What are the principal criticisms of the 2010 book The New Jim Crow: Mass Incarceration in the Age of Colorblindness by Michelle Alexander?

Critics from the far left have claimed The New Jim Crow: Mass Incarceration in the Age of Colorblindness supports the status quo by using a mainstream, white, middle-class theoretical framework and have dismissed it as a "white liberal consumer product." Joseph Osel, for example, claims that the author's language "misleads its readers, mystifying and obscuring the true coordinates of the problem" in order to hide the author's deeper allegiance to the current power structure. Careening from initial enthusiasm to outright rejection, these critics dismiss The New Jim Crow as "white capitalist bourgeoisie rhetoric, dressed-up as black social concern."
These critics suggest the book provides a cathartic release for white liberals without threatening the "oppressive hegemonic assumptions" of capitalism; a word the book fails to mention. The New Jim Crow, they claim, excludes the work of radical black thinkers and black power advocates. These left-wing critiques often reflect the basic assumptions of neo-Marxism, Critical Race Theory, or neo-Gramscianism.
Another principle critique is the argument that Alexander fundamentally misdiagnoses the incarceration epidemic as stemming from the war on drugs. The book Locked In, for example, points out that drug offenders are only a small minority of the prison population, and that the majority of those drug offenders are in prison for violent crime.

In The New Jim Crow, Michelle Alexander reveals how the modern day prison system in the U.S. systemically oppresses African Americans, inflicting upon many a caste system that permanently relegates them to a lower class. A high proportion of black men in urban areas are either currently imprisoned or hold criminal records, a status which deprives them of the right to vote, the right to serve on a jury; it also affects education, employment, and housing opportunities. Alexander criticizes the justice system as a whole, the prison system in particular, and asserts that large-scale campaigns such as the War on Drugs unfairly target African Americans and impede justice. Although Jim Crow laws were banished in the 1960s, the system of segregation and oppression has simply reformed itself into the current prison system rather than disappearing altogether. This is evident through statistics cited in the book, including the fact that African Americans are convicted at disproportionately high rates compared to their white counterparts, allowing a system of legalized discrimination to disrupt black lives in what Michelle Alexander shows to be a modernized version of Jim Crow subjugation.
I'm interpreting this question to refer to the principal criticisms highlighted by Michelle Alexander in the The New Jim Crow, rather than criticisms of the book by readers. I hope the information is helpful as you delve into the subject matter, and I'm including a link below to the feedback page on the book's website, in case you are actually searching for reader responses.
http://newjimcrow.com/praise-for-the-new-jim-crow

What is capitalism and why is it important for supporting free and open markets? Why do you think countries such as China (with planned economies) have moved toward a market economy that supports private enterprise?

I don't see how it is possible to sustain free and open markets without capitalism. By definition, capitalism is made up of buyers and sellers who exercise free choice in all they produce and consume. There is no such thing as pure capitalism, as every capitalist economy has some restraints upon it, which may be to create a level playing field, protect consumers, or protect the environment. The whole idea is to allow people to make what they wish to make—and as much as they want to make—for whatever price they wish, and to allow people to decide what they wish to buy, how much of it they want, and the price they are willing to pay. In a capitalist society, people are far more highly motivated to produce and consume than they are in a planned economy.
Motivation is only one drawback to the planned economy. In a planned economy, the government decides who is going to produce what. The government decides quantity and price. This restricts what is available to the consumer. The government is not prescient, so it often does not know what there will be a demand for, which means goods may very well go unsold. The government may not order the production of goods that people actually want or need. If the needs or desires in an economy shift—which they do—the government may not be flexible or resilient enough to keep up with these shifts. Of course, when people are told what they have to do, they are singularly unmotivated to do it better or faster or to try to do it more creatively. A planned economy stifles creativity. 
China is one country that has been moving toward private enterprise for a while now. I am of the opinion that its re-acquisition of Hong Kong made its rulers see capitalism's advantages quite dramatically. For China to grow its GDP; be part of the modern world; and feed, clothe, and house over 1.3 billion people, capitalism makes a much better model.

Which of Franklin's aphorisms express values that are still widely held in America?

Benjamin Franklin (1706–1790) was an American statesman and humorist whose extensive writings generated a great quantity of pithy observations on the nature of the times in which he lived and the human experience more generally. Many of these aphorisms, printed in his encyclopedic Poor Richard's Almanac, express values that are still relevant in contemporary America.
One of Franklin's aphorisms that holds true today is "write injuries in dust, benefits in marble." Here, Franklin suggests not to be consumed by one's mistakes but, rather, remember the successes of one's life and career. The importance of remembering one's successes continues to be a mantra important in modern times. Heather Yamada-Hosley, writing in 2015 in Lifehacker, affirms this as a modern virtue by referencing other authors who also believe in its importance.
Another aphorism with contemporary relevance is "there are no gains, without pains." In other words, hard work is needed to achieve meaningful results. This has been reimagined in contemporary times into the exercise slogan "no pain, no gain." Underscoring its currency is the fact that Google returns more than 13 million search results for the modern iteration of the phrase.

Franklin wrote and published Poor Richard's Almanack under the pseudonym of Richard Saunders. The purpose of the publication was to promote what Franklin considered to be important cultural values.
Saunders was characterized as a poor yet ambitious man who succeeded by means of hard work and exceptional moral character. He embodies the values of the "American Dream," a phrase that refers to the popular notion that no matter where you come from, if you work hard for long enough, you can earn a comfortable life for yourself and your family.
The American Dream is something many people still cling to today, so the values associated with it are still widely held. Here are just a few quotes with aphorisms that touch on notions related to the American Dream and the value of hard and diligent work. You can find many more in the text. 

No man e'er was glorious, who was not laborious.


He that waits upon Fortune, is never sure of a Dinner.


Early to bed and early to rise, makes a man healthy, wealthy, and wise.

Precalculus, Chapter 1, 1.2, Section 1.2, Problem 62

Find the intercepts of the equation $4x^2 + y^2 = 4$ and test for symmetry.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

4x^2 + y^2 =& 4
&& \text{Given equation}
\\
4x^2 + (0)^2 =& 4
&& \text{To find the $x$-intercept, we let } y = 0
\\
4x^2 =& 4
&&
\\
x^2 =& 1
&&
\\
x =& \pm 1

\end{aligned}
\end{equation}
$



The $x$-intercepts are $(-1,0)$ and $(1,0)$

$y$-intercepts:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$


The $y$-intercepts are $(0,-2)$ and $(0,2)$

Test for symmetry

$x$-axis:


$
\begin{equation}
\begin{aligned}

4x^2 + y^2 =& 4
&& \text{Given equation}
\\
4x^2 + (-y)^2 =& 4
&& \text{To test for $x$-axis symmetry, replace $y$ by $-y$ and see if the equation is still the same}
\\
4x^2 + y^2 =& 4
&&

\end{aligned}
\end{equation}
$


The equation is still the same so it is symmetric to the $x$-axis

$y$-axis:


$
\begin{equation}
\begin{aligned}

4x^2 + y^2 =& 4
&& \text{Given equation}
\\
4(-x)^2 + y^2 =& 4
&& \text{To test for $y$-axis symmetry, replace$ x$ by $-x$ and see if the equation is still the same}
\\
4x^2 + y^2 =& 4
&&

\end{aligned}
\end{equation}
$


The equation is still the same so it is symmetric to the $y$-axis

Origin:


$
\begin{equation}
\begin{aligned}

4x^2 + y^2 =& 4
&& \text{Given equation}
\\
4(-x)^2 + (-y)^2 =& 4
&& \text{To test for origin symmetry, replace both $x$ by $-x$ and y by $-y$ and see if the equation is still the same}
\\
4x^2 + y^2 =& 4
&&

\end{aligned}
\end{equation}
$


The equation is still the same so it is symmetric to the origin.

Therefore, the equation $4x^2 + y^2 = 4$ has an intercepts $(-1,0), (1,0), (0,-2)$ and $(0,2)$ and it is symmetric to the $x$-axis, to the $y$-axis and to the origin.

What most likely changed when cottage industries started to disappear?

When cottage industries started to disappear, what most likely changed was the honor bound tradition of the self-employed craftsman. These skilled craftsmen were increasingly overshadowed by manufacturers who could create the same product in factories in much less time, thus overtaking the market for a product once made with great care relatively slowly. If the skilled craftsman wanted to keep working but did not have the staff or managerial skills to compete with a factory, he or she would have to be retrained to work on a machine that produced the same or similar product that he or she made before. The craftsman, in order to keep working competitively, would have to participate in an endeavor that originated in someone else's mind. Craftsmen did not have the training that factory managers had because it was not needed on such a small scale. With the loss of creative and managerial control came the loss of status the craftsmen once enjoyed, with factory owners and managers replacing craftsmen as part of the new middle class.

What is the significance or symbol in the uniforms of both the Nazis and the prisoners in the book?

The Nazi's clean-cut, black uniforms represent authority, power, and an oppressive force to the Jewish prisoners at Auschwitz. The swastikas on the Nazi soldiers' armbands represents the Third Reich and their loyalty to Adolf Hitler. The color black also symbolically represents the evil, wicked deeds of the Nazi regime, such as the systematic annihilation of the European Jewish population. The Nazi uniforms stand in stark contrast to the worn, dirty uniforms that resemble striped pajamas that the Jewish prisoners are forced to wear.
The prisoners' uniforms do not fit properly and are reused by other prisoners when someone dies. The prisoners' uniforms symbolically represent their oppression and servitude. The stripes on their uniforms also relate to prison bars and represent their seclusion in the violent, harsh concentration camps. The fact that the prison uniforms resemble pajamas symbolically represents Bruno's naive, innocent perspective. He does not understand that the people inside the fence are prisoners and suffer under the horrific conditions of their environment. Overall, the uniforms are symbols of separation, reflect the balance of power at Auschwitz, and represent the Nazi authority and Jewish servitude in the concentration camp.

There are two distinct "uniforms" in The Boy in the Striped Pajamas. The Nazi officers wear official Officers uniforms to signify authority and power; these uniforms symbolize control and higher status over the prisoners. The prisoners in the camp wear striped grey clothes (which Bruno mistakes for pajamas on Shmuel). These clothesstrip the prisoners of their identities and ensure they conform to their lower status in the camp.
The striped "pajamas" are significant because they represent the branding that occurred on a larger scale in Europe (Jews were forced to wear yellow Stars of David; Nazi supporters wore red armbands with black swastikas to show allegiance to Hitler's cause).The pajamas may also represent Bruno's childish innocence (or naivety) about the outside world. When he puts on the "smelly" old, grey pajamas to sneak into the concentration camp with Shmuel, he is mistakenly killed alongside his Jewish friend. This shows readers the true horrors of artificial branding; even the Commandant's own son can be killed if he innocently ignores the division established by the uniforms.

What is a secondary character who functions as a contrast to a major character called?

Secondary characters are reoccurring characters who are of lesser importance than the primary or main characters. Secondary characters who function as a contrast to the major characters are called foils. In Shakespeare's classic play Romeo and Juliet, Mercutio serves as Romeo's foil. Mercutio is considered Romeo's foil because he expresses a different opinion on love and has opposite character traits. Unlike Romeo, who is passionate and serious about love, Mercutio mocks love and is rather cavalier about the subject. Mercutio is also portrayed as charismatic and enthusiastic while Romeo is depicted as depressed and melancholy before attending the Capulet ball. Another secondary character who acts as a foil is Rosaline. Rosaline is Juliet's foil and is portrayed as aloof and uninterested in Romeo. Unlike Juliet, who is infatuated and loyal to Romeo, Rosaline has sworn off marriage and remains distant. Overall, foils are secondary characters who contrast primary characters, and both Mercutio and Rosaline act as foils in the play.

A secondary character who serves to contrast the traits of a major character, often the protagonist, is called a foil.  Rosaline, for example, serves as a foil to Juliet.  Rosaline is, apparently (for she never appears on stage), emotionally distant and does not return Romeo's affections; in fact, she has sworn to remain chaste and never indulge in fleshly pleasures.  Juliet, on the other hand, is very passionate and romantic, and she marries Romeo within twenty four hours of meeting him for the first time.
Tybalt, Juliet's cousin, also serves as a foil for Benvolio, Romeo's cousin.  Benvolio, as the root of his name suggests, is good and peace-loving.  He is constantly trying to break up fights between the Capulets and Montagues, and he encourages others to use good sense in their dealings.  Tybalt, on the other hand, hates peace and seems to thrive on violence.  He often instigates fights himself or adds fuel to the disagreements begun by others.  Their contrast makes Tybalt seem so much more evil and Benvolio so much more benevolent.

How would history have been different if Lincoln had not been assassinated?

We can only speculate how history would have been different if President Lincoln wasn’t assassinated. One difference might have been in the Reconstruction plan that was eventually enacted. When the Civil War ended, President Lincoln knew he had to heal the country. The terms of the agreement at Appomattox Court House, ending the Civil War, were very easy on the South. President Lincoln believed this would start the healing process and help with the reunification of the country.
President Lincoln had proposed a plan of Reconstruction. His plan called for having states write new constitutions that would ban slavery when ten percent of the voters in the state pledged to be loyal to the United States. He also offered amnesty or forgiveness to southerners, except for the leaders of the Confederacy. It is possible that, if Lincoln’s plan was accepted, there might have been less resistance and opposition in the South to Reconstruction. President Lincoln was a very skilled leader, so it is reasonable to assume that he might have been able to persuade Congress to adopt his plan, or one that was less harsh, over the plan that was eventually enacted by the Radical Republicans. It's reasonable to assume that President Lincoln would have continued to work to help heal the wounds from the Civil War.
While it might be a stretch to say that race relations might have been better in the South, if there was less opposition to Reconstruction, African Americans might not have faced as much resistance as they faced after Reconstruction ended.
https://www.history.com/this-day-in-history/lincoln-issues-proclamation-of-amnesty-and-reconstruction

https://www.u-s-history.com/pages/h177.html

Calculus of a Single Variable, Chapter 3, 3.1, Section 3.1, Problem 13

You need to evaluate the critical numbers of the function and for this reason, you must differentiate the function with respect to t, using the product and chain rules, such that:
g'(t) = (t*sqrt(4 - t))'
g'(t) = t'*sqrt(4 - t) + t*(sqrt(4 - t))'
g'(t) = sqrt(4 - t) + t*((4-t)')/(2sqrt(4 - t))
g'(t) = sqrt(4 - t) + (-t)/(2sqrt(4 - t))
You need to solve for t the equation g'(t) = 0:
sqrt(4 - t) + (-t)/(2sqrt(4 - t)) = 0
2(4 - t) - t = 0 => 8 - 2t - t = 0 => 3t = 8 => t = 8/3
Hence, evaluating the critical values of the given function, yields t = 8/3.

What is Bradbury trying to say about Montag’s state of mind in the "one drop of rain" paragraph on page 15? How is Montag changing?

This paragraph is meant to show how quickly Montag is changing his view of the world and how, in this moment, he is overwhelmed by that change.
He has just met the lively and curious Clarisse, who made him question whether or not he's happy, and come to the conclusion that he "wore his happiness like a mask" and is not truly happy with his life. Right after this encounter, he came home to find his wife, Mildred, nearly dead from an overdose and had to call in emergency services to save her life.
The "one drop of rain" paragraph comes after Mildred has been saved by some callous, uncaring medical machine operators. With Mildred now asleep, Montag thinks about how only an hour ago, he had been on the street with Clarisse and that it was "Only an hour, but the world had melted down and sprung up in a new and colorless form." When he opens the window, he can hear Clarisse and her family talking in their house, and he wishes he could join them. The one snippet of conversation that he catches is Clarisse's uncle talking about how people in their society use each other and move through the world without knowing how to care about others.
Montag's "one drop of rain" sequence shows us that he is taking in all the information of the past hour and searching frantically for answers to try to make sense of what's going on in his life. This is a turning point for Montag—he knows that he is not content with the life he has, mindlessly burning books, and that something needs to change. His statement after the end of the paragraph, "I don't know anything any more," shows that he is questioning everything now, rather than blindly following, and is starting his journey towards individualism.

y = 5lnx Determine whether the function is a solution of the differential equation y^((4)) - 16y = 0

Given
y = 5ln(x)
y' = 5/x
y''=-5/x^2
y'''=10/x^3
y''''=-30/x^4
so we have to check whether y^((4)) -16y=0
y'''' -16y=-30/x^4 -16(5ln(x)) != 0   
So it's not a solution to the differential equation.

How and why did agriculture develop differently in the middle colonies and in the southern colonies?

In both the middle colonies and the southern colonies, farming was an important economic activity. However, there were some differences between these regions.
In the southern colonies, farming was the main economic activity. There was very little industry in the southern colonies. The soil was fertile, and the climate was suited for farming. In the southern colonies, farmers grew tobacco, indigo, and rice. Many slaves were used on the large farms in the South.
In the middle colonies, there were a variety of economic activities. There was more manufacturing in the middle colonies than in the southern colonies. Farming was important, but it wasn’t the only economic activity. Farmers in the middle colonies were known for the grains they grew. Wheat was one crop that was grown and sold. The middle colonies are often called “the breadbasket colonies” because of the grain that was grown in this region. Slavery did exist in the middle colonies. However, since the farms in the middle colonies weren’t as large as the plantations in the South, there weren’t as many slaves in the middle colonies.
While farming occurred in both regions, there were some differences between the regions related to farming.
https://thomashagen.wordpress.com/history-papers/major-differences-between-the-colonies/

https://www.ushistory.org/us/5.asp

What is an example of human nature in Leo Tolstoy's short story "How Much Land Does a Man Need?"

The term human nature refers to the ways in which people naturally behave, feel, and think, without any influences from society. These are behaviors, feelings, and thoughts that all human beings share, regardless of culture. One element of human nature found in Leo Tolstoy's short story "How Much Land Does a Man Need?" is greed.At first, the protagonist Poham only wants to own enough land to bring him financial security. When he hears his wife and sister-in-law bickering about which life is better, the peasant life or the urban life, Poham thinks to himself, "Our only trouble is that we haven't land enough. If I had plenty of land, I shouldn't fear the Devil himself!" (Ch. 1). Land brings financial prosperity; therefore, in saying the above, he is saying that if he had enough financial prosperity, he wouldn't be tempted into sinful behaviors by the Devil. Yet, the more land he acquires, the greedier he becomes.At first, he purchases 40 acres from a wealthy landowner, along with other peasants in the village. But, when the neighbors begin quarreling and moving elsewhere, he imagines himself buying up his neighbors' land as well. This vision lasts until a peasant from the other side of the Volga comes to visit and tells him about all of the fertile, inexpensive land there. The peasant tempts him with the following:

The land was so good, he said, that the rye sown on it grew as high as a horse, and so thick that five cuts of sickle made a sheaf. One peasant, he said, had brought nothing with him but his bare hands, and now he had six horses and two cows of his own. (Ch. 3)

After hearing this, Pahom's greed for prosperity drives him to purchase 125 acres across the Volga; then, he nearly settles a contract to purchase another 1300 acres to grow more wheat. Either of these purchases could have provided him with plenty. Yet, his greed does not allow him to stop there. Instead, once he hears that inexpensive, fertile land could be purchased from the Bashkirs, he makes yet another deal that costs him his life.
http://w3.salemstate.edu/~hbenne/pdfs/reflections.pdf

Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 27

To find the equation of the graph passing through the point (9,1), we need to solve the given differential equation:
y' = y/(2x) .
First, rewrite it as
(dy)/(dx) = (y)/(2x) . This equation can be solved by the method of separating variables.
Multiply by dx and divide by y:
(dy)/y = (dx)/(2x) . Now we can integrate both sides:
lny = 1/2lnx+C = lnx^(1/2)+C , where C is an arbitrary constant.
Rewriting this in exponential form results in
y = e^(ln(x^(1/2)) + C) = e^C*x^(1/2) .
Since the graph of this equation passes through the point (9,1), we can find C:
1 = e^C*9^(1/2)
e^C = 1/3
C = ln(1/3) = -ln3 .
So the equation of the graph passing through the point (9,1) with the given slope is
y(x) = 1/3x^(1/2) = 1/3sqrt(x) .

int (4x^2+2x-1)/(x^3+x^2) dx Use partial fractions to find the indefinite integral

int (4x^2+2x-1)/(x^3+x^2)dx
To solve using partial fraction method, the denominator of the integrand should be factored.
(4x^2+2x-1)/(x^3+x^2)=(4x^2+2x-1)/(x^2(x+1))
Take note that if the factor in the denominator is linear and non-repeating, each factor in the denominator has a partial fraction form of A/(ax+b) .
And if the factor is linear and repeating, its partial fraction decomposition has a form A_1/(ax+b) + A_2/(ax+b)^2+... +A_n/(ax+b)^n .
So, expressing the integrand as sum of fractions, it becomes:
(4x^2+2x-1)/(x^2(x+1))=A/x+B/x^2+C/(x+1)
To determine the values of A, B and C, multiply both sides by the LCD of the fractions present.
x^2(x+1)*(4x^2+2x-1)/(x^2(x+1))=(A/x+B/x^2+C/(x+1))*x^2(x+1)
4x^2+2x-1=Ax(x+1)+B(x+1)+Cx^2
Then, assign values to x in which either x, x^2 or x+1 will become zero.
So plug-in x=0 to get the value of B.
4(0)^2+2(0)-1=A(0)(0+1)+B(0+1)+C(0)^2
-1=A(0)+ B(1)+C(0)
-1=B
Also, plug-in x=-1 to get the value of C.
4(-1)^2+2(-1)-1=A(-1)(-1+1)+B(-1+1)+C(-1)^2
1=A(0)+B(0)+C(1)
1=C
To get the value of A, plug-in the values of B and C. Also, assign any value to x. Let it be x=1.
4(1)^2+2(1)-1=A(1)(1+1)+ (-1)(1+1)+1(1)^2
5=A(2)-2+1
5=2A-1
6=2A
3=A
So, the partial fraction decomposition of the integrand is:
int(4x^2+2x-1)/(x^3+x^2)dx
= int (4x^2+2x-1)/(x^2(x+1))dx
= int (3/x -1/x^2+1/(x+1))dx
Then, express it as three integrals.
= int 3/x dx - int 1/x^2 dx + int 1/(x+1)dx
= 3int 1/x dx- int x^(-2) dx + int 1/(x+1)dx
For the first and third integral, apply the formula int 1/u du = ln|u|+C .
And for the second integral, apply the formula int u^n du = u^(n+1)/(n+1)+C .
= 3ln|x| + x^(-1) + ln|x+1| +C
=3ln|x| +1/x + ln|x+1| +C
 
Therefore, int(4x^2+2x-1)/(x^3+x^2)=3ln|x| +1/x + ln|x+1| +C .

What is the main and moral ideas of the book The Story of My Life from chapter 1-14?

The main idea of the first part of Helen Keller's The Story of My Life (Chapters 1-13) is the way in which Keller, who was stricken with an illness that made her blind and deaf as a young child, is able to overcome her so-called disabilities to have a full education and a full life. At the end of these chapters, Keller writes of her friends, "In a thousand ways they have turned my limitations into beautiful privileges, and enabled me to walk serene and happy in the shadow cast by my deprivation." In other words, she feels that her friends--people like Dr. Alexander Graham Bell, who directed Keller's father to the Perkins Institute in Boston, and like Keller's teacher Miss Sullivan--helped Keller in her journey from childhood misfortune to later triumph. The moral of the book is also the way in which people who have limitations imposed on them as Keller did can, though education, will, and patience, work to overcome these limitations. Keller became a well-educated, worldly person with many friends through hard work and the help of her family, teachers, and friends.

Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 24

The sum of two numbers is two. The difference between eight and twice the smaller number is two less than four times the larger. Find the two numbers.

If we let $x$ and $y$ be the smaller and larger numbers, respectively, then we have

$x+y = 2$

$x = 2-y \qquad$ Equation 1

And


$
\begin{equation}
\begin{aligned}

8-2x =& 4y-2
\\
8+2 =& 2x+4y
\\
10 =& 2x+4y \qquad \text{Equation 2}

\end{aligned}
\end{equation}
$



By substituting equation 2 with 1, we get


$
\begin{equation}
\begin{aligned}

10 =& 2(2-y) + 4y
\\
10 =& 2(2) - 2(y) + 4y
\\
10 =& 4 - 2y + 4y
\\
10-4 =& 2y
\\
6 =& 2y
\\
\frac{6}{2} =& \frac{2y}{2}
\\
3 =& y

\end{aligned}
\end{equation}
$


Then, by applying back substitution, we get


$
\begin{equation}
\begin{aligned}

x = 2-y = 2-3 = -1

\end{aligned}
\end{equation}
$


Therefore, the two numbers are -1 and 3.

Why did the ghost appear in a dark room?

In "The Canterville Ghost," the ghost almost always appears in a dark room. We see this in Chapter Two when the ghost makes his first appearance before the family. He waits until all of the lights have been turned off before he rattles his chains along the corridor.
Arguably, the ghost appears in a dark room because he wants to maximise his chances of scaring the Otis family. By appearing at night and in the dark, the ghost has a better chance of frightening the new residents of Canterville Chase which is, in fact, the reason for his existence, as is made clear in Chapter Four:

"It was his solemn duty to appear in the corridor once a week, and to gibber from the large oriel window on the first and third Wednesdays in every month."

Ultimately, however, the ghost fails to frighten the family, despite his many appearances in the darkest recesses of the house. In an ironic twist, the ghost becomes the terrified victim of the Otis family and decides to leave the house in Chapter Five so that he can rest eternally in the Garden of Death. 

What does candida mean when she says that morell is spoiled with love and worship?

The overeager young poet Eugene Marchbanks has fallen for Candida Morell in a big way. He puts her on a pedestal; he treats her like a goddess; he's convinced himself that his love for her is truly divine. For her part, Candida encourages Eugene's attentions, not least because she's a tad jealous of the effect her husband James's preaching seems to have on the ladies of the congregation—and not only them, but his secretaries too, like Prossy, who used to perform all manner of menial jobs around the house for the Reverend Morell in return for a pittance. Candida suggests that she only did this because she was in love with him.
However, Candida soon changes her tune and claims that she was only kidding. She is jealous, she says, not for herself, but for someone else who isn't as loved as he ought to be. Morell thinks his wife might be referring to himself, but she actually means Eugene. James, on the other hand, is positively spoiled with love, says Candida; he gets far too much of it. And not just love, but worship too. Candida is referring not just to the love that she gives to her husband, but that which he's received from the ladies of the congregation and his former secretaries. It is Eugene, she claims, who needs love so much more than James. It's simply unfair that all the love should go to James and none to Eugene.

What is the plot and the significance of the main characters in the book The Alienist by Caleb Carr?

Caleb Carr's 1994 crime novel The Alienist follows John Moore, a New York Times crime reporter, as he and his friend Laszlo Kreizler (a famed psychiatrist) recount the grisly 1896 murder spree of a serial killer in Manhattan and their attempts to uncover his identity. 
Their journey begins on March 3, 1986, when Kreizler has Moore brought to the horrific crime scene, where a 13-year-old boy named Georgio "Gloria" Santorelli has been disfigured and killed: his eyes gouged out, right hand cut off, buttocks sheared off, throat slit, cut across his body, and genitals cut off and stuffed into his mouth. Santorelli was a sex worker who dressed as a girl in order to pick up johns. Despite this kind of case normally being ignored, Moore and Kreisler decide to investigate, and Kreizler realizes that there seems to be a connection to another murder case in which two children had had their eyes gouged out. 
Police Commissioner Theodore Roosevelt (yes, that Theodore Roosevelt... the future president!) understands that this is actually the third murder in this pattern, but to avoid controversy due to Kriezler's reputation, he decides to stay away from the case and allow Kriezler to work on it behind the scenes.
The pair are joined by detective brothers Lucius and Marcus Isaacson, as well as one of the first female employees of the NYPD, Sara Howard. Together, the team develops a profile of the serial killer in hopes of predicting his next attempted murder. They contact various mental institutions to see if anyone matching this profile had once been cared for in such an establishment.
After visiting Washington, DC, the team discovers another similar murder--this time, one that has taken place in rural New York. A visit to the site of this murder and a talk with the surviving brother of the killer reveals to them the killer's name: John Beecham (born Japheth Dury). The team discovers that Japheth had been unwanted by his parents and sexually abused by George Beecham, which was the cause of his vengeful behavior. Ultimately, John/Japheth is killed by a gang of thugs before Kreizler can interview him, and although he manages to conduct an autopsy of the body, only the knowledge of the killer's childhood of abuse can offer insight into his deranged actions. 

Example of Antony being clever.

Antony is diabolically clever in his speech to the crowd after Caesar's murder. After essentially promising that he will not oppose Brutus and the conspirators, he asks that he be allowed to speak. Brutus naively trusts him and gives his consent, thinking that by speaking first, he can avert any damage that might come from having Antony speak. He also gets Antony to swear that he will not say anything negative about the conspirators and instead will only eulogize Caesar. He cleverly adheres to this promise in his speech, appealing to the sentimentality of the people by emphasizing Caesar's virtues.
Throughout, however, he reminds the crowd sardonically that Brutus is an "honorable" man. He does not directly call for the people to avenge Caesar's death, but he stokes their fury by reading Caesar's will after repeatedly saying (with sarcasm and mock decorum) that he does not want to move them to violence. Having worked the crowd to a fever pitch, he then describes the murder as an act of traitors but still repeats that Brutus is honorable. So Antony is very clever in securing permission to speak and by stirring up the crowd to avenge Caesar's death through innuendo and suggestion.

How does Shakespeare's theater differ from a modern day theater?

I think you are asking about the physical theaters in which Shakespearean plays were first performed, and how these might compare to the theaters in which we'd expect to see the plays now. Shakespeare's plays are most associated with the Globe Theatre in London, which was actually the first purpose-built playhouse of its kind and was financed by Shakespeare's acting troupe.
Prior to the building of The Globe, plays were regularly performed in any space that was large enough to host them, be it a village square, a pub, a schoolhouse, or a royal court. The Globe, then, has far more in common with our modern theaters than it did with the "theaters" of the time before it. Still, it differed somewhat from the modern understanding of a theater.
In the first place, it had no roof, being open to the air and shaped like a Roman amphitheatre. Only the stage had a roof ("the heavens") for the purposes of hanging scenery from it. People would sit all around the circular theater on the raised banks of seats, but there was also a "pit" in front of the stage where people could stand, for a smaller fee than a ticket with a seat. There was also a balcony above the stage, probably for musicians.
https://www.shakespearesglobe.com/discover

What are some characteristics of Miranda?

When Katherine Anne Porter's short story "Old Mortality" opens, one of the characters, Miranda, is just eight years old. But she feels much older:

 Maria and Miranda, aged twelve and eight years, knew they were young, though they felt they had lived a long time. They had lived not only their own years; but their memories, it seemed to them, began years before they were born, in the lives of the grown-ups around them, old people above forty, most of them, who had a way of insisting that they too had been young once. It was hard to believe.

Right off the bat, we can see that Miranda is mature  beyond her years, that she is highly observant, and that she knows how to behave around adults. 
We see these characteristics quite clearly in another scene, in which the two sisters watch their grandmother crying over old keepsakes during one of her periodic spells of sentimentality:

If Maria and Miranda were very quiet, and touched nothing until it was offered, they might sit by her at these times, or come and go. There was a tacit understanding that her grief was strictly her own, and must not be noticed or mentioned.

We also see that Miranda aspires to great beauty, and that she is concerned with outward image:

Miranda persisted through her childhood in believing, in spite of her smallness, thinness, her little snubby nose saddled with freckles, her speckled gray eyes and habitual tantrums, that by some miracle she would grow into a tall, cream-colored brunette, like Cousin Isabel; she decided always to wear a trailing white satin gown.

Later, when she's a bit older, Miranda is an avid reader:

During vacation on their grandmother’s farm, Maria and Miranda, who read as naturally and constantly as ponies crop grass...

And we learn that she's ambitious:

Her hope of being a beauty died hard, until the notion of being a jockey came suddenly and filled all her thoughts. Quietly, blissfully, at night before she slept, and too often in the daytime when she should have been studying, she planned her career as a jockey. It was dim in detail, but brilliant at the right distance. 

Again and again, we'll see examples of how detail-oriented Miranda is, and how much she pays attention to things that might escape others' notice:

The jockeys sat bowed and relaxed, their faces calm, moving a little at the waist with the movement of their horses. Miranda noted this for future use; that was the way you came in from a race, easy and quiet, whether you had won or lost. 
 

What do the Sealanders think of wacknuck

This answer can be found at the very end of the story. David has been rescued by the Sealand woman, and the conversation that follows gives David and readers great insight into exactly how the Sealanders view the Waknuk people. As the Sealand woman explains that the plastic threads contract enough to kill anybody caught in them, Rosalind shivers at the thought. The woman's nonchalant attitude toward the deaths of all of those people surprises David.

We were puzzled, too, by the Sealand woman, for there was no callousness in her mind, nor any great concern either: just a slight distaste, as if for an unavoidable, but unexceptional, necessity.

The very next paragraph has the woman explaining her apparent callousness. She explains that death is necessary in order to put meat on the plate in order to eat. This comment doesn't mean she thinks the Waknuk people are a food source. Instead, it shows that her attitude is that the Waknuk people are equivalent to an animal of some sort. If readers question this concept, the Sealand woman makes it abundantly clear at the end of the paragraph that she consideres the Waknuk people a completely different species than her own.

"And just as we have to keep ourselves alive in these ways, so, too, we have to preserve our species against other species that wish to destroy it — or else fail in our trust."

The woman believes that Waknuk people are an inferior species that is now being naturally selected to eventually disappear from the planet.

"Your minds are confused by your ties and your upbringing: you are still half-thinking of them as the same kind as yourselves. That is why you are shocked. And that is why they have you at a disadvantage, for they are not confused. They are alert, corporately aware of danger to their species. They can see quite well that if it is to survive they have not only to preserve it from deterioration, but they must protect it from the even more serious threat of the superior variant.
For ours is a superior variant, and we are only just beginning."

What are the effects of globalization on the culture of the people affected?

To a degree, this depends on which people you are discussing. A subsistence farm in sub-Saharan Africa and a hedge fund manager based in London have very different cultural experiences. It is also not really possible to separate the effects of globalization from those of technology.
International trade mean many types of material culture are available globally rather than just locally. For example, on the level of cuisine, one can buy sushi in the United States, fried chicken in Paris, and halal meat in South America. As a wide range of consumers become familiar with international cuisines, creative fusions are also common, such as chicken tikka masala pizza. 
Another important effect of globalization has been the increasing dominance of English as a global language. This affects both business and the arts.
Internet technology and globalization have combined to make many forms of entertainment, including films and video games shared among a global audience and thus designed to meet international demands rather than merely domestic ones. 

A satellite of mass 2500 kg is orbiting the Earth i n an elliptical orbit. At the farthest point from the Earth, its altitude is 3600 km, while at t he nearest point, it is 1100 km. Calculate the energy and angular momentum of the satellite an d its speed at the aphelion and perihelion.

Let's start with the equations you will need for this problem.
Gravitational potential energy, U:
U= -(G*M*m)/r
where: G = gravitational constant, m = satellite's mass, and M = Earth's mass
Aphelion is where the satellite is furthest away:
r_1= R_E + 3600 km=9.967*10^6 m
Perihelion is where the satellite is the closest:
r_2= R_E + 1100 km=7.467*10^6 m
Conservation of Energy:
K_1+U_1 = K_2+U_2
1/2*m*v_1^2-G*m*M/r_1=1/2*m*v_2^2-G*m*M/r_2
Conservation of Angular Momentum:
mv_1 r_1=mv_2 r_2
Solve system of equations for v2.
1/2*m*(v_2*r_2/r_1)^2-G*m*M/r_1=1/2*m*v_2^2-G*m*M/r_2
v_2^2 = 2GM*(1/r_1-1/r_2)/((r_2/r_1)^2-1)
Plug in numerical values to and solve to get the velocities. 
v_1 = 4387.3 m/s at aphelion, and 5856.2 m/s at perihelion.
Next, plug in either position 1 or position 2 values to get E at BOTH aphelion and perihelion of E=K+U=1/2*m*v_1^2-G*m*M/r_1=7.603*10^10 J
Your angular momentum will also be the same for both aphelion and perihelion
J=m*r_1*v_1=1.09x10^14 (kgm^2)/s
Therefore this problem was completly solved by the conservation of energy and angular momentum.
I included a link that attempts to solve this same problem in more detail. There numerical values are incorrect because they are missing a factor of two when they solve for the velocity.
https://www.assignmentexpert.com/homework-answers/physics-Answer-61340.pdf

Describe the general process by which new elements are synthesized

New elements are synthesized by the highly energetic collisions between nuclei of different elements that may result in the generation of nuclei with a higher atomic number. Particle accelerators are commonly used to provide very high speeds to the ions of colliding elements to generate synthetic elements.
Of the known elements, only 94 are naturally occurring elements and 24 others have been synthesized from these elements.
One of the first synthetic elements to be produced by humans was Curium (atomic number = 96) in the year 1944. Since then, 23 other elements (such as Americium, Berkelium, Fermium, Mendelevium, Nobelium, Bohrium, etc.) have been synthesized.
It should be noted that the process of synthesizing new elements from existing elements is a very expensive and time-consuming process. An example is the attempts made at producing a synthetic element with an atomic number 119. Experiments have been conducted to try to combine Einsteinium and Calcium; Berkelium and Titanium; Curium and Vanadium, etc. However, scientists have not been successful so far.

Glencoe Algebra 2, Chapter 2, 2.6, Section 2.6, Problem 36

f(x) = |x- (1/4)| , the the domain and range is given as follows
(i)Domain definition:
The domain of a function is the set of the input or argument values for which the function is real and defined.
In this function, The function has no undefined points, so the domain is
-oo (ii)Range definition
It is the set of values of the dependent variable for which a function is defined.
For this function the interval has a minimum point at x= 1/4 with value f(x) = 0
so the range of |x- (1/4)| is f(x) >= 0
It can also be observed from the graph below:

How does Holden describe Sunny?

In chapter 13, Holden Caulfield solicits a prostitute named Sunny, who arrives at his apartment expecting to have sex and get paid. Holden initially describes Sunny as "young as hell" and believes that she is around his age. Sunny is also wearing a green dress and Holden mentions that she seems nervous by the way that she continually bounces her leg up and down while sitting cross-legged on a chair. Whenever Holden offers Sunny a cigarette, she rudely declines it, and he mentions that she has a "tiny little wheeny-whiny voice." Holden also notices that she doesn't thank him, which is why he says, "She just didn't know any better" (Salinger, 51). During their conversation, Holden comments that she sounds like a "real kid" before refusing to have sex with her. After she initially leaves the apartment, Holden also refers to Sunny as a "pretty spooky kid." Overall, Holden pities Sunny and sympathizes with her because she is so young and in sad situation. He feels sorry that she is forced to earn a living being a prostitute and is skeptical about her unsettling presence.

In chapters thirteen and fourteen, Holden describes Sunny, the prostitute, as having dyed blonde hair and being "young as hell," meaning around the same age as Holden. Her manners are coarse. Holden thinks she is nervous because she jiggles her "foot up and down" when she sits on the chair in Holden's hotel room. Holden describes her voice as very small and "whiny" and characterizes her expression "like fun you are" as childish. He also describes her as "a pretty spooky kid" when she becomes insistent about how much money Holden owes her.
When Sunny returns with Maurice in tow to collect the rest of the money, they say Holden owes them. Sunny urges Maurice not to hurt Holden after she takes an extra five dollars from Holden's wallet.
Overall, Holden's description of Sunny is sympathetic. He seems a bit appalled at the state of her life at such a young age.

In the poem "Mending Wall" by Robert Frost, how does the speaker feel about the gaps in the wall?

The speaker seems to feel that, because the gaps keep forming, there is some element in the world "that doesn't love a wall." Nature "sends the frozen-ground-swell under it" so that the rocks on top spill off and land on the ground. Hunters and their dogs, also, must make some gaps as well, as the narrator says he frequently has to make repairs when they come through. However, he says,

The gaps, I mean,No one has seen them made or heard them made,But at spring mending-time we find them there.

So, each spring, the narrator and his neighbor pick a day to walk the line of the wall and "set the wall between" them again, repairing these gaps that appear throughout the year. They "wear [their] fingers rough with handling" the stones, some of them quite large, and this is frustrating, it seems, for the narrator, because "we do not need the wall." He reiterates to his neighbor, "Something there is that doesn't love a wall, / That wants it down." Nevertheless, his neighbor insists, time and time again, that "Good fences make good neighbors," and the narrator carries on, really, only because that is what the two have always done. He helps to repair the gaps because it is routine and keeps the peace.

In the poem, the speaker is unhappy about the gaps; the reason for this is that, once the gaps are discovered, he and his neighbor must work together again to put up the wall that separates their properties.
The speaker doesn't specifically care how the gaps are made, whether it is the work of hunters or of nature; he just doesn't think a wall is necessary between neighbors. He states that his neighbor grows pines, while he grows apples; meanwhile neither of them raise cattle, so there isn't any fear of cows venturing onto the other's property.
We get the idea that the speaker thinks the gaps a nuisance of sorts; he would rather leave them alone than decide which fallen boulders belong to whose side of the property. To the speaker, the wall is a waste of time, as he and his neighbor aren't enemies:

Before I built a wall I’d ask to know/ What I was walling in or walling out,/ And to whom I was like to give offense.

The speaker disagrees with his neighbor's belief that "Good fences make good neighbors."

Show how deprivation and suffering are portrayed in the novel Oliver Twist.

Desperation and suffering are everywhere in Oliver Twist and are portrayed in minute detail. Oliver grows up in a workhouse, a place where poor people are housed to stop them from begging in the streets. These were places of hopelessness and squalor, and conditions are incredibly harsh for Oliver as they were for many workhouse inmates in real life. Everyone is expected to work hard, children included. What makes life even harder is that there's not enough food to eat; and the little that's available is absolutely disgusting. It tells you how hungry Oliver is that he asks for more of the revolting slop.
Even after Oliver leaves the workhouse, he constantly finds himself exploited by adults. Noah Claypole, the undertaker's apprentice, treats him like dirt because of his workhouse background. The detestable Monks—Oliver's half-brother—tries to cheat him out of his inheritance. And when Oliver rocks up in London, he becomes part of a gang of young thieves, used by Fagin and Bill Sikes to steal for their own selfish gain. Deprivation and suffering go hand in hand in Oliver Twist. The more deprived you are—whether it's of love, money, food, or a place to live—the more likely you are to suffer.

When did the Indians first inhabit the US?

Scientists disagree about the precise date that indigenous people first came to what is now North America. It was traditionally believed that they traveled to America from northeast Asia roughly 12,000 years ago by making their way across a treacherous sheet of ice between Siberia and Alaska. This is the so-called "Bering Strait" theory, named after the stretch of water that separates Siberia from Alaska.
However, scientists from the University of Barcelona in Spain have challenged the traditional account. Skulls unearthed in Baja California in Mexico appear to have shed new light on the racial origins of the first American settlers. Although the skulls themselves are only a few hundred years old, they display certain features that set them apart from modern-day Native Americans. According to the university's findings, the more slender faces of these skulls share affinities with those of southeast Asians, who are now thought to have occupied Australia some 60,000 years ago before expanding into the Americas some 13,500 years ago.
The scientists involved in this study concluded that, instead of there being one mass migration to America, there was actually a continuous influx from Asia. Despite the findings of this research and the growing rejection of the "Bering Strait" theory by a number of Native American tribes, there is no scientific consensus on the issue. The debate and the controversy continues.
https://www.sciencedaily.com/releases/2013/04/130417092013.htm

What is definition of protagonist?

The definition of protagonist is the character around which the plot of the story centers. Although many misinterpret protagonist to mean the hero or “good guy,” this is not always the case. If one examines the main conflict within a story, then one should be able to determine the protagonist by simply asking oneself: whom or what is most affected by the main conflict in the story?
In the case of William Faulkner’s famous short story, “A Rose for Emily,” the central conflict is the pressure of society and its judgment. The person who suffers at the hands of society’s unyielding judgment is, of course, Miss Emily Grierson of title fame.
Although the reader never hears from Miss Emily directly, the narrator focuses his or her story on the circumstances of Emily’s life and death, and her impact on the people of Jefferson.

Is Waverly happy with her gift? How do you know?

When Waverly and her brothers attend the annual Christmas celebration at the First Chinese Baptist Church, Waverly receives a twelve-pack of Life Savers as a gift. Waverly's brother, Vincent, receives a chess set, which is missing a black pawn and a white knight. Waverly becomes enchanted with the game of chess as she watches her brothers play and even offers two of her Life Savers to fill in as the missing pieces. Waverly is much more interested in the chess set that her brother received than she is with her gift of Life Savers. Waverly develops an affinity for chess and dedicates herself to learning the rules and techniques of the game. Waverly even uses her Life Savers to bet against her brother and an old man named Lau Po in games of chess. Waverly's willingness to sacrifice her candy indicates that she does not really cherish her gift of Life Savers. However, Waverly does use her Life Savers to gain valuable playing experience and become a better chess player.

When Waverly and her family go to the First Chinese Baptist Church's annual Christmas party, every child at the party gets to talk with Santa, and then choose one present from a stack of gifts. There are separate gift stacks for boys and girls, and for different age groups.
When Waverly goes about choosing her gift, she is very strategic, knowing she only has one chance at getting a present she'll actually like. She watches other children choose before her, and notes that "big gifts were not necessarily the nicest ones," and "the sound of the box was also important." She digs through the presents, "testing their weight, imagining what they contained." Waverly ends up choosing a present that turns out to be a 12 pack of Life Savers candies, and she "spent the rest of the party arranging and rearranging the candy tubes in the order of [her] favorites." She is obviously very pleased with her choice, as she says that her brother "chose wisely as well," indicating the she believes that she herself chose wisely. Later on, she is also able to use the candies to bribe people into playing chess with her.

In ''The Last Leaf," how does the doctor feel about painting?

Johnsy, the young painter, is feeling very sick. She's laid up in bed with a particularly nasty bout of pneumonia. Johnsy's from California, so isn't used to the harsh winters of New York. Her friend Sue, deeply concerned, calls for the doctor. He examines Johnsy and unfortunately his prognosis isn't good. He gives her a one in ten chance of making it, and even that's dependent on her wanting to live. The doctor, however, has concluded that Johnsy has effectively given up the ghost; she must have something on her mind, he thinks. The doctor asks Sue what that something might be:

     "She - she wanted to paint the Bay of Naples some day" said Sue.
     "Paint? - bosh! Has she anything on her mind worth thinking twice - a man for instance?"

Clearly, the doctor's no fan of painting. He thinks that Johnsy's desire to paint the Bay of Naples is a waste of time. The doctor cannot believe that something he regards as so trivial, so unimportant could possibly be the cause of Johnsy's malaise. The only reasonable explanation he can think of is that she must be pining over a man. 
http://www.eastoftheweb.com/short-stories/UBooks/LasLea.shtml

sum_(n=1)^oo 5^n/n^4 Use the Root Test to determine the convergence or divergence of the series.

To determine the convergence or divergence of a series sum a_n using Root test, we evaluate a limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
We may apply Root test on the given series sum_(n=1)^oo 5^n/n^4 when we let:  a_n =5^n/n^4 .
Applying the Root test, we set-up the limit as: 
lim_(n-gtoo) |5^n/n^4|^(1/n) =lim_(n-gtoo) (5^n/n^4)^(1/n)
Apply Law of Exponent: (x/y)^n = x^n/y^n and (x^n)^m= x^(n*m) .
lim_(n-gtoo) (5^n/n^4)^(1/n) =lim_(n-gtoo) (5^n)^(1/n)/(n^4)^(1/n)
                        =lim_(n-gtoo)5^(n*1/n)/n^(4*1/n)
                        =lim_(n-gtoo)5^(n/n)/n^(4/n)
                        =lim_(n-gtoo)5^1/n^(4/n)
                        =lim_(n-gtoo)5/n^(4/n)
Evaluate the limit.
lim_(n-gtoo) 5/n^(4/n)=5 lim_(n-gtoo) 1/n^(4/n)         
                =5 *1/oo^(4/oo)
                =5 *1/oo^(0)
                =5 *1/1
                 = 5*1
                =5
The limit value L =5 satisfies the condition: Lgt1 since 5gt1 .
Conclusion: The series sum_(n=1)^oo 5^n/n^4 is divergent.

Characteristics of Joan of Arc.

Joan of Arc was an immensely brave young woman. She fought courageously on the field of battle, leading a whole army at a time when war was considered man's work and opportunities for women outside the home and convent were limited, to say the least. As well as possessing great physical bravery, Joan also displayed immense moral courage. When she was hauled up before the court on charges of heresy and witchcraft, she remained calm and defiant in the face of her prosecutors. She knew that she'd effectively been found guilty already and was scheduled to die a painful death as a consequence. Yet she remained true to her beliefs, genuinely convinced that she had been chosen by God as an instrument with which to expel the English from France once and for all.
As this would suggest, she was also a very devout woman. This was a time when religion dominated the lives of just about everyone. Yet even by the standards of the time, Joan was considered deeply devout, even in childhood. And on the day of her death, she humbly begged the pardon of all who witnessed her execution, as well as pardoning those who had wronged her. So saintly was Joan's demeanor at the stake that day that even many of her erstwhile enemies wept bitterly and proclaimed that she bore all the hallmarks of a saint. However, it wasn't until 1920, some 489 years after her death, that she was finally canonized by the Roman Catholic Church.
https://www.history.com/topics/middle-ages/saint-joan-of-arc

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 72

Graph the family of polynomials $P(x) = x^3 + cx; c = 2, 0 , -2 , -4$ in the same viewing rectangle. Explain what are the effects of changing the value of $c$.


Based from the graph, when the value of $c$ is positive, its graph will never cross the $x$-axis other than the origin. On the other hand, when the value of $c$ is negative, its graph crosses the $x$-axis that makes the functions local extrema defined. All the functions have the same end behaviours and their graphs are all symmetric to the origin. As the value of $c$ increases positively, the graph of $P(x) = x^3$ where $c$ is 0 became more compressed. On the other hand, when the value of $c$ increases negatively its graph expands.

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 47

The table below shows the Temperature $T$(in$^\circ\rm{F}$) in Oklahoma $t$ hours after
midnight on June 12, 2003. Estimate the value of $T'(10)$ and state what does that mean.



$
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline\\
t & 0 & 2 & 4 & 6 & 8 & 10 & 12 &14\\
\hline\\
T & 73 & 73 & 70 & 69 & 72 & 81 & 88 & 91\\
\hline
\end{array}
$







Based from the graph, $\displaystyle T'(10) \approx 3.9\frac{^\circ\rm{F}}{\rm{hour}}$. This means the rate at which
the temperature around 10:00 AM is increasing by $\displaystyle 3.9\frac{^\circ\rm{F}}{\rm{hour}}$. Also,
it shows in the graph that the temperature starts increasing at 6:00 AM in the morning.

Where does Ichabod Crane live? Why does he need to be able to have all of his belongings in a small bundle?

Ichabod Crane, a school teacher in the fictional town of Sleepy Hollow, is the main character in the short story "The Legend of Sleepy Hollow" by Washington Irving. In the short story, Irving describes Crane as being a "huge feeder," meaning he has a big appetite. Since his job as a teacher does not pay well and is barely enough to provide him with enough food for the day, he does not have a permanent residence. Instead, Ichabod lodges at various farmers' houses. These farmers are the families of the students Ichabod instructs at his schoolhouse. Each week, Ichabod packs up his belongings and lodges at a different farmer's home. Due to the fact that Ichabod must move around so frequently, he must keep his belongings small enough to tie up in a "cotton handkerchief" so he can move on to the next place. 

Calculus of a Single Variable, Chapter 5, 5.5, Section 5.5, Problem 62

y = log_10 (2x)
The line is tangent to the graph of function at (5,1). The equation of the tangent line is _______.
To solve this, we have to determine the slope of the tangent. Take note that the slope of a tangent is equal to the derivative of the function.
To get the derivative of the function, apply the formula d/dx [log_a (u)] = 1/(ln(a)*u)*(du)/dx .
Applying this, the y' will be:
y' = d/dx [log_10 (2x)]
y' = 1/(ln(10) * 2x) * d/dx (2x)
y'=1/(ln(10) * 2x) *2
y'=1/(xln(10))
Then, plug-in the given point of tangency to get the slope.
y'= 1/(5ln(10))
So the line that is tangent to the graph of the function at point (5,1) has a slope of m=1/(5ln(10)) .
To get the equation of the line, apply the point-slope form
y - y_1 = m(x - x_1)
Plugging in the values, it becomes:
y - 1 = 1/(5ln(10))(x - 5)
y - 1 = 1/(5ln(10))*x - 1/(5ln(10))*5
y - 1 =x/(5ln(10)) -1/(ln(10))
y=x/(5ln(10)) - 1/(ln(10))+1

Therefore, the equation of the tangent line is y=x/(5ln(10)) - 1/(ln(10))+1 .

What is Helen Keller's family background?

Helen Keller came from a distinguished American pedigree. On her father's side, her ancestors included a governor of the Virginia colony, Colonel Alexander Spottswood, while her mother was descended from important Massachusetts families. Helen's maternal grandfather, Charles Adams, though from Massachusetts, fought on the Confederate side in the Civil War, where he rose to become an acting brigadier general, while Helen's father, Arthur Keller, fought as a Confederate captain during the same war. 
Although the Keller family became poorer after the Civil War, they were hardly impoverished. Helen's father was a newspaper editor and when Helen was five, he became Marshall of North Alabama under President Cleveland's administration.
Helen was fortunate to grow up with privilege. Her family had servants and the financial resources to seek help for their blind and deaf daughter, which included the money to hire Anne Sullivan. Without these resources, Helen's fate likely would have been very different. 
https://www.afb.org/about-afb/history/helen-keller/biography-and-chronology/biography

Helen Keller has long been venerated as an example of courage and determination. Rendered blind and deaf due to a disease she had at 19 months old, Helen eventually became an author, public speaker, and benefactor of other similarly affected people.
Helen was aided by a strong family who was not content to let her remain isolated. Her father, Arthur Keller, was the editor of a newspaper called the North Alabamian in Tuscumbia, Alabama. Her mother, Kate Adams, was the daughter of Charles Adams, who reached the rank of brigadier general in the Confederate army during the Civil War. She also had three brothers and one sister.
Helen was undoubtedly helped by the fact that her family was financially stable and had the connections to help them find the assistance Helen needed. A child from a less prosperous family would probably not have had the opportunity to overcome Helen's limitations.
Perhaps the most important person in Helen's life was her teacher, Anne Sullivan. Although not technically a member of her family, she lived with Helen for almost 50 years. Sullivan was able to open up Helen's world by teaching her to communicate.
https://www.afb.org/about-afb/history/helen-keller/biography-and-chronology/biography

https://www.biography.com/activist/helen-keller

What innovation allowed humans to settle permanently?

Approximately 10,000 years ago, humans discovered that they could cultivate the land and grow crops to feed themselves, as well as tame and raise animals for food. This innovation, known as the Agricultural Revolution, allowed humans to stop their constant search for food by means of hunting and gathering, and instead allowed them to build permanent settlements around farming and animal husbandry. The Agricultural Revolution turned the process of procuring food from a 24-7 job into a more manageable, less time intensive pursuit.
The extra time left over allowed these first non-nomadic humans to create better tools, devise mathematics and come up with philosophies and religions to explain the world around them. Soon, humans began to use written language in order to safeguard their knowledge and build upon it. The Agricultural Revolution also brought about efficiencies that allowed humans in settled villages to turn their expertise to activities other than producing food. This development is known as the Division of Labor. This change in turn led to trading in early barter economies, the building of the cities, and ultimately, the so-called birth of civilization.

To what extent do you agree that friendship is more important than love in act 1 and act 2?

This is an opinion question, so you can feel free to disagree with the idea that friendship is more important than love in these two acts; however, I do believe that friendship is shown as being more important. Bassanio says that he loves Portia and that he wants to woo her in order to make her his wife. Whether you believe that Bassanio is truly in love with her or just in love with the idea of marrying an attractive and rich woman is up to you. In order for Bassanio to pursue Portia, he needs money. Unfortunately, Bassanio is broke at the moment, so he asks Antonio for a loan. Antonio's money is tied up at the moment, but Antonio agrees to take a loan from Shylock in order to help his friend. This is a huge testament to Antonio's friendship because Shylock is known for charging ridiculously high interest rates on his loans.

Shylock, albeit I neither lend nor borrow
By taking nor by giving of excess,
Yet to supply the ripe wants of my friend,
I’ll break a custom.

Additionally, the "pound of flesh" arrangement brings the deal to a whole new level of dangerous. Antonio is a good friend to Bassanio. To Bassanio's credit at this point, Antonio's welfare is more important to him than pursuing Portia. Bassanio tells Antonio to not take the deal. His friend is more important than his pursuit of love.

You shall not seal to such a bond for me!
I’ll rather dwell in my necessity.

What is the purpose of the short scene depicting the interaction between Herrick and the prisoners in the jails?

There are a number of possible reasons for this scene's inclusion in the play. One of these is that it somewhat lightens the generally somber mood of the drama. There's something almost comical about the way in which Tituba interprets the lowing of a cow as a sign of Satan at work. Outside the jailhouse, such ludicrous babbling would've been taken with the utmost seriousness by the credulous townsfolk. But inside the jail, away from the mass hysteria raging outside, it just sounds ridiculous.
One could argue that Miller is attempting to impress upon the audience the point that environment is a key determining factor in fueling the kind of mass hysteria that we witness in the play. In this reading, society is largely to blame for creating the conditions that allow the delusional ramblings of naive young girls like Tituba and Sarah Good to be taken seriously and that form the basis of a judicial process that results in the destruction of innocent lives.

At the beginning of act 4, there is a short scene in the jail that includes Marshal Herrick, Sarah Good, and Tituba. Herrick is drunk, and he comes to wake the two prisoners up. When he does, the two women start talking about how the Devil is coming and how he's going to help them fly to Barbados so they can be happy. One purpose of this scene is to show the terrible hypocrisy of those in Salem: Tituba and Sarah Good are saying the kinds of things that would have been taken incredibly seriously just a couple of months ago, things that would have scared everyone in the town. Now, however, no one regards them or takes seriously anything they say at all. The marshal is drunk and even shares his drink with them. If these types of statements are no longer taken seriously, then why are individuals still going to be hanged for being accused of similar things?  

No party dominated politics through most of the Gilded Age; did this situation have a positive or negative effect on American government? Why? Explain how politics functioned during that time period.

"The Gilded Age" is a term that generally refers to the period between 1877 and 1897 in American history. This was a period of rapid growth for American industry and the population, as many immigrants entered the country from Europe.
Politics in this period were characterized by strong competition between the two main parties, the Democrats and the Republicans, just like today. However, unlike in the modern United States, voters turned out for general elections at a rate of over 80%, reflecting the extreme loyalty of most citizens to their parties of choice. Arguably, the extremely close elections were reflective of the fact that party loyalties across the country were divided approximately equally, and the high voter turnout meant that the ideas of almost everyone who could vote were represented. The economic effects of the Civil War in the South contributed to the fact that many Southern states, very impoverished at this time, tended to vote Democrat where now we would see Republican leanings. New waves of immigrants also supported both parties in roughly equal measure (Catholics would vote Democrat, and Protestants often voted Republican).
This type of evenly-matched politics had generally negative effects upon the government. The major downside was that because both parties were very aware that the election would be extremely close, corruption was encouraged: potential opponents in the form of minor parties—who might take a needed share of the vote—were often paid off by the main parties. Bribes were also offered to important and wealthy voters, particularly large business owners, who were then able to dictate what politicians could and could not do in terms of controlling big business. Additionally, because Congress was so evenly matched, it was extremely difficult to pass any laws, as a majority was very hard to come by in the House.

What were the reasons for the small number of enslaved Africans in the Caribbean before 1600?

There were not many whites in the Caribbean to own slaves before 1600. The French and Spanish debated the morality of the African slave trade, but they also noted that poor whites died soon due to the intense work in the sugarcane fields and the prevalence of malaria, which Africans did not seem to get as often. One also has to consider that before 1600 the Spanish and French were the key players in the New World, and the Spanish were still trying to get the gold out of the North American continent. The English would not be major players until after 1600, though there would be considerable numbers of English pirates preying on the supplies of Spanish and French colonies in the Caribbean.
While slavery would be vital to the history of the Caribbean, it would not explode until the 1700s. During that time, many in Spain, France, and England would consider the Caribbean islands more productive than North America due to their sugarcane fields worked by slaves.

A few different instances resulted in African slaves being brought over to the New World, including the Caribbean, in the 1500s. Most of the events that resulted in slaves being brought to the Caribbean only brought a few slaves at a time.
The first record of African slaves in the Caribbean occurred during Diego Cólon's time as the governor of the Spanish empire in the Caribbean. Cólon believed that Native American slaves were not hard workers, therefore he started the process of petitioning for African slaves to be shipped there. King Ferdinand of Spain allowed for the shipping of 50 African slaves to be sent to the Caribbean in 1510.
Throughout the course of the rest of the century, slaves were sent to places like the West Indies and Jamaica, to work in tobacco and sugar fields, but the slave trade did not increase to large numbers before 1600 because several countries, including France and even Spain, fiercely debated the legality and ethics of slave trade.
http://www.brycchancarey.com/slavery/chrono3.htm

Describe Bacon's vision about death in his essay "Of Death."

In this essay, Bacon attempts to take some of the fear out of death by situating it in a larger context. It is not the worst thing in the world, he says; it is just another one of life's processes. He says it is unfortunate that people develop an irrational fear of it. He notes that, despite exaggerated reports that people die in horrible pain and with convulsions, many also die with little bother. People even welcome death as a release from grief or from their world-weariness:

A man would die, though he were neither valiant nor miserable, only upon a weariness to do the same thing so oft over and over.

He also argues that death allows people to love people unconditionally in memory because we no longer envy them.
While Bacon takes a clear-eyed, sensible, and rational view of death (illustrating his role as one of the fathers of the Enlightenment), we also notice that he is still firmly influenced by Renaissance ideas: he relies heavily on the authority of classical authors of antiquity (on tradition) to buttress his claims about death. He also assumes that his audience is fluent in Latin—the international language among the educated classes in his time—which is why there are so many Latin quotes in the essay. This would seem to fly in the face of the "plain" language for which he is famous, but it would have seemed perfectly ordinary to use Latin during this period.

In Francis Bacon's essay "Of Death", he rejects the framework that death is an event to be feared and despised and further rejects that death is the ultimate perversion and enemy of life. Rather, Bacon argues that death is as natural as birth and is an integral part of the delicate cycle of nature. Death, according to Bacon, is something to ponder and reflect upon but not to be feared—as is often the case and how it is often depicted in literature and art. Bacon sees fear of death as a weakness and as the failing of a mind that is unwilling to understand how death is a part of life. Bacon argues that death should not be seen as the ultimate form of torture but rather as a natural, and often not uncomfortable, closing to a story, one in which the person who dies is often revered and cherished after passing.

Bacon's view on death is well-summarized by his opening comparison to children's fear of the dark: while some amount of fear makes sense, it should be overcome. However, he argues that, rather than demystifying the objects of our fear, all too often humans magnify these fears—making them more monstrous and ghastly than they are in reality.
Just as ghost stories and monster stories make the dark more scary, Bacon discusses the way in which writings about death—often pushed by religious figures—describe it as far more gruesome and painful than it is. He frames it simply as a natural process and as the completion and end of a life. Showing an impressive level of detachment, Bacon suggests that, if we do not invest ourselves in the unrealistic idea that we could live forever, there's no reason to be distraught by the idea that at some point our life will end. Bacon points out that one can leave behind a legacy and that people are generally remembered better after they have died, which are two comforting thoughts.

In his essay "Of Death," Francis Bacon claims that the fear of death is both childish and irrational. It is perfectly right and proper to contemplate death from a religious standpoint, as its being the wages of sin, for example, but to fear death is a sign of weakness. All too often, men—especially religious men such as monks—mistake the horrible accompaniments of death for death itself. Although death is often attended by such unpleasant trappings as facial disfigurement, groans, and convulsions, in itself it is nothing and can just as easily happen without the presence of these and other mortal horrors.
Bacon holds death to be as natural as life itself. Indeed, he believes that the end of life is one of the true benefits of nature. Throughout this essay, we see Bacon the empiricist philosopher, Bacon the man of science, going out of his way to demystify death, to make it seem perfectly natural and therefore absolutely nothing to be afraid of. But we also see Bacon the courtier and politician, Bacon the man of the world, for whom reputation is all-important; a man who thinks that death performs a valuable service to humankind by ensuring that those who are envied in this life shall be loved when they are gone.

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 29

If $\displaystyle f(x) = \frac{1}{\sqrt{x + 2}}$, find $f'(a)$.

Using the definition of the derivative


$
\begin{equation}
\begin{aligned}

f'(a) &= \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}
&& \\
\\
f'(a) &= \lim_{h \to 0} \frac{\displaystyle \frac{1}{\sqrt{a + h + 2}} - \frac{1}{\sqrt{a + 2}}}{h}
&& \text{Substitute $f(a + h)$ and $f(a)$}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\sqrt{a + 2} - \sqrt{a + h + 2}}{(h)(\sqrt{a + h + 2})(\sqrt{a + 2})}
&& \text{Get the LCD of the numerator}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\sqrt{a + 2} - \sqrt{a + h + 2}}{(h)(\sqrt{a + h + 2})(\sqrt{a + 2})}
\cdot \frac{\sqrt{a + 2} + \sqrt{a + h + 2}}{\sqrt{a + 2} + \sqrt{a + h + 2}}
&& \text{Multiply both numerator and denominator by $(\sqrt{a + 2} + \sqrt{a + h + 2})$}\\
\\
f'(a) &= \lim_{h \to 0} \frac{a + 2 - ( a + h + 2)}{(h)(\sqrt{a + h + 2})(\sqrt{a + 2})(\sqrt{a + 2} + \sqrt{a + h + 2})}
&& \text{Simplify the equation}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\cancel{a} + \cancel{2} - \cancel{a} - h - \cancel{2}}{(h)(\sqrt{a + h + 2})(\sqrt{a + 2})(\sqrt{a + 2} + \sqrt{a + h + 2})}
&& \text{Combine like terms}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\cancel{-h}}{\cancel{(h)} (\sqrt{a + h + 2}) (\sqrt{a + 2})(\sqrt{a + 2} + \sqrt{a + h + 2})}
&& \text{Cancel out like terms}\\
\\
f'(a) &= \lim_{h \to 0} \left[ \frac{-1}{(\sqrt{a + h + 2})(\sqrt{a + 2})(\sqrt{a + 2} + \sqrt{a + h + 2})}\right] = \frac{-1}{(\sqrt{a + 0 + 2})(\sqrt{a + 2})(\sqrt{a + 2} + \sqrt{a + 0 + 2})}
&& \text{Evaluate the limit}\\
\\
f'(a) &= \frac{-1}{(\sqrt{a + 2})(\sqrt{a + 2})(\sqrt{a + 2} + \sqrt{a + 2})} = \frac{-1}{(a + 2)(2 \sqrt{a + 2})} = \frac{-1}{(a + 2)(2)(a + 2)^{\frac{1}{2}}}
&& \text{Simplify the equation}

\end{aligned}
\end{equation}
$


$\qquad\fbox{$f'(a) = \displaystyle \frac{-1}{2(a + 2)^{\frac{3}{2}}}$} $

How does Goethe's variation of the Faust legend differ from that in Washington Irving's The Devil and Tom Walker?

In Goethe's Faust Mephistopheles tempts Faust by appealing to his desire for knowledge and control of nature. Faust then falls prey to sensuous delights after Mephistopheles promises him a moment of strong experience and restores his youth. Faust falls in love with the young and beautiful Gretchen. Faust is lured by the devil with the promise of knowledge and later the promise of sensual pleasures. Faust does the devil's work by killing Gretchen's brother and mother and then striving to achieve earthly accomplishments. In the end Faust, who recognizes that God is a higher power than himself, is redeemed and welcomed into heaven.
Tom Walker, on the other hand, is lured into doing the devil's work by the promise of finding Captain Kidd's treasures. Instead of being tempted by sensuous delights or the promise of knowledge, Tom Walker is tempted by greed. He lives his life as a rapacious money lender. Eventually he tries to repent but, unlike Faust, he is never given the chance for redemption. Instead, after he dies, he is said to haunt the swamp where he first encountered the devil. While Faust undergoes a true redemption and accepts God, Tom Walker only undergoes the outward manifestations of redemption. He attends church, but he remains a miserly and self-interested moneylender. Therefore, in the end, while Faust flies to God and achieves true salvation, Tom Walker is forever claimed by the Devil. 

In Chapter 16 of the book Guns, Germs, and Steel, how, according to Jared Diamond, did the Chinese develop and maintain Sinification?

Diamond maintains that, unlike other races, it makes no sense to ask how the Chinese became Chinese. China has been China since the very beginning of its existence, displaying a degree of cultural uniformity almost without parallel in human history.
The main reason for this is that China had a head start in food production. It was the highly sophisticated food production techniques of the Chinese that led to other hallmarks of civilization such as writing, technology, and state formation. These innovations quickly spread throughout Southeast Asia, transforming primitive hunter-gatherer societies into more technologically advanced civilizations. These civilizations—Burmese, Laotians, and Thais—rapidly expanded southward, completing the Sinification of tropical Southeast Asia. All of these cultures still exist to this day, but they share a common origin in South China, from which their ancestors hailed.

Diamond portrays the relative cultural homogenization in China as almost without parallel around the world. "Sinification," he says, "involved the drastic homogenization of a huge region in an ancient melting pot," and indeed this process "offers the key to the history of all of East Asia" (324). It took place, for one thing, because China has some geographic characteristics that encouraged cultural unity. Long rivers that ran from east to west, like the Yangtze and Yellow, meant that similar crops were grown along the coast and far inland. Nor is it divided by a major desert. So when northern Chinese peoples developed what might be called advanced civilization, they spread their culture southward--it was their form of writing, for example, that caught on throughout China, because it had no competitors. Indeed, Chinese culture was heavily influential in the Korean Peninsula and Japan as well as Southeast Asia, in addition to what is today the nation-state of China. As Diamond puts it:

Within East Asia, China's head start in food production, technology, writing, and state formation had the consequence that Chinese innovations also contributed heavily to developments in neighboring regions. (332)

Within China itself, the ruling elites were deliberate in their promotion of Chinese culture and writing, taking sometimes brutal measures to stamp out what they regarded as the primitive culture of people in South China. Because of all these factors, Diamond tells us, the "Sinification" of East Asia was really complete by 100 B.C.E.

Why is The Merchant of Venice named for Antonio?

It's difficult to say with definite certainty why Shakespeare chose the name The Merchant of Venice, but it's possible to guess with reasonable accuracy. In general, it's reasonable to assume that The Merchant of Venice is named after Antonio (who is a merchant and is from Venice) because, in many ways, most of the play's plot revolves around him. Consider, for instance, that Portia and Bassanio's courtship relies upon Antonio's help, as the merchant needs to secure a loan to allow Bassanio to pursue the heiress of Belmont. Furthermore, Antonio's inability to repay this loan results in the dramatic conflict with Shylock. In that case, it appears as though most of the play's action depends upon and revolves around Antonio, and so naming the play after him makes sense.
It's very interesting, therefore, that the character that audiences usually find most memorable is not Antonio, but Shylock. Indeed, the marginalized, Jewish moneylender's oppressed existence, along with his arguably tragic downfall, proves to be more engaging, memorable, and sad than anything Antonio does in the play. Therefore, it's understandable that the title of the play is confusing, as it's Shylock, not Antonio, that we remember once the final curtain falls.

How do we use solvents in our lives?

A solvent is a substance that is used to dissolve another substance (called solute) into it. For example, when we mix salt and water together, salt is the solute and the water is the solvent because water dissolves the salt.
Here are some examples of solvents in our daily lives:
1. As nail polish remover: acetone is a commonly used solvent in nail polish removers.
2. Rubbing alcohol: isopropanol is commonly used as rubbing alcohol for degreasing surfaces.
3. Oils, such as turpentine and gasoline (petrol): are commonly used for removing oily deposits.
4. Dry-cleaning chemicals: TCE (trichloroethylene) was the most commonly used chemical for dry-cleaning of clothes. Trichloroethane is another alternative for the same.
5. Water: the most important solvent in our lives. It dissolves minerals and is also used for cleaning purposes (as well as many other uses it serves in our daily lives).
Thus, we commonly use solvents in our day-to-day life for cleaning purposes and also for transport of minerals and nutrients (through water), and so on.

How is masculinity treated in Chopin's 'The Awakening'?

As presented through the main male characters of Leonce Pontellier and Robert Lebrun, masculinity is portrayed in The Awakening as domineering and uncomfortable with challenges to its power.
Leonce Pontellier is a wealthy man with a fairly high social position. He expects his wife Edna to follow all of the rules of social propriety and to fulfill her duties as a wife and mother as well as a member of the upper class. After a somewhat carefree summer in Grand Isle, the family returns to New Orleans and to their "normal" lives. At this point, though, Edna has progressed and evolved as a character and no longer wants to play the role for which she is supposed to be fitted. For example, she goes out on walks and does what she feels like doing when she is supposed to be home receiving visitors from the Pontelliers' social class. Leonce chastises Edna for not following these norms. She becomes bolder and acquires a smaller house—the pigeon house—where she decides to live on her own, disgusted by the extravagance and obligations of Leonce's family house. Leonce is, of course, embarrassed and concerned about his reputation as a man and a husband. He is also told at one point by Edna's father that he needs to crack down on her and control her more, as though she is a piece of property or an animal. Masculinity, through Leonce, is portrayed as not flexible or open to challenges and also domineering in the sense that he feels it is his right to control his wife and force her to fulfill certain duties.
Robert Lebrun is a different character from Leonce in many ways; he seems more sensitive, and maybe even more feminine to an extent. However, it turns out that Robert is not so different from other men of his class after all. It is implied that he has an affair with a young Mexican girl, which is accepted (seemingly by all, other than Edna, who is offended because she loves him), and this points to the double standard that men can have sexual experiences outside of marriage while women cannot (contrast this to the way women are judged when they spend time with Alcee Arobin). The best piece of evidence that Robert is basically like other men of his time and class occurs after he and Edna confess their feelings for one another near the end of the novel. Robert says that he wants to marry Edna; in other words, he wants to possess her. Edna is disappointed that Robert still thinks in such traditional ways about the potential relationships of men and women. She finds marriage and gender roles restrictive, but Robert wants to put her in the role of wife all over again. This shows that the male characters are conservative and enjoy their power over women; they want to maintain control over their wives and still think (if subconsciously) of women as belongings rather than independent people with their own wills and desires.

Masculinity is treated as something that is somewhat fragile, especially in the face of an empowered woman.  In Grand Isle, when Edna does not leap from her sleep to listen to Leonce's tales of the club and that night's game, he seems to feel that his position is threatened by her failure to play her role.  He lies and says that one of their sons is sick, and he reproaches her for her inattention as a mother (when what he is really irritated with is her inattention as a wife).  On another, later evening, Edna will not come inside and prefers to remain in the hammock alone rather than come in and give in to her husband's sexual advances, as she becomes aware that, in the past, she would simply have done as he'd asked.  With his masculinity threatened by her refusal, Leonce comes outside and refuses to go in as well, as if to make it seem like it is he who is refusing Edna and not the reverse.  
Likewise, Robert Lebrun's masculinity cannot handle the unconventional relationship that Edna proposes near the novel's end.  He hopes that Leonce will divorce her and that he and Edna can get married and be accepted by society; however, Edna sees that this can never happen and also expresses her desire that it not happen, even if it could.  Who would Robert be if he could not perform his masculinity in the way that his society tells him it should be performed: as a husband to a conventional wife and not simply the lover of a disgraced woman?  He does not know, and he cannot imagine it, and so he leaves her, this woman he obviously loves.
This seems to be why Edna's failure to be feminine in the proper way is so threatening: it prevents the men in her life from being masculine in what society has dictated to them to be the proper way.  Thus, we see that their masculinity is fairly fragile, because it cannot withstand one woman's deviation from her socially-prescribed role.  Femininity and masculinity seem to be rooted together, and if the former shifts, the latter will crumble.  

Is there justice in Maycomb County?

One would have to say no. Tom Robinson has been falsely convicted of the rape and assault of Mayella Ewell. This wasn't even a borderline case; it was physically impossible for Tom to have carried out the deed. But in Maycomb County, as elsewhere in the Deep South, that doesn't really matter, because the trial of a black man accused of rape has less to do with achieving justice and more to do with reinforcing the dominance of the white race.
As soon as Tom was accused of the crime, the vast majority of people in Maycomb made up their minds that he was guilty as sin. Why? Because Tom is black, and in the South at that time, the prevailing prejudice held that black men were always on the lookout for white women to rape and as such needed to be kept firmly in line by the law.
Mayella's accusation, though patently false, is tantamount to a conviction in such a deeply racist society. The members of the jury—all but one of them, anyway—have already made up their minds as to Tom's guilt before even setting foot inside the courtroom. They know what's expected of them; they know that their deliberations have absolutely nothing to do with any meaningful notion of justice, but everything to do with keeping African Americans firmly in their place.

Judging from the verdict of the Tom Robinson trial, one could argue that there is no justice in Maycomb County. Tom Robinson becomes the victim of racial injustice after being wrongly convicted of assaulting and raping Mayella Ewell. During the trial, Atticus proves that Bob and Mayella's stories were fabricated and shows that Bob had the motivation to assault his daughter. Atticus also proves that Tom Robinson could not have inflicted the injuries to Mayella's face and neck because of his obvious physical handicap. Despite Atticus's efforts, the racist jury wrongly convicts Tom Robinson of assaulting and raping Mayella simply because he is black. This blatant example of racial injustice is enough evidence to state that there is no justice in Maycomb County. In addition to Tom becoming a victim of racial injustice, the Old Sarum bunch is not punished for attempting to lynch Tom before the trial, and Bob Ewell is allowed to freely roam throughout the community after committing obvious perjury.

Calculus of a Single Variable, Chapter 9, 9.10, Section 9.10, Problem 70

From the table of power series, we have:
(1+x)^k = 1 +kx+ (k(k-1))/2! x^2 +(k(k-1)(k-2))/3!x^3 + ...
To apply this on the given integral int_0^0.2 sqrt(1+x^2)dx , we let:
sqrt(1+x^2) =(1+x^2)^(1/2)
Using the aforementioned power series, we may replace the "x " with "x^2 " and "k " with "1/2 or 0.5 ".
(1+x^2)^(1/2) =1 +0.5x^2+ (0.5(0.5-1))/2! (x^2)^2 +...
= 1 +0.5x^2 -0.25/2! x^4 +...
= 1 +x^2/2-x^4/8 +...
The integral becomes:
int_0^0.2 sqrt(1+x^2)dx = int_0^0.2[1 +x^2/2-x^4/8 +...]dx
To determine the indefinite integral, we integrate each term using Power Rule for integration: int x^ndx =x^(n+1)/(n+1) .
int_0^0.2[1 +x^2/2-x^4/8 +...]dx = [x +x^3/(2*3) -x^5/(8*5) +...]|_0^0.2
= [x +x^3/6 -x^5/40+...]|_0^0.2
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
F(0.2)=0.2 +0.2^3/6 -0.2^5/40+ ...
=0.2+1.3333x10^(-3)-8x10^(-6)+ ...
F(0) =0+0^3/6-0^5/40+ ...
= 0+0-0+...
All the terms are 0 then F(0)= 0.
We can stop at 3rd term (8x10^(-6) or 0.000008) since we only need an error less than 0.0001 .
Then,
F(0.2)-F(0) = [0.2+1.3333x10^(-3)-8x10^(-6)] -[0]
= 0.2013253
Thus, the approximated integral value is:
int_0^0.2 sqrt(1+x^2)dx ~~0.2013

Why does Mr. White say that Herbert’s death is particularly hard?

The next day after Mr. White uses the monkey's paw to wish for two hundred pounds to pay off their mortgage, he and his wife receive the tragic news that their son Herbert has died in an unfortunate work accident. In Part Two, a messenger from Herbert's place of work visits the White's home and informs them that their son lost his life when he got caught in a piece of machinery. The messenger also mentions that the Whites will receive two hundred pounds as compensation for Herbert's death. After learning about his son's death, Mr. White comments, "He was the only one left to us. . . It is hard" (Connell, 9). These two sentences are significant and indicate that Herbert was not their only child. It is also written that Mr. and Mrs. White have been married for nearly forty years and have apparently endured many hardships. Mr. White's comment also indicates that they have outlived all of their children. Overall, Herbert was their last remaining child alive, which makes his death extremely difficult for Mr. and Mrs. White.

Mr. White says that Herbert’s death is particularly hard because “He was the only one left to us.” Although Mr. White’s explanation is short, the implication is that he is their last remaining child, and their other children have died. Elsewhere in the story we learn that Mr. White and his wife have been married for approximately forty years, and based on the rest of the story, it seems that they have faced many hardships. It appears that Herbert’s death is the death of their last surviving child.
But there is an additional reason that it is particularly hard for Mr. White: Mr. White made the wish that resulted in Herbert’s death. Although this reason is not explicitly provided by Mr. White when he explains that it is hard, it is important to keep in mind that Mr. White is, essentially, responsible for Herbert’s death.

Discuss the difference between acids, alkalis, and bases. Discuss and compare the reactivity of alkali metals with those of alkali earths.

Differences between acids, alkali, and bases:
Acids are chemicals that have a pH of less than 7.0, while bases are substances that have a pH of more than 7.0.
Acids can also be thought of as chemicals that donate protons, while bases are chemicals that accept protons.
An acid can also be thought of as a chemical that can neutralize a base. Similarly, a base can neutralize an acid.
Acids turn litmus paper red, while bases make litmus paper turn blue.
Some examples of acids are sulfuric acid, hydrochloric acid, nitric acid, and so on. Some examples of bases are sodium hydroxide, potassium hydroxide, and so on.
Acids generally taste sour, while bases have a bitter taste.
Alkalis are the bases that are water-soluble, which means that they dissolve in water. In other words, not all bases are water-soluble, and only the water-soluble bases are known as alkalis. An example of an alkali is sodium hydroxide. It is a base because it can neutralize an acid, and because it is water-soluble, it is an alkali. An example of a base that is not alkali is copper oxide. This chemical can neutralize an acid, but it is insoluble in water.
In other words, all alkali are bases but not all bases are alkalis.
Also, an alkali has a hydroxide group, while a base has an oxide group in it.
Reactivity of Alkali metals with Alkaline Earth metals:
Alkali metals are group I (or group IA) elements in a periodic table of elements. These include metals such as sodium, lithium, potassium, and so on. Alkaline earth metals are group II (or group IIA) elements and include metals such as calcium, magnesium, barium, and so on. Both the alkali and alkaline earth metals are very reactive due to the loosely associated valence electrons.
In case of alkali metals, only one electron is present in the outermost shell. It is easier to lose this electron to attain a filled electronic configuration. In case of an alkaline earth metal, there are two valence electrons. Since two electrons are a little more difficult to lose when compared to one electron, alkaline earth metals are less reactive when compared to the alkali metals. For example, it is easier for a sodium atom to lose one electron than it is for a magnesium atom to lose two electrons. This means that sodium is more reactive when compared to magnesium.
If we go down a group in the periodic table, the reactivity increases. This is mostly due to an increase in the size of atoms, which results in less nuclear attraction for the valence electrons. This makes the electrons easier to lose, which results in an increase in the reactivity of the atom.
Hope this helps.

What were Sparta's cultural achievements and legacy?

The cultural achievements of Sparta include a well-organized society, gender empowerment, and military prowess. Sparta was made up of three main communities: Spartans, Perioeci, and Helots. The Spartans held the administrative and military positions. The Helots were Greeks captured from other lands conquered by Sparta. They were used as slaves for menial jobs, such as cleaning, farming, and other house chores. The Perioeci were passers-by, mostly traders that visited Sparta to make money.
In all of Greece, Sparta was one of the few areas where women were given the freedom to go to school, own property, and engage in sports.
The government of Sparta paid for the Spartan's military training. It was compulsory for all able-bodied male children to begin military training when they were 7 years old. The training taught them to be patriotic, obedient, and learn to endure tough times. They would become secret police officers by 13, and then graduate to full-time soldiers by 20.
Sparta's legacy was that they had one of the strongest armies in the world at the time.
https://www.history.com/topics/ancient-history/sparta

Through the years, Hollywood has trumpeted the military acumen of the ancient Spartan people, but the city-state also enjoyed tremendous cultural advancement. The Spartans built a very well organized culture which combined elements of democracy, oligarchy, and monarchy. They were strong architects and builders as seen in their remarkable temples, government buildings, and monuments. While the Athenians are generally regarded as artists, the Spartans were known to be gifted in the musical arts including dancing. Their sculpting ability was the envy of the ancient world, particularly their work with bronze. The Spartans are also on the historical record as being respected poets and the oldest love poem in the world is believed to be one written by a Spartan. The Spartans also created a very unique social structure that granted women a great deal of responsibility and respect.