Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 62

Suppose $f(x) = x+4$ and $h(x)=4x-1$, find $a$ function $g$ such that $g \circ f = h$.
Both equations are linear functions so function $g(x)$ must be a linear function as well.
Let $g(x) = Ax + B$, where $A$ and $B$ are constant.



$
\begin{equation}
\begin{aligned}

g \circ f(x) =& g(f(x))\\
g(x + 4) =& Ax + B\\
g(x + 4) =& A(x + 4) + B\\
g \circ f =& Ax + 4A + B


\end{aligned}
\end{equation}
$


To obtain $g \circ f = h$

$Ax + 4A + B = 4x - 1$
By grouping the equation in terms of the linear equation $Ax + B$


$
\begin{equation}
\begin{aligned}

\frac{Ax}{x} =& \frac{4x}{x}\\
A =& 4\\
\\
4A + B =& -1\\
4(4) + B =& -1\\
16 + B =& -1\\
B =& -17

\end{aligned}
\end{equation}
$


Substituting to the function $g(x) = Ax + B$

$g(x) = (4)(x) + (-17)$
$\fbox{$g(x) = 4x - 17$}$

In Newjack by Ted Conover, what do you think Conover learned about himself and about his relationships with staff and inmates?

Conover worked as a guard at Sing Sing to understand the reality of the inmates' and correction officers' lives. In writing his book, he was both a journalist and an ethnographer, as he worked alongside the people he wrote about. In the end, he understands that the reality of the lives of the correctional officers (or COs, as they are known) and the inmates is different than the way the public has understood it. He also has a great deal of empathy for both the COs and inmates and understands that both the COs and inmates are scared and human, just as he was during his time working at Sing Sing.
He writes in the Afterword to his book that he has only just begun to understand "the depth of the stigma they [the officers] felt, the pain of society's disregard" (page 315). He goes on to write that "the antidote" to the stigma is "recognition and an appreciation of the job's unique difficulties" (page 315). In other words, the COs are misunderstood by society, and only by living in a CO's shoes does he understand the reality of how difficult their work is. He also comes to understand the lives of the inmates in their blocks, which he describes as "massive human warehouses" (page 6). He comes to understand that prisons have to be reformed to prevent recidivism, and he comes to know that many of the prisoners are scared or mentally ill human beings. In short, he comes to understand that he has to experience someone's reality to truly understand it.  

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 32

Factor the polynomial $P(x) = x^5 - 4x^3$ and use the factored form to find the zeros. Then sketch the graph.

$
\begin{equation}
\begin{aligned}
P(x) &= x^5 - 4x^3 \\
\\
&= x^3(x^2 - 9) && \text{Factor out } x^2\\
\\
&= x^3(x+3)(x-3) && \text{Difference of squares}
\end{aligned}
\end{equation}
$

Since the function has an odd degree of 5 and a positive leading coefficient, its end behaviour is $y \rightarrow -\infty \text{ as } x \rightarrow -\infty \text{ and } y \rightarrow \infty \text{ as } x \rightarrow \infty$. To find the $x$ intercepts (or zeros), we set $y = 0$.
$0 = x^3(x+3)(x-3)$

By zero product property, we have
$x^3 = 0, \quad x + 3 = 0$ and $x - 3 = 0$

Thus, the $x$-intercept are $x =0, -3$ and 3

What are some important quotes spoken by the character Macbeth in Shakespeare's play?

It is difficult to choose only a few lines to pull out of the play for Macbeth, but here are some examples that indicate Macbeth’s journey and are important to showing who he is as a character, his state of mind, and the direction of the plot.
The first important one is Macbeth’s reaction to Malcolm being named successor to the throne.  The witches indicated that Macbeth would be king, and he really wants to be king.  He does not take Duncan’s announcement that his son will be king well.

MACBETH
[Aside] The Prince of Cumberland! that is a stepOn which I must fall down, or else o'erleap,For in my way it lies. Stars, hide your fires;Let not light see my black and deep desires … (Act 1, Scene 4) 

This shows that Macbeth is ambitious, and that he is worried about the effects of his ambitions.  He does not want to show others how much he wants to be king, and how disappointed he is in not being chosen.  This is especially true because no one probably expects him to think he will be king, since it makes more sense for the king’s son to be king. 
Another significant quotation from Macbeth comes from when he is trying to decide what to do about this discrepancy between his wishes and Duncan’s.  He imagines a fantasy dagger, and wonders where it came from.  Does this mean that he is meant to kill Duncan and become king himself?

Is this a dagger which I see before me,The handle toward my hand? Come, let me clutch thee.I have thee not, and yet I see thee still.Art thou not, fatal vision, sensibleTo feeling as to sight? or art thou butA dagger of the mind, a false creation,Proceeding from the heat-oppressed brain? (Act 2, Scene 1)

Macbeth’s wife wants him to be a man and swallow his doubts, but he is grappling with the moral and practical questions of killing the king.  When he sees the dagger, it is partly a manifestation of his ambition.  It gives him the courage to do the deed, but it does seem to add to the impression that he is hardly sane!
Another significant quote is Macbeth’s reaction to his wife’s death.  He seems to ponder his own mortality along with hers.  She has succumbed to her own guilt at their deed, and he is getting more and more unstable.

To-morrow, and to-morrow, and to-morrow,Creeps in this petty pace from day to dayTo the last syllable of recorded time,And all our yesterdays have lighted foolsThe way to dusty death. Out, out, brief candle!Life's but a walking shadow, a poor playerThat struts and frets his hour upon the stageAnd then is heard no more: it is a taleTold by an idiot, full of sound and fury,Signifying nothing. (Act 5, Scene 5)

Macbeth has seen nothing turn out as he hoped.  He did become king, but he had to hold on to his power with more and more bloodshed, always fearing to lose it.  As he makes this speech, his wife is dead and Malcolm’s troops are storming the castle.  Macbeth’s power is threatened, and his own mortality is on his mind.

How does the relationship among Agatha, Felix and their father compare with the relationship between Victor, Elizabeth, and Victor's father?

Both the DeLacey and the Frankenstein families are close, loving families, although Felix and Agatha are much more devoted to their father and each other than is Victor Frankenstein to his family.
Initially, in Chapter 1 of Shelley's novel, narration about the Frankenstein family describes them as in relationships that involve the one cared for and the caretaker. For instance, Alphonse Frankenstein comes "like a protecting spirit" to the rescue of Caroline Beaufort who has been orphaned by the death of her father, a true friend of the senior Frankenstein. Further, Caroline Frankenstein rescues Elizabeth Lavenza, saving her from a life of poverty, and she is received by Victor as though she is a cousin. There is love in this family; as Victor tells Walton, "Everyone loved Elizabeth."Similarly, the DeLacey family, although having fallen upon misfortune, are a loving, caring family. The children of M. Delacey, a man who has lost his affluent social position in France and is now blind, are extremely respectful and devoted to him, and care for him as best they can; for instance, they go without food so that their father can eat, and they do what they can to cheer him and protect him. For example, when the creature enters the cottage in their absence, hoping to have human contact by speaking to M. DeLacey, they attack the creature upon their return and chase him out of the cottage, fearing that he means harm to their father.
Whereas the DeLaceys seem of all one mind, there is, however, diversity in the thinking of Victor, Elizabeth, and Alphonse Frankenstein. For one thing, a young Victor becomes greatly taken with the writings of Cornelius Agrippa, but his father tells him not to waste his time reading these writings: "...it is sad trash." Later, he rejects Agrippa, but he involves himself in yet another aspect of science of which his father would not approve as he commences upon the creation of a living being.
Of course, unlike Agatha and Felix DeLacey, Victor Frankenstein possesses a selfish pride that keeps him from preventing the death of his brother William and his cousin Elizabeth. Nor does he admit to his responsibility for these tragedies. He also does nothing to prevent Justine's condemnation, and he later places Elizabeth's life in danger by marrying her. Believing that the creature intends to kill him for having destroyed the female creature no matter what he does, Victor decides to have what little joy he can before his inevitable death. "Well, be it so," he says, and he marries Elizabeth. Unfortunately, this selfish attempt to attain some happiness results in not his death, but that of Elizabeth.
Certainly, then, the simple, loving relationships in the DeLacey family differ from the loving relationships of the Frankenstein family that become tragic because of the selfish interests of Victor.

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 24

Make the substitution u = sqrt(4x^2 - 9), then du = (4x)/sqrt(4x^2 - 9) dx. Inversely, dx =sqrt(4x^2 - 9)/(4x) du = u/(4x) du and 4x^2 = u^2 + 9. The limits of integration become from sqrt(3) to 3sqrt(3).
The indefinite integral becomes
int u/(4 u x^2) du = int (du)/(u^2 + 9) = 1/3 arctan(u/3) + C,
where C is an arbitrary constant.
Thus the definite integral is 1/3 (arctan(sqrt(3)) - arctan(1/sqrt(3))) = 1/3 (pi/3 - pi/6) = pi/18.

In "The Adventure of the Speckled Band," what kind of character is Helen Stoner?

Helen Stoner in "The Adventure of the Speckled Band" is a relatively flat character—to an extent, she could even be called a "stock" character, in that she represents a damsel in distress figure who comes to Holmes in order to present him with a mystery to be solved. She serves an expository function; part of the story, which is mainly narrated by Watson, is narrated by Stoner, as she explains the events which have brought her to Baker Street. The structure of this story echoes that of many of Doyle's others, in which a client comes to Baker Street and sets out their case to Holmes.
There are hints that Stoner is not an entirely reliable narrator in telling her own story. Holmes notices that she has been "cruelly used," spotting bruises on her arm and suggesting that she has been "screening" her stepfather in the telling of her tale. As such, Holmes does not pry further, but suggests that he and Watson should proceed to Stoke Moran in order to ascertain further details himself.

Helen Stoner is a typical young middle-class Victorian woman. She has always led a sheltered, protected, domestic life. She comes to Sherlock Holmes because she wants guidance. The fact that she is so frightened and helpless appeals to the compassionate side of Holmes' nature. He will help her even though she can't afford to pay him. Her stepfather, Dr. Grimesby Roylott, controls most of her resources. Helen Stoner might be termed "a maiden in distress." Holmes often gets involved with young women who are in need of help. His desire to help them provides his motivation which drives the story. Other examples of maidens in distress in Sherlock Holmes stories can be found in: "The Adventure of the Solitary Cyclist," "The Adventure of the Copper Beeches," and "A Case of Identity."
Helen Stoner is not a particularly well-rounded character. She serves mainly to involve the great detective in a perplexing case. She also gives Holmes a great deal of information in the backstory she tells when she first comes to Baker Street. Holmes not only saves Helen's life but solves the "locked room murder mystery" of her sister Julia's death two years earlier.

Is Gertrude protecting Hamlet when she says he is mad (4.1.7), or does she believe that he is mad? If she believes he is mad, does it follow that she no longer feels ashamed and guilty? Explain.

It would be difficult for Gertrude, or for any mother under the circumstances, not to believe that her son is mad after the way he has behaved. But, of course, she's nevertheless trying to protect him, to tell the others that, in spite of his violently disruptive behavior, Hamlet, given his mental condition, should not be harmed.
Gertrude does not come off as one of the more intelligent or perceptive of Shakespeare's characters. From the start, she seems not to grasp the extent to which Hamlet is traumatized by the death of his father. Nor does she grasp the hostility he feels toward his new stepfather, Claudius. Even if she is more sensitive than she seems to the real reason for Hamlet's dysfunctional manner, she's in denial about it. She wishes above all to maintain the status quo of her new marriage. To recognize why Hamlet acts as he does would destroy that marriage. At the same time, it's probable that she does feel guilt and shame—again, this is almost instinctive for any mother to do when her child is so obviously pathologically disturbed, as Hamlet is.
When Hamlet confronts her in act 3, scene 4, Gertrude is stunned into recognizing how warped Hamlet's personality has become. When she tells him, "Thou hast cleft my heart in twain," it is not only because of his hateful posture toward her but also, arguably, because she feels responsible for the situation, for what Hamlet has become and for the mayhem he's causing. At Ophelia's funeral, before Hamlet bursts onto the scene, Gertrude sadly remarks that she had wished Ophelia for his wife. This remark, perhaps more than anything else, reveals the plans Gertrude had entertained for her son to have a normal life, to become a functional person.
One could, of course, argue that even if she did not believe Hamlet to be insane, she would still try to make the others think he was in order to protect him. But, especially after he has killed Polonius without showing the slightest regret, and, moreover, after he has hallucinated a ghost (because Gertrude herself does not see the ghost, she naturally would believe Hamlet is hallucinating), why would Gertrude not think him insane? Even if Hamlet were shamming madness as part of an elaborate hoax for his purpose of revenge, any person would, in my view, have to be insane first in order to perpetrate such a ruse.

Gertrude certainly appears to think that Hamlet is insane. She tells Claudius frankly in act 4, scene 1, that he is as mad as the sea and the wind in a storm. Whether Gertrude really does think that Hamlet is mad is a matter of debate, but there seems to be little doubt that by telling Claudius that Hamlet is mad, she is putting her faith in her new husband. Now, whatever Hamlet's true psychological state, she has effectively thrown in her lot with Claudius. Her greater loyalty appears to be to him and not to her son. Gertrude's description of Hamlet's mental state validates Claudius in his plan to send Hamlet to England to have him assassinated. Of course, this is not intentional on Gertrude's part; there is nothing to suggest that she wants any harm to come to her son. However, at the very least, her growing estrangement from Hamlet means that she is no longer fully able to protect him, even if she wants to.

Using complete sentences, explain what upwelling is, how it occurs, and its importance to ocean life

Ocean upwelling is a really interesting phenomenon. Upwelling occurs when deeper ocean water near a coastline rises up to the surface region. The deeper water essentially replaces the surface waters because the surface waters have been driven away by winds. Upwelling typically occurs along coastlines that are oriented in a North-South direction. The west coast of the United States is a good example of this. Winds from the north will blow down south along the coastline. This wind direction, in combination with the rotation of the earth, causes the ocean water to move away from the coastline. The deeper water is then drawn up from below and replaces the surface waters.
Upwelling is important for ocean life because the deeper waters are nutrient rich waters. These nutrients aid in seaweed growth as well as supporting phytoplankton blooms. Both of those things have a ripple effect on the food web because they are the base organisms of many food chains.
Upwelling isn't always a blessing for marine organisms. There are many ocean organisms that produce microscopic larvae that drift in the ocean water for months. Their natural habitat might be shallower, coastal waters. Upwelling will move those surface waters away from the coast, and those organisms will be removed from their natural habitat. This will reduce their chances for survival.
https://governmentshutdown.noaa.gov/

Upwelling refers to the process of deeper ocean water rising upward to replace surface water that has been displaced by blowing winds. Upwelling can occur in coastal areas and out in the open waters of the ocean. This water from beneath is usually colder and filled with nutrients that contribute to the flourishing of seaweed and plankton near the water’s surface. As a result, marine life of various sorts are drawn to areas of upwelling, where rich ecosystems tend to exist. The location of the thermocline, which is the transition boundary between the upper, warmer waters and the deeper, colder waters impacts the processes of upwellings, with more nutrients rising to the surface in areas of shallow thermoclines than in areas of deep thermoclines.
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/eln/upw.rxml

https://governmentshutdown.noaa.gov/

https://www.nationalgeographic.org/encyclopedia/upwelling/

Describe the relationship between Robbie and Cecilia

Atonement opens with at the Country Estate of the Tallis family. Cecilia has just arrived and is reunited with Robbie, the son of the Tallis family’s cleaning lady who lives with his mother in a nearby cottage. We learn that The Tallis' more or less adopted Robbie as a child and made sure he had a proper upbringing and education. He and Ceclia grew up together, and they are on the cusp of discovering that they are in love with each other. Briony--Cecilia's 13-year-old sister--is also in love with Robbie and is jealous of the developing relationship she sees between Robbie and Cecilia. After Briony discovers Robbie and Cecilia in the middle of a sexual encounter, she is enraged and jealous and tells a lie that sends Robbie to prison for years. We then believe that Robbie Cecilia have a brief time together after the war, but we then learn in section three of the novel that both Robbie and Cecilia were killed in 1940 during the war, so their time together was actually very brief.
https://newrepublic.com/article/63386/atonement-ian-mcewan-fiction

Robbie and Cecilia are faced with feeling romantic affection towards one another while navigating the societal demands of their time that frowned upon inter-class relationships. Robbie is a young man who belongs to the working class and is dedicated to improving his social and class position through education. Cecilia is a young woman of the upper crusts of society who is expected to marry within her class to a man of prestigious standing. A tension and low-level conflict exist between the two despite their affectionate feelings for each other that could be attributed to the social and class tension that are ever present between them. The possibilities of their love are never able to be explored as Robbie is sent away to prison (when he is falsely accused of sexual assault by Cecilia's younger sister), and then onto war, while Cecilia becomes a nurse during the war. Tragically, the two never see one another again.

The relationship between Robbie and Cecilia is a bit of a mystery since the whole novel is told from Briony's perspective. Briony is younger than her sister Cecilia and is not necessarily the most reliable source. 
What we can assume about Robbie and Cecilia's relationship is that they are attracted to one another despite the socioeconomic barriers present. Robbie's family, including Robbie himself, works for Cecilia's wealthy family. He is a young working-class man, while Cecilia is a privileged daughter of an upper-class family. It is probable that a serious relationship between them, like a marriage, would be forbidden. Briony witnesses a scene between Robbie and Cecilia at the fountain of the Tallis family estate, and though she doesn't quite understand what she is seeing, it seems as though there is some underlying sexual tension between the characters. Later, Robbie gives Briony a note to deliver to Cecilia. He thinks he is giving Briony a note with an apology for breaking a valuable vase earlier that day, but actually, he hands her a note with a sexually explicit message that he wrote but did not intend to give to Cecilia. Briony's opinion of Robbie is sealed by this note, and she feels she must protect her sister from him. Later, when Lola is sexually assaulted in the dark on the estate grounds, Briony accuses Robbie. He is sent to jail and later goes to war. He and Cecilia never see each other again.
The relationship between Cecilia and Robbie is a tragic love story, one that never really properly started. It is likely that their difference in class status would have kept them apart anyway, but ultimately, it is Briony's accusation that severs the pair's budding romance forever.

In Animal Farm, what rank is Napoleon?

In Orwell's allegory for the communist Russian Revolution, Napoleon is the embodiment of complete dictatorial control in what was supposed to be a “populist” movement. He is the ultimate authority over the animal population on the farm, just as the Communist party leadership assumed absolute control over the rest of the Russian population once in power. In chapter 9, there must be a Presidential election among the farm animals, and “there was only one candidate, Napoleon, who was elected unanimously.”
Though he begins his ascent to power ostensibly as equal to the other animals, he clearly has the ambition to obtain complete control, as he does in a variety of manipulations and power grabs. Napoleon's ultimate rank as the absolute leader of the power structure on the farm is earned patiently but persistently. By the story's end, Napoleon has full authority over the lives of the other animals, much like Soviet leadership did in the years following the Bolshevik Revolution. Orwell satirically puts this hypocrisy on full display when we read his single commandment in chapter 10: “All animals are equal, but some animals are more equal than others.”

Napoleon is the highest ranking animal on the farm and is referred to as "our Leader, Comrade Napoleon." After successfully usurping power and chasing Snowball off of the farm, Napoleon rules as the farm's dictator. As a dictator, Napoleon attains supreme authority on the farm and rules with absolute power. Napoleon employs Squealer and other high-ranking pigs to enforce his political agenda, which oppresses the other animals on the farm. Napoleon is portrayed as an unscrupulous, selfish leader, who is quick to execute any animal who disagrees with his political decisions. As the supreme leader of the farm, Napoleon enjoys the privilege of living in the farmhouse, wearing Mr. Jones's clothes, drinking liquor, and amassing wealth, while the other animals toil. Napoleon also gives himself the military decorations "Animal Hero, First Class" and "Animal Hero, Second Class," which enhance his image as Commander-in-Chief.

College Algebra, Chapter 1, 1.6, Section 1.6, Problem 44

Solve the nonlinear inequality $5x^2 + 3x \geq 3x^2 + 2$. Express the solution using interval notation and graph the solution set.

$
\begin{equation}
\begin{aligned}
5x^2 + 3x & \geq 3x^2 + 2\\
\\
5x^2 - 3x^2 + 3x - 2 & \geq 0 && \text{Subtract } 3x^2 \text{ and } 2\\
\\
2x^2 + 3x - 2 & \geq 0 && \text{Factor}\\
\\
(x+2)(2x-1) & \geq 0
\end{aligned}
\end{equation}
$


The factors on the left side are $x+2$ and $2x - 1$. These factors are zero when $x$ is -2 and $\displaystyle \frac{1}{2}$ respectively. These numbers divide the real line into intervals.
$\displaystyle (-\infty, -2], \left( -2, \frac{1}{2} \right), \left[ \frac{1}{2},\infty \right)$



From the diagram, the volutions of the inequality $5x^2 + 3x \geq 3x^2 + 2$
are $(-\infty, -2] \bigcup \left[\frac{1}{2}, \infty \right)$

Firms can achieve overall, organization-wide competitive advantage through the following strategies: Competing on Differentiation Competing on Low Cost Competing on Response Pick a company you are familiar with and identify which of the above strategies it has selected. Based on this strategy, discuss how the company may have implemented each of the ten strategic OM decisions to achieve competitive advantage. (Company suggestions if needed: Walmart or Apple Inc.)

There are several companies a student might select for this assignment. One of the most interesting is Amazon, a company that has very effectively used network effects and data analytics to grow and capture market share over the past decade.
It competes in two areas, responsiveness and cost, simultaneously. Due to its storefronts existing in the cloud, it avoids many of the costs that bricks and mortar stores incur while managing to serve a national market effectively due to a superb logistics networks. Although in one sense it does not differentiate itself in terms of products, as the items it sells are normally available from other retailers, its Amazon Prime membership tends to facilitate customer loyalty, and the sheer breadth of its offerings makes it a go-to place for many shoppers. In terms of responsiveness, it offers a simple interface and sophisticated search options for shoppers, and its logistics networks ensure ultra-fast delivery.
Of the OM decisions, perhaps the most important for Amazon are logistical, encompassing supply chains, inventory, location, and scheduling. Amazon saves money by having numerous third-party sellers for which it acts as a platform, meaning that it does not deal with the physical inventory for those sellers at all. For the products that Amazon itself sells, it has an extensive regional warehouse network, has invested heavily in logistics companies, and uses data analytics extensively to predict demand and ensure it has the capability for same-day (or in some markets, one-hour) delivery.
Amazon also uses data analytics to maximize the effectiveness of human resources by analyzing multiple metrics to streamline its processes.

The story ends with a misinterpretation. How has the author prepared us to understand simultaneously how the doctor might arrive at this conclusion and how this conclusion is wrong?

First, the misinterpretation: the doctor concludes that Louise's death was precipitated by a grave shock. Since Louise suffers from a heart condition, this interpretation is only natural.
However, the author does prepare us to understand how the doctor arrives at this conclusion. She begins the first line of the story with pointed information: Mrs. Mallard has "heart trouble," so she must not receive sudden shocks. Any bad news must be broken to her gently.
The author also prepares us to understand how the doctor's conclusion is wrong. After Louise retires to her room, Chopin introduces the idea of a foreign emotion holding Louise in its grip. Until she entered her room, Louise had only shown one emotion: unrestrained grief. Now, a separate emotion threatens her composure.

There was something coming to her and she was waiting for it, fearfully. What was it? She did not know; it was too subtle and elusive to name. But she felt it, creeping out of the sky, reaching toward her through the sounds, the scents, the color that filled the air. Now her bosom rose and fell tumultuously. She was beginning to recognize this thing that was approaching to possess her, and she was striving to beat it back with her will—as powerless as her two white slender hands would have been.

At first, the emotion is "too subtle" to name. When Louise finally recognizes it for what it is, she tries to reject it. However, Chopin tells us that she is powerless to do so. In fact, the repetitively murmured "free, free, free" alerts us to Louise's frank, unadorned glee. We suddenly realize that Louise is actually looking forward to life away from the shadow of a "powerful will."
This sense of freedom is an "elixir of life" to Louise. The first moments of sheer grief have given way to a pragmatic assessment of her situation. The doctor, however, is not privy to Louise's private "feverish triumph" over her initial emotions. Because of his knowledge of Louise's heart condition, he misinterprets her cause of death.

How does Philip answer question number four on his English exam?

In Avi's Nothing But the Truth, question number four on Philip's Winter Term English exam for Margaret Narwin's class is:

What is the significance of Jack London's choice in making Buck, the dog in The Call of the Wild, the focus of his novel? Is the dog meant to be symbolic? Explain your answer. Can people learn from this portrayal of a dog? Expand on these ideas. 

Rather than provide a serious answer to this question, Philip chooses to be glib and to let his poor attitude spoil his efforts. He replies:

The significance of Buck in Jack London's novel The Call of the Wild is that Buck is symbolic of a cat. You might think that cats have nothing to do with the book, but that is the point. Dogs are willing to sit around and have writers write about them, which, in my personal opinion, makes them dumb. I think cats are smart. Cats don't like cold. A book that takes up so much time about a dog is pretty dumb. The book itself is a dog. That is what people can learn from Jack London's novel The Call of the Wild.

Miss Narwin is troubled by Philip's persistent disrespect and his lack of thoughtful intention, commenting that he needs to be "more than lazy in [his] thinking." She writes on his exam that she knows that he has the potential to do good work, particularly since his previous work has been much better; she also warns him that he is in danger of failing the class and gives him a "C-" on the grade.
This grade puts Philip's position on the track team in jeopardy, but still Philip can't seem to take responsibility for his own poor work ethic. He lashes out and tells Coach Jamison that he is only doing poorly because Miss Narwin doesn't like him and is too "old-fashioned" and "boring." Coach Jamison is sympathetic but informs Philip that he won't even be allowed to try out for the team. 

Why does George not want Lennie to talk to their boss when they report for work in the morning?

Before George and Lennie meet the boss, George tells Lennie to "jus' stand there and don't say nothing." He explains to Lennie that if he starts talking, the boss will find out that he's "crazy" and then they won't get the jobs on the ranch. Although George appreciates that the boss will hear Lennie talk eventually, he knows that if he sees Lennie work first, then he will be so impressed by Lennie's strength and work ethic that it will make no difference if he then hears Lennie talk afterwards.
The novel is set in the 1930's, and the need to secure a job was especially important at this time. Indeed, because of the Great Depression, jobs were relatively scarce, and this situation was exacerbated by the huge dust storms which destroyed the fertile topsoil of much of the farmland across America. Consequently, many migrant workers, like George and Lennie, travelled to California, where the land was still fertile, in search of work. This meant that more and more workers, like George and Lennie, were competing for fewer and fewer jobs. George is very much aware of this, and so is desperate to secure the jobs on the ranch. He tells Lennie not to speak because he knows that if he does, the boss may think that Lennie is crazy and offer the jobs to some other men. And if this happens, it could be a long time until George and Lennie find employment again.

George does not want Lennie to speak to their new boss because he fears that Lennie might say something that would jeopardize their jobs. George is also aware that Lennie's mental handicap is obvious and fears that their new boss will get the impression that Lennie is useless and immediately fire them after speaking to him. Lennie has difficulty speaking to others and will surely come across as unintelligent and lost. An intolerant, impatient boss would more than likely fire Lennie on the spot after assuming that he is too stupid to follow directions, complete tasks, or contribute to the farm. The boss could very well view Lennie as useless after speaking to him, which is exactly what George wants to avoid. When the boss does question Lennie, he remains silent and George continually answers for him. George then admits that Lennie is unintelligent but compliments his friend's impressive work ethic and strength. Overall, George fears that the boss will get the wrong impression of Lennie after speaking to him and fire them on the spot.

George does not want Lennie to talk when they meet the boss because Lennie may say something that may cause them not to get the job.
While they are in the clearing the night before they go to the ranch and their new job, George instructs Lennie to keep quiet when they meet the boss. He tells Lennie that he will give the boss their work tickets, "but you ain't gonna say a word."George instructs Lennie to just stand there and not say anything when they meet the new boss. "If he finds out what a crazy bastard you are, we won't get no job." However, if they do get on the job, and the boss sees how strong Lennie is and how hard he works before he hears Lennie talk, George feels that they will be "set." That is, the boss will not care that Lennie is slow mentally because he is a virtual work horse.
George has Lennie repeat over and over, "I ain't gonna say nothin'" Also, he has Lennie repeat, "An' you ain't gonna do no bad things like you done in Weed, neither.""Lennie looked puzzled. 'Like I done in Weed?'"George cannot believe that Lennie has forgotten. He says that he will not remind him for fear that Lennie will do it again.
Lennie understands and tells George that they were run out of Wood, but George counters, saying they ran on their own: "They was lookin' for us but they didn't catch us." Lennie chuckles and says that he has not forgotten that.
This conversation between Lennie and George hints at what will follow. For, the reader understands that Lennie somehow gets himself into predicaments that cause both men problems.
 
 

What is the difference between a solar flare and a prominence?

A solar flare, as defined by NASA, is an intense burst of radiation that results from the release of magnetic energy associated with the sunspots. A typical solar flare may last from few minutes to few hours and can be observed as bright areas on the Sun. Solar flares may also be accompanied by coronal mass ejection (significant release of plasma and magnetic field) and this ejection can extend up to thousands of miles from the Sun's surface. The solar flares have very broad spectrum emissions. A solar flare may present a radiation hazard to spacecraft and astronauts, and may adversely impact satellite communication.
A solar prominence, on the other hand, is a large and bright feature that extends from the Sun's surface. A prominence is anchored to the Sun's surface, unlike a flare, and is often characterized by a loop shape. A prominence is bound by the Sun's magnetic field and can last for months. A prominence can also extend up to thousands (or hundreds of thousands) of miles from the Sun's surface. These are typically harmless as compared to the solar flares.
Hope this helps.

Calculus of a Single Variable, Chapter 7, 7.6, Section 7.6, Problem 20

For an irregularly shaped planar lamina of uniform density (rho) , bounded by graphs y=f(x),y=g(x) and a<=x<=b , the mass (m) of this region is given by:
m=rhoint_a^b[f(x)-g(x)]dx
m=rhoA , where A is the area of the region.
The moments about the x- and y-axes are given by:
M_x=rhoint_a^b 1/2([f(x)]^2-[g(x)]^2)dx
M_y=rhoint_a^bx(f(x)-g(x))dx
The center of mass (barx,bary) is given by:
barx=M_y/m
bary=M_x/m
We are given:y=sqrt(x)+1,y=1/3x+1
Refer to the attached image, plot of y=sqrt(x)+1 is red in color and plot of y=1/3x+1 is blue in color.The curves intersect at (0,1) and (9,4) .
Now let's evaluate the area of the region bounded by the graphs of the given equations,
A=int_0^9((sqrt(x)+1)-(1/3x+1))dx
A=int_0^9(sqrt(x)+1-1/3x-1)dx
A=int_0^9(sqrt(x)-1/3x)dx
Evaluate using power rule,
A=[x^(1/2+1)/(1/2+1)-1/3(x^2/2)]_0^9
A=[2/3x^(3/2)-1/6x^2]_0^9
A=[2/3(9)^(3/2)-1/6(9)^2]
A=[2/3(3^2)^(3/2)-1/6(81)]
A=[2/3(3)^3-27/2]
A=[18-27/2]
A=9/2
Now let's find the moments about the x- and y-axes using the formulas stated above,
M_x=rhoint_0^9 1/2([sqrt(x)+1]^2-[1/3x+1]^2)dx
M_x=rhoint_0^9 1/2([x+2sqrt(x)+1]-[(1/3x)^2+2(1/3x)(1)+1^2])dx
M_x=rhoint_0^9 1/2(x+2sqrt(x)+1-x^2/9-2/3x-1)dx
Take the constant out,
M_x=rho/2int_0^9(x-2/3x+2sqrt(x)-x^2/9)dx
M_x=rho/2int_0^9(x/3+2(x)^(1/2)-x^2/9)dx
Apply the basic integration rules i.e sum and power rules,
M_x=rho/2[1/3(x^2/2)+2x^(1/2+1)/(1/2+1)-1/9(x^3/3)]_0^9
M_x=rho/2[x^2/6+2(2/3)x^(3/2)-x^3/27]_0^9
M_x=rho/2[x^2/6+4/3x^(3/2)-x^3/27]_0^9
M_x=rho/2[9^2/6+4/3(9)^(3/2)-9^3/27]
M_x=rho/2[81/6+4/3(3^2)^(3/2)-9^3/(9*3)]
M_x=rho/2[27/2+4/3(3^3)-27]
M_x=rho/2[27/2+36-27]
M_x=rho/2[27/2+9]
M_x=rho/2((27+18)/2)
M_x=45/4rho
M_y=rhoint_0^9x((sqrt(x)+1)-(1/3x+1))dx
M_y=rhoint_0^9x(sqrt(x)+1-1/3x-1)dx
M_y=rhoint_0^9x(x^(1/2)-1/3x)dx
M_y=rhoint_0^9(x^(3/2)-1/3x^2)dx
M_y=rho[x^(3/2+1)/(3/2+1)-1/3(x^3/3)]_0^9
M_y=rho[2/5x^(5/2)-1/9x^3]_0^9
M_y=rho[2/5(9)^(5/2)-1/9(9)^3]
M_y=rho[2/5(3^2)^(5/2)-81]
M_y=rho[2/5(3)^5-81]
M_y=rho[2/5(243)-81]
M_y=rho[486/5-81]
M_y=rho[(486-405)/5]
M_y=81/5rho
Now let's evaluate the coordinates of the center of mass by plugging in the values of the moments and area,
barx=M_y/m=M_y/(rhoA)
barx=(81/5rho)/(rho9/2)
barx=(81/5)(2/9)
barx=18/5
bary=M_x/m=M_x/(rhoA)
bary=(45/4rho)/(rho9/2)
bary=(45/4)(2/9)
bary=5/2
The center of mass is (18/5,5/2)

Show how Oscar Wilde has made the Canterville Ghost almost human by giving him complex emotions.

The Canterville Ghost is made almost human because Wilde gives him a range of complex, human emotions. We see this most clearly when the ghost has interactions with members of the Otis family. For example, when the Canterville Ghost first meets with Mr. Otis and is offered some lubrication to oil his chains, he is described as feeling "grossly insulted." Similarly, when the ghost appears before the family for the second time and is forced to flee, he is described as having broken down entirely.
In addition, in chapter 5, we see the ghost's vulnerability when he has a heart-to-heart with Virginia and asks for her help in getting to the Garden of Death.
By giving the ghost this range of emotions, Wilde transforms him into an almost human character with whom the reader can empathize and sympathize.

Can we make a comparison between Shakespeare's Julius Caesar and Othello? What are the differences and the similarities?

There are many similarities between Shakespeare's classic plays Julius Caesar and Othello. Both plays are tragedies, where the tragic heroes have inherent character flaws that lead to their demise. In Julius Caesar, Brutus's tragic flaws are his nobility and naive personality, while Othello's tragic flaw is his jealous nature. Both tragic heroes are manipulated by characters they believe are genuine, trustworthy friends. For example, Cassius manipulates Brutus into joining the conspirators and assassinating Julius Caesar, while Iago continually manipulates Othello into believing that Desdemona is having an affair with Michael Cassio. Both tragic heroes also commit suicide at the end of each play.
Despite the many similarities, both plays have significantly different themes, settings, and elements. Julius Caesar focuses on the assassination of Julius Caesar and its outcome, while Othello concerns Iago's attempts to undermine and ruin Othello, who overlooked him in favor of Michael Cassio. Julius Caesar examines political upheaval, ambition, and codes of honor, while Othello explores the themes of jealousy, prejudice, and manipulation. The settings are also significantly different. Othello is set in Venice and Cyprus, while Julius Caesar takes place in ancient Rome.

You absolutely can compare Julius Caesar with Othello. The two plays are both tragedies, so they share many similarities. Both focus on tragic heroes (Brutus in Julius Caesar and Othello in Othello) who meet their end when external forces exploit their weaknesses. Brutus, for instance, allows his sense of honor to blind him to the cruel reality of politics, while Iago uses Othello's tendency to be jealous to destroy him. Thus, at a very basic level, the two plays have similar structures and focus on similarly tragic heroes. 
Although there are similarities between the two plays, there are also many differences. Julius Caesar, for instance, is a sweeping investigation of political scheming, the value of freedom and representational government, personal codes of honor, and the power of mob mentality. It is, in other words, a sprawling and epic look at the nature of government and the perils of trying to correct a corrupt system. Othello, on the other hand, is much more tightly constructed, as it focuses almost completely on Othello's relationship with Desdemona and Iago's efforts to destroy it. The play focuses on domestic themes, such as infidelity and jealousy, and it largely avoids tackling the public world of politics. As such, if both plays are similarly tragic, then they approach their tragic subject matter very differently, as Julius Caesar opts for epic political drama, while Othello examines the much more intimate world of relationships. 

In The Great Gatsby, what argument is F. Scott Fitzgerald making about the American Dream, based on the desires and fates of the characters?

The essence of the American Dream is the rags-to-riches tale where someone achieves greatness through their own hard work. In this story, Gatsby comes from extremely humble origins but has managed, by the time he is a young man, to make a modest success of himself. He wins Daisy's love, even though she is his social better, but even at this point he still feels that she is too good for him and feels a sense of conquest in achieving her. His feeling that she will not stay with him, however, seems borne out by the fact that when he is away at war, she does not wait for him, but marries someone of her own social class. This is the end of Gatsby's first American Dream: he's been taught that making a success of oneself does not actually enable someone to become equal with people who were born rich.
After this knockback, then, instead of abandoning the American Dream, Gatsby simply doubles down in his pursuit of it. Having found that honest hard work has not allowed Gatsby access to the upper echelons of society as promised, he instead sets out to make himself phenomenally wealthy through illegal pursuits and lying about his upbringing. When everyone believes that Gatsby is an Oxford graduate from a rich family, he is then able to become the center of social activity in the area, but he still cannot have Daisy. The difference between Gatsby, "new money," and Daisy, "old money," is symbolized by the space between West Egg and East Egg. Gatsby has done all of this to make himself someone Daisy might be willing to be with in public, but he still does not achieve what he wanted; he has put in a huge amount of hard work but he still does not win Daisy.
When, at the end of the novel, Gatsby is revealed to have come from humble origins, he loses everything in the eyes of the shallow, "old money" crowd of East Egg. Thus, being a self-made man has not enabled him to make his own destiny: he is still distanced from those who were born into money because they do not actually respect him, knowing that he has come from nothing. In this novel, then, it seems that the argument Fitzgerald is ultimately making is that the American Dream is hollow, or else that Gatsby himself has misunderstood the dream.

Fitzgerald examines the vain pursuit of the American Dream throughout the novel The Great Gatsby. The idea of the American Dream revolves around the assumption that individuals can attain social status and wealth by working hard. Jay Gatsby embodies the idea of the American Dream throughout the novel. His quick ascension to the upper class and extraordinary wealth is the result of his hard work and dedication. However, his dream of marrying Daisy is unfulfilled because he lacks the ability to provide a secure relationship due to his illegal occupation as a bootlegger. As a result, Gatsby's amassed wealth means nothing. His emphasis on superficial items was not enough to win Daisy's heart. Even though he attained what many consider to be the American Dream, he died lonely and unappreciated. Other characters who also attained the American Dream through financial freedom and social status live fruitless, superficial lives. Both Tom and Daisy have attained the American Dream, but they are not happily married and continually cheat on one another. Myrtle Wilson is another character who attempts to climb the social ladder in hopes of attaining the American Dream. Unfortunately, she dies in a fatal accident and never achieves her goal of living a wealthy, secure life with Tom. Once again, Fitzgerald illustrates how the vain pursuit of money and social status, the preeminent characteristics of the American Dream, is unfulfilling and empty.

The idea of the American Dream is a huge theme in The Great Gatsby. Each character is searching for his/ her version of the American Dream. Typically, the American Dream refers to the belief that one can start with nothing and ultimately succeed through hard work. For Jay Gatsby, this belief is extremely important. He started with nothing, and through hard work was able to amass a great deal of wealth. Gatsby is considered "new money," while other main characters (Tom and Daisy) are "old money." Gatsby wants to be on Daisy's level, and he tries to show off his wealth to her every chance he gets with lavish parties and his collection of custom shirts. His American Dream is to prove his worth to and win over Daisy, by proving he can provide for her.
Fitzgerald seems to be warning his audience about the pitfalls of pursuing the American Dream. Gatsby is never truly accepted by Tom and Daisy, and in the end, Daisy chooses not to be with Gatsby despite his wealth. Gatsby ultimately dies in pursuit of his American Dream—shot and left for dead in his swimming pool. His attempt to achieve the American Dream was unsuccessful.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 95

Solve for the value of constant $c$ such that the line $\displaystyle y = \frac{3}{2}x + 6$ is tangent to the
curve $y = c \sqrt{x}$

If the line is tangent to the curve at some point, it means that the first derivative of the curve is equal
to the slope of the line and by inspection, the slope of the line $\displaystyle \frac{3}{2}$ by the formula
$y = mx + b $, where $m$ is the slope.

Taking the first derivative of the curve with respect to $x$

$
\begin{equation}
\begin{aligned}
y &= c \sqrt{x}\\
\\
y'&= \text{slope} = c \left( \frac{1}{2\sqrt{x}}\right)\\
\\
\frac{c}{\cancel{2}\sqrt{x}} &= \frac{3}{\cancel{2}} && \text{Using cross multiplication}\\
\\
c &= 3\sqrt{x}
\end{aligned}
\end{equation}
$


Also, if the line is tangent to the curve, they instersect at one point and the line passes through
the curve therefore we can equate both equations.
$\displaystyle c \sqrt{x} = \frac{3}{2}x + 6$
but the value of $c = 3\sqrt{x}$
$ \displaystyle 3 \sqrt{x}(\sqrt{x}) = \frac{3}{2}x +6$
$\displaystyle 3x = \frac{3}{2}x +6 $

Solving for $x$:
$x = 4$

Now, solving for $c$, we substitute the value of $x$

$
c = 3 \sqrt{x}\\
c = 3 \sqrt{4}\\
\boxed{c = 6}
$

College Algebra, Chapter 3, 3.5, Section 3.5, Problem 54

The graph of $g$ is given below. Sketch the graphs of the following functions.







a.) $y = g(x + 1)$

The graph of $y = g(x + 1)$ is the graph of $g(x)$ that is shifted 1 unit to the left.







b.) $y = g(-x)$

The graph of $y = g(-x)$ is the graph of $g(x)$ that is reflected about $y$-axis.







c.) $y = g(x - 2)$

The graph of $y = g(x - 2)$ is the graph of $g(x)$ that is shifted 2 units to the right.







d.) $y = g(x) - 2$

The graph of $y = g(x) - 2$ is the graph of $g(x)$ that is shifted 2 units downward.







e.) $y = -g(x)$

The graph of $y = -g(x)$ is the graph of $g(x)$ that is reflected about $x$-axis.







f.) $y = 2g (x)$

The graph of $y = 2g (x)$ is the graph og $g(x)$ that is stretched vertically by a factor of 2.

College Algebra, Chapter 1, 1.6, Section 1.6, Problem 10

Suppose that $\displaystyle s = \left\{ -2, -1, 0, \frac{1}{2}, 1, \sqrt{2}, 2, 4 \right\}$. Determine which element of $s$ satisfy the inequality $\displaystyle x^2 + 2 < 4$.


$
\begin{equation}
\begin{aligned}

& x^2 + 2 < 4
&& \text{Subtract } 4
\\
\\
& x^2 - 2 < 0
&& \text{Difference of squares}
\\
\\
& (x + \sqrt{2})(x - \sqrt{2}) \text{ and } x + \sqrt{2} < 0
&&
\\
\\
& x - \sqrt{2} < 0 \text{ and } x + \sqrt{2} < 0
&&
\\
\\
& x< \sqrt{2} \qquad x < - \sqrt{2}

\end{aligned}
\end{equation}
$


Thus, the solution set is the union of the two intervals $\displaystyle \left\{ -2, -2, 0, \frac{1}{2}, 1 \right\}$ satistfy the inequality.

Calculus: Early Transcendentals, Chapter 5, 5.5, Section 5.5, Problem 73

You need to solve the definite integral, using fundamental theorem of calculus, such that:
int_a^b f(x) dx = F(b) - F(a)
First, you need to solve the indefinite integral int (dx)/((1+sqrt x)^4) , using the substitution 1 + sqrt x = t such that:
1 + sqrt x = t => 1/(2sqrt x) dx = dt => dx = 2(t-1)dt
int (dx)/((1+sqrt x)^4) = int (2(t-1)dt)/(t^4)
int (2(t-1)dt)/(t^4) = int (2t)/(t^4)dt - int 2/(t^4) dt
int (2(t-1)dt)/(t^4) = int 2/(t^3)dt - int 2/(t^4) dt
int (2(t-1)dt)/(t^4) = int 2*(t^(-3))dt - int 2*(t^(-4)) dt
int (2(t-1)dt)/(t^4) = 2*(t^(-2))/(-2) - 2(t^(-3))/(-3) + c
int (2(t-1)dt)/(t^4) = -1/(t^2) + 2/(3t^3) + c
Replacing back 1 + sqrt x for t yields:
int (dx)/((1+sqrt x)^4) = -1/((1 + sqrt x)^2) + 2/(3(1 + sqrt x)^3) + c
Calculating the integral yields:
int_0^1 (dx)/((1+sqrt x)^4) = (-1/((1 + sqrt x)^2) + 2/(3(1 + sqrt x)^3))|_0^1
int_0^1 (dx)/((1+sqrt x)^4) = (-1/((1 + 1)^2) + 2/(3(1 + 1)^3) + 1/((1 + 0)^2) - 2/(3(1 + 0)^3))
int_0^1 (dx)/((1+sqrt x)^4) = -1/4 + 1/12 + 1 - 2/3
int_0^1 (dx)/((1+sqrt x)^4) = (-3 + 1 + 12 - 8)/12
int_0^1 (dx)/((1+sqrt x)^4) = 2/12
int_0^1 (dx)/((1+sqrt x)^4) = 1/6
Hence, evaluating the definite integral, using the fundamental theorem of calculus, yields int_0^1 (dx)/((1+sqrt x)^4) = 1/6.

A major issue in Chapter 21 surrounds the determination of whether a case falls within UCC Article 2. First, think about about the type of item involved. Next, determine if the contract is for the sale of goods, services, or a mixture of both. With this in mind, please discuss the relevant issues from the following fact pattern. Mrs. Downing was fitted for dentures by her dentist, Dr. Cook. After she received her dentures, Mrs. Downing began experiencing mouth pain that she attributed to Dr. Cook's manufacture of dentures that did not properly fit her properly. Mrs. Downing filed suit against Dr. Book for breach of warranty under Article 2 of the UCC. Dr. Cook defended on the grounds that his denture work was a service and therefore not covered under Article 2 warranties. Decide the case. Explain your reasoning.

Article 2 of the UCC was intended to refer to goods—“all things that are movable at the time of identification to a contract for sale.” It does not provide any direct advice concerning mixed goods and service contracts, where services are “intangible commodit[ies] in the form of human effort, such as labor, skill, or advice.” As such, suppliers of mixed goods and services often argue that Article 2 does not apply by declaring that they have provided a service only. 
In this case, the contract was evidently for a mixture of goods and services. The dentist's work in assessing Mrs. Downing's mouth and then fitting the dentures constituted a service. However, it is stated that he manufactured the dentures himself; thus, he is responsible for creating an inappropriate good: the dentures were "movable at the time of identification to a contract for sale." Unfortunately for Mrs Downing, this does not mean she is entitled to claim under Article 2. 
A number of courts have considered whether mixed contracts contain "implied warranties." The dentist here is arguing that they do not: he suggests that because the contract was not purely one in goods, common law, rather than UCC, must apply. It can be argued that this interpretation is a form of deception—the seller (the dentist) did not stipulate outright at the point of sale that an implied warranty did not exist here. However, it is usually only if the seller can be proven to have used this deception—failure to declare the non-application of an implied warranty—repeatedly that a court would rule in favor of Mrs. Downing. Because there was no warranty specifically agreed on at the point of sale, Mrs. Downing cannot sue for breach of warranty in this case.
https://digitalcommons.law.yale.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1047&context=student_papers

Write, using historical evidence, your interpretation of John Winthrop's statement about the Massachusetts bay colony being "a city on top of a hill" and "a beacon to mankind."

John Winthrop stated that the Massachusetts Bay Colony would be “a city on top of a hill” and “a beacon to mankind.” John Winthrop believed this colony would be a shining example for the rest of the world about living rightfully. The city on a hill refers to the city of Boston.
The Puritans came to the New World because they wanted religious freedom. They believed that each person’s fate was predetermined at birth by God. A person could not alter one’s fate. The Puritans hoped to show the world that they could establish a colony that successfully followed the religious principles in which they believed. They established an elected legislature allowing for the Puritans to govern themselves. Over 14,000 Puritan settlers came to this colony to practice their religious beliefs. The Puritans showed that their plan could be successful and be a model for others to follow.
The Puritans believed that God will take out his wrath on those who did not follow God’s will. Winthrop hoped that by showing the world that people could care for and love each other—while not forcing religion onto anybody—religious faith would naturally be developed. This is the same idea that the Quakers believed and used in their settlements many years later.
Being a city on a hill will shine a spotlight on this colony. Winthrop believed previous settlements, such as the one at Jamestown, had failed because God did not want these settlements to thrive. Winthrop wanted the people of his settlement to choose life and show the world that a settlement could thrive following the virtues in which the Puritans believed. In some ways, this idea was very idealistic. This idealism was seen in future American documents such as the Declaration of Independence and the Constitution.
John Winthrop hoped that his settlement would become a model for others to follow in the future. Some of the Puritan ideals and beliefs can be seen in the Quaker settlements and in future documents in American history. The American Revolution also became a model for other revolutions elsewhere.
https://thehistoricpresent.com/2010/06/28/the-city-upon-a-hill-and-puritan-hubris/

https://www.ushistory.org/us/3c.asp

Calculus of a Single Variable, Chapter 8, 8.2, Section 8.2, Problem 30

int e^(4x)cos(2x)dx
To solve, apply integration by parts int u dv = u*v - int vdu .
In the given integral, the let the u and dv be:

u = e^(4x)
dv = cos(2x)dx

Then, take the derivative of u to get du. Also, take the integral of dv to get v.

du = e^(4x)*4dx
du = 4e^(4x)dx
intdv = int cos(2x)dx
v = (sin(2x))/2

Substituting them to the integration by parts formula yields
int e^(4x)cos(2x)dx= e^(4x)*(sin(2x))/2 - int (sin(2x))/2 * 4e^(4x)dx
int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 - int 2e^(4x)sin(2x)dx
For the integral at the right side, apply integration by parts again. Let the u and dv be:

u = 2e^(4x)
dv = sin(2x)dx

Take the derivative of u and take the integral of dv to get du and v, respectively.

du = 2e^(4x)*4dx
du = 8e^(4x)dx
int dv = int sin(2x)dx
v = -cos(2x)/2

Plug-in them to the formula of integration by parts.
int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 - int 2e^(4x)sin(2x)dx
int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 - [2e^(4x)*(-(cos(2x))/2) - int (-(cos(2x))/2)*8e^(4x)dx]
int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 - [-e^(4x)cos(2x)+int 4e^(4x)cos(2x)dx]
int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 +e^(4x)cos(2x) - 4int e^(4x)cos(2x)dx
Since the integrals at the left and right side of the equation are like terms, bring them together on one side.
int e^(4x)cos(2x)dx+4int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 +e^(4x)cos(2x)
The left side simplifies to
5int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/2 +e^(4x)cos(2x)
Isolating the integral, the equation becomes
int e^(4x)cos(2x)dx= ((e^(4x)sin(2x))/2 +e^(4x)cos(2x)) * 1/5
int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/10 +(e^(4x)cos(2x))/5
Since it is an indefinite integral, add C at the right side.
Therefore,
int e^(4x)cos(2x)dx= (e^(4x)sin(2x))/10 +(e^(4x)cos(2x))/5+C .

Can I have a summary of the car ride up to Jay Mountain from Johnny's point of view in chapter 6 please?

In chapter 6, the boys are eating at Dairy Queen when Johnny mentions that he is going to turn himself in. Johnny elaborates on his reasoning before asking Dally if his parents asked about him. Dally directly responds by saying "No," which upsets Johnny. On the car ride back to Jay Mountain, Ponyboy mentions that he felt bad for Johnny before Dally begins questioning his decision to turn himself in. Johnny admits to being scared of the police and simply stares at the floor of the car. Dally then tells Johnny that he is not mad at him and is worried about what will happen to Johnny when he goes to jail. Dally says,

You get hardened in jail. I don't want that to happen to you. Like it happened to me" (Hinton, 76).

Johnny then asks Dally if he would prefer Johnny to live in hideouts his entire life. Dally responds by saying "yes," at which point the boys arrive at the top of Jay Mountain to discover that it is in flames.
Throughout the car ride, Johnny experiences several different emotions. Initially, Johnny is upset at the fact that his parents do not care about him. Johnny is more than likely thinking about how no one, except for his friends, cares about him in the world. When Dally questions Johnny about turning himself in, Johnny more than likely begins to question his decision. Johnny probably begins to realize that Dally really cares about him when he mentions that he is worried about what will happen to him in jail. Dally's display of affection more than likely cheers up Johnny, who continues to think about his decision to turn himself in. 

"Romance at short notice was her speciality." Justify this observation about Vera.

The term "romance" is usually associated with love stories, but the definition of the word, according to the Merriam-Webster online dictionary includes these meanings:


a (1) :  a medieval tale based on legend, chivalric love and adventure, or the supernatural (2) : a prose narrative treating imaginary characters involved in events remote in time or place and usually heroic, adventurous, or mysterious 


2:  something (as an extravagant story or account) that lacks basis in fact

When the narrator of "The Open Window" says that "Romance at short notice was her specialty" it means that Vera was adept in making up "extravagant" stories full of mysterious events. No doubt Vera likes that kind of reading material herself. H. Ryder Haggard's popular Victorian novels would be good examples. Vera is obviously bored with her confinement in an English country manor and must be indulging in escapism in her reading as well as in her own imagination. 
 
Vera invents two stories on the spur of the moment. One she tells her visitor Framton Nuttel when they first meet. She only has a few minutes before her aunt will appear and take over as hostess. During that time Vera tells Nuttel how her aunt's husband and two brothers were sucked into a bog three years ago and never seen again. Her story sets Framton up to believe he is seeing ghosts when the three men appear outside headed towards the open window. Then at the end Vera invents another lurid story to explain Framton Nuttel's sudden disappearance.


"A most extraordinary man, a Mr. Nuttel," said Mrs. Sappleton; "could only talk about his illnesses, and dashed off without a word of goodby or apology when you arrived. One would think he had seen a ghost."
"I expect it was the spaniel," said the niece calmly; "he told me he had a horror of dogs. He was once hunted into a cemetery somewhere on the banks of the Ganges by a pack of pariah dogs, and had to spend the night in a newly dug grave with the creatures snarling and grinning and foaming just above him. Enough to make anyone lose their nerve."

Vera is an exceptionally intelligent and creative girl. Yet she must have gotten some help from her reading when she invented the story about a man being hunted by a pack of pariah dogs and spending the night in a newly dug grave.

In what ways is Douglass’s Narrative a work of abolitionist propaganda? In what ways is it a historical source on the nature and arguments of the abolition movement in antebellum America?

Propaganda is information used to promote or support a particular point of view. Propaganda is usually understood to be distorted or false, but Douglass's work is not that type of propaganda. It is propaganda, however, in that it is consistently "on message" that slavery is an indefensible and immoral evil.
The Narrative also acts as abolitionist propaganda in that it weaves in answers to the objections to freeing slaves that white people most often made in that period. One objection was that slaves, if questioned, usually said they were content and happy with their lot. Douglass vehemently opposes the truth of that idea, stating that slaves are afraid of severe reprisals if they do not lie. He recounts the story of a slave who complained about his lot, only to be sold down South into a much worse situation.
Whites also used the argument that the slaves' tendency to sing showed they were happy. Douglass argues that this singing derives from their deep grief over their enslavement. Finally, pro-slavery individuals often stated that the Christianity of the owners made them more compassionate to the slaves: Douglass argues that the opposite is true, stating that "conversion experiences" create harsher masters, who now have Biblical dispensation to oppress the slaves.
The Narrative is most powerful as an authoritative first-person account of what it was like to be a slave from the perspective of a slave. It aligns with abolitionist aims in unequivocally showing slavery to be a cruel and dehumanizing institution that destroys the lives of slaves and corrupts the souls of masters. Near the end of the account, Douglass also provides information about abolitionism directly, such as describing the way The Liberator, an abolitionist newspaper, spoke to his condition and fired him up to become part of the abolitionist movement.

In Frederick Douglas's autobiographic novel Narrative of the Life of Frederick Douglass, An American Slave, Douglas tells the horrific story of his life under slavery and his path to freedom. The books serves as an abolitionist piece due to the horrifying truths that are told by Douglas and due to the fact that Douglas was a staunch abolitionist who spent his life as a free man working to end the evils of slavery. He wrote from an abolitionist perspective and it permeates the pages of his novel.
This book is a historical source on the abolitionist movement, as it is Douglas's true story. Readers are able to gain perspective from a man who was both formerly enslaved as well as a fierce and determined abolitionist. Exposing the horrors of slavery and making moral arguments against its use was a major part of the abolitionist movement. Douglas's autobiography uses this strategy to bring the antislavery appeal to the hearts and minds of those reading and to provide hope and encouragement to anyone who was still enslaved and reading his words.

Frederick Douglass's narrative is preceded by two introductions. The first is by William Lloyd Garrison, the editor of the abolitionist newspaper The Liberator. Garrison recalls having seen Douglass speak at an abolitionist conference in Nantucket in 1841. Garrison is a white man who must vouch for the credibility of Douglass, a black man. Many readers might have thought at the time that a former slave could not have been as eloquent and learned as Douglass, who writes with a literary, learned style. At the time, Garrison, and Wendell Phillips, a white Boston abolitionist who wrote the next introduction, had to give Douglass his bona fides, or his credibility. Douglass's work is a product of the abolitionist movement and uses its arguments, such as that slavery degrades the white people who perpetuate it. The work is also an artifact of the abolitionist movement and shows that it was controlled by whites, not by blacks.

Frederick Douglass's Narrative is one of the best known slave narratives. New England abolitionists, particularly William Lloyd Garrison, the editor of the abolitionist newspaper The Liberator, encouraged Douglass to tell his story of life on a Maryland plantation in an effort to end slavery.
Because the narrative is based on the actual events of Douglass's life, it serves as a historical source. It is a key piece of abolitionist propaganda because the tales of Douglass's suffering gave credence to abolitionists' insistence on the evils of slavery. 
Douglass was the product of rape, like many slave children. His mother, also a slave, had been raped by an unknown white man. He witnessed brutal whippings, including the brutalization of his aunt, and he suffered periods of starvation and cold. 
After spending several comfortable years in Baltimore with the ship carpenter, Hugh Auld, where he had learned to read, he was sent to work on a farm in Maryland. There, he came under the control of the slave-breaker, Edward Covey. "Slave-breaking" involved daily beatings, starvation, and, sometimes, more creative methods of cruelty. Covey's treatment left Douglass "broken" spiritually.
It is possible that if not for his literacy, which allowed him to access a world beyond that of cruelty, Douglass might not have escaped to the North to become not only an abolitionist but a living example of resilience.

What is Creon's reason for not wanting to be king?

When Oedipus accuses Creon of conspiring to depose him and take over the rule of Thebes, Creon explains that he already gets all the benefits of being king without any of the downsides. Because he is so close to Oedipus, people fawn over him, wishing him "Godspeed." They try to gain his favor. He has a voice in policy, in fact, what he calls "boundless influence," but without any worries. He tells Oedipus:

Why should I leave the better, choose the worse?That were sheer madness, and I am not mad.No such ambition ever tempted me ...

Creon is saying that he has no ambitions of becoming ruler. He has everything he wants. This rings true, because when Laius was killed, Creon could have had the throne—in fact, that was what Laius wanted. Instead, he offered it to anyone who could free Thebes from the Sphinx by solving its riddle. Oedipus did so, and Creon had him crowned and gave him Jocasta as his wife. Creon has not shown any resentment of Oedipus since. It is clear that Oedipus's accusations come from his own growing desperation. He lashes out because he doesn't want to face the truth.

Creon presents several arguments for why he would not want to be king. First, he asks Oedipus,

I bid thee think, Would any mortal choose a troubled reign Of terrors rather than secure repose, If the same power were given him? As for me, I have no natural craving for the name Of king, preferring to do kingly deeds, And so thinks every sober-minded man.

In other words, he asks why someone would choose to reign during troubled times instead of resting, secure in one's position and family ties? Creon believes that he already wields a great deal of power and has a high status in the kingdom (as brother-in-law to the king); why would he trade his ability to relax for an obligation to rule? Further, he says that he is simply not ambitious to be the king; he would rather do "kingly deeds," perhaps aiding the kingdom and its citizens, without actually having all the responsibilities a king must take on. Moreover, he says,

were I king, My acts would oft run counter to my will. How could a title then have charms for me Above the sweets of boundless influence?

If he were the king, Creon argues, he would have to do things that he does not want to do and make decisions, perhaps, that he does not want to make. Therefore, why would he trade his "boundless influence" and lack of responsibility for the title of king? It would only guarantee him more troubles and concerns.

Creon doesn't want to be the king because he gets a lot more stress and responsibility without extra benefits.
Creon is the brother-in-law of Oedipus Rex, the king of Thebes. His sister married Oedipus. If he wanted to be the king, Creon could have been—he was already ruling over the city after the death of the last ruler. He gave Oedipus the crown after Oedipus defeated the Sphinx and saved the city.
Creon explains that he doesn't want to be the king because it brings a lot more problems and stress to him. As the brother-in-law of the king, he already has access to the power and favor that Oedipus had. People come to him for favors, and he has lots of influence over the country and its people.
If he became the king, he'd have the same influence but a lot more problems. He'd be responsible for Thebes. He'd have to keep its people safe and secure. Currently, he's not responsible for those things. He says:

As for me, I have no natural craving for the name / Of king, preferring to do kingly deeds, / And so thinks every sober-minded man. / Now all my needs are satisfied through thee, / And I have naught to fear; but were I king, / My acts would oft run counter to my will. / How could a title then have charms for me / Above the sweets of boundless influence?

Throughout the play, Creon is displeased with the potential necessity of becoming king. He wants to stay in the position he has—but of course, things don't work out for him in the long run.

Why is chapter 10 in Gary Schmidt's Okay for Now called "The Arctic Tern"?

"The Arctic Tern" refers to the title of the very first plate drawn by John James Audubon that Doug looked at and admired his first time visiting the library. The plate depicts a bird called an Arctic tern that is actually very symbolic of Doug and the young woman who becomes his girlfriend, Lil. Since seeing the drawing of the bird for the first time, Doug has learned how to create his own drawings, and the lesson of drawing, as well as the Audubon plates, has changed his life. The title of the final chapter of the book reflects just how much Doug's life has been changed by The Arctic Tern and what the bird symbolizes.As soon as Doug sees the plate of the bird, he thinks it's the most beautiful picture he has ever seen. He sees it as a picture of the bird being all by itself and falling without a "single thing in the world that cared at all" (p. 21). What strikes Doug most is bird's "round and terrified eye" (p. 14). He is so struck by the drawing that he visualizes himself as having made the drawing and uses his hand to mimic the motions the artist might have used. As soon as Mr. Powell, an employee of the library, sees his interest in drawing the bird, he begins teaching Doug how to draw. Through Mr. Powell's lessons, Doug learns how to use drawing to forget his troubled home life:

You know one thing that Mr. Powell taught me? He taught me that sometimes art can make you forget everything else around you. (p. 297)

Sadly, however, the city soon begins selling the Audubon plates to pay off the city's debts. Doug makes it a personal mission to restore the plates to the library. Doug sees who has bought the plates, and by performing services, doing favors, and making compromises, Doug convinces the owners to return each plate back to the library. As a result of all he does to restore the plates, Doug matures from a troubled, scared young boy to a brave young man who is now unafraid to tackle his future. Not only does the bird's "terrified eye" in the drawing symbolize Doug's emotions at the beginning of the story, the bird itself is known for its brave and adventurous spirit. Scientists now know the Arctic tern follows the longest migratory route of any bird on record. By the end of the story, Doug and Lil are a bit terrified of their future because Lil is fighting cancer. However, Doug has confidence that they'll bravely, successfully take on the future together and likens the two of them to Arctic terns flying side by side, with Doug being the one ready to "show [her] the next spectacular thing that's going to come into [her] life" (p. 310).
http://www.bbc.com/earth/story/20160603-mystery-migration-solved

How does Nick meet Gatsby?

It's chapter 3 when Nick first meets the elusive Gatsby. He's received a personal invitation to one of Gatsby's legendarily lavish parties. This is a rare privilege indeed. Most of Gatsby's freeloading guests just show up when they feel like it and proceed to help themselves to his food and illegal booze.
While Nick's engaged in conversation with Jordan Baker, a man comes over and starts chatting to him. The man says that Nick looks kind of familiar and wonders if perhaps he served in the war. Nick doesn't know it yet, but the man in question is none other than Jay Gatsby. This scene is important because it shows us what kind of a person Gatsby is. Not only does Nick gain the privilege of a personal invitation to the party, he also gets to see a side of Gatsby that few people ever get a chance to see. The first meeting between the two men foreshadows the friendship that will develop throughout the book.

College Algebra, Chapter 10, 10.5, Section 10.5, Problem 10

Find the expected value (or expectation) of the games described.

A card is drawn from a deck. You win $\$104$ if the card is an ace, $\$26$ if it is a face card, and $\$13$ if it is the 8 of clubs.

The deck of 52 cards has four ace with probability $\displaystyle \frac{4}{52} = \frac{1}{3}$, twelve face card with probability
$\displaystyle \frac{12}{52} = \frac{3}{13}$ and one 8 of clubs with probability $\displaystyle \frac{1}{52}$.
So you get $\$104$ with probability $\displaystyle \frac{1}{3}, \$26$ with probability $\displaystyle \frac{3}{18}$
and $\$13$ with probability $\displaystyle \frac{1}{52}$. Thus, the expected value is

$\displaystyle 104 \left( \frac{1}{13} \right) + 26 \left( \frac{3}{13} \right) + 13 \left( \frac{1}{52} \right) = \frac{57}{4} = 14.25$

This means that if you play this game, you will make, $\$14.25$ per game.

What is the plot line of the story Macbeth?

The plot of William Shakespeare's Macbeth concerns the tragic downfall of the titular character as a result of his misguided ambition. In the play, Macbeth is given a prophecy that he will become king of Scotland. At the time of the prophecy, Macbeth is a hardened, loyal soldier. However, the prophecy causes him to begin to think of ways to become king. His own desires, coupled with the influences of his wife, cause him to murder Duncan, the current king of Scotland. Duncan's two sons, Malcolm and Donalbain, flee the country in fear, and Macbeth takes the throne. Once Macbeth becomes king, Scotland begins to fall into disarray. He is a terrible leader, and his paranoia causes him to fall apart and grow more fearful of almost everybody around him. After the murder of Duncan, Macbeth begins to grow more calloused toward murder, having his close friend Banquo killed, as well as the entire family of Macduff, as he begins to feel more and more afraid that his rule is being threatened. The play ends with those who love Scotland coming together under the combined might of Malcolm and Macduff, overthrowing Macbeth, and once again leading Scotland towards a bright, prosperous future.

In "Half and Half," by Amy Tan, what does the metaphor mean when the narrator writes, "My mother believed in God's will for many years. It was as if she had turned on a celestial faucet and goodness kept pouring out"?

It's a way of expressing An-mei's simple faith in God. An-mei firmly believes that her faith is responsible for all the blessings and good things she's received in life. The faucet metaphor is very useful, because it perfectly encapsulates a comforting, uncomplicated understanding of what faith in God entails. Just as when we're thirsty, we turn on a faucet to get a drink of water; when An-mei wants to enjoy the blessings of life, she places her unconditional faith in God.
But as her faith is based largely upon an almost constant flow of blessings, it's inevitable that when the "faucet" is turned off, then that faith will falter. And that's precisely what happens in the case of An-mei. For when Bing, her youngest child, falls into the sea, An-mei implores God to give her son back to her. Sadly, her prayers go unanswered and An-mei loses her faith.

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 13

f(x)=sinx+cosx
differentiating,
f'(x)=cosx-sinx
Now let us find the critical points by setting f'(x)=0,
cosx-sinx=0
cosx=sinx
tanx=1
x=pi/4 , 5pi/4
Now let us check the sign of f'(x) to find the intervals of increase or decrease by plugging test value in the intervals (0,pi/4) , (pi/4,5pi/4) and (5pi/4,2pi)
f'(pi/6)=cos(pi/6)-sin(pi/6)=(sqrt(3)-1)/2=0.36603
f'(pi)=cos(pi)-sin(pi)=-1-0=-1
f'(3pi/2)=cos(3pi/2)-sin(3pi/2)=0-(-1)=1
Since f'(pi/6) is positive , so the function is increasing in the interval(0.pi/4)
f'(pi) is negative , so the function is decreasing in the interval (pi/4,5pi/4)
f'(3pi/2) is positive , so the function is increasing in the interval (5pi/4,2pi)
So the function has Local maximum at x=pi/4 and Local minimum at x=5pi/4
f(pi/4)=sin(pi/4)+cos(pi/4)=1/sqrt(2)+1/sqrt(2)=sqrt(2)
f(5pi/4)=sin(5pi/4)+cos(5pi/4)=-1/sqrt(2)-1/sqrt(2)=-sqrt(2)
Now to find the intervals of concavity and points of inflection, let us find the second derivative of the function,
f''(x)=-sin(x)-cos(x)
-sinx-cosx=0
tanx=-1
x=3pi/4 , 7pi/4
Now let us find the sign of f''(x) by plugging test points in the intervals (0,3pi/4) , (3pi/4,7pi/4) and (7pi/4,2pi)
f''(pi/2)=-sin(pi/2)-cos(pi/2)=-1-0=-1
f''(pi)=-sin(pi)-cos(pi)=-0-(-1)=1
f''(15pi/16)=-sin(15pi/16)-cos(15pi/16)=0.78569
Since f''(pi/2) is negative , so the function is concave down in the interval (0,3pi/4)
f''(pi) is positive , so the function is concave up in the interval (3pi/4 , 7pi/4)
f''(15pi/16) is positive , so the function is concave up in the interval (7pi/4,2pi)
Since the concavity is changing so x=3pi/4 and 7pi/4 are the inflection points

Explain what brought about the economic depression of the late 1830s and the emergence of the Whig party.

The economic depression of the 1830s occurred because of a series of poor decisions made by Andrew Jackson and state banks. Andrew Jackson disliked the national bank and, in 1832, vetoed the extension of its charter. However, the national bank’s charter ran until 1836, meaning the bank would continue to exist for the next four years. To reduce the effectiveness of the national bank, President Jackson deposited federal funds in state banks (also called "pet banks"). These banks had more lenient lending policies, and many Americans went to get loans from these banks in order to buy western land.
When Andrew Jackson realized that the speculation in western land was getting out of control, he issued the Specie Circular, which stated that land sales had to be made with gold and silver. However, this policy wouldn’t take effect until after the election of 1836. Once the policy went into effect, the economy slowed significantly, in part because people didn't have access to gold and silver.
The Whig Party emerged to challenge Andrew Jackson, whom they referred to as King Andrew. This party disliked Andrew Jackson’s policies toward the national bank and disliked how he ignored decisions of the Supreme Court. When the economy slumped in 1837, Martin Van Buren followed a laissez-faire policy regarding the government’s role in ending the depression. As the depression lingered, people grew frustrated with Van Buren’s hands-off policy. The Whig Party, on the other hand, wanted the federal government to take steps to ease the effects of the depression. These steps included re-establishing a national bank, passing legislation to provide relief for the American people, and giving a portion of land sales to the states. The willingness of the Whig Party to try to do things to help end the depression helped them win the presidency in 1840.

The Panic of 1837, one of the largest economic depressions in American history, was caused when Andrew Jackson did not renew the charter of the Bank of the United States. Instead, he put money into state banks which curried his favor.  These state banks made bad loans and right before the Panic there was a bubble in land speculation.  When the bubble burst, the economy crashed and people blamed Martin Van Buren, Jackson's handpicked successor, even though it was due to Jackson's fiscal policies.  
The Whig Party started because of Jackson's use of the veto.  Jackson issued more vetoes than any president before him.  They resented that Jackson did not want to use federal dollars on internal improvements.  The Whig Party formed in order to create what would be called the National System, so the nation would become more self-sufficient with tariffs and a national infrastructure.  They also resented Jackson's campaign strategists, who tried to appeal to the common man through parades and barbecues.  Additionally, they resented Jackson's use of what would be called the spoils system, a practice in which Jackson would reward those who helped him win.  The Whig Party would adopt the spoils system for its own use and adopted many of the campaign strategies that they hated about Jackson.  

How is Dr. Manette's life in French jail?

Dr. Alexandre Manette’s life in French prison is miserable and unjust. A casualty of class warfare, he is imprisoned in the infamous Bastille for daring to expose the truth about the wickedness of rich and powerful aristocrats. The irredeemably vile Evrémonde Brothers seize Dr. Manette’s letter to the Minister of State that would have revealed their sins, and they lock him away for eighteen painful years.
While under confinement, the doctor is restricted to dark, damp quarters where human waste and infectious diseases run amok. He often suffers from hunger and exhaustion and loneliness, constantly battling for his sanity and humanity. He refuses to become a zombie, one of the “living dead.”
Dr. Manette is a man of strong will and conviction, but even the toughest men can break down in the face of such physical, emotional, and psychological torture. The doctor’s saving graces during this arduous ordeal are the love and loyalty of his daughter Lucie, his adopting the craft of shoemaking, and his ability to forgive, not holding the sins of the father and uncle against Charles Darnay.
The difficulties experienced by Charles Dickens’s own father while incarcerated in debtor’s prison when Dickens was a child greatly influenced his depictions of Dr. Manette’s prison sentence.
https://dickensmuseum.com/blogs/charles-dickens-museum/what-inspired-a-tale-of-two-cities-by-professor-michael-slater

Dr. Alexandre Manette is sent to prison on a trumped-up charge. This is his punishment for daring to expose the wicked crimes of two members of the aristocratic Evrémonde family. Dr. Manette isn't just sent to any prison; he's sent to the notorious Bastille, hated symbol of repression under the ancien regime. The Bastille is a truly horrible place. Conditions are appalling, with filth everywhere and contagious diseases running rampant. The prisoners are constantly hungry, and without any adequate exercise, they're cooped-up in their dank, dismal cells practically the whole time.
Many prisoners go out of their minds in such conditions. Amazingly, Manette somehow manages to endure eighteen long years of this mental and physical torture. But he's never quite the same again. Although he managed to stop himself from going insane in the Bastille by becoming a shoemaker, Manette has been mentally destroyed by his lengthy incarceration.

In "A Sound of Thunder" by Ray Bradbury, is it fair for Eckels to die?

This question is asking about the final moments of the story.  Eckels, Travis, and the rest of the safari group have returned to the present.  Unfortunately, it is not the present that they left earlier that day.  In the past, Eckels stepped on a butterfly which caused cataclysmic changes to occur in the timeline.  Eckels is completely blown away that such a small change in the past could have such huge consequences.  He begs for the possibility of going back in time and correcting the mistake.  That possibility is not even entertained, and Travis shoots and kills Eckels.  

Eckels moaned. He dropped to his knees. He scrabbled at the golden butterfly with shaking  fingers. "Can't we," he pleaded to the world, to himself, to the officials, to the Machine, "can't we take it back, can't we make it alive again? Can't we start over? Can't we-­" 
He did not move. Eyes shut, he waited, shivering. He heard Travis breathe loud in the room; he heard Travis shift his rifle, click the safety catch, and raise the weapon.
There was a sound of thunder.

Whether or not it is fair that Eckels dies is entirely up to individual reader opinion.  You can safely state your opinion, but remember to explain why you think what you think.  
Personally, I don't think it's fair or justified that Eckels dies.  I believe that Travis shoots Eckels more out of anger and revenge than punishment.  Nothing can be done about the changes that happened, so I don't feel that Travis shooting Eckels is a punishment.  If it were a punishment, it's a useless punishment.  It doesn't solve the problem in any way.  Killing Eckels doesn't help the situation.  Leaving Eckels alive won't cause any additional harm, either; therefore, I don't believe it is fair that Eckels dies. 

3 elements creating suspense or horror in the cask of amontillado

The foreshadowing in the first two paragraphs helps to create suspense. Montresor says that he "vowed revenge" on Fortunato, and he explains his criteria for how this must be achieved. He says, "I must not only punish, but punish with impunity [....]. I continued, as was my wont, to smile in his face, and he did not perceive that my smile now was at the thought of his immolation." Thus, we know that Montresor is going to do something horrible—something absolutely destructive—to Fortunato, as he refers to his enemy's "immolation." We also learn that Fortunato has no clue that he is in such grave danger, and we must wait to find out what horrors Montresor is going to unleash on his nemesis.
The revelation of Montresor's manipulative and cunning character also creates some horror. We learn that he is absolutely capable, intellectually and emotionally, to achieve the revenge he seeks. He tells us that his servants were all away from home: "I had told them that I should not return until the morning, and had given them explicit orders not to stir from the house. These orders were sufficient, I well knew, to insure their immediate disappearance, one and all, as soon as my back was turned." Montresor knows just how to fix things without arousing suspicion in his household. He also deflects suspicion from anyone who sees them together outside by wearing a black mask and a long black cape to disguise his identity.
Moreover, Montresor describes the nitre that clings to the walls in his vaults, calling it "'the white webwork which gleams from these cavern walls.'" Such a metaphor seems to compare the nitre to a spider's web, which makes Montresor, himself, the spider. This metaphor creates horror, indeed, because we imagine Montresor as a terrible predator and even begin to feel a little bit sorry for Fortunato, the prey who has absolutely no idea what's coming.

What is the name of Tony's grandfather's friend?

Tony's grandfather's friend is named Adam Hibbs.
According to the story Tony tells his friends, Adam Hibbs disappeared on Levy Lake (Lake Levart) years ago. At the time of Adam's disappearance, he and Tony's grandfather had been camping out along the lake.
Accordingly, Adam had awoken in the night and gone in search of his canteen, which was supposedly hung on the branches of a tree. Strangely, Adam never returned to the tent he shared with Tony's grandfather. For his part, Tony's grandfather remembered hearing the sounds of someone getting into a boat.
When Tony's grandfather investigated, he found that Adam was out in a rowboat in the middle of the lake. At the time, there was a three-quarter moon, and Adam seemed to be smiling happily. Tony's grandfather called to his friend, but Adam never answered. Eventually, some clouds eclipsed the moon, shrouding the lake area in momentary darkness. Tony's grandfather went in search of a lantern. When he returned, Adam had disappeared. No one ever heard from Adam again.
Tony tells his friends that five more people disappeared in a similar fashion within the next fifty years. All disappeared under the same conditions, and they were never heard from again.

Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 114

Graph $x-2y = -4$ using a graphing device. Verify that the graph has the correct $x-$ and $y$-intercepts.







$x$-intercept:


$
\begin{equation}
\begin{aligned}

x-2y =& -4
&& \text{Given equation}
\\
x-2(0) =& -4
&& \text{To find the $x$-intercept, let } y = 0
\\
x =& -4
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(-4,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

x-2y =& -4
&& \text{Given equation}
\\
0-2y =& -4
&& \text{To find the $y$-intercept, let } x=0
\\
-2y =& -4
&& \text{Divide by } -2
\\
y =& 2
&&

\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,2)$

a_n = sin(npi/2) Write the first five terms of the sequence.

a_n=sin (npi/2)
The subscript n represents the term number. It usually starts with n=1 which tells that a_1 is the first term.
So to determine the first five terms, plug-in n={1,2,3,4,5}.
When n=1 , the first term is:
a_1=sin (1*pi/2)
a_1=1
 When n=2 , the second term is:
a_2=sin (2*pi/2)
a_2=0
 When n=3 , the third term is:
a_3=sin (3*pi/2)
a_3=-1
 When n=4 , the fourth term is:
a_4=sin (4*pi/2)
a_4=0
And when n=5 , the fifth term is:
a_5=sin (5*pi/2)
a_5=1
 
Therefore, the first five terms of the sequence are {1, 0, -1, 0, 1}. 

y = ln(cosx) , [0,pi/3] Find the arc length of the graph of the function over the indicated interval.

The arc length of a function of x, f(x), over an interval is determined by the formula below:
L=int_a^bsqrt(1+((dy)/(dx))^2)dx
So using the function given, let us first find (dy)/(dx):
d/(dx)(ln(cos(x)))=(1/(cos(x)))*(-sin(x))=-(sin(x))/(cos(x))=-tan(x)
We can now substitute this into our formula above:
L=int_a^bsqrt(1+((dy)/(dx))^2)dx=L=int_0^(pi/3)sqrt(1+(-tan(x))^2)dx
Which can then be simplified to:
L=int_0^(pi/3)sqrt(1+tan^2(x))dx=int_0^(pi/3)sqrt(sec^2(x))dx=int_0^(pi/3)sec(x)dx
Then you find the definite integral as you normally would.  (Using the method shown on the link below, you can find the integral of sec(x).)
L=int_0^(pi/3)sec(x)dx=ln|sec(x)+tan(x)|_0^(pi/3)
L=ln(sec(pi/3)+tan(pi/3))-ln(sec(0)+tan(0))=ln(2+sqrt(3))-ln(1+0)
L=ln(2+sqrt(3))-ln(1)=ln(2+sqrt(3))~~1.32
So the exact value of the arc length of the graph of the function over the given interval is ln(2+sqrt(3))
which is approximately 1.32.
http://www.math.ubc.ca/~feldman/m121/secx.pdf

Who is Mr. Murdstone in David Copperfield?

David Copperfield first meets Mr. Murdstone as early as chapter II, "I Observe." He describes him as a large man with black hair and whiskers. From the beginning, David doesn't like him and professes that he feels jealous that his mother is giving him so much attention.
What he calls "a child's distinctive dislike" becomes a genuine hatred after Mr. Murdstone marries David's mother. One of the first things Mr. Murdstone does as David's stepfather is threaten to beat David if he upsets his mother again. As the story progresses, and Mr. Murdstone's equally cruel sister arrives, life becomes a unbearable until Mr. Murdstone finally sends David to boarding school. The school is somewhat of a relief to receiving the beatings at the hand of Mr. Murdstone and seeing the unhappiness of his own mother.

Mr. Murdstone is David Copperfield's wicked stepfather. He marries David's mother when the boy is conveniently away at the coast. When David returns home, he's in for a nasty surprise, because his new stepdad is a cruel, sadistic bully. He regularly beats David for no good reason; he dominates and controls David's mother; and for good measure, he brings his equally disgusting relatives into the house, which they proceed to take over and treat as their own.
Murdstone provides David with what he fancifully regards as gainful employment in the family wine-bottling factory, "Murdstone & Grinby." Unfortunately, this isn't much of a career move, as David is forced to slave away in a menial job, treated little better than a slave. We get the impression that his evil stepdad sent him out to work just so that he could get him out of the way.
Life at the factory becomes so utterly wretched and unbearable that David is forced to run away and find refuge with his eccentric but lovable great-aunt, Miss Betsey Trotwood. When Murdstone discovers that David has gone AWOL from the factory, he sees an opportunity to remove him from his life altogether and arranges for Miss Betsey to become David's legal guardian, but not before Betsey gives him a richly-deserved tongue-lashing for his appalling treatment of the young lad and his family.

In "Black and Latino," by Roberto Santiago, do any of the characters change? If so, what caused them to change?

"Black and Latino" is a personal essay written by Robert Santiago and originally printed in Essence magazine. As such, it is not a story but a reflection on being born and raised with a foot in two worlds, that of his heritage, which was Puerto Rican, and that of the African American, because his skin was of a dark hue.
Santiago claims that he has a black heritage as well, since Puerto Rico is close to Haiti and states that his grandparents " . . . were the classic Negro como carbon (black as carbon) people, but despite the fact that they were as dark as can be they are officially not considered black" (1). It is in this way that Santiago discusses his growing up in East Harlem and looking black but not being accepted as African American.
Santiago narrates this essay in first person, so he is not really a character. He discusses his own childhood and one incident where he faced racial discrimination. He does not change his viewpoint on racial issues throughout this essay. Instead, he is puzzled why race issues exist at all.
http://harvey.binghamton.edu/~pgay/etext/Black_and_Latino.html

Compare the Mississippi black codes, found in document 15-3, with the Civil Rights Act of 1866, found in document 15-4. Why do you think Congress believed that it had to pass the Civil Rights Act and then adopt the Fourteenth Amendment?

Since there were no documents attached, I have located a copy of the black codes in Mississippi. I am using that source along with the source for the Civil Rights Act of 1866 to respond to your question.
The black codes of Mississippi, and for that matter other states, attempted to strip African-Americans of some of the freedoms they gained after the Civil War ended. For example, these laws prohibited most former slaves from carrying weapons. Additionally, former slaves could be fined if they didn’t have a job.
These black codes convinced some people that there had to be some guarantees of the rights of the freedman. The Civil Rights Act of 1866 gave full citizenship to African-Americans. The federal government would protect these rights. When President Johnson vetoed this bill, Congress overrode the veto. This convinced the Radical Republicans that a constitutional amendment was needed to guarantee the freedoms of the former slaves. While a law can be reversed at any time, it is much more difficult to change the Constitution. Thus, if an amendment to the Constitution was made guaranteeing freedoms for all citizens, including the former slaves, it would be much more difficult to take these freedoms away.
https://www.blackpast.org/african-american-history/1866-mississippi-black-codes/

College Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 78

Suppose that $f(x) = \sqrt{x}$ and $\displaystyle g(x) = \frac{2}{x-4}$ find $f \circ g$, $g \circ f$, $f \circ f$ and $g \circ g$ and their domains

$
\begin{equation}
\begin{aligned}
f \circ g &= f(g(x)) = f\left( \frac{2}{x - 4} \right) = \sqrt{\frac{2}{x-4}}\\
\\
g \circ f &= g(f(x)) = g(\sqrt{x}) = \frac{2}{\sqrt{x}-4}\\
\\
f \circ f &= f(f(x)) = f(\sqrt{x}) = \sqrt{\sqrt{x}} = \sqrt[4]{x}\\
\\
g \circ g &= g(g(x)) = g\left( \frac{2}{x-4} \right) = \frac{2}{\frac{2}{x-4}-4}\\
\\
&= \frac{2(x-4)}{2-4(x-4)} = \frac{2(x-4)}{2-4x+16} = \frac{2(x-4)}{-4x+18} = \frac{2(x-4)}{-2(2x-9)} = \frac{-(x-4)}{2x-9}
\end{aligned}
\end{equation}
$


To find the domain of $f \circ g$, we want...

$
\begin{equation}
\begin{aligned}
x - 4 &> 0 && \text{Add } 4\\
\\
x &> 4
\end{aligned}
\end{equation}
$

Thus, the domain of $f \circ g$ is $(4, \infty)$

To find the domain of $g \circ f$, we want $\sqrt{x } - 4 \neq 0$. The denominator is zero when...

$
\begin{equation}
\begin{aligned}
\sqrt{x} - 4 &= 0 && \text{Add } 4\\
\\
\sqrt{x} &= 4 && \text{Square both sides}\\
\\
x &= 16
\end{aligned}
\end{equation}
$


Also, the function involves square root that is defined for only positive values. Thus, the domain of $g \circ f$ is $[0,16)\bigcup(16,\infty)$

To find the domain of $f \circ f$, recall that the function with even roots is defined only for positive values of $x$. Thus, the domain of $f \circ f$ is $[0, \infty)$

To find the domain of $g \circ g$, we want $2x - 9 \neq 0$ the denominator is zero when...

$
\begin{equation}
\begin{aligned}
2x - 9 &= 0 && \text{Add } 9 \\
\\
2x &= 9 && \text{Divide } 2\\
\\
x &= \frac{9}{2}
\end{aligned}
\end{equation}
$

Thus, the domain of $g \circ g$ is $\displaystyle \left( -\infty, \frac{9}{2} \right)\bigcup \left( \frac{9}{2}, \infty \right)$

Compare "The Destructors" to Lord of the Flies.

The most obvious similarity between the two stories is that they both deal with the savagery of a group of boys. In "The Destructors," an urban street gang willfully destroys an old building that has stood for hundreds of years. In Lord of the Flies, a group of schoolboys crash-land on a remote desert island, where they quickly degenerate into savagery and turn on each other.
Social class is an important theme in both stories. In "The Destructors," the Wormsley Common gang consists of poor, working-class boys who have nothing; they have no money, no real family to speak of, and certainly no education. Nevertheless, the gratuitous act of vandalism and destruction they carry out is inspired by their new leader Trevor, who, unlike them, comes from a good home and really ought to know better. Trevor abuses his position of leadership to incite the other boys to commit a serious, and utterly needless, criminal act.
A similar abuse of leadership is practiced in Lord of the Flies by Jack Merridew. Like all the boys on the island, he comes from a privileged, elite background. As a scion of a good family, he really should know the value of a well-structured, ordered society. But before long, he disregards all notions of order to make a shameless grab for dictatorial power. In doing so, Jack has derogated from his duty as one of society's natural leaders to transform himself into a blood-crazed savage.
Ralph and Piggy, on the other hand, though from the same social background as Jack, do take their responsibilities seriously. They know that civilization is something that has to be painstakingly built and preserved over time if it is to endure. Even when civilization is sustained, as in the England of "The Destructors," barbarism is never very far away. Thus, it is necessary that the privileged classes exercise responsibility along with their power.