Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 198

A 50-pond weight is applied to the left end of a seesaw that is 10 ft long. The fulcrum is 4 ft from the 50-pound weight. A weight of 30 lb is applied to the right end of the seesaw. Is the 30-pound weigh adequate to balance the seesaw?

Using the Lever System Equation

$F_1 x = F_2 (d-x)$

Solving for $x$,


$
\begin{equation}
\begin{aligned}

F_1 x =& F_2 (d-x)
&& \text{Apply Distributive Property}
\\
\\
F_1 x + F_2 x =& F_2 d
&& \text{Add } F_2 x
\\
\\
x(F_1 + F_2) =& F_2 d
&& \text{Factor out } x
\\
\\
x =& \frac{F_2 d}{F_1 + F_2}
&& \text{Divide by } F_1 + F_2
\\
\\
x =& \frac{50(10)}{30+50}
&&
\\
\\
x =& \frac{500}{80}
&&
\\
\\
x =& \frac{25}{4}
&&
\\
\\
x =& 6.25 \text{ ft}
&&

\end{aligned}
\end{equation}
$


The distance of a 30-pound weight to the fulcrum is $6.25$ ft or $\displaystyle 6 \frac{1}{4} $ ft. This means that the 30-pound weight is not adequate to balance the seesaw.

What was the significance of fletcher vs peck?

The case of Fletcher v. Peck (1810) culminated in a landmark decision by the United States Supreme Court. For the first time ever, the Court ruled that a state law was unconstitutional. This was a radical judgment, not least because many Americans passionately believed that state law should take precedence over federal law. To them, Fletcher v. Peck was another example of a disturbing trend in public life, a move towards greater centralization of power in American government.
The case also established an important legal precedent in relation to the sanctity of contractual agreements. The Court held that, whatever the Georgia state legislature's admirable motives in invalidating the relevant contracts may have been, it did not have the constitutional authority to do so. Even though the contracts had been made by crooked individuals they were legally valid nonetheless and should be upheld. In its well-meaning efforts at tackling corruption, the Georgia state legislature was essentially seizing property without compensation, and that was clearly unconstitutional.
The Marshall Court, in keeping with its Federalist bias, was overwhelmingly partial to business interests as well as strengthening central government. Allowing private property rights to override state laws was a useful tool in enabling not just the growth of federal power but also facilitating the rapid expansion of the United States economy in the early nineteenth century and beyond.
https://constitutionallawreporter.com/2015/06/16/fletcher-v-peck-contract-clause/

As the story ends, what do you think Orwell has to say about the Russian Revolution and the people who were behind it? Explain what it says about when leaders forget or lose their original visions.

Orwell's wonderful tale depicts the utter failure of the Russian Revolution and the betrayal of its purpose by its leaders. The premise of the Revolution was to ensure equality for all. Its goal was to uplift those who were victims of a system of abuse and prejudice and to ensure that each citizen directly shared in the wealth and privilege which had been the preserve of the privileged few--the Russian aristocracy and upper class.  
The novel, furthermore, exposes how power corrupts over time. After the Rebellion, the pigs, who had assumed leadership, almost immediately begin abusing their authority to benefit themselves, to the exclusion of all others. They use the milk to mix into their mash and claim the windfall apples for themselves. On a question as to why they have  done so, they use propaganda, fear, and misinformation to easily convince the largely unintelligent general animal populace. Squealer tells them that they need the sustenance provided by the milk and apples to effectively perform their task of running the farm, otherwise Jones will come back.
This response to the animals' queries becomes a trend. Whenever the pigs change a commandment, they use Squealer's excellent oratory to persuade the animals that they are not doing anything wrong, and that they are acting in everyone's best interests. The pigs' sly tactics quickly lead to much more extreme action. Napoleon expels Snowball from the farm and later has some animals slaughtered by his vicious dogs under the pretext that they have been betraying their comrades by trying to destroy whatever has been achieved. An atmosphere of fear and anxiety now permeates every aspect of the animals' lives.
By using these incidents, Orwell illustrates how Joseph Stalin assumed leadership and became a dictator. Just like Napoleon, Stalin also used brutal measures to get rid of his enemies. He, for example, had Leon Trotsky exiled, just as Napoleon has done with Snowball. Once Snowball is gone, Napoleon becomes a dictator and imposes tyrannical rule on the animals. All the original ideals of Animalism are quickly forgotten and the pigs assume human characteristics and indulge in human behavior. Napoleon's absolute authority has corrupted him absolutely.
At the end of the novel, all the original commandments are replaced by a single paradoxical tenet:

All animals are equal but some animals are more equal than others 

The pigs start walking on their hind legs and carry whips in their trotters. Napoleon starts wearing clothes and begins smoking a pipe. When the animals see him conversing with humans during a meeting, he cannot be distinguished from the humans, as the following excerpt indicates:

The creatures outside looked from pig to man, and from man to pig, and from pig to man again; but already it was impossible to say which was which.

Things on the farm have come full circle. The Rebellion has been a disaster that only succeeded in ensconcing the pigs in the same positions of entitlement that Mr. Jones and his men had occupied. The ironic difference is that now, the abuses, exploitation, and oppression of the animals are imposed upon them by their own kind and not by some uncaring and ruthless humans. Stalin and his cronies had, similarly, enslaved their comrades and exercised their brutality on them. 

At the heart of Orwell's story is the message that the leaders of the Russian Revolution (who are represented by the pigs) treated the people no better than those who came before. In fact, as the story closes,  the reader is left with the powerful image of the pigs walking on two legs, drinking alcohol and living in the farmhouse. This suggests that the leaders of the Revolution sought to emulate the power and lifestyle of previous leaders, the very people whom they claimed to hate at the beginning of the story.
Moreover, through the Seven Commandments, Orwell shows that the leaders broke their promises to create equality. This is shown most clearly when it is revealed that the Commandments have been replaced by a single rule:

"All animals are equal but some animals are more equal than others."

Finally, through the portrayal of Napoleon, Orwell shows that the original leaders did not forget their vision. In fact, he suggests that they deliberately set out to create a totalitarian regime. In the story, this begins when Napoleon steals the milk and apples so that it can be mixed into the pigs' mash. This demonstrates his selfishness and political ambition, marking the beginning of his rise to absolute leader.

Calculus of a Single Variable, Chapter 8, 8.5, Section 8.5, Problem 7

int 5/(x^2+3x-4)dx
To solve using partial fraction, the denominator of the integrand should be factored.
5/(x^2+3x-4)=5/((x+4)(x-1))
Then, express it as sum of fractions.
5/((x+4)(x-1))=A/(x+4)+B/(x-1)
To determine the values of A and B, multiply both sides by the LCD of the fractions present.
(x+4)(x-1)*5/((x+4)(x-1))=(A/(x+4)+B/(x-1))*(x+4)(x-1)
5=A(x-1)+B(x+4)
Then, assign values to x in which either x+4 or x-1 will become zero.
So plug-in x=-4 to get the value of A.
5=A(-4-1)+B(-4+4)
5=A(-5)+B(0)
5=-5A
-1=A
Also, plug-in x=1
5=A(1-1)+B(1+4)
5=A(0)+B(5)
5=5B
1=B
So the partial fraction decomposition of the integrand is
int 5/(x^2+3x-4)dx
= int 5/((x+4)(x-1))dx
= int (-1/(x+4)+1/(x-1))dx
Then, express it as two integrals.
= int -1/(x+4)dx + int 1/(x-1)dx
= - int 1/(x+4)+int 1/(x-1)dx
To take the integral, apply the formula int 1/u du = ln|u| + C .
= -ln|x+4| + ln|x-1| + C

Therefore, int 5/(x^2+3x-4)dx= -ln|x+4| + ln|x-1| + C .

Did the United States ever join the League of Nations?

The United States never joined the League of Nations. This was one of the reasons why the League of Nations wasn’t successful in accomplishing its goals.
Some United States senators were opposed to parts of the charter of the League of Nations. The part that raised the most concern was the provision requiring member nations to help with actions, either military or non-military, against countries that failed to comply with requests made by the League of Nations. These senators believed this would limit flexibility in foreign policy and that the United States might have to become involved in actions that didn’t directly affect the United States. The senators were also concerned we might have to take actions against another country that wouldn’t be in the nation's best interests. They asked President Wilson to negotiate some changes. When he refused, the United States didn’t join the League of Nations. We also didn’t ratify the Versailles Treaty because the League of Nations was part of that treaty.
https://www.history.com/this-day-in-history/league-of-nations-instituted

Discuss the life of Emily Dickinson (one aspect of her life, such as her family, her education, religion, or her personal relationships) and how it affected her work (discuss at least one poem in detail).

Emily Dickinson lived an introverted life, rarely venturing from her Amherst, Massachusetts home, save for a year at Mount Holyoke Female Seminary and an eight-month stay in Cambridge for treatment of an eye affliction.
Though she herself was an introvert, Emily Dickinson lived among family members who had careers that required a notable public presence. Her grandfather, a lawyer, founded Amherst College, and her father, too, was a lawyer who practiced in Amherst. Moreover, Emily Dickinson's father was the treasurer of Amherst College for nearly forty years and served in the Massachusetts state legislature and also Congress. He sat on many boards and was prominent in many reform movements.
Emily Dickinson's brother, Austin, followed in his father's and grandfather's footsteps and also practiced law in Amherst and had a busy career in civic affairs.
In their close-knit family, Emily Dickinson had ample opportunity to observe the demands of community prominence and careers in public service. As a recluse who rarely strayed far from her house, her contemplation of the lives of her grandfather, father, and brother seems clear in this poem:

I’m Nobody! Who are you?
Are you – Nobody – too?
Then there’s a pair of us!
Don’t tell! they’d advertise – you know!

How dreary – to be – Somebody!
How public – like a Frog –
To tell one’s name – the livelong June –
To an admiring Bog!

The poem is an imagined conversation with an introverted person like herself, one who relishes the anonymity of a life lives away from the public eye. The speaker in the poem has no desire to have a public persona, judging such an existence as "dreary" like a frog croaking to the denizens of its swamp. The speaker takes amusement in finding someone like herself with whom to share her witty analogy.

What is the purpose, creative intention, and performance style of The Sound of Music and West Side Story?

Both The Sound of Music and West Side Story are performed as musicals, meaning singing and dancing are an essential part of their storytelling technique. Personally, this is one of my favorite film styles.
These movies are distinctive in that they use the platform of a musical style to tell a serious story. The Sound of Music, set in 1938, tells of the von Trapp family having to flee Austria because of conscientious objection to joining the German Navy during the Nazi regime. West Side Story, a Romeo and Juliet-inspired tale set in the 1950s, explores such social problems as prejudice and animosity between those of different ethnic backgrounds and the repercussions of gang violence.
The creative intent of such musicals is to both further the plot and develop the characters by means of song and dance. For example, in The Sound of Music, the song "Maria" is used to give us insight into the protagonist's character—such as her liveliness and youthful energy. In West Side Story, the song "America" gives context to the story by examining the pros and cons of being an immigrant in that country.

x=6t^2 , y=2t^3 , 1

The formula of arc length of a parametric equation on the interval alt=tlt=b is:
L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt
The given parametric equation is:
 x=6t^2
y=2t^3
The derivative of x and y are:
dx/dt= 12t
dy/dt = 6t^2
 So the integral needed to compute the arc length of the given parametric equation on the interval 1lt=tlt=4 is:
L= int_1^4 sqrt ((12t)^2+(6t^2)^2) dt
The simplified form of the integral is:
L= int_1^4 sqrt (144t^2+36t^4)dt
L=int_1^4 sqrt (36t^2(4+t^2))dt
L= int_1^4 6tsqrt(4+t^2)dt
To take the integral, apply u-substitution method.

u= 4+t^2
du=2t dt
1/2du=tdt
t=1 ,  u =4+1^2=5
t=4 ,  u = 4+4^2=20

Expressing the integral in terms of u, it becomes:
L=6int_1^4 sqrt(4+t^2)* tdt
L=6 int _5^20 sqrtu *1/2du
L=3int_5^20 sqrtu du
L=3int_5^20 u^(1/2)du
L=3*u^(3/2)/(3/2)  |_5^20
L=2u^(3/2)  |_5^20
L = 2usqrtu  |_5^20
L=2(20)sqrt20 - 2(5)sqrt5
L=40sqrt20-10sqrt5
L=40*2sqrt5 - 10sqrt5
L=80sqrt5-10sqrt5
L=70sqrt5
Therefore, the arc length of the curve is  70sqrt5  units.

Describe the early feminist movement, factors that encouraged rebirth of the feminist movement, its recent goals and successes, and how the new wave of feminism differs from that of the 1960s and 1970s.

The early feminist movement grew out of the desire to grant women certain personal rights (e.g., access to education and the right to inherit property) and political rights (e.g., suffrage). The focus of the feminist movements in both the US and Europe was to secure women the right to vote, perhaps as the first and most important step in addressing the other issues that confronted them.
In the United States, The Seneca Falls Convention of 1848 was the first major conference involving both men and women who supported women's suffrage. It led to the trend of having conferences every year. In fact, just two weeks later, another major convention—even bigger than that at Seneca Falls—was held in Rochester. Two of the participants at Seneca Falls, Lucretia Mott and Elizabeth Cady Stanton, had met in London at an anti-slavery convention. Many suffragists found their voices and discovered the language to describe their own oppression by speaking out for the abolition of slaves. Lucy Stone, for example, was forbidden to take speech classes while a student at Oberlin College. She practiced speech alone in the woods near the college and later gave anti-slavery speeches, like Mott and Stanton.
Suffragists were ambivalent about the passage of the Fifteenth Amendment, which granted all men the right to vote, because it did not include women. Women were not granted universal suffrage in the US until 1920. In Britain, suffrage was first granted to property-owning women over 30, but the voting age was not lowered to 21 until 1928. Some countries had much longer to wait—women were not granted suffrage in France until 1945. New Zealand was the first Western country to grant women suffrage in 1893, followed by Australia and the Scandinavian countries. Under Leninist Communism, Russia granted women the right to vote in 1917.
The second-wave feminist movement was revived in the United States in 1963. I will focus on the US, not only because it is the country that I know the most about, but also because it is a country that tends to serve—for better or worse—as a role model to other nations. Betty Friedan published The Feminine Mystique in that year, a book which illuminated the oppression of white, middle-class women by gender stereotypes, advertising, and unfair cultural expectations nurtured by scholarship, film, the publishing industry, and educational institutions. The book articulated for many women what Friedan described as "the problem that has no name." The "mystique" was a stereotype of femininity that many women felt pressure to live up to, despite how oppressive the image was.
Though Friedan's book is credited with sparking the second-wave, she was very often at odds with other feminists, including Gloria Steinem, but also lesbian feminists whom she characterized as "the lavender menace." Friedan wanted women to be full participants in society as it was, while other feminists sought to revolutionize or overturn the systems that Friedan valued, such as capitalism and marriage. However, Friedan agreed with the importance of reproductive freedom. The birth control pill became widely available around the time her book was published and abortion became legal throughout the US in 1973, after the Supreme Court decided Roe v. Wade. Other goals of that movement, which were accomplished, included granting women their own lines of credit and eliminating discrimination in employment, education, and sports at educational institutions. What did not get accomplished was the passage of the Equal Rights Amendment in 1979, which would have included a constitutional amendment saying that men and women were equal under the law.
The current feminist movement is harder to peg. All kinds of people identify as feminists—conservative and progressive women, Republicans and Democrats, libertarians and socialists. The current feminist movement exists as more of an ideology than a movement with clear social goals. Arguably, only the recent rise of the "Me Too" movement has done work similar to that of the second-wave movement in addressing an ongoing problem related to women's oppression and suggesting steps on how to remedy the problem of routine harassment and assault. There is also the issue of "equal pay for equal work," but this problem has proven to be more difficult to address.
https://www.worldatlas.com/articles/first-15-countries-to-grant-women-s-suffrage.html

What does Coach's tattoo say?

Coach has a tattoo on his back that says, "The Good Shepherd." The phrase is taken from the Gospel of John 10:11-18, where Jesus says:

I am the good shepherd: the good shepherd giveth his life for the sheep. (KJV).

The tattoo is important as it symbolizes Coach's role in the story. He's not quite a Christlike figure, but he's certainly a good man who sees it as his responsibility to show kids in the neighborhood that there is a world beyond the poverty and crime of the barrio. Coach grew up in the neighborhood himself so he knows all about the struggles that Eddie and his friends encounter on a daily basis. Unlike many in the barrio, Coach has experience of the wider world. His service in Vietnam is an example of this. In fact, Coach had his tattoo done just before he headed overseas; and though the tattoo is a perfect expression of Coach's personality, he still regrets having it done.

What government replaced Kaiser Wilhelm in Germany?

Kaiser Wilhelm reluctantly capitulated in 1918. German armies had been defeated and communist revolutionaries were a threat inside Germany. The tumultuous situation finally led to the Kaiser's exile in neutral Holland.
The end of the Kaiser's government created an opportunity for communist agitators. The communists had seized Russia after the czar's recent abdication, and they tried to seize power in Germany, too. The German military and other conservative elements of society were determined to keep communism out of Germany.
There was chaos in Germany until Friedrich Ebert (1871–1925), a socialist leader, set up a provisional government. Communists attempted to seize power by force, but they were defeated and their leaders—Rosa Luxemburg and Karl Liebknecht—were executed in January 1919. Ebert then founded the Weimar Republic.
Although Ebert was a capable and earnest leader, his government faced numerous obstacles, and Weimar Germany's instability eventually led to the rise of Adolph Hitler.

Wilhelm II of Germany was forced to abdicate as Kaiser in November 1919. Following his abdication, the Weimar Constitution was signed, declaring that the state of monarchy and aristocracy in Germany would be null and void, and all such titles were to be renounced. The signing of this constitution issued in the so-called Weimar Republic, which governed Germany between late 1919 and 1933.
The leaders of the Weimar Republic were those in power in Germany when the Treaty of Versailles was signed. Because of this, the people of Germany distrusted the Republic's commitment to the German people, believing the terms of the treaty to have been unfair and unfavorable. Under the Weimar Republic, Germany also suffered enormous monetary inflation and an unstable economic climate which endured for many years, in part due to the terms enforced by the Treaty of Versailles. As such, the unpopularity of the Weimar Republic left it open to attack from other quarters: communism was popular in Germany during the 1920s, and during this period, Adolf Hitler and the Nazi party also grew in prominence.

Would "rising in thunderheads of tobacco smoke" be an example of personification or a metaphor?

The quote in the question is an example of a metaphor.  A metaphor is a comparison of two unlike things and does not use the words "like" or "as."  In this case, the quote being used is describing the smoke that is surrounding Captain Beatty.  The smoke isn't thin wisps of tobacco smoke.  It's as thick as the biggest and most dangerous storm clouds.    

Captain Beatty there, rising in thunderheads of tobacco smoke.

The comparison being made portrays Captain Beatty and his movements as similar to a big, powerful storm cloud.  He is imposing and dangerous looking.  Because the quote says that Beatty is in the cloud, I picture Beatty as enshrouded by the cloud.  The line gives Captain Beatty a sort of Satanic presence, which is exactly the kind of person that he is.  He is the ruthless, malicious, shrewd, and destructive antagonist of the story.  At times he comes across as friendly and soft, but that is only to gain an advantage over some other person.  

Write a refection of about 500 words on the significance of being "perfected by society" within the meaning of the following quote from Aristotle: "Man perfected by society is the best of all animals; he is the most terrible when he lives without law, and without justice."

To be "perfected by society" means to be shaped by the laws and social mores of one's community. Aristotle saw man as just another animal but this animal had the benefit of having regulations instead of only acting for his own selfish interests. By acting according to these laws, man can better fit into society and his natural nature of greed and malice is replaced by a need to do the right thing in order to make society run—hence, he is "perfected by society."
According to Aristotle, the man who lives without being "perfected by society" is little more than an animal. He does not feel an urge to fit into society and he does whatever he wishes. He does not have any sense of what the Romans would later call "virtue," which is an urge to do the right thing in order to make society run smoothly. He acts according to his own selfish interests without any fear of being penalized. According to Aristotle, one needed to be constantly "perfected by society" in order to feel fully comfortable within a community. Aristotle wrote these lines in order to point out the importance of laws and social mores in making a community function properly.

Calculus and Its Applications, Chapter 1, 1.1, Section 1.1, Problem 80

The given function is
$
g(x) =
\left\{
\begin{equation}
\begin{aligned}
&x^2 - 2, && \text{for } x < 0\\
&2 - x^2, && \text{for } x \geq 0
\end{aligned}
\end{equation}
\right.
$.
By using the GRAPH and TRACE features determine the limit
$
\displaystyle
\lim_{x \to \infty}
g(x)
$
and
$
\displaystyle
\lim_{x \to -\infty}
g(x)
$.





Based from the graph, the
$
\displaystyle
\lim_{x \to \infty}
g(x)
=
\lim_{x \to -\infty}
g(x)
=
0
$

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 61

Equation of a tangent line to the graph of function f at point (x_0,y_0) is given by y=y_0+f'(x_0)(x-x_0).
The first step to finding equation of tangent line is to calculate the derivative of the given function. To calculate this derivative we will have to use the chain rule (u(v))'=u'(v)cdot v'
y'=1/(1+(x/2)^2)cdot1/2
Now we calculate the value of the derivative at the given point.
y'(2)=1/(2(1+(2/2)^2))=1/2(1+1)=1/4
We now have everything needed to write the equation of the tangent line.
y=pi/4+1/4(x-2)
y=x/4+(pi-2)/4
Graph of the function along with the tangent line can be seen in the image below.

In "A Jury of Her Peers," what aspects of the Wright’s farm suggest that this was not a happy place for Minnie?

When Mrs. Hale gets to the Wright property near the start of "A Jury of Her Peers," she notes the lonely and isolated appearance of the farm. The narrator writes,

Mrs. Hale scarcely finished her reply, for they had gone up a little hill and could see the Wright place now, and seeing it did not make her feel like talking. It looked very lonesome this cold March morning. It had always been a lonesome-looking place. It was down in a hollow, and the poplar trees around it were lonesome-looking trees.

Mrs. Hale feels silenced by the look of the place, and the word "lonesome" is repeated three times in the short paragraph. This sets the tone for the rest of the story. The further sense of Minnie Wright's loneliness is described when Mrs. Hale hesitates to open the door:

Even after she had her foot on the door-step, her hand on the knob, Martha Hale had a moment of feeling she could not cross that threshold. And the reason it seemed she couldn't cross it now was simply because she hadn't crossed it before.

Mrs. Hale does not want to go into the house, and the reason she gives is that she has not visited before. Minnie's lack of friendly visitors both suggests her isolation and Mrs. Hale's guilt for contributing to that isolation.
While exploring the house, the men point out that they had found Minnie sitting in a rocking chair. It is described by the narrator as follows:

Everyone in the kitchen looked at the rocker. It came into Mrs. Hale's mind that that rocker didn't look in the least like Minnie Foster—the Minnie Foster of twenty years before. It was a dingy red, with wooden rungs up the back, and the middle rung was gone, and the chair sagged to one side.

Mrs. Hale notices that the rocker does not match the former personality of Minnie, so she must have changed for the worse, or she does not feel at home in her surroundings. The description of the "dingy" color and "sagg[ing]" chair that stands in a state of disrepair adds to the depressing mood that pervades the farm. It is difficult to imagine anyone living a happy life in that setting.
A conversation between two characters later in the story furthers the idea of the dour and lonely life on the farm but also shifts the attention from Minnie to her husband, the murder victim, and the role he played in contributing to the homestead:

"It never seemed a very cheerful place," said she, more to herself than to him.
"No," he agreed; "I don't think anyone would call it cheerful. I shouldn't say she had the home-making instinct."
"Well, I don't know as Wright had, either," she muttered.
"You mean they didn't get on very well?" he was quick to ask.
"No; I don't mean anything," she answered, with decision. As she turned a little away from him, she added: "But I don't think a place would be any the cheerfuller for John Wright's bein' in it."
"I'd like to talk to you about that a little later, Mrs. Hale," he said. "I'm anxious to get the lay of things upstairs now."

The exchange between Mr. Henderson and Mrs. Hale begins with Mr. Henderson basically blaming Minnie for the inhospitable feel of the home: "I shouldn't say she had the home-making instinct." Mrs. Hale quickly turns this idea on its head, saying that John Wright certainly wouldn't have done anything to make the home happier or more welcoming. This eventually leads to the discovery by the women of the dead bird that symbolizes Minnie. This symbol suggests that Mr. Wright oppressed Minnie and didn't allow her to be herself. When he killed her bird, she snapped and killed him. Mrs. Hale expresses her empathy for Minnie:

Mrs. Hale had not moved. "If there had been years and years of—nothing, then a bird to sing to you, it would be awful—still—after the bird was still."

Mrs. Hale understands how changed Minnie was by life on the Wright farm and with her husband. She is compassionate and also feels guilty that she did not do more to ease Minnie's troubles. Ultimately, she protects her former friend because she can understand why Minnie was so desparate to escape her lonely prison of a life.

y = x^3 - 2x , (-1,1) Set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point.

First we need to calculate equation of the tangent line for which we use the following formula
y=y_1+f'(x_1)(x-x_1)
where y=f(x) is the curve and (x_1,y_1) is the point where the tangent touches the curve.
We will first calculate the derivative f'(x).
f'(x)=3x^2-2
f'(-1)=3-2=1
Now we calculate the equation of the tangent line.
y=1+x-(-1)
y=x+2
In order to determine the upper bound of integration we need to calculate the the point of intersection of the tangent line and the graph of the given function. Hence, we need to solve the following system of equations.
y=x+2
y=x^3-2x
x^3-2x=x+2
x^3-3x-2=0
Factor the equation.
x^3-x-2x-2=0
x(x^2-1)-2(x+1)=0
x(x-1)(x+1)-2(x+1)=0
(x+1)[x(x-1)-2]=0
(x+1)(x^2-x-2)=0
(x+1)(x+1)(x-2)=0
From this we see that the points of intersection are x=-1 (which we already knew) and x=2. Those are also the bounds of integration.
To calculate the area between two curves we simply subtract area under the lower curve from the area under the upper curve. Looking at the image below, we see that the upper curve is the tangent line. Therefore, we get
A=int_-1^2(x+2-(x^3-2x))dx=
int_-1^2(-x^3+3x+2)dx=(-x^4/4+(3x^2)/2+2x)|_-1^2=
-4+6+4-(-1/4+3/2-2)=6+3/4=27/4
The area of the region bounded by the graph of the given function and tangent to the graph at point (-1,1) is equal to 27/4.  
https://en.wikipedia.org/wiki/Tangent

In the play Death of a Salesman by Arthur Miller, Willy misses the distinction between being loved and being well-liked. What are the consequences of Willy's failure to distinguish between the two?

Willy misses the point and confuses "being loved" with being "well-liked" as it is evidenced in the fact that he takes almost for granted the love of his wife, Linda, and seems more eager to please and satisfy someone who shows him only shallow emotions when he enters the affair with "The Woman."
Linda gives Willy every possible validation he would need. She calls him "handsome," "smart,"  and she continuously showers him with complements and kind comments that would assure any normal man that he is loved.
Still, Willy grew up without real love. His father and, later on, his brother left him at an early age having to fend for himself in all matters of support and personal worth. Willy may very well have never known what it feels to feel loved, and so he embarked in a never-ending quest to be "liked." After all, to be "liked" often carries with it a lot of instant gratification, which Willy savors.
In his affair with "The Woman," Willy constantly asks her why she picked him, why she likes him, and other things that have nothing to do with true, emotional connection. As such, he also lacked this connection with just about everyone, including his own adult children.
The consequences of this lack of distinction are crass. Because of his ridiculous need for validation, Willy nearly destroys his marriage. While the marriage was saved, his relationship with Biff became permanently damaged when the latter found out about the affair. Willy also breaks relationships with coworkers, going as far as (supposedly) slapping someone when he heard the person call him a "Walrus."

I’m fat. I’m very—foolish to look at, Linda. [...] a salesman I know, [...] I hear him say something about—walrus. And I—I cracked him right across the face. I won’t take that. I simply will not take that. But they do laugh at me. I know that.

Willy is aware, fully aware, that he is NOT well-liked. Perhaps, he has never been well-liked, judging from the poor way that the treats his friends and neighbors. Therefore, this is one of the consequences of his desire to be well-liked: he fails. He tries too hard, and he loses each and every time. If he knew and validated love, and those who love him, he would not have to be in this endless cat-and-mouse chase for validation that has led him nowhere.

What is one of the themes of William Blake's poem "The Tyger?"

One theme of Blake's poem is the mystery of how a God that could create a creature as gentle as a lamb—and identify the lamb with his son, Jesus—could also make a creature as fearful and bloodthirsty as a tiger.
The poem thus explores two sides of God. One side is gentle, comforting, and inviting—like a lamb. The other is sublime: it strikes us with fear and awe.
The tiger, because of the fear it raises in us, is an example of the sublime. The sublime, usually associated with nature, includes those elements of the natural world that are both beautiful and yet fill us with a sense of God's grandeur and vast might. Mighty waterfalls crashing down or the view from icy mountain tops could fill us with a sense of awe and terror. So does Blake's tiger.
In the poem, the speaker wonders why God is both so gentle as to create the lamb and so terrifying as to create a dangerous predator. The poem dwells in the space of mystery, not offering answers but asking questions.

The divine source of creation is a theme in William Blake's poem "The Tyger," keeping suit with Blake's Pre-Romantic aesthetic and simultaneous interest in the Bible and irreverence toward the Church of England.
The poem questions, "What immortal hand or eye, / Could frame thy fearful symmetry?" In other words, the poet is questioning what kind of god could be responsible for creating a creature who is inherently destructive in nature. This is an especially potent question within the context of the Lamb referenced in the fifth stanza. How could a divine creator create two such seemingly opposite animals--one that is the pinnacle of innocence and one that is a killer? Blake does not provide any answers to these questions, but rather simply opens a dialogue for a discussion of this duality.
This poem is ultimately also a reflection of the limitations of human understanding, particularly as we try to discern the moral questions of good versus evil. 

Why is Ponyboy famous now?

In chapter 5 of The Outsiders, Ponyboy and Johnny are hiding in the church when Dally comes to check on them. After telling the boys that they look pale and thin, Dally informs Ponyboy that he has a letter from Soda. Although Dally tells Soda that he doesn't know where Johnny and Ponyboy are hiding, Soda doesn't believe him. In the letter, Soda explains that Darry is worried about him, and that he wishes they would turn themselves in.
At the end of the letter, Soda says, "You sure are famous," explaining that Ponyboy and Johnny are mentioned in a paragraph in the newspaper. They are in the newspaper as a result of Johnny killing the Soc while trying to defend Ponyboy. Ponyboy, however, doesn't seem too impressed with his celebrity status. After reading the letter a few times, Ponyboy seems more concerned with his brother's spelling errors in the letter.

Do fruit flies and humans have the same evolutionary relationship to wheat?

A good way to address your question is to look at a cladogram, which is a branching diagram showing the evolutionary relationships between organisms. Cladograms always begin with a single stem, which is divided again and again, representing separations into different related groups. A cladogram of the animal kingdom, for instance, could illustrate the relationship between the group that includes humans, Chordata (animals having a spinal cord) and the group that includes fruit flies, Arthropoda (animals having jointed legs).
In a cladogram, branch points represent the most recent common ancestor of the organisms in the two branches. Ever since that ancestor, the two branches have developed separately. Thus we can describe the evolutionary relationship between two organisms by finding their most recent common ancestor, that is, the point where their portions of the diagram branched apart.
Wheat would not be featured on a diagram of the animal kingdom, because it is not an animal. It is a plant. To find an evolutionary relationship to wheat, we must go back farther. At the link below, there is a cladogram showing the most fundamental division of life into six kingdoms. You will have to scroll down past the chart and the first graphic until you see two images next to each other. The one on the left, that looks like a candelabra, is a cladogram of the kingdoms of life.
On this diagram, plants are indicated by a tree and the label Plantae, the biologists' name for the plant kingdom. Animals have a giraffe and the label Animalia. Looking below those labels, you can find the branch point, the most recent common ancestor between animals and plants. It is the second branch point down from the top; the left-hand branch becomes the Plantae, and the right-hand branch then divides into the Fungi and Animalia. All plants, including wheat, are in kingdom Plantae, so they are all in that left-hand branch. All animals, including fruit flies and humans, are in the kingdom Animalia, so they are all in the right-hand branch. That branch point represents the single common ancestor of wheat, humans, and fruit flies. The evolutionary relationship of humans to wheat is that our lineage separated at that point. The evolutionary relationship between fruit flies and wheat is also that their lineage separated at that same point.
Note that there are some differences between cladograms, and some of the relationships are different. This has to do with exciting new information scientists are learning from DNA regarding relationships and time since most recent common ancestor. It does not affect the answer to your question, however.
http://domainsoflife.yolasite.com/kingdom.php

What was the author “shouting” to the reader in "A Good Man is Hard to Find"?

This is certainly an interesting question, and you could find textual evidence to support many ideas for what is being shouted at the reader in "A Good Man is Hard to Find." One idea that the author, Flannery O'Connor, could be "shouting" at readers is the idea that people are not capable of knowing right and wrong without God. The evidence for this would be when the grandmother tries to express that Jesus could help the Misfit. He responds:

"Jesus was the only one who ever raised the dead," The Misfit continued, "and He shouldn't have done it. He thown everything off balance. If He did what He said, then it's nothing for you to do but thow away everything and follow Him, and if He didn't, then it's nothing for you to do but enjoy the few minutes you got left the best way you can."

Additionally, O'Connor paints the Misfit as a sympathetic character in many ways, blurring the lines between good and evil. While he has murdered, he also extends social graces and kindness. In this way, he is better than the children who show nothing but selfishness and rudeness.
Another thing that could be shouted at readers is the idea that each generation has thought that the younger generation has become less respectful and has morally declined. The textual evidence for this would be the disrespectful behavior of June Star and John Wesley toward their parents, grandmother, Red Sammy and his wife, and toward the murderer, Bobby Lee.
Flannery O'Connor herself said of her own story that what was most significant about it was the "moment of grace" the grandmother experiences. In her essay "A Reasonable Use of the Unreasonable," O'Connor spoke of the heroine of her story, the grandmother. She is a hypocritical woman who wears her faith on the outside but doesn't let it change her heart. However, at the moment when her death is imminent, she has a genuine change of heart and experiences the power of grace. Here is what O'Connor wrote about the grandmother's experience:

I often ask myself what makes a story work, and what makes it hold up as a story, and I have decided that it is probably some action, some gesture of a character that is unlike any other in the story, which indicates where the real heart of the story lies. This would have to be an action or gesture which was both totally right and totally unexpected; it would have to be one that was both in character and beyond character; it would have to suggest both the world and eternity. The action or gesture I'm talking about would have to be on the anagogical level, that is the level which has to do with the Divine life and our participation in it. It would be a gesture that transcended any neat allegory that might have been intended or any pat moral categories a reader could make.

O'Connor goes on to describe the grandmother's moment of clarity when she realizes she is responsible for the Misfit and bound to him by the bonds of kinship, as are all men. She has been talking about the mysteries of the Divine, but until this point in the story, it's been empty talk. In this moment, she experiences the grace and the mystery of the Divine interacting with the common.

What is the purpose of the balcony scene in Romeo and Juliet?

The "balcony scene" act 2, scene 2, is a pivotal moment in the play for several reasons. First of all, it is key to demonstrating the difference in approach between the two protagonists. While both are extremely young and impulsive, having fallen in love mere moments after meeting, Romeo's verbose language, which utilizes the trappings of courtly romantic poetry, betrays him as a rather impractical slave to love, happy to soliloquize about the beauty of his "bright angel." By contrast, Juliet's thoughts have taken a different turn, and she sets out the key conflict in the play:

O Romeo, Romeo! wherefore art thou Romeo?Deny thy father and refuse thy name;Or, if thou wilt not, be but sworn my love,And I'll no longer be a Capulet.

Juliet is concerned with the fact that, although she loves Romeo, he is a member of an opposing family. In this scene, the two lovers discuss the difficulties which this presents to them, and we see how they approach the issue. Romeo's inclination is to belittle it, so swept away is he in his romantic daze—he is happy to dismiss the issue, stating "henceforth I never will be Romeo." Juliet is concerned that Romeo will be killed in the orchard "if any of my kinsmen find thee here," to which Romeo says his love will protect him.
The key intrigue in this scene is the question of which of the two attitudes will win out: Romeo's romanticism, or Juliet's pragmatic concern, despite her new passion for Romeo. Ultimately, at the end of the scene, they agree that Romeo should "send...word tomorrow" if he intends to truly marry Juliet, and she will follow him "throughout the world." By the end of the scene, then, the events of the play have been set in motion. We have seen the lovers' concerns raised and interrogated, to a certain extent, and have seen them decide to pursue love over common sense. This allows the audience to settle in, ready to observe how this will play out, and whether the central conflict—that of Montagues against Capulets—will be resolved as a result of this love pact, even if the lovers in a tragedy cannot be expected to survive.

What is one motif in "A White Heron" by Sarah Orne Jewett?

Motifs are recurring symbols which support the themes or main ideas in any story. In A White Heron, the young sportsman's gun is a recurring motif.
To Sylvia, the gun represents strange emotions associated with masculinity, an area she's too young to explore but which, nevertheless, fascinates her.

Sylvia would have liked him vastly better without his gun; she could not understand why he killed the very birds he seemed to like so much. But as the day waned, Sylvia still watched the young man with loving admiration. She had never seen anybody so charming and delightful; the woman's heart, asleep in the child, was vaguely thrilled by a dream of love.

Sylvia is only nine and for her, the realm of love is still hidden in shadows. For her part, she's fascinated as well as horrified by the hunter's nonchalance in killing his animal prey. The gun, of course, is a phallic symbol, and it underlines the theme of nature versus man in the story. Sylvia's conflict is with herself: should she choose to humor the sportsman by revealing the white heron's hiding place or should she protect the birds that have given her so much joy in her young life?
In the end, Sylvia makes her decision on the side of nature. Although her heart is broken as she remembers the "sharp report" of the young sportsman's gun and the "sight of thrushes and sparrows dropping silent to the ground, their songs hushed and their pretty feathers stained and wet with blood," the author suggests that Sylvia has made the better choice. The young protagonist foregoes financial remuneration and a promising friendship with the huntsman in order to protect the beautiful white heron.
So, in the story, the gun is used as a motif to underline the theme of conflict between nature and man. Certainly, the gun can be a useful weapon when one lives in the wilderness: Sylvia's grandmother shares with the sportsman how her son, Dan, used to keep her pantry well-stocked with partridges and squirrels when he was home. However, the gun can also represent the loss of innocence. Sylvia, who doesn't understand how the sportsman can shoot the birds he purports to love, must suddenly begin to contemplate how nature fits into the larger story of humanity.

How can Blanche's madness be shown using quotes?

Although we don't discover the true depths of Blanche's mental illness until later, the signs are certainly there early on in the play, as we see from the following words she speaks to Stella:

I want to be near you, got to be with somebody, I can’t be alone! Because - as you must have noticed - I’m – not very well… [Her voice drops and her look is frightened.] (Scene 1).

We sense that something's not quite right with Blanche. When she says she's not very well, we know that she's not referring to her physical well-being. Ironically, it's not her being alone that eventually leads to her being committed but spending time with other people.

And funerals are pretty compared to deaths. Funerals are quiet, but deaths – not always. (Scene 1).

Blanche has experienced a number of deaths in her unhappy life. She can handle funerals, but the deaths themselves have clearly had a deeply damaging effect upon her mental health. The aching fragility of Blanche's mind is in evidence here; she is simply too delicate to survive in such a harsh, unforgiving world.

There’s so much – so much confusion in the world… [He coughs diffidently.]Thank you for being so kind! I need kindness now. (Scene 3).

Blanche desperately needs someone to help her make it through each day in this confusing world, a world in which she does not really belong. For a brief hopeful period, she thinks that Mitch is the one to help her. Sadly, Blanche becomes as thoroughly disillusioned of Mitch as of everyone else. Once he's rejected her, then there's no one left to help, and so there's a frightening sense of inevitability about her subsequent descent into madness.

I don’t want realism. I want magic! [Mitch laughs] Yes, yes, magic! I try to give that to people. I misrepresent things to them. I don’t tell the truth, I tell what ought to be truth. And if that is sinful, then let me be damned for it! – Don’t turn the light on! (Scene 9).

As Blanche increasingly comes to feel that she cannot handle this world, she retreats deeper and deeper into a world of fantasy, of the imagination. Only there can she be safe. But, try as she might, she cannot fully escape the world nor its lurid, glaring light, the truth that exposes her sordid past for all to see. Blanche is painting herself into a corner, leaving madness as her only refuge, the only available source of comfort and repose.

You know what I shall die of? I shall die of eating an unwashed grape one day out on the ocean. I will die – with my hand in the hand of some nice-looking ship’s doctor, a very young one with a small blond mustache and a big silver watch. […] And I’ll be buried at sea sewn up in a clean white sack and dropped overboard – at noon – in the blaze of summer – and into an ocean as blue as my first lover’s eyes! (Scene 11).

Blanche has effectively given up her struggle with reality. In the face of all her troubles she's retreated completely into a world of fantasy and delusion. There's no going back for Blanche now; but then, she wouldn't want to return to the real world, in any case. It's only in madness that she can find any glimmer of hope. She's safe in her own little fantasy world, and it's a telling indictment of society and how it's treated her that the attractions of insanity are so much greater than those of the so-called real world.

Why must the development of technology must be monitored following WWII?

World War II awakened many people around the world to the destructive potential of technology. This was most famously and tragically illustrated by the destruction wrought by the atomic bombs dropped by the United States on the Japanese cities of Hiroshima and Nagasaki. It was clear, with the development of atomic weapons, that human beings had developed technology capable of wiping out the human race itself.The use of air power more generally had devastated Japan and Germany as well, and Nazi scientists had developed rockets capable of delivering bombs to faraway targets. So this conflict illustrated that sophisticated technology carried terrible dangers.
The new military technology was fostered by cooperation between scientists and the state. Governments spent a great deal of money on developing weapons and other technologies, and this contributed to the rise of what President Dwight Eisenhower would famously call the "military-industrial complex." He meant that governments would spend more and more on weapons, and that there was a risk that the motive for all this spending was industry profits more than national security or the maintenance of peace. Indeed, the rapid buildup of weapons in both the United States and the Soviet Union during the Cold War seemed to confirm his concerns. So the advent of highly destructive and very expensive technologies during World War II posed a major challenge for the human race in the immediate aftermath of the war and beyond.
https://www.history.com/this-day-in-history/eisenhower-warns-of-military-industrial-complex

What was the Aubigny household plantation like prior to Armand's marriage?

Armand Aubigny is lord and master of the L'Abri plantation; he treats his slaves with great harshness and cruelty. At home, he's also a dominant character, controlling his wife in keeping with prevailing gender relations. The brooding, oppressive atmosphere on the plantation is reflected in its physical appearance. Whenever Madame Valmondé arrives at L'Abri, she always shudders at the very sight of it:

The roof came down steep and black like a cowl, reaching out beyond the wide galleries that encircled the yellow stuccoed house. Big, solemn oaks grew close to it, and their thick-leaved, far-reaching branches shadowed it like a pall.

The connotations of death are hard to miss. The tense, overhanging atmosphere is dark and funereal, reflecting the fact that it has been without "the gentle presence of a mistress" for some time. Old Monsieur Aubigny's first wife passed away and is now buried in France; one senses quite strongly that when she died, the plantation died with her. She was the very soul of L'Abri, but since her death, the place has turned into a gigantic mausoleum, savoring of death and decay.

Summary of Frederick Douglass's speech "The Meaning of July Fourth for the Negro."

Douglass gave this speech in 1852, almost a decade before the outbreak of the Civil War and in a period before the Emancipation Proclamation. While Douglass himself was no longer a slave, he was very conscious, as he says at the beginning of the speech, of the great distance between that plantation and the hall in which he was now being granted a platform—and of the difficulties he had faced in moving from one to the other.
He begins the speech by noting that the United States, at seventy six years of age, is still a young nation, in the "impressible" stage of its existence, and suggests a hope that this means it can still be changed. In reference to the Revolutionary War, he describes how "your fathers" "went so far in their excitement as to pronounce the measures of government unjust, unreasonable, and oppressive, and altogether such as ought not to be quietly submitted to. I scarcely need say, fellow-citizens, that my opinion of those measures fully accords with that of your fathers." Throughout the speech, Douglass is sure to maintain this distinction between "us" and "you," reminding his audience that the freedom fought for by "their" fathers has not been passed on equally to Douglass and his people.
"Oppression makes a wise man mad," Douglass says. He reminds the audience that the Revolutionary War was not, at one point in time, universally popular and that the idea of breaking from England "tried men's souls," while today the "sovereignty" of the nation is a source of pride for all. He is indicating that times, and beliefs, change. Those who opposed the revolution, he says, are the same people who have always existed and who hate all kinds of change except "silver, gold and copper change." Today, their opposition is seen as unpatriotic.
Douglass expresses his personal respect for the signers of the Declaration of Independence, describing them as "brave men" and stating that it is natural for "you," the audience, to want to celebrate the rewards now being reaped because of the signers' actions. For a time, Douglass elaborates upon the bravery of those who were driven to revolution and his own admiration of, and understanding of, their reasons. He then states:

We have to do with the past only as we can make it useful to the present and to the future.

At this point, Douglass makes explicit what has been implied in the speech to this point: the fact that the same oppression against which the early Americans fought is still being visited upon blacks in America. He notes, "Sydney Smith tells us that men seldom eulogize the wisdom and virtues of their fathers, but to excuse some folly or wickedness of their own." Douglass reminds his audience of "the disparity between us," and states:

I am not included within the pale of this glorious anniversary! Your high independence only reveals the immeasurable distance between us.

Wondering why he has been called upon to give this speech today, Douglass describes the invitation as tantamount to "inhuman mockery." He has been brought "in fetters" into the "illuminated temple of liberty" and asked to extol its virtues when, in fact, those virtues are not espoused in the behavior of white America towards the black man. The soul of the nation, Douglass states, "never looked blacker to me than on this fourth of July," in the knowledge that the "wail of millions" rises above, and is mocked by, the joy of those celebrating ideals that are actually hypocritical. Americans have already declared, he says, that a man is entitled to his own body and his own liberty; black men have already proved, Douglas says, that they are men. And yet, the one concept somehow does not connect to the other, and the celebration of American liberty and justice is a cruel and inhumane one for as long as that liberty and justice are held away from a significant proportion of the country's inhabitants. Douglass reminds his audience that the American slave trade is alive and well, and extremely prosperous, and that this is conveniently put out of the minds of those who believe America to be a forward-thinking and free nation.
In summarizing his complaints against America's inconsistencies, Douglass also notes that the "gospel" preached in America is itself not free of hypocrisy, such that even atheism would be better than it:

The existence of slavery in this country brands your republicanism as a sham, your humanity as a base pretense, and your Christianity as a lie. It destroys your moral power abroad: it corrupts your politicians at home.

For as long as the USA allows slavery, Douglass says, it will not really be the land of liberty "your fathers" once envisioned, but a sham of itself.

Douglass's purpose in writing and delivering the speech was to illustrate that black people did not have any cause to rejoice in the anniversary of America's independence from Britain when they had not been granted freedom and independence on American soil. To illustrate this point, he offered the following rhetorical questions: 

Fellow-citizens, pardon me, allow me to ask, why am I called upon to speak here to-day? What have I, or those I represent, to do with your national independence? Are the great principles of political freedom and of natural justice, embodied in that Declaration of Independence, extended to us? and am I, therefore, called upon to bring our humble offering to the national altar, and to confess the benefits and express devout gratitude for the blessings resulting from your independence to us? 

In the last statement, there is a tone of both absurdity and irony. In historical context, it was not unusual for white slave owners to believe that slaves should have been grateful to their masters for clothing them, feeding them, and delivering them from a dark, heathen land. Douglass likely may have been alluding to that particular attitude.
Black people, he asserts, have nothing to do with "your independence." That is, those who are slaves cannot take part because they cannot identify with the nation's celebration of liberation.
The tone of speech becomes more indignant. He claims that no nation on earth is guilty of crimes "more shocking and bloody" than the United States. He says its "celebration is a sham" and its "shouts of liberty and equality" are "hollow mockery." Thus, in the speech, he not only ridicules the idea that black people should take part in Fourth of July celebrations, but ridicules white America's participation in the ritual; for they are failing to live up to their own promises and ideals.

Why did Chaucer bring the gods into "The Knight's Tale"?

The action of "The Knight's Tale" is set in Athens and Thebes in ancient Greece. Given the setting, it was perhaps inevitable that the ancient gods would be invoked by Chaucer at some point. But he introduces them mainly to highlight the superiority of Christianity over pagan religion in explaining what happens in the world, especially in relation to love and death.
Here, the gods intervene in human affairs as they often do in Greek mythology. The gods have their champions, and in this tale Mars and Venus squabble over which of the warring knights will prevail. On the face of it, it seems that we're being presented with a pagan worldview, where the gods are all-powerful and everyone just has to accept the fate that the immortals have laid down for us. Theseus, however, is given to us as a kind of proto-Christian, a Christian before his time. He advances the notion of God as a prime mover, a superior being that sets the ball rolling, as it were, creating the entire cosmos as a great chain of love that holds the everything together. So the death of Arcite, like all deaths, is not as the result of some arbitrary act by the gods but part of a divine, orderly plan in which there is a reason for everything and everything has its proper place.

Where is foreshadowing in Leiningen Versus the Ants?

Foreshadowing in the suspense-filled "Leiningen Versus the Ants" comes mainly in the exposition of the story, but there are other incidences of foreshadowing near the middle of the story as the narrative develops.
The exposition of this story immediately reveals the circumstances that threaten Leiningen's coffee plantation. A Brazilian official has made a special trip to warn Leiningen of the aggressive approach of an army of voracious ants capable of destroying vegetation, beasts, and man. "Unless they alter their course, and there's no reason why they should, they'll reach your plantation in two days at the latest," the Brazilian tells Leiningen.
A self-assured Leiningen does not heed the official's warning. He thanks the man for "paddling all this way" to give him "the tip," however, he is not afraid. Leiningen tells the Brazilian that even "saurians" (crocodiles, lizards, and other reptiles) could not drive him out. In great frustration, the official throws up his arms. He shouts at Leiningen, accusing the plantation owner of being insane: "They're not creatures you can fight--they're an elemental--an 'act of God.' Ten miles long, two miles wide--ants, nothing but ants!" Undaunted, Leiningen argues that he can use his intelligence against any foe; besides, he adds, when he built his plantation and farm, he considered all that could happen, so he is ready for "anything and everything." Realizing that his warning is wasted on Leiningen, the official rises from his chair and informs the owner that if he and his workers do not leave the area, he will endanger not only himself but all his four hundred workers.
Leiningen accompanies the Brazilian official to the launch where the boat is moored. As he watches this boat move away, he sees the official waving his arms and still imploring him. As the man's voice grows dimmer, Leiningen hears, "You don't know them, I tell you! You don't know them!"
The official's words are a strong example of foreshadowing in Stephenson's exciting story that has as its central conflict one of Man vs. Nature. This foreshadowing suggests that Leiningen does not realize what he is up against with a mile long army of voracious large ants, as the battle against them will involve much more than he thinks. Later in the narrative, there is more foreshadowing of disaster as Leiningen surveys "twenty square miles of life-destroying ants," and he sees the vast army of ants ruining his plantation: "...that wide vista was being mown as by a giant sickle, leaving only the vast moving shadow."
It is then he realizes that the ants are a true "elemental," and Leiningen "could not free himself from a qualm of malaise...Hadn't his brain for once taken on more than it could manage?" At this point in the narrative, the foreshadowing of Leiningen's anxiety about what can yet occur starts to become a reality with the dangerous action that follows. After his desperate, but successful last attempt to save his plantation, a badly wounded--in some parts of his body so much flesh is eaten that his bones are visible--Leiningen finally realizes the strong significance of the Brazilian official's having called the voracious ants "an elemental."

Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 1

The volume of the solid obtained by rotating the region bounded by the curves y=2 - x/2, y=0, x=1,x=2 , about x axis, can be evaluated using the washer method, such that:
V = int_a^b pi*(f^2(x) - g^2(x))dx
Since the problem provides you the endpoints x=1,x=2, you may find the volume such that:
V = int_1^2 pi*(2 - x/2 - 0)^2 dx
V = pi*int_1^2 (2 - x/2)^2dx
V = pi*int_1^2 (4 - 2x + x^2/4)dx
V = pi*(int_1^2 dx - 2int_1^2 x dx + (1/4)int_1^2 x^2 dx)
V = pi*(x - x^2 + x^3/12)|_1^2
V = pi*(-2 + 2^2 - 2^3/12 - 1 + 1^2 + 1^3/12)
V = pi*(2 - 8/12 + 1/12)
V = (17pi)/12
Hence, evaluating the volume of the solid obtained by rotating the region bounded by the curves y=2 - x/2, y=0, x=1,x=2 , about x axis , using the washer method, yields V = (17pi)/12.

What are the different ranks of coal?

Coal originates from dead plant material. Plants photosynthesize by use of light energy to produce glucose they use as a food source. When these plants die, the decay process is sometimes stopped and the energy is kept within the plant debris. This is known as an organic sediment called "peat." This eventually becomes buried and subjected to pressure underground, facilitating the coalification process.
Coal has several "ranks" and is consecutively transformed from the highest to the lowest.
Lignite: lowest rank, peat transformed into rock, used to fuel generation of electricity
Sub-butiminous: metamorphosed lignite, loss of oxygen and hydrogen yielding more carbon content
Butiminous: metamorphosed sub-butiminous coal, most abundant (50% of coal produced in the US), higher carbon content than sub-butiminous
Anthracite: highest rank, highest carbon content (>87%)
Coal is considered a "nonrenewable resource" because of its difficulty to reproduce. Coal is believed to be abundant in North America, Russia, China, and India to name a few. In terms of contribution to the world's coal supply, China leads with 22% followed by the US (19%), former Soviet Union members (16%), Germany (10%) and Poland (5%).
https://geology.com/rocks/coal.shtml

https://www.encyclopedia.com/earth-and-environment/minerals-mining-and-metallurgy/mineralogy-and-crystallography/coal

Calculus and Its Applications, Chapter 1, 1.7, Section 1.7, Problem 84

Differentiate $s = \sqrt[4]{t^4 + 3t^2 + 8} \cdot 3t$

By using Product Rule and Chain Rule, we get

$
\begin{equation}
\begin{aligned}
s'(t) &= \left( t^4 + 3t^2 + 8 \right)^{\frac{1}{4}} \cdot \frac{d}{dt} (3t) + (3t) \cdot \frac{d}{dt} \left( t^4 + 3t^2 + 8 \right)^{\frac{1}{4}}\\
\\
s'(t) &= \left( t^4 +3t^2 + 8 \right)^{\frac{1}{4}} (3) + 3t \cdot \frac{1}{4} \left( t^4 + 3t^2 + 8 \right)^{\frac{1}{4} - 1} \cdot
\frac{d}{dt} \left( t^4 + 3t^2 + 8 \right)\\
\\
s'(t) &= 3 \left( t^4 +3t^2 + 8 \right)^{\frac{1}{4}} + \frac{3t}{4} \left( t^4 +3t^2 + 8 \right)^{-\frac{3}{4}} (4t^3 + 6t)\\
\\
s'(t) &= 3\left( t^4 +3t^2 + 8 \right)^{\frac{1}{4}} + \frac{3t^4 + \frac{9t^2}{2}}{\left( t^4 +3t^2 + 8 \right)^{\frac{3}{4}}}\\
\\
s'(t) &= \frac{3\left( t^4 +3t^2 + 8 \right) + 3t^4 + \frac{9}{2}t^2 }{\left( t^4 +3t^2 + 8 \right)^{\frac{3}{4}}}\\
\\
s'(t) &= \frac{3t^4 + 9t^2 + 24 + 3t^4 + \frac{9}{2}t^2 }{\left( t^4 +3t^2 + 8 \right)^{\frac{3}{4}}}\\
\\
s'(t) &= \frac{6t^4 + \frac{27}{2}t^2 + 24 }{\left( t^4 +3t^2 + 8 \right)^{\frac{3}{4}}}
\end{aligned}
\end{equation}
$

How can I describe the relationship between Beatrice Hunsdorfer and her daughter Ruth in Paul Zindel's play The Effect of Gamma Rays on Man-in-the-Moon Marigolds?

Beatrice and Ruth have a very problematic relationship. It is easy to see their personalities are similar, and this causes them to clash frequently. They are both outgoing, vain, and very sensitive to what others think about them. Beatrice talks about her younger days and how attractive and popular she was. We learn from Ruth that some people in the community used to refer to her mother as "Betty the loon." When Ruth repeats this in her mother's presence, Beatrice is visibly wounded and upset. It is obvious this gossip causes pain and humiliation for both of them, but Ruth retaliates against her mother's criticism of her by taunting her with this information.
Their relationship is characterized by oversensitivity and hyper-criticism; it is volatile, dysfunctional, and often passionate. Beatrice is protective of Ruth due to her illness, but just as Ruth is ashamed of her mother, there seems to be some embarrassment on the part of Beatrice because of Ruth's ailment. Clearly, the similar personality traits and psychological issues affecting both women are a factor in their relationship. There is also shame connected to Beatrice's husband leaving her years ago, and Ruth's interest in boys is overshadowed by her mother's failed marriage.

How are young people presented by Shakespeare in Romeo and Juliet?

Though Romeo and Juliet are young and impulsive at times, Shakespeare doesn't limit his young characters to being constantly foolish. Instead, both Romeo and Juliet, and their respective cousins, Benvolio and Tybalt, show several different aspects of what it means to be a young person.
Starting with Romeo, Shakespeare shows us the impulsive, head-over-heels romantic love of a teenager who has fallen for someone. And believe it or not, that person isn't Juliet! Romeo starts off the play sighing for Rosaline. It isn't until after the party at the Capulets that he falls for Juliet. His impulsivity is also seen later in Friar Lawrence's cell when he learns he is banished. He acts out of emotion that feels over-the-top, and Friar Lawrence has to correct him and instruct him in behaving more maturely.
Juliet, too, shows some teenage impulsiveness, but once she and Romeo are married, she develops more mature feelings towards him, responding with genuine sorrow when she learns that Tybalt is dead and Romeo is banished, and resolving to take action and defy her father's wishes. She chooses to remain faithful to her new husband, which takes courage and confidence in the face of her father's anger.
The other young men in the play, Mercutio, Tybalt, and Benvolio, show still more sides of adolescence. Mercutio, who is most likely older than Romeo, is young but worldly, with knowledge and experience that he uses to convince Romeo to move on from Rosaline. His death shows that he is still lighthearted and witty, even while acknowledging the seriousness of the feud that has cost him his life.
Tybalt, on the other hand, is not lighthearted--he has fully bought in to the feud in Verona. Whether this shows maturity or singleness of purpose, Tybalt's role in the play grounds all the other young characters by showing that young people are capable of violence. It seems improbable to everyone that Romeo, the romantic dreamer, could challenge Tybalt, but in their final confrontation, Romeo manages to find the will to avenge Mercutio's death.
Benvolio, Romeo's young cousin, is perhaps the wisest of all the young people in the play. It is Benvolio who, full of sorrow, explains the tragic ironies of Romeo and Juliet's deaths to everyone. He is the voice of reason who shows that even young people can demonstrate wisdom beyond their years.
As you can see, Shakespeare doesn't limit young people to being merely foolish, impulsive children. He gives them their own voices and their own story arcs, showing that teens have more inside them than some adults give them credit for!

Although this is a tragedy, Shakespeare must have had fun writing this play. The young people in it, like many adolescents, are emotional, impulsive, and live intensely in whatever moment they happen to be in.
For example, the play opens with Romeo pining away for Rosaline. When his friends persuade him to go with them to the Capulet's masked ball, Romeo attends reluctantly. He can't believe it is possible he could meet any young woman in Verona who could tempt him away from his undying love for Rosaline. However, once he gets to the party, he falls in love with Juliet with breathtaking speed. We never hear of Rosaline again. 
Romeo and Juliet's emotions are so strong they want to get married the next day. Juliet is as impatient for the wedding as Romeo. She can hardly wait to let her nurse get the words out of her mouth about the hasty marriage plans. 
Romeo also acts impulsively when he thinks Juliet is dead, not stopping to find out what might be going on. He immediately kills himself, and Juliet does the same when she finds him dead. While the overarching tragedy is the feud between the two families, the impulsive nature of adolescence also plays a strong role in the death of the young lovers. 

How can we relate Romeo and Juliet to other plays by Shakespeare (Hamlet, Othello, The Tempest, A Midsummer Night's Dream)?

This is an interesting question. Shakespeare's plays are sometimes thematically similar, but the ones you have selected are not unified by any one obvious factor. However, we can certainly draw some points of comparison.
To begin with, Romeo and Juliet is a tragedy centered around a young couple whose love ends in suicide. In this way, it has thematic similarities to Hamlet, in which the love between the young prince and Ophelia ends with Ophelia drowning herself.
In Othello, romance and tragedy go hand and hand. Numerous misunderstandings lead Othello to kill his wife, Desdemona, and then himself. Iago has persuaded Othello that Desdemona has been unfaithful to him, but the audience knows this to be untrue. Likewise, at the end of Romeo and Juliet, Romeo believes Juliet to be dead and kills himself, at which point Juliet then also commits suicide.
A Midsummer Night's Dream is quite dissimilar in tone to Romeo and Juliet—it is a comedy that ends in marriage, rather than death. However, it shares themes of young romance and the common Shakespearean trope of misunderstanding driving the plot. Confusion and misunderstanding is central to this play.

What are some similarities and differences between today's society and the society in Hemingway's The Sun Also Rises?

Despite the long span of years that separates contemporary society from the society of Ernest Hemingway's The Sun Also Rises, the novel is still relevant and contains many similarities to the current cultural climate. The two similarities that I want to focus on are gender roles and technological advancement.
The Sun Also Rises chronicles a time of great social change, especially in terms of gender roles. Published in the middle of the 1920s, the novel arrived at a time when women were gaining greater independence in many countries and challenging traditional gender roles that subordinated women to men. In the novel, one of Hemingway's primary goals is to find a definition for masculinity within the context of rapidly evolving gender roles. This trend has definite similarities to contemporary society; while the United States has come a long way since the 1920s, society still has much progress to make before true gender equality can be realized. Thus, as in Hemingway's time, many individuals, both men and women, are still trying to redefine masculine and feminine roles in society.
Additionally, the society in The Sun Also Rises experienced rapid technological advancement. Cars were becoming more accessible, economies were adapting to increased manufacturing, and the world had just witnessed the atrocities that advanced weaponry had brought on the battlefield in World War I. Likewise, our own society is seeing a glut of technological evolution, with cell phones, social media, and computers taking on roles of greater and greater importance. Just as individuals struggled to make sense of human life in the midst of the increased technological presence during the '20s, so too are members of our own society trying to define what it means to be human in the age of Facebook and iPhones. 
In short, the 1920s were a period of swift advancement in all spheres of life, and society was changing rapidly. As such, it bears many similarities to our own quickly changing society, despite the fact that the book was published nearly 100 years ago. 

What characters best exemplify courage, and what point does Harper Lee want to make about courage through her use of these characters in To Kill a Mockingbird?

Using Atticus Finch's definition of courage-- 

"It's when you know you're licked before you begin, but you begin anyway and you see it through no matter what"--

Mrs. Dubose, of whom Atticus speaks in this quote, is courageous, and, of course, Atticus is also courageous, as well as Boo Radley.
Mrs. Dubose
Jem is assigned to read to Mrs. Dubose after he angrily destroys her camellias because she has insulted his father by saying,

"Your father's no better than the n****rs and trash he works for."

During these visits, Mrs. Dubose lies in a semi-conscious state as Jem reads. But sometimes she utters "blood-curdling inventions." It is not until after her death that Jem learns that Mrs. Dubose has been a morphine addict; however, before she passed away, she bravely decided to die aware of the world in her last moments by withdrawing from this powerful drug. Atticus tells Jem,

"According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew."

Atticus Finch
Knowing that it will certainly be surprising if Tom Robinson is declared innocent of the charges brought against him by Bob and Mayella Ewell, Atticus takes the case and becomes the attorney for the defense in Tom's trial. Atticus is brave because he also knows he is "licked" before he begins, but he begins anyway and "sees it through no matter what."
Atticus takes this brave move as he feels he must. He explains to his daughter Scout that Tom Robinson's case goes to "the essence of a man's conscience." Further, he allows others their opinions, but he says that he must live with himself. For, "[T]he one thing that doesn't abide by majority rule is a person's conscience."And, so, he tells his children to be prepared for vituperation, but not to lash back. Atticus bravely protects Tom at the jailhouse and endures the insults and affronts by many in community before and after the trial. 
Boo Radley
When the reclusive Boo hears the frightened cry of Jem as he is attacked by Bob Ewell, Arthur Radley bravely rushes out of the house which he hardly ever leaves. He rushes Ewell and saves the lives of Jem and Scout by wrestling Bob's knife from him. Without question, he risks his life to save the Finch children.

College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 16

Find the complete solution of the system
$
\left\{
\begin{equation}
\begin{aligned}

x-y =& 3
\\
2x + y =& 6
\\
x - 2y =& 9

\end{aligned}
\end{equation}
\right.
$
using Gauss-Jordan Elimination.

We transform the system into reduced row-echelon form

$\displaystyle \left[
\begin{array}{ccc}
1 & -1 & 3 \\
2 & 1 & 6 \\
1 & -2 & 9
\end{array}
\right]$

$R_2 - 2 R_1 \to R_2$

$\displaystyle \left[
\begin{array}{ccc}
1 & -1 & 3 \\
0 & 3 & 0 \\
1 & -2 & 9
\end{array}
\right]$

$R_3 - R_1 \to R_3$

$\displaystyle \left[
\begin{array}{ccc}
1 & -1 & 3 \\
0 & 3 & 0 \\
0 & -1 & 6
\end{array}
\right]$

$\displaystyle \frac{1}{3} R_2$

$\displaystyle \left[
\begin{array}{ccc}
1 & -1 & 3 \\
0 & 1 & 0 \\
0 & -1 & 6
\end{array}
\right]$

$R_3 + R_2 \to R_3$

$\displaystyle \left[
\begin{array}{ccc}
1 & -1 & 3 \\
0 & 1 & 0 \\
0 & 0 & 6
\end{array}
\right]$

$\displaystyle \frac{1}{6} R_3$

$\displaystyle \left[
\begin{array}{ccc}
1 & -1 & 3 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}
\right]
$

$R_1 - 3 R_3 \to R_1$

$\displaystyle \left[
\begin{array}{ccc}
1 & -1 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]$

$R_1 + R_2 \to R_1$

$\displaystyle \left[
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}
\right]$

This is in reduced row echelon form. If we translate the last row back into equation, we get $0x + 0y = 1$, or $0 = 1$, which is false. This that the system has no solution or it is inconsistent.

What methods and leadership were most effective of the abolitionist movement?

I would argue that John Brown's raid on Harper's Ferry in Virginia was extremely effective in inflaming the sectarian tensions that led to the Civil War. The issue of slavery more than likely would not have been resolved without the war.
Brown led his raid on the night of October 16, 1859 with twenty-two men, six of whom were prominent abolitionists. By the end of the fight that broke out between Brown's "army" and the US Marines who were dispatched to the site, ten of Brown's men were killed, including two of his sons. Brown was later tried for treason and executed. Before his execution, he passed a note to his guard that read, "I, John Brown, am now quite certain that the crimes of this guilty land will never be purged away but with blood."
Brown was no stranger to guerrilla warfare. Earlier in the 1850s, he traveled to Kansas with five of his sons to stop the development of slavery in the new territory. Slavery was permitted in neighboring Missouri and there was a desire to expand it westward. Brown lost another son in the battle now referred to as "Bleeding Kansas."
Brown remains a controversial figure. Some historians laud him as a radical hero, while others suggest that he may have been mentally unstable. However, Brown was raised in a Calvinist family that was strongly against slavery and, after a lifetime of failed business ventures, he believed that he had found his calling to fight for abolition while attending an anti-slavery convention in Cleveland, Ohio in 1837. Brown's Calvinist faith, which includes the notion of predestination—that all events in one's life are willed by God, or fated—may have also influenced his decision to become a radical abolitionist.
Though Brown's act of defiance is one of the most memorable in history, its effectiveness could be the results of both timing—the North and South were strongly divided over the westward expansion of slavery and the Fugitive Slave Act of 1850, which demanded that slaves who escaped to the North be returned to the South—and the fact of Brown's being a white man who had led a raid with other white men. Previous revolts against slavery were insurrections led by slaves. A white man's commitment to die to end an unjust system likely drew more attention and was probably taken more seriously.
The anti-slavery convention at which Brown was moved to radicalize is also important. Anti-slavery conventions, which were held frequently and internationally (London was the site of an anti-slavery convention which included the suffragists Lucretia Mott and Elizabeth Cady Stanton), drew large crowds and included the voices of men and women who had escaped from slavery—particularly Frederick Douglass, who began his career giving speeches about his life story at anti-slavery conventions, leading to the publication of his narrative.
Douglass worked closely with William Lloyd Garrison, the Boston-based publisher of The Liberator, an abolitionist newspaper. Douglass went on to publish his own abolitionist newspaper, The North Star. Abolitionist media was banned in some Southern states. Southern legislatures even attempted to stop the dissemination of anti-slavery newspapers and petitions through the mail. These attempts by Southern legislatures to prevent the dissemination of this literature—the most prominent of which was published by Douglass and Garrison—indicates that media was quite effective in changing some hearts and minds.
https://www.history.com/this-day-in-history/john-browns-raid-on-harpers-ferry

Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 19

Given,
lim_(x->oo) sech(x)
to find the value of lim_(x->oo)sechx
we need to find the value of
lim_(x->-oo) sechx and lim_(x->+oo)sechx
so,
the value of
lim_(x->-oo)sechx is as x tends to negative infinity the sech(x) -> 0
and similarly as
lim_(x->+oo)sechx is as x tends to positive infinity the sech(x) -> 0
So,
lim_(x->-oo)sechx=lim_(x->+oo) sechx=0
the limit exits forlim_(x->oo)sechx
and the value islim_(x->oo)sechx=0

In business, what is the differences between infrastructure and superstructure?

In business, infrastructure refers to underlying components of necessary elements that make business activity possible. Infrastructure is exemplified by such things as roadways and waterways; transportation; telecommunications; waste removal and processing; and power. Some definitions include human resources as part of infrastructure.In contrast, superstructure refers to the overlaying construction of business activity supported by the infrastructure. The difference between the two is that the infrastructure forms the base or foundation of business activity, while the superstructure forms the facilities and operational procedures of business activity.An infrastructure (the base or foundation upholding business activity) is that which of necessity must be gone through to achieve business activity, while a superstructure has optional and alternative route-ways for conducting business activity. As an illustration, business needs the infrastructure components of communications connections in order to communicate with buyers and suppliers. It also needs the infrastructure component of transportation via road-, rail-, air- or waterways in order to deliver goods and receive resources. In the superstructure, a business can optionally employ telephone or Internet communications. Also in the superstructure—when more than one transportation infrastructural component is at hand—a business can optionally employ trucking, railway lines, airfreight or shipping for delivery of goods and receipt of resources.
http://www.businessdictionary.com/definition/infrastructure.html

http://www.businessdictionary.com/definition/superstructure.html

What sustains the Pilgrims during their initial hardships ?

The winter of 1620-1621 was a very disturbing time for the Pilgrims at Plymouth. It can be said that nothing sustained the Pilgrims during this time because a majority of them died from illness during what has been dubbed the "starving time." Pilgrims that survived this winter did so by chance and through their powerful faith in their destiny and their God. In the spring, the natives in the area made contact with the Pilgrims. Having been decimated by a deadly plague themselves, the Native Americans came in peace. One of them, the last surviving member of the Patuxet, was extremely helpful to the survival of the Plymouth Colony. Having been abducted and brought to Spain, Squanto escaped and was hired by an English company, where he learned to speak the language. He returned to the area of New England in 1618. After meeting the Pilgrims, he taught them how to sustain themselves with agriculture (corn) and fishing. He showed them the lay of the land and acted as a mediator between the Europeans and the Indians. Had it not been for the help of Squanto, it is unlikely that the Pilgrims would have survived.
http://www.millsgen.com/gen/hist/pilstor4.htm

In Rumble Fish, what does the river symbolize?

The river could symbolize a couple of things that are closely related. I think the river is symbolic of rebirth and/or freedom.
The Motorcycle Boy uses the term "Rumble Fish" to describe the Siamese fighting fish that he likes from Mr. Dobson's pet store. The Siamese fighting fish have to be kept apart from each other because otherwise they would fight to the death.

They try to kill each other. If you leaned a mirror against the bowl they'd kill themselves trying to fight their own reflection.

The Motorcycle Boy sees similarities between the fish and the gang members that Rusty-James associates himself with. The Motorcycle Boy has tried to distance himself from the gangs and violence. The Motorcycle Boy is also curious if the Siamese fighting fish would act that way in the river.

"Wonder if they'd act that way in the river," the Motorcycle Boy went on.

He eventually steals the fish from the pet store in order to release them into the river. His hope is that their newfound environment and freedom will cause them to change their ways. They are free from captivity by being in the river, so it makes sense that the river is symbolic of freedom. If the new environment does cause them to change their ways, then the fish will have essentially been reborn with a new outlook on life. This is what happened to the Motorcycle Boy when he spent time away from the gang violence in Tulsa.

What is the most meaningful stanza in the poem "Psalm of Life" and why?

The poem's second stanza carries great meaning:

"Life is real! Life is earnest! 
   And the grave is not its goal; 
Dust thou art, to dust returnest, 
   Was not spoken of the soul."

Henry Wadsworth Longfellow's speaker suggests to the reader that simply living out our mortal lives is not fully living out our potential. He asserts that we begin and end as dust, but that our souls aren't concerned with the mechanics of our brief earthly lives. Overall, the poem's message is that great men know that they must take action to achieve immortality. The speaker contends that it is up to us to make our lives "sublime," and that in doing so, we are not only remembered, but also help others when they are feeling abandoned, lonely, and despairing. The poem's overall sentiment is that great men live lives that serve as inspiration to those who come along after them. This stanza speaks directly to the poem's larger theme.

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 33

At what rate is $R$ changing when $R_1 = 80 \Omega$ and $R_2 = 100 \Omega$?
$\displaystyle \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}$

$
\begin{equation}
\begin{aligned}
\text{Given: } \frac{dR_1}{dt} &= 0.30 \frac{\Omega}{s} \\
\\
\frac{dR_1}{dt} &= 0.20 \frac{\Omega}{s}\\
\\

\end{aligned}
\end{equation}
$


Required: $\displaystyle \frac{dR}{dt}$ when $R_1 = 80 \Omega$ and $R_2 = 100 \Omega$



$\displaystyle \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \qquad \Longleftarrow \text{ Equation 1}$
By getting the derivative with respect to time


$
\begin{equation}
\begin{aligned}
\frac{-\frac{dR}{dt}}{R^2} &= \frac{-\frac{dR_1}{dt}}{R_1^2} + \frac{-\frac{dR_2}{dt}}{R_2^2}\\
\\
- \frac{dR}{dt} &= R^2 \left[\frac{-\frac{dR_1}{dt}}{R_1^2} + \frac{-\frac{dR_2}{dt}}{R_2^2} \right]
\end{aligned}
\end{equation}
$


We will use Equation 1 to get the value of $R$

$
\begin{equation}
\begin{aligned}
\frac{1}{R} &= \frac{1}{80}+ \frac{1}{100}\\
\\
R &= \frac{400}{9} \Omega
\end{aligned}
\end{equation}
$


Now, to solve for the required

$
\begin{equation}
\begin{aligned}
-\frac{dR}{dt} &= \left( \frac{400}{9}\right)^2 \left[ \frac{-0.30}{(80)^2} + \frac{-0.20}{(100)^2}\right]
\end{aligned}
\end{equation}\\
\boxed{\displaystyle \frac{dR}{dt} = \frac{107}{810} \frac{\Omega}{s}}
$

What were the fundamental differences in political, social, and economic ideas that separated the American colonies and Great Britain after 1763?

An important social difference between the colonies and Great Britain in the 18th Century involved notions of aristocracy and land ownership. For centuries, most land in Great Britain had been owned and managed by an aristocratic population. They ran this land on the age-old feudal system. There was only a limited amount of land to go around in Great Britain, and this system of dividing its ownership and use was well-established there.
The colonies were less beholden to the notion of class-divisions. It did exist but was much less important. Very few members of the nobility settled in the colonies. They had no reason to since their holdings were back in Great Britain. In North America, there seemed to be a limitless amount of land to be had. It was usually available to anyone willing to manage it. Therefore, the notion of a noble class in control of the land did not apply in the colonies. That is why one of the first things the founders of the United States got rid of was official social distinctions made between aristocracy and peasants.
The colonists also had well-defined notions of their political involvement in local matters. For generations, they were responsible for managing their own politics and laws with little interference from Parliament and the King in London. After the French and Indian War, the English started to change their policy of letting the colonies essentially run themselves. The King and Parliament began to make laws that directly dictated many aspects of colonial life and the colonial economy. They felt that as the imperial power they had the authority to do so. This was not well-received in North America, where the colonists had grown accustomed to their relative independence.

Politically, the colonists after 1763 became more and more committed to the ideas of Enlightenment philosophy, including the concepts that "men" were born with natural rights that were given to them by God and thus "inalienable" (couldn't be legitimately taken away) and that "the consent of the governed" was the basis of government. As the 1770s wended along, the idea of republicanism also gained more and more traction. This had nothing to do with a political party but was the idea that governments could be created from democratic elections in which leaders were chosen by the people. This anti-monarchial theory was in radical opposition to the British, who were wedded to monarchy.
Socially, as more and more Americans were born in the colonies of families that had lived in North America for generations, ties with and feelings of allegiance to Britain began to fade. This, coupled with the immigrants who came from other countries, such as Germany or Holland, weakened the connection between the colonists and Britain.
The economic differences between the colonies and England diverged markedly after 1763 and was a key trigger point in starting the American Revolution. The Americans wanted to be left alone, as had long been the case, to run their economy as they saw fit. This policy, called "salutary neglect" had benefited both the colonies and Britain for many years. Now, however, Britain wanted to recoup some of its expenses from the French and Indian War. The war had been vastly expensive, and the English naturally felt the Americans, who were the chief beneficiaries of it, should help pay. The Americans felt quite differently and balked at anything that looked like an extra tax or anything that might incite more taxes.
In all these areas, the colonists wanted to loosen ties with the British and become as autonomous as possible. The British wanted to strengthen ties, stay in control, and earn money from the colonies. But after the French and Indian war ejected the French, ridding the colonists of a threat of a French takeover, the colonists no longer needed the British.

One key political difference between the two groups would be the concept of representation. The colonists believed that a representative should speak for the people that he represented in a particular district. This is why the cry, "No taxation without representation," was heard so loudly during the Revolutionary period. Parliament, on the other hand, claimed that any member of Parliament could speak for the good of the entire realm. They also claimed that Parliament was not a representative body and that the colonists had no alternative but to pay the taxes as British subjects. This was the argument that ultimately caused the conflict.
A social difference between the two groups would be how each group viewed land. The colonists, who had always had cheap sources of land, viewed open space as a natural right and thought that it was proper for young men to own land for successful farms. Britain, on the other hand, viewed land as something that should mainly be owned by the wealthy. This explains the large estates held by the nobility who owned land but had no intention of farming it themselves. While many Southern planters owned land tended by slaves, many Americans also desired their own plot of land to work.
Another social difference would be the American attachment to religion. During this period and the period immediately before, Americans flocked to churches to hear clergy such as John Edwards deliver fiery sermons. This is not as common in Britain as the Church and and State were entirely locked together.
An economic difference would be the South's reliance on slaves; compared to the British Isles where slavery would become illegal soon after the War of 1812. Another economic difference that is tied to a political difference is how readily Americans took to smuggling. While Britain had Navigation Acts on the books, Americans often would not follow them and there was a comfortable business going on between tax collectors and those paying bribes. Americans thought nothing of trading with the Spanish or French, two of Britain's enemies.

sum_(n=0)^oo 2^n/(n!) Use the Root Test to determine the convergence or divergence of the series.

It is usually easier to use ratio test on these types of series that contain factorials. However, we can also use root test if we rewrite factorial using exponentials. This can be accomplished using Stirling's approximation
n! approx sqrt(2pi n)(n/e)^n
The reason why we can use this approximation is because it becomes more precise for greater values of n, in fact the ratio of the left and right hand side of the approximation converges to 1 as n tends to infinity.
lim_(n to infty)root(n)(2^n/n!) =lim_(n to infty) root(n)(2^n/(sqrt(2pi n)(n/e)^n))=lim_(n to infty)2/(root(n)(sqrt(2pi n))n/e)=
In order to calculate lim_(n to infty) root(n)(sqrt(2pi n)) we need to use the following two facts:
lim_(n to infty) root(n)(c)=1, c in RR and lim_(n to infty)root(n)(n^p)=1, p in RR.
                                                                                                                    Applying this to our limit yields
lim_(n to infty)2/(root(n)(sqrt(2pi n))n/e)=lim_(n to infty)2/(n/e)=lim_(n to infty)(2e)/n=(2e)/infty=0
Since the value of the limit is less than 1, the series is convergent. 
https://en.wikipedia.org/wiki/Root_test

https://en.wikipedia.org/wiki/Stirling%27s_approximation

What country did Daniel's family live in, and how long had they lived there?

The story begins with Daniel’s family in Frankfurt, Germany, in 1933. Eight years later, Daniel’s family is caught in the holocaust, and the family is deported to a Jewish ghetto in Poland. The family is transferred to a concentration camp, Auschwitz, in August 1944. On arrival, the men are separated from the women. Daniel and his father stay in Auschwitz until December 1944, when they are transferred to another camp, Buchenwald. The horrors of the holocaust are etched in Daniel’s mind, and, like many prisoners, he even questions his own faith. The crimes committed were of an extreme nature and included the murder of babies. Daniel and his father stay at Buchenwald until the end of the war, after which Daniel and a friend embark on a mission to find their friends and family.
Daniel's family lived in Frankfurt, Germany for eight years before being deported to Lodz in Poland.

What is the theme of "The Story of an Hour"?

"The Story of an Hour" is specifically about the ways in which marriage constrained nineteenth-century women from living life as they wished. Marriage was not an equal partnership but an arrangement in which, more often than not, the man was the one in charge.
The most obvious way to show this would have been to make Louise's husband out to be a tyrannical ogre figure, but Chopin is much more clever and realistic in her treatment of him. He is described as pretty normal and a decent fellow who never intended to hurt his wife. He simply assumes, as all of society did in the Victorian era, that women are meant to serve men within a marriage and have no life of their own outside the domestic sphere. Even Louise has some affection for him, which Chopin wryly alludes to: "She did love him. Sometimes." However, this is not enough for Louise, and Chopin seems to suggest it should not be for women in general.
Louise has no identity aside from "wife" until she believes her husband has been killed. With him no longer there, she realizes she can do whatever she wishes without having to run all her plans by a husband. She starts to feel an intense connection with the natural world outside her window, examining the birds in particular, evoking the notion that Louise is a bird about to be free of its cage.
Chopin hammers in the idea of marriage as existential imprisonment for women by having the story end with Louise realizing her husband survived the accident and subsequently dying from shock. Now that Louise has known true joy, having it revoked so suddenly not only triggers her heart trouble, it spiritually destroys her.

One of the themes in “The Story of an Hour” by Kate Chopin is freedom. The news of the sudden death of her husband, Brently Mallard, is given to Mrs. Mallard as gently as is possible by her sister Josephine and her husband's friend, Richards. The information is delivered in this manner because Mrs. Mallard is known to have a heart condition that is sensitive to shocking news. On receiving the news, Mrs. Mallard weeps. She is grief-stricken.
Later, after calming down a little, she retires to her room. It is while sitting in her room that she realizes the freedom that the death of her husband would bring her way. The thought possesses her so much that the words “free, free, free” escape her lips. She is excited by the thought of the new independence she will have, for with these thoughts, “her pulses beat fast, and the coursing blood warms and relaxes every inch of her body.”
She understands that her joy for her newfound freedom and independence does not mean that she hated her husband. What she hated was to live a life in which her will was constantly bent by another person. She would, from then on, live for herself. She is thrilled by the power that lies in being in control of one’s life without the interference of a spouse. She thinks of the many springs and summers yet to come that she would enjoy alone, doing whatever she wanted to do. When Brently walks into the house at the end of the story, he unknowingly tears this freedom from his wife.