What particular event took place that made Nelson Mandela want things to be different?

One event that motivated Nelson Mandela to turn to more radical means of changing South Africa during Apartheid was the Sharpeville Massacre of 1960. At this point, Mandela was already a long-time member of the ANC, or African National Congress, formed to fight against Apartheid, and he had been arrested in 1956 and tried (but acquitted) on the charge of treason.
In the Sharpeville Massacre, the police fired on protestors who were peacefully demonstrating against pass laws, and 69 people were killed. In the aftermath of the event, the country was convulsed by riots and unrest. The Sharpeville Massacre had motivated him to turn to new means of creating change. In 1961, Mandela became the founder and leader of Umkhonto we Sizwe (Spear of the Nation), a paramilitary wing of the ANC. In 1962, Mandela was jailed for 5 years for instigating a workers' strike, and the following year, he was arrested in the so-called Rivonia Trial for threatening to overthrow the government. Sentenced to life in prison in 1964, he served 27 years before his release. He went on to serve as President of South Africa. 

One of the primary events that occurred that made Nelson Mandela want things to be different was the white only election in 1948, in which the National Party won on the platform of apartheid. Another important moment came in 1950, with the violent government reaction to the joint strike called by the ANC, the Communist Party, and the South African Indian Congress to protest the ban of the Communist Party.
By the time of the election, Mandela was already involved with the African National Congress (ANC).  After the election, Mandela (along with other leaders such as Oliver Tambo and Walter Sisulu) began to lobby the ANC to protest militarily against the multitude of new laws enacted by the Nationalists.
In the bloody aftermath of the government crackdown against the so-called May Day strike, Mandela made the decision that freedom could only occur with a broad based alliance against apartheid.  The Africanist wing of the ANC disagreed, but Mandela held his ground and helped form the Congressional Alliance.
In 1952, the Congressional Alliance launched its Defiance Campaign.  While the campaign did not stop apartheid, it did solidify the ANC as a formidable force against white minority rule.
Source: South African History Online

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 38

Determine an equation of the line that satisfies the condition "through $(-1,6)$; slope $\displaystyle - \frac{5}{6}$".

(a) Write the equation in standard form.

Use the Point Slope Form of the equation of a line with $(x_1,y_1) = (-1,6)$ and $m = \displaystyle - \frac{5}{6}$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&& \text{Point Slope Form}
\\
\\
y - 6 =& - \frac{5}{6} [x - (-1)]
&& \text{Substitute $x = -1, y = 6$ and } m = - \frac{5}{6}
\\
\\
y - 6 =& - \frac{5}{6}x - \frac{5}{6}
&& \text{Distributive Property}
\\
\\
6y - 36 =& -5x - 5
&& \text{Multiply each side by $6$}
\\
\\
5x + 6y =& -5 + 36
&& \text{Add each side by $(5x + 36)$}
\\
\\
5x + 6y =& 31
&& \text{Standard Form}

\end{aligned}
\end{equation}
$



(b) Write the equation in slope-intercept form.


$
\begin{equation}
\begin{aligned}

5x + 6y =& 31
&& \text{Standard Form}
\\
\\
6y =& -5x + 31
&& \text{Subtract each side by $5x$}
\\
\\
y =& - \frac{5}{6}x + \frac{31}{6}
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$

How did the printing press impact the Protestant Reformation?

It is safe to say that the printing press, embodied by the use of Gutenberg's inventional genius in the 16th century, was the primary reason that the Protestant Reformation was able to come to life and spread as rapidly as it did. While the ideas of reformation leaders such as Martin Luther, John Calvin, etc. were, in themselves radical enough to acquire popularity on their own, the printing press provided a more reasonable method for these ideas to be passed on to other people - particularly in the common language of the day. This is what led to the transmission of Luther's ideas at such a rapid pace. Because of this, before the Catholic Church could quell the heresies (according to Rome) that Luther was teaching, hundreds of copies of his beliefs had been printed. 
For example, Bibles at the time of the Reformation were usually copied by the hands of  monks and were not available in German (the common language of Luther's region). Because Bibles were in Latin and were incredibly time-consuming and expensive to produce, the prospect of a Bible in German was vehemently opposed by the Catholic Church yet because of the printing press, German translations of the Bible were able to be produced at an alarming rate to the Catholic Church. This led many in Germany to read, or at least hear the direct words of the Bible themselves, rather than hearing it interpreted from Latin by their priest. 
Thus, without the printing press, the Protestant Reformation may never have occurred. 
 

I'll start by providing a bit of context about the printing press to better answer your question. The printing press was a groundbreaking invention created by Johann Gutenberg in 1488. Before this invention, it was extremely difficult to produce books and other publications in mass quantities and at an affordable price, therefore most people did not have easy access to printed material. 
With this new technology, books and other printed materials were able to be mass produced for the first time and at an affordable cost, resulting in the spread of ideas throughout much of Europe. The Bible, for example, was able to be disseminated throughout society, and even translated into different languages. The printing press acted as a catalyst for access to printed materials, educating people, and intellectual conversations about religion and other happenings. 
During this time, people looked to the Catholic Church for most of their information and the Church often used censorship to maintain their power. With the invention of the printing press, however, people of the Protestant faith, most notably Martin Luther, were able to dissent from the Catholic Church by producing large quantities of informational pamphlets to spread throughout Europe.

The growth of the printing press was an absolutely crucial factor in the rise, and subsequent development, of the Protestant Reformation. For one thing, Protestantism is a denomination of a book—the book in question being, of course, the Bible. The printing press allowed new Bibles to be published more rapidly, leading to their wider dissemination in society.
Bibles could also be printed in native languages, or the vernacular, which made the Christian message more easily understood. Previously, Bibles were only available in Greek or Latin, and as such unavailable to the vast majority of Europe's literate population. Even then, their use was restricted by the Catholic Church, which didn't want its position as an intermediary between God and man to be undermined by individual believers' own interpretations of Scripture.
The printing press also allowed the extensive spread of pamphlets, books, and religious treatises written from the Protestant point of view. Many of these publications were highly polemical, as they conveyed their message in an often crude, unsophisticated style that was nonetheless easily comprehended by large swathes of the population. Luther was particularly adept at writing in such a style, combining the Protestant message with scathing criticism and abuse of his opponents.

What's the impact of literature on journalism?

The impact of literature on journalism is most keenly felt by the development of New Journalism. New Journalism developed in the 1960s and was made famous first by Truman Capote who employed narration more often associated with fiction in his "non-fiction novel," as he called it, In Cold Blood. Tom Wolfe's book, The Electric Kool-Aid Acid Test, is another example of New Journalism, as are many of Joan Didion's essays on politics and popular culture in the 1960s.
While traditional journalism focuses solely on the facts of an event or a person of interest to maintain a distant, objective stance, New Journalism allows the writer's personal views and perceptions into the text. The writer of the piece is often a character, or participant, in the story's events. This is most evident in Gay Talese's work The Voyeur's Motel.
New Journalism focuses on character development and is more descriptive than a traditional article. Voices come alive through sustained dialogue. As opposed to merely reporting what someone says, a New Journalist will describe the context in which the quote was said and the mood of the speaker.
These days, this style of writing is particularly evident in magazines, such as The New Yorker and Harper's.
The main impact is that of a more elastic idea of the truth. Is the truth only the facts, or does it also include how those facts are expressed? Does personal narrative diminish the validity of a journalistic piece or enhance it?
https://www.britannica.com/topic/New-Journalism

Calculus and Its Applications, Chapter 1, 1.8, Section 1.8, Problem 30

Determine the $y'$ of the function $\displaystyle y = 3x^{\frac{4}{3}} - x^{\frac{1}{2}}$
By using Chain Rule,

$
\begin{equation}
\begin{aligned}
y' &= \frac{d}{dx} \left( 3x^{\frac{4}{3}} - x^{\frac{1}{2}} \right)\\
\\
y' &= 3 \cdot \frac{d}{dx} \left( x^{\frac{4}{3}} \right) - \frac{d}{dx} \left( x^{\frac{1}{2}} \right)\\
\\
y' &= 3 \cdot \frac{4}{3} \left( x^{\frac{4}{3} - 1} \right) - \frac{1}{2} x^{\frac{1}{2} - 1}\\
\\
y' &= 4x^{\frac{1}{3}} - \frac{1}{2} x^{-\frac{1}{2}} \text{ or } 4x^{\frac{1}{3}} - \frac{1}{2x^{\frac{1}{2}}}
\end{aligned}
\end{equation}
$


Then,

$
\begin{equation}
\begin{aligned}
y'' &= \frac{d}{dx} \left[ 4x^{\frac{1}{3}} - \frac{1}{2} x^{- \frac{1}{2}} \right]\\
\\
y'' &= 4 \cdot \frac{d}{dx} \left( x^{\frac{1}{3}} \right) - \frac{1}{2} \cdot \frac{d}{dx} \left( x^{-\frac{1}{2}} \right)\\
\\
y'' &= 4 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} - \frac{1}{2} \cdot \left( - \frac{1}{2} \right) x^{-\frac{1}{2} - 1}\\
\\
y'' &= \frac{4}{3} x^{-\frac{2}{3}} + \frac{1}{4} x^{-\frac{3}{2}} \text{ or } \frac{4}{3x^{\frac{2}{3}}} + \frac{1}{4x^{\frac{3}{2}}}
\end{aligned}
\end{equation}
$

Compare and contrast Mildred and Clarisse. Can either character survive in their society? What roles do they play in their society? How did their personalities develop?

Clarisse is Montag's affable neighbor who enjoys nature, conversations, and leisure time with her family. Clarisse's positive attitude and love for life make Montag aware of his own meaningless existence. Clarisse is scrutinized by her teachers and essentially shunned by society because she is vibrant and acts differently than her peers. Clarisse inherits her lively, curious personality from her family. They are loving, intelligent people who raised a charismatic daughter.
Mildred is Clarisse's foil throughout the novel. Mildred is shallow, callous, and insensitive. She constantly watches the parlor televisions and listens to her Seashell radios to escape from reality. Mildred is unaware of her meaningless existence and is content living a superficial, unexamined life. Mildred's personality has been shaped by the authoritarian government that promotes constant entertainment and violence.
Clarisse does not fit into the dystopian society and is viewed as an outcast, while Mildred is the typical, ignorant citizen who passively accepts the authoritarian agenda. In my opinion, neither character can survive in the dystopian society. Clarisse will eventually be arrested by the government or killed by a savage citizen. Although Mildred might live longer, she will probably die of an overdose. Interestingly, both characters do not survive in the story.

How does Shakespeare present Mark Anthony in act 3 scene 1?

Antony is portrayed as cunning and clever but also as loyal to Caesar. The first scene of act 3 is when Caesar is assassinated by the conspirators, who then learn that Antony has "fled to his house, amazed" at Caesar's death. Brutus then receives Antony's servant, who comes from his master seeking assurance that the conspirators don't want him dead as well. Once he receives this assurance, he arrives and is so overcome with grief at seeing Caesar's corpse that he actually suggests that Brutus should go ahead and kill him as well. Antony shakes hands with each of the conspirators and says, despite being clearly distraught, that he will support them, and he asks to speak to the crowd assembled outside.
It is at this point that we see Antony's plans. He will not actually support Brutus and Cassius but will conspire against them. In a soliloquy he reveals that he plans to foment a civil war in Rome with the support of Octavian. But he pragmatically determines to gauge the reaction of the Roman crowd to the eulogy he is about to give for Caesar. He will exploit Brutus's decision to allow him to speak to stir up the Roman crowd to avenge Caesar's death.

Newton's laws of motion

Isaac Newton's three laws of motion describe the relationship that exists between an object, the forces that are acting on an object, and the object's motion in response to those forces.
Newton's first law of motion states that an object at rest remains at rest and an object in motion remains in motion at constant speed in a straight line unless acted upon by an unbalanced force. This law is sometimes called the law of inertia. If you break this law apart a little bit, you can see that there are two parts to the law. The first part of the law is the "objects at rest" part. An object at rest is not moving relative to whatever point of reference happens to be in use. The stationary object will remain that way unless an unbalanced force does something to the object. The second part of the law is very similar to the first part except that it deals with moving objects. It says that an object will forever move at a constant velocity unless an unbalanced force is applied that causes the object to speed up, slow down, or turn. This is probably the most difficult part of Newton's laws of motion to explain to students, because they always imagine objects on Earth. Students are familiar with thrown baseballs and fired bullets slowing down and dropping. Friction and gravity are the unbalanced forces in this situation. If those forces were not present, that thrown baseball would move at the initial velocity forever.
Newton's second law of motion states that the acceleration of an object depends on the mass of the object and the amount of force applied. In other words, an object will accelerate faster if you push it harder. If you cannot push it harder, you can accelerate the object faster by reducing the mass. Acceleration and force are a direct proportion. Acceleration increases as force increases. However, acceleration and mass are an inverse proportion. Acceleration increases as mass decreases. Newton's second law can be written mathematically. Acceleration = Force/Mass. Sometimes, the law is written to highlight force. Force = mass x acceleration.
Newton's third law of motion states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. This law is often reworded to say that every action has an equal and opposite reaction. I want to make it clear that the two forces involved do not act on the same object. When a person kicks a soccer ball, they apply a force to the ball. The ball then applies a force that is equal in size but in the opposite direction to the foot kicking the ball. Guns and bullet mechanics work well to explain this. When the gun is fired, the force of the powder charge propels the bullet forward, but an equal and opposite force is applied to the gun. This is why guns recoil. However, the recoil of the gun is not the same speed as the bullet. This is because of Newton's second law. The gun is much bigger than the bullet; therefore, the bullet has a large acceleration from that force due to the low mass of the bullet. Conversely, the gun's much larger mass prevents it from accelerating at the same rate that the bullet accelerated.
http://www.pas.rochester.edu/~blackman/ast104/newton3laws16.html

What are five legacies of Puritanism that influence us in 2018?

Many aspects of the Puritan worldview affect us today. I will answer this question from an American perspective, since it is in this country that Puritanism remains most influential.
The first is directly related to the idea of American exceptionalism. The puritan John Winthrop, in an address to the early settlers at Massachusetts Bay, exhorted them to be as a "city on a hill." He meant that the nature of their religious experiment made them different, but this idea has made its way into American politics and culture. Many politicians, ranging across the spectrum from Ronald Reagan to Barack Obama, have repeated the claim that the United States is a divinely-chosen nation that serves as an example to the rest of the world.
Another political aspect of Puritanism, at least as it was established here in North America, that remains today is the concept of participatory government. Puritan towns featured a "town meeting" in which the people (i.e., church members) made important decisions that affected everyone. These included naming ministers, constructing town buildings, and so on. Many American towns still have this form of government, and the idea of civic engagement still permeates American political culture.
Long ago, a sociologist named Max Weber identified a "Protestant [by which he basically meant Calvinist or Puritan] work ethic." This was the idea that a person could glorify God through his work and that making money was not inherently sinful. This encouraged people to work hard and to invest their money in smart ways. American culture continues to celebrate work for the sake of financial gain, and, in many ways, associates work with religious virtue. In no other country are religion (especially Protestantism) and economic philosophy (i.e., capitalism) so intertwined.
Another way in which Puritanism remains influential is in its links between sexual behavior and morality. While Puritans were never as prudish as portrayed in popular memory, they certainly placed an emphasis on sexual behavior as a marker for one's virtue. This was especially true of female sexual behavior. While sex is very prominent in American popular culture, it is indisputable that modern mainstream evangelicals place a heavy emphasis on sexual behavior, especially outside of marriage.
Finally, as the above answers have suggested, the ideas of Puritanism, especially the concept of a "fallen" world in which people were in need of God's mercy and grace, are fundamental to many branches of modern evangelical Christianity. Evangelicalism remains a powerful cultural, political, and religious force in American society, with many Puritan values at its heart.
https://www.nytimes.com/2012/08/05/opinion/sunday/are-americans-still-puritan.html

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 9

Integral test is applicable if f is positive, continuous and decreasing function on infinite interval [k,oo) where k>=1 and f(n)=a_n . Then the series sum_(n=k)^ooa_n converges or diverges if and only if the improper integral int_k^oof(x)dx converges or diverges.
Given series is ln2/2+ln3/3+ln4/4+ln5/5+ln6/6+........
The series can be written as sum_(n=1)^ooln(n+1)/(n+1)
Consider f(x)=ln(x+1)/(x+1)
Refer the attached graph for f(x),
From the graph, we observe that the function is positive, continuous and decreasing for x>=2
We can also determine whether f(x) is decreasing by finding the derivative f'(x), such that f'(x)<0 for x>1
Since the function satisfies the conditions for the integral test , we can apply the same.
Now let's determine the convergence or divergence of the integral int_1^ooln(x+1)/(x+1)dx
int_1^ooln(x+1)/(x+1)dx=lim_(b->oo)int_1^bln(x+1)/(x+1)dx
Let's first evaluate the indefinite integral,intln(x+1)/(x+1)dx
Apply integral substitution:u=ln(x+1)
=>du=1/(x+1)dx
intln(x+1)/(x+1)dx=intudu
=u^2/2+C , where C is a constant
Substitute back u=ln(x+1)
=1/2[ln(x+1)]^2+C
lim_(b->oo)int_1^ooln(x+1)/(x+1)dx=lim_(b->oo)[1/2(ln(x+1))^2]_1^oo
=lim_(b->oo)[1/2(ln(b+1))^2]-[1/2(ln(2))^2]
lim_(x->oo)(x+1)=oo
lim_(u->oo)ln(u)=oo
=1/2oo^2-1/2(ln(2))^2
=oo-1/2(ln(2))^2
=oo
Since the integral int_1^ooln(x+1)/(x+1)dx diverges, so the given series also diverges as per the integral test.

Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 40

Determine the slope and $y$-intercept of the line $\displaystyle \frac{-3}{4}x + \frac{1}{2}y = 0$. Graph the line, labeling any intercepts.

We write the equation $\displaystyle \frac{-3}{4}x + \frac{1}{2}y = 0$ in slope intercept form to find the slope. We get


$
\begin{equation}
\begin{aligned}

\frac{-3}{4}x + \frac{1}{2}y =& 0
&& \text{Given equation}
\\
\\
\frac{1}{2}y =& \frac{3}{4}x
&& \text{Add } \frac{3}{4}x
\\
\\
y =& \frac{3}{2}x
&& \text{Multiply both sides by } 2

\end{aligned}
\end{equation}
$



The slope is $\displaystyle \frac{3}{2}$. To find the $y$-intercept, we let $x = 0$ and solve for $y$. So we have


$
\begin{equation}
\begin{aligned}

y =& \frac{3}{2} (0)
\qquad x = 0
\\
y =& 0

\end{aligned}
\end{equation}
$


The $y$-intercept is .

Is Dickon's upbringing different than that of Mary and Colin? If yes, how?

Certainly--Dickon is a boy from the working class. His sister, Martha, is a maid at the manor, and Dickon has been brought up in the dales among the animals. He lives in a small cottage with his family, and they have never had very much money. Additionally, he has never been properly educated. Dickon can expect to go into a far different life as an adult than Colin.
It is worth noting, however, that Mary's upbringing is also different to Colin's. While they are both of the middle class, Mary spent her early childhood in India with distant parents. She was mostly looked after by her Indian governess. This has led her to behave as if she is of a far more aristocratic class than she actually is, having been treated as such by her Indian servants. The family of a diplomat would not have been able to live so lavishly in England. Meanwhile, Colin has lived a strangely segregated existence in a house in which there is money, though little sign of it being spent recently. His father is often away, and Colin has always been taught that he is going to die. As such, he has had a rather sad life, despite the fact that he comes from a higher social class than Dickon and has spent little time with other children.

College Algebra, Chapter 3, 3.7, Section 3.7, Problem 78

The amount of a commodity that is sold is called the demand for the commodity. The equation $D(p) = -3p + 150$ represents the demand for a certain commodity as a function of price.

a.) Find $D^{-1}$. What does $D^{-1}$ represent?

b.) Find $D^{-1} (30)$. What does it represent?

a.) To find $D^{-1}$, we set $y = D(p)$.


$
\begin{equation}
\begin{aligned}

y =& - 3p + 150
&& \text{Solve for $t$; add $3p$ and subtract $y$}
\\
\\
3p =& 150 - y
&& \text{Divide by } 3
\\
\\
p =& \frac{150 - y}{3}
&& \text{Simplify}
\\
\\
p =& 50- \frac{y}{3}
&& \text{Interchange $y$ and $p$}
\\
\\
y =& 50 - \frac{p}{3}
&&

\end{aligned}
\end{equation}
$


Thus, the inverse of $D(p)$ is $\displaystyle D^{-1} (p) = 50 - \frac{p}{3}$.

If $D(p)$ represents the amount of commodity sold, then $D^{-1} (p)$ represents the amount of commodity that has been unsold.

b.)


$
\begin{equation}
\begin{aligned}

D^{-1} (30) =& 50 - \frac{30}{3}
\\
\\
=& 50 - 10
\\
\\
=& 40

\end{aligned}
\end{equation}
$


$D^{-1} (30)$ means that there are 40 items unsold at the price of 30.

Why might you conclude that Macbeth's character is not all bad?

At the beginning of the play, Macbeth is presented as an honorable, courageous soldier, who valiantly fights for King Duncan. Only after meeting with the Three Witches does Macbeth's ambitious nature begin to develop. Despite his ambitious feelings, Macbeth is still a loyal soldier and is ashamed to admit his thoughts about murdering the king. Macbeth recognizes that his violent thoughts are terrible and treacherous. After Macbeth initially refuses to harm King Duncan, it is Lady Macbeth who coerces her husband into committing regicide. Immediately after killing the king, Macbeth displays his guilt and feels sorry for his actions. As the play progresses, Macbeth's ambitious nature becomes unhinged; he orders the death of Banquo and Macduff's family. Despite his tyrannical nature, Macbeth's hallucinations are a result of his guilty conscience. Another significant argument that can be made is that Macbeth is a victim of fate. The Three Witches' prophecies came true, and one cannot help but think that Macbeth's actions were unavoidable. One can argue that Macbeth was manipulated by both the witches and his wife throughout the play, which is the reason audiences can sympathize with his character.

How would you compare and contrast the characters of Roger and Mrs. Jones in the short story "Thank You, M'am"?

Both Mrs. Jones and Roger are denizens of Harlem and, as such, have shared some of the same experiences. However, Mrs. Jones is an adult who has profited from her experiences and is now wiser than the young Roger.
After she resists his attempts to steal her purse and captures him, Mrs. Jones tells Roger to pick up her purse, then asks him, “Now ain’t you ashamed of yourself?" He replies that he is, although it may be out of fear that he answers. Nevertheless, from his next responses to Mrs. Luella Bates Washington Jones it becomes apparent that Roger learns to respect this woman. Then, after she takes him home and feeds him, Roger certainly acquires gratitude for her kindness to him.
Here, then, are some comparisons and contrasts between the two characters:
--Comparisons
Both are from the inner city and have not lived a comfortable, stable life.
Both have done things that are illegal.

“I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know," Mrs. Jones reveals to Roger.

Both have learned respect for others. Mrs. Jones tells Roger, “You ought to be my son. I would teach you right from wrong." Only later on does Roger speak very respectfully, and he makes sure that she knows he is not looking at her purse nor is he near it.
Both demonstrate concern for the welfare of others. Mrs. Jones takes Roger home; Roger tries to be helpful.
--Contrasts
Mrs. Jones is a trustworthy, hard-working, and compassionate woman. However, Roger has no consideration for her when he tries to steal her purse; instead, he merely pursues his selfish desire for a pair of shoes. Whereas Mrs. Jones no longer believes in breaking the law, Roger defies it.
Early in the narrative, Mrs. Jones treats Roger kindly, offering to take him home and wash his face [which implies more than is said]. On the other hand, Roger selfishly preys on her, and after he is stopped, he simply wants to get away.
Mrs. Jones displays a respect for Roger as a person early on; later, she offers to feed him and directs him to wash his face and clean up before eating while he is in her rooms. Roger's respect is merely given out of fear at first. But, after learning to respect Mrs. Jones, he is concerned about her, offering to run errands:

“Do you need somebody to go to the store,” asked the boy, “maybe to get some milk or something?"Also, Roger even thanks her as he departs.

Roger only learns from his experience with Mrs. Jones to respect people; Mrs. Jones already displays sympathy for others.
Where she lives, Mrs. Jones has people with whom she can interact. Alone at home at night, Roger is deprived of parental attention and guidance.
 

How did Alexander the Great unify his empire?

Alexander the Great conquered vast stretches of territory. He conquered nearly 3,000 miles in a matter of thirteen years. Unlike other conquered empires, the empire of Alexander the Great was unique in that its conquered residents were relatively united. Alexander the Great was able to accomplish this unity by employing several strategies.
1. He did not want his subjects to think he was trying to exploit them. So instead of destroying local languages, religions, and customs, Alexander preserved local cultures in the areas he conquered.
2. He allowed Persians to serve as administrators in his new empire. This strategy incorporated locals into the decision-making process, enabling them to take part in government.
3. In keeping with his theme of respecting local cultures, he married Eastern women. His wife Roxana was Persian.
These are a few strategies Alexander employed to unite his vast empire despite its size and variety of cultures.

Comment on the narrator's description of camping out.

The narrator's description of camping out is hilarious. It is all the more hilarious if you have ever actually "camped out." The reason that his several-paragraph description of camping out is hilarious is because it is the standard, stereotypical vision of what camping out should be like. People always imagine that camping out, and "getting back to nature," is a wonderfully harmonious experience in which relaxation is the main attraction and all of nature bows down to you, the human, in an effort to make sure that everything is perfect. The narrator explains a scene in which the stream is utterly peaceful and the birds cheerfully chirp at volumes low enough for gentle conversation to occur. The food is easily made and easily cleaned up. The moon lovingly kisses and embraces the scene, and the men peacefully put out their pipes and fall asleep quickly and gently.

Then we run our little boat into some quiet nook, and the tent is pitched, and the frugal supper cooked and eaten. Then the big pipes are filled and lighted, and the pleasant chat goes round in musical undertone; while, in the pauses of our talk, the river, playing round the boat, prattles strange old tales and secrets, sings low the old child’s song that it has sung so many thousand years—will sing so many thousand years to come, before its voice grows harsh and old—a song that we, who have learnt to love its changing face, who have so often nestled on its yielding bosom, think, somehow, we understand, though we could not tell you in mere words the story that we listen to.

Camping, according to the narrator, is a gloriously wonderful endeavor, and that is what makes it hilarious for experienced campers. Anecdotally, I like camping; however, it is never as wonderful as the narrator describes. Sleeping on the ground is not as nice as sleeping in my bed. Tents can easily be far too hot or cold to sleep comfortably in. Nature loves it when I camp because the bugs seem to want to embrace me and my dinner. I always imagine camping will be just as the narrator describes it, and that is probably why I keep camping.

What effect does religion have on the character Dolly Winthrop in Silas Marner?

Dolly Winthrop is one of the few genuinely decent people in Raveloe. She's certainly one of the only people in the village to accept Silas Marner for who and what he is. At the same time, unlike Silas, she is possessed of a conventional Christian piety, one that manifests itself in kindness, care, and concern. Her faith is simple and unreflective, largely conditioned by her environment and upbringing. For instance, it's telling that when Dolly brings Silas some lardy cakes, she doesn't understand that the special letters on them—I.H.S—are the first three letters of Jesus in Greek. Dolly's Christianity is the kind common to unlettered country folk in her neck of the woods, simple and unaffected.
Dolly is no fanatical proselytizer, but she does gently insist on Silas attending church and giving up weaving on Sundays. She also strongly advises him that little Eppie should be baptized and given Christian instruction. The formalities of Christianity are clearly very important to Dolly, and due proprieties must be maintained lest Silas feel guilty if the child ever goes off the rails. Religion is of the utmost importance to Dolly, influencing everything she does. It's what enables her to be such a kind, patient advisor and confidante to Silas, and what eventually makes him realize that he can start to trust people at long last.

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 3

Determine the $\lim\limits_{x \rightarrow -2} (3x^4+2x^2-x+1)$ and justify each step by indicating the appropriate limit law(s).


$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow -2} (3x^4+2x^2-x+1) &= \lim\limits_{x \rightarrow -2} 3x^4 +
\lim\limits_{x \rightarrow -2} 2x^2 -
\lim\limits_{x \rightarrow -2} x +
\lim\limits_{x \rightarrow -2} 1
&& \text{(Sum and difference Law)}\\
\lim\limits_{x \rightarrow -2} (3x^4+2x^2-x+1) &= 3\lim\limits_{x \rightarrow -2} x^4 +
2\lim\limits_{x \rightarrow -2} x^2 -
\lim\limits_{x \rightarrow -2} x +
\lim\limits_{x \rightarrow -2} 1
&& \text{(Constant Multiple Law)}\\
\lim\limits_{x \rightarrow -2} (3x^4+2x^2-x+1) &= 3\lim\limits_{x \rightarrow -2} x^4 +
2\lim\limits_{x \rightarrow -2} x^2 -
\lim\limits_{x \rightarrow -2} x +
1
&& \text{(Special Limit, Constant Multiple Law.)}\\
\lim\limits_{x \rightarrow -2} (3x^4+2x^2-x+1) &= 3(-2)^4 +
2(-2)^2 -
(-2) +
1
&& \text{(Power Special Limit)}
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow -2} (3x^4+2x^2-x+1) = 59}
$

What is the significance of the title of The Book of Three by Lloyd Alexander?

Taran is a young boy who is beginning to grow into a man. He lives in Caer Dalben with Coll, Hen Wen (an oracular pig), and Dalben. Dalben is a 379-year-old wizard with many mysterious powers. He owns an important book called the Book of Three. Sometimes, he reads the stories in the Book of Three to Taran. The stories are about important people, like kings, princes, and bards. 
As a young orphan who doesn't know anything about his parentage, Taran is fascinated by these stories. He dreams that he could be unknowingly born of royal blood and that he too may have adventures one day. Taran leads a sheltered lifestyle in Caer Dalben, without much excitement or exposure to the outside world. The Book of Three symbolizes the excitement and glory he imagines will be waiting for him in the outside world. It tells stories of those who have done great deeds and acts of heroism. It is also something that is forbidden to Taran, who is not allowed to read the book himself.
When Taran sees Dalben napping, he decides to try and read the Book of Three without permission, thinking that the contents of the book will reveal to him new ideas and stories that Dalben is holding back from him. But as soon as he touches the book, it stings and burns his hands! Shortly after this, he leaves Cair Dalben alone to chase after Hen Wen after she escapes while under his watch. This catapults Taran into a series of adventures undertaken while he is trying to recapture Hen Wen.
The title The Book of Three symbolizes the adventures that Taran has throughout the course of the book, which were previously forbidden to him as too dangerous (just like the Book of Three was). It also symbolizes his need to learn more about the world and be a hero, just like the heroes in the stories in the Book of Three. He finds out that heroism is not quite all that it is portrayed as, and no longer values the excitement of violence and war the way he did when he first left Caer Dalben.
When Taran returns to Caer Dalben, he finds Dalben in his cottage, writing in the Book of Three. While this is not expressly stated, we can guess that Dalben is writing about Taran and his companions' adventures while Taran was away trying to find Hen Wen. This is a fitting culmination to the book because it shows how Taran's dreams were actualized through his own effort and bravery. In the end, he didn't merit glory because he found out his parents were royalty, or because of grand deeds. He earned it through his own bravery and effort, and by helping his friends succeed in their efforts to save Hen Wen and fight off the Horned King (one of the major antagonists in the story).
The title The Book of Three symbolizes Taran's intense need for adventure and glory, and his desire to learn and make his mark on the world.

Calculus and Its Applications, Chapter 1, 1.5, Section 1.5, Problem 48

If $\displaystyle y = x^{-\frac{3}{4}} - 3x^{\frac{2}{3}} + x^{\frac{5}{4}} + \frac{2}{x^4}$, find $y'$

$
\begin{equation}
\begin{aligned}
y' &= \frac{d}{dx} \left( x^{-\frac{3}{4}} - 3x^{\frac{2}{3}} + x^{\frac{5}{4}} + \frac{2}{x^4} \right)\\
\\
&= \frac{d}{dx} \left( x^{-\frac{3}{4}} \right) - \frac{d}{dx} \left( 3x^{\frac{2}{3}}\right) + \frac{d}{dx} \left( x^{\frac{5}{4}} \right)+ \frac{d}{dx} \left( \frac{2}{x^4} \right)\\
\\
&= \frac{d}{dx} \left( x^{-\frac{3}{4}} \right) - 3 \cdot \frac{d}{dx} \left( x^{\frac{2}{3}} \right) + \frac{d}{dx} \left( x^{\frac{5}{4}} \right) +
2 \cdot \frac{d}{dx} \left( x^{-4} \right)\\
\\
&= -\frac{3}{4} \cdot x^{-\frac{3}{4}-1} - 3 \cdot \frac{2}{3} x^{\frac{2}{3} - 1} + \frac{5}{4} \cdot x^{\frac{5}{4}-1} + 2 \cdot (-4) x^{-4-1}\\
\\
&= -\frac{3}{4}x^{-\frac{7}{4}} - 2 x^{-\frac{1}{3}} + \frac{5}{4} x^{\frac{1}{4}} - 8x^{-5}\\
\\
&= \frac{-3}{4x^{\frac{7}{4}}} - \frac{2}{x^{\frac{1}{3}}} + \frac{5}{4} x^{\frac{1}{4}} - \frac{8}{x^5}

\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 2, Review Exercises, Section Review Exercises, Problem 19

Show that the statement $\lim \limits_{x \to 2} (14 - 5x) = 4$ using the precise definition of a limit.

Based from the definition,

$\qquad$ if $0 < | x - a | < \delta $ then $|f(x) - L | < \varepsilon $

$\qquad$ if $0 < | x - 2 | < \delta $ then $|(14-5x)-4| < \varepsilon$

But,

$\qquad$ $|(14-5x)-4| = |14 - 5x -4| = |10 - 5x| = |-5 (x - 2)| = 5 |x - 2|$

So we want

$\qquad$ if $0 < |x - 2| < \delta$ then $5| x - 2 | < \varepsilon$

That is,

$\qquad$ if $0 < | x - 2 | < \delta$ then $|x - 2| < \displaystyle \frac{\varepsilon}{5}$

The statement suggest that we should choose $\displaystyle \delta = \frac{\varepsilon}{5}$.

By proving that the assumed value of $\displaystyle \delta = \frac{\varepsilon}{5}$ will fit the definition.

$\qquad$ if $0 < |x - 2| < \delta$ then,

$\qquad$ $|(14-5x)-4| = |14 - 5x -4| = |10 - 5x| = |-5 (x - 2)| = 5 |x - 2| < 5 \delta = \cancel{5} \left( \frac{\varepsilon}{\cancel{5}} \right) = \varepsilon$

Thus,

$\qquad$ if $0 < | x - 2 | < \delta $ then $|(14-5x)-4 | < \varepsilon$

Therefore, by the precise definition of a limit

$\qquad$ $\lim \limits_{x \to 2} (14-5x) = 4$

What goods were exchanged with the Columbian exchange?

The Columbian Exchange, named for the explorer Christopher Columbus, describes the transmission of plants, animals, goods, and slaves between Europe, the Americas, and Africa. While it had numerous positive benefits for the Europeans, who established farming properties and gained access to lucrative raw materials, the Columbian Exchange also opened the door to the enslavement of indigenous people, who were forced to work on newly-created plantations and farms. The Columbian Exchange also brought new diseases to the Americas, decimating the indigenous populations. This prompted a rise in the slave trade from Africa, as African slaves had immunities to the diseases that killed so many indigenous people.
Among the most lucrative goods transmitted in the Columbian Exchange were sugar, corn, and tea. Columbus himself is credited with bringing sugar to Hispaniola, setting up sugar cane plantations after Spanish miners had exhausted the gold stores there. Sugar quickly became the primary good traded in the Columbian Exchange, and the rapid increase in plantations led to a increase in the slave trade as more and more people were needed to produce sugar cane.
Unlike sugar cane, corn was native to the New World. Not only did corn play a major role in the diets of indigenous Americans, but it was valued for its cultural worth as well, appearing in many myths and legends. Columbus is credited with bringing corn back from the New World to Europe, where it quickly became a staple in the European diet. Corn could be grown in many climates and provided significant nutrition, making it a particularly useful crop. Eventually, corn was grown and consumed in the Americas, Europe, and even China, where it often was planted to replace flooded rice fields.
Tea was introduced to Europe thanks to trade routes through Asia. Though initially considered a curiosity, tea quickly became popular among Europeans in part due to its reported medicinal values. Eventually, tea was brought to the New World by Jesuit missionaries. Because tea couldn't be grown in Europe, the tea trade through Asia expanded enormously. As its cache grew, so too did the desire for sugar, which was used to sweeten tea. The tea trade and the sugar trade, then, increased in relation to one another.
The Columbian Exchange, however, was not limited to the trade of goods and products. It also was a vessel for diseases, like smallpox. While Europeans weren't entirely immune to smallpox, its widespread presence in the Old World led many Europeans to develop immunity. In the New World, however, indigenous people lacked immunity, leading millions of people to contract smallpox and die. While it's unclear whether Europeans understood the spread of disease, most scholars agree that they were likely surprised by the high death toll of European diseases in the New World. High death tolls of indigenous people also increased the need for African slaves who had more immunities, boosting the trade of slaves in the Columbian Exchange.

The Columbian Exchange involved the transfer of American plants and animals and the products made from them to Europe, Asia, and Africa as well as the transfer of European, Asian, and African plants and animals to America.
Among the most important American contributions to the Columbian Exchange were potatoes, tomatoes, tobacco, chocolate, maize, and cassava root, which became a staple food in Africa. While the Columbian Exchange is best known for benefitting the European economy, it benefitted Africa and Asia as well. It led to a considerable expansion in the global food base, and this, in turn, substantially diminished the frequency of famines in the entire Old World and facilitated steadier population growth.
Among the most important Old World contributions to the Columbian Exchange were grains, such as barley, rye, and wheat; livestock, particularly cattle, horses, pigs, goats, and sheep; and sugar cane and coffee. These importations dramatically changed the way of life and economy in the Americas. For example, they led to explosive growth in cattle husbandry in Spanish America, and soon the Spanish American colonies became the main exporter of hides to Europe. The appearance of horses in the Great Plains transformed the habits and society of Native Americans there, as they began to use horses for hunting and transportation. The development of sugar cane and coffee plantations in Cuba, Brazil, and the Caribbean led to an enormous demand for slaves and shaped the development of the Transatlantic slave trade. More than 70 percent of the people crossing the Atlantic from the Old World to America before 1800 were black slaves.
The Columbian Exchange also included the exchange of bacterial and viral pools. Tens of millions of Native Americans died from European diseases, such as small pox. These devastating diseases were among the most powerful factors facilitating the European conquest of America. It is also quite possible that syphilis may have come to Europe and Asia from America, although this remains a matter of scholarly debate.

How could I create a PowerPoint presentation (6-8 slides) discussing gang problems and offering alternatives to gangs for adolescents in my community that could be shown at my school? I am supposed to suggest ways for young people to focus on the positive within their community while avoiding the traps of gang involvement.

First, this assignment has a very specific audience of students attending a school in your community. This means you should tailor it quite specifically to the demographic and cultural nature of your region. A presentation in rural Montana, where populations are primarily white with a significant Native American minority, would be quite different from one in New Mexico, which has more people of Hispanic origin than any other ethnic group. An impoverished urban school will face different issues than a wealthy suburban one. 
Your slides and associated talk should be accessible to students. Talk in concrete terms and use familiar examples instead of abstract generalizations.
Your first slide might discuss what attracts people to gangs, including lack of other things to do after school, a sense of community, a desire for respect, fear, economic necessity, and peer pressure. Each subsequent slide should address one of these issues. For example, your second slide could discuss locally available after-school activities that are good alternatives to hanging out with gangs, including sports and clubs. On economic issues, you could supply resources for finding part-time jobs. For building community, you might discuss not just local clubs and groups but online communities.
Your final slide might conclude with a list of local and web resources of potential use to students searching for alternatives to gang life or gang members trying to leave gangs.

Intermediate Algebra, Chapter 1, 1.4, Section 1.4, Problem 16

Simplify the expression: $6a + 5a$.

$6a + 5a = 11a \qquad$ Combine like terms

What is the definition of texture as it is used in paragraph 20 in "A Mother in Mannville"?

The word "texture" in paragraph 20 of "A Mother in Mannville," by Marjorie Kinnan Rawlings, is used to describe Jerry's wood chopping. The first two lines of the paragraph read,

At daylight I was half wakened by the sound of chopping. Again it was so even in texture that I went back to sleep.

Texture is commonly used to describe something we physically touch, and it's an important part of how we identify the things around us. We know that sandpaper is rough and silk is smooth.
However, texture is also a characteristic used in music and literature to create a feeling. In paragraph 20, the texture, or regularity and evenness, of Jerry's chopping is calming and soothing to the narrator, and she goes back to sleep. At the beginning of the story, the narrator tells us she is looking for "quiet, isolation" in which to work. Jerry's chopping isn't a distraction; it is part of the peaceful environment of the isolated cabin. This type of texture contributes to the mood and setting of the story.

In Marjorie Kinnan Rawlings's short story, "A Mother in Mannville," the word texture in paragraph twenty is used to describe the rhythm of chopping wood when Jerry returns after the first morning. Here is the quote:

At daylight, I was half wakened by the sound of chopping. Again it was so even in texture that I went back to sleep. 

The first time Jerry chopped wood for the narrator, it is described it as rhythmic and even. 

I went back to work, closing the door. At first the sound of the boy dragging the brush annoyed me. Then he began to chop. The blows were rhythmic and steady, and shortly I had forgotten him, the sound no more an interruption than a consistent rain.

According to the Merriam-Webster dictionary, texture comes from a Latin word meaning to weave. In using the context clues surrounding the word, readers understand that Rawlings is referring to the steady rhythm that Jerry is weaving with his skillful chopping.
https://www.merriam-webster.com/dictionary/texture

What does Squealer say will happen when some of the animals complain that the pigs get all the milk and apples?

I assume that you're referring to Animal Farm by George Orwell. Squealer is effectively the pigs' chief propagandist, devising ever more elaborate (and unconvincing) justifications for their tyrannical behavior. When some of the animals complain about the pigs getting all the milk and apples, he says,

"Comrades!" he cried. "You do not imagine, I hope, that we pigs are doing this in a spirit of selfishness and privilege? Many of us actually dislike milk and apples. I dislike them myself. Our sole object in taking these things is to preserve our health. Milk and apples (this has been proved by Science, comrades) contain substances absolutely necessary to the well-being of a pig. We pigs are brainworkers. The whole management and organization of this farm depend on us. Day and night we are watching over your welfare. It is for YOUR sake that we drink that milk and eat those apples."

Squealer's little speech is meant to be persuasive, but no one is really convinced. The use of science to justify the pigs being "more equal than others" is a cynical attempt by the pigs to cloak their greed in the language of selflessness. "Well," Squealer says, "we'd really rather not drink this milk and eat these apples, but you know, science tells us that we must. In any case, it's not just good for us, it's good for you too. We are the brain-workers. If we're not healthy, then the whole farm will go to wrack and ruin. Then where would you be? You need us, and you need us to be healthy. That is why we keep the milk and apples for ourselves."
Orwell is making a satirical point. Communist regimes claim to be built on the principle of equality, yet those in charge enjoy a much better standard of living than everyone else. If anyone should challenge them (if anyone dared to, that is) they would use the kind of phony arguments used by Squealer to justify their cynical, self-serving actions.

So is a blue moon not actually blue?

I suppose to be entirely accurate, yes, a blue moon is actually blue; however, the modern day usage of "blue moon" isn't referring to a blue-colored moon.
As we use it today, the phrase "once in a blue moon" means seldom or rarely; however, the phrase does have astronomy roots. Today a "blue moon" refers to the 2nd of two full moons in a single calendar month. An even older definition says that a blue moon is the 3rd or even 4th full moon in a single season. Regardless of which historical definition you would like to use, the event is fairly rare, but it is predictable.
An actual, real blue moon is not predictable. On rare occasions, volcanic eruptions or large fires can put into the atmosphere enough particles of the right size to act like a color filter. The result is a moon that is tinged a bit blue.
https://earthsky.org/astronomy-essentials/when-is-the-next-blue-moon

https://www.spaceweather.com/glossary/bluemoonstories.html

When did the Olympics begin?

The Olympic Games of antiquity date back to 776 BC in Greece. There are written documents supporting the date of the first Games, which were held in the southern region of Greece known as the Peloponnese, in the city of Olympia. This region of Greece is located on a peninsula of the same name. The city of Olympia is located in the western part of the region. A stadium which held thousands of people was located there, along with other ancient structures, which accommodated large numbers of people every four years when the Olympic Games were held. Temples in honor of the Greek god Zeus and the goddess Hera stood near the Olympic stadium.
History and mythology become intertwined when the origins of the games are discussed. Most of the myths provide evidence of the Games being held in honor of the Greek god Zeus. Young men came together each Olympiad to demonstrate their prowess in ancient athletic endeavors.

What are the differences between a graphic novel and a conventional novel? Here's the information I know through comparison between the two. What could I say about a traditional novel in words, anything more descriptive to support my idea? Conventional uses diction; graphic novel uses color and shading to create the mood. Graphic: Zip line and shading are used to create and express action and emotion. Traditional Novel: Detailed word description. Graphic novels can present different scene at exactly the same time, and use illustration to create a distinction between the two, creating parallelism. Conventional novels, however, focus on one scene.

The differences you have listed between conventional and graphic novels are valid and quite thorough. However, I would like to add one or two points that would enhance the distinctions you have outlined.
If one looks at a specific graphic novel such as Art Spiegelman's Maus, one can see immediately a striking effect that is impossible in the conventional format, despite the fact that in the twentieth century and later, written prose, through stream-of-consciousness and other techniques, has already been able to achieve surreal and dreamlike effects diverging from photographic reality. In Maus,Spiegelman casts people as animals: specifically as mice, cats, and pigs. Given the use of anthropomorphism (the ascription of human characteristics to nonhumans) in cartoons and children's literature, one would not necessarily think that Spiegelman's technique is necessarily revolutionary or novel. However, in Maus, he is using this method to symbolize the dynamic among the different groups during historical events: World War II and the Holocaust. A conventional novel, regardless of how imaginative and surreal it might be, would never achieve the striking effect of Spiegelman's images upon the reader or effectively utilize the grim symbolism inherent in his use of animal characters as humans. History is thus given a new kind of life in which the immense tragedy of the Holocaust strikes the reader with an immediacy that neither the conventional novel nor film is capable of.

It sounds like you have a great understanding of the structural differences between graphic and traditional novels, including uses and effects of such differences for the author's purposes. Perhaps the next item of comparison should be how these two types of texts affect readers differently.
While reading a traditional novel, we experience the flow of "natural reading," meaning that our brains register whole sets of words simultaneously, rather than focusing on individual words (which can happen in short dialogue bubbles of graphic texts). Therefore, we cover more text in the same amount of time we would spend on a graphic novel, which generally has shorter groupings of text. As we read a traditional novel, our brain registers the word groupings using various area of the brain (touch, vision, emotion, etc.) To fully make meaning of the words, the brain then associates them with our own real-life experiences. Of course, all this happens within milliseconds as our eyes scan across the page. However, this also means that we don't take much time to consider any one idea (generally required for retention of data) unless we choose to stop and re-read or take notes.
Due to the verbal-visual blend of a graphic novel, there is generally less text to be read on each page, and the flow of reading is interrupted more often as our eyes scan to the pictures. However, studies show that this multi-modal method of reading is actually more effective for retention of data. Rather than relying only on textual evidence, our brains must also decipher visual and spacial evidence on the page. As a result, our neuron activity is increased as we read and even afterwards, as we remember the story and accompanying graphic images. For this very reason, foreign language learners not only have an easier time reading a graphic novel in the new language, but it also helps them acquire and retain the language faster. The same is true for anyone wanting to acquire new data.
One study done at Ankara College Foundation Private High School compared similar-level students’ comprehension of Shakespeare’s Macbeth. Not surprisingly, the group using a graphic novel approach scored significantly higher on the posttest than did those reading the traditional play format. The days of believing that comic books are just for young children are past. We live in a multi-modal, digital world, and whether we simply want to enjoy a colorful story or acquire some new knowledge, choosing a graphic text is not only fun but an effective brain activity.
https://www.futurity.org/reading-brains-1133942-2/

https://www.scribendi.com/advice/reasons_to_start_reading_comic_books.en.html

Why does Harry look for the woman on the third day?

The three men see the woman on the rooftop one day in June as they are working on a roof gutter. She is all naked, save for a “brief red scarf tied around her breasts and red bikini pants.” They see her on the very “first day of the sun,” sunbathing on her roof. She is oblivious to her surroundings and does not seem worried that her presence on the rooftop may bother others. Harry, the oldest of the three workers, is not very keen on watching the sunbathing woman. He tries to dissuade his colleagues from looking at her by telling them that “small things amuse small minds.” On their second day of work, they again see the woman, sunbathing on her roof. This time around, all three men “whistle and yell” at her because she is indifferent to them watching her. Of the three, Stanley is the most affected by the woman’s indifference. In fact, the woman quite upsets him. He thinks that she is wrong to display her body in that manner. Tom is attracted to the woman and has crazy sexual fantasies about her.
On their third day of work, Harry is keen on knowing whether the woman is at her usual place on the rooftop. Therefore, immediately the three men get to the roof, he is the first to look for her presence. Tom knows that Harry does this so as to stop Stanley from looking out for her; he hopes to stave off Stanley’s bad humor. Harry is relieved to find that the woman is absent from the roof. The woman often distracts them from their work and especially puts Stanley in a bad mood. The day progresses smoothly with few incidents. However, later on in the evening, just as they prepare to leave for home, they realize that the woman had been on her roof after all, only that, she had hidden away from them in a different section of her roof.

Why doesn't Hamlet react angrily immediately after his father's murder?

Hamlet does not react angrily immediately after his father's murder because he does not actually know that his father has been murdered. Hamlet does not learn until act 1, scene 5, when he speaks with his father's ghost, that old King Hamlet was, in fact, murdered, and by the king's own brother, Claudius. Hamlet's father's ghost tells him,

'Tis given out that, sleeping in my orchard,A serpent stung me. So the whole ear of DenmarkIs by a forged process of my deathRankly abused. But know, thou noble youth,The serpent that did sting they father's lifeNow wears his crown. (1.5.42–47)

In other words, the ghost says that everyone in the country has been told a lie: that he was killed by a snake that bit him while he was asleep in the orchard. In truth, that "serpent" is actually the man who now wears the crown of Denmark, the dead king's own brother, Claudius. It is only at this point that Hamlet can respond with anger to his father's murder because he's only just learned of it.
Hamlet is angry at the start of the play, but his anger is the result of his mother's hasty remarriage to her own brother-in-law. When he speaks to his friend Horatio, he tells Horatio, sarcastically, that

The funeral baked meatsDid coldly furnish forth the marriage tables.Would I had met my dearest foe in heavenOr ever I had seen that day, Horatio! (1.2.187–190)

In other words, he caustically jokes that the leftovers from the funeral fed people at the wedding because the wedding followed the funeral so quickly. He is exaggerating of course, but it shows how angry he is at his mother's choice.

Hamlet is fairly angry from the very beginning of the play. There may have been a period between his father's death and his return to Elsinore when he was merely sad, but we don't see this. Hamlet's initial anger at both his mother and Claudius is driven by the fact that he returns home to find them married mere months after Old Hamlet's death. Whether or not the old king was murdered, Hamlet's angry reaction is first driven by his fury at his mother for marrying with such "wicked speed." He also feels that the marriage is "incestuous" and that Claudius is unworthy of his mother.
It isn't until after the Ghost asks Hamlet to "revenge his foul and most unnatural murder" that Hamlet begins to think there is something even more sinister behind the king's death and his mother's hasty remarriage. Prior to this, he agreed with his mother that his father's death had been "common" (that is, natural and usual), but he was very upset about it all the same.

Why was the narrator’s father not happy about the Captain’s extended stay at the inn?

Jim Hawkin's father and owner of the Admiral Benbow Inn certainly is not fond of Billy Bones, aka "The Captain." It probably does not help that Mr. Hawkins is in poor health, meaning that his son, Jim, is picking up the slack around the inn. Billy Bones is certainly not a model guest. His clothes are bad and his language foul. He is extremely anti-social, which would have been frowned upon in a public space, such as an 18th Century English inn. He sang loud sea shanties without a care for the other guests and would subject them to terrifying tales of the sea. Furthermore, Billy Bones is almost constantly drunk. He also stops paying for his accommodations after a time, even though he stays at the inn for several months. When Jim's father would bring up the issue of payment with Billy Bones, the guest would intimidate the innkeeper into leaving him be. We can easily suppose that all these things meant that Jim's father was not at all happy to host the Captain at the inn.

What is your interpretation of the relationship between Mary and Billy (Will)?

The relationship between Billy and his mother Mary is a codependent one. By vying for his mother's love and approval in the shadow of his abusive father, Billy gives Mary power she would not have otherwise. When he gets older and grows up, she loses that power and the two eventually have a less personal, less codependent relationship. 
As a child, Billy relies on the love, protection, and acceptance his mother offers him. He is unable to get it from anyone else. As a result, Billy shapes himself into the kind of person she expects throughout his childhood. 
Mary's husband Constantine abused his wife and children, especially Billy. For example, one night when Billy finds his parents filling their Easter baskets, Constantine thinks of his son's small frame and how at five he already "had a scrawny neck and a squeaky, pleading voice." He is annoyed by his son's presence and disappointed in Billy, so he shakes him hard after Mary tries to defuse the situation by telling Billy that it is just a dream. Mary intervenes for him and makes her husband stop.
Constantine decides he has not done enough and slaps Billy's behind hard—making him fall. He goes to hurt him more, and Mary gets in between them. This type of interaction explains the relationship between Billy and Mary during his childhood. Because her husband is abusive toward Billy, Mary is more focused on him; she dotes on him more than his sisters—always in an attempt to stop Constantine from abusing Billy.
Billy wants to please Mary. At one point, she chooses to buy him a stuffed monkey because that is what Mary wants him to prefer. Billy himself wants a Barbie, but he does not tell his mother. Part of the reason he wants to please her is because she is his protector and the one who stands up for the person Billy is inside. His father sees Billy as he wants him to be—a boy who wants to buy a football rather than replace a broken toy horse. Mary accepts the desires that Billy voices and continues to love him, even though that love stifles him.
Billy is appreciative of the love Mary has for him. At the same time, though, it overpowers him and prevents him from coming into his own. Cunningham writes the following:

She smiled, deeply pleased, and told him he was a good little boy, a prize. She told him he deserved all sorts of good things, and if anyone tried to tell him differently, that person didn't know what he was talking about. Billy stared at her gratefully. She offered a practiced smile, one he'd seen thousands of times: a quick jerking upward of the corners of her mouth, a squeezing shut of the eyes, as if the act of smiling caused her a sharp and exquisite pain. Something bucked inside him, a feeling so unruly he thought he might be sick. She was his friend. She was the one who allowed. How could he dislike her? 

Mary appreciates Billy because he is the kind of child she can connect with. Cunningham says that "of Mary's children, only Billy wanted the things she wanted to give." He is happy to do as she asks. He is polite and studious and does not rebel. Billy is the only one of her three children that Mary really understands.
As he gets older, Billy separates himself from his mother and she feels desperate over the loss of the relationship. She does not understand why he might not want to attend Harvard and why he is not lining up for the life she imagined for him. In the same token, Billy sees her as a barrier to having his own life shaped by his own desires. 
When he leaves home, Billy changes his name and goes by Will instead, further separating himself from the child Mary understood so clearly. This puts Mary more in line with her husband, who has never understood Billy. When they visit him at college, the changes are more clear to them. Cunningham says:

Again, her emotions rose in such confusion that she felt the moisture break out along her upper lip. She wanted to defend Billy from his father. She wanted to stand next to Constantine and demand to know who Billy had turned himself into. How had he gotten so lost? Her lungs clenched up and she struggled for a breath.

She sees Billy as a reflection of herself, and, now that he has changed into a more sullen, unkempt person, she does not have that connection anymore. It frightens and upsets Mary and keeps her from being able to connect with the person Will is. She is faced with this when she visits him on the day he is about to graduate from college. It is clear to her that she does not know him. "Although she thought of Billy constantly, she thought of him in faintly abstract terms, the way she'd think of a character in a television show when the show wasn't on."
As Will gets older, she is able to visit with him a couple times every year in Boston. She still thinks of him as Billy, though she calls him Will when she speaks to him. Even though they are together, the relationship between them is more stiff and formal than in the past. 
Mary is aware that her son is gay and is happy not speaking about it. Once Will meets Harry, however, she has to acknowledge and accept it on a more significant level. It is the first time in years that she sees him as the son she once had—recognizing the same pride and embarrassment in his declaration of love for Harry that he had when he brought home a necklace he had made at summer camp as a child. 
Mary recognizes that she can hurt him for the first time in years when he asks if she finds his orientation strange. However, she says she is not shocked, and she asks to know more. It is the right choice for their relationship. Even though she still feels anger for all the things he did not achieve, she still loves him. Her acceptance of him is the first time they have really connected since before he left for college. 
In the end, the codependent relationship between Billy and Mary gave Mary power that she did not have otherwise. Her husband controlled her, and the world she lived in was not the one she wanted. Young Billy worked for her attention and approval until he finally left the family home to grow into an adult. In the end, Cunningham writes,

By accepting him she had lost much of her power, and she saw that she would not be able to get it back even if she wanted to. He’d moved beyond the reach of her disapproval. She had released him.

She did accept Will. Mary recognizes who her son is and is able to love him for that. She also recognizes that Harry is a good man—the kind of man she might have chosen for herself if things were different. This creates a bridge between them that allows them to have a less codependent relationship and develop a more normal one, even if they are not particularly close. Mary still feels more connected to him than to her daughters. She recognizes that she has to love him as he is; there is no other option. 

How was the conflict in The Boy with the Striped Pajamas resolved?

The conflict at the heart of the story is a culture clash between the two different worlds that Bruno and Shmuel occupy. Though physically separated by nothing more than a fence, the two boys might as well live on different planets. Bruno is a German; his father, the commandant of Auschwitz, plays a key role in the Nazi genocide against the Jews. Shmuel is himself a Jew, a victim of the campaign of terror and physical annihilation waged against his people by the Nazis.
It seems scarcely believable that two boys from such radically different backgrounds should be able to forge any kind of meaningful friendship. That they do so is a testament to the power of humanity to transcend the artificial racial and ethnic barriers that people construct to keep themselves separate.
And it is this unique friendship that ultimately resolves the book's central conflict, albeit tragically. For it is only when Bruno goes with Shmuel to die in Auschwitz's notorious gas chambers that the divisions between them finally collapse. That it takes their deaths to resolve this conflict speaks volumes about the world that Bruno's father has helped to create.

The main conflict throughout the novel involves the circumstances surrounding Bruno and Shmuel's friendship. Since Bruno is the son of a Nazi Commandant and Shmuel is a Jewish prisoner, their friendship is forbidden. Bruno and Shmuel are forced to meet in secret and talk between the fence that separates them. Despite the fact that they cannot play together and are forbidden from interacting, Bruno and Shmuel develop a strong friendship. Shmuel listens to Bruno, and Bruno brings Shmuel food each trip. Bruno eventually agrees to help Shmuel find his father and crawls underneath the fence. Unfortunately, the boys are forced to march with a group of Jewish prisoners to a gas chamber. Although the two boys die, the conflict is resolved because their friendship and loyalty transcend their terrible environment. At Auschwitz, the boys' friendship was forbidden, but in death, they are given the chance to be together for eternity. 

What kind of a letter did the kidnappers write to Ebeneezer Dorset? What were its contents?

Sam and Bill concoct a surprisingly credible and grammatically correct ransom letter. Ordinarily this would be effective, because it would show the father than he was dealing with intelligent men and not with a couple of ignorant hoodlums. The entire text of the letter Sam and Bill sent to Ebeneezer Dorset is shown below.

Ebenezer Dorset, Esq.:
We have your boy concealed in a place far from Summit. It is useless for you or the most skilful detectives to attempt to find him. Absolutely, the only terms on which you can have him restored to you are these: We demand fifteen hundred dollars in large bills for his return; the money to be left at midnight to-night at the same spot and in the same box as your reply--as hereinafter described. If you agree to these terms, send your answer in writing by a solitary messenger to-night at half-past eight o'clock. After crossing Owl Creek, on the road to Poplar Cove, there are three large trees about a hundred yards apart, close to the fence of the wheat field on the right-hand side. At the bottom of the fence-post, opposite the third tree, will be found a small pasteboard box.
The messenger will place the answer in this box and return immediately to Summit.
If you attempt any treachery or fail to comply with our demand as stated, you will never see your boy again.
If you pay the money as demanded, he will be returned to you safe and well within three hours. These terms are final, and if you do not accede to them no further communication will be attempted.
TWO DESPERATE MEN.

Bill had talked Sam out of asking for two thousand dollars because Bill was having such a hard time controlling the boy who called himself Red Chief that he was already desperate to get rid of him. The ransom letter demanded a reply at eight-thirty that night but gave Ebeneezer Dorset until midnight of that same night to pay the actual money. Sam's intention was to be hiding up in the tree above the spot where Dorset's messenger was supposed to leave the reply; but he gave him some extra hours in which to raise the fifteen-hundred-dollars in cash. Sam wanted to know exactly when the reply would arrive. He did not want to be seen crossing any open space in case Dorset should go to the law authorities and they should have a stakeout waiting. As it turned out, there was to be no ransom money. Dorset sent them a reply at exactly eight-thirty in which he stated that instead of paying them $1500, he would take his son off their hands if they paid him $250.
The story is based on heavy situational irony. The two kidnappers did not foresee what a problem they would have with their hostage. Neither did they foresee how indifferent a father might be to getting his son back. O. Henry may have given the father the first name of Ebeneezer as an allusion to Charles Dickens' miserly and hard-bargaining character Ebeneezer Scrooge in A Christmas Carol. 
 

How can I write an eight-page research essay on the theme of family in The Shining by Stephen King using five critical scholarly sources?

First, you need to narrow your topic down to a specific aspect of family in The Shining. Here are a few suggestions:
Familial abuse
Cycles of domestic abuse (consider Jack's childhood and how it might affect his relationship with his son)
Wendy as wife and mother or Jack as husband and father
How the book treats family versus how the 1980 Kubrick movie does (considering the differences between the book and movie, you could get a lot of mileage out of this one)
Second, you need to seek out articles or books which either approach The Shining from your chosen viewpoint or relate to it indirectly. For example, if you write about domestic abuse in the novel, you could research what domestic abuse is typically like in reality then compare it to what King has in the novel. If you compare the book and the movie, you could use movie reviews and studies on the topic (of which there are too many to count).
Once you've done your research, you need to formulate an argumentative thesis statement, which will go at the end of your opening paragraph. Each body paragraph will provide different points of your argument, backed up by both evidence from King's novel and from the scholarly sources you selected.

Your first step in approaching this assignment should be to think about a particular stance and theoretical approach. 
Your introductory section should set out how you will approach the work. You could focus on a feminist reading in which you looked at the role of Wendy, especially how she seems a figure who almost exists to react to the dynamic between Jack and Danny rather than a strong figure in her own right. A second possibility would be to focus on issues of patriarchy, and specifically how Jack is affected and harmed by his own ideals of masculinity. A third possibility is to examine the child-with-special-powers trope, one that is quite successful in popular fiction. A fourth possibility would be do a reception study, looking at how the family is portrayed in the book vs. the film or how the sequel, Doctor Sleep, makes us rethink the family dynamics of the original novel. 
The second section might look at the period and setting and King's own statements about the genesis of the novel and his own struggles with alcoholism. It would be useful to indicate the ways in which the family was changing in the 1970s, in which the male single-earner household was more common than it is today.
For your main body paragraphs, you want to organize your sections analytically rather than simply following the narrative flow of the novel. For example, if you are focusing on Wendy's role, you might write one section on how the narrator describes her, another on what she says in dialogue, another on her interactions with Jack, and another on her interactions with Danny. Whichever theme you choose, you should break it down into sections, and look at the theme in terms of different literary elements of the book (i.e. how the writer expresses the theme) rather than simply focusing on the story. 
For citations, you can find scholarly works about this novel by searching the MLA International Bibliography, which should be accessible from your university library's website. If you do not have access to that, Google Scholar is another solid resource. 
https://www.mla.org/Publications/MLA-International-Bibliography

Explain lines 45 through 66 of the poem "The Last Ride Together" by Robert Browning. The explanation should cover the lines of the stanza beginning "Fail I alone, in words and deeds?" through "My riding is better, by their leave."

The lines you have described constitute the fifth and sixth stanzas of Robert Browning's "The Last Ride Together." The poem itself consists of ten stanzas, each 11 lines long. The poem is written in iambic tetrameter, with each stanza rhymed AABBCDDEEEC.
The poem is a dramatic monologue narrated in the first person. In earlier stanzas we have discovered that the narrator is in love with a woman who is not in love with him and that she has effectively ended the relationship. Nonetheless, she agrees to his request that they go riding together one last time. The situation of these two stanzas is that the poet and the woman he loves unrequitedly are now riding together. There is no detail regarding where they are riding, the precise time of day, the weather, or the landscape. The lack of detail is deliberate, as the narrator wants to emphasize the emotion and spiritual aspects of the situation, which he considers more important than material details.
The fifth stanza begins with the following:

Fail I alone, in words and deeds?
Why, all men strive and who succeeds?

The narrator worries he has "failed" at love and wonders if he is unique in being a failure or whether, in fact, all people in some way feel that they fail to achieve the ideals towards which they strive. These lines introduce a theme common in Browning, sometimes called his doctrine of imperfection, the belief that it is our imperfections and the way they make us strive towards self-improvement that are characteristic of our humanity. Without imperfection and failure, we would lack ambition and goals.
The poem takes a metaphysical turn as the narrator contemplates traveling past unknown regions and cities. On a literal level, this could not be accomplished in a single ride; instead, the narrator is talking about his mental state rather than the physical journey, suggesting that as he rides he thinks about humanity as a whole, not just his immediate situation. He thinks that most people have this awareness that their actual deeds never fully measure up to their hopes and dreams. Even if he has not found eternal love and is disappointed with how things turned out, he takes solace in his ability to savor the moment of the ride, suggesting that even as we strive towards goals we cannot attain, we will achieve moments of joy that would not have existed without that striving; thus, rather than be disappointed in our failures, we should appreciate our positive experiences.
The sixth stanzas expands on this theme. The narrator considers that statesmen and soldiers also never achieve their grand goals, and that the greatest heroes end up dead, with only an impressive grave to show for their efforts. As a result, he feels increasingly appreciative of how—at least in his attempt to attain love—he has achieved this wonderful ride in which he can feel joy at contemplating his beloved and what he has enjoyed of the relationship.

Was Romeo's reaction to his banishment in Act 3, scene 3 understandable or excessive?

I think a lot of this answer depends on the reader. Personally, I think it's excessive; however, many of my students fiercely defend his response as completely understandable. I suppose it's both. He's a young, impulsive teenager, and his response to banishment is a typical teenager's excessive overreaction to bad news. The friar comes in and tells Romeo that he has been banished instead of sentenced to death. Romeo's reaction is classic over-exaggeration. Romeo says that banishment is far worse than death.

Ha, banishment! Be merciful, say “death,”
For exile hath more terror in his look,
Much more than death. Do not say “banishment.”

Friar Lawrence tries to talk some sense into Romeo, but Romeo isn't having any of it. Romeo goes so far as to say that the only world is Verona because that is where Juliet is. If he can't be there with her, there is no world worth living in. Death would simply be a kinder punishment.


There is no world without Verona walls
But purgatory, torture, hell itself.
Hence “banishèd” is banished from the world,
And world’s exile is death. Then “banishèd,”

Is death mistermed. Calling death “banishment,”
Thou cutt’st my head off with a golden ax
And smilest upon the stroke that murders me.





The friar continues to try and talk some sense into Romeo. He stresses that Romeo is alive even though his crime demands his death.


O deadly sin! O rude unthankfulness!
Thy fault our law calls death, but the kind Prince,
Taking thy part, hath rushed aside the law,
And turned that black word “death” to “banishment.”
This is dear mercy, and thou seest it not.



This back and forth between these characters continues far too long. Friar Lawrence attempts to persuade Romeo for much longer than I would have. I would have given up and started laughing at his excessive whining, but many of my students that claim to have loved and lost love are proud of the friar for his continued efforts. They empathize with Romeo's response; therefore, they see it as understandable. Eventually, Romeo's suicide comes up in the discussion, and this is the moment when Friar Lawrence has had enough. He firmly puts Romeo in his place through a long "suck it up" type speech.


Thy wild acts denote
The unreasonable fury of a beast.
Unseemly woman in a seeming man,
And ill-beseeming beast in seeming both!
Thou hast amazed me. By my holy order,
I thought thy disposition better tempered.
Hast thou slain Tybalt? Wilt thou slay thyself,
And slay thy lady that in thy life lives
By doing damnèd hate upon thyself?

How are Nadine Gordimer’s political beliefs reflected in the story "Once Upon a Time"?

Nadine Gordimer expresses a strong opposition to the apartheid of South Africa in her short story "Once Upon a Time."  In this story, structured like a fairy tale, Gordimer shows the detrimental effects of apartheid on those at the top of the power structure.  Gordimer's story describes a family living in a community in which they fear the invasion of the "other."  To keep their possessions safe, they and their neighborhoods put up neighborhood signs to discourage intruders with words such as "You have been warned," purchase electronic security systems, build higher fences, and install vise-like contraptions over these fences.  
All these precautions ironically result in a less safe and less attractive community.  With their tall fences, the neighborhood begins to look like a concentration camp. To protect themselves, they imprison themselves. The alarm system provides cover for thieves.  The Dragon Tooth contraption results in the death of their son.  Through this story, Gordimer shows quite clearly what an apartheid system does to those who continue to enforce it. 
But we also see more socialistic tendencies in the story.  The story itself is a frame story.  The frame is the author's writing a children's story when she is awakened and frightened by a noise she heard.  She finds out that the noise was caused by the fact that her house was built over an underground mine that had perhaps in earlier years collapsed upon and interred the workers down below.  This small detail is important because it can serve as a metaphor for Gordimer's political leanings.  The foundation of the house is shaky (like the apartheid government), and its first victims are those down below or the lower class, but eventually the tremors that have such devastating effects on the lower class will result in the collapse of the entire household or government.  In other words, when one segment of society keeps getting poorer while another segment of society keeps increasing their wealth and possessions, that society is no longer stable and will eventually fall.  A vastly uneven distribution of wealth negatively affects the entire society.  

In That Was Then, This is Now by S.E. Hinton, how is Cathy involved in the separation of Bryon's and Mark's relationship?

Cathy is a part of the emotional change that leads Bryon to distance himself from Mark.
Cathy is a significant part of Bryon's emotional maturation.  She enables him to see beyond the things that used to define him.  Cathy allows Bryon to see that his life of hanging and hustling with Mark, living solely in the moment, and engaging in self-destructive behavior are not ways to live. Cathy encourages Bryon to embrace more sensitive and thought-provoking approaches.  For example, he takes an active role in helping Cathy find her brother.  Bryon displays care and warmth in her time of need.  At the same time, Cathy is instrumental in helping Bryon understand his feelings of regret over Charlie's sacrifice.  She allows him to expand his emotional scope.
Since Mark does not possess such a perspective, Cathy's influence over Bryon facilitates the brothers' separation. Cathy does not intentionally drive a wedge between them. She is not jealous or possessive.  Rather, her goodness is contagious.  It rubs off on Bryon and causes him to ask questions about the person he is and the one he is going to become.  Cathy's effect on Bryon is evident in his betrayal of Mark as he can no longer passively watch what Mark does.  He must take action against it.  Cathy awakens a sense of duty and responsibility in Bryon that Mark lacks.

What happens when Fotheringay orders the earth to stop its movement?

The clergyman Mr. Maydig is very impressed with Fotheringay's miracle-working abilities—so much so that the challenges him to make the earth stand still and stop time. Foolishly, Fotheringay accedes to Maydig's request, asking for the earth to stop rotating. (Later, he asks to be brought back down to earth safe and sound.)
The earth duly grinds to a halt, and, as we might expect, people, animals, and things of various kinds start flying through the air. Fotheringay is one of them, but thanks to his miracle-working abilities, he is able to survive. However, the same can't be said of anyone else, because thanks to this particular miracle, every living thing on the planet has been completely destroyed and will remain destroyed until Fotheringay "undoes" all his miracles at the end of the story.

How is moral education addressed in To Kill a Mockingbird, and which characters reveal this education? Could you please include techniques used?

Morality is central to To Kill a Mockingbird, so moral education occurs throughout the story. The character who tells this story is a child who is observing an adult world and seeing how morality is undercut in society. The narrator, Scout, is about eight years old, and her sense of right and wrong is abiding, but her observations of how right and wrong play out among adults reveal society's hypocrisy.
Two of the best quotes from Atticus (Scout's father) help indicate how moral values are taught in the book. Atticus says,

You never really understand a person until you consider things from his point of view, until you climb into his skin and walk around in it.

He also notes,

When a child asks a question, answer him for goodness sake, but don't make a production out of it. Children are children, but they can spot evasion quicker than adults.

Atticus and other adults in the book give advice and have specific attitudes that reveal their moral character.
Calplurnia, the family maid, is big on enforcing rules about how to act. Early in the book, when Scout brings home a backwoods classmate for supper (lunch) and he pours half the jar of syrup on his food, Scout comments. Calpurnia pulls her aside and tells her to be gracious to her guests and to keep her mouth shut.
Miss Maudie, the optimistic and non-conformist neighbor, is an example to Scout of an independent woman. Her morality is to keep her spirits up and to provide an example. She also tells Scout directly what is important in how to treat others.
Atticus is fond of making short speeches about right and wrong, but his actions back them up. He speaks of courage and acts courageously, for example when he shoots the rabid dog that threatens the neighborhood. His quotes reveal that he tells children what they need to know; his actions provide an example, and there are many instances of this throughout the book. His handling of the court proceedings, for example, shows his courage and his adherence to his convictions.
Tom Robinson provides moral education by standing upright, telling the truth, and representing the outsider who is unjustly accused. Boo Radley does the same by acting kindly even though he is an outcast. After the children have to evacuate their home and stand out in the cold during the fire at Miss Maudie's house, Boo—under cover of darkness—puts a blanket over Scout. This gentle act prompts Scout to fess up to Atticus about her and Jem's ongoing attempt to figure Boo Radley out, leading to another lesson of morality from Atticus about leaving people be.
Scout's mistakes, missteps, and experiences of adversity almost always lead to a morality lesson—one she learns internally, from a specific scolding, or from a piece of advice she receives from an adult.
As for the effects of the moral education, it can be seen clearly in both Jem and Scout as they mature over the course of the story. Scout learns to appreciate what she has, to understand the hypocrisy of a racist society, and to respect others who are different. Jem learns courage and compassion through taking care of their neighbor Mrs. Dubose, who demonstrated courage in the face of great pain.
The kids both learned their lessons through observation and having reliable, loving, and kind adults in their lives—not just Atticus but most of the adults they encountered.

Moral education is addressed through Jem and Scout's relationship with their father. Throughout the novel, Atticus teaches both of his children important life lessons on perspective, real courage, sympathy, and tolerance. Atticus not only has one-on-one conversations with his children, explaining to them the importance of self-control, integrity, and respect, he also acts as a role model and demonstrates how to behave morally in difficult situations. Jem and Scout watch as their father treats Mrs. Dubose with respect, forgives Walter Cunningham, sympathizes with Bob Ewell, and valiantly defends Tom Robinson in front of a racist jury. Jem and Scout listen to their father's advice and develop into well-behaved children with perspective on the world around them. The children learn the importance of protecting innocent beings, standing up for what they believe in, and being tolerant toward people with different ideologies.
Atticus also challenges his children to forgive others by purposefully putting them in difficult situations. For example, Atticus makes Jem read to their racist neighbor as punishment for destroying her camellias and also makes Scout apologize for getting an attitude with Aunt Alexandra. Overall, Jem and Scout are morally educated by listening to Atticus's life lessons and witnessing their father behave morally in difficult situations.

Which character celebrates a birthday on the day Myrtle dies?

On the same day that Myrtle is killed, Nick celebrates his thirtieth birthday. When Nick realizes that it is his birthday and tells Tom, he has a moment of clarity in which he becomes daunted by the prospect of entering another decade. In fact, he calls it a "portentous, menacing road of a new decade."
Although he does not yet know it, this day will become "portentous" and "menacing" for another reason. The death of Myrtle Wilson, which takes place shortly after this realization, sets in motion a chain of menacing events, which will affect Nick in a far more significant way than simply turning thirty. It will lead, for example, to Gatsby's murder and the end of his American Dream, alongside Nick's decision to leave the East and return home to the West.

Calculus of a Single Variable, Chapter 6, 6.2, Section 6.2, Problem 4

Apply direct integration both sides: intN(y) dy= int M(x) dx to solve for the general solution of a differential equation.
For the given first order ODE: (dy)/(dx)=6-y it can be rearrange by cross-multiplication into:
(dy)/(6-y)=dx
Apply direct integration on both sides: int(dy)/(6-y)=int dx
For the left side, we consider u-substitution by letting:
u=6-y then du = -dy or -du=dy
The integral becomes: int(dy)/(6-y)=int(-du)/(u)
Applying basic integration formula for logarithm:
int(-du)/(u)= -ln|u|
Plug-in u = 6-y on -ln|u| , we get:
int(dy)/(6-y)=-ln|6-y|
For the right side, we apply the basic integration: int dx= x+C

Combing the results from both sides, we get the general solution of the differential equation as:
-ln|6-y|= x+C
y =6-e^((-x-C))
or
y = 6-Ce^(-x)

a) showing details of the work, write an expansion in Fourier series of the signal f(x) which is assumed to have the period 2pi f(x) = "Please refer to the attached image" Use Integration by parts show detailed work for each calculation of a0,an,bn. also show the values of all coefficients a1, b1, a2, b2, a3, b3, a4, b4, a5, b5 b) Graph both the f(x) and the partial sums up to that including cos 5x and sin 5x, for the interval −4pi

This function is odd, thus its Fourier expansions contains only sin(nx) terms, i.e. a_n=0, ngt=0. This expansion has the form  sum_(n=1)^(oo) b_n sin(nx)  where  b_n = 1/pi int_(-pi)^(pi) f(x) sin(nx) dx.
Find these coefficients:
b_n = 1/pi int_(-pi)^(pi) f(x) sin(nx) dx = 2/pi int_0^(pi) f(x) sin(nx) dx =
= 2/pi int_0^(pi/2) f(x) sin(nx) dx + 2/piint_(pi/2)^(pi) f(x) sin(nx) dx) =  
= 2/pi int_0^(pi/2) x sin(nx) dx + 2/piint_(pi/2)^(pi) pi/2 sin(nx) dx.
The second integral is obviously
-(cos(nx))|_(x=pi/2)^pi = -1/n (cos(n pi)-cos((n pi)/2)).
To find the second, use integration by parts:
2/pi int_0^(pi/2) x sin(nx) dx =
= |u=x, du=dx, dv=sin(nx)dx, v=-1/n cos(nx)| =  
= -2/(n pi) (x cos(nx))|_(x=0)^(pi/2) + 2/(n pi) int_0^(pi/2) cos(nx) dx =
= -1/n cos((n pi)/2) + 2/(n^2 pi) (sin(nx))|_(x=0)^(pi/2) =
= 2/(n^2 pi)sin((n pi)/2)-1/n cos((n pi)/2).
 
This way  b_n =2/(n^2 pi)sin((n pi)/2)-1/n cos(n pi).   Therefore  b_1=1+2/pi, b_3=1/3 -2/(9 pi), b_5=1/5+2/(25 pi).
The graphs are attached (the function is in blue, the approximation is in green). They are not so close but are somewhat similar. Note that on (-4pi,4pi) the function is 2pi -periodic.
http://tutorial.math.lamar.edu/Classes/DE/FourierSineSeries.aspx

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 20

The First Derivative f'(c) can be interpreted as:
- derivative of f(x) when x=c
- slope of a tangent line at a point (c, f(c))
- instantaneous rate of change of f(x) at x=c. f
The First Derivative test is commonly used to determine the possible local extrema: local minimum point or local maximum point. These can also be called as relative maximum or relative minimum
Local extrema exists at x=c when f'(c) =0.
To predict the concavity of the function f(x) at x=c,we follow:
f'(a) >0 and f'(b) <0 in the interval a
f'(a) <0 and f'(b) >0 in the interval aSign table:
If f'(x) >0 or f'(x) = positive value then function f(x) is increasing or has a positive slope of tangent line (slant line going up).
If f'(x)< 0 or f'(x) = negative value then function f(x) is decreasing or has a negative slope of tangent line (slant line going down).

As for Second Derivative Test, a critical point at x=c such that f'(c) =0 and f"(c) is continuous around the region of x=c follows:
f"(c) >0 then local minimum occurs at x=c.
f"(c) < 0 then local maximum occurs at x=c.
f"(c) =0 the inflection point, local extrema or neither will occur at x=c.
A real inflection points occurs at x=c such that f"(c)=0 if concavity changes before and after x=c.

For the given function f(x) = x^2/(x-1) , we can solve for first derivative f'(x) using product rule or quotient rule.
Using Product Rule:
f(x) =x^2/(x-1) is the same as f(x) =x^2*(x-1)^(-1)
f'(x) = 2x*(x-1)^(-1) + x^2 (-1)*(x-1)^(-2)
f'(x)= (2x)/(x-1) - x^2/(x-1)^2
f'(x) = (2x*(x-1) -x^2)/(x-1)^2

f'(x)= (2x^2-2x-x^2)/(x-1)^2
f'(x)= (x^2-2x)/(x-1)^2
Applying first derivative test, let f'(x) =0
(x^2-2x)/(x-1)^2 =0
Cross-multiply (x-1)^2 to the other side.
x^2-2x =0
Factoring common factor "x":
x(x-2)=0
Apply zero-factor property: a*b =0 if a=0 or b=0
x=0 and x-2=0 or x=2.
Sign table:
x -1 0 0.5 2 3
f'(x) 3/4 ---- -3 --- 3/4
f inc. dec. inc.
Concavity <--down nnn --> <---up uuu --->
Based on the table f'(-1)>0 and f'(0.5) <0 indicates a local maximum at x=0 while f'(0.5) <0 and f'(3)>0 indicates a local minimum at x=2.


Solve for the second derivative f"(x) using product rule derivative onf'(x)= (x^2-2x)/(x-1)^2 or f'(x)= (x^2-2x)*(x-1)^(-2) :
f"(x) = (2x-2)(x-1)^(-2)+ (x^2-2x)*(-2)(x-1)^(-3)

= ((2x-2)(x-1)+ (-2x^2+4x))/(x-1)^(3)
= ((2x^2-4x+2)+ (-2x^2+4x))/(x-1)^(3)
= 2/(x-1)^(3)
Applying second derivative:
f"(0) = 2/(0-1)^(3)
= 2/(-1)^3
=2/(-1)
=-2 negative value or f"(0)<0
then f"(0)<0 indicates a local maximum at x=0
f"(2) = 2/(2-1)^(3)
= 2/(1)^3
=2/(1)
= 2 positive value or f"(2)>0
then f"(2)>0 indicates local minimum at x=2

In my opinion, I would prefer the second derivative test in this problem since f"(x) can be easily simplified and there is no need to use additional x-values to be plug-in.

What is the difference between abiotic and biotic?

Biotic and abiotic are terms commonly used in ecology to describe the living and non-living components of the system.
Biotic components of an ecosystem represent all the living beings in that particular ecosystem. The examples of biotic factors are animals, plants, microorganisms (such as bacteria, fungi, and the like). The biotic factors of an ecosystem are defined as the living things that directly or indirectly affect the life of organisms. These may include interactions, waste, parasitism, and such.
Abiotic or non-biotic components of an ecosystem represent all the non-living things that affect the ecosystem. The examples of abiotic components are water, air, minerals, light, humidity, temperature, wind, and more. These components influence the ability of a biotic component to survive and prosper and may limit its population in a given ecosystem.
Together, the biotic and abiotic components create an ecosystem.
Hope this helps.

What does the title character experience while he is sleeping in Washington Irving's short story "Rip Van Winkle"?

In Washington Irving's short story "Rip Van Winkle," the titular character falls into a deep sleep following his consumption of the proverbial strange brew, initially described by Irving's unseen narrator as "a stout keg that seemed full of liquor" and "had much of the flavor of excellent Hollands." Finding the taste of this beverage very much to his liking, the perpetually irresponsible protagonist proceeds to drink a quantity sufficient to render him unconscious or, as the narrator suggests, throw him into a "deep sleep." With this development, Irving concludes Part I of his story.
With the beginning of Part II, Rip awakens from his sleep, certain that he has merely slept through the night and concerned about the reaction he will encounter from his far more responsible spouse, Dame Van Winkle. Rip's story proceeds to its conclusion, which entails his discovery that he has actually slept for twenty years and that his daughter is now grown and married, but the friends and neighbors he knew are dead.
As for what Rip experienced while sleeping, no one knows. Irving simply allows his protagonist to fall asleep and wake up two decades later. There is no sense of Rip having dreamt of anything in particular. His only experience is that of the natural aging process. In describing Rip's appearance following his long sleep, Irving's narrator notes the now-aged man's "long, grizzled beard, his rusty fowling piece, his uncouth dress, and an army of women and children at his heels...." What we can conclude, therefore, is that Rip experienced the aging process while sleeping.

Rip falls asleep after drinking a flagon of the beer with the odd, old-fashioned Dutch people he runs into in the mountains. We learn that his senses are overpowered, his eyes swim, and his head gradually droops before he falls into a deep sleep, indicating that this beer is more powerful than what Rip is used to consuming.
We don't learn anything about his sleep, such as whether he dreamed, but when he wakes up he is surprised that he might have slept all through the night. Although he has been snoozing deeply for 20 years, on awakening, he has no inkling of this. Instead, he worries about what excuse he can give Dame Van Winkle when he gets back home and wonders why his body feels so stiff in his joints, not yet associating this with aging.