How was immigrant labor beneficial to the United States?

The United States owes a lot to immigrant labor. Immigrants provided a lot of the unskilled labor which built this country. Irish and German immigrants helped make Henry Clay's American System thrive by building the necessary infrastructure such as the canal and railroad system. These immigrants came looking for work and they often took jobs for low wages that native-born Americans would take only as a last resort.
Even though anti-immigrant bias has been common since the country's inception, immigrants have been valuable in performing jobs that Americans needed. Chinese immigrants were quite successful in the gold fields of California—so successful that they were wrongfully accused of stealing claims and this was part of the reason why the nation passed the Chinese Exclusion Act in the 1880s, the first time the nation attempted to restrict the immigration of a specific group.
After the Civil War, thousands of immigrants came from Southern and Eastern Europe in order to work in the factories of the major metropolitan areas. This led to friction between the new immigrants and native-born Americans who feared for their jobs and their way of life as these new immigrants were slow to assimilate due to their settling in already-established immigrant communities. Immigrants also provided valuable skilled labor over the years as well, as most of America's early work on outer space would not have been possible without German rocket scientists.
Currently, the United States still needs immigrant labor. The H-1B visa program brings in skilled laborers from all over the world to work in fields such as IT and medicine. Undocumented workers are controversial; yet without them, much of the nation's manual labor would go undone. There would be virtually no one to harvest our food. Also, these workers contribute to the local economy by spending their wages in the US. While minimum wage floors have allowed the immigrants not to compete for lowered wages like they did in the 1800s, the plight of unskilled immigrant workers is still scary.

Using "The Monkey's Paw" and "What Do You Wish For?" please answer the following: What benefits might you get from working to make a wish come true rather than having it come true through magic?

The benefits from working to make a wish come true are profound. When a person works to achieve a dream, it is, psychologically speaking, worth more because of the effort expended to obtain it. Perhaps Thomas Paine said it best: "What we obtain too cheap, we esteem too lightly." To continue in this line of thinking, if a person is granted a wish with no effort expended by him or her, the wish will hold less value.
In the process of working to make a wish come true, the person has ample opportunity to continually weigh whether the wish is worth the effort or whether the wish is no longer as important as it seemed at first. Life changes a person's circumstances and desires, and it is possible that the wish will diminish in importance or completely evaporate over time.
In "The Monkey's Paw," the wife's wish for her deceased son's return is not a carefully considered wish. It is the result of an impulsive, emotional reaction, and it carries some pretty horrific possibilities. The magic that reanimates her son offers no guarantees that negative consequences will not accompany the wish. Handing one's life over to "magic" removes control over a situation that one might otherwise have.

Single Variable Calculus, Chapter 4, 4.5, Section 4.5, Problem 28

Use the guidelines of curve sketching to sketch the curve. $\displaystyle y = x^{\frac{5}{3}} - 5x^{\frac{2}{3}}$

The guidelines of Curve Sketching
A. Domain.
Since the function is continuous everywhere. It's domain is $(-\infty, \infty)$

B. Intercepts.
Solving for $y$-intercept, when $x= 0$
$y = (0)^{\frac{5}{3}} - 5(0)^{\frac{2}{3}} = 0$
Solving for $x$-intercept, when $y = 0$

$
\begin{equation}
\begin{aligned}
0 & = x^{\frac{5}{3}} - 5x^{\frac{2}{3}}\\
\\
5x^{\frac{2}{3}} &= x^{\frac{5}{3}}\\
\\
5 &= x^{(5/3 - 2/3)}\\
\\
x &= 5
\end{aligned}
\end{equation}
$



C. Symmetry.
The function is not symmetric to either $y$-axis or origin by using symmetry test.

D. Asymptotes.
The function has no asymptotes.

E. Intervals of Increase or Decrease.
If we take the derivative of $f(x)$

$
\begin{equation}
\begin{aligned}
f'(x) &= \frac{5}{3} x^{\frac{2}{3}} - 5 \left( \frac{2}{3} x^{\frac{-1}{3}} \right)\\
\\
f'(x) &= \frac{5}{3} \left[ x^{\frac{2}{3}} - 2x^{\frac{-1}{3}} \right]
\end{aligned}
\end{equation}
$


when $f'(x) = 0$

$
\begin{equation}
\begin{aligned}
0 &= x^{\frac{2}{3}} - 2x^{\frac{-1}{3}}\\
\\
0 &= x \left( x^{\frac{-1}{3}} - 2x^{\frac{-4}{3}} \right)
\end{aligned}
\end{equation}
$

We have, $x=0$ and $x^{\frac{-1}{3}} - 2x^{\frac{-4}{3}} = 0$

Therefore, the critical numbers $x = 2$ and $x = 0$. Hence, the interval of increase or decrease is.

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


F. Local Maximum and Minimum Values.
Since $f'(x)$ changes from negative to positive at $x=2$. Thus $f(2) = -4.76$ is a local minimum. On the other hand, since $f'(x)$ changes from positive to negative at $x = 0$, thus, $f(0) = 0$ is a local maximum.

G. Concavity and Points of Inflection.

$
\begin{equation}
\begin{aligned}
\text{if } f'(x) &= \frac{5}{3} \left[ x^{\frac{2}{3}} - 2x^{\frac{-1}{3}} \right], \text{ then}\\
\\
f''(x) &= \frac{5}{3} \left[ \frac{2}{3} (x)^{\frac{-1}{3}} -2 \left( \frac{-1}{3}\right) (x)^{\frac{4}{3}} \right]\\
\\
f''(x) &= \frac{10}{9} x^{\frac{-1}{3}} + \frac{10}{9} x^{\frac{-4}{3}}
\end{aligned}
\end{equation}
$


when $f'(x) = 0$

$
\begin{equation}
\begin{aligned}
0 &= \frac{10}{9} \left( x^{\frac{-1}{3}} + x^{\frac{-4}{3}} \right)\\
\\
0 &= x^{\frac{-1}{3}} + x^{\frac{-4}{3}}\\
\\
0 &= x \left( x^{\frac{-4}{3}} + x^{\frac{-7}{3}} \right)
\end{aligned}
\end{equation}
$

We have $x = 0$, as our inflection points
Hence, the concavity is...

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f''(x) & \text{Concavity}\\
\hline\\
x < 0 & - & \text{Downward}\\
\hline\\
x > 0 & + & \text{Upward}\\
\hline
\end{array}
$


H. Sketch the Graph.

What action does Claudius take against Hamlet after the play in act 3?

After Hamlet stages the "mousetrap" play, Claudius knows beyond the shadow of a doubt that Hamlet is aware that he, Claudius, killed the senior Hamlet to get the throne. Claudius now knows the reason why Hamlet has been acting so strangely. Then, after Hamlet kill Polonius, Claudius has to assume that he was the target, not Polonius. He also recognizes that Hamlet is capable of killing. Claudius understands he has to act fast and get rid of Hamlet for good.
Hamlet is popular in Denmark, so rather than jail him for murdering Polonius, Claudius sends him to England with his courtiers Rosencrantz and Guildenstern. He sends the duo with a sealed letter ordering that Hamlet be killed when he gets to England.
Since the two courtiers are fools, it doesn't take long for Hamlet to open the letter, read it, and write a new letter condemning Rosencrantz and Guildenstern to death. Having dodged this bullet, Hamlet returns to Denmark. So does Laertes, bent on killing Hamlet to avenge his father. Claudius manipulates the hot-headed Laertes into fighting Hamlet with a poisoned rapier.
Claudius does not last long as a monarch. If Hamlet had not killed him at the end of the play, he would have been deposed by Fortinbras arriving with an army. As it happens, Hamlet is wounded with the poisoned rapier and dies, but it does Claudius no good.

In act three, Hamlet has a private conversation with Gertrude and kills Polonius, who was secretly listening in on their conversation. Following Polonius's death in act 3, Claudius believes that he will be held responsible for Polonius's death, and he moves forward with his plan to send Hamlet to England alongside his friends, Rosencrantz and Guildenstern. Claudius also secretly sends a letter with Rosencrantz and Guildenstern instructing the authorities in England to murder Hamlet upon his arrival. However, Hamlet ends up discovering Claudius's letter and returns back to Denmark. Claudius then plots Hamlet's death by setting up a fencing match between Hamlet and Laertes, who wishes to avenge his father's death. Claudius also has Hamlet's drink poisoned as a backup plan in the event that Laertes fails to strike the prince with his poison-tipped sword. Tragically, Claudius's plan backfires as Gertrude drinks the poison, and Hamlet kills Claudius before dying alongside Laertes.

In Chapter 3 of Lord of the Flies, how does Jack display animal-like behavior?

In the chapter's opening line, Jack is hunkered down, sniffing the earth like an animal. Golding refers to him as "dog-like." Jack ignores his own discomfort as he proceeds on all fours to track pigs that have passed through the underbrush. Except for "a pair of tattered shorts," he is naked.
Moments later, Golding describes Jack as "ape-like." When he is suddenly startled by a forest cry, he shrinks "with a hiss of indrawn breath," suggesting that he is guided by instinct rather than reason.
When Jack later meets up with Ralph, he has trouble conveying (in words) to him "the compulsion to track down and kill," a primitive, unreasoned, and animalistic behavior. Later in their conversation, Jack tells Ralph that sometimes when he is in the jungle he senses that he is being hunted. Since there are no predators of man on the island, it is as if Jack is slipping into animalistic, instinctive thoughts and behaviors, as opposed to the higher thinking of Ralph, Piggy, and Simon.

At the beginning of Chapter 3, Jack acts like an animal as he attempts to track pigs. Jack gets down on all fours like a sprinter and looks closely at the forest floor in order to spot any signs that indicate pigs are nearby. Golding describes Jack's mannerisms as being "dog-like" as he crawls on the ground looking for evidence of pigs. Jack even closes his eyes and breathes in the air to pick up a scent, which is something a dog would do. As Jack enters the forest, he travels in silence and examines pig droppings, which indicate the pigs are somewhere nearby. Overall, Jack's appearance and actions at the beginning of Chapter 3 resemble that of an animal, particularly a bloodhound. Unfortunately, Jack is unable to successfully kill a pig in Chapter 3 and begins arguing with Ralph about the importance of obtaining meat for the boys. 

At the start of the chapter Jack is on the hunt and most of the descriptions regarding his actions equate him to an animal on the prowl - a predator seeking its prey. In the first paragraph we read:

Jack was bent double. He was down like a sprinter, his nose only a few inches from the humid earth......Then dog-like, uncomfortably on all fours yet unheeding his discomfort, he stole forward five yards and stopped.

The highlighted words indicate that he has assumed the position of an animal. In paragraph two it is suggested that even his body seemed like that of some creature:

...his bare back was a mass of dark freckles and peeling sunburn.

He is described as naked (except for his shorts) and that his nostrils were flared - a description usually used to describe an animal.
To further emphasize Jack's animal-like behavior, we read in paragraph three that:

...he stole forward and cast this way and that over the ground.

And, in paragraph four:

Jack himself shrank at this cry with a hiss of indrawn breath, and for a minute became less a hunter than a furtive thing, ape-like among the tangle of trees...

The terminology makes it clear that Jack had become like an animal. In the first instance, he was casting his eyes around, as a predator would when seeking its prey. The highlighted words in paragraph four are self-explanatory.
Even after he has completed his unsuccessful hunt, Jack does not lose his bestiality, as illustrated by the following extract:  

Jack took up a coconut shell that brimmed with fresh water from among a group that was arranged in the shade, and drank. The water splashed over his chin and neck and chest. He breathed noisily when he had finished.

He drinks as an animal would.
He later declares that he has an instinctual sense which he shares with the animals: 

“There’s nothing in it of course. Just a feeling. But you can feel as if you’re not hunting, but—being hunted, as if something’s behind you all the time in the jungle.”
“Only I know how they feel. See? That’s all.”

His actions in this chapter foreshadow Jack's actions later when he rebels against rules and order, abandons civilized behaviour and adopts savagery. He and his hunters become savages and form a tribe. They are later primarily responsible for Simon's death and kill Piggy. They also capture others, such as Sam and Eric and hold them captive. Eventually, they hunt Ralph and plan to kill him. 

Precalculus, Chapter 5, 5.2, Section 5.2, Problem 38

Verify the identity: [tan(x)+tan(y)]/[1-tan(x)tan(y)]=[cot(x)+cot(y)]/[cot(x)cot(y)-1]
Divide every term on the left side of the equation by tan(x)tan(y)
[[tan(x)/{tan(x)tan(y)]]+[tan(y)/[tan(x)tan(y)]]]/[[1/[tan(x)tan(y)]]-[[tan(x)tan(y)]/[tan(x)tan(y)]]]=[cot(x)+cot(y)]/[cot(x)cot(y)-1]
Simplify each term.
[[1/tan(y)]+[1/tan(x)]]/[[1/[tan(x)tan(y)]]-1]=[cot(x)+cot(y)]/[cot(x)cot(y)-1]
Simplify the left side of the equation using the reciprocal identity.
[cot(y)+cot(x)]/[cot(x)cot(y)-1]=[cot(x)+cot(y)]/[cot(x)cot(y)-1]
[cot(x)+cot(y)]/[cot(x)cot(y)-1]=[cot(x)+cot(y)]/[cot(x)cot(y)-1]

Intermediate Algebra, Chapter 2, 2.6, Section 2.6, Problem 60

For compound inequality $2x - 6 \leq -18$ and $2x \geq -18$, decide whether intersection or union should be used. Then give the solution set in both interval and graph form.

We solve the inequality individually


$
\begin{equation}
\begin{aligned}

2x - 6 \leq & -18 && \qquad \text{and} &&& 2x \geq & -18
\\
2x \leq & -12
\\
x \leq & -6 && \qquad \text{and} &&& x \geq & -9

\end{aligned}
\end{equation}
$


By graphing the two intervals, we have













We can see from the graph on each set that it intersects on the interval $[-9,-6]$.

What are the basic principles and values of a republic?

The most basic principle of a republic is that the power is vested in the people of the country. The key example of this is the electoral process. The will of the people is the lifeline of a republic.
A republic creates a constitution that outlines the rule of law within the country. It is important to remember that, in terms of the United States, the republican form of government is a balance between the monarchy our Founding Fathers faced and a direct democracy.
Another principle of a republic is that representatives wield the political power. (In a direct democracy, the people have the power in all situations.) James Madison was a key proponent of "filtering" the popular voice before it came to power. This is where the importance of elected representatives is found.
https://fee.org/articles/the-founding-of-the-american-republic-17-principles-of-the-constitution/

There are a number of defining principles of a republic.
A republic is a self-governing state or country in which members of society have the power to elect officials who represent them in government matters. This differs from a pure democracy in which individual people cast votes directly on the issues of importance to society.
The officials are elected to serve at the will of the people, and to vote according to the values they are chosen to represent
In a republic, there is generally one elected official such as a president, chosen to represent the entirety of the population. This person is not a sovereign ruler such as a king or queen, nor is his or her position based on blood lineage.
In addition, in a republic there are different levels of elected officials such as local, state, and national, who represent different groups of constituents. Voting on those who represent the different populations takes places at regularly set intervals.
https://www.civiced.org/resources/curriculum/lesson-plans/450-lesson3-what-is-a-republican-government

Calculus of a Single Variable, Chapter 8, 8.5, Section 8.5, Problem 14

int(5x-2)/(x-2)^2dx
Let's use partial fraction decomposition on the integrand,
(5x-2)/(x-2)^2=A/(x-2)+B/(x-2)^2
5x-2=A(x-2)+B
5x-2=Ax-2A+B
comparing the coefficients of the like terms,
A=5
-2A+B=-2
Plug in the value of A in the above equation,
-2(5)+B=-2
-10+B=-2
B=-2+10
B=8
So now int(5x-2)/(x-2)^2dx=int(5/(x-2)+8/(x-2)^2)dx
Now apply the sum rule,
=int5/(x-2)dx+int8/(x-2)^2dx
Take the constant's out,
=5int1/(x-2)dx+8int1/(x-2)^2dx
Now let's evaluate each of the above two integrals separately,
int1/(x-2)dx
Apply integral substitution u=x-2
=>du=dx
=int1/udu
Use the common integral :int1/xdx=ln|x|
=ln|u|
Substitute back u=x-2
=ln|x-2|
Now evaluate the second integral,
int1/(x-2)^2dx
Apply integral substitution:v=x-2
dv=dx
=int1/v^2dv
=intv^(-2)dv
Apply the power rule,
=v^(-2+1)/(-2+1)
=-v^(-1)
=-1/v
Substitute back v=x-2
=-1/(x-2)
:.int(5x-2)/(x-2)^2dx=5ln|x-2|+8(-1/(x-2))
Add a constant C to the solution,
=5ln|x-2|-8/(x-2)+C

Which techniques and practices should be applied to combat soil degradation?

Soil degradation is caused by too much erosion. Often this is due to poor agricultural and industrial processes. One's land should be treated with care. Hilly acreage should be left as pasture so that the soil is not left barren for any length of time. Terraces are useful as well, as this slows runoff, but does not entirely eliminate it. In recent years many farmers have turned to no-tilling their row crops; this reduces the amount of soil exposed to the wind and rain and still allows for good crops. Farmers even report having to fertilize less with this method. Many mining companies plant trees and shrubs over areas that they have mined in order to control toxic runoff into streams.
It is also important not to take all the nutrients out of soil. Controlling erosion will help the soil stay fertile, but it is also important not to grow the same crop in a field every year as it can sap nutrients. Corn is especially bad for this, as it takes a great deal of nitrogen to grow a good corn crop. Many farmers use a green manure crop, such as winter wheat as both a soil cover in the winter and as nutrients in the spring when the wheat is turned under by the plow.

Soil is mostly degraded through erosion, agricultural activities, and industrial activities. Soil erosion occurs when it rains on areas with loose soils. Soil degradation occurs through agricultural and industrial activities because of the chemicals applied to or released in the soil.
Soil erosion can be controlled by growing some vegetative cover on the soil. The plants will stop soil degradation by holding the soil together and preventing soil erosion. Plants will also slow down the surface runoff caused by rain water. Building gabions in areas suffering extreme soil erosion will help stop the degradation.
Soil degradation caused by agricultural activities can be controlled by ensuring farmers use the correct types and amounts of agrochemicals. Constructing terraces in hilly areas can also prevent excessive surface runoff and erosion.
Soil degradation caused by industrial activities can be remedied through the restoration of utilized areas such as quarries. Stronger regulations and restrictions can also be imposed to control the industrial dumping of wastes, which contaminate the environment.
https://www.worldwildlife.org/threats/soil-erosion-and-degradation

Two cars are driving towards each other from towns that are 150 miles apart. The first car is traveling 45 miles per hour, and the second is traveling 55 miles per hour. If each leaves at 2:15, when will the two cars pass on the road?

To solve, refer to the figure.
Let d1 be the distance traveled by the first car and d2 be the distance traveled by the second car.
Since the two cars are 150 miles apart at the start, when they meet, the sum of their distances traveled is 150 miles.
d_1+d_2=150
Then, express the equation in terms of time. Let t be the number of hours that the cars been traveling. The two cars have the same variable t since they start at the same time. Applying the formula
distance =speed *time
the distance traveled by each car expressed in t are
45t + 55t = 150
The left side simplifies to
100t=150
Dividing both sides by 100, it becomes
(100t)/105=150/100
t=1.5
So the value of t is 1.5 hours.  To get the time, express the value of t in hours and minutes. To do so, convert the decimal part to minutes.
t = 1 hr + 0.5 hr
t = 1 hr + 0.5 h * (60 min)/(1hr)
t = 1 hr + 30 min
It is after 1 hour and 30 minutes that the two cars will meet. Since the cars left at 2:15, therefore, they will pass each other at 3:45.

What would be some points from Elie Wiesel's Night to prove the lesson that silence can be dangerous?

Well answered. Thank you. 

The concept of silence is a very important one in Night. Wiesel uses his narrative to display the dangers of silence.
Wiesel sees silence as dangerous because it allows abuse to happen. In Night, when people are silent, abuse is perpetrated.  There is a danger in being silent when we know injustice is taking place.
One instance where the dangers of silence can be seen is with Moshe the Beadle.  The Nazis deport Moshe, and he bears witness to their extraordinary cruelty.  However, he ends up surviving the ordeal.  Convinced that God spared his life so that he could tell the other people in Sighet about what he experiences, Moshe returns and tells the town what the Nazis are going to do to them if they remain in Sighet. However, Moshe is met with scorn, ridicule, and silence. People do not pay attention to him. They silence his narrative through rejection and apathy. The sad truth is that Moshe was right and people did not listen to him.  Wiesel uses the story of Moshe the Beadle to demonstrate the dangers of silencing voices.
Another instance where silence is shown to be dangerous is with Madame Schächter.  In the train to Auschwitz, Madame Schächter begins to scream out that she sees "fire."  She is met with silence.  When she begins to shout again, people on the train beat her up in order to get her to be quiet. Madame Schächter's voice is silenced, and even her son simply watches as the others beat up his mother.  Madame Schächter demonstrates the dangers of silence. When people are not heard or are silenced from telling their stories, Wiesel believes that bad things usually follow.  This becomes poignantly true when Eliezer's father reminds his son that what Madame Schächter said was actually true.  The fires of crematorium greeted all who entered Auschwitz-Birkenau.
The Nazis show the dangers of silencing voices.  They silenced millions of people's voices during the Holocaust. In this instance, look no further than Eliezer, who saw his family separated in the lines at Auschwitz-Birkenau. When the Nazi official says, "Men to the left!  Women to the right," it silences the voices of Eliezer's mother and sister. He never got the chance to say farewell, and could only watch as a part of his life was annihilated. 
I think that there is one more sad lesson about the dangers of silence in Night.  It takes place at the narrative's end.  Eliezer must watch his father die a slow and agonizing death. The doctors refuse to help and Eliezer is condemned to watch his father die.  In his last night, Eliezer's father is writhing and moaning in pain.  He is beaten by a Nazi officer, and Eliezer is scared that such a fate would be in store for him, as well.  After the beating, Eliezer's father continues to call out his son's name.  Eliezer hears the cries and he does not respond.  
The next morning, Eliezer wakes up to find his father gone.  Another prisoner has replaced him.  Eliezer reasons that "they must have taken him away at daybreak."  It is at this point that Eliezer's words about his father's death reflect one final lesson about the dangers of silence:  "No prayers were said over his tomb. No candle lit in his memory. His last word had been my name. He had called out to me and I had not answered."  No one could possibly blame Eliezer for being silent.  However, that does not remove the guilt he feels for being silent when his father called out to him.  Eliezer lives with the reality that he remained silent when someone yearned for him.  This demonstrates the ultimate danger of silence.  Silence is a form of negating the bonds that exist between human beings.  Whether it is seen in the Holocaust on a large scale or in the sad interactions between a dying father and his son, the lesson is clear that when we are silent, we fail to acknowledge the connections between human beings. Even as Eliezer is liberated from the camps, he carries this lesson with him for the rest of his days.

Can you give me some tips about how I can write a synopsis of the movie The Crucible?

A synopsis should cover the main elements of the movie. You can use headings to separate out these different elements and create a clear structure for your paper. One possible way to organize this would be:
Introduction. This should discuss the author Arthur Miller, and the political background of the McCarthy era. It should introduce the purpose of the play and the main points Miller was making about mass hysteria. 
Setting: This section should give information about the period in which the play was set and the degree to which it provides an historically accurate portrait of the Salem witch trials.
Characters: You should include short descriptions of the main characters including John and Elizabeth Proctor, Tituba, Abigail Williams, Mary Warren, Rebecca Nurse, and John Hale.
Plot: In your description of the plot, you should describe the main events of the play in chronological order. You might start with Abigail's affair with John Proctor and then move through the various witchcraft accusations and Proctor's final refusal to submit a signed confession.
https://www.newyorker.com/magazine/1996/10/21/why-i-wrote-the-crucible

How do Cassie and her brothers react to the news of the Berrys being burned in Roll of Thunder, Hear My Cry?

In Chapter 1, Cassie and her brothers are greatly disturbed to hear that men of their congregation have been set on fire.
This incident creates anxiety in itself, but when their father issues them an order not to go to the Wallace store for any reason, the children are, indeed, worried about what changes are occurring in their environment. Of course, this incident foreshadows the main conflict in the narrative; for, later in Chapter 3 when Mr. Avery comes to the Logan home, this same problem is discussed.
When he first arrives, Mr. Avery asks Mrs. Logan if her husband is home because he wants to inform him of a growing problem: "It's...it's them again. They's ridin' t'night." When Mrs. Logan asks why they are "riding," Mr. Avery replies that he does not really know, but as they are aware,

"Anytime they thinks we steppin' outa our place they feels like they gotta stop us. You know what some of 'em done to the Berrys...."

The pretext of the burning of the Berrys was that one of them flirted with a white woman, and the other two relatives tried to defend him.
As the Logan children listen to what Mr. Avery tells their mother, they become frightened, worried that the white men will come after them because they have sabotaged the school bus carrying the white children in retaliation for the driver's veering into the muddy water that splashes onto them. They do not yet understand the greater threat.

What were the various motives of Progressive reformers?

The Progressive Era—and the reformers who populated it—sprung from dissatisfaction with the status quo of the Gilded Age. The laissez-faire, business-first attitude of many nineteenth-century politicians horrified a growing number of progressive reformers, who believed that people, not money, should be America's first priority.
The Populists and Progressive reformers shared many of the same motives (namely, helping the disempowered and working towards a balance of political and economic control between the wealthy and the poor), but they come from very different backgrounds and used vastly different tactics. The populists were primarily from working class cooperatives and unions, and used collective bargaining and striking to try and make change from the bottom up. The Progressives, on the other hand, attacked the problems from the top, attempting to change legislation, build charitable organizations, and create more moral communities.
Progressivism is difficult to discuss in general terms, as it was an enormously diverse movement, led by a wide swath of Americans with nearly endless motives and goals.
Some Progressives, like Oregon senator William U’Ren, went directly towards the motive of political reform, aiming to dissolve political machines and give people more of a voice in the legislature. Beginning in his own state, U’Ren passed measures that allowed citizens to propose laws in the legislature (1902), recall elected officials for misconduct (1908), and vote in “primary” elections to reduce the power of political machines (1911). These bills would eventually make their way to the nationals stage.
Other Progressives, like Eugene V. Debs, focused on the motive of easing tensions between the working class and the employing class by establishing labor unions and instituting collective bargaining measures. Wealthy Progressives also shared this motive, but used different techniques: industrialists like Andrew Carnegie created lasting foundations to fund programs in the humanities and sciences, purchased large tracks of land that were donated to the state, supported aid and education programs for immigrants and black Southerners, and even helped professionalize aid organizations like the Red Cross.
Progressive reform also became a popular pastime for the middle and upper classes. Women in particular took up the mantle of reform, particularly in the areas of temperance, suffrage, housing reform, and healthcare. Most famously, women like Jane Addams established settlement houses, situated in poor immigrant communities. Educated, civic-minded young women would live in these houses and provide free services to their communities, including classes in various fields, recreation, lectures, and childcare. They also conducted research into the community's social ills, and used that research to push for reforms.
Progressivism also owes a lot to the work of the "muckrakers," groundbreaking investigative journalists who worked to upset the power balance between the weak and the strong by exposing the true underbelly of government, industry, and social inequality. They were a diverse group, including women, Black Americans, and immigrants, and used new techniques—such as research, flash photography, and interviews—to reveal, for the first time, the reality of life in America. The muckrakers raked the muck up, and the Progressive reformers washed it away through legislation.

Single Variable Calculus, Chapter 6, 6.1, Section 6.1, Problem 18

Sketch the region enclosed by the curves $y = 8 - x^2$, $y = x^2$, $x = -3$ and $x = 3$. Then find the area of the region.


By using vertical strips
$\displaystyle A = \int^{x_2}_{x_1} \left(y_{\text{upper}} - y_{\text{lower}} \right) dx$
In order to get the values of the upper and lower limits, we equate the two functions to get its point of intersection. Thus


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

we have, $x = 2$ and $ x = -2$
Let's divide the shaded region on three parts. Let $A_1$, $A_2$ and $A_3$ be the area of left most part, middle part and the right most part respectively. Thus,

$
\begin{equation}
\begin{aligned}
A_1 &= \int^{-2}_{-3} \left[ x^2 - \left( 8 - x^2 \right)\right] dx\\
\\
A_1 &= \int^{-2}_{-3} \left[ 2x^2 - 8 \right] dx\\
\\
A_1 &= \left[ \frac{2x^3}{3} - 8x \right]^{-2}_{-3}\\
\\
A_1 &= \frac{14}{3} \text{ square units}

\end{aligned}
\end{equation}
$

For the middle part,

$
\begin{equation}
\begin{aligned}
A_2 &= \int^{2}_{-2} \left[ x^2 - \left( 8 - x^2 \right)\right] dx\\
\\
A_2 &= \int^2_{-2} \left[ 8 - 2x^2 \right]dx \\
\\
A_2 &= \left[ 8x - \frac{2x^3}{3} \right]^2_{-2}\\
\\
A_2 &= \frac{64}{3} \text{ square units}

\end{aligned}
\end{equation}
$


For the right most part,

$
\begin{equation}
\begin{aligned}
A_3 &= \int^3_2 \left[ x^2 - \left( 8 - x^2 \right)\right] dx\\
\\
A_3 &= \int^3_2 \left[ 2x^2 - 8 \right]\\
\\
A_3 &= \left[ \frac{2x^3}{3} -8x \right]^3_2\\
\\
A_3 &= \frac{14}{3} \text{ square units}
\end{aligned}
\end{equation}
$



Therefore, the area of the entire region is $\displaystyle A_1 + A_2 + A_3 = \frac{14}{3} + \frac{64}{3} + \frac{14}{3} = \frac{92}{3}$ square units

Why does Claude Frollo kill Captain Phoebus?

In Victor Hugo's famous novel The Hunchback of Notre-Dame, Claude Frollo is the corrupt archdeacon of the titular Notre Dame Cathedral. Captain Phoebus de Châteaupers is the Captain of the King's Archers, and while he is not as bad as Frollo, he isn't such a great guy either.
We see Claude Frollo's dark personality in many ways, including when he becomes obsessed with and pursues Esmeralda relentlessly. And by pursues, I mean tries to kidnap her because he wants to possess her, like an object, so that no one else can have her. Phoebus saves Esmeralda from the attempted kidnapping, and she consequently falls in love with him. Later on, the two agree to meet up again; Esmeralda wants to tell Phoebus that she loves him, while Phoebus just wants to have sex with Esmeralda (he's already engaged to someone else).
Frollo finds out about their relationship and the possibility of Esmeralda having sex with someone besides himself, and he becomes enraged. He disguises himself and pays Phoebus to let him hide in the room where the two lovers are going to meet. Phoebus agrees to this because he has no money, and while he is seducing Esmeralda, Frollo jumps out and stabs Phoebus. Esmeralda faints, and when she wakes up, she has been accused of murdering Phoebus (who later turns out isn't actually dead). So essentially, Frollo stabs Phoebus because he is insanely jealous of him due to his obsession with Esmeralda. He also uses the incident as a way to frame Esmeralda for murder so that he can try to take her again while she's imprisoned.

Compare and contrast the author's treatment of the husband-wife relationship in the two stories "The Lovely Leave" by Dorothy Parker and "Doors" by Chitra Divakaruni, taking into account the spouses' needs and couples' communication styles.

The short stories are similar in that the respective authors highlight how opposing viewpoints can create conflict within a marriage. However, "The Lovely Leave" differs from "Doors" in that the conflict in the latter leads to a dangerous marital schism.
Even though the parting between the couple in "The Lovely Leave" is somewhat tense in nature, the wife still remains committed to her husband's vision for their lives. In "Doors," however, the husband and wife decide to sleep in separate rooms due to their inability to reconcile their differing views about privacy.
In both "Doors" and "The Lovely Leave," the wives accuse their husbands of not sympathizing with their positions. Mimi in "The Lovely Leave" can't bring herself to enjoy Steve's 24 hour leave, as she knows that their time together is short-lived. She remembers the nights of worry and loneliness she has endured. When Steve arrives, she pours out her frustrations to him despite her earlier resolution not to burden him with her struggles. For her part, Mimi is too frustrated to restrain her overpowering emotions.

"...No, you're the one that's awful, Steve. You really are. I'm trying to show you a glimpse of my heart, to tell you how it feels when you're gone, how I don't want to be with anyone if I can't be with you. And all you say is I'm not doing any good to anybody. That'll be nice to think of when you go. You don't know what it's like here for me alone. You just don't know."
"Yes, I do," he said. "I know, Mimi."

For his part, Steve responds sympathetically to Mimi. Since his 24 hour leave has been cut short, he refrains from engaging in heated words with her. Steve decides to take a bath before he leaves. Despite their strained words, Mimi and Steve share an emotional parting hug; it is obvious that their bond is still strong.
In "Doors," Preeti and Deepak also argue, but their disagreement results in a terrible schism in their marriage. The bond between them threatens to rupture, precipitated by their differing cultural values. Although both are Indian, Preeti is American-raised. Deepak, the more traditional of the two, is bewildered by the American emphasis on privacy and individualism. Like Raj (his brother-in-law), Deepak cannot understand why closed doors are so important to Preeti.
After Raj leaves, Deepak and Preeti engage in a war of words. When Preeti suggests moving into Cathy's apartment, Deepak is flabbergasted. His response (unlike Steve's response to Mimi) is explosive:

You can't leave. What would people say? Besides, you're my wife. You belong in my home.

To Deepak, a wife's understanding and submission is expected. His cultural sensitivities demand it. Meanwhile, Steve (although distressed by Mimi's words) shares his wife's frustrations about prolonged absences from home. Therein lies the difference between how marriage is portrayed in both stories. While Preeti and Deepak argue from the vantage point of differing cultural prisms, Steve and Mimi share similar views about war and the western idea of freedom. Although frustrated by his absences, Mimi still supports Steve's mission. On the other hand, Preeti is unable to reconcile her very western ideas about privacy with Deepak's conventional views about family life.

f(x)=lnx, n=4,c=2 Find the n'th Taylor Polynomial centered at c

Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of f^n(x) centered at x=c . The general formula for Taylor series is:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...
To determine the Taylor polynomial of degree n=4 from the given function f(x)=ln(x) centered at x=2 , we may apply the definition of Taylor series.
We list f^n(x) up to n=4  as:
f(x) = ln(x)
f'(x) = d/(dx)ln(x) =1/x
Apply Power rule for derivative: d/(dx) x^n= n *x^(n-1) .
f^2(x) = d/(dx) 1/x
           = d/(dx) x^(-1)
           =-1 *x^(-1-1)
           =-x^(-2) or -1/x^2
f^3(x)= d/(dx) -x^(-2)
           =-1 *d/(dx) x^(-2)
           =-1 *(-2x^(-2-1))
          =2x^(-3) or 2/x^3
f^4(x)= d/(dx) 2x^(-3)
            =2 *d/(dx) x^(-3)
           =2 *(-3x^(-3-1))
            =-6x^(-4) or -6/x^4
Plug-in x=2 , we get:
f(2) =ln(2)
f'(2)=1/2
f^2(2)=-1/2^2 = -1/4
f^3(2)=2/2^3 =1/4
f^4(2)=-6/2^4 = -3/8
Applying the formula for Taylor series, we get:
sum_(n=0)^4 (f^n(2))/(n!) (x-2)^n
=f(2)+f'(2)(x-2) +(f^2(2))/(2!)(x-2)^2 +(f^3(2))/(3!)(x-2)^3 +(f^4(2))/(4!)(x-2)^4
=ln(2)+1/2(x-2) +(-1/4)/(2!)(x-2)^2 +(1/4)/(3!)(x-2)^3 +(-3/8)/(4!)(x-2)^4
=ln(2)+1/2(x-2) -(1/4)/2(x-2)^2 +(1/4)/6(x-2)^3 -(3/8)/24(x-2)^4
=ln(2)+1/2(x-2) -1/8(x-2)^2 + 1/24(x-2)^3 -1/64(x-2)^4
The Taylor polynomial of degree n=4  for the given function f(x)=ln(x) centered at x=2 will be:
P_4(x)=ln(2)+1/2(x-2) -1/8(x-2)^2 + 1/24(x-2)^3 -1/64(x-2)^4

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 70

Determine an equation of the line that satisfies the condition "through $(-1,3)$; parallel to $-x + 3y = 12$".

(a) Write the equation in slope intercept form.

We find the slope of the line $-x + 3y = 12$ and write it in slope intercept form


$
\begin{equation}
\begin{aligned}

-x + 3y =& 12
&& \text{Given equation}
\\
\\
3y =& x + 12
&& \text{Add each side by $x$}
\\
\\
y =& \frac{1}{3}x + \frac{12}{3}
&& \text{Divide each side by $3$}
\\
\\
y =& \frac{1}{3}x + 4
&&

\end{aligned}
\end{equation}
$



The slope is $\displaystyle \frac{1}{3}$. Using the Point Slope Form, with point $(-1,3)$, we have


$
\begin{equation}
\begin{aligned}


y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
\\
y - 3 =& \frac{1}{3} [x - (-1)]
&& \text{Substitute } x = -1, y = 3 \text{ and } m = \frac{1}{3}
\\
\\
y - 3 =& \frac{1}{3}x + \frac{1}{3}
&& \text{Distributive Property}
\\
\\
y =& \frac{1}{3}x + \frac{10}{3}
&& \text{Add each side by $3$}
\\
\\
y =& \frac{1}{3}x + \frac{10}{3}
&& \text{Slope Intercept Form}


\end{aligned}
\end{equation}
$


(b) Write the equation in standard form.


$
\begin{equation}
\begin{aligned}

y =& \frac{1}{3}x + \frac{10}{3}
&& \text{Slope Intercept Form}
\\
\\
3y =& x + 10
&& \text{Multiply each side by $3$}
\\
\\
-x + 3y =& 10
&& \text{Standard Form}

\end{aligned}
\end{equation}
$

What is the meaning of Watchmen reference?

In the story, we see references to the Watcher. There are a number of interpretations of this usage. First, Oscar refers to himself as the Watcher or a pariguayo, which in Dominican slang refers to someone who stands apart from a group. The pariguayo is always on the outside, looking in. He doesn't seem to belong anywhere; he's the ultimate loner. Here is one definition from the text:

...pariguayos- a word that in contemporary usage describes anybody who stands outside and watches while other people scoop up the girls. The kid who don't dance, who ain't got game, who lets people clown him- he's the pariguayo. If you looked in the Dictionary of Dominican Things...pariguayo would include a wood carving of Oscar.

The word pariguayo was originally used during the US occupation of the Dominican Republic in 1916-1924. Then, US Marines would attend Dominican parties and just watch. Eventually, they were referred to as the Party Watchers. In the story, Oscar is a pariguayo. The narrator, Yunior, tells us that Oscar is overweight (he weighs in at 245 pounds) and can never seem to keep a girlfriend.
Meanwhile, Yunior is a Watcher as well. Although he is more successful at getting girlfriends than Oscar, Yunior is still a pariguayo of sorts. He fails in wooing and keeping Lola, the woman he most wants in his life. On another level, Yunior is a Watcher much like Uatu, who is mentioned in the story. In the Marvel world of comics, Uatu is a member of the Watchers, powerful alien beings who watch and record events across the galaxy. Uatu is important because he has been assigned to watch over Earth. Yunior even makes a reference to the Marvel Comics' Uatu in the novel:

"No matter how far you travel...to whatever reaches of this limitless universe...you will never be... ALONE!" (The Watcher, Fantastic Four #13 May 1963)

So, much like Uatu, Yunior watches over the main characters in the novel, and he provides engaging commentary about their actions. Through Yunior's comments (indirect characterization), the main characters come alive before our very eyes.
Toward the end of the novel, Yunior resigns himself to returning back to the shadows, to the Blue Area of the Moon (where the comic-book Uatu lives). In the end, Yunior is as much a pariguayo as Oscar is; because of his poor choices, Yunior can only observe, not participate, in Lola and her daughter's lives.

Intermediate Algebra, Chapter 2, Test, Section Test, Problem 20

Evaluate the compound inequality $3x \geq 6$ and $x-4 < 5$


$
\begin{equation}
\begin{aligned}
3x &\geq 6 && \text{and} & x - 4 &< 5
&& \text{Solve for } x\\
\\
x &\geq 2 && \text{and} & x &< 9
\end{aligned}
\end{equation}
$

Since the inequalities are joined with $and$, find the intersection of the two solution.
The intersection is shown and is written as $[2,9)$

Rousseau says, "property is the most sacred of all the rights of citizenship": What do you think he means by this, and why might property be the most important right of a citizen?

For readers in contemporary developed countries, where property rights are taken for granted, this saying can appear puzzling. It is important to read it in historical context, against the background of feudalism. The idea of property rights was enshrined for the English in the Magna Carta, signed by King John of England in 1215, along with the idea that even the king was not above the law and that everyone had the right to a fair trial. The French, under the power of an absolute monarch, lacked such rights.
Under the feudal system, all people were vassals of the king, holding land and property in return for service to the king. This meant, in theory, that the king could, at will, strip an individual of all property and rights. That meant that no one was truly free to criticize the king or oppose his policies until private property rights became established.
Property gives people freedom of action. In other words, someone who owns a home, and has an adequate income for necessities such as food, clothing, and medical care, is in a position to criticize injustice and speak freely. Someone who is dependent on the government or can be deprived of their property by a vindictive or authoritarian ruler simply for expressing an unpopular opinion, has no real freedom.
Also, as Marx later stated, freedom is freedom from economic necessity. In other words, a serf, who owned almost nothing and simply worked the land for a noble, on terms dictated by the noble, had no freedom to make any life choices. As one accumulates property (whether in the form of real property such as land or money), one is able to choose where to live, what employment to seek, whether to marry or remain single, and many other things, but without inalienable property, one lacks freedom of choice.

What is the relationship between Rolf and Azucena? What do they give to each other? What kind of love do they share?

Rolf and Azucena share a dynamic relationship in “And of Clay Are We Created” by Isabel Allende.
Originally, when Rolf arrives at the site of the mudslide he is working as a reporter for a major news outlet, but he leaves a changed man. He locates Azucena, the little girl partially buried in the clay. While observing her situation, he realizes her situation is not just a story to be covered as a job. He knows he must stay with her and facilitate her rescue. At first he frantically tries to get aid for her, but as time passes he realizes he has become an emotional support system for the girl. As night falls, she pleads with him to stay with her.

“Don’t leave me alone,” she begged.
“No, of course I won’t leave you.”

During the hours the two spend together, they connected. The little girl demonstrated her bravery as she faced increasingly dire circumstances. As Rolf observes Azucena’s strength, he changes from her support system to a man who bravely faces his difficult past. This is something he never allowed himself to do.  Although, he sets out to save the little girl’s life, she ends up allowing him to face his past so that he can heal and move forward with his life as she loses her.
Do they demonstrate “love”? Can you develop love in three days? In this story, some would say the two characters developed an unconditional love which allows them to bare their hearts and souls to each other.  When help does not arrive, Rolf stays with the little girl, singing and talking to her through the hours. His job as a photo journalist is forgotten, instead he focuses all his attention on bolstering the girl. But as time passes, and she becomes weaker, his disastrous childhood creeps into his consciousness. Although, he cannot tell Azucena all the sordid details, he allows her to have a cathartic effect on him. One of her final expressions is that of never being loved by a boy. Rolf assures her he loves her more than anything. Her death allows him to live a life unencumbered by his past.
Rolf's partner was a distant observer, and she says,

I was there when she told him that in all her thirteen years no boy had ever loved her and that it was a pity to leave this world without knowing love. Rolf assured her that he loved her more than he could ever love anyone, more than he loved his mother, more than his sister, more than all the women who had slept in his arms, more than he loved me, his life companion, who would have given anything to be trapped in that well in her place, who would have exchanged her life for Azucena’s, and I watched as he leaned down to kiss her poor forehead, consumed by a sweet, sad emotion he could not name. I felt how in that instant both were saved from despair, how they were freed from the clay, how they rose above the vultures and helicopters, how together they flew above the vast swamp of corruption and laments. How, finally, they were able to accept death. Rolf Carlé prayed in silence that she would die quickly, because such pain cannot be borne.

From The House on Mango Street, please provide three examples of imagery with page numbers.

Imagery has to do with phrases, references, or figurative language that uses one or more of the fives senses. The creation of imagery happens when an author uses the senses of sight, smell, taste, touch, or sound to describe something. The following example from the first vignette mentions at least two of these senses:

"It's small and red with tight steps in front and windows so small you'd think they were holding their breath. Bricks are crumbling in places, and the front door is so swollen you have to push hard to get in" (4).

Notice that this passage has visual images: small, red, tight steps, bricks crumbling, and a swollen door. Next, it shows the sense of touch with words such as "push hard," and "holding their breath." One might identify with how it feels to push hard to open an old door, or to hold one's breath, for example. 
Another example of the use of imagery can bee seen in the following passage:

". . . and nobody looked up not once the day Angel Vargas learned to fly and dropped from the sky like a sugar donut, just like a falling star, and exploded down to earth without even an 'Oh'" (30).

The senses of sight, sound, and taste can be found in this quote. Words such as "sugar donut" and "falling star" can both be visualized. The sugar donut can be tasted; however, since a donut is also easily broken, the image shows that it is fragile to the touch. Then because the falling star "exploded," the sense of hearing can be employed. 
One final example of a passage that uses imagery is one that focuses on Esperanza's blind aunt.

"My aunt was blind by then. She never saw the dirty dishes in the sink. She couldn't see the ceilings dusty with flies, the ugly maroon walls, the bottles and sticky spoons. I can't forget the smell. Like sticky capsules filled with jelly. My aunt, a little oyster, a little piece of meat on an open shell for us to look at" (60).

Many people can identify with having dirty dishes in a sink. Readers can also visualize what flies on ceilings might look like, so visual images are strong in this passage. It might also be easy to imagine what maroon walls, bottles, and sticky spoons lying around the house look and smell like. Esperanza describes the smell of the apartment like "capsules filled with jelly," which smell may or may not be easy to imagine based on one's personal experience. However, the rest of the description of her aunt describes her as little as an oyster, and maybe only as significant as a tiny "piece of meat." Readers can visualize what an oyster in its shell looks like and apply it to how Esperanza's aunt appears to be and act like. Anyone who has eaten oysters might also apply the sense of taste when reading this description, too. Therefore, there are many visual images to ponder in this passage. The senses of smell and taste coincide with the descriptions of the objects in the apartment as well.
 
 

Slavery was an integral part of American southern life. How did it shape that life and culture?

Slavery was one reason why the South was a society based on class. The rich had slaves to do all of their manual labor—this meant that they had little reason to hire other working-class people or poor whites to do things around the plantation. While this gave the rich leisure time to study in prestigious universities or run for public office, it also created a system where poor whites would nearly always stay poor unless they moved away from the South and traveled North for factory work or West for cheaper land. Poor whites also resented the slaves for taking their jobs, thus creating racism from all sides for the African Americans of the region. As cotton prices grew alongside worldwide demand for textiles, southern planters saw no reason to expand into industry or allow slaves to work on infrastructure projects which might help the South in the long-term. Slavery allowed a small group of people to control much of what happened politically in the South; unfortunately, these people led the South to secession and war.

What were the principle causes of the Civil War?

The American Civil War occurred as a result of conflicting views with regards to slavery. The Southern states forming the Confederate States of America were in support of slavery because they relied on the brutal practice to provide labor to run their farms and homes. On the other hand, the North, as the Union, was against slavery. Initially, some of the Northerners believed that slavery should not be allowed to spread, and eventually, sustained pressure from the South forced them to take measures to abolish the practice altogether.
Seven Southern states seceded after President Abraham Lincoln assumed control of the executive branch. Tensions flared, and Confederate soldiers attacked Fort Sumter. Confederates' push against Lincoln was based on the knowledge that Lincoln was anti-slavery. As president, Lincoln was forced to respond with violence to address antagonism by the Confederates in the South.
https://www.battlefields.org/learn/articles/brief-overview-american-civil-war

Why did the frog sing? How did others like his song?

The frog sings his songs for the entire bog to hear each night under the sumac tree simply because he enjoys singing and has an inherent desire to express himself in an artistic manner. Vikram Seth writes that the frog was determined "to display his heart's elation," which is why he sang each night. Despite the frog's personal feelings regarding his affinity for singing, the other animals in the bog "loathe" his deep voice. Whenever the nightingale initially sings her beautiful song, the animals in the bog applaud her pleasant song. The next day, the frog approaches the naive nightingale and mentions that he is well known for his "splendid baritone." The frog's comment implies that he lacks a certain self-awareness and is proud of his voice. After manipulating the nightingale and witnessing her die of exhaustion, the frog calls her stupid and says,

"Well, poor bird—she should have known That your song must be your own. That's why I sing with panache" (Vikram Seth).

The frog's comment gives further insight into why he feels the need to sing each night under the sumac tree. The frog has an inherent desire to express himself in an artistic way that is uniquely his own. The frog feels fulfilled when he sings his heart out and does not care whether or not any other creature enjoys his voice. In contrast, the nightingale values the opinion of others and dies while trying to please the frog and her audience.

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 26

The equation $\displaystyle f= \frac{1}{2L} \sqrt{\frac{T}{\rho}}$ represents the frequency of vibrations of a vibrating violin string. Where $L$ is the length of the string, T is its tension, $\rho$ is its linear density

a.) Find the rate of change of the frequency with respect to
$(i)$ the length (when $T$ and $\rho$ are constant)
$(ii)$ the tension (when $L$ and $\rho$ are constant), and
$(iii)$ the linear density (when $L$ and $T$ are constant)
b.)The pitch of a note is determined by the frequency $f$. Use the signs of the derivative in part(a) to determine what happens to the pitch of a note.
$(i)$ when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates.
$(ii)$ when the tension is increased by turning a tuning peg.
$(iii)$ when the linear density is increased by switching another string.


$
\begin{equation}
\begin{aligned}
\text{a.) } & (i) & \frac{df}{dL} &= \frac{1}{2} \sqrt{\frac{T}{\rho}} \frac{df}{dL} \left( \frac{1}{L} \right)\\
\\
& \phantom{x} & \frac{df}{dL} &= \frac{1}{2} \sqrt{\frac{T}{\rho}} \left( \frac{-1}{L^2} \right)\\
\\
& \phantom{x}& \frac{df}{dL} &= \frac{-1}{2L^2} \sqrt{\frac{T}{\rho}}\\
\\
\\
\\
& (ii) & \frac{df}{dT} &= \frac{1}{2L(\rho)^{\frac{1}{2}}} \cdot \frac{d}{dT} (T)^{\frac{1}{2}} \\
\\
& \phantom{x} & \frac{df}{dT} &= \frac{1}{2L(\rho)^{\frac{1}{2}}} \cdot \frac{1}{2} T^{\frac{-1}{2}}\\
\\
& \phantom{x} & \frac{df}{dT} &= \frac{1}{4L\sqrt{\rho T}} \\
\\
\\
& (iii) & \frac{df}{d\rho} & = \frac{\sqrt{T}}{2L} \cdot \frac{d}{d\rho} (\rho)^{\frac{-1}{2}}\\
\\
& \phantom{x} & \frac{df}{d\rho} &= \frac{T}{2L} \cdot -\frac{1}{2}(\rho)^{\frac{-3}{2}}\\
\\
& \phantom{x} & \frac{df}{d\rho} &= \frac{-1}{4L} \sqrt{\frac{T}{\rho^3}}

\end{aligned}
\end{equation}
$


b.) $(i)$ A decrease in length $L$ is associated with the increase in the frequency since $\displaystyle \frac{df}{dL}$ from part(a) is negative.
$(ii)$ An increase in the tension $T$ is associated with an increase in frequency since $\displaystyle \frac{df}{dT}$ from part (a) is positive.
$(iii)$ An increase in the linear density $\rho$ is associated with a decrease in frequency since $\displaystyle \frac{df}{d\rho}$ from part (a) is negative.

Does Othello feel any remorse or regret for what he did?

Othello feels regret the moment he learns Desdemona remained true to him to the end of her life, but even before that, he is reluctant to go through with murdering her, or at the very least, sorry that he must carry out his idea of justice. He kisses her as she sleeps, almost tempted not to go through with his bloody deed. Unfortunately he does and learns too late his wife was not the adulteress he believed. Othello weeps and cries out several times, realizing what he has lost.
Othello ends up committing suicide after this. He will likely be executed by the state for murder anyway, but his suicide is more motivated by that same sense of honor and justice that made him murder Desdemona in the first place. Thus, he kills his wife's murderer, both from remorse and from his sense of honor that proved both his greatest virtue and his final undoing.
http://www.shakespeare-online.com/plays/othello/examqo/othellosuicide.html

Othello feels regret as soon as he discovers from Emilia that Iago has been plotting against him. Emilia tells Othello, who has just killed his wife, that Iago asked her to get the handkerchief—a gift from Othello to Desdemona—for him. Iago then used it to convince Othello that his wife was having an affair with Michael Cassio. Othello is overcome with rage and grief, chasing Iago from the room and launching into a heartrending speech in which he imagines that Desdemona's look alone will "hurl my soul from heaven." He is filled with remorse and begs to know why Iago has "ensnared [his] soul and body." After another long speech in which he begs his comrades to remember him not as an evil murderer but as a man who had loved with too much passion, he kills himself. So Othello, an overly proud and hotheaded man, is forced at the end of the play to come to terms with the fact that Iago has skillfully and diabolically played on his emotions to bring Othello's marriage to a tragic end.

Calculus: Early Transcendentals, Chapter 7, 7.2, Section 7.2, Problem 30

int_0^(pi/4) tan^4(t) dt
Express the integrand in factor form.
= int _0^(pi/4) tan^2(t) *tan^2(t) dt
Plug-in the trigonometric identity tan^2(t) = sec^2(t)-1 to one of the factors.
= int_0^(pi/4) tan^2(t)*(sec^2(t)-1) dt
= int_0^(pi/4) (tan^2(t)sec^2(t)-tan^2(t)) dt
= int _0^(pi/4) tan^2(t)sec^2(t) dt - int_0^(pi/4)tan^2(t) dt
Plug-in again the trigonometric identity tan^2(t) =sec^2(t) - 1 to the second integral.
= int_0^(pi/4) tan^2(t)sec^2(t)dt- int_0^(pi/4) (sec^2(t) - 1) dt
= int_0^(pi/4) tan^2(t) sec^2(t) dt - int_0^(pi/4) sec^2(t)dt + int_0^(pi/4) dt
For the first integral, apply the u-substitution method.
u=tan (t)
du = sec^2(t) dt
>> int tan^2(t) sec^2(t)dt = int u^2du=u^3/3 = (tan^3(t))/3
For the second integral, apply the formula int sec^2 x dx = tanx .
>> int sec^2(t)dt = tan (t)
And for the third integral, apply the formula int adx = ax .
gtgt int dt = t
So the integral becomes:
int_0^(pi/4) tan^2(t) sec^2(t) dt - int_0^(pi/4) sec^2(t)dt + int_0^(pi/4) dt
= ((tan^3(t))/3 -tan(t) + t) |_0^(pi/4)
=((tan^3(pi/4))/3 - tan(pi/4) + pi/4) - ((tan^3(0))/3 - tan(0) + 0)
= (1/3 - 1 + pi/4) - 0
=pi/4 - 2/3
Therefore, int_0^(pi/4) tan^4(t) dt = pi/4 - 2/3 .

What are the claims Martin Luther King makes in his "Letter From Birmingham City Jail"?

Dr. Martin Luther King, Jr. penned this letter in response to criticism he received from eight white clergymen for his peaceful protests in Birmingham, Alabama. He makes many claims in the lengthy letter, some of which are described below.
Right from the beginning of the letter, King asserts that he receives much criticism and doesn't have the time to respond to most of it; otherwise, he would do little work besides responding to his critics. Yet the claims made by these eight white clergymen are worth taking the time to compose a response, particularly the labels they have attributed to Dr. King's work as "unwise and untimely."
King claims that he has to be in Birmingham because injustice is in Birmingham. Since he deeply believes in the interconnectedness of all people, he says that he cannot simply sit in Atlanta knowing of the injustices in Birmingham and take no action. After all, he notes, "Injustice anywhere is a threat to justice everywhere."
King also claims that sometimes tension is needed to bring about social change, and he isn't afraid of situations that stimulate healthy tension. King hopes that this type of tension can lead to negotiations that foster brotherhood.
King also makes the claim that the oppressed must demand freedom from their oppressors as those with power never volunteer to relinquish it. He goes on to say that African Americans have waited for three hundred and forty years for their Constitutional and God-given rights to be fully recognized. He says that they cannot stand to wait any longer because they are always fighting a sense of "nobodyness" and are tired of being ignored, treated without respect, and facing violence.
A further claim King makes in response to those who ask why he wants to obey some laws (such as desegregating schools) and ignore others (laws that enforce segregation in some areas) is that there are two types of laws: just laws and unjust laws. He sides with St. Augustine that "an unjust law is no law at all."
King also says that white moderates impede a path to social justice through their focus on order over justice and who feel that they can set a timetable for another man's freedom. He also makes this claim in response to white moderates who tell King and his supporters that their rights will come in "time" and they shouldn't rush so quickly:

It is the strangely irrational notion that there is something in the very flow of time that will inevitably cure all ills. Actually, time is neutral. It can be used either destructively or constructively. I am coming to feel that the people of ill will have used time much more effectively than the people of good will. We will have to repent in this generation not merely for the vitriolic words and actions of the bad people but for the appalling silence of the good people. We must come to see that human progress never rolls in on wheels of inevitability. It comes through the tireless efforts and persistent work of men willing to be coworkers with God, and without this hard work time itself becomes an ally of the forces of social stagnation.

King's letter is an assertion that the oppressed cannot remain oppressed forever, and that eventually freedom will demand to be acknowledged. This letter makes various claims that demand that whites acknowledge both the timeliness and inherent justice in King's work.

The letter, written on April 16, 1963, is addressed to Martin Luther King’s fellow clergymen and tries to explain his presence in Birmingham while also addressing various criticisms made by these people towards him. He claims that there are racial injustices in Birmingham in the form of brutality, segregation, unfair treatment of African Americans within the judicial system, unsolved bombings of black homes and churches, and so on. He states that his presence in Birmingham is based on an invitation by the Alabama Christian Movement for Human Rights to be available to engage in a nonviolent call for action against the appalling racial conditions in the city.
He claims that nonviolent direct action is important as it creates the tension necessary to force a society that has repeatedly refused to negotiate deal with underlying difficult issues. He states that historically, privileged groups rarely give up their privileges easily, unless when pushed into action.
He states that they aim to disregard all laws that are unjust, such as the segregation statutes that “give the segregator a false sense of superiority, and the segregated a false sense of inferiority.” This is in response to criticism leveled towards his group and its willingness to “break laws.” He states that his group’s actions are meant to bring to the surface the underlying societal problems—to expose existing injustices.
In response to calls for patience in agitation for justice, he states that “human progress never rolls in on wheels of inevitability; it comes through the tireless efforts of men willing to be coworkers with God, and without this hard work, time itself becomes an ally of the forces of social stagnation.” He denies claims that his and his group’s actions are extreme, stating that theirs is a point between two existing stances: one agitating for inaction, the other standing for hatred and despair.

Using Aeschylus's Orestia Trilogy, select two speeches by Clytemnestra that support what we have been calling Aeschylus's "protofeminism." Tips 1: You may wish to specifically pay attention to Aeschylus's interest to give voice to a woman whose interest to claim a right to her own child (Iphegenia) would have been rendered "voiceless" by a culture which gave primacy to the father's (versus the mother's) right to the child. Tip 2: As a response, you may wish to attend to (and write about) whatever signals exist in Aeschylus's "Clytemnestra" language to kindle our sympathy and compassion for Clytemnestra's plight—in other words, talk about certain phrases and words from her speeches which ignite our sympathies for her. Thank you!

First, protofeminism refers to the philosophical construct that anticipates modern-day feminism by endorsing concepts of gender equality before its time.
In light of this, many argue that Aeschylus's Orestia shows hints of protofeminism at play. Since you asked for two of Clytemnestra's speeches to support Aeschylus's protofeminism, I will refer to the queen's speeches during Agamemnon's homecoming and following the murder of Cassandra and Agamemnon.
In the first speech, Clytemnestra can be seen acting the part of the faithful and adoring spouse. Agamemnon has just returned, and he is victorious. The people welcome him, and Clytemnestra, although still grieving the death of Iphigenia, dares not betray her true emotions. Instead, she talks about how she suffered during the absence of her husband.

First, that a wife sat sundered from her lord, In widowed solitude, was utter woe And woe, to hear how rumour's many tongues All boded evil-woe.

She then tells Agamemnon that Orestes is safe but not presently at home. Instead, he is with Strophius. Here, Clytemnestra is extremely careful not to mention Iphigenia. The Chorus, however, warns us that the queen is merely playing a part:

At home there tarries like a lurking snake, Biding its time, a wrath unreconciled, A wily watcher, passionate to slake, In blood, resentment for a murdered child

Even the watchman at the beginning of the play warns that Clytemnestra is a woman "in whose . . . breast beats [the] heart of man."
Clytemnestra then does something out of the ordinary: she tells her lord to walk on the purple carpets she has ordered her maids to lay out. For his part, Agamemnon initially balks; after all, purple is reserved for the gods, and he certainly does not consider himself one. Clytemnestra answers the king's refusal with a stalwart "Nay, but unsay it—thwart not thou my will!" Gone is the simpering, adoring wife; in its place is the imperious queen, confident of her lord's acquiescence to her will. In ancient Greece, Clytemnestra's reference to her will would have been considered unfeminine at the very least.
However, Aeschylus has Clytemnestra hold her ground. She does not back down and, instead, taunts Agamemnon for fearing the "voice of human blame." This is almost too much for Agamemnon, who was lulled into complacence by Clytemnestra's initial subservience. He barks out an angry but helpless proclamation that "war is not woman's part, nor war of words." However, Agamemnon eventually succumbs to Clytemnestra's unusually confident stance; he must sense that his queen is not to be crossed at this moment. After all, he has just willingly paraded Cassandra, his new concubine, in front of the crowd. Agamemnon humors Clytemnestra and soon comforts himself that all is well.
He enters the palace, however, and meets his doom there. Clytemnestra also kills Cassandra, who sensed that all was not well from the very beginning. Here is part of Clytemnestra's speech after killing her husband and his lover. She is adamant that she has done the right thing, despite protestations from the Chorus.
Oh, lies enough and more have I this day Spoken, which now I shame not to unsay. How should a woman work, to the utter end, Hate on a damned hater, feigned a friend; How pile perdition round him, hunter-wise, Too high for overleaping, save by lies? . . . and with two cries His limbs turned water and broke; and as he lies I cast my third stroke in, a prayer well-sped To Zeus of Hell, who guardeth safe his dead! Wouldst fright me, like a witless woman? Lo, This bosom shakes not. And, though well ye know, I tell you . . . Curse me as ye will, or bless, 'Tis all one . . . This is Agamemnon; this, My husband, dead by my right hand, a blow Struck by a righteous craftsman. Aye, 'tis so . . . Aye, now, for me, thou hast thy words of fate; Exile from Argos and the people's hate For ever ! Against him no word was cried, When, recking not, as 'twere a beast that died, With flocks abounding o'er his wide domain, He slew his child, my love, my flower of pain.
Clytemnestra is unrepentant. Aeschylus lets her speak boldly and plainly. Gone are the careful words of the subservient wife. Clytemnestra glories in the blow she has struck her faithless husband. She also flaunts her own love affair with Aegisthus before the Chorus and argues that she only acted to protect her self-interest. The language Clytemnestra uses is dominant, uncompromising, and unapologetic. We are led to sympathize with Clytemnestra when she proclaims, in righteous anger, Agamemnon's sin: "He slew his child, my love, my flower of pain."
What should I fear, when fallen here I hold This foe, this scorner of his wife, this toy And fool of each Chrysei's under Troy; And there withal his soothsayer and slave, His chanting bed-fellow, his leman brave, Who rubbed the galleys' benches at his side.
Clytemnestra maintains that Agamemnon has scorned her and murdered her child, both terrible wrongs indeed. By her words, we are led to sympathize with her even as she stands with her bloody ax over the bodies of Agamemnon and Cassandra.

Of all men on the ship, who could have put the carved head in the hold?

Since the text does not reveal who put the carved head in the hold, we can only make guesses as to who may have done so. While Mr. Barlow could have placed the head there, it is also possible that another member of the crew did so. 
Whoever put the head in the hold clearly did not want Charlotte to explore the area. In chapter 6, Mr. Barlow warned Charlotte about going down to the hold. When she questioned him, he mentioned that the hold contained extra cargo. However, he also warned that there were rats, roaches, and "foul bilge" down there. Additionally, Mr. Barlow mentioned that the brig or the "ship's jail" was located in the hold.
He cautioned that Captain Jaggery never sailed without a brig on board. This new knowledge made Charlotte uncomfortable, but Mr. Barlow might have intended his words to elicit this reaction from her. It was while Mr. Barlow was helping Charlotte retrieve her trunk that he took the opportunity to warn her about Captain Jaggery. According to Mr. Barlow, the captain was not what he seemed. Mr. Barlow also divulged the fact that Captain Jaggery was abusing his crew.
Prior to Mr. Barlow's warning, Zachariah had also warned Charlotte about the captain's misconduct. However, Charlotte refused to believe either man. It is entirely possible that either Mr. Barlow or Zachariah could have put the head in the hold. The men might have wanted to spare Charlotte the sight of the filthy prison. 

How does Rikki-tikki’s decision to destroy Nagaina’s eggs contribute to the story?

Rikki-tikki's decision points the story toward its climatic battle between Rikki and Nagaina. Even though Nagaina's husband, Nag, has been killed, Rikki realizes that he must destroy her eggs to prevent more cobras in the garden. Darzee, a helpful bird, tells Rikki the location of Nagaina's eggs, then lures her away from them by pretending to have a crippled wing.
While Rikki-tikki is destroying the eggs, however, Nagaina stops chasing Darzee and instead corners Teddy to exact revenge for Teddy's father shooting Nag. Rikki saves one egg, then rushes over and taunts Nagaina, distracting her just long enough for Teddy's father to yank his son out of reach.
After saving Teddy's life, Rikki-tikki chases Nagaina into her hole, then emerges victorious a few minutes later. His heroic actions endear him to the family, whom he represents in the "man vs. nature" conflict against the snakes. His decision to destroy the eggs symbolized his devotion to Teddy, who had found him unconscious after a flood and nursed him back to health, and Teddy's family.
https://www.storyboardthat.com/storyboards/anna-warfield/rikki-tikki-tavi-plot-diagram

Rikki-tikki's decision to destroy Nagaina's eggs is significant because he is able to get her attention while she stares down Teddy in the bungalow. Rikki-tikki wisely destroys twenty-four of Nagaina's twenty-five eggs and carries the last remaining egg with him into the bungalow, where Nagaina is focused on killing Teddy. Rikki-tikki is able to get Nagaina's attention by mentioning her eggs. As soon as Nagaina turns her head to look at her nest, Teddy's father grabs his son and pulls him to safety. Rikki-tikki holds onto Nagaina's last remaining egg as he begins dancing around her in circles. If Rikki-tikki had not destroyed twenty-four of Nagaina's twenty-five eggs, he would not have been able to get her attention while she prepared to strike Teddy. Rikki-tikki's decision to destroy Nagaina's eggs saves Teddy's life and allows Rikki-tikki to take the offensive in their conflict.

College Algebra, Chapter 7, 7.3, Section 7.3, Problem 28

Solve the system of equations $\left\{
\begin{equation}
\begin{aligned}

-7x + 4y =& 0
\\
8x -5y =& 100

\end{aligned}
\end{equation}
\right.
$, $\displaystyle \left[ \begin{array}{cc}
\displaystyle \frac{-5}{3} & \displaystyle \frac{-4}{3} \\
\displaystyle \frac{-8}{3} & \displaystyle \frac{-7}{3}
\end{array} \right] $ by converting to a matrix equation and using the inverse of the coefficient matrix $\left[ \begin{array}{cc}
-9 & 4 \\
7 & -3
\end{array} \right]$

We write the system as a matrix equation of the form $AX = B$







Using the rule for finding the inverse of a $2 \times 2$ matrix, we get

$\displaystyle A^{-1} = \left[ \begin{array}{cc}
-7 & 4 \\
8 & -5
\end{array} \right]^{-1} = \frac{1}{-7 (-5) - 4(8)} \left[ \begin{array}{cc}
-5 & -4 \\
-8 & -7
\end{array} \right] = \frac{1}{3} \left[ \begin{array}{cc}
-5 & -4 \\
-8 & -7
\end{array} \right] $

Multiplying each side of the matrix equation by this inverse matrix, we get


$
\begin{equation}
\begin{aligned}

\left[ \begin{array}{c}
x \\
y
\end{array} \right] =&
\frac{1}{3}
\left[ \begin{array}{cc}
-5 & -4 \\
-8 & -7
\end{array} \right]

\left[ \begin{array}{c}
0 \\
100
\end{array} \right] = \left[ \begin{array}{c}
\displaystyle \frac{-5}{3} \cdot 0 + \left( \frac{-4}{3} \right) \cdot 100 \\
\displaystyle \frac{-8}{3} \cdot 0 + \left( \frac{-7}{3} \right) \cdot 100
\end{array} \right]
=
\left[ \begin{array}{c}
\displaystyle \frac{-400}{3} \\
\displaystyle \frac{-700}{3}
\end{array} \right]

X =& A^{-1} \qquad B

\end{aligned}
\end{equation}
$


So $\displaystyle x = \frac{-400}{3}$ and $\displaystyle y = \frac{-700}{3}$

In The Boy in the Striped Pajamas, how does the story of Bruno and Shmuel embody heroic qualities?

In their willingness to go on an adventure, donning "armor," and in their spirit of sacrificing for one another, Bruno and Shmuel embody heroic qualities.
The hero must embrace adventure.  We tend to valorize people as heroes when they undertake something that most of us could not.  Bruno and Shmuel fit this pattern when they decide to take one “final adventure.”  Both boys are dismayed when they realize that Bruno will be leaving for Berlin.  In order to commemorate their friendship, they decide to take a  “great adventure." Bruno and Shmuel are heroes in the way they fearlessly embrace the spirit of adventure.
Heroes have to don "armor" as a part of their adventure. The hero has external clothing which represents the their quest.  In Bruno's and Shmuel's case, it would be the "striped pajamas," or the uniform that prisoners had to wear in Auschwitz.  Bruno sheds his "civilian" clothes as he crosses under the fence and wears "the striped pajamas."  At this moment, both boys are ready to go on their quest.  Even though, Bruno realizes that the clothes do  “not smell very nice,” he sees the clothes as a part of his adventure.  Like a hero, he remembers the words of his "sage" grandparents who told him that "You wear the right outfit and you feel like the person you’re pretending to be."  Bruno and Shmuel are heroic in how their clothing, their "armor," represents their quest.
Heroes inspire because they sacrifice so much for others. This heroic quality is seen in Bruno's and Shmuel's journey.  Bruno has second thoughts about his quest when he sees the people on the other side of the fence "looking horribly sad.”  While he wants to abandon his initial commitment, Bruno is heroic when he realizes that he would be forsaking Shmuel.  He does not want to let his friend down.  Bruno is heroic in the way he sees something more than himself at stake.  He continues his quest because of it. When Bruno and Shmuel are in the gas chamber, unaware of what will happen, Bruno reminds him that they will be "best friends for life."  Bruno and Schmuel die in the gas chamber, having undertaken an adventure and shown unwavering commitment to their friendship.  In this way, their heroism lies in how they sacrifice for something larger than themselves.

Some authoritarian regimes allow at least some institutionalized limits on rulers’ power. Why does this happen? Provide examples.

An authoritarian regime is often led by a single dictator or an oligarchy. Since the leadership is a very small minority, they cannot rule without the active support of a strong inner circle and the complicity of a substantially larger group of people, including the police and the military. Thus, many authoritarian regimes use some form of institutionalized limits on power, whether real or merely for optics, in order to maintain their legitimacy. Another issue is that because many wealthy democracies insist on human rights as a precondition of trade, aid, or diplomacy, maintaining at least a facade of legitimacy is important to many regimes. Finally, companies that want the benefits of trade and foreign direct investment must show some evidence of rule of law, which constitutes a constraint on the authority of the government.
Russia (under Putin), Egypt (under Sisi), Uzbekistan, Kazakhstan, and Turkmenistan are among the recent examples of countries that stage elections while not allowing genuine democracy. Although China is authoritarian, Xi Jinping, despite the increasing centralization of power, is enforcing anti-corruption regulations and limiting the ability of politicians to be corrupt in commercial endeavors or take bribes. These limits on his own power, especially the emphasis on cracking down on corruption, solidifies his power and makes the middle classes less likely to rebel against his authority since he is offering a guarantee of lawfulness and stability, rather than the sort of caprice associated with unlimited power.

Authoritarian regimes may be structured as dictatorships run by a single strongman or junta, with a straightforward, top-down flow of power, but not all cases are so simple. Structures of government are often the result of generations of historical development, including existing constitutional and legal provisions. Governments may also contain, in practice, multiple or even competing sectors that effectively limit the power of the top leadership, although this structure does not have to resemble democratic governments with their constitutional checks and balances between executive, legislative, and judicial branches.
An interesting example to consider is the government of the Islamic Republic of Iran, formed following the Islamic revolution of 1979. The lion's share of power in Iran is held by the Supreme Leader, currently Ayatollah Ali Khamenei, who sits atop a complex of clerical institutions and also controls the Revolutionary Guard and its Quds Force. However, Iran also has a popularly elected President, although candidates for that office must be approved by the Supreme Leader. The regime squashed a civic protest movement in 2009 following the disputed presidential election of 2009.
Venezuela's government, considered by some to have authoritarian qualities, represents a contrasting example. In this case, a democratically elected and highly popular leader, Hugo Chavez, implemented policies that simultaneously broadened democratic participation in civic life and concentrated political power in the office of the President. Chavez and his successor, Nicolas Maduro, represented a movement they styled as a "Bolivarian revolution," intended to distribute the nation's wealth equitably and uplift the working class. However, their actions were intended to stymie the united political opposition, which managed to capture a legislative majority in 2015. Maduro's government reacted by trying to dissolve the assembly, bringing about an ongoing constitutional crisis.

What are the advantages and disadvantages of rural industrialization?

There are several advantages of rural industrialization beyond the obvious economic ones such as higher wages, less dependence on related agricultural industries, and employment opportunity. While the most significant advantage is economic, several advantages are bonuses that increased economic activity indirectly impacts. Some research seems to support the idea school systems benefit and academic achievement appears to rise. An expanding tax base, particularly in the form of increased property taxes paid by the new residents relocating to rural industries, generates new sources of revenue for school systems. Though possibly an overgeneralization, when industry chooses to locate from a more urban setting to a rural area, they recognize the skill level of the workforce is probably inadequate to staff the plant. To support the relocation and construction of a new manufacturing plant or reinvestment in an industry that may have a location in a rural area draws people with the skills needed to operate the plant to the area. New people create a short term economic boom as they need housing and bring new dollars into the area. Many of the efforts to relocate industry to rural areas have built into them substantial state guarantees of tax subsidies and promises to increase the skill level of potential new employees by investing in the education system. Opportunities also slow the number of people who rather than leave an area choose to stay, which is an economic benefit as well. A better-educated population tends to draw complementary industries to the area to support the significant manufacturer relocating to a rural area.
The disadvantages are equally apparent. The major disadvantage is the character of the rural area is compromised. More people, traffic, and higher costs are associated with increased economic activity. New people bring new ideas about how an area should develop (some good, some bad), and these ideas may contradict longstanding beliefs that form the character of the rural community. Industrialization may displace people from the property they have owned for generations or may change the use of the land to the extent it impacts farmers who remain committed to agriculture. Studies have shown that not everyone benefits economically from industrialization in rural areas. Significant amounts of economic development from construction work and delivery of materials leak out of the community to outside contractors. Non-residents and commuters comprise a substantial part of the workforce, and they tend to spend their money where they live. There is always a possibility a rural area will become too dependent on one large industrial plant, and when the economy or industry changes the plant moves to a different area, wiping out any long term benefits the community received. Some industries use their size and status to monopolize the workforce and prevent other similar industries for relocating to the area.
In a global economy, the lesson learned by the industrial base relocating to rural communities is the economic benefit, while very attractive, can disappear in the blink of an eye. What was once a promising economic development can abandon a community in moment's notice leaving the community worse off than before it located in the rural area. Both the positive and negative advantages have to be weighed from a long-term perspective.
https://www.census.gov/newsroom/blogs/random-samplings/2016/12/beyond_the_farm_rur.html

https://www.investopedia.com/ask/answers/072815/what-are-some-drawbacks-industrialization.asp

https://www.whatworksforamerica.org/ideas/community-development-in-rural-america-collaborative-regional-and-comprehensive/

The major advantages of industrialization in rural areas are employment, infrastructure, and education. Rural areas are often left behind when it comes to economic opportunities. For families that do not farm, rural areas can mean a lengthy commute to the nearest job sites, but more often, those in rural areas experience higher rates of unemployment. Industrialization can bring jobs to those remote areas, and with jobs, better infrastructure. Building a factory means building roads to the factory, ensuring quick shipping routes, and providing adequate housing for employees. Finally, with better infrastructure and job opportunities often come better schools. The tax base in a community increases around industry, small businesses come in to serve that industry (such as restaurants and hotels). As property values increase, the demand for and funding for public schools increase.
The major disadvantages of industrialization in rural areas are pollution, displacement of residents, and loss of natural spaces. Rural areas can be more susceptible to groundwater and/or freshwater pollution when industry moves in because they do not have the safeguards already in place in industrialized areas. The issue is compounded if the rural area is home to livestock and/or crop farming. When industry comes to a rural area, bringing jobs and tax breaks with it, it may need to displace homes, businesses, schools, and wildlife to set up operations. Finally, rural areas are marked by unspoiled acreage, which may not generate revenue, but preserves green spaces and wildlife.  Loss of green spaces is one of the major reasons rural residents protest industrialization.

Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 50

Graph $\displaystyle y = \frac{1}{2}x$ by using the slope and $y$-intercept.

$y$-intercept:


$
\begin{equation}
\begin{aligned}

y =& \frac{1}{2}x
&& \text{Given equation}
\\
y =& \frac{1}{2} (0)
&& \text{To find the $y$-intercept, let } x = 0
\\
y =& 0
&&

\end{aligned}
\end{equation}
$


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


$
\begin{equation}
\begin{aligned}

m =& \frac{\text{change in } y}{\text{change in } x}
\\
\\
m =& \frac{1}{2}

\end{aligned}
\end{equation}
$


Beginning at the $y$-intercept, move to the right 2 units and then up 1 unit.







$(2, 1)$ are the coordinates of a second point on the graph.

Draw a line through $(0,0)$ and $(2, 1)$

Describe the setting of "The Sniper." Why do you think this setting is so limited?

"The Sniper" is set in the city of Dublin during the Irish Civil War. This places the story somewhere in 1922 or 1923.  Beyond this general setting, the bulk of the story takes place on a building rooftop near O’Connell Bridge where the protagonist has inserted himself.  We are told that night has just fallen.  That is basically all the information that readers are given for this story's setting.  As the question states, the setting details are fairly limited.  
There could be a couple of reasons for why the author chose to limit the setting details so much.  One reason could be basic genre conventions.  O'Flaherty is writing a short story, and a lengthy setting description works against his ability to keep the story intense and short.  
A more likely reason for keeping setting details to a minimum is that it fits better with what O'Flaherty does with other details in the story.  Very few details are given about anything in the story.  Other than a description of the protagonist's face and eyes, we do not get any other details about him.  We are not given an age, height, or description of clothing.  It is the same with the other characters as well.  Readers are given almost zero details about the old woman, the other sniper, or the man in the car.  In fact, O'Flaherty does not even bother naming the characters in the story.  Keeping the setting details to a minimum fits with the story's lack of detail regarding its characters. 

what food does helen keller love to eat?

Helen enjoys eating candies, which everyone in her family gives her (probably because they feel bad for her and want a way to communicate their love for her). Since she is blind and deaf, she cannot easily communicate or understand what is happening around her.
Before Annie Sullivan arrives to teach Helen, several members of the household give Helen sweet treats, not realizing that others have already given her treats. First, her mother (Kate) gives her a peppermint drop. She says,

"I don't think one peppermint drop will spoil your supper."

Soon later, Viney, their servant, gets Helen a tea-cake. She thinks aloud,

"Guess one little tea-cake ain't [going to] ruin your appetite."

Moments later, Helen's father is talking with her. He hands her a large stick candy, saying,

"Here. I brought you some stick candy, one nibble of sweets can't do you any harm."

Within moments, Viney calls out to him, reprimanding him for filling her up with "that trash" before her dinner.
Overall, the family loves Helen, and everyone wants her to be happy. They find ways, such as giving her sweets, to show their concern for her. However, giving her so many treats causes her to think she can have whatever she wants. Most members of the household begin to give into Helen's every wish whenever she gets upset. Her stubborn behavior, caused by spoiling her with everything she wishes for, is part of what Annie Sullivan seeks to fix while teaching Helen.

Use context clues to determine the meaning of the word tradition as it is used in paragraph 5 of “The Lottery.” Write your definition of “tradition” and explain how you figured out the meaning.

The narrator explains to the reader that the old box used for the lottery has become really dilapidated and worn, with chipping paint and stains and faded areas. Mr. Summers, the man in town who runs the lottery each year, has tried to convince the townsfolk to make a new box, "but no one liked to upset even as much tradition as was represented by the black box." The meaning of the word tradition in this context seems to be the status quo, or the way things are already done. People seem to want to continue to do things the way they have been doing them because that is the way they have been done before. They seem to want to avoid thinking about what might be replaced, as this could open up a whole can of worms, so to speak: just the box? Or the box and how families draw? Or the box and the lottery in general? Where does the replacement stop once it begins? Rather than address these questions, the villagers would rather "not upset" any even seemingly minor part of their lives.

In the fifth paragraph of Jackson's "The Lottery," the word "tradition" appears as follows: "no one liked to upset even as much tradition as was represented by the black box." In the story, the black box holds the slips of paper representing each member of the village, with one slip bearing the infamous black spot that signifies the stoning of that person. The black box is old and splintered, but it is the original box that was used when the villagers first began the practice of the lottery. Because the villagers are quite tied to their traditional practices, they do not want to replace the box with a newer one. The villagers do not want to "upset" any aspect of their ongoing practice, and for them, the black box is one of the iconic elements of this practice. "Tradition" in the context of the story refers to the act of blindly following a long-held practice, even if—like the black box—time prompts a revision of the practice.

Was Bruno's grandmother against the Nazis? If so, how was she not killed?

Nathalie, Bruno’s grandmother, was a singer and what we can see in the story is that she still loves to sing and art related events. Every year for Christmas, she organizes a play for the family where she and the kids participated. She hates the idea of the Nazis and the concentration camps. She was outspoken about that. When Father was named Commandant of “Out-With”, she was very angry and upset. Bruno’s Grandfather was proud, but she was irritated, offended by that. She knew what was happening in those concentration camps and the suffering of all who went there. When all the family was congratulating Father, she was thinking that probably she made a mistake while raising Father because that new uniform was more no reason to be proud but a statement of how low he has gone.
Being a critic of the Third Reich and their plans was a criminal offense. Most people would have been in trouble, but Grandmother was safe. Probably because her son was the Commandant of Auschwitz. If the people knew that his mother was against the plan it could have been a humiliation and probably cause outrage in the community. The events at those camps were military secret and nothing that could alter that order was going to be allowed.

Bruno's grandmother is deeply hostile towards the Nazis. She bravely expresses her utter loathing for them and their sadistic cruelty. Much of her ire is directed towards her grandson, Bruno's father. For him to take over as commandant of Auschwitz represents a source of abiding shame for his grandmother. She knows full well what goes on there, what horrors await those unfortunate enough to enter its gates.
Despite her very public condemnation of the Nazis, Bruno's grandmother seems never to get into any trouble with the authorities. Publicly criticizing the Nazis in any way was a serious criminal offense in the Third Reich, one that could lead to imprisonment or even death. One possible reason for the authorities leaving Bruno's grandmother alone is that arresting her would potentially cause quite a scandal. The last thing the Nazis would want is for it to get out that the commandant of Auschwitz's own grandmother was against the regime in any way. Also any publicity could reveal what the Nazis were up to at Auschwitz, something they wanted to keep secret.

What is the most important thing that happens in The Outsiders in chapters 1–8?

I'm not sure if this question is asking for the single most important thing that happened in all of those chapters or is asking for an important thing that happened in each chapter. I'm going to choose an event from each chapter just to be safe.  
Chapter 1: This chapter is mainly an introduction to each gang member, but one important event that happens is Ponyboy almost getting beat up by the Socs.  
Chapter 2: I think this is the most important chapter in the book.  Ponyboy meets Cherry, and she helps Ponyboy begin seeing that Greasers and Socs aren't all that different from each other.  This chapter also has the flashback that explains what happened to Johnny when the Socs jumped him.  
Chapter 3: Darry hits Ponyboy.  This causes Ponyboy to run away with Johnny.
Chapter 4: Johnny kills Bob in order to save Ponyboy's life. This forces the two boys to flee and hide out in an old abandoned church. 
Chapter 5: Not much action happens in this chapter.  It's focused on Johnny and Ponyboy spending the better part of a week hiding out in the church.  Readers do find out at the end of the chapter that Cherry Valence is spying on the Socs for the Greasers. 

"Hey, I didn't tell you we got us a spy."
"A spy?" Johnny looked up from his banana split. "Who?"
"That good-lookin' broad I tried to pick up that night you killed the Soc. The redhead, Cherry what's-her-name."

Chapter 6: The church burns down, and Ponyboy and Johnny rescue some kids; however, Johnny is hurt during the rescue. 
Chapter 7: Randy comes to speak with Ponyboy.  Randy is amazed at what Pony and Johnny did, and Randy admits that he's tired of all of the fighting. The exchange is important because it's further evidence that the Greasers and Socs aren't that different.  
Chapter 8: I think probably the most important thing that happens in this chapter happens at the end.  It's when Ponyboy admits that he would help Cherry and Randy out.  They are no longer Soc enemies.  They are just people with problems that watch sunsets like him.  

I'd help her and Randy both, if I could. "Hey," I said suddenly, "can you see the sunset real good from the West Side?"
She blinked, startled, then smiled. "Real good."
"You can see it good from the East Side, too," I said quietly.