any law that degrades human personality is unjust." (para. 16)
"An unjust law is a code that a numerical or power majority group compels a minority group to obey but does not make binding on itself. This is difference made legal. By the same token, a just law is a code that a majority compels a minority to follow and that it is willing to follow itself. This is sameness made legal." (para. 17)
"Lukewarm acceptance is much more bewildering than outright rejection."

Do you think someone born in 1750 would have found the Britain of 1500 more familiar than the Britain of 1900?

This assignment seems designed to encourage you to think about the effects of the Industrial Revolution. Thus your instructor is probably seeking an answer which emphasizes the increasing pace of technological and social change in the late eighteenth and nineteenth centuries.
Thus you could make the point that to a peasant farming the land, the main source of power in both 1500 and 1750 would have been human or animal, while steam power and other mechanical devices would have been increasingly common in 1900. The great manufacturing towns that arose in the Victorian era would have been unfamiliar in 1500 and 1750.  Another dramatic change was in transportation. In 1500 and 1750, transportation was by foot or animal, while in 1900, railways, steam powered boats, and cars existed. 
Religious diversity increased dramatically in the period after 1750. Women gained the right to own property and began to enter the work force in the late 19th century in ways that were unknown earlier.

Intermediate Algebra, Chapter 1, 1.4, Section 1.4, Problem 54

Complete the statement so that the indicated property is illustrated. Simplify the answer if possible.


$
\begin{equation}
\begin{aligned}

0(35t^2 - 8t + 12) =& \underline{0}
\qquad \text{(distributive property)}

\end{aligned}
\end{equation}
$

What series of events led the characters to resolve a problem, in chapter 4 of lightning theif

Chapter 4 of The Lightning Thief finds Percy in the car with his mother and his best friend, Grover, heading to what Percy believes is a summer camp and being chased by something that has both Grover and Percy’s mom incredibly scared.
There are two problems to examine in Chapter 4.  The first and more obvious is the fact that a mythological creature is chasing them down, wanting to kill Percy and probably everyone with him.  The second problem is that Percy is just now discovering that the mythical world he’d learned about in school is real. He is completely unprepared for the world he is about to be launched into.
How do they solve the problem of the Minotaur? The car goes into a ditch, possibly hit by lightning, and the three of them have to abandon it.  That’s when Percy realizes that the man after him is Not a Man.  Percy’s mom wants him to leave them and run to safety, but Percy refuses to leave them behind.  He gets her to help drag a nearly unconscious Grover out of the car. 
Percy learns from his mom that the creature has several weaknesses, much like a regular bull. Percy's mom gives him the plan: when the creature charges, wait until the last second then jump to the side. It works the first time, but now Percy is separated from the others.
The Minotaur charges again, this time at Percy’s mom. She tries the same trick as before, but the creature catches her in his massive hand. The shock and grief of seemingly watching his mother die right before his eyes gives Percy a rush of energy and strength.  He distracts the Minotaur from his friend on the ground by waving his red jacket and yelling, positioned in front of a massive pine tree. Instead of jumping to the side at the last minute, he jumps straight up and lands on the back of the creature’s neck while it brains itself on the tree.  During the ensuing struggle he manages to break off a horn, which gets him thrown off and bashed against a rock on the ground.  When the Minotaur charges again, Percy stabs it with its own horn and succeeds in killing it.  He watches as it turns to dust and blows away: more evidence that he’s in a whole new reality.
The problem of Percy’s lack of knowledge is far more central to the plot.  The events that led the supporting characters, Grover and his mom, to expose themselves to Percy actually happen in Chapter 3 when Percy is attacked and they make the decision to get Percy to camp.  By Chapter 4, Percy has discovered that his best friend is not human; he’s a satyr with goat legs. Grover admits that it was his job to “watch” Percy and that part of that job was to make sure Percy remained oblivious.  He inadvertently drops a comment that “You started to realize who you are,” which alerts Percy to the fact that he may be more than human.  Grover then further admits that Mrs. Dodds was real and that the old ladies at the fruit stand were actually the Fates.
Percy discovers that his mother knows all about the reality of mythological creatures and has been keeping this from him his whole life. His mom drops hints that the summer camp they are racing towards is not just an ordinary camp, but a place where he will be safe.  In the middle of the fight with the Minotaur, she reveals that she can’t go with them—she can’t cross the property line.  At the time, Percy doesn’t understand why that is.
All these hints and introductory “reveals” are not enough to make Percy aware of who he is and the nature of the world he belongs to, but Grover and Percy’s mom do provide a solid foundation to help prepare Percy for the revelations that will be coming in the subsequent chapters.

How do System 1 and System 2 contribute to the use of heuristics and cognitive bias?

The concept of "System 1" and "System 2" were created by Israeli-American Nobel Laureate and psychologist Daniel Kahneman, Ph.D. He uses "System 1" to refer to the emotional, intuitive part of our minds, while "System 2" refers to the analytical and controlled part of our minds. Kahneman believes that these different systems lead to our use of heuristics, or mental shortcuts, and cognitive biases because System 1 is what he refers to as a "storyteller" (see the APA Monitor article with an interview of Kahneman at the link below). That is, System 1 likes to make up a coherent story using the information readily available to it. This system, as it is highly intuitive, does not pause to realize the information that it has left out. Instead, it relies on the idea of what Kahneman calls "WYSIATI: What You See Is All There Is."
For example, we make snap judgments about others based on limited information, such as their appearance, without stopping to consider what we don't know. This is how we often practice bias. In addition, we might rely on heuristics such as "anchoring and adjustment" (see the list of heuristics below). In this heuristic, one assumes there is a given starting point from which one can operate. An example is a salesperson starting at a very high quote and going down from that quote, leading the buyer to believe he or she is getting a good deal when he or she isn't. In order to check System 1, we need to employ System 2, or our deliberate, analytical side, to ask what we are missing. We need to determine when we are not seeing the whole story and resist only relying on System 1, which is the more automatic and easier system to use.

Precalculus, Chapter 1, 1.3, Section 1.3, Problem 66

Determine the equation of the line that is perpendicular to the line $y = 2x-3$ containing the point $(1,-2)$. Express your answer using the general form or the slope intercept form of the equation of a line, which ever you prefer.

Since the two lines are perpendicular, the product of their slopes must be $-1$. We use the given equation to find the slope. The line $y = 2x-3$ has a slope $2$. So, any line perpendicular to this line will have slope $\displaystyle \frac{-1}{2}$. By using the point slope form to find the equation with point $(1,-2)$. We have,


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x- x_1)
&& \text{Point Slope Form}
\\
\\
y - (-2) =& \frac{-1}{2} (x-1)
&& \text{Substitute } m = \frac{-1}{2}, x = 1 \text{ and } y = -2
\\
\\
y =& \frac{-1}{2}x + \frac{1}{2} - 2
&& \text{Simplify}
\\
y =& \frac{-1}{2}x - \frac{3}{2}
&& \text{Slope Intercept Form}
\\
\\
\text{or} &
&&
\\
\\
\frac{1}{2}x + y =& \frac{-3}{2}
&& \text{General Form}

\end{aligned}
\end{equation}
$

What does Tom agree to with the devil?

When Tom Walker initially meets Old Scratch in the swamp, the devil tells him about Kidd's buried treasure and informs Tom that nobody will be able to discover the buried money, because it is under his protection. The devil then offers to place the money within Tom's reach under "certain conditions." While Irving never directly states the terms of their agreement, it is implied that the devil offers Tom the buried treasure in exchange for his soul. Tom does not initially accept the devil's offer and meets with him once again after his wife disappears. In their second meeting, Tom haggles with the devil about the terms of their agreement, because the devil insists that the buried treasure is used to advance his evil agenda. Initially, the devil wants Tom to be a slave trader, but Tom refuses. Tom finally agrees to be a usurer and ends up taking advantage of people with financial difficulties by foreclosing on their mortgages. Tom also agrees to sell his soul to the devil to become wealthy. Tom and Old Scratch strike a deal and Tom lives his life as a wealthy, callous man until the devil visits him to take his soul.

In "The Devil and Tom Walker," Tom is desperate to have possession of the hidden treasure and is prepared to make a deal with the Devil in order to get it. Firstly, the Devil offers Tom the treasure in return for his soul, but Tom categorically refuses.
Later in the story, however, the pair do come to agreeable terms. The Devil will give Tom the treasure so long as Tom uses the money to make the Devil a profit. The Devil asks Tom to become a slave trader, but Tom has no desire to join this profession. Instead, Tom suggests that he will become a usurer (a moneylender), an occupation to which the Devil agrees.
After the bargain is struck, Tom sets up his moneylending business in Boston. He is so successful in this business that it does not take long for him to become extremely wealthy and completely driven by financial gain.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 25

Differentiate $\displaystyle F(y) = \left( \frac{1}{y^2} - \frac{3}{y^4} \right)(y + 5y^3)$



$
\begin{equation}
\begin{aligned}

F(y) =& \left( \frac{1}{y^2} - \frac{3}{y^4} \right)(y + 5y^3)
&& \text{Expand the equation}
\\
\\
F(y) =& \left( \frac{y}{y^2} - \frac{3y}{y^4} + \frac{5y^3}{y^2} - \frac{15y^3}{y^4} \right)
&& \text{Reduce to lowest term}
\\
\\
F(y) =& \frac{1}{y} - \frac{3}{y^3} + 5y - \frac{15}{y} = y^{-1} - 3y^{-3} + 5y - 15y^{-1}
&& \text{Combine like terms}
\\
\\
F(y) =& -3y^{-3} + 5y - 14y^{-1}
&& \text{Apply Power Rule}
\\
\\
F'(y) =& -3 \frac{d}{dy} (y^{-3}) + 5 \frac{d}{dy} (y) - 14 \frac{d}{dy} (y^{-1})
&&
\\
\\
F'(y) =& (-3)(-3y^{-4}) + (5)(1) - (14)(-y^{-2})
&& \text{Simplify the equation}
\\
\\
F'(y) =& 9y^{-4} + 5 + 14 y^{-2}
&&



\end{aligned}
\end{equation}
$

What is the motif of the animals throughout the novel, and how is it being used throughout the story? What theory is the author intending to show with this motif?

The central motif of We The Animals is the depiction of children as animals. A secondary motif broadens the original one to include all humans in the story. In this particular "animal farm," some animals are also more equal than others—or, at the very least, they think they are. Adult onlookers describe the children as "dogs" and "locusts," but they are really no better. In fact, if anything, the kids are more human than the adults, filled as they are with normal human foibles, desires, and insecurities.
However, the point of view is important here. We are given a child's view of the world, one in which it is the adults who seem like strange, exotic creatures:

Her mascara was all smudged and her hair was stiff and thick, curling black around her face and matted down in the back. She looked like a raccoon caught digging in the trash: surprised, dangerous.

The brothers are practically feral children. They frequently live down to the low expectations set for them by society. They fight, they get into scrapes, and they flip off their neighbors. However, at the same time, they are trying—in their own imperfect way—to find a place in the world and to forge their own identities without parental guidance in an environment hostile to mixed-race relationships. By getting in touch with their raw animality, the boys are also simultaneously discovering what it means to be human. These kids may be wild, but they are still kids. Unlike the adults in the story, this particular species of animal evolves.
The narrator's developing sexuality is also related to the animal motif. Over time, he comes to realize that he is gay. Along with his mixed-race heritage, this adds to his outsider status. In a harsh, brutally unforgiving environment, he is now doubly "other," not just estranged from the world around him, but also from his brothers. Their violent homophobia confirms that there is a distinct hierarchy in this "animal kingdom." If you are gay, like the narrator, then you are not just inhuman, you occupy the lowest ladder on the evolutionary scale.
The animal motif allows Torres to get to the truth with pinpoint accuracy. He does not preach; he does not judge; he is not making grand, sweeping statements about the human condition. What he does do, however, is describe what happens with unerring detail. This is what we would expect if we were reading an animal fable. The harshness of nature needs to be laid bare by keen observation of what unfolds before our eyes. In We The Animals, that is precisely what Torres does.

In what ways does Troy resemble the antihero? In what ways does he resemble the tragic hero?

An antihero is a protagonist of a work who does not possess traditional heroic qualities. Troy Maxson, the self-aggrandizing protagonist of August Wilson's play Fences, can be viewed as an antihero due to his many character flaws. At the start of the play, Troy is 53 years old and what one might consider "all washed up." He was a star in the Negro Baseball League but his glory days have long since passed. Troy lives in the past, spinning tall tales of his own former "heroics," and refusing to see any reality other than the one he himself inhabits. He butts heads with both of his sons, one who wants to be a musician and the other who wants to play football, and his quick temper and stubborn refusal to be swayed in their father-child conflicts, combined with his tendency towards hyperbole (if not outright lies) are all excellent examples of traits Troy exhibits that would never be exhibited by a traditional hero. Over the course of the play, Troy cheats on his wife, the extremely sympathetic Rose, alienates both of his sons, and, through his ignorance, confines his brother to an asylum.
All that said, there are many ways in which Troy is sympathetic. Perhaps if the audience had met him in his heyday, during the height of his baseball career, he would have appeared to be a true hero, as opposed to the antihero or tragic hero he is now that he's past his prime. He's the patriarch and the breadwinner in his family, and, though perhaps its old-fashioned, he believes that, as such, he deserves respect. Though this belief sometimes translates into him behaving like a tyrant, it is also understandable in the context of the time. Troy is also consistently portrayed as a good brother to Gabriel before signing the papers to commit him because he is too proud to admit that he doesn't know how to read.
Outside of his family life, in his professional one, many of Troy's actions could actually be seen as heroic. Troy successfully campaigns to become the first black garbage truck driver in the city, calling out a racist system and getting it abolished. His words and actions are often hypocritical, his worst moments balanced out by his brighter ones.
Given Troy's many sympathetic, even heroic, traits, the appellation of tragic hero better applies to the character than antihero does. A tragic hero, in the classical sense, is one who, through a specific personality defect/error in judgement, brings about his own downfall. Troy's fatal flaw is his pride, which, given how deep it runs, may even be called hubris. It is this pride that leads to his brother's commitment to the asylum. It is this pride that prevents Troy from seeing eye-to-eye with his sons, who, in their differences of opinion from their father, represent changing times and voices of a younger generation.
The main thing distinguishing a tragic hero from an antihero is while an antihero can descend into total amorality, a tragic hero always believes himself to be right and acts according to a set of moral principles that just may turn out to not be the right ones. Each of Troy's actions throughout the play is motivated by his belief that he knows what's best. And it's this exact belief that, in true tragic hero style, is his ultimate demise.

Explain Baudrillard's theories of advertisement and simulation.

Baudrillard's simulation argument focuses on the role of maps and models in our lives and how these have become paramount to our perceptions of reality. Basically, Baudrillard is saying that we have come to rely on models so much that these have become reality and precede the natural world. We can posit several different examples of this, but video games are probably the easiest to understand.
If you look at a game such as Grand Theft Auto, Baudrillard would say that people are totally engrossed with everything going on in the game to the exclusion of anything else. They come to believe that the actions by characters controlled by other online players are as real as if they actually happened. It is as though the simulation of real life has replaced real life experiences.
In terms of advertising, Baudrillard argues that the media manipulates individuals' desires according to the media's objectives (selling products and making money). Advertisements are thus a means by which corporations shape individuals' wants and demands; individuals do not determine what corporations make through free exchange on the open market. Baudrillard is therefore saying that the open market is not open because individuals are not choosing what to buy, but they are buying what media and corporations have convinced them to buy.
There are a lot of criticisms of Baudrillard's work, as with postmodernism generally—perhaps the most crucial being his subjective interpretations that are posited as fact. Postmodernism rejects objectivity and the scientific method (although they still use words such as "theory"). And similar to many other postmodernists, Baudrillard's work has been highly criticized for being purposefully obscure. He makes interesting points, but it also seems as though these points are intentionally placed in a fog of academic jargon in order to give them greater validity.
https://plato.stanford.edu/entries/baudrillard/

How could I write an essay about The Song of the Lark?

There are different critical essays you could write on The Song of the Lark. One theme running throughout the book is the sacrifices that Thea makes for her art (which turns out to be singing). She must, over time, repudiate the demands of her family and upbringing to become a truly great artist.
Even while living in Moonstone (in Colorado), she shows independence of spirit by befriending people like Professor Wunsch and Spanish Johnny, who are both culturally and morally at odds with people in the town. Later, when Thea dedicates herself to singing, she leaves Moonstone and cannot return even to attend her mother's funeral. As an opera singer, she dedicates herself fully to her career and does not have time at the height of her career for a family. The novel speaks about what it means to be an artist, and Cather suggests that artists are freethinkers who are willing to separate themselves from what they know and the life they are born into. One of the themes you could write about, then, is the life of an artist. 
You could also focus on the mentors who help Thea become a great artist, including Dr. Archie and Frederick Ottenburg. What is Cather suggesting about an artist's need for understanding and mentorship to develop his or her art? These two men are critical to Thea, and their support is vital in helping her flourish. 

Calculus and Its Applications, Chapter 1, 1.7, Section 1.7, Problem 48

Determine $\displaystyle \frac{dy}{du}, \frac{du}{dx}$ and $\displaystyle \frac{dy}{dx}$ if $\displaystyle y = \frac{u+1}{u-1}$ and $u = 1 + \sqrt{x}$.

We first find $\displaystyle \frac{dy}{du}$ and $\displaystyle \frac{du}{dx}$.



$
\begin{equation}
\begin{aligned}

\frac{dy}{du} =& \frac{\displaystyle (u-1) \cdot \frac{d}{du} (u+1) - (u+1) \cdot
\frac{d}{du} (u-1)}{(u-1)^2} \qquad \text{ and } &&& \frac{du}{dx} =& \frac
{d}{dx} (1) + \frac{d}{dx} (x)^{\frac{1}{2}}
\\
\\
=& \frac{(u-1) (1) - (u + 1)(1)}{(u - 1)^2} &&& =& 0 + \frac{1}{2} (x)^{\frac{-1}{2}}
\\
\\
=& \frac{u-1-u-1}{(u-1)^2} &&& =& \frac{1}{2 \sqrt{x}}
\\
\\
=& \frac{-2}{(u-1)^2}

\end{aligned}
\end{equation}
$


Then,


$
\begin{equation}
\begin{aligned}

\frac{dy}{dx} =& \frac{dy}{du} \cdot \frac{du}{dx}
\\
\\
=& \frac{-2}{(u-1)^2} \cdot \frac{1}{2 \sqrt{x}}
\\
\\
=& \frac{-2}{2(u - 1)^2 \sqrt{x}}
\\
\\
=& \frac{-1}{(1 + \sqrt{x} - 1)^2 \sqrt{x}}
\qquad \text{Substitute $1 + \sqrt{x}$ for $u$}
\\
\\
=& \frac{-1}{(\sqrt{x})^2 \sqrt{x}}
\\
\\
=& \frac{-1}{x \sqrt{x}}

\end{aligned}
\end{equation}
$

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 9

You need to evaluate the limit, hence, you need to replace 0 for x in expression under the limit, such that:
lim_(x->0) (e^(4x) - 1 - 4x)/(x^2) = (e^0 - 1 - 0)/(0) = (1-1)/0 = 0/0
Hence, since the result is indeterminate 0/0 , you may use l'Hospital's theorem, such that:
lim_(x->0) (e^(4x) - 1 - 4x)/(x^2) = lim_(x->0) ((e^(4x) - 1 - 4x)')/((x^2)')
lim_(x->0) ((e^(4x) - 1 - 4x)')/((x^2)') = lim_(x->0) (4e^(4x) - 4)/(2x)
Replacing 0 for x yields:
lim_(x->0) (4e^(4x) - 4)/(2x) = (4e^0 - 4)/(2*0) = (4-4)/0 = 0/0
Hence, since the result is indeterminate 0/0, you may use again l'Hospital's theorem, such that:
lim_(x->0) (4e^(4x) - 4)/(2x) = lim_(x->0) ((4e^(4x) - 4)')/((2x)')
lim_(x->0) ((4e^(4x) - 4)')/((2x)') = lim_(x->0) (16e^(4x))/2
Replacing 0 for x yields:
lim_(x->0) (16e^(4x))/2 = (16e^0))/2 = 16/2 = 8
Hence, evaluating the given limit yields lim_(x->0) (e^(4x) - 1 - 4x)/(x^2) = 8.

Miranda's appeal lies in her sweet innocence, gentle nature, and pure, unselfish love for Ferdinand. Referring closely to the text, bring out the truth of this statement.

When Ferdinand first sees Miranda in act 1, scene 2, of Shakespeare's The Tempest, he mistakes her for a goddess of the isle on which he has been shipwrecked. He is shocked to see another living soul on what he had taken for a deserted island and delighted that they speak the same language. Almost immediately, he casts off thoughts of his drowned father in order to ask if Miranda is a maid. Ferdinand's infatuation at first sight could be due partly to shock, but in this introductory scene there is also a hint that he admires the qualities listed in your question. Ferdinand is a prince and accustomed to court and courtly ladies. He mistakes Miranda for a goddess not because she is so glamorous—she isn't—but because he's never seen a woman so earthy, natural, and free.
The best textual examples of Ferdinand's love for Miranda being based on her innocence, gentle nature, and unselfishness can be found in their next scene together, act 3, scene 1. In Ferdinand's speech that opens the scene, he calls Miranda "gentle creature." In the courting scene that follows between the two of them, Miranda's actions repeatedly betray the fact that she is ignorant of the ways of the world and the rules of courtly love, while Ferdinand grows more and more charmed by her and exclaims about her perfection. This is the scene to look at when harvesting your quotes for this assignment.

How does Doyle build tension in Chapter Ten of The Sign of Four?

Doyle effectively builds tension in chapter 10 by creating a sense of anticipation in the reader. In this chapter, we anticipate that Holmes and Watson are finally going to catch Jonathan Small, the key to the mystery of the secret treasure. The sense of anticipation lends tension to the chapter. We wonder if our heroes will be successful in their efforts to capture Small.
Doyle begins building the tension at the beginning of the chapter. After their meal, Holmes asks Watson if he has his service revolver handy. When Watson replies in the affirmative, Holmes tells him to take it with him. He tells Watson that they must be prepared for what lies ahead. At this point, we don't know what lies ahead of this excursion into dangerous waters.
When they are safely settled in their police boat, Holmes tells Watson that their craft is a fast one. It even manages to overtake a river steamer. Holmes then mentions that the Aurora (the boat they are after) has a reputation for swiftness. So, at this point, we anticipate an eventful boat ride on the waters. Essentially, Holmes and Watson may be in for a difficult time, and we don't yet know how it will end. To add to the tension, Holmes has elected not to have police backup for their mission.
Jones, the detective, voices what all of us feel at this point:

You have planned it all very neatly, whether they are the right men or not . . . but if the affair were in my hands I should have had a body of police in Jacobson's Yard, and arrested them when they came down.

Soon, Holmes spots the Aurora, and he orders Jones to give chase. Here, Doyle adds to the tension by having Holmes speak in short exclamatory sentences:

"We MUST catch her!" cried Holmes, between his teeth. "Heap it on, stokers! Make her do all she can! If we burn the boat we must have them!"
"Pile it on, men, pile it on!" cried Holmes

Of course, the chapter ends with the capture of Jonathan Small. Doyle certainly uses every tool at his disposal to build tension in the chapter. As the chapter comes to a close, we are led to wonder whether Jonathan Small will tell the entire truth about the treasure. So, the chapter ends on an eventful, tense note.

Ah, I think modern readers must find this chapter especially exciting! Are you familiar with the trope of a car chase in films, where the "good guys" must rush to catch up with the "bad guys?" Chapter Ten has very much the same content, except Mr. Holmes and Dr. Watson are chasing down their bad guys in a boat!
Doyle opens the chapter with Holmes and Watson enjoying a meal before they must do their work for the evening. They and their police fellow, Jones, set off to the wharf. Here, they get into a police boat that has been disguised by removing its identifying green lamp. Already, we can sense the seriousness of what is about to occur. 
En route to their destination, Holmes explains why they are headed there. He knows that the man they are after uses a nearby dock, and Holmes has guessed that it is most likely Jacobson's Yard. Holmes also explains that the man they are looking for has acquired a boat from a local drunkard. While they are waiting in the dark just near the docks of Jacobson's Yard, the very boat they are waiting for zips behind them! 
The Aurora is fast, but so is the police boat Holmes and Watson are in! On both boats, men are furiously shoveling coal into the steam-engines. As the police boat closes in on the Aurora, Dr. Watson fires at one of the men they are chasing and he falls overboard. Holmes, Watson, and their police fellows are able to rope the boats together and board the Aurora. 
The sense of excitement and tension drawn from two well-matched means of transport is certainly nothing new, and it was just as powerful to Doyle's readers in 1890 as it is to us watching a car chase today!

What is a feminist criticism of the story "The Lady with the Dog" by Anton Chekhov? Explain how and why the feminist mode of criticism could help talk and write about this story. What issues in the story are women's (feminist) issues?

In Anton Chekhov’s short story “The Lady with the Dog,” the main character, Dmitri Dmitritch Gurov, has an ambivalent relationship with women. Even though he thinks that women are inferior to men, he still prefers to be in their company. About his own wife, Gurov resents the fact that she has aged, and he is threatened by her intellectual pursuits. His attraction to Anna Sergeyevna seems predicated on her youth and “diffidence.” When he returns to Moscow without her, Gurov imagines Anna as “lovelier, younger, tenderer than she was.” Gurov is not threatened by Anna, and it is clear that he has felt threatened by some of the women in his past, whom he describes as “very beautiful, cold women, on whose faces he had caught a glimpse of a rapacious expression, ­an obstinate desire to snatch from life more than it could give, and these were capricious, unreflecting, domineering, unintelligent women not in their first youth.” Once Gurov “grew cold to them, their beauty excited his hatred.” Gurov feels victimized by the pull women hold over him, and he doesn’t seem capable of true empathy with those who belong to what he calls “the lower race.” When Gurov and Anna begin their adulterous affair, Anna is certain that Gurov will despise her, but his morality is never questioned.

How has Edward's experience as a pauper influenced him in The Prince and the Pauper?

Edward, Prince of Wales and son of King Henry VIII, exchanges clothes with Tom Canty, a poor beggar boy who looks very much like him. In his ragged clothes, Edward is mistaken for a beggar and thrown out of the palace.
As he wanders the streets, hungry and forlorn, he learns how rough life is for the poor. Nobody puts on a show for him because nobody knows he is a prince. Nobody feels compelled to show him kindness. He is exposed to a gang of thieves and to living in a hut. He learns to appreciate getting something to eat. He comes to understand what is like when nobody will believe what you say and when people treat you as if you are crazy--or when you are at the mercy of a truly crazy person who wants to kill you.
After he regains his rightful position, now as King of England after his father dies, Edward rights some of the wrongs the poor suffer. He can no longer dismiss their plight, having experienced it firsthand.

“What dost thou know of suffering and oppression? I and my people know, but not thou.”

The statement by King Edward VI summarized his experience as a pauper, and how the incident influenced him. After he was thrown out of the royal court, Edward ended up mingling with some local boys. The boys made fun of him, and he was determined to improve their lives by getting them an education when he ascended the throne. Edward also met with other individuals who had suffered great ills at the hands of their tormentors, and he planned to make things right. Edward got an opportunity to live among his people and understand their challenges and suffering. He was made aware of issues and circumstances that would otherwise be hidden from him given his status and the protection of the royal court. His exposure to the reality of the lives of his people helped him develop care and compassion towards his subjects, which made him an agreeable king.
https://www.owleyes.org/text/prince-pauper/read/dedication

Why was Mrs. Mary Maloney to be divorced by her husband in "Lamb to the Slaughter" by Roald Dahl?

A careful examination of the text shows readers that Patrick or Mary never says the word "divorce." We can't be 100% sure that Patrick wants a divorce:

"This is going to be a bit of a shock to you, I’m afraid," he said. "But I’ve thought about it a good deal and I’ve decided the only thing to do is tell you right away. I hope you won’t blame me too much."
And he told her. It didn’t take long, four or five minutes at most, and she sat very still through it all, watching him with a kind of dazed horror as he went further and further away from her with each word.
"So there it is," he added. "And I know it’s kind of a bad time to be telling you, but there simply wasn’t any other way. Of course I’ll give you money and see you’re looked after. But there needn’t really be any fuss. I hope not anyway. It wouldn’t be very good for my job."

It is conceivably possible that he wants to separate from Mary and live separate lives but not tell anybody and not have a legal document attached to his name that says he is divorced. This arrangement could be why he says the line about "it" not being good for his job. Perhaps a divorce would reflect badly on him and his work situation.
Regardless of what Patrick wants, it is clear that the marriage is over. Unfortunately, readers never learn what Patrick's motive is. That's okay because it's not the point of the story. Mary's transformation from hearing his terrible announcement is way more important to the story. Additionally, Dahl has created an interesting discussion topic by not telling readers why Patrick does what he does. Perhaps he has found another woman. Perhaps the thought of being a father is too much for him to handle. Perhaps Mary is too much the doting wife, and he feels stifled at home.

In "Lamb to the Slaughter," Dahl does not reveal to the reader Patrick's reason for wanting to divorce his wife, Mary. Instead, the reader experiences this moment from Mary's perspective. As we might expect, such a shocking announcement happens in a blur for Mary: she is unable to grasp the details because his announcement is so unexpected. This is shown through Dahl's description of Mary's reaction:

She sat still through it all, watching him with puzzled horror.

In contrast, Patrick is relatively calm and collected: he responds to her in a very matter-of-fact way by emphasising the practical matters of the divorce, like the financial settlement. Ironically, he thinks that the worst is over because he has broken the news to Mary, not realising that his murder, the worst possible outcome, is about to take place.

Why did Theodore Taylor dedicate The Cay to Dr. Martin Luther King, Jr.?

While a central conflict of The Cay is a man vs. nature struggle for survival, the book also has an emphasis on racial conflicts.  Phillip has been raised to believe that his white skin makes him superior to people of different colors.  Throughout the book, Phillip learns that his parents are wrong.  He learns that Timothy is absolutely not an inferior human being.  Phillip learns that Timothy is an equal.  Phillip's blindness is most definitely a literal plot device, but it is also a metaphorical device too.  Phillip becomes blind to Timothy's skin color.  It simply doesn't matter, and the two characters are able to sit down with each other in mutual respect.  
Dr. King's "I Have a Dream" speech displays the same kind of vision for race relations.  

"I have a dream that one day on the red hills of Georgia, sons of former slaves and the sons of former slaveowners will be able to sit down together at the table of brotherhood."

The Cay, through the characters of Phillip and Timothy, echoes Dr. King's speech.  That is why I think Taylor dedicated it to Dr. King.  

What was the question of religious principle that gave rise to the war between Lilliput and Blefuscu?

In the novel Gulliver's Travels, Gulliver lands on the island of miniaturized people Lilliput, and finds them very trivial in nature. They are constantly at odds with their neighboring island, Blefuscu, and they end up engaging in war. They ask the giant Gulliver to help them conquer and enslave Blefuscu but he refuses, resulting in his eventual departure.
The reasoning behind this war was one of "religious principle" as a certain religious debate had come up between the two that was irreparable. This debate was which end of an egg to crack when cooking it—the big end or the small end. The Blefuscuns were "Big Endians" and this angered the Lilliputians to no end.
The resulting war was used to satirize the petty squabbles and drama that would cause countries such as England, France, and Portugal to engage in war.

The cause of the seemingly never-ending conflict between Lilliput and Blefuscu is almost breathtaking in its triviality. The whole thing started over a dispute about the correct end at which to break an egg. The Lilliputians believe that an egg should be broken from the small end. The Blefuscans, however, are so-called "Big Endians," believing with equal conviction that the big end of the egg is the correct place at which to break it.
Gulliver's Travels is a work of satire, and in the pointless, drawn-out conflict between Lilliput and Blefuscu, Swift is poking fun at the ridiculous reasons that countries often give for going to war with each other. During Swift's lifetime, conflicts of one kind or another frequently broke out in Europe. And though the causes of such conflicts were never quite as trivial or absurd as the great egg controversy, Swift nonetheless suggests that the regular wars plaguing Europe in the early 18th century were still wholly unnecessary.

How is poverty a cycle for Junior's family?

The Absolutely True Diary of a Part Time Indian is fiction. But it’s based, at least in part, on the real-life experiences of the author, Sherman Alexie. Alexie came of age on the Spokane Indian Reservation and identifies as Spokane-Couer d’Alene; in the novel, his protagonist, fourteen-year-old Arnold Spirit Jr (a.k.a. Junior) lives on the same reservation in the state of Washington. The book deals with poverty, violence, and alcoholism, particularly as it relates to the indigenous community that’s central to the narrative.
Poverty is a cycle across cultures, but in Junior’s case, the family’s poverty is tied to larger issues on the reservation. In real life, both of the author’s parents were alcoholics, which made it difficult to hold down steady jobs. The same is true of Junior’s parents in the novel, though his mother is in recovery from her addiction. Alexie has spoken and written extensively on the subject of alcohol abuse in Native American communities and the ways in which it prevents individuals and families from making upward progress.
Another factor that perpetuates poverty in Junior’s world is lack of access to educational and professional opportunities. Junior has talent; he’s an aspiring cartoonist. But most of the kids living on the reservation don’t have the resources to develop their talents. Junior, at least, is an exception to that rule: one of his teachers notices his abilities and encourages him to enroll in a school off the reservation. Junior’s experiences as the only indigenous student at an all-white high school—the challenges he faces there, as well as the new opportunities he finds—form the basis of the novel.

What are the 5 themes of geography?

The five themes are geography are:

Location—our position on Earth, both relative and absolute. Think of the US—it has an absolute position on earth that can be located and pinpointed on a map and with coordinates (this is where latitude and longitude factor in to the conversation). It also has a relative location in terms of economy, society, politics, and so on. The United States's capacity for producing oil is relative to where the oil exists.

Place—these are the physical and human characteristics that help define a location. How the physical and human relate to and impact one another is a key study in geography. Questions about place could include things like "what are the physical attributes of the Amazon rainforest" as well as "which peoples live in the Andes Mountains."

Human-Environment Interaction—this concerns the impact humans have had on the environment. For example: how have irrigation efforts in the American Southwest impacted the environment?

Movement—Continuing with our "human" theme, how have people and goods moved across the environment? Walking? Boat? Car? Airplane? Electronically? And how has this movement impacted the way humans live and interact with the environment, both absolute and relative?

Region—how do regions form and change? The fertile crescent is a band of earth (in a crescent shape) from the Eastern Mediterranean across to the Tigris and Euphrates Rivers in modern-day Iraq and Iran. How did this form? How does it change with human interactions? How do boundaries change over time with political changes? What is the location and place of the fertile crescent? And so on . . . How about the Northeast? It is not a formal region with delineated borders or boundaries, and yet it is considered a "region" of the United States.

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 54

Determine $y'$ if $x^y = y^x$

$
\begin{equation}
\begin{aligned}
\ln x^y &= \ln y^x\\
\\
y \ln x &= x \ln y\\
\\
\frac{d}{dx}(y \ln x) &= \frac{d}{dx} ( x \ln y)\\
\\
(y) \frac{d}{dx} (\ln x) + (\ln x) \frac{d}{dx} (y) &= x \frac{d}{dx} (\ln y) + (\ln y) \frac{d}{dx} (x)\\
\\
y \cdot \frac{1}{x} + \ln x \frac{dy}{dx} &= x \cdot \frac{1}{y} \frac{dy}{dx} + \ln y (1)\\
\\
\frac{y}{x} + y' \ln x &= \frac{x}{y} y' + \ln y\\
\\
y' \ln x - \frac{x}{y} y' &= \ln y - \frac{y}{x}\\
\\
y' \left( \ln x - \frac{x}{y} \right) &= \ln y - \frac{y}{x}\\
\\
y' &= \frac{\ln y - \frac{y}{x}}{\ln x - \frac{x}{y}}
\end{aligned}
\end{equation}
$

What main changes does Paul Fisher go through?

In Edward Bloor's novel Tangerine, Paul Fisher is the main character and narrator. He is also a dynamic character. The main change he goes through is finding his identity in the shadow of his older brother, Erik. He also finds the courage to confront Erik at the end of the novel, which no one else in his life has been able to do.
Paul is dealing with a move from Houston, Texas to Florida. He has a pragmatic mother and a nearly absent father. His father focuses most of his energy on his dreams of football glory for his oldest son, Erik. Paul also has a disability, he is vision impaired, and has fuzzy memories of the accident that caused this.
Paul has confidence in his abilities in soccer but gets kicked off the team at Lake Windsor Middle School because he is on an IEP, or individualized education plan, and the school can't insure him as a player. Due to a sinkhole which destroys most of the portable classrooms at Lake Windsor Middle, Paul is able to transfer to Tangerine Middle School. He convinces his mother to not transfer the IEP so he can play soccer. Through this experience, he learns a lot about being a team player and a good friend. He gains confidence as well as friends. His changes run parallel to his older brother Erik, a static character, who continues the same pattern of self-promotion and self-absorption he has maintained all his life.
Paul sees the injustice that his brother Erik is responsible for in the death of his friend's relative, Luis. He also sees Erik lie and manipulate the situation so that he won't face consequences. At the same time, fragments of memories of the accident that damaged his eyesight come to him. He eventually puts the pieces together and discovers that Erik's cruelty is responsible for his vision impairment as well as Luis's death. He confronts his parents and Erik, and as a result, justice is finally served. At the beginning of the novel, Paul lives in the wake of Erik's shadow. He feels inferior to Erik, and as a result, he struggles to find his worth. At Tangerine Middle School, he finds a group of friends who help him grow in confidence. He also grows in self-worth, realizing he has many valuable things to contribute, both on and off the field. Even though he goes through many struggles in the book, he realizes that those struggles have made him stronger. In contrast, no one ever allowed Erik to go through struggles, and it made him into a cruel and careless individual. Paul accepts the consequences to his actions but also gains the perspective that it is not the end of the world, but only a temporary, light affliction.

Paul Fisher goes through a variety of changes. He is a dynamic character who grows and develops throughout the book.
At the beginning of Tangerine, Paul was  a weak pushover who allows his brother to mercilessly bully him. He had low self-esteem due to Erik’s relentless taunting. However, at the end of Tangerine, he became an empowered and decisive young man with the power to  stand up for himself and his friends. These changes were primarily motivated by his move to Tangerine Middle School and his growing understanding of Erik's cruelty. 
 First of all, Paul's family moved to Tangerine from Houston. This major change should have allowed  Paul to begin anew, but his hopes for a self-reinvention were dashed by his parents’ focus on Erik’s burgeoning superstardom on the football team. It was a negative change, given that Tangerine held new dangers (muck fires and sink holes) and the same old problems as Houston; for example, Erik quickly got up to his old tricks and found new lackeys to torment Paul. Consequently, the first major change to positively impact Paul was his move to Tangerine Middle School, where he was able to make new friends, experience success on the soccer team, and gain the necessary confidence to confront Erik.
When Paul saw  Erik’s lackey, Arthur Bauer, demean his new Tangerine friends and fatally injure Luis Cruz, Paul underwent  a change of heart. He found himself no longer able to stomach Erik’s cruelty, and he joined his friends by attacking Erik and the football team at an awards ceremony. He also regained his memory of how he lost his sight back in Houston (Erik and one of his friends spray-painted his eyes.) Consequently, Paul gained both knowledge and power. 

What is the difference between market failure and government failure?

A government failure and a market failure can be roughly compared to a person drowning and to a lifeguard who drowns trying to save that person.
Market failures can occur for many reasons, including inefficient delivery of goods, lack of supply to meet demand, drastic overpricing or underpricing, or overinvestment in aspects of business that fail to produce results. Market failures are typically the fault of businesses because of improper long-term planning or poor customer research.
By contrast, a government failure is an attempt to solve a market failure that obviously does not succeed. For example, the US government bailed out the automobile industry during the Great Recession: while this was not a failure, it could have been if the government intervention was not strong enough, if it was directed toward the improper channel, or if the government put in subsidies to keep businesses alive at the cost of efficiency.
Government failures are less common in market economies than they are in planned economies, where the state decides the output of industries. Even so, they are not uncommon in market economies like that of the United States. It has been argued that subsidies to boost the coal mining industry are government failures, since the cost of coal is higher than some other energy sources like oil and gas: the government is thus promoting inefficiency by funneling resources to coal.

Government failures cannot occur unless market failures have already happened. When the government involves itself in the economy in order to try and rectify an existing market failure, this can sometimes resolve the failure, or it can generate further inefficiency, such that the market failure is not resolved. In this situation, a government failure is said to have occurred. This may be because the government has altered prices, which has led to a lack of competition or to shortages or monopolies, or because the government has allocated too much budget to a failing company in subsidies, meaning that other companies are unable to compete, leading to antitrust issues.
A market failure is what happens when the balance between supply and demand is disrupted. This can be because one firm has developed a monopoly over an entire market, because resources have been incorrectly allocated and there are shortages, or because poor decision-making has resulted in excessive costs being passed on to the consumer (unfair price rises relating to manufacturing decisions or shortages).
https://www.economicsonline.co.uk/Market_failures/Government_failure.html

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 50

Use the Intermediate Value Theorem to show that $\tan x = 2x$ has root on the interval $(0.5, 1.4)$

Let $f(x) = \tan x - 2x$
Based from the definition of Intermediate Value Theorem,
There exist a solution c for the function between the interval $(a,b)$ suppose that the function is continuous on that
given interval. So, there exist a number $c$ between 0.5 and 1.4 such that $f(x) = 0$ and that is, $f(c) = 0 $.


$
\begin{equation}
\begin{aligned}

f(0.5) & = \tan(0.5) - 2(0.5) = -0.4537\\
f(1.4) & = \tan(1.4) - 2(1.4) = 2.9978

\end{aligned}
\end{equation}
$


By using Intermediate Value Theorem. We prove that...


So,
$
\begin{equation}
\begin{aligned}
& \text{ if } 0.5 < c < 1.4 \quad \text{ then } \quad f(0.5) < f(c) < f(1)\\
& \text{ if } 0.5 < c < 1.4 \quad \text{ then } \quad -0.4537 < 0 < 2.9978

\end{aligned}
\end{equation}
$

Therefore,

There exist a such solution $c$ for $\tan x -2x =0 $

Why does more than one story arc make a novel interesting?

Novels (as with any art form) are successful when they speak to the real lived experiences of readers. If you think about the life of even the most ordinary person, it is connected with other lives; stories branch out into other places and connect with unknown people. This connectivity means that we are all familiar with the relationship between different stories, and how to use one to understand another. As we experience this in life, so too do we desire it in literature. Multiple story arcs not only give us a greater volume of material to appreciate, but also resonate with the patterns of our own lives, the many overlapping and undulating stories within.
There are innumerable instructive quotes on the joys and benefits of reading books. One particular quote, however, offers some explanation as to why multiple narratives within a work are particularly enjoyable:
“A great book should leave you with many experiences, and slightly exhausted at the end. You live several lives while reading.”
- William Styron, from an interview in Writers at Work, First Series (1958), edited by George Plimpton.

Show how Doctor Faustus is a tragedy of Presumption.

Tragedy of presumption isn't generally a well-defined term in literary studies, but it implies situational irony, and in Faustus's case cosmic irony as well. Situational irony occurs when events turn out differently than one expects and cosmic irony occurs when that situation is elevated to expectation of divine realities. In Marlowe's play, Faustus engages in presumptions about these realities and about his own human nature that lead not only to his death and damnation but also, in a more traditional tragic sense, to the loss of the quality that had made him most admirable.
Faustus is among the most gifted minds of his day, and having seemingly exhausted what conventional studies can offer seeks the intrigue of necromancy. After this decision, he is repeatedly disappointed in the results of his choice but unwilling to repent. Further, the quality of mind that made him heroic in the first scene becomes increasingly debased as he continues in his soul-selling bargain.
The first ironic presumption he makes is to say "I think hell is a fable," while speaking to a devil. He then seeks astrological knowledge that medieval scholasticism had failed to supply but which humanist ones were unfolding. Similarly, his magic accomplishes little more than humanist Europe was supplying: stage plays in which ancient figures come to life and distribution channels for exotic goods (such as grapes out of season). The middle section of the play functions largely through these types of ironies, a quality Marlowe was deft at deploying without turning the play into pure satire or farce. The play moves from ironic comedy to ironic tragedy with a tonal complexity of which Marlowe was a master.
At the end, we see Faustus's final presumption. Hours and even minutes before his death, he retains the promise of salvation through repentance. His tragedy might be seen as one of presumption in that he presumes—in the same overweening pride that initiates his story—that he is too great in his error to be forgivable, that his evil is greater than God's ability to pardon. As a result, he dies talking about the value of repentance and regret without actually repenting.

In relation to the character of Dr. Faustus, presumption can be defined as behavior that is arrogant, disrespectful, and which transgresses established social norms and boundaries. Faustus comfortably ticks all of these boxes. Although a learned, intelligent man with a lot going for him, Faustus is profoundly dissatisfied with his life. He feels frustrated by the limits of human knowledge, which severely impede the attainment of the earthly power he so desperately craves.
Egged on by the Evil Angel, Faustus begins dabbling in black magic, hungry for the enormous power and fame it will give him. Even though Faustus knows that messing around with the forces of darkness is in danger of arousing God's "heavy wrath," he still goes ahead anyway. This is a classic example of Faustus's presumption: he's acting like God and defying Him at the same time. Black magic will indeed give Dr. Faustus more power than he could ever have dreamed of. But it will also endanger his mortal soul, and therein lies the tragedy of his presumption.

Find information on 5 trade agreements. Talk about the countries involved and when the agreement was implemented. Then discuss the pros and cons of each agreement in terms of gains and losses for the countries involved. An example of NAFTA is provided for you below. Needless to say, NAFTA cannot be used as an example in your own papers. Name of agreement NAFTA (North American Free Trade Agreement) Countries involved United States, Canada, and Mexico. (USDA, n.d.) Date agreement implemented January 1, 1994 (USDA, n.d.) Pros of agreement The agreement between Canada, the U.S. and Mexico links 450 million people and produces $17 trillion in goods and services annually. Some of the advantages include a 5-fold increase of trade between the NAFTA signatories from $297 billion in 1993 to $1.6 trillion in 2009. (Amadeo, 2012) Cons of agreement Critics say that the agreement has led to a net loss of 500,000 – 750,000 jobs in the U.S., and a decline in labor protection and degradation of the environment in Mexico. (Amadeo, 2012) References: Amadeo, Kimberly (2012,February 12). NAFTA Pros and Cons, Retrieved from http://useconomy.about.com/b/2008/04/24/nafta-pros-and-cons.htm United States Department of Agriculture.Foreign Agricultural Service (n.d.). North American Free Trade Agreement (NAFTA). Retrieved fromhttp://www.fas.usda.gov/itp/Policy/nafta/nafta.asp Make sure you clearly state theSOURCEfor each set of information that you use to fill out your tables and provide APA CITATIONS within parentheses in your text. Without in-text citations and references your work will be considered plagiarized and you will get a ZERO. What your presentation should look like – APA formatted title slide One paragraph Introduction to the presentation At least 5 slides (you can have more than 5) – one for each agreement – using the format for NAFTA presented above. Make sure you have in-text citations for each point (again as shown above) One paragraph Conclusion References (APA formatted) All text must have citations as well as references. What is the difference between the two? When you get ideas from a source that is not your own, you must give credit. This is a citation and will take the form of a parenthetical citation at the end of the paragraph/sentence as in the example below: With obesity concerns gripping the nation many non-exercisers have turned to cycling as a leisure activity that helps fight the battle of the bulge. Cycling is a great low impact way to increase your heart rate and burn calories without causing undue strain and pressure to your joints and muscles. This is especially important with an ageing baby boom population seeking an easier way to stay fit (Foley, 2005). This article is then fully referenced in the references page at the end of the paper as Ryan Foley A.P. (2005) The Lance Factor. Retrieved from the Honolulu Advertiser October 8th, 2005 the.honoluluadvertiser.com/article/2005/Jul/24/bz/507240340.html Remember that citations are required not only when you are directly quoting from a source. Even if you “borrow” an idea from a source but paraphrase it in your own words you must give credit. Otherwise you are trying to pass off someone else’s ideas as your own. And that is plagiarism. A plagiarized paper will get a grade of zero. Since social science disciplines use the APA style of formatting you must follow the APA style throughout the paper. The following website will give you information about the APA style of formatting.

Free trade agreements (FTA's) are an integral practice within an ever-growing globalized market economy, and, in America especially, free trade agreements have resulted in huge economic gains. As stated by the International Trade Administration, the "reduction of trade barriers and the creation of a more stable and transparent trading and and investment environment make it easier and cheaper for the U.S. to export their products and services." From this statement, it is clear that the U.S. has benefitted greatly from past FTA's with countries that range from each end of the globe.
Here are some examples: 
1)
Name of agreement                          The Central American-Dominican Republic Free Trade Agreement 
 
Countries involved                           United States, Costa Rica, Dominican Republic, Guatemala, Honduras, Nicaragua, El Salvador. (Arnadeo, 2017)       
 
Date agreement implemented         August 5, 2004 (Arnadeo, 2017)          
 
Pros of agreement                           71% increase in trade of goods since 2005. 4.7% economical growth in Nicaragua (2014). Greater foreign investment in Costa Rican telecommunication and insurance industries. Growth of gold and silver exports in Dominican Republic, as well as an increase in tourism. (Arnadeo, 2017) 
 
Cons of agreement                          This trade deal resulted in a massive upheaval due to an increase in exports of low-cost grains and a change of location for low-cost labor. Many jobs moved overseas to countries like China and Vietnam. (Arnadeo, 2017) 
2)
Name of agreement                          Trans-Pacific Partnership
 
Countries involved                           United State and 11 countries that border the Pacific (Arnadeo, 2017)
 
Date agreement implemented         February 4, 2016 (Arnadeo, 2017)          
 
Pros of agreement                            The creation of jobs due to an increase in exports and economic growth. Specifically, this agreement would help to improve the plastics, machinery, auto, and agricultural industries. (Arnadeo, 2017) 
 
Cons of agreement                           A majority of the growth that would incur would primarily benefit higher wage earners. This is a result of an increase of production of textiles and cheap goods. (Amadeo, 2017)
3)
Name of agreement                          Transatlantic Trade and Investment Partnership 
 
Countries involved                           United States and the European Union (Arnadeo, 2017).  
Date agreement implemented        In progress... (Arnadeo, 2017)          
 
Pros of agreement                            Economic growth and the creation of up to 2 million jobs. This agreement would also strengthen the relationship of Transatlantic partnerships in the face of a rise in economic power from China, India, and other Pacific nations. (Amadeo, 2017)
 
Cons of agreement                           A growth in the European economy could result in a reduction of jobs for American workers. Companies like Boeing and those that produce French champagne would be especially damaged. (Amadeo, 2017)
4)
Name of agreement                          Israel Free Trade Agreement 
 
Countries involved                           United States and Israel (Arnadeo, 2017).
 
Date agreement implemented         1985 (Arnadeo, 2017)          
 
Pros of agreement                            Resulted in a decrease in trade restrictions that limited exports between the two countries. Also resulted in greater transparency in regard to trade regulations. (Amadeo, 2017)
 
Cons of agreement                           The strengthening of ties between Israel and the U.S. resulted, in part, in the alienation of Middle Eastern and neighboring countries like Palestine. (Amadeo, 2017)
5)
Name of agreement                         Jordan Free Trade Agreement
 
Countries involved                           United States and Jordan (Arnadeo, 2017)       
 
Date agreement implemented         December 17, 2001 (Arnadeo, 2017)          
 
Pros of agreement                            Reduced trade barriers in the meat and poultry industries, specifically. Also benefitted Jordan's agricultural industry. (Amadeo, 2017)
 
Cons of agreement                           May have resulted in an increase in violations of labor-rights due to the increase in production of cheap goods. (Amadeo, 2017)
In conclusion, all of the aforementioned trade agreements have resulted in an increase in the production and export of trade goods between the countries involved. Consequently, all of the countries involved have experienced economic growth to some degree since these agreements have been signed into action. Unfortunately, this economic growth primarily benefits higher-wage earners as free trade agreements tend to help more industrialized countries. As a consequence, economies that cannot compete to the same degree tend to suffer. (Arnadeo, 2017)
References
Amadeo, K. (n.d.). The Top 12 U.S. Bilateral Trade Agreements. Retrieved June 26, 2017, from https://www.thebalance.com/what-are-bilateral-trade-agreements-pros-cons-and-list-3305911
Amadeo, K. (n.d.). Will the World's Largest Trade Agreement Be Signed This Year? Retrieved June 26, 2017, from https://www.thebalance.com/transatlantic-trade-and-investment-partnership-ttip-3305582
Amadeo, K. (n.d.). The 2004 Trade Agreement That Made Bananas Cheaper. Retrieved June 26, 2017, from https://www.thebalance.com/what-is-cafta-3305580
Amadeo, K. (n.d.). What Does Trump's Executive Order to Withdraw from the TPP Mean? Retrieved June 26, 2017, from https://www.thebalance.com/what-is-the-trans-pacific-partnership-3305581
 
https://www.thebalance.com/multilateral-trade-agreements-pros-cons-and-examples-3305949

https://www.thebalance.com/what-is-the-trans-pacific-partnership-3305581

In what ways did the Mexican-American War impact national politics?

The Mexican-American War resulted from years of disputes between the United States and Mexico over territory in present day Texas, California, and New Mexico. These disputes arose in large part because of American ambitions surrounding western expansion and "Manifest Destiny," the belief that America's expansion across North America to the Pacific was ordained by God and necessary to civilize the continent, no matter who might already inhabit it. In fact, President James K. Polk won the 1844 election with his slogan "54-40 or fight," referring to his desire to take all of the Oregon Territory that was shared with Britain, and he proved himself a staunch advocate of expansion. In the 1830s, the Mexican government invited US citizens to settle in Texas as a way to encourage the development of the region. However, when Mexico outlawed slavery and attempted to impose Catholicism on settlers, Texans led by Stephen Austin declared independence and created the Republic of Texas. The Republic of Texas sought annexation by the US, but controversies over slavery and the possibility of war with Mexico caused most presidents to avoid the issue. However, when gold was discovered in California, President Polk decided that it was time to gain the territory held by Mexico. The resulting Mexican-American War lasted from 1846 to 1848 and resulted in the Treaty of Guadalupe-Hidalgo.
The treaty proved favorable to the United States, which received the territories of Texas, New Mexico, and California in exchange for just $15 million. However, this land quickly fueled debates in the United States. Slaveholding states feared that abolitionists would outlaw slavery in the new territories, tipping the balance between slave and non-slave states in Congress in favor of non-slave states, particularly northern states. On the other hand, northerners and abolitionists feared that the growing cotton industry would spread to these new territories, taking slavery with it. As the California Gold Rush intensified, the population increase in the territory made it eligible for statehood. The Missouri Compromise (1820) that had set a precedent for keeping the balance between free and slave states only applied to the Louisiana Territory, and new debates broke out over whether to extend the 36-30 compromise line to the Pacific, to outlaw the spread of slavery altogether, or to allow slavery in territories based on popular sovereignty (letting the people of the territory decide). Ultimately Congress agreed to the Compromise of 1850, which admitted California as a free state and allowed for popular sovereignty in the territories of Utah and New Mexico. It also outlawed the slave trade in Washington, DC, and included a much stricter Fugitive Slave Law that was abhorred by many northerners. Ultimately, although it ended in compromise, the debates surrounding the territories from the Treaty of Guadalupe-Hidalgo revealed the growing tensions between the North and South. The Compromise of 1850 succeeded in keeping a tenuous peace for just four years. Then, the issue of slavery in Kansas and Nebraska led to violent disputes between proslavery and antislavery factions.

First, there was the impact of the war itself:  many Northerners saw this as a Southern conspiracy to spread slavery.  The war was ordered by a Southern president (James K. Polk) and instigated by a Southern general (Zachary Taylor).  Taylor moved his forces into the disputed boundary between Mexico and the United States between the Nuecces and the Rio Grande Rivers.  Mexico fired on the American soldiers, and Polk declared war.  Abraham Lincoln, who was then a Whig, argued that American blood was not shed on American soil and that the United States instigated the conflict.  Of course, his pro-expansionist constituency in Illinois did not like this, and he lost in the next election.  
After the war, there was a question of whether or not the new land would be free or slave.  Southerners did not want to lose the split between free states and slave states in the Senate, and Northerners wanted to control the spread of slavery.  All of this would lead to the Compromise of 1850 which, ultimately, made no one happy.  

How does Oates mix the real with the fantastic in this story? Who is Arnold Friend? What is the significance of his name?

The encounter between Connie and Arnold Friend at the end of this story does have some fantastical elements. It has been said that Friend is, on some level, a symbolic character and a sort of composite as well. The name "Friend" refers to a number of things, one being the character's embodiment of popular music, which Connie is obsessed with. Music is something that helps her become who she wants to be. As the story says, she has "two sides" that represent who she is at home and who she is elsewhere. Music is a "friend" that understands and supports her. Her family does not like her music and tell her to turn it down. The story's dedication to Bob Dylan signifies its connection to popular music and the spirit of rebellion that Dylan's songs and persona represented to youth culture.
Friend is someone from the "other side" of Connie's home life; she meets him when she is hanging out one night with her friends. When Friend shows up at Connie's house, these two sides, these two worlds, meet for the first time, and Connie is unsure of how to connect them together. The door that stands between her and Arnold is a symbol of the safety of her home and the divide between her family life and the life of freedom, expression, and exploration that she craves. The screen on the door is also a symbol of her virginity (this is a common trope in coming-of-age literature and film).
The fact that this man is named "Friend" is also meant to allay Connie's fears about exploring her sexuality and rebelling against her family's attitudes about her encounters with boys. When she opens the door to go for a ride with him, she merges the two sides of her world: home, safety, and innocence merges with life, danger, and exploration.

The Scarlet Letter - Why is the "witch" tolerated and Hester is punished? What does this say about the kinds of sins that bother us the most?

In this novel, the witch, Mistress Hibbins, is tolerated because she is the sister of a prominent politician in the colony, Governor Bellingham.  I'm not sure that we can, with total accuracy, say that her activities are tolerated much better than Hester's because the narrator does tell us that she was "executed as a witch" a few years after the bulk of this story takes place.  But it is possible that she is also tolerated for as long as she is because people are afraid of her: she does seem to have a lot of knowledge about individuals' private conversations and whereabouts as well as admitting to meeting with the Devil in the woods.  However, the fact that Hester's sins are punished so swiftly may indicate that sexual sinfulness, especially in a woman, is considered to be the most egregious type of sinfulness. 

int e^x/((e^x-1)(e^x+4)) dx Use substitution and partial fractions to find the indefinite integral

inte^x/((e^x-1)(e^x+4))dx
Let's apply integral substitution:u=e^x
=>du=e^xdx
=int1/((u-1)(u+4))du
Now create partial fraction template of the integrand,
1/((u-1)(u+4))=A/(u-1)+B/(u+4)
Multiply the above equation by the denominator,
=>1=A(u+4)+B(u-1)
1=Au+4A+Bu-B
1=(A+B)u+4A-B
Equating the coefficients of the like terms,
A+B=0    ----------------(1)
4A-B=1   ----------------(2)
From equation 1, A=-B
Substitute A in equation 2,
4(-B)-B=1
-5B=1
B=-1/5
A=-B=-(-1/5)
A=1/5
Plug in the values of A and B in the partial fraction template,
1/((u-1)(u+4))=(1/5)/(u-1)+(-1/5)/(u+4) 
=1/(5(u-1))-1/(5(u+4))
int1/((u-1)(u+4))du=int(1/(5(u-1))-1/(5(u+4)))du
Apply the sum rule,
=int1/(5(u-1))du-int1/(5(u+4))du
Take the constant out,
=1/5int1/(u-1)du-1/5int1/(u+4)du
Now use the common integral:int1/xdx=ln|x|
=1/5ln|u-1|-1/5ln|u+4|
Substitute back u=e^x and add a constant C to the solution,
=1/5ln|e^x-1|-1/5ln|e^x+4|+C
 

Does Mary have a guilty conscience?

We don't know for sure if Mary does have a guilty conscience. However, if she does, then she doesn't really show it. Although her killing of Patrick is carried out in the heat of the moment, it is still a crime all the same. And Mary's subsequent behavior doesn't suggest that she feels any remorse for what she's done. She meticulously sets about covering up her crime and establishing an alibi. There's the coldly methodical way she concocts a story for the police. Then, of course, there's her novel method for disposing of the evidence. Again, one would have to say that this doesn't appear to be the behavior of someone with a guilty conscience.
Besides, if Mary really did feel any guilt or remorse for what she's done, then she has ample opportunity to confess to the police when they arrive. It's clear from all the available evidence that this is not a premeditated act; no charge of murder would've been filed against Mary as a consequence. Yet she chooses not to confess, and this, in conjunction with all the other evidence, indicates that Mary doesn't really have a guilty conscience at all.

y=sqrt(4-x^2) , -1

To calculate the surface area generated by curve y=f(x) revolving about x-axis between a and b, we use the following formula
S_x=2pi int_a^b y sqrt(1+y'^2)dx
Let us therefore first find the derivative y'.
y'=1/(2sqrt(4-x^2))cdot(-2x)=-x/sqrt(4-x^2)
y'^2=x^2/(4-x^2)
We can now calculate the surface.
S_x=2pi int_-1^1sqrt(4-x^2)sqrt(1+x^2/(4-x^2))dx=
2pi int_-1^1sqrt(4-x^2)sqrt(4-x^2+x^2)/sqrt(4-x^2)dx=
2pi int_-1^1 2dx=4pi x|_-1^1=4pi(1+1)=8pi
The area of surface generated by revolving the given curve about x-axis between -1 and 1 is 8pi.
Graphs of the curve and the surface generated by curve's revolution can be seen in the images below.

College Algebra, Chapter 4, 4.6, Section 4.6, Problem 72

Find the slant asymptote, the vertical asymptotes, and sketch a graph of the function $\displaystyle r(x) = \frac{2x^3 + 2x}{x^2 - 1}$.

By applying Long Division,







By factoring,

$\displaystyle r(x) = \frac{2x^3 + 2x}{x^2 - 1} = \frac{2x (x^2 + 1)}{(x - 1)(x + 1)}$

Thus,

$\displaystyle r(x) = \frac{2x^3 + 2x}{x^2 - 1} = 2x + \frac{4x}{x^2 - 1}$

Therefore, the line $y = 2x$ is the slant asymptote.

The vertical asymptotes occur where the denominator is , that is, where the function is undefined. Hence the lines $\displaystyle x = 1$ and $x = -1$ are the vertical asymptotes.

To sketch the graph of the function, we must first determine the intercepts.

$x$-intercepts: The $x$-intercepts are the zeros of the numerator, in our case, $x = 0$ is the only real $x$-intercept.

$y$-intercept: To find $y$-intercept, we set $x = 0$ into the original form of the function

$\displaystyle r(0) = \frac{2(0) (0^2 + 1)}{(0 -1)(0 + 1)} = 0$

The $y$-intercept is .

Next, we must determine the end behavior of the function near the vertical asymptote. By using test values, we found out that $y \to \infty$ as $\displaystyle x \to 1^+$ and $x \to - 1^+$. On the other hand as $y \to -\infty$ as $x \to -1^-$ and $\displaystyle x \to 1^-$. So the graph is

A 200-gallon tank is half full of distilled water. At time t = 0, a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 5 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 3 gallons per minute. At what time will the tank be full?

Total volume of the tank=200 gallon
Given that, tank is half full,
so remaining volume of the tank to be filled=200-100=100 gallon.
Since 5 gallons of solution comes into the tank per minute and 3 gallons of solution goes out each minute,
Net flow of solution in the tank=5-3= 2 gallons per minute.
Time required=100/2=50
So, the time required for the tank be full = 50 minutes 

Is Sara a flat or dynamic character?

Sarah Ruth is a flat character as she remains religious, unattractive and uninterested in frivolities throughout the story. When Parker first meets her, he observes that he wouldn’t want anything to do with her, because of her “dry hot and rough hands” and her plain looks. Also, she is not attracted to his tattoos, something that quite surprises Parker as he had never before met a woman who did not like his tattoos. She refers to the tattoos as “vanity of vanities." It is her rejection of his tattoos that torments Parker.
Later on, after he marries her, Parker observes that she has not changed much. She is plain-looking and, to make matters worse, pregnant—something that makes her even less attractive to him. He thinks that she obsesses over righteousness. This is why she does not imbibe, smoke, use foul language, or even use body makeup.
However, Parker forgets that Sarah comes from a religious family and lives her life the only way she knows how to. Her father was a preacher who must have taught her the scriptures well. Parker may have thought that marriage would finally change Sarah Ruth into a doting, more agreeable wife. However, she remains unchanged and this makes him “gloomier than ever." The text states that each morning, Parker would leave determined not to return, yet came back in spite of everything.

In Cranes by Hwang Sun-won, what was Songsam's relationship with Tokchae like when they were children?

Although now torn apart by war and the separation of North Korea and South Korea, Songsam and Tokchae were quite close when they were children, as indicated by a few flashbacks throughout “Cranes.” In one particularly touching flashback, Songsam and Tokchae are stealing chestnuts from a tree when Songsam falls and suffers being pricked by chestnut needles all over his bottom. Tokchae patiently removes the needles and then hands his friend a bunch of chestnuts to enjoy.
The pivotal flashback is to when the boys were twelve and decided to secretly catch and keep a crane, only to let it go free when they feared it would be captured or killed by someone else. It is this memory that triggers Songsam’s drastic act of compassion; he forms an idea, using this memory of crane-catching, to let his old friend Tokchae escape capture and execution.

When Tokchae and Songsam were children, they were childhood friends with each other. 
The story gives some small details from the characters' pasts that indicate that the two men were fairly close friends.  For example, Songsam initially thinks that offering Tokchae a cigarette is bad timing, but then he remembers that Tokchae and he shared stuff with each other when they were children.

Then suddenly he thought that Tok-chae, too, must want a puff. He thought of the days when they used to share dried gourd leaves behind walls, hidden from the adults.

Near the story's conclusion, Tokchae and Songsam arrive at a field together.  The reader is told that this is the same field where the two men captured and freed a crane together as young boys.  

Once, when Song-sam and Tok-chae were about twelve, they had set a trap here, without the knowledge of the adults, and had caught a crane, a Tanjong crane.

Tokchae believes that he is about to be executed in this very same field, but because of their childhood bond, Songsam decides to let Tokchae run away.  Just as the two men let the crane go free as boys, Songsam is now letting Tokchae go free as well.  

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 6

a.) Find all zeros of $P(x) = x^5 + 9x^3 $ of $P$, real and complex

b.) Factor $P$ completely.



a.) We first factor $P$ as follows.


$
\begin{equation}
\begin{aligned}

P(x) =& x^5 + 9x^3
&& \text{Given}
\\
\\
=& x^3 (x^2 + 9)
&& \text{Factor out } x^3

\end{aligned}
\end{equation}
$


We find the zeros of $P$ by setting each factor equal to :

Setting $x^3 = 0$, we see that $x = 0$ is a zero. More over, setting $x^2 + 9 = 0$, we get $x^2 = -9$, so $x = \pm 3i$. So the zeros of $P$ are $0, 3i$ and $-3i$.

b.) Since the zeros are $0, 3i$ and $-3i$, by the complex Factorization Theorem $P$ factors as


$
\begin{equation}
\begin{aligned}

P(x) =& x (x - 3i) [x - (-3i)]
\\
\\
=& x (x - 3i)(x + 3i)

\end{aligned}
\end{equation}
$

Why does Beatty believe that sports are good for society?

Captain Beatty supports government censorship and is vehemently opposed to literature, preserving knowledge, and engaging in intellectual pursuits. Beatty is in favor of any type of entertainment that distracts the citizens and prevents them from exercising their minds or analyzing their superficial society. Therefore, Captain Beatty is a proponent of sports because they are a form of mindless entertainment that amuses the vast majority of the population. In Bradbury's dystopian society, sports have become an outlet for citizens to exert their pent-up energy in a harmless way that poses no threat to the government or upsets the majority of the population. The citizens are particularly attracted to violent sports, which is something Beatty also supports. Overall, Beatty is a proponent of virtually any form of mindless entertainment that allows the population to remain passive and ignorant. Similar to interactive televisions and psychological medications, sports distract the population from recognizing and analyzing society's ills.

Beatty believes that sports are good for society because sports, like cartoons and pictures, reduce the need for the mind to work and to learn. Books are dangerous because they encourage thinking, and if the people in society are thinking, they may realize they are unhappy and want to do something about it.
Sports are straightforward and simple to understand. The point of sports is to give the participants and audience members an opportunity to be distracted; everyone can enjoy mindless entertainment and forget about their questions and problems. Also, it is the nature of sports to enjoy them in groups. As a result, the spirit of fun is contagious amongst a group of people, and this group experience minimizes opportunities for society members to be individuals and think independently for themselves.

Can you help me scan "The West Wind" by John Masefield?

Although the poem does seem to have an inconsistent number of syllables in each line, the scansion of its rhythms and meter are actually fairly consistent if you emphasize the appropriate words. Sometimes with a poem like this, you have to read it aloud to find the appropriate emphasis, as it does not just fall in line with the number of syllables. The emphasis in terms of scansion is on the words that create the image or meaning in each line. Modern poetry often does not conform precisely to these meters in the same way poetry from earlier centuries does.
If one considers Masefield may be paying homage to Percy Bysshe Shelley's poem "Ode to the West Wind," which is written in iambic pentameter, then we can see Masefield's poem may be scanned as if it is also in iambic pentameter.
In this way, we san see a reading of the first line of Masefield's poem should emphasize the words "warm," "west," "full," and "cries." This gives the poem an iambic meter and feeling and is appropriate to its structure.
https://poets.org/poem/ode-west-wind

How does Hamlet work to examine human behavior and psyche, and what role does Act V play in establishing this depth/connection? Why is Hamlet so often referred to as Shakespeare's (and literature's) greatest achievement and how is Act V the crowning moment?

Hamlet examines human behavior and the psyche in several different ways. One is by its portrayal of madness. Hamlet announces that he will feign madness, but his behavior, as well as several of his soliloquies, suggest that his madness may be authentic. He experiences bouts of melancholy, expresses uncontrollable rage, and generally behaves erratically throughout the play. The characters in the play are generally convinced that he is insane, and the audience is forced to contemplate the fine line between madness and sanity as part of the human condition as well as in the title character. Beyond this, we encounter in Hamlet a character wracked by self-doubt, a trait most people can identify with. At times he doubts himself capable of avenging his father's death and continues to stall throughout much of the play. He declines, for example, to kill Claudius when it would have been very easy to do so, citing the fact that his uncle is praying. His tortured relationship with his mother and with Ophelia (whose own decline into madness also suggests the frailty of the human psyche) show him to be a intensely conflicted character. Act V is in many ways the crowning achievement of the play, as the audience witnesses a resolution to the conflicts between Hamlet and Claudius, Hamlet and his father's ghost, and Hamlet and himself. The first scene of the act witnesses Ophelia's tragic death and Hamlet's extended and melancholy speech on mortality (occasioned by his discovery of Yorick's skull). The second scene closes the play with the death of Claudius and Hamlet, whose vacillations in seeking revenge give way to focus as he kills his uncle.

Why were freedmen not able to enjoy the freedom that they received as a result of the 13 amendment

 
The 13th Amendment to the United States Constitution states as follows:

Section 1. Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
Section 2. Congress shall have power to enforce this article by appropriate legislation.

By "freedmen," the generally understood meaning is former slaves who were under involuntary servitude (slavery) to slave masters in southern states where slavery was legal prior to the ratification of the 13th Amendment. Perhaps the most significant reason why many freedmen were unable to enjoy fully the freedoms provided under the 13th Amendment was the substantial efforts many (if not all) Democrat-controlled states in the South (the Confederate States) immediately undertook in a deep-seated effort to preserve a culture of racism.
As a direct response to the passage and ratification of the 13th Amendment across southern states, state and local jurisdictions in southern states enacted a series of racially-restrictive statutes, ordinances, and rulings (commonly referred to as "Black Codes"). For example, without the ability for now-former slave masters to lawfully secure labor at low or no cost through the mechanism of slavery, the assumption was that Black Codes permitted a way around the intent of the 13th Amendment while in principle not directly violating the 13th Amendment. Black Codes went far beyond merely creating barriers to reasonable wages and fair labor laws but also affected the ability of blacks to obtain and enjoy such rights as equal access to housing, a fair and speedy trial, the right to bear arms, the ability to attend public schools, and a host of other rights provided to non-black citizens of the United States.
State and local laws viewed as Black Codes, in many cases, were painstakingly-crafted not to be outright racist against blacks on their face. However, the application of such laws created a net effect that such laws were in fact racist in a way that unfairly, unjustly, and unconstitutionally violated the rights of blacks to access and benefit from equal rights and liberties as enumerated under the United States Constitution.
That said, many of the state and local laws passed following the ratification of the 13th Amendment outright prohibited blacks from enjoying equal rights. Many of these Black Codes were quickly challenged at the state and federal level as unconstitutional and subsequently repealed. However, many of these laws remained in full force and effect for a number of years to follow. Southern states also worked around the invalidation of Black Codes by coming up with a more insidious plan to preserve de jure segregation in most sectors of society. State and local laws (commonly referred to as "Jim Crow laws") enforcing racial segregation for the remainder of the 19th century until 1965 continued to restrict the civil rights and civil liberties of blacks, particularly in southern states where the bulk of Jim Crow laws existed.

Why was Putnam brought into the court?

Giles Corey storms into the courtroom at the beginning of act 3, insisting that "Thomas Putnam is reaching out for land!" Deputy Governor Danforth has Giles removed from court and questions him outside. When Danforth glances over Giles's deposition, he asks that Mr. Putnam—who is already in the courtroom—be brought in to this other room by Reverend Parris. When Putnam enters, Danforth says,

"Mr. Putnam, I have here an accusation by Mr. Corey against you. He states that you coldly prompted your daughter to cry witchery upon George Jacobs that is now in jail."

Putnam, of course, denies this charge. As Giles points out, if Jacobs is convicted of witchcraft, then his land goes up for public auction, and, he says, "there is none but Putnam with the coin to buy so great a piece." Giles believes that Putnam prompted his daughter, Ruth, to accuse George Jacobs so that his land would become available and Putnam would then be able to purchase it legally. Putnam is essentially asked to address this charge, and all he has to say is that it is untrue. At this point, the magistrates begin to question Giles as to the identity of his supposed informant. However, because Giles knows that this man will be arrested and likely found guilty of wrongdoing himself, he will not give the name. Eventually, Danforth holds him in contempt of court for his refusal to do so.

Mr. and Mrs. Putnam are two of the main characters perpetuating witchcraft hysteria throughout the community. They are both deeply involved in the witch trials, and Giles Corey mentions that Thomas Putnam is reaching out for land at the beginning of act 3. Deputy Governor Danforth calls into the court to speak with Thomas Putnam, who is more than likely watching the witch trials with the rest of the community. Deputy Governor Danforth then tells Thomas Putnam that Giles Corey has a deposition from a respected community member who claims to have heard Putnam telling his daughter to accuse George Jacobs of witchcraft. According to Salem's laws, if any citizen admits to being involved in witchcraft, their land automatically goes up for sale. Because Thomas Putnam is the only citizen with enough money to purchase extensive plots of land, he uses his daughter to accuse innocent citizens of witchcraft so that he can acquire more land. However, Thomas Putnam denies Giles Corey's claim, and Giles is arrested after refusing to name the citizen who said he overheard Thomas Putnam speaking to his daughter. 

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 42

Determine the $\displaystyle \lim_{x \to 0^+} \sin x \ln x$. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.
$\displaystyle \lim_{x \to 0^+} \sin x \ln x = \lim_{x \to 0^+} \frac{\ln x}{\csc x} $


By applying L'Hospital's Rule...

$
\begin{equation}
\begin{aligned}
\lim_{x \to 0^+} \frac{\ln x}{\csc x} &= \lim_{x \to 0^+} \frac{\frac{1}{x}}{-\csc x \cot x} \\
\\
&= \lim_{x \to 0^+} \frac{\left( \frac{1}{x} \right)}{-\frac{1}{\sin x} \left( \frac{\cos x}{\sin x} \right)}\\
\\
&= \lim_{x \to 0^+} \frac{- \sin^2 x}{x \cos x}
\end{aligned}
\end{equation}
$


We can rewrite the limit as...

$
\begin{equation}
\begin{aligned}
\lim_{x \to 0^+} \frac{-\sin^2x}{x \cos x} &= - \lim_{x \to 0^+} \left( \frac{\sin x}{x} \cdot \frac{\sin x}{\cos x} \right)\\
\\
&= - \left[ \lim_{x \to 0^+} \frac{\sin x}{x} \cdot \lim_{x \to 0^+} \tan x \right]\\
\\
\text{Recall that } \lim_{x \to 0^+} \frac{\sin x}{x} &= 1 \text{ ,so...}\\
\\
&= - \left[1 \cdot \lim_{x \to 0^+} \tan x \right]\\
\\
&= -[1 \cdot 0]\\
\\
&= 0
\end{aligned}
\end{equation}
$

Describe the first plan that Faber and Montag come up with.

When Montag initially visits Faber's home, he suggests that they get a printing press and begin making copies of illegal books to distribute throughout society. Faber immediately tells Montag that he would not be interested in the plan and suggests that he might participate in a plan that would destroy the fireman structure from the inside. Faber then suggests that they could possibly make copies of books and plant the illegal novels inside firemen's homes, which would sow seeds of suspicion throughout the organization. After describing his plan, Faber immediately retracts his statement and mentions that his plan would be far from a guarantee. Before Faber can dismiss Montag, Montag grabs his attention by ripping pages out of the Bible. Faber then agrees to help Montag and gives him a two-way communication device known as the green bullet.