Why is a government needed?

Government is necessary to establish and maintain order and social control. At its fundamental level, government is responsible for the safety and welfare of its individuals. As John Locke famously stated, it is necessary to enter into a “social contract," giving up some of our innate rights, for the general welfare and safety of the population at large.
While it has expanded and developed in leaps and bounds, especially in a country as massive as the United States, the government still maintains its fundamental role in society: protect the safety of the citizens and ensure freedom and integrity. This is maintained through business regulations, environmental conservation, foreign policy, regulation of the economy, civil rights, and much more. The government is intended to be the protector of the people.

There are various reasons why we need to have a government. One reason is that a government provides order within a society. Without a government, there might not be laws. People would feel they could do whatever they wanted, whenever they wanted to do these things. We likely would be less safe without laws.
There are various services that government provides that are important to people. Without a police force, it would be harder to deal with illegal activities. In colder climates, roads need to be plowed in the winter. State and local governments set up public schools and public universities. In some places, the government arranges to have garbage collected and materials recycled. The government monitors the activities of businesses to help to ensure that consumers are being treated fairly. The government also provides relief to people when natural disasters, such as tornadoes, hurricanes, and earthquakes, occur.
Conducting relations with other countries would be very difficult if a government didn't exist. The government is responsible for making treaties and, if needed, going to war. The government is responsible for maintaining a military.
Governments take on many roles that help to ensure that society can function smoothly.
https://www.thoughtco.com/why-do-people-need-government-721411

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 29

Given f(x)=2sin(x)+sin(2x) on the interval [0,2pi], find the points of inflection and discuss the concavity:
Find the second derivative:
f'(x)=2cos(x)+2cos(2x)
f''(x)=-2sin(x)-4sin(2x)
Inflection points occur when the second derivative is zero (and changes sign.)
-2sinx-4sin(2x)=0
-8sin(x)cos(x)-2sin(x)=0 Using the identity sin(2x)=2sin(x)cos(x)
-2sin(x)[4cos(x)+1]=0
-2sin(x)=0 ==> x=0,pi,2pi on the interval
4cos(x)+1=0 ==> cos(x)=-1/4 ==> x=1.823,4.460
The second derivative is:
positive to the immediate left of 0negative on (0,1.823)positive on (1.823,pi)negative on (pi,4.460)positive on (4.460,2pi)negative to the immediate right of 2pi
---------------------------------------------------------------------------------------
There are inflection points at 0,1.823,pi,4.460,2pi
The function is concave down on (0,1.823), up on (1.823,pi), down on (pi,4.460), and up on (4.460,2pi)
---------------------------------------------------------------------------------------
The graph:

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 8

For the given integral: int 1/(xsqrt(x^4-4))dx , we may apply u-substitution by letting:
u =x^4-4 then du = 4x^3 dx .
Rearrange du = 4x^3 dx into (du)/( 4x^3)= dx
Plug-in u =x^4-4 and (du)/( 4x^3)= dx , we get:
int 1/(xsqrt(x^4-4))dx =int 1/(xsqrt(u))* (du)/( 4x^3)
=int 1/(4x^4sqrt(u))du
Recall u =x^4-4 then adding 4 on both sides becomes: u + 4 = x^4 .
Plug-in x^4 =u+4 in the integral:
int 1/(4x^4sqrt(u))du =int 1/(4(u+4)sqrt(u))du
Apply the basic integration property: int c*f(x) dx = c int f(x) dx :
int 1/(4(u+4)sqrt(u))du=1/4int 1/((u+4)sqrt(u))du
Apply another set of substitution by letting:
v =sqrt(u) which is the same as v^2 =u .
Then taking the derivative on both sides, we get 2v dv = du .
Plug-in u =v^2 , du = 2v dv , and sqrt(u)=v , we get:
1/4 int 1/((u+4)sqrt(u))du = 1/4int 1/((v^2+4)v)(2v dv)
We simplify by cancelling out common factors v and 2:
1/4int 1/((v^2+4)v)(2v dv) =1/2int (dv)/(v^2+4) or1/2int (dv)/(v^2+2^2)

The integral part resembles the integration formula:
int (du)/(u^2+a^2) = (1/a) arctan (u/a) +C
Then,
1/2 int (dv)/(v^2+4) =1/2 *(1/2) arctan (v/2) +C
=1/4 arctan (v/2) +C
Recall that we let v =sqrt(u) and u =x^4-4 then v = sqrt(x^4-4)
Plug-in v = sqrt(x^4-4) in 1/4 arctan (v/2) +C to get the final answer:
int 1/(xsqrt(x^4-4))dx =1/4 arctan (sqrt(x^4-4)/2) +C

How does Shakespeare portray Lady Macbeth as rejecting her femininity through the course of the play?

Lady Macbeth begins rejecting the femininity of her gender when she demands that she be unsexed. There seems to be a visible mid-way transition in what she rejects when Macbeth declines to disclose his plans for Banquo to her: "Be innocent of the knowledge, dearest chuck,/ Till thou applaud the deed." In the end, it seems the only thing Lady Macbeth rejects is her actions when she laments that there is neither enough water nor perfume in Arabia to cleanse the blood and smell from her hands.
After reading Macbeth's letter—which he closes by saying that he doesn't want her to be "ignorant of what greatness is promised thee [her]"—she begins the process of rejecting her feminine qualities by contemplating the need to chastise Macbeth and to pour the "valour" of her words into his—the warrior's—ears. By saying this, she identifies herself with masculine traits relating to war, killing, and ambition. As her ambition heats up for the attainment of Macbeth's kingship and her own queenship, Lady Macbeth goes further and further in rejecting feminine characteristics by demanding that the spirits "unsex me here, / And fill me. . . top-full / Of direst cruelty!" and that they come to "my woman's breasts, / And take my milk for gall."
It can be argued that in the midst of Macbeth's torment over the role Banquo might play, Lady Macbeth begins a transition away from vehement rejection of feminine qualities. This is evident when she laments the unfolding outcome of events: "Nought's had, all's spent." Immediately after this reflection, Macbeth enters. Instead of pouring valor and venom into Macbeth's ears, she consoles him, calling upon the feminine trait of comfort-giving to do so: "Things without all remedy / Should be without regard: what's done is done."  
Shortly after that, we see Lady Macbeth be secretly observed by a doctor attempting to diagnosis her strange behavior. Macbeth has already seen Banquo's ghost at the banquet. Lady Macbeth has already tried to rouse him and accused him of being "quite unmann'd in folly." Now she is walking in her sleep, pantomiming washing her hands "this a quarter of an hour"—an ironic turn of events, as she earlier told Macbeth that a little water would wash Duncan's blood from his hands—and she is longing for the perfume of Arabia to get rid of the scent of blood from her hands. Here we see a Lady Macbeth who now rejects her past actions that her mind is unhinged.
https://www.bl.uk/shakespeare/articles/unsex-me-here-lady-macbeths-hell-broth

How was Jem affected by Boo Radley? - To kill a Mockingbird

Jem is affected in several ways by Arthur "Boo" Radley. 
With the arrival of Dill Harris, who spends the summer at the home of his aunt's, Jem's interest in the strange recluse increases because of Dill's curiosity.

The first raid came to pass only because Dill bet Jem The Gray Ghost against two Tom Swifts that Jem wouldn't get any farther than the Radley gate. In all his life, Jem had never declined a dare.Jem thought about it for three days. I suppose he loved honor more than his head, for Dill wore him down.

Jem runs up to the Radley house and slaps it with his palm and races back in fear. When they get on the Finch porch, they look down the street, but nothing has changed. During the summer, the children playact various scenes based on the rumors about the Radleys. After some time, however, Jem and the others become deceptive about roleplaying about the Radley family because Atticus has told them to leave Arthur alone. One day Atticus comes home unexpectedly and catches Jem, Dill, and Scout when they have been told to end such play.  Although Jem tries to deceive Atticus, Atticus uses one of his legal tricks and leads Jem into admitting that they are engaged in reenacting Boo's history. 
One night after being scolded, however, Dill and Jem decide to peep into one of the windows at the Radley house. Someone from inside the house steps out onto the porch and fires a rifle. The children scatter, but Jem catches his pants on the barbed wire. He is forced to remove them so he can escape. Having heard the report of the rifle, the neighbors come outside. When Atticus sees that Jem is not wearing pants, he asks Jem what he has done with his pants. Dill quickly says that he won Jem's pants from him when they were playing strip-poker. "Were you all playing cards?" Atticus asks pointedly. Jem intervenes and says that they were using matches. That night as he and Scout lie on the porch, Jem says that he is going to retrieve his pants from the Radley yard because he does not want his father to know that he has been deceitful again.
Despite their invasions of the Radleys' privacy and acts of imitation, Boo leaves gifts for the children in the knothole of one of the trees that the children pass each day on their way home. When they find two soap figures carved in their likenesses, Jem is very touched. He saves them in his trunk of mementos. Then, after Nathan Radley cements this hole to prevent his brother from giving Jem and Scout anything else, Jem is affected by the cruelty of Nathan Radley, and he sheds tears of anger and disappointment. Later, after the travesty of the trial of Tom Robinson, a disgruntled Jem remarks, "I think I'm beginning to understand why Boo Radley's stayed shut up in the house all this time...it's because he wants to stay inside." 
In the final chapters, Boo Radley demonstrates his love for the Finch children again when he becomes aware of the children's distress as they attempt to reach home but are attacked by the scoundrel Bob Ewell. Boo comes outside and intervenes, and in the struggle between the two men, Ewell dies. Afterwards, Boo carries Jem home because Jem's arm has been broken. A deeply moved Atticus thanks Arthur for saving his children's lives after Sheriff Tate explains what has happened. From then on, Jem bears the reminder of the loving intervention of Boo Radley since his injured arm is shorter than the other. 

Calculus of a Single Variable, Chapter 9, 9.1, Section 9.1, Problem 38

Before we start calculating the limit, we will simplify the expression for the general term of the sequence. To that end we shall use recursive definition of factorial.
n! ={(1 if n=0),(n(n-1)! if n>0):}
a_n=((n-2)!)/(n!) =((n-2)!)/(n(n-1)(n-2)!)=1/(n(n-1))
Now it becomes easy to calculate the limit and determine convergence of the sequence.
lim_(n to infty)a_n=lim_(n to infty)1/(n(n-1))=1/(infty cdot infty)=1/infty=0
As we can see the sequence is convergent and its limit is equal to zero.
The image below shows the first 15 terms of the sequence. We can see they are approaching x-axis i.e. the sequence converges to zero.

College Algebra, Chapter 9, 9.6, Section 9.6, Problem 34

Determine the first fifth terms in the expansion $(ab-1)^{20}$
Recall that the Binomial Theorem is defined as
Substituting $a = ab$ and $ b = -1 $ gives

$
(ab - 1)^{20} =
\left(
\begin{array}{c}
20\\
0
\end{array}
\right)
(ab)^{20} +
\left(
\begin{array}{c}
20\\
1
\end{array}
\right)
(ab)^{19} (-1) +
\left(
\begin{array}{c}
20\\
2
\end{array}
\right)
(ab)^{18} (-1)^2 +
\left(
\begin{array}{c}
20\\
3
\end{array}
\right)
(ab)^{17} (-1)^3 +
\left(
\begin{array}{c}
20\\
4
\end{array}
\right)
(ab)^{16} (-1)^4 +
....
$

Thus, the 5th term is

$
\begin{equation}
\begin{aligned}
&=
\left(
\begin{array}{c}
20\\
4
\end{array}
\right)
(ab)^{16}(-1)^4\\
\\
&=
\left( \frac{20!}{4!(20-4)!} \right) (ab)^{16}(-1)^4\\
\\
&= 4845 a^{16} b^{16}

\end{aligned}
\end{equation}
$

8. You roll a 16 pound bowling ball down the lane at 8 meters per second. Assume no slippage and ignore friction and air resistance. The radius of the bowling ball is 4.25 inches. a. What is Ω (the rotation rate in radians per second)? b. What is the angular momentum? c. What is the rotational energy? d. As you look down the lane, in which direction does the angular momentum vector point?

A bowling ball weighing 16 pound rolls down the lane at 8 m/s. The ball does not slip, and friction, as well as air resistance, can be ignored.
The mass of the ball is 16 pound which is equivalent to 7.25748 kg. The linear velocity of the ball is 8 m/s. The radius of the ball is 4.25 inches or 0.10795 m.
Linear velocity v and rotational velocity w are related by w = v/r.
Substituting the values given,
w = 8/0.10795 = 74.1 rad/s
The angular momentum of a body is given by L = I*w, where I is the moment of inertia and w is the angular speed. For a solid spherical body of mass m and radius r, moment of inertia I = (2/5)*m*r^2
The moment of inertia of the bowling ball is I = (2/5)*7.25748*(0.10795)^2 = 0.03383 kg*m^2
The angular momentum is equal to 0.03383*74.1 = 2.507 kg m^2/s
The rotational energy of the ball is (1/2)*I*w^2 = (1/2)*.03383*74.1^2 = 92.877 J
The right hand rule gives us the direction of the angular momentum vector. It is pointing to the left.

What is the theme of "One of These Days" by Gabriel Garcia Marquez?

The short story "One of These Days" by Gabriel Garcia Marquez has a seemingly simple plot. A dentist wakes early and goes about his work. Although he does not possess a degree, he performs his work skillfully and with dedication. When the mayor arrives to have a tooth pulled, the dentist does not want to help him, knowing that the mayor has been responsible for the deaths of many people. He sees that the mayor's condition is serious, though, and he changes his mind. However, he informs the mayor that the procedure has to be performed without anesthetic, and as he begins to pull, he states: "Now you'll pay for our twenty dead men." He pulls the tooth, and the mayor leaves.

It would be simple to say that the theme of the story is revenge. However, the revenge element is secondary to the more important themes of the use or abuse of power, and the adherence to professionalism by the dentist. If revenge were the main theme, it would have been more fitting if the dentist had shot the mayor with the revolver he had in his drawer. Instead, he closes the drawer and agrees to perform the procedure.

One of the main themes in the story is the way that power is used by the two main characters. Overall, the corrupt mayor obviously has far greater power in his ability to use his office to justify the threat of violence. In this situation, though, he is helpless before the dentist. There are limits to the mayor's power. He cannot pull his own tooth. Despite all the power he wields in his office, he must sit in the chair and make himself vulnerable to the dentist. He must also accept the conditions under which the dentist performs the procedure. He has no way of knowing if the dentist's explanation of the abscess is accurate or not. For this reason, he allows the dentist's moment of revenge without retaliation, but as soon as the tooth is pulled, the mayor is back in control.

The dentist's adherence to professionalism is another important theme. Marquez touches on this early as he describes the dentist working on false teeth, gold teeth, and bridges. The dentist has an opportunity to shoot the hated mayor, but he does not take it when he sees the man's condition. His professional ethics cannot allow him to turn away a patient in need. However, he uses the brief period in which the mayor is under his control to inflict at least some pain in return for the atrocities the mayor has committed. In the overall exchange, the dentist comes out as the far better man.

Often we can find several different themes in a story, and it's possible to find evidence for each. "One of These Days" is a powerful story with many themes, but I think that power is one of the strongest themes.
The story is very much a play of power, and as we read, we see power exchanged between the dentist and the mayor. There is a bit of a back-and-forth on who holds the most power and who is most in control of the situation.
In the beginning of the story, the dentist is in control. We see him working slowly, taking his time and not paying attention to much. When the mayor arrives and asks for help, the dentist denies him. However, power changes hands when the mayor threatens to shoot the dentist.
Of course, it quickly switches back when we find out that the dentist also has a gun, and is ready to shoot the mayor as soon as he walks in. He doesn't, but he maintains control of the situation because the mayor's tooth has incapacitated him. The dentist uses his power to deny the mayor anesthesia and to make the extraction especially painful.
But, by the end of the story, power returns again to the mayor, and we know that even while the dentist held control over this situation, the mayor always had more power and always will. This is solidified with the comment that charging him and charging the town is the same, because in the end, bad tooth or not, the mayor has always been in control.

Revenge, power, and corruption are three main themes in Gabriel Garcia Marquez’s "One of These Days." Garcia Marquez conveys the theme of revenge by having the dentist Aurelio Escovar insist on completing the Mayor’s tooth extraction without anesthesia. In the story, the Mayor is suffering from an abscess. Although it is true that many abscesses do not respond well to anesthesia, there are other pain-control methods that dentists can use to deal with tooth abscesses. Because the dentist doesn’t even investigate any of these methods, the reader can assume that he is quite happy to extract the Mayor’s tooth without anesthesia. The reason behind this decision is simple: the dentist wants revenge. After all, while extracting the tooth, the dentist exclaims, "Now you’ll pay for our twenty dead men."
The theme of power is also evident in this story. The dentist, by pulling the tooth from the Mayor’s mouth, exhibits a certain amount of power. (Any reader who has been to the dentist has likely felt that power. After all, there are few experiences that make a person feel more exposed than having a stranger’s hands in the raw, inner-workings of his/her mouth.) However, in “One of These Days,” the dentist's power is brief. In reality, the true power belongs to the Mayor. It is, after all, the Mayor who tells the dentist’s young son that he will shoot the dentist if the dentist does not treat him immediately. Only a person with immense power would make that threat.
Finally, we come to Garcia Marquez’s last theme, that of corruption. We know that both the dentist and the Mayor are corrupt in their own way. The dentist is operating without a degree, and he has a gun in his office. So, in that sense, he is not law-abiding. However, the true corruption lies with the Mayor. Garcia Marquez highlights this fact when, at the story’s end, the dentist asks where he should send the bill. Should he send it to the Mayor or the town? When the Mayor responds, “It’s the same damn thing,” the Mayor’s true corruption is revealed. Clearly, Garcia Marquez is using the Mayor’s corruption as a metaphor for the corruption of all powerful politicians. By the end of "One of These Days," the reader sees the dentist as a weak, vengeful everyman who will employ all that is in his power to exact revenge on the corrupt and powerful.
https://www.dentalfearcentral.org/fears/not-numb/

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 68

Find a.) $F'(x)$ and b.) $G'(x)$ where $F(x) = f(x^{\alpha}$ and $G(x) = [f(x)^{\alpha}]$. Suppose that $f$ is differentiable everywhere and $\alpha$ is a real number.


$
\begin{equation}
\begin{aligned}

\text{ a.) } F'(x) = \frac{d}{dx} [f(x)] =& f'(x^{\alpha}) \cdot \alpha (x^{\alpha - 1})
\\
\\
F'(x) = \frac{d}{dx} [f(x)] =& \alpha x^{\alpha - 1} f'(x^{\alpha})
\\
\\
\\
\text{ b.) } G'(x) = \frac{d}{dx} [G(x) ] =& \alpha [f(x)]^{\alpha - 1} \cdot f'(x) \cdot 1
\\
G'(x) = \frac{d}{dx} [G(x) ] =& \alpha [f(x)]^{\alpha - 1} \cdot f'(x) \cdot 1
\\
\\
G'(x) = \frac{d}{dx} [G(x) ] =& \alpha [f(x)]^{\alpha - 1} f'(x)

\end{aligned}
\end{equation}
$

Precalculus, Chapter 9, 9.2, Section 9.2, Problem 37

Given a_8=26, a_12=42
The equation for an arithmetic sequence is
a_n=a_1+(n-1)d
a_8=a_1+(8-1)d
26=a_1+7d
Equation 1: 26=a_1+7d

a_n=a_1+(n-1)d
a_12=a_1+(12-1)d
42=a_1+11d
Equation 2: 42=a_1+11d

Using equation 1 and equation 2 solve for the a_1 and d using the substitution method or the elimination method. The substitution method is shown below.
26=a_1+7d
a_1=26-7d

42=a_1+11d
42=(26-7d)+11d
42-26=-7d+11d
16=6d
d=4

a_1=26-7d
a_1=26-7(4)
a_1=26-28
a_1=-2

Find the equation of the arithmetic sequence using the a_1 and d .
a_n=a_1+(n-1)d
a_n=-2+(n-1)(4)
a_n=-2+4n-4
a_n=4n-6

Find the first 5 terms of the sequence.
a_n=4n-6
a_1=4(1)-6=4-6=-2
a_2=4(2)-6=8-6=2
a_3=4(3)-6=12-6=6
a_4=4(4)-6=16-6=10
a_5=4(5)-5=20-6=14

What are some interesting facts in the book The Underdogs by Mariano Azuela?

Although this is a novel, Azuela, working as a medic, was an eye-witness to the Mexican revolution, so his work gives us a bird's-eye view of the times.
In the book, real historical characters make an appearance, such as Pancho Villa. Villa was a famous general in the revolutionary army and Azuela actually served under him. Another historical character, Francisco Modero, who was assassinated but had earlier overthrown the repressive former regime to become President of Mexico, is invoked. The reflections on Modero reveal some of the cynicism expressed by the common people, who felt that once they had helped Modero achieve power, they were turned on and told to go back to work, "half naked and hungry," just as they had been before.  
Most interestingly, the novel offers facts about the social history of Mexico in this time period. We witness the primitive conditions in which the peasants lived: in the opening scene we find a room lit by a tallow candle and a children lying on a bed, covered in rags.
We learn too that not only today are people concerned about a surveillance state. The passage below, where the policeman has his ear to the door, indicates that the same issue bothered people more than a century ago and gives us a colorful picture of what life was like in Mexico at that time:

I was born in Limon, close by Moyahua, right in the heart of the Juchipila canyon. I had my house and my cows and a patch of land, see: I had everything I wanted. Well, I suppose you know how we farmers make a habit of going over to town every week to hear Mass and the sermon and then to market to buy our onions and tomatoes and in general everything they want us to buy at the ranch. Then you pick up some friends and go to Primitivo Lopez' saloon for a bit of a drink before dinner; well, you sit there drinking and you've got to be sociable, so you drink more than you should and the liquor goes to your head and you laugh and you're damned happy and if you feel like it, you sing and shout and kick up a bit of a row. That's quite all right, anyhow, for we're not doing anyone any harm. But soon they start bothering you and the policeman walks up and down and stops occasionally, with his ear to the door. 

Towards the end of the novel, the modernity of the early twentieth century collides with the world of the peasants when government forces use machine guns to great effect: "They mowed us down like wheat,"  reports Solis. Finally, the novel is unflinching in its assessment of the failed dreams of the revolution.  As Solis says:

What a colossal failure we would make of it, friend, if we, who offer our enthusiasm and lives to crush a wretched tyrant, became the builders of a monstrous edifice holding one hundred or two hundred thousand monsters of exactly the same sort. People without ideals! A tyrant folk! Vain bloodshed!

In fact, the lower classes in Mexico remain poor to this day. 

Why did Mrs. Olinski pick those kids for the team?

Mrs. Olinski might be expected to choose students for the Academic Bowl competition on the basis of book smarts or intellect. However, she does not do this. Although "The Souls" she eventually picks are not her first choice, she has been influenced by how she has been treated by her students since her return to class. Mrs. Olinksi was involved in a serious car accident that left her a paraplegic. Some of the students have been very cruel and inconsiderate toward her, and this has been very upsetting. But not all Mrs. Olinksi's students have been so mean; she observes that a number of them have engaged in acts of kindness toward others. They made a big impression on her, so much so that she wants them to represent the class in the Academic Bowl.

Who does "she" refer to in "she is like most artists" in "The Nightingale and the Rose" by Oscar Wilde?

In the passage you reference, "she" refers to the Nightingale. Here's the passage in full:

“She has form,” he said to himself, as he walked away through the grove, “that cannot be denied her; but has she got feeling? I am afraid not. In fact, she is like most artists; she is all style, without any sincerity. She would not sacrifice herself for others. She thinks merely of music, and everybody knows that the arts are selfish. Still, it must be admitted that she has some beautiful notes in her voice. What a pity it is that they do not mean anything, or do any practical good.”

In the story, the young student cannot understand what the nightingale is saying to him; he only knows what he reads in books, and the language of the nightingale's song appears strange to him. While professing to be a student of logic, he is blind to the logic of true self-sacrifice.
In reality, the nightingale has already consented to sacrifice her life's blood for him, but the young student is unaware of this. He accuses the nightingale of being selfish, but it is he who lacks true discernment. What he considers as the vain song of a bird is in reality a song of self-sacrifice. All the nightingale asks in exchange for forfeiting her life is that the young student will be a "true lover."
Ironically, the young student can appreciate the "beautiful notes" in the nightingale's song but fails to recognize the "feeling" and "sincerity" in her anthem of love.

How does Jonathan Swift use ethos, logos, and pathos in "A Modest Proposal"?

Because “A Modest Proposal” is such a deeply ironic work, the use of ethos, pathos and logos differs markedly from their normal usage in, for instance, a political speech. All these rhetorical devices are typically used to persuade the audience to agree with the speaker or writer. Here, they are all used to horrify the reader by the callous inhumanity of the argument. This is the principal reason why logos is the most prevalent device. The cool appraisal of what a child is worth considered as a piece of meat is intended to provoke outrage at the heartlessness of such a calculation. This effect is exacerbated by the references to women as “breeders” and the constant comparisons with sheep and cattle.
Swift’s calculations are a particularly effective way of using logos to convey human tragedy more effectively than pathos could, by including a mass of human misery in apparently dispassionate statistics:

I again subtract fifty thousand for those women who miscarry, or whose children die by accident or disease within the year. There only remains one hundred and twenty thousand children of poor parents annually born.

Of the apparent pathos in the essay, only the pathos in the opening is not entirely ironized, since the sight of beggars on the streets is indeed melancholy, though not for the reasons Swift is to profess. His solution is the principal source of irony, since it is worse than the problem:

It is a melancholy object to those who walk through this great town or travel in the country, when they see the streets, the roads, and cabin doors, crowded with beggars of the female sex, followed by three, four, or six children, all in rags and importuning every passenger for an alms.

Ethos is also used ironically in the final paragraph, when the author protests his own disinterest, as though there are so few legitimate objections to his proposal that this is the most serious of which he can conceive and he must dispel it by insisting on the purity of his own motives:

I profess, in the sincerity of my heart, that I have not the least personal interest in endeavoring to promote this necessary work, having no other motive than the public good of my country, by advancing our trade, providing for infants, relieving the poor, and giving some pleasure to the rich. I have no children by which I can propose to get a single penny; the youngest being nine years old, and my wife past child-bearing.

The speaker employs ethos, attempting to establish his own credibility with his audience, when he talks about being "assured by our merchants" as to the value of young children or being "assured by a very knowing American" who has, apparently, experienced a system very like the one the speaker proposes. He makes it sound as though he has consulted experts who support his idea, lending him credibility.
The speaker employs pathos, appealing to his audience's emotions, at the start of the text when he says,

It is a melancholy object to those, who walk through this great town, or travel in the country, when they see the streets, the roads and cabin doors crowded with beggars of the female sex, followed by three, four, or six children, all in rags, and importuning every passenger for an alms. These mothers instead of being able to work for their honest livelihood, are forced to employ all their time in strolling to beg sustenance for their helpless infants.

He attempts to draw an incredibly sympathetic picture of the poor Irish peasants who are forced to beg for their sustenance, especially the women and children, dressed "all in rags" and seeking kind souls who are willing to spare a few pennies. In this way, he tries to win over his audience's hearts so that they will be more open to listen to his proposal.
The speaker employs logos when he begins to make his mathematical calculations:

The number of souls in this kingdom being usually reckoned one million and a half, of these I calculate there may be about two hundred thousand couple whose wives are breeders; from which number I subtract thirty thousand couple, who are able to maintain their own children, . . . but this being granted, there will remain an hundred and seventy thousand breeders. I again subtract fifty thousand, for those women who miscarry, or whose children die by accident or disease within the year. There only remain an hundred and twenty thousand children of poor parents annually born. The question therefore is, How this number shall be reared, and provided for? which, as I have already said, under the present situation of affairs, is utterly impossible by all the methods hitherto proposed.

He attempts to present very logical calculations about how the community cannot go on the way it is with the sheer number of children born to the poor Irish. This way, his proposal will seem all the more logical to his audience.

One of the strengths of Swift's satire is his relentless use of logos. Swift's narrator employs one statistic after another to demonstrate the efficacy of his "proposal." He points out that there are over one hundred thousand children born in Ireland that could be profitably sold for food. This, he computes, will have a dramatic effect on the economy of the kingdom:

Whereas the Maintainance of an hundred thousand Children, from two Years old, and upwards, cannot be computed at less than Ten Shillings a piece per Annum, the Nation's Stock will be thereby encreased fifty thousand pounds per Annum, besides the profit of a new Dish, introduced to the Tables of all Gentlemen of Fortune in the Kingdom, who have any refinement in Taste, and the Money will circulate among our selves, the Goods being entirely of our own Growth and Manufacture.

In many ways the appeal to logos in the essay is exactly what Swift is satirizing. He is claiming that attacking the social problems of a society in an overly rational way (without considering morality) can lead mankind to make decisions with terrible consequences. However, Swift also appeals to pathos, citing the "melancholy sight" of beggars and orphans on street corners and the "horrid practice of women murdering their Bastard children" for want of means to support them. He uses ethos when he points out, sardonically, that he has no financial interest in the "proposal" because his children are past the age where they are edible.  

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 25

Determine the derivative of the function $\displaystyle F(z) = \sqrt{\frac{z-1}{z+1}}$

$
\begin{equation}
\begin{aligned}
F'(z) &= \frac{d}{dz} \left( \frac{z-1}{z+1} \right)^{\frac{1}{2}}\\
\\
F'(z) &= \frac{1}{2} \left( \frac{z-1}{z+1} \right)^{\frac{-1}{2}} \frac{d}{dz} \left( \frac{z-1}{z+1}\right)\\
\\
F'(z) &= \frac{1}{2} \left( \frac{z-1}{z+1} \right)^{\frac{-1}{2}} \left[ \frac{(z+1) \frac{d}{dz}(z-1)-(z-1)\frac{d}{dz}(z+1)}{(z+1)^2}\right]\\
\\
F'(z) &= \frac{1}{2} \left( \frac{z-1}{z+1} \right)^{\frac{-1}{2}} \left[ \frac{(z+1)(1)-(z-1)(1)}{(z+1)^2}\right]\\
\\
F'(z) &= \frac{1}{2} \left( \frac{z-1}{z+1} \right)^{\frac{-1}{2}} \left[ \frac{\cancel{z}+1 - \cancel{z} +1 }{(z+1)^2}\right]\\
\\
F'(z) &= \frac{1}{\cancel{2}} \left( \frac{z-1}{z+1} \right)^{\frac{-1}{2}} \left[ \frac{\cancel{2}}{(z+1)^2}\right]\\
\\
F'(z) &= \frac{(z-1)^{\frac{-1}{2}}}{(z+1)^{\frac{-1}{2}}} \left[ \frac{1}{(z+1)^2} \right]\\
\\
F'(z) &= \frac{(z-1)^{\frac{-1}{2}}}{(z+1)^{\frac{3}{2}}}\\
\\
F'(z) &= \frac{1}{(z+1)^{\frac{3}{2}} (z-1)^{\frac{-1}{2}}}
\end{aligned}
\end{equation}
$

What was the role of the knights in Murder in the Cathedral?

Murder in the Cathedral tells the story of the events that led to the demise of Thomas Becket, Archbishop of Canterbury. The Archbishop is murdered in the cathedral by four knights in the last part of the verse drama. The four knights were a carrying a plot to assassinate the Archbishop, which was supposedly sanctioned by King Henry II. Thomas Becket contradicted the king’s position over the rights and privileges of the church.
The king had successfully managed to limit the clergy’s independence and reduce Rome’s influence on the realm. Although most of the members of the clergy had consented to the king’s plans, Thomas Becket resisted. Henry’s attempts at convincing Becket failed, and he instituted contempt proceeding against him. Becket lost the case and was forced to flee to France. After negotiations, he returned; however, the conflict persisted, leading up to his assassination by the four knights believed to be at the behest of the King.
The knights justify their actions at the end of the drama. They believe that they were performing their social and moral duty for the good of the public.
https://www.britannica.com/biography/Saint-Thomas-Becket

The four knights in Murder in the Catherdral act as agents of King Henry II and actually carry out the murder of Thomas Becket, Archbishop of Canterbury. At the end of the play, three of the four offer justifications for the murder. The second knight asks that they be pitied, saying they were only following orders for the good of the people of England. The third knight says that the archbishop was a guilty criminal, and so his murder was justified. The fourth knight argues that Becket brought the murder on himself, so in reality, the murder was a suicide.
The play was commissioned by George Bell, the bishop of Chichester, as a protest against the Night of the Long Knives of June 1934, in which Hitler turned on his dear old friend Röhm and had him and others who stood in his way murdered. The knights in the play represent the strongmen in Germany who carried out Hitler's orders and the justifications they used to rationalize their crime.

How many people does Poirot observe as he eats lunch with M. Bouc?

Poirot observes thirteen people as he eats lunch with M. Bouc. 
Opposite Poirot's table, there are three men: an Italian, an Englishman, and an American. The men appear to be single travelers who just happen to be seated together. Meanwhile, at a small table, sits the ugliest old woman Poirot has ever seen. M. Bouc tells Poirot that the woman is Princess Dragomiroff, a Russian. Her husband is rumored to have realized great gains before the Russian revolution and to have invested those gains abroad.
Princess Dragomiroff is clothed in an expensive sable coat; she also wears a necklace of large pearls and many rings on her fingers. As Poirot observes her, she orders mineral water and orange juice to be placed in her compartment. For dinner, she orders simply-cooked chicken and boiled fish.
Next, Poirot observes Mary Debenham and two other women seated at a larger table. Near them, Colonel Arbuthnot sits at a small table by himself. Meanwhile, a middle-aged woman sits on the other side of the carriage. Poirot thinks that she looks either German or Scandinavian; he speculates that she is someone's maid. Beyond her sits a couple. The man appears to be in his thirties and has a powerful set of shoulders. His beautiful companion appears to be barely into her twenties.
Both M. Bouc and Poirot agree that the man and his companion make a handsome couple. The last two in the lunchroom carriage are MacQueen (Poirot's fellow traveler) and Mr. Ratchett.

In Things Fall Apart, would silence be characterized as positive or negative?

Throughout the novel, Chinua Achebe characterizes silence as being ominous and negative. In Chapter 7, Okonkwo and the boys work in "complete silence" until the locusts descend onto the village. Shortly after, Ezeudu tells Okonkwo that Umuofia has decided to kill Ikemefuna. When Okonkwo receives the news, he tells Ikemefuna that he will be taking him home but does not say a word to Nwoye. The next day, the men of the village begin their journey with Ikemefuna. Achebe writes, "A deathly silence descended on Okonkwo's compound" (58). As the group of men travel nearer to the outskirts of Umuofia, they become "silent." As they continue their journey, Achebe describes their surroundings and writes, "All else was silent" (58). The silence provides an ominous mood before Okonkwo kills Ikemefuna.
Later in the novel, Obierika travels to visit Okonkwo and tells him that the village of Abame has been wiped out by white men. Obierika tells him that the villagers of Abame killed a messenger who spoke a strange language, which provoked the other white men to destroy the village. When Uchendu asks Obierika what the white man said before he was killed, one of Obierika's companions says, "He said nothing" (139). Uchendu responds by saying, "Never kill a man who says nothing" (140). Again, silence is associated with impending destruction.
In Chapter 23, the leaders of Umuofia are taken captive, and the villagers are frightened. Achebe writes, "It was the time of the full moon. But that night the voice of children was not heard. . . Young men who were always abroad in the moonlight kept their huts that night. Their manly voices were not heard on the village paths as they went to visit their friends and lovers" (196). Eventually, the elders return and Okonkwo makes the fateful decision to kill a white messenger. The silence in the village is associated with negative emotions and provides an ominous mood to the story. Silence almost always precedes a destructive event throughout the novel and would be characterized as negative.

After reading case 24-3, Figgie International, Inc. v. Destileria Serralles, Inc. , please identify a significant ambiguous phrase that affects your ability to accept the court's conclusion. Explain the ambiguity and why it matters

This case, decided by the Fourth Circuit Court of Appeals in 1999, involves a dispute between a Destileria Serralles, Inc. (“Serralles”), a bottler of rum, and Figgie International, Inc. (“Figgie”), a manufacturer of bottle-labeling equipment. Figgie could not provide bottle making equipment in a satisfactory way to Serralles, so Serralles received a refund after they returned the equipment. The question in this case was whether Serralles was limited to what was is referred to as "the exclusive remedy of repair, replacement, or return of the equipment." Serralles also wanted Figgie to pay for alleged losses that were incurred as a result of the bottle equipment that did not work.
In its decision, the court stated that Figgie had submitted several affadavits by people in the bottling industry to the effect that sellers in the industry limit remedies to the repair, replacement, or return of equipment and do not include other damages. In their decision, the court said that "Serralles asserts that it did not 'acquiesce' in this practice." The court does not define the precise meaning of the word "acquiesce," so it is ambiguous as to what Serralles meant by saying that they did not acquiesce in this situation. The reason it matters is that it is not clear whether Serralles agreed to this practice of limited damages or not. There are other examples of ambiguity you can find in the court's decision. 

Are personal qualities the sole reason one becomes an outlier?

No, personal traits are not the sole factors determining one's success. In fact, in Outliers, Malcolm Gladwell notes that personal traits are often not even the most important factor. Each section of the book covers different ways that success is impacted by outside factors. For example, among Canadian hockey players, one's birthdate is important. Those born earlier in the year are often much stronger and more developed than those born later in the year. They perform better in practice and are selected for additional training opportunities, further increasing the gap between them and younger players in the same class. Cultural factors also determine the skills people develop, leading to significant differences in skill levels in specific subject areas between cultures.

No. Innate talent is only one of the attributes needed to become an outstandingly successful person. Malcolm Gladwell begins with these definitions of “outlier:”
something that is situated away from or classed differently from a main or related body.
a statistical observation that is markedly different in value from the others of the sample.
We’re used to hearing the stereotypical stories of folks who overcome insurmountable odds to make their rags-to-riches climbs to the top of their fields. After Gladwell analyzes the histories of Silicon Valley computer geeks, Jewish immigrant garment workers, Asian rice farmers and math students, Korean pilots, and many more examples, he comes to another conclusion: the stereotype is a myth. There are almost always hidden advantages of some kind. Cultural legacies and perfect timing by the calendar can combine to produce the right people doing the right thing at the right time. Sometimes, it’s a matter of where you were born and when, and how much time you could devote to your project.

They are products of history and community, of opportunity and legacy. Their success is not exceptional or mysterious. It is grounded in a web of advantages and inheritances, some deserved, some not, some earned, some just plain lucky—but all critical to making them who they are. The outlier, in the end, is not an outlier at all (285).

How does Bassanio know that he is a welcome suitor?

In Shakespeare's play The Merchant of Venice, Bassanio is in love with the beautiful lady Portia. He feels that he must make expensive gestures to win Portia's love, not realizing that she already loves him. Portia is speaking to her maid, Nerissa, early in the play about how she dislikes all of her current suitors and how much she enjoyed a previous visit from Bassanio:

NERISSA: Do you not remember, lady, in your father's time, aVenetian, a scholar and a soldier, that came hitherin company of the Marquis of Montferrat?PORTIA: Yes, yes, it was Bassanio; as I think, he was so called.NERISSA: True, madam: he, of all the men that ever my foolisheyes looked upon, was the best deserving a fair lady.PORTIA: I remember him well, and I remember him worthy ofthy praise.

Meanwhile, her current suitors try to win Portia's hand by passing a strange test her father mandated in his will: anyone who wishes to marry Portia must choose one of three caskets (gold, silver, and lead). If he chooses the casket which contains Portia's portrait, he can marry her; otherwise, he must leave. No suitor has yet passed this test, and there are some scenes showing suitors picking the wrong caskets (gold and silver). Portia is very tired of this whole charade, so when Bassanio arrives at her house to declare his love and try the test, she is sad, as she doesn't want to lose the possibility of marrying him:

PORTIA: I pray you, tarry: pause a day or twoBefore you hazard; for, in choosing wrong,I lose your company: therefore forbear awhile . . . I would detain you here some month or twoBefore you venture for me.

Bassanio nevertheless is determined to try, saying "Let me choose / For as I am, I live upon the rack," tormented by his love for Portia. Portia very reluctantly agrees to let him try, but "with much, much more dismay / I view the fight than thou that makest the fray."
To their joy, Bassanio passes the test by choosing the casket with Portia's portrait inside—the lead casket which the other suitors automatically passed over in favor of the gold and silver caskets. Bassanio is not taken in by the more expensive caskets, indeed he reasons:

ornament is but the guiled shoreTo a most dangerous sea . . . The seeming truth which cunning times put onTo entrap the wisest. Therefore, thou gaudy gold,Hard food for Midas, I will none of thee;Nor none of thee, thou pale and common drudge [silver]'Tween man and man: but thou, thou meagre lead,Which rather threatenest than dost promise aught,Thy paleness moves me more than eloquence;And here choose I; joy be the consequence!

Bassanio is not deceived by appearances but believes true beauty is more than mere outward spectacle. He is correct, and he wins Portia's hand in marriage.
http://shakespeare.mit.edu/merchant/full.html

In My Side of the Mountain by Jean George, why does Sam decide to run away from home?

While Sam Gribley does originally plan to run away from home, his father discovers his plans and tells him that he will be allowed to travel to the abandoned Gribley farm to attempt to live off of the land provided that he let people in town know where he is. In this way, he does not "run away" in the traditional sense but is allowed to go by his father, who believes that after a very short time without modern comforts, Sam will return. This turns out to not be the case at all. Sam leaves his home because he finds his cramped living situation completely unbearable and craves the freedom and adventure provided by living in open nature and off the land. Sam carefully studies survival skills and proves to be extraordinarily talented in regard to being self-sufficient. With his accumulated skills, Sam proves that he is able to live in the wild indefinitely.

In the first two chapters, you’ll find three reasons why Sam Gribley left his home in New York City to run away to the Catskill Mountains. Near the end of Chapter One, titled “In Which I Hole Up in a Snowstorm,” Sam shares some details about his family life. He has four sisters and four brothers; so together with his parents, they total eleven people living in one apartment. It must have been a tight and uncomfortable space.

And not one of us liked it, except perhaps little Nina, who was too young to know. Dad didn’t like it even a little bit. He had been a sailor once, but when I was born, he gave up the sea and worked on the docks in New York.

Sam evidently wanted to get out, to a place where he could be on his own and could breathe. Then we learn that Sam’s ancestors once owned property in the Catskills. His father told him:

“That land is still in the family’s name. Somewhere in the Catskills is an old beech with the name Gribley carved on it. It marks the northern boundary of Gribley’s folly – the land is no place for a Gribley.”

Sam lets us know that he has since found the beech tree and the carved name, and that he thinks the area is just the right place for a Gribley to live.
In the second chapter, titled “In Which I Get Started on This Venture,” Sam tells us that his father once ran away from home but chickened out and was back before nightfall. Sam wanted to do likewise, but instead go off to the famous Gribley land.

Everybody laughed at me. Even Dad. … He had roared with laughter and told me about the time he had run away from home. … Then he told me, “Sure, go try it. Every boy should try it.”

So Sam did. And he found success living on his own, on or near the Gribley land. And part of him wanted to prove especially to his father that he could do it.

Explain why Syme believes the narrowing of the range of thought is necessary.

Syme is the most intelligent person Winston knows but paradoxically the most zealous supporter of the Party. The ideology of the Party, as in all totalitarian regimes, demands unquestioning acceptance from its members, and the more limited people's thoughts are, the less likely they are to have "heretical" thoughts and rebel against the Party. Hence Syme's desire for narrowing the range of thought of which the citizens of Oceania are capable.
During lunch in the canteen at the Ministry, Syme explains to Winston his work on the Newspeak dictionary and the obvious delight he takes in it, saying, "the destruction of words is a beautiful thing." The Party's intention is to reduce the vocabulary of the English language to such an extent that eventually, anti-Party thought will become impossible because there will be no words available in which to express it. Orwell's own theory, expressed in the appendix of 1984 and in his earlier essay "Politics and the English Language," is that there is a direct connection between clarity of thought and the way in which people use words. If a politician or a writer, for example, uses unclear, sloppy language, it facilitates his ability to engage in deception and to make lies sound convincing. Similarly, if (as in the dystopia of 1984) the vocabulary is cut down to an absolute minimum of words required for communication, then people will not even be able to think anything not dictated to them by the Party.
One of the unique features of the English language as it exists today is the size of its vocabulary, since English, probably more than any other language, has undergone a process over the centuries of borrowing an immense number of words from other languages. Though Syme doesn't mention this fact—which he may not even be aware of because the citizens of Oceania are forbidden to learn foreign languages—he states that, for instance, all the synonyms for the word "good" are useless and should just be replaced by prefixes to show the degree of "goodness"—plusgood, doubleplusgood, and so on. Even antonyms are seen as superfluous, so that "bad" is replaced by "ungood." Insofar as thought is dependent upon words—a point Orwell makes clear in the appendix—the intention of the Party is not merely to limit thought and make heretical thoughts impossible but to eliminate the ability to express emotion, and thus to turn people into robot-like beings.
Syme himself, because he understands this purpose so clearly, is, as Winston realizes, a danger to the Party in spite of his unquestioning devotion to it. His intelligence makes him the opposite of the unthinking machines into which the Party is trying to transform the masses. So Winston is not surprised when Syme vanishes, when all references to his existence have been eliminated. Syme has been "vaporized." One wonders if this fate is worse than what ultimately happens to Winston, who is imprisoned and "reeducated." Winston survives but is turned into the zombie-like being the Party intends everyone to become.

What was Andrew Jackson’s relationship with the Native Americans before he became president? How do his attitudes toward them reflect Southern ideals?

Andrew Jackson was already a nationally prominent figure before his election as President in 1828—and even before his entrance into national politics a few years earlier. He had earned part of his fame at the Battle of New Orleans, where he successfully organized the defense of the city, repulsing a massive assault by British forces. More importantly, especially to the "common man" that Jackson drew upon for his political support, was his record as an Indian fighter. Jackson led American forces (as well as some Cherokee fighters) who were involved in an internecine conflict among the Creeks known as the "Red Stick" War. This conflict, which, from its outset, intertwined with the larger War of 1812, culminated in the destruction of a large Red Stick force at the battle of Horseshoe Bend in 1814. This led to a massive cession of Creek lands (much of which belonged to those who had not fought against Jackson's force). Four years after his success at Horseshoe Bend, Jackson led American forces against Seminole towns (and, ultimately, Spanish ones) in Florida. This campaign began as a punitive expedition; the Seminole people often provided safe havens for fugitive slaves from Georgia. Jackson was also involved in repeated negotiations with Cherokee and other Southeastern Native peoples over land cessions. Accordingly, it can be understood that long before he was elected President Jackson was an instrument of American expansion and the expropriation of Native lands, in what is today the American Southeast. This process converted this region from Native lands into a planation belt where Southerners migrated in large numbers (bringing with them thousands of enslaved African Americans) to raise cotton. It was thus strongly supported by Southerners, who were always eager to bring new lands under cultivation by slaves.
https://www.loc.gov/collections/andrew-jackson-papers/articles-and-essays/andrew-jackson-timeline-1767-1845/the-war-of-1812-and-indian-wars-1812-1821/

Before he became President, Andrew Jackson was one of the key American leaders in the war against the Creek Indians.  Jackson also controversially invaded Florida, and this was one of the sparks of the First Seminole War.  Jackson's reputation as an "Indian fighter" made him quite popular with his Western constituents, who desired more Western land for their growing cotton plantations.  It was important to keep acquiring land because cotton is very hard on the soil's nutrients; new ground must be continually obtained for its growth.  This became essential after cotton became a multimillion dollar industry in the United States.  
After Jackson became President, he authorized the Indian Removal Act, which sent what scholars refer to as the "Five Civilized Tribes" of the southeastern United States to Oklahoma.  Jackson's argument for doing so was that the white culture which surrounded the Native Americans would eventually extinguish the native culture.  Jackson was claiming to act in the best interests of the Native Americans.  This paternalistic attitude was not uncommon, as Thomas Jefferson recommended moving all Indians west of the Mississippi River in order to preserve tribal traditions.  In reality, this attitude was really a mask to cover up the fact that Jackson wanted to acquire millions of acres for his Western constituents.  

Before he became president, Andrew Jackson fought in the war against the Creeks in 1813–1814. He and his nephew, John Coffee, were then part of what the author Anthony Wallace calls "Alabama fever." Using his influence in Washington, Jackson was able to have Coffee appointed the head government surveyor of Alabama lands. In his position, Coffee was aware of the location of valuable land, and he made his relatives aware of profitable deals. He also formed a land company that Andrew Jackson was part of, and Jackson was able to buy land near the shoals in Alabama without any competing bids. He later bought land in Mississippi as well. 
As the author writes, Jackson was not an exceptionally greedy person but reflected the general southern interest at the time in getting one's hands on Native Americans' land. This desire was most feverish in the southern slave-owning states out of a desire to have land on which to grow cotton, which was then a very profitable crop. Jackson became a proponent of Indian removal during his presidency, and he was long interested in the acquisition of Native American lands to further the economic interests of the slave holders in the South.

Does it make sense to say that characters in Pride and Prejudice are true to themselves?

Yes, it does. Elizabeth Bennet, for example, knows that she must marry for love, and she is unwilling to compromise her principles, even when presented with financially advantageous proposals from her cousin Mr. Collins and Mr. Darcy (the first time he proposes). Though either match would make her mother so happy and would, at least, secure her family against future financial strain, she cannot bring herself to entertain either of these men when she does not love them.
Charlotte Collins, née Lucas, on the other hand, really doesn't care about love. As she is nearing spinsterhood, financial security and avoiding becoming a drain on her family are her priorities. Therefore, when presented with a marriage proposal from Mr. Collins—a man she knows cannot possibly love her, as he just proposed to her best friend a few days earlier—she accepts with alacrity. She has said more than once that she is "not romantic," and she proves it by marrying someone she does not love so that she can maintain respectability and peace in her own life. These are her priorities, and she acts in accordance with them.
We might also consider Lady Catherine. We may not like her very much, but we have to concede that she sticks to her principles as well. Family is her priority, and when she hears a rumor that her nephew—who she intends her own daughter to marry—has proposed to a relatively penniless young woman with questionable relatives, she flies into action. In her own way, she is attempting to protect her family, and she shows her continued displeasure by refusing to attend the wedding of Darcy and Elizabeth. Again, we may not like her, but she sticks to her guns, so to speak.
Thus, these characters, and others, do behave in ways that feel "true to themselves." Most of them are fairly uncompromising of their principles, and when they do seem to change—as Elizabeth and Darcy do—it is due to a sincere reassessment of their prior behaviors and not a failure to be true to themselves.

Gulliver says, "[...] I always believed it would be, some Time or other, my fortune to do." What did Gulliver want to do, and how did he prepare for it?

Gulliver believed that it would be his fortune, at some point, to travel.  In order to prepare himself for a life of travel, he continued his education for some time, procuring money enough to do so.  He studied medicine, what he calls "Physick," because he knew that such a course of study would be useful and practical on voyages.  After school, he got a recommendation to serve as the "Surgeon" on board a ship called the Swallow, and he was gone about three and a half years.  When he returned, he tried to settle in London, set up a practice, and got married, but business was poor and his practice failed because, as Gulliver says, he was unwilling to "imitate the bad Practice of too many among [his] Brethren."  He went again to sea, making several trips over the next six years, and he eventually returned home.  Another business failure led him to try his hand, again, at travel, and thus begins the story.

Why does young Marguerite make the choice to speak to Ms. Flowers?

Young Marguerite makes the choice to speak to Mrs. Flowers because she senses that the older woman is different from the other adults in her life. Mrs. Flowers never makes Marguerite feel like she's at fault for not wanting to talk. She accepts Marguerite for who she is and never belittles her for her fears.
For her part, Marguerite is fascinated by Mrs. Flowers. The older woman reminds Marguerite of "women in English novels who walked with their dogs" and "who sat in front of fireplaces, drinking tea and eating cookies." In other words, Mrs. Flowers is refined and sophisticated. Marguerite thinks that Mrs. Flowers is as "well-mannered and civilized as white folks in the movies and books." Despite her obvious education, Mrs. Flowers remains friendly and modest.
It is Mrs. Flowers who tells Marguerite that "language is man’s way of communication with other people and it is language alone which separates him from the lower animals." Additionally, during her visit with Mrs. Flowers, Marguerite is made to feel right at home. She enjoys cookies that Mrs. Flowers has baked just for her, and she revels in the thought that she will be able to bring some of those cookies home to share with her brother. Later, Mrs. Flowers reads to Marguerite from A Tale of Two Cities.
Although Marguerite has read the book herself, she is held spellbound by Mrs. Flowers' voice as she reads. Throughout her whole experience at Mrs. Flowers' home, Marguerite is made to feel like she is valued for who she is rather than who she is related to. This makes all the difference in how Marguerite responds to Mrs. Flowers. While the other adults in her life try to control Marguerite, Mrs. Flowers is more focused on communicating with her young friend.
Mrs. Flowers' unique perspective on life and her kindness to Marguerite inspires Marguerite to open up to her.

Why does it make sense that this story takes place in a cantonment?

A cantonment is a military base in India.  The Kipling Society notes that the Segowlee Cantonment is a fictitious location; however, a cantonment is a real place where soldiers live and train.  A cantonment is a place for warriors.    
It makes sense that this story happens in a place where warriors live because Rikki-tikki is a warrior.  He may not be fighting humans, and he may not have human weapons of war, but that doesn't mean Rikki-tikki isn't a warrior with warrior weapons.  He's very quick, and has teeth that are capable of stabbing flesh for the killing blow.  Rikki-tikki is asked to put his warrior skills into practice during this story too.  He kills three deadly snakes over the course of the short story.  For a children's story, the body count is fairly high.  
The opening paragraph of the story also helps sell the cantonment setting.  

This is the story of the great war that Rikkitikki-tavi fought single-handed. . . 

Readers are introduced to a character fighting a war.  Active combat soldiers live in military bases.  Rikki-tikki is an active warrior in this story, and he is housed in a cantonment.  
http://www.kiplingsociety.co.uk/rg_rikkitikki_notes.htm

Beginning Algebra With Applications, Chapter 7, 7.3, Section 7.3, Problem 98

Multiply: $(2x - 9y)(8x - 3y)$

$
\begin{equation}
\begin{aligned}
&= 2x(8x) - 2x(3y) - 8x(9y) - 9y(-3y)
&& \text{Use foil method}\\
\\
&= 16x^2 - 6xy - 72xy + 27y^2
&& \text{Evaluate the expression}\\
\\
&= 16x^2 - 78xy + 27y^2
&& \text{Combine like terms}
\end{aligned}
\end{equation}
$

Precalculus, Chapter 6, 6.4, Section 6.4, Problem 62

You need to evaluate the projection of vector u onto vector v using the formula, such that:
proj_v (u) = ((u*v)/(|v|^2))*v
You need to evaluate the product of vectors u = u_x*i + u_y*j and v = v_x*i + v_y*j , such that:
u*v = u_x* v_x + u_y* v_y
u*v = (-3)*(-4)+ (-2)* (-1)
u*v = 12+2
u*v = 14
You need to evaluate the magnitude of the vector v, such that:
|v| = sqrt((-4)^2+(-1)^2) => |v|^2 = 17
proj_v (u) = (14/17)*v => proj_v (u) = (14/17)*<-4,-1>
proj_v (u) = <-56/17,-14/17>
Hence, evaluating the projection of vector u onto vector v yields proj_v (u) = <-56/17,-14/17> .

Assuming that the mass of the Milky Way Galaxy is 10^11 times that of the Sun and that the Sun is 2.45 × 10^20 meters from its center, what is the Sun's orbital speed around the center of the Galaxy? How long does it take the Sun to orbit the Milky Way? (In this problem, we assume that the Galaxy can be treated as a single body. Strictly speaking, this isn't correct, but the more elaborate math needed to calculate the problem properly ends up giving almost the same answer.) V = ___ × 10^___ m/s Time = ___ × 10^___ years

Hello!
Kepler's first law states that an orbit of a planet around the Sun is an ellipse with the Sun being at one focus of it. Our problem is close enough: the Milky Way Galaxy may be considered as a sun (large central body), and the Sun may be considered as a planet orbiting it. I assume this ellipse is almost a circle, because in the opposite case the speed of the Sun would be different at the different points of its trajectory.
Denote the radius of this orbit as R, it is given, and the speed as V, it is unknown. Also denote the given mass of the Milky Way Galaxy as M and the Sun's mass as m, it is about 2*10^(30) kg. Then the Newton's Law of Universal Gravitation tells us that the gravity force F is G*(M*m)/R^2, so by Newton's second law the acceleration is F/m = (GM)/R^2.
We also know that the acceleration of a body in uniform circle motion is V^2/R, so (GM)/R^2 = V^2/R, or V^2 = (GM)/R, or V = sqrt((GM)/R) = sqrt((G*10^11*m)/R).
Numerically it is about
sqrt((6.7*10^(-11)*10^11*2*10^30)/(2.45*10^20)) = sqrt(5.5*10^10) approx 2.3*10^5 (m/s),
or about 230 km/s.
The time needed is about (2piR)/V approx 6.7*10^15 (s) approx 212,000,000 years.
 
https://en.wikipedia.org/wiki/Galactic_year

https://www.physicsclassroom.com/class/circles/Lesson-3/Newton-s-Law-of-Universal-Gravitation

By what principle does Swift arrange his list of advantages in A Modest Proposal?

Swift arranges the list of advantages of killing and eating the babies of the poor on the basis of utilitarianism. It is important, however, to note that while Swift wrote the essay, it does not express his point of view. It is the point of view of a clueless person who is so fixated on economics and utilitarianism that he has lost his moral compass; Swift wants us to be horrified by this person's ideas.
Since the narrator is chiefly concerned with economics—making the poor pay their own way—his first priority and first selling point is that his proposal can be described as,

[A] fair, cheap and easy method of making these children sound and useful members of the commonwealth.

He seems to lose sight of that fact that by making poor children sound and useful members of the commonwealth through killing them, he will also render them no longer members of the commonwealth.
He then moves onto his more "humanitarian" points, although they make no sense in the context of killing these babies: he argues that his scheme will prevent abortions and will give mothers an incentive not to murder their newborns. The mothers will instead wait until their babies are a year old to sell them for slaughter.
Swift wants us to see how inhumane and senseless it is to approach poverty and suffering only from an economic perspective without keeping in mind that those who suffer are also human beings.

Tom is faced with an internal conflict. What is it?

While much of “Contents of the Dead Man’s Pocket” revolves around Tom Benecke’s external conflict, the drama of the external conflict is heightened by the twin internal conflicts with which the short story begins.
The first internal conflict that Tom faces is whether or not to go to the theater with his wife. This conflict manifests in the form of a heat that Tom ultimately recognizes as guilt.
The second and much longer internal conflict that Tom faces is whether or not to climb out onto the ledge of his high-rise apartment to retrieve the paper that has blown there. It is an important paper, just out of reach, and to Tom it represents both months of work and a path to success. Ultimately, the pressure to succeed at the workplace overrides Tom’s better judgment and he talks himself into climbing out of his window.
Both of these internal conflicts heighten the sense of dread and regret that Tom experiences while on the ledge. Twice Tom faces an internal conflict, and in both cases acting on them differently would have kept Tom safe during the night. This realization—by both Tom and the reader—produces a sense of regret. Ultimately, realizing the error of his ways provides Tom with the strength to smash through the window, reenter his apartment, and find his wife at the theater.

What is an atom?

An atom is the smallest piece of an element which maintains the chemical properties of that element. It is made up of smaller bits of particles called subatomic particles. There are three different types of subatomic particles: protons, neutrons and electrons.
The nucleus of an atom is at the center and it contains protons and neutrons. The proton carries a positive charge but the neutron is neutral and carries no electric charge. The nucleus of the atom is surrounded by electrons which are negatively charged and they are arranged in shells referred to as energy levels.
Atomic number refers to the number of protons in the atom. Atoms have no electrical charge overall because the number of protons which carry positive charge in the atom is the same as the number of electrons which carry negative charge.
https://www.bbc.co.uk/bitesize/guides/zwn8b82/revision/3

How is whiteness socially constructed?

Whiteness has been socially constructed in a variety of ways. Beginning with the social construction of race through global exploration in the late 1700s. Scientists began to create categories for racial classification and used these categories to justify European colonialism through racial superiority. These European scientists claimed that white people were the superior race and therefore justified the often sub-human treatment of colonial subjects. Society continued to construct whiteness in the United States as people immigrated and people tried to maintain a rigid social hierarchy. Initially there was a clear distinction between African Americans, Native Americans, and European immigrants. However, in the 1800s as increasing numbers of European immigrants arrived in the US, White Americans felt that their whiteness was being threatened. These new European immigrants were undesirable and therefore were not granted the same status of whiteness as the established white American residents. We see this in history with the various waves of anti-immigrant sentiment directed at the Polish, Irish, Italian, and Jewish. However, given time each of these immigrant groups was enveloped into the American construction of Whiteness. America continues to construct whiteness today through the systemic oppression of people of color. White people in the United States are afforded increased access to education, economic opportunities (ex. loans), higher wages, decreased arrest rates, etc. In order to be considered "white" in the United States people not only have to look a certain way but also have to comport themselves in specific ways. There are clear unspoken expectations in this country about what is and is not acceptable to the dominant (white) culture and in this country the dominant culture is White culture. A further way that Whiteness is constructed and works to oppress people of color is through forced assimilation into White culture. Dominant culture (white culture) expects people of color to speak and act in certain ways and when they do not the dominant (white) culture punishes these people by refusing to promote them, denying them access to loans, marketing them as dangerous, etc. Whiteness is a meaningless social construction like every other racial category. However, what gives these racial categories power is the way which we validate them and use them to oppress certain people and privilege other people.

Whiteness is socially constructed inasmuch as certain characteristics are assigned to it, and boundaries are drawn around it. Historically, "whiteness" has been constructed by societies that have assigned benefits to it. In slave societies, for example, laws have determined who was legally white and who wasn't. This was because not being white carried the stigma of slavery. Over time, legal mechanisms established whiteness in the South, where eventually anyone with an African-American ancestor was deemed to be nonwhite and subjected to the discrimination of Jim Crow laws. This might be the case irrespective of skin color, which demonstrates the constructed nature of "whiteness": a person, like Homer Plessy of the famous Supreme Court decision Plessy v. Ferguson, could be deemed non-white. There have been times in American history when Irish immigrants, regardless of skin color, were portrayed and imagined as non-whites, and the same was true of Eastern European immigrants later. Both of these peoples "became white" as legal distinctions against them were dropped over time. So "whiteness" describes a group of people whose members correspond to a certain "race," that are designated as privileged by a society. Because scientists have observed that race itself is essentially a meaningless, spurious means of categorizing people, the concept of "whiteness" is a complete social fabrication devoid of any meaning beyond maintaining power and privilege.

In "The Lottery" by Shirley Jackson, why did the lottery officials and people prefer a male from the family to draw?

One of the fascinating aspects of Shirley Jackson's short story, "The Lottery," is the strong adherence to tradition evinced by the actions and words of the townspeople before, during, and after the lottery. Not only are the traditions of the lottery followed uncritically, what conversation that does occur among characters concerning the traditional nature of the lottery is primarily to decry other places that have slipped in following tradition or that have discontinued the lottery entirely. Further, things that disrupt the strict adherence to tradition, such as Tessie Hutchinson's futile protestations over her fate, lead to discomfort and unease among the townsfolk.
One such tradition apparent in the story is that the head of household is responsible for drawing in the first stage of the lottery, the one that determines from which household the sacrifice will be taken. It is also apparent that, traditionally, the head of household duties are performed by the eldest adult male present from the household. This is best shown by the exception that occurs. Mrs. Dunbar has to draw for her husband because he is unable to attend the lottery due to a broken leg and their eldest son is not yet old enough to serve as head of household for the lottery. However, it is clear form the conversation between Mr. Summers and Mrs. Dunbar that it would be preferable for her son to draw instead of her if he were old enough. Further, the "Watson boy" is praised for being old enough to draw for his mother and himself, further showing that, traditionally, the eldest adult male in a family was considered the head of that household, at least for the purposes of the lottery.
Like with the lottery itself, the purpose behind the tradition of a male being the head of household and drawing during the first stage of the lottery is not important. What is important to the townspeople is that the traditions of the lottery be adhered to as closely as possible. Anything else brings to the surface the discomfort and unease that they all seem to feel about the lottery. By following the traditions as closely as possible, including the tradition of the male head of household drawing in the first stage of lottery, the townspeople are able to blindly follow the traditions rather than focus on the horror of the sacrifice.
 
 
 

How could I summarize the plot of Every Day by David Levithan in five to seven sentences?

Because the plot of a story has exactly six elements, your question sets up a perfect scenario for a tiny plot summary of Every Day.  The plot always begins with the exposition, when the reader learns about the character and the setting.  During this part of the story, the reader learns about A, who lives in a body only for 24 hours before switching to another one.  Next comes the inciting incident (that some call the conflict):  the problem in the story that needs to be solved.  This particular incident here is when A falls in love with Rhiannon when he inhabits the body of Justin.  This is followed by the rising action, when the tension begins to mount.  Many things happen in the rising action of Every Day.  In fact, in almost every moment of the rising action, A is trying to reach Rhiannon through another body.  Meanwhile, he is foiled a bit by other bodies that he has previously inhabited. The tension continues until it reaches the story's climax:  the height of the tension.  There is no doubt that the climax of the story is when Rhiannon and A figure out that they cannot have a regular relationship.  The climax is followed by the falling action, when things begin to return to normal:  A knows the result of their climactic decision is best for Rhiannon.  By the time of the resolution, the original conflict has been solved in some way.  In fact, A takes his "new" body (Katie) on an adventure in order to disappear.  If you apply these ideas to your assignment for Every Day, it should be easy to write five to seven sentences having to do with the plot.

Who was Assef in The Kite Runner most like in A Thousand Splendid Suns and The Thorn Birds?

It can be argued that Assef is most like Rasheed in A Thousand Splendid Suns. Assef's equivalent in The Thorn Birds, however, would be a combination of Mary Carson and Luke O'Neill. Let me explain.
Like Assef, Rasheed in A Thousand Splendid Suns harbors a violent streak. In The Kite Runner, Assef is guilty of rape, murder, and theft. Although Rasheed does not kill anyone, he comes close to it. Without Mariam's intervention, Rasheed would have choked Laila to death. Both Rasheed and Assef are capable of great violence. The only difference between the men is that Assef has committed actual murders.
When we turn to The Thorn Birds, the closest equivalent to Assef (based on the capacity for violence) is Luke O'Neill. Luke does not kill anyone, but he enjoys his wedding day privileges at Meggie's expense. It can be argued that Luke actually raped Meggie during their first sexual encounter. The text is clear that Luke demonstrated little regard for his bride's sexual inexperience and made no effort to spare her physical agony:

She fought like one possessed to be rid of that ghastly, painful thing, but his weight pinned her down and his hand deadened her cries, the agony went on and on. Utterly dry because he hadn't roused her, the even drier condom scraped and rasped her tissues as he worked himself in and out, faster and faster. . . then some change stilled him, made him shudder, swallow hard. The pain dulled to raw soreness and he mercifully rolled off her to lie on his back.

Here, Luke's actions mirror that of Assef's in The Kite Runner. In his youth, Assef raped the helpless Hassan and as an adult, he makes Sohrab (Hassan's son) his sexual slave. Assef also participates in the murder of thousands of Hazaras and religious minorities. Rasheed in A Thousand Splendid Suns comes closest to Assef in terms of pure malice and savagery. Consider how Rasheed treats Mariam during their first sexual encounter after their wedding:

He slid under the blanket beside her. She could feel his hand working at his belt, at the drawstring of her trousers. Her own hands clenched the sheets in fistfuls. . . . The pain was sudden and astonishing. Her eyes sprang open. She sucked air through her teeth and bit on the knuckle of her thumb. She slung her free arm over Rasheed's back and her fingers dug at his shirt.

To get back to The Thorn Birds, Luke O'Neill is similar to Assef in the sense that both men are self-absorbed, violent, and reckless. However, Luke is not a sadist or a sociopath, at least not in the typical sense. On the other hand, Assef is openly malicious and sadistic in nature. He revels in forcing his fellow Muslims to watch his brutal executions of religious minorities or other Muslims he deems "unrighteous." Assef even gloats in Sohrab's sexual slavery and openly taunts Amir when the latter begs for Sohrab to be released into his custody. Based on his sadistic nature, Assef's equivalent is Mary Carson in The Thorn Birds.
Knowing that her sexual passion for Father Ralph de Bricassart will never be reciprocated, Mary Carson leaves the priest with a terrible choice upon her death: he can either leverage Drogheda and the 13 million pounds she bequeaths him to fulfill his ambitions in the Catholic Church or deprive Meggie (the woman he loves) of her inheritance. Mary understood the immense emotional agony Ralph would suffer in making his choice, and she delighted in that knowledge. Mary's sadistic nature is equivalent to Assef's nature: both derive actual delight from being the cause of another's suffering.

What effect do you think the Industrial Revolution had on the quality of life of those most affected by it?

The Industrial Revolution had a tremendous impact on the labor force. When the Industrial Revolution began, most people who worked in manufacturing were negatively impacted by it. Prior to the Industrial Revolution, many people were working in small, worker-friendly environments. The business owners and the workers knew each other and their families very well. The workers were treated well by the business owners. This changed with the start of the Industrial Revolution.
When the Industrial Revolution began, people went to work in factories since expensive machines were being used to manufacture products. There were hundreds of people working in these factories. The owners and workers had little to no contact with each other. Working conditions were poor, and the pay was very low. They also worked very long hours. There was very little regard for those who worked in the factories. Supervisors were more concerned with production than they were with the overall well-being of the workers. As a result, workers were negatively impacted when the Industrial Revolution began.

How would you describe Atticus Finch as a parent?

Atticus Finch is a single father to his two children, Scout and Jem. He tells Jem to read a newspaper to Ms. Dubose, who is trying to die without being addicted to morphine. Atticus does this because he considers Mrs. Dubose's determination to overcome her addiction to be very courageous, and he wants Jem to see that courage and learn from it. Atticus also takes Scout and Jem to the courtroom with him during Tom's trial, showing he does not shelter his children from the reality of race relations in Maycomb. Additionally, Atticus teaches his children that cruelty for the sake of cruelty is wrong. An example of this would be when Atticus tells Jem that it's a sin to kill a mockingbird because they are innocent. Atticus does kill a rabid dog in the story, though, which shows Jem and Scout that sometimes one has to fight to protect oneself and others from danger. Atticus tells Jem to take care of and watch out for Scout, and Atticus does not make Scout dress up in girly clothes. He also talks to his children like they are adults. By letting his children be themselves and showing them respect, Atticus makes Jem and Scout more responsible and mature.  

What is the theme of "Once upon a Time" by Nadine Gordimer?

A theme is a universal truth about life or mankind that a work of art seeks to convey. A literary work can have many themes. Three themes in Nadine Gordimer's short story are explained below.
1. Living in fear creates a prison of one's own making. In the story frame and in the bedtime story the narrator tells herself, the characters allow fear to dictate how they act. The narrator, lying in bed, is "a victim already." She feels trapped in her room, unable to rest or sleep but also unable to rise up and put her fears to rest. The family, attempting to protect themselves from rioters, murders, and burglars, enclose themselves behind walls, bars, and finally an ugly Auschwitz-like coil. What they do to their property symbolizes what they are doing to their souls and spirits—cutting themselves off and stunting their lives because of their fears.
2. Avoiding and withdrawing from what we fear, especially if it is fear of "the other," cannot solve the problem. The more effort the family makes to escape from the racial/ ethnic group they distrust, the more the problems between their community and the other community grows. The wife's instinct to reach out to the other group with compassion is quickly squelched, yet that is the only glimmer of possibly bringing an end to the escalating fear and isolation the family feels.
3. To live "happily ever after" requires more than material possessions. Looking for root causes of the tragedies that occur in the story, we must follow the money, and we find that love of money is the root of this evil. The family has arrived at their "house in a suburb" where they "had a car and a caravan trailer for holidays, and a swimming-pool." This good life that they have achieved requires protection. They fear losing it, so they insure it and participate in Neighborhood Watch. They can't insure against riot, though, so they go to drastic measures to make sure their property can't be taken from them. In the family's obsessive desire to protect their material wealth, their relationships suffer. The mother-in-law is a "witch," and they are unable to show basic human kindness to outsiders that would enrich their own souls and spirits. Ultimately, they lose their most precious "possession," their son, because of their fixation on protecting their material goods.
These strong themes of fear, prejudice, and materialism make "Once upon a Time" a powerful short story.

 There are two dominant themes that arise from Gordimer's work.  The first one being the fear of "the other."  The family's drive to protect themselves and essentially shield themselves from the outside world represents an inherent fear of that which is unknown.  This fear is the driving force behind inwardly drawn communities and also represents a large and underlying rationale of apartheid in Gordimer's own native South Africa.  The attitudes of the family help to develop this theme of a fear of that which is unknown or misunderstood.  The tragic condition of the family at the end, resulting the death of their child, is a result of this fear.  Another theme in the work is the idea of the idealistic and reciprocal nature of creation and destruction.  This holds the idea that each act of creation is an inevitable step towards destruction.  The family seeks to create a "perfect" solution to their fear of the outside world.  In barricading themselves off, they feel they have "the answer."  However, with each advancing step in this vein, they actually move a step closer to destruction and terror, as they move farther away from rationality and understanding and closer to a domain where destruction is the only logical end. 

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 18

a.) By using Pythagorean Theorem, we have...
$x^2 + 90^2 = z^2$; when $x = 45$ft; $z = \sqrt{45^2 + 90^2} = 45 \sqrt{5}$ft


Taking the derivative with respect to time,
$\displaystyle 2x \frac{dx}{dt} + 0 = 2z \frac{dz}{dt}$

$
\begin{equation}
\begin{aligned}
x \frac{dx}{dt} &= z \frac{dz}{dt}\\
\\
\frac{dz}{dt} &= \frac{x}{z} \frac{dx}{dt}
\end{aligned}
\end{equation}
$

Plugging in all the values we have,

$
\begin{equation}
\begin{aligned}
\frac{dz}{dt} &= \frac{\cancel{45}}{\cancel{45}\sqrt{5}} (24)\\
\\
\frac{dz}{dt} &= \frac{24}{\sqrt{5}} \text{ or } \frac{24\sqrt{5}}{5} \frac{\text{ft}}{s}
\end{aligned}
\end{equation}
$


The distance of the battler from the second base is decreasing at a rate of $\displaystyle\frac{24\sqrt{5}}{5}\frac{\text{ft}}{s}$
b.)



Again, by using Pythagorean Theorem,
$x^2 + 90^2 = z^2$; when $x = 45$ft; $z = \sqrt{45^2 + 90^2} = 45 \sqrt{5}$ft
Taking the derivative with respect to time,

$
\begin{equation}
\begin{aligned}
0 + 2x \frac{dx}{dt} &= 2z \frac{dz}{dt}\\
\\
x \frac{dx}{dt} & = z \frac{dz}{dt}\\
\\
\frac{dz}{dt} & = \frac{x}{z} \frac{dx}{dt}
\end{aligned}
\end{equation}
$


Plugging all the values we obtain,


$
\begin{equation}
\begin{aligned}
\frac{dz}{dt} &= \frac{45}{45\sqrt{5}} (24)\\
\\
\frac{dz}{dt} &= \frac{24}{\sqrt{5}} \text{ or } \frac{24\sqrt{5}}{5} \frac{\text{ft}}{s}
\end{aligned}
\end{equation}
$

Thus shows that the distance of the batter from the third base is increasing at a rate equal to the decreasing rate of the batter's distance from the second base.

What are the drawbacks of modernism?

One of the possible drawbacks of modernist art, depending on one's perspective, is that it borrowed heavily from West African influences in sculpture but took little interest in the cultures from which the artifacts were derived.
In Paris, West African masks and sculptures were sought after as early as 1906 but became particular objects of interest during the period between the wars, collected by the American expatriate writer Gertrude Stein and the gallery owner Paul Guillaume. African art also had a substantial influence on the development of Cubism, particularly as it was envisioned by Pablo Picasso.
Many European critics at the time, particularly French critics, believed that European culture could rejuvenate itself through a superficial exploration of African art and cultures. I write "superficial" because Europeans expressed little interest in learning about African cultures as they actually were; instead, they superimposed their own ideas about the region and its peoples, which were often very stereotypical. They believed, for example, that African culture amounted to little more than primeval expressions of sexuality and sensuality, as well as more primitive forms, and sought to superimpose that in European art. The interest in African art was a rejection of the machine age. Machinery was integral, after all, in the destructive war that had broken the European spirit. In France, where the interest in African art was particularly pronounced, the nation suffered massive losses in World War I.
So, I would argue that one of the drawbacks of modernism was that it fetishized African, as well as Black American, cultures with the misguided belief that these cultures could rejuvenate artistic production and culture in Europe. On the other hand, without these influences, we would not have Cubism, and jazz would never have made it to Europe, especially France, where it retains cultural influence.

Although modernism was an important movement in the arts and resulted in many outstanding works, there are several possible criticisms of it.
First, modernism (and postmodernism, to an even greater degree) is essentially parasitic on earlier traditions. Breaking the boundaries of meter, for example, only has meaning if regular meter is a standard poetic convention. Once a convention disappears, fighting against it is meaningless; this means that modernist works can appear dated once their project succeeds. Many aspects of modernism embody ironic re-appropriation of Victorian material, something only relevant at a time when Victorian standards were commonly accepted.
Next, modernist art is inherently elitist. It is highly allusive, hermetic, and cerebral, appealing only to a limited audience. This tends to weaken public support for the arts. Taken with the standard mode of modernism being critique, artistic modernism can end up in unintended de facto opposition to the arts.
At times, modernist works in their explicit self-reflexivity become almost a commentary on art, so that what the reader experiences in not so much the sense of discovering a beautiful poem or painting but of reading a scholarly journal.

Modernism was an important aesthetic and cultural movement that is generally thought to have begun in the late 19th century and to have remained extremely influential at least until the WWII era. Though it is an important historical period, especially in terms of the art it produced, the Modernist era also wrestled with some seriously negative ideas, and these could be seen as potential drawbacks. For instance, Modernist literature often explores the lives of individuals that have been alienated from society, or who feel isolated from the culture they live in. Moreover, many Modernist writers tended to suggest that, since many traditional values were destroyed by advancements in science, philosophy, and more, existence was meaningless and lacked any kind of solid foundation. Now, it's important understand that these were and are important concepts to explore. That said, these ideas could also be seen as the drawbacks of Modernism, as they advance a thoroughly pessimistic and depressing view of life. 

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 65

Suppose that $f$ and $g$ are the functions whose graphs are shown, let $u(x) = f(g(x)), v(x) = g(f(x))$ and $w(x) = g(g(x))$. Find each derivative, if it exist, explain why.







a.) $u'(1)$


$
\begin{equation}
\begin{aligned}

u'(x) =& f'(g(x)) g'(x)
\\
\\
u'(1) =& f'(g(1)) g'(1)
\\
\\
u'(1) =& f'(3) g'(1)
\\
\\
u'(1) =& \left( \frac{3 - 4}{6 - 1} \right) \left( \frac{0 - 6}{2 - 0} \right)
\\
\\
u'(1) =& \left( \frac{-1}{4} \right) (-3)
\\
\\
u'(1) =& \frac{3}{4}

\end{aligned}
\end{equation}
$


b.) $v' (1)$


$
\begin{equation}
\begin{aligned}

& v'(x) = g'(f(x)) f'(x)
\\
\\
& v'(1) = g'(f(1)) f'(1)
\\
\\
& v'(1) = g'(2) f'(1)
\\
\\
& v'(1) \text{ does not exist because $g'(2)$ doesn't exist.}

\end{aligned}
\end{equation}
$



c.) $w' (1)$


$
\begin{equation}
\begin{aligned}

w'(x) =& g'(g(x)) g'(x)
\\
\\
w'(1) =& g'(g(1)) g'(1)
\\
\\
w'(1) =& g'(3) g'(1)
\\
\\
w'(1) =& \left( \frac{2 - 0}{5 - 2} \right) \left( \frac{0 - 6}{2 - 0} \right)
\\
\\
w'(1) =& \left( \frac{2}{3} \right) (-3)
\\
\\
w'(1) =& -2

\end{aligned}
\end{equation}
$

Why does Shylock hate Antonio and Christians in general?

Shylock hates Antonio because Antonio has the privilege of being a wealthy Venetian who charges no interest on his loans, and he also hates Antonio for being a Christian. Additionally, Shylock hates Antonio for the outspoken disdain that Antonio displays towards him.
Early in act I, Shylock expresses his hatred for Antonio.

I hate him for he is a Christian. . .He lends out money gratis and brings downThe rate of usance here with us in Venice.If I can catch him once upon the hip,I will feed fat the ancient grudge I bear him. (1.3.34-38)

Antonio not only loans money interest-free to many, he has also covered the loans of Shylock's victims without charging them interest to repay him. This action has enabled Shylock's victims to escape total ruin, as they pay off their loans to Shylock quickly without having to pay most of the added charges for these loans. Then, they can repay Antonio simply for the amount of their loan. Furthermore, Antonio's action also undercuts Shylock and forces him to lower his interest rates in order to get others to borrow from him. 
In addition to undercutting Shylock, Antonio has denounced Shylock in public, calling him a dog. He has even kicked and spat upon Shylock. Shylock reminds Antonio of these insults: 


In the Rialto you have [be]rated me
About my moneys and my usances.
Still have I borne it with a patient shrug. . .
You call me misbeliever, cutthroat dog,
And spet upon my Jewish gaberdine—
And all for use of that which is mine own. (1.3.105-111)
 



Antonio's insults help motivate Shylock to loan Antonio money with a horrific penalty for failure to make repayment. If Antonio fails to repay Shylock, Shylock can exact a brutal revenge against his enemy.
 
Shylock would hate Christians in general since, at the time of this play, Jews in Venice were made to live in a ghetto and were prohibited from being in Venetian society. The word ghetto may have been derived from the Italian word, getto, meaning foundry. (The first ghetto was established on the site of a foundry in Venice in 1516), or from the Italian word borghetto, which is the diminutive of the word borgo that means borough.

In Shakespeare's The Merchant of Venice, Shylock hates Antonio for many reasons. First, Shylock claims that he hates Antonio because he is a Christian. Historically, many tensions have existed between Christian and Jewish communities, with Jews often facing significant persecution at the hands of Christians. As such, it's hardly surprising that Shylock would regard any Christian with distaste. Second, Shylock hates Antonio because he lends money without charging interest. As a moneylender, Shylock makes his money by charging interest on loans, and any competitors who charge lower rates (or no rates at all) are likely to cut into his profits. Finally, and most importantly, Antonio proves himself to be anti-Semitic, bullying and abusing Shylock on several occasions simply because he is Jewish. As such, it's hardly surprising that Shylock hates both Antonio and Christians in general, as it seems that he is regularly oppressed by Antonio and the general Christian community in Venice. 
Understanding the reasons for Shylock's hatred of Antonio changes the meaning of the play. Before delving into the many motivations behind Shylock's anger, it's possible to feel sorry for Antonio and see him as a victim. However, once we realize the full extent of Antonio's abuse of Shylock, it becomes much more difficult to feel bad for him. Sure, he may not deserve to be carved up, but Antonio's oppressive treatment of Shylock certainly does not earn our respect. Indeed, by the end of the play, it becomes much easier to sympathize with the oppressed Shylock.

How is Romeo a tragic character?

Romeo is a tragic hero for two reasons. First, his situation is tragic. He is a Montague and he falls in love with a Capulet. The two families, bitter enemies, have been feuding for many years. His is truly a forbidden love. As Juliet reminds him as he scales the garden wall to visit her, if her male relatives find him, they will kill him.
Second, Romeo has a tragic personal flaw: he is too impulsive. Like a typical teenager, he lives very passionately in the moment. For instance, he and Juliet marry a day after they meet, and even that feels too long to him (and to her as well for that matter). Therefore, when he does not receive the message that Juliet is faking death and finds what he thinks is her corpse, we are not surprised when he acts impulsively and immediately kills himself. If only he had waited a little while! But that would not be Romeo. He commits suicide. Juliet kills herself when she finds him dead, and for both the end is tragic.

Why was the delegates' meeting for the Constitutional Convention so secretive?

At the Constitutional Convention of 1787, the Founding Fathers' deliberations were held in total secrecy. The reason for this is that those attending the Convention did not want any information getting out which might lead to misunderstanding or the deliberate distortion of what they were doing. This may seem like an overreaction, but these concerns were perfectly valid under the circumstances. The political atmosphere was deeply acrimonious at the time, with people holding many different competing visions for what the United States should look like in future. The fierce partisan debate was reflected in the press, which routinely engaged in outright slander against individuals whose positions they disagreed with. In such a toxic environment, it is not surprising that the delegates of the Convention agreed to hold it in secret.
Secrecy allowed the delegates to have a vigorous, open, honest debate without worrying about what their political opponents and scurrilous journalists would say. It also meant that some of the heat could be taken out of an increasingly fractious political environment, greatly conducive to the overall stability of the country. The making of the Constitution was an important business and needed to take place in an appropriately serious atmosphere, one in which differences could reasonably be aired without being subject to the dictates of ill-informed opinion.
http://law2.umkc.edu/faculty/projects/ftrials/conlaw/convention1787.html