How does Watson change throughout the novella? How does Conan Doyle structure him?

In the opening scene of The Sign of the Four Watson is intimidated by Sherlock Holmes and upset with himself for not having the courage to confront him about his frequent injections of cocaine and morphine. Despite his medical expertise, Watson describes himself as "diffident" and Holmes as "masterly." Watson summons the courage to point out the possible permanent consequences on Holmes's brain, only to hear Holmes say that his brain needs stimulation, whether it is a puzzle, problem, or drug. Also in this scene, Holmes belittles Watson's attempt at writing, and as Watson defends his work he reflects resentfully on Holmes's ego and vanity.
However, Watson must credit Holmes for his extraordinary powers of deduction, and he is quick to abandon his negative thoughts about Holmes when Miss Morstan arrives and Watson is asked to accompany Holmes in the investigation.
Watson gradually becomes more assertive; he is both attracted to and protective of Miss Morstan and engages with her while Holmes retreats into his own thoughts. Watson, however, retains his diffidence; when he understands that Miss Morstan may become a very rich heiress, his confidence falters. They do, though, fall in love and she accepts Watson's proposal.
Holmes often needs Watson as a sounding board for his theories about the case, and Holmes also knows that Watson is much better in dealing with people than he is himself. He tells Watson that he needs his help, and Watson seems to gain confidence as a result.
When the case is solved, Holmes falls back into his same pattern of solitude and drug abuse while Watson becomes less preoccupied with feelings of inferiority and more humanized and developed through his assistance with the case and his romance with Miss Morstan.

In Number the Stars why does uncle Henrik state it is easier to be brave if you don’t know everything in chapter 9?

Uncle Henrik believes that there are times that if you don’t know everything, you are then able to act bravely. There are times when not having all of the details allows a person to act more freely. Without knowing everything, a person can act naturally and do what he or she thinks is the right thing to do.
When a person has all the details, that person may overthink the situation. The person might start weighing the risks and the rewards of a situation. This analysis might cause the person to hesitate or not take action because the possible dangers might be perceived as too great. The person might also share information that could be harmful to the mission.
Annemarie is upset because she believed her uncle and mother weren’t being truthful to her about the death of an aunt. Annemarie never heard of this aunt and thought it was strange that no phone call was made to inform the family of the death. When her uncle asks Annemarie if she is brave, Annemarie says that she isn’t really brave. Her uncle assures her that she is brave and that there are times when it easier to be brave if a person doesn’t know all the details. Not knowing all the details can free a person to do the right thing without overanalyzing the situation.
Later in the story, Annemarie shows her bravery by taking the packet that has fallen to her uncle. When she encounters the German soldiers, she is able to still keep the packet because she has no idea how the packet would be used. She is able to get the packet to her uncle, which is essential for the success of the mission of smuggling the Jews to Sweden.

How do Bulgaria’s and Estonia’s culture, geography, laws, politics, social issues, and current trade affect Canadian businesses and consumer spending?

Bulgaria was a Soviet satellite state from 1946 to 1989; it is now a member of the European Union (despite concerns over its high incidence of corruption) and NATO. The country has been criticized by the EU for its lack of high-profile cases cracking down on corruption. Its climate has produced a great deal of biodiversity. According to the Canadian government (see the link below), Canada and Bulgaria have good bilateral trading and cultural relations. Both countries are members of the Organization for Security and Cooperation in Europe (OSCE), la Francophonie, and NATO allies. More than 30,000 Canadians who have Bulgarian origin live in Canada. In addition, in 2012, trade between the two countries totaled $369.3 million. Bulgarians have a developed mining industry that is interested in Canadian gas and oil, and Canadians have invested in Bulgarian telecommunications, airport services, and agriculture. Canadians are particularly interested in exporting electrical products, machinery and equipment, and chemicals and plastics to Bulgaria. 
Canada and Estonia are both NATO members. Canada did not recognize Soviet control of Estonia, one of the Baltic states, and Canada was one of the first nations to recognize Estonia as an independent country in 1991 (following the collapse of the Soviet Union). Canada was also the first member of NATO to accept Estonia into the organization, and Canada is home to the second-largest Estonian community outside of Estonia (numbering 24,000 people). In 2010, the two nations signed a Youth Mobility Agreement that allows members of one country (of the ages 18–35) to work for a short time in the other country. In 2012, Canada exported $22.9 million in goods to Estonia, including lumber, seafood, and machinery, and Canada imported $48.4 million in goods from Estonia, including telephone sets, chemical products, and fishing articles. Therefore, consumers and businesses spend money on Estonian imports. 
https://www.international.gc.ca/country-pays/latvia-lettonie/index.aspx?lang=eng

Calculus of a Single Variable, Chapter 6, 6.1, Section 6.1, Problem 24

To determine whether the given function is a solution of the given differential equation, we first need to find the derivative of the function.
y'=2x(2+e^x)+x^2e^x
Now we plug that into the equation.
x[2x(2+e^x)+x^2e^x]-2x^2(2+e^x)=
2x^2(2+e^x)+x^3e^x-2x^2(2+e^x)=
x^3e^x
As we can see, after simplifying the left hand side we get the right hand side of the equation. This means that the given function is a solution of the given differential equation.
Of course, this is only one of the solutions. The general solution of this equation is y=x^2(c+e^x).
The image below shows graphs of several such functions for different values of c. The graph of the function from the beginning is the green one.

a_n = ln(n^3)/(2n) Determine the convergence or divergence of the sequence with the given n'th term. If the sequence converges, find its limit.

a_n=(ln(n^3))/(2n)
The first few terms of the sequence are:
0 ,  0.5199 ,  0.5493 ,  0.5199 ,  0.4828 ,  0.4479 ,  0.4170 ,...
To determine if the sequence converge as the n becomes larger, take the limit of the nth-term as n approaches infinity.
lim_(n->oo)a_n
 =lim_(n->oo) (ln(n^3))/(2n)
To take the limit of this, apply  L'Hospital's Rule.
=lim_(n->oo) ((ln(n^3))')/((2n)')
=lim_(n->oo) (1/n^3*3n^2)/2
=lim_(n->oo) (3/n)/2
=lim_(n->oo) 3/(2n)
= 3/2 lim_(n->oo) 1/n
=3/2*0
=0
Therefore, the sequence is convergent.  And the terms converges to a value of 0. 

How does S.E. Hinton develop Soda's character throughout the novel?

Hinton uses a combination of direct and indirect characterization to develop and fully realize Soda's character. Direct characterization occurs when the author or narrator tells readers an explicit detail about a character. This is how Ponyboy first tells readers about his second brother. Ponyboy tells us Soda's exact age and that Soda is always smiling.

I love Soda more than I've ever loved anyone, even Mom and Dad. He's always happy-go-lucky and grinning . . .

Ponyboy also tells readers that he doesn't think Soda will ever grow up, and this is a bit of indirect characterization. It lets us know that Soda is a kid at heart, and he is likely always to have that sense of play about him. These feelings are confirmed when we see Soda flipping and cartwheeling around.

"Yeah!" screamed Soda as he too did a flying somersault off the steps. He flipped up to walk on his hands and then did a no-hands cartwheel across the yard to beat Darry's performance.

This brief sequence also lets us know that Soda is extremely athletic. All of these early details help readers form the idea that there isn't much emotional depth to Soda; however, that couldn't be further from the truth. As the novel progresses, we see that Soda has emotional depth and a well-aimed moral compass. This is evidenced through his commitment to Sandy and the unborn child that isn't even his. Chapter 12 gives readers a really good look at how deeply Soda cares and feels for the health and wellness of his family. His parents are gone, so all he has is his brothers. It tears him apart when the family fights, and that is a far cry from the "happy-go-lucky" person we were introduced to.

"It's just . . . I can't stand to hear y'all fight . . . Sometimes I have to get out or . . . It's like a middleman in a tug o' war and I'm being split in half . . . We're all we've got left. We ought to be able to stick together against anything. If we don't have each other, we don't have anything."

S.E. Hinton develops Soda's character throughout the novel by gradually depicting his emotional depth and sensitive nature, which is something Sodapop rarely displays. Towards the beginning of the novel, Sodapop is depicted as a happy-go-lucky teenager who enjoys joking around and does not take life too seriously. However, Hinton gradually develops his character by depicting some of his difficulties in life, which warrant Soda's emotional reactions. Hinton begins developing Soda's character through Ponyboy's story about his brother's horse, Mickey Mouse. Pony's story portrays Sodapop as a sensitive, compassionate person, who has experienced tragedy before. Later on, Soda's character is further developed by his reaction to Sandy's letter as well as Darry and Ponyboy's heated arguments. After Darry and Pony catch up to Soda when he runs out of the house, Hinton once again displays Soda's vulnerable, sensitive personality. Overall, Hinton develops Sodapop's character by depicting various moments where he displays a myriad of emotions, which portray him as a compassionate, vulnerable teenager who typically suppresses his difficult emotions.

What are two anecdotes in Jerome's novel Three Men in a Boat?

The dictionary defines an anecdote as “a short, entertaining account of some happening, usually personal or biographical.” Three Men in a Boat is told in anecdotal style, with one story following another. The challenge is to find ones that are short, since the narrator tends to ramble. Let’s confine our search to anecdotes that he shares from the past or from someone else, and not events as they develop on the current river trip.
One such story arises in Chapter IV, when the friends consider whether or not to take cheese along on the boat now. J. is reminded of a time when another friend asked him to take care of some cheeses for him. They had a strong smell; and everywhere J. went, the odor followed him. After he finally delivered the cheeses to his friend, he too decided that they smelled too much. He had to bury them on a beach to get rid of them.
George tells a story about boat tow lines in Chapter IX. On a previous trip, he and some friends came upon a young couple who were walking along the tow path dragging a rope behind them. But whatever boat they had thought they were pulling was nowhere in sight. The two were so lost in conversation that they hadn’t paid attention to the boat. So George and his friends hitched their craft to the couple’s line, allowing them to pull them along. When the young people finally turned around and saw a boat behind them with strangers in it, the woman exclaimed, “Oh Henry, then where is auntie?”

Why does the speaker admire his father?

The speaker admires his father for his ability to dig and work the land of a potato farmer, just as his grandfather had done. The description given about how well his father handles a spade and the amount of earth moved in a day show the author's respect for his father's abilities. He further describes the ability of his father and grandfather to dig down to the most fertile soil, which is necessary for successful potato farming. It is not just the physical ability to dig that the author admires. He also acknowledges his father's ability to know where the most fertile soil is and how to work the soil to grow potatoes.
The author himself has no such abilities and does not have a spade to use. If he did, he likely wouldn't know how to use it efficiently or where to find the most fertile soil. Instead, the author cultivates with pen and paper, as a writer. He compares using the pen to write with his father using the spade to dig up potatoes and spread the sprouts into the fertile soil.

How did Congress respond to Castro's actions in Cuba?

Many of the actions taken against Cuba in the wake of the revolution were undertaken by the President, as well as the State Department, which handles diplomacy. Congress responded to the Cuban Revolution, which resulted in the establishment of a communist state under Fidel Castro, by enacting an embargo, which John F. Kennedy made official in 1962. American companies were no longer allowed to trade with Cuba, which had formerly been more or less in the economic orbit of the United States. This placed an extreme strain on the government and the people of the island nation, and they turned to the Soviet Union as a trading partner. Congress made the embargo permanent in the 1990s. Congress had actually extended official recognition to Cuba in the wake of Castro's overthrow of Fulgencio Batista, but the State Department cut off all diplomatic ties to the country, with the support of both houses, when the revolutionaries nationalized American industries and executed many of Batista's loyalists..
http://content.time.com/time/nation/article/0,8599,1891359,00.html

After reading the "Slim Greer in Hell," identify, as specifically as possible, what you see as one core reversal in the poem. What expectations—of Slim, St. Peter, Heaven, Hell, "Dixie," The United States, intelligence, or whatever else strikes you—are reversed in Brown's poem? How are they reversed? Point to textual evidence here. Then, reflect on the point of the reversal. How does the reversal present the world differently?

"Slim Greer in Hell" by Sterling A. Brown portrays the titular character's journey into Hell at the request of St. Peter. Once Slim arrives in hell, he is shocked by what he sees: there are bloodhounds chasing African Americans, rowdy cabarnets, a preacher with a brown-skinned woman on each knee, and, most tragically, a giant furnace in which black folks are thrown in. The poem reads:

Den he took him to de furnace
Dat somem devils was firing,
Hot as Hell, an' Slim start
A mean presspirin'.

White devils with pitchforks
Threw black devils on,
Slim thought he'd better
Be gittin' along.

It is interesting to note that while the African Americans are being burned, the white folk continue to have fun.
After Slim returns to heaven to brief St. Peter on his experience in Hell, Slim seems perplexed that he was simply sent to the racist antebellum South. In a shocking reversal of expectations, St. Peter denies Slim entrance into heaven not for a lack of virtues, but for a lack of what he considers intelligence. He insults Slim by saying,

Git on back to de yearth,
Cause I got de fear,
You'se a lettle too dumb,
Fo' to stay up here.

This depiction of St. Peter is a far cry from the solemn figure that guards Heaven's gates and decides who is morally and spiritually fit to enter. In "Slim Greer In Hell," he seems to discipline Slim for his ignorance. This, of course, mirrors the false ideas that existed during the time of this poem's inception that African Americans were inherently less intelligent than whites. Brown seems aware of this stereotype and plays with it, including it in his satirical vision of heaven.
Another important thing to note in "Slim Greer In Hell" is the way the characters speak to one another. The poem uses a style of stereotypical African American speak (also seen in other works of the time, such as Huckleberry Finn and the "Goophered Grapevine"). This style can be seen in any line of the poem. In the beginning of the poem, St. Peter speaks to Slim,

You been travelin' rascal
In yo'day.
You kin roam once mo';
Den you come to stay.

Compare this to the traditional image of St. Peter, particularly his manner of speaking. In religious circles, St. Peter is quoted as saying, "Man's salvation and perfection consist of doing the will of God, which he must have in view of all things and at every moment of his life." Thus, Brown's image of St. Peter speaking colloquially with Slim Greer seems at odds with the typical idea of how St. Peter spoke.
The core reversal in "Slim Greer In Hell" is an interpretation of Hell and Heaven as an extension of racist America. Hell is the South in the days of slavery, the Devil is a racist white sheriff, and St. Peter spites Slim because of his inability to recognize the South as Hell. Brown seems to satirically suggest that Slim Greer is mired in not only a racist country and racist world, but also a racist universe, with Satan and St. Peter himself participating.
Of course, this poem presents the entire world as being a hellish, racist place. It is far different from many poems and art forms that glamorize it (even those that glamorize the slavery-era south): "Slim Greer In Hell" confidently has something to say about the way the world works. Even those in power were frequently racist, and Brown extends this idea to include Heaven and Hell.
https://poets.org/poem/slim-greer-hell

https://www.openbible.info/topics/st_peter_at_heavens_gates

How does Milton make his description of Paradise Lost dramatic?

John Milton's dramatic descriptions in Paradise Lost are effective because they appeal to all of the senses. For instance, Heaven is associated with light and brightness. He describes God's throne as shrouded in a cloudy type of mist because the light that emanates from him is so strong. The contrast to this, of course, is his depiction of Hell as dark. He writes,

As one great furnace flamed, yet from those flames
No light, but rather, darkness visible (I. 62-63).

It is paradoxical that the flames in Hell somehow give off darkness instead of light. Adding to his lurid depiction of Hell is the mention of the sulfuric fumes that attack Lucifer's sense of smell as the flames burn his body.
In book 1, Lucifer rallies his other fallen angels by saying,

Seest thou yon dreary Plain, forlorn and wilde,
The seat of desolation, voyd of light,
Save what the glimmering of these livid flames
Casts pale and dreadful? (I. 180-183).

This description is particularly powerful because Lucifer is admitting their loss of the light of Heaven and he does not make any attempt to glorify their new, painful surroundings. This makes his subsequent statement, that they lift themselves from the "fiery waves" and consider their next move, particularly poignant.
It is Milton's appeal to the senses that makes the descriptions dramatic. He elevates the light and goodness of Heaven in order to contrast it with the darkness and pain of Hell.

What worries were often prevalent in Robert Louis Stevenson's life?

Three major worries for the somewhat melancholic Stevenson were health, his career path, and religion.
Robert Louis Stevenson's health was poor throughout his life. When he was an infant and a young child, he came close to death many times. His family had to hire a nanny to be with him full-time. As a school-aged child, he missed a lot of school because he was confined to bed.  
Stevenson made it to adulthood, but poor health continued to plague him from time to time. As young man, he lost a lot of weight, became depressed, and nearly had a nervous breakdown (more on that later). After Stevenson married, he and his family moved to the Pacific with the hope that the warmer climate would help his health. (He had tuberculosis, a wasting cough, which was not helped by the cold rainy climate in his native Scotland.)
Stevenson died of tuberculosis at age 44. Despite his poor health, he had lived a full life, had many adventures, and wrote prolifically.
Stevenson was a sensitive, intuitive type who seemed born to be a writer. This caused him some worries about the path he would take in life. He came from a family of engineers and lighthouse keepers, and it was expected he would follow in their footsteps. Stevenson could not make himself stay interested in engineering. To please his father (who was a loving parent but also put some pressure on Robert, his only child), Stevenson then earned a law degree. He had no enthusiasm for law either, and by his early twenties, he was writing full-time. His gift was so strong that it could not be restrained.
Finally, religion was a problem for the sensitive Stevenson. His loving parents were Calvinists, a sect of Christianity. Calvinism, with its emphasis on people's inherent sinfulness and inability to save themselves unless God changes their hearts, is considered by many to be a strict and gloomy form of Christianity. When Stevenson was a young man, he was forced into a confrontation with his parents in which he admitted he no longer believed in God. They were bitterly disappointed. The conversation resulted in a long-term strain on the relationship, and cast Stevenson into a depression. It was after this that he came near to having a nervous breakdown. He was saved by the support and listening ear of a few good friends. 
Although Stevenson officially rejected the God of his parents, his outlook on life remained shaped by what he had been taught. The Strange Case of Dr. Jekyll and Mr. Hyde, particularly, shows Stevenson knew well the deceitfulness of the human heart. It is a book that could have been written by a Calvinist. Dr. Jekyll's experience in the book also suggests Stevenson was familiar with dynamics of addiction.
http://robert-louis-stevenson.org/

https://thehumanist.com/magazine/september-october-2015/features/robert-louis-stevenson-says-no-to-religion

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 42

Find $f''(e)$ if $\displaystyle f(x) = \frac{\ln x}{x}$


$
\begin{equation}
\begin{aligned}

\text{if } f(x) =& \frac{\ln x}{x}, \text{ then by using Quotient Rule}
\\
\\
f'(x) =& \frac{\displaystyle x \cdot \frac{d}{dx} (\ln x) - (\ln x) \cdot \frac{d}{dx} (x) }{x^2 }
\\
\\
f'(x) =& \frac{\displaystyle x \left( \frac{1}{x} \right) - \ln x (1)}{x^2}
\\
\\
f'(x) =& \frac{1 - \ln x}{x^2}

\end{aligned}
\end{equation}
$


Again, by using Quotient Rule


$
\begin{equation}
\begin{aligned}

f''(x) =& \frac{\displaystyle x^2 \cdot \frac{d}{dx} (1 - \ln x) - (1 - \ln x) \cdot \frac{d}{dx} (x^2)}{(x^2)^2 }
\\
\\
f''(x) =& \frac{\displaystyle x^2 \left( - \frac{1}{x} \right) - (1 - \ln x)(2x)}{x^4}
\\
\\
f''(x) =& \frac{x(-1 - 2 + 2 \ln x)}{x^4}
\\
\\
f''(x) =& \frac{-3 + 2 \ln x}{x^3}

\end{aligned}
\end{equation}
$


Thus,


$
\begin{equation}
\begin{aligned}

f''(e) =& \frac{-3 + 2 \ln (e)}{e^3}
\\
\\
f''(e) =& \frac{-3 + 2 (1)}{e^3}
\\
\\
f''(e) =& \frac{-1}{e^3}


\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 10, 10.3, Section 10.3, Problem 45

The formula of arc length of a parametric equation on the interval alt=tlt=b is:
L = int_a^b sqrt((dx/dt)^2+(dy/dt)^2) dt
The given parametric equation is:
x=3t + 5
y=7 - 2t
The derivative of x and y are:
dx/dt = 3
dy/dt = -2
So the integral needed to compute the arc length of the given parametric equation on the interval -1lt=tlt=3 is:
L = int_(-1)^3 sqrt(3^2+(-2)^2) dt
The simplified form of the integral is:
L = int_(-1)^3 sqrt13 dt
Evaluating this yields:
L = sqrt13t |_(-1)^3
L = sqrt(13)*3 - sqrt13*(-1)
L=3sqrt13 + sqrt13
L=4sqrt13
Therefore, the arc length of the curve is 4sqrt13 units.

How did the actions of Japan, Germany, and Italy in the first half of the 1930s serve as warning signs of an impending war?

The seeds for the start of World War II were sown by the eventual Axis powers of Japan, Italy, and Germany in the first half of the 1930s. The Western powers, still wearied from World War I, hoped that appeasement would keep the peace, but their reaction only emboldened the dictators into believing that their actions would have no consequences. This led to further aggressiveness later in the decade until the West had no choice but to go to war to stop the Axis powers.
The first action that presaged world war was Japan's invasion of Manchuria in 1931. The Japanese coveted resources on the Chinese mainland and used the pretext of an explosion that destroyed a railway owned by the Japanese to invade the region. The Chinese army was ill-prepared to stop the Japanese, who quickly took control and turned Manchuria into the puppet state of Manchukuo. The West's response was simply not to recognize the new state or any treaties that it made.
Next to test the Western powers was Italy, which decided to resume hostilities with Ethiopia in 1935. The Italians had tried to invade Ethiopia in 1896 but were humiliated in battle. They were determined to win this time and overwhelmed the Ethiopians with modern weaponry. The League of Nations, created after World War I to try to resolve conflicts without warfare, voted to impose sanctions upon Italy for its aggression, but the sanctions were weak, and member nations were lax in enforcing them. The Italians ignored the sanctions and completed their takeover.
Finally, it was Germany's turn to take action. After Adolf Hitler took power in 1933, the Germans had steadily increased its resistance to the restrictions imposed upon it by the Treaty of Versailles that had ended WWI. Finally, in March 1936, the Germans marched into the Rhineland region—an egregious violation of the Treaty, which provided for the region to be a demilitarized buffer zone between Germany and France. If the West had called Hitler's bluff and met might with might, he would have been forced to retreat, as the German army was not yet ready to fight a major conflict with France and England. Instead, the West protested but did nothing else. Hitler learned the same lesson the Japanese and Italians had learned earlier—he could act with impunity with little resistance from the West.
https://history.state.gov/milestones/1921-1936/mukden-incident

https://www.britannica.com/event/Italo-Ethiopian-War-1935-1936

https://www.nationalarchives.gov.uk/education/resources/german-occupation/

College Algebra, Chapter 1, 1.7, Section 1.7, Problem 44

Solve the inequality $\displaystyle 2\left| \frac{1}{2}x + 3 \right| +3 \leq 51$. Express the answer using interval notation.

$
\begin{equation}
\begin{aligned}
2\left| \frac{1}{2}x + 3 \right| +3 &\leq 51\\
\\
2\left| \frac{1}{2}x + 3 \right| &\leq 48 && \text{Subtract 3}\\
\\
\left| \frac{1}{2}x + 3 \right| &\leq 24 && \text{Divide by 2}
\end{aligned}
\end{equation}
$



We have,


$
\begin{equation}
\begin{aligned}
\frac{1}{2}x + 3 &\leq 24 && \text{and}& -\left( \frac{1}{2}x + 3 \right) &\leq 24 && \text{Divide each side by -1}\\
\\
\frac{1}{2}x + 3 &\leq 24 && \text{and}& \frac{1}{2}x + 3 &\geq -24 && \text{Subtract 3}\\
\\
\frac{1}{2}x &\leq 21 && \text{and}& \frac{1}{2}x &\geq - 27 && \text{Multiply by 2}\\
\\
x &\leq 42 && \text{and}& x &\geq -54
\end{aligned}
\end{equation}
$


The solution set is $[-54,42]$

Why is the Constitution important and how does it work?

The United States Constitution is the document that set up our entire system of government.  It tells us the distribution of power amongst the three branches of government and the distribution of power between the federal government and the state governments.  It sets forth the rights and duties of federal government.  It also sets forth the ways that Americans are protected from the government.  In some ways, it could be thought of as the Bible of American government.  It has, in my opinion, created the most successful democracy of all time, recent and current events notwithstanding.
The way the Constitution works is that anyone who thinks that the government is acting in a way that violates it has the right to go to court and seek relief from that violation.  Sometimes it is one branch of government accusing another branch of government of violating the Constitution. Sometimes it is a private organization or a private citizen making that claim. The court decides whether or not that is the case, and if someone in government is violating the Constitution, he or she is ordered to stop doing so.
The court must read the Constitution and interpret it to apply to the case at hand.  Reading it literally is often of no use.  For example, there is nothing in the Constitution that says Congress is supposed to fund interstate highways.  There were no interstate highways when it was written.  But the Constitution has been interpreted to mean that Congress can do this because it is part of our national defense, which Congress is constitutionally responsible for.   In this way, too, the Constitution is like the Bible.  For instance, there is nothing in the Bible about cars, yet observant Jews will not drive on the Sabbath because that has been interpreted to be a form of work, which is forbidden on the Sabbath.  Any document must be read in accordance with the time and place it is meant to be applied to.
I should also say that the Constitution is to some degree a kind of social contract.  The courts do not have soldiers to enforce their orders.  We all agree to abide by the Constitution in order to live in a civilized democracy.  If that social contract breaks down, for example, if a president refuses to abide by a constitutional ruling by the court, the nation and the Constitution are in a great deal of trouble. 

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 72

Use a graphing calculuator to check the results of the function $\displaystyle y = \frac{3x^4 + 2x}{x^3 - 1}$ and its derivative
$\displaystyle y' = \frac{3x^6 - 16x^3 - 2}{(x^3 - 1)^2}$




Based from the graph, we can see that the function has a positive slope or positive derivative when it is increasing.
On the other hand, the function has a negative slope or negative derivative when the function is decreasing.
Also, the function has a zero slope at the minimum and maximum point of the graph.
Moreover, the function is not differentiable at $x=1$ because the function is undefined at that point.

What are some examples of hyperbole in the story "The Interlopers?"

When the author describes the history of the feud between the two families, he notes that Georg and Ulrich wish misfortune on one another. They have continued this inherited feud simply out of tradition and out of a continued personal ill will for one another. But it would be an exaggeration (hyperbole) to say that "they had thirsted for one another's blood." It is possible that their mutual hatred is so great that Georg and Ulrich both wish each other dead, but that does not mean they have an actual cannibalistic thirst for human blood. 
After they become trapped, Ulrich says his men are close behind and will arrive first. Georg says the same thing. Both men are being hyperbolic. Neither Georg nor Ulrich know how long it will be until either party reaches them: 

Both men spoke with the bitterness of possible defeat before them, for each knew that it might be long before his men would seek him out or find him; it was a bare matter of chance which party would arrive first on the scene. 

When Ulrich manages to get a drink of wine, it is described as a "heaven-sent draft." It only seems this good because he is in such a dire predicament and it serves to calm his nerves. Their reconciliation is "dramatic" but this is a fitting description and not really an exaggeration. 

Does the play end in total gloom?

It does indeed, especially for Oedipus, both literally and figuratively. Having gouged his own eyes out, he can't see a thing, and in the metaphorical sense he can't see any kind of way forward either. And it's not hard to see why—he's lost everything: his wife/mother, his kingdom, his reputation. The man is utterly destroyed.
However, there's still a glimmer of hope for Thebes. Now that the terrible truth about Oedipus's sordid past has been revealed, there's a chance for the city and its people to move on under the wise leadership of Creon. That's the theory, at any rate, because as we know from Antigone, Creon proves to be anything but a wise leader. But that's all in the future. For now, the Theban people can get over their troubles and look forward with some degree of confidence to a future without the man who inadvertently brought them so much misery and suffering.

It's pretty doom and gloom in the end. Jocasta has taken her own life, and Oedipus has scratched out his own eyes with the brooches from her robes. His children are revealed to be the monstrous offspring of a mother and son, and everyone now knows that Oedipus killed his own father and then sired children with the same woman who gave birth to him. He has banished himself from Thebes and will now be turned loose into the world, with nowhere to go and no one to comfort him. If there is one even remotely positive thing to come out of these events, it is that Creon, a person who has been revealed to be sagacious and wise, fair and thoughtful, will now rule Thebes. Compassionately, Creon even has Oedipus's daughters brought in to say goodbye to him. He ought to be a good and just ruler to help lead Thebes away from the tragedy of Oedipus and his family.

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 29

Determine the $\displaystyle \lim \limits_{t \to 0} \left( \frac{1}{t \sqrt{1 + t}} - \frac{1}{t} \right)$, if it exists.


$
\begin{equation}
\begin{aligned}

& \lim \limits_{t \to 0} \left( \frac{1}{t \sqrt{1 + t}} - \frac{1}{t} \right)
= \lim \limits_{t \to 0} \frac{1 - \sqrt{1 + t}}{t \sqrt{1 + t}}
&& \text{ Get the LCD.}\\
\\
& \lim \limits_{t \to 0} \frac{1 - \sqrt{1 + t}}{t \sqrt{1 + t}} \cdot
\frac{1 + \sqrt{1 + t}}{1 + \sqrt{1 + t}}
= \lim \limits_{t \to 0} \frac{1 - (1 + t)}{t(\sqrt{1 + t})(1 + \sqrt{1 + t})}
&& \text{ Multiply the numerator and the denominator by $1 + \sqrt{1 + t}$ and simplify.}\\
\\
& \lim \limits_{t \to 0} \frac{-1}{(\sqrt{1 + t})(1 + \sqrt{1 + t})}
= \frac{-1}{(\sqrt{1 + 0})(1 + \sqrt{1 + 0})}
= \frac{-1}{(\sqrt{1})(1+\sqrt{1})}
= \frac{-1}{(1)(2)}
= \frac{-1}{2}
&& \text{ Substitute value of $t$ and simplify}\\
\\
& \fbox{$ \lim \limits_{t \to 0} \displaystyle \left( \frac{1}{t\sqrt{1 + t}} - \frac{1}{t} \right) = -\frac{1}{2}$}


\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 28

Determine the integral $\displaystyle \int \tan^3 (2x) \sec^5 (2x) dx$

Let $u = 2x$, then $du = 2 dx$, so $\displaystyle dx = \frac{du}{2}$. Thus,


$
\begin{equation}
\begin{aligned}

\int \tan^3 (2x) \sec^5 (2x) dx =& \int \tan^3 u \sec^5 u \cdot \frac{du}{2}
\\
\\
\int \tan^3 (2x) \sec^5 (2x) dx =& \frac{1}{2} \int \tan^3 u \sec^5 u du
\\
\\
\int \tan^3 (2x) \sec^5 (2x) dx =& \frac{1}{2} \int \tan^2 u \sec^4 u \sec u \tan u du
\qquad \text{Apply Trigonometric Identity } \sec^2 u = \tan^2 u + 1 \text{ for } \tan^2 u
\\
\\
\int \tan^3 (2x) \sec^5 (2x) dx =& \frac{1}{2} \int (\sec^2 u - 1) \sec^4 u \sec u \tan u du
\\
\\
\int \tan^3 (2x) \sec^5 (2x) dx =& \frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du

\end{aligned}
\end{equation}
$


Let $v = \sec u$, then $dv = \sec u \tan u du$. Thus,


$
\begin{equation}
\begin{aligned}

\frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du =& \frac{1}{2} \int (v^6 - v^4) dv
\\
\\
\frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du =& \frac{1}{2} \left( \frac{v^{6 + 1}}{6 + 1} - \frac{v^{4 + 1}}{4+1} \right) + c
\\
\\
\frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du =& \frac{1}{2} \left( \frac{v^7}{7} - \frac{v^5}{5} \right) + c
\\
\\
\frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du =& \frac{v^7}{14} - \frac{v^5}{10} + c
\qquad \text{Substitute value of } v
\\
\\
\frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du =& \frac{(\sec u)^7}{14} - \frac{(\sec u)^5}{10} + c
\\
\\
\frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du =& \frac{\sec^7 u}{14} - \frac{\sec^5 u}{10} + c
\qquad \text{Substitute value of } u
\\
\\
\frac{1}{2} \int (\sec^6 u - \sec^4 u) \sec u \tan u du =& \frac{\sec^7 (2x)}{14} - \frac{\sec^5 (2x)}{10} + c


\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 5, 5.2, Section 5.2, Problem 10

Estimate $\displaystyle \int^{\frac{\pi}{2}}_0 \cos ^4x dx, n = 4$ using Midpoint Rule

The width of each sub-intervals is given to be $\displaystyle \Delta x = \frac{\displaystyle \frac{\pi}{2} - 0}{4} = \frac{\pi}{8}$. So the endpoints of the four sub-intervals are $\displaystyle 0, \frac{\pi}{8}, \frac{\pi}{4}, \frac{3 \pi}{8}$ and $\displaystyle \frac{\pi}{2}$. Thus, the midpoints are $\displaystyle \left( \frac{\displaystyle 0 + \frac{\pi}{8} }{2}\right) = \frac{\pi}{16}, \left( \frac{\displaystyle \frac{\pi}{8} + \frac{\pi}{4}}{2} \right) = \frac{3 \pi}{16}, \left( \frac{\displaystyle \frac{\pi}{4} + \frac{3 \pi}{8}}{2} \right) = \frac{5 \pi}{16}, \left( \frac{3 \pi}{8} + \frac{\pi}{2} \right) = \frac{7 \pi}{16}$.

Therefore, the Midpoint Rule gives..



$
\begin{equation}
\begin{aligned}

\displaystyle \int^{\frac{\pi}{2}}_0 \cos^4 x dx \approx & \Delta x \left[ f\left( \frac{\pi}{16} \right) + f \left( \frac{3 \pi}{16} \right) + f \left( \frac{5 \pi}{16} \right) + f \left( \frac{7 \pi}{16} \right) \right]
\\
\\
\approx & \frac{\pi}{8} [0.9253 + 0.4780 + 0.0953 + 0.0014]
\\
\\
\approx & 0.5891

\end{aligned}
\end{equation}
$

x=t^2-t+2 , y=t^3-3t Find all points (if any) of horizontal and vertical tangency to the curve.

Parametric curve (x(t),y(t)) has a horizontal tangent when its slope dy/dx is zero, i.e. dy/dt=0 and dx/dt!=0 .
Curve has a vertical tangent if its slope approaches infinity i.e. dx/dt=0 and dy/dt!=0
Given equations of the parametric curve are:
x=t^2-t+2
y=t^3-3t
dx/dt=2t-1
dy/dt=3t^2-3
For horizontal tangents:
dy/dt=0
3t^2-3=0
=>3t^2=3
=>t^2=1
=>t=+-1
Corresponding points on the curve can be found by plugging the values of t in the parametric equation,
For t=1,
x_1=1^2-1+2=2 
y_1=1^3-3(1)=-2
For t=-1,
x_2=2^2-2+2=4
y_2=2^3-3(2)=2
Horizontal tangents are at the points (2,-2) and (4,2)
For vertical tangents,
dx/dt=0
2t-1=0
=>t=1/2
Corresponding points on the curve for t=1/2 are,
x=(1/2)^2-1/2+2
x=1/4-1/2+2
x=(1-2+8)/4
x=7/4
y=(1/2)^3-3(1/2)
y=1/8-3/2
y=(1-12)/8
y=-11/8
Vertical tangent is at the point (7/4,-11/8)
 

Give evidence of the disadvantages and advantages of Hong Kong using a market economic system.

The advantages and disadvantages of free markets are much the same for Hong Kong as they are for anywhere else. In my opinion and that of the vast majority of economists, the advantages outweigh the disadvantages; but we should be honest about the fact that there are real disadvantages for many people.The chief advantage of free market globalization is increased economic efficiency. This benefit must not go unappreciated; it sounds like we're just saying some numbers go up on a graph. But improved economic efficiency means better lives for millions of people. It means more goods for less work, more wealth and less poverty. The expansion of free markets around the globe is the chief reason why global extreme poverty is now at the lowest level it has ever been.The chief disadvantage of free market globalization is increased economic inequality. When we open ourselves to free markets, we make both winners and losers, and as a result some people become much wealthier while others remain the same or may even become poorer. Another disadvantage, particularly applicable to Hong Kong, is volatility. Markets can shift suddenly and randomly, and particularly when a small country is linked by trade to larger countries, GDP can rise and fall dramatically as the tides of global finance change. Hong Kong only has a population of about 7 million, compared to its chief trading partners China and the US with 1.368 billion and 321 million respectively. An economic shock that may feel minor to China or the US could nonetheless have huge effects for Hong Kong. These are indeed the results we've observed. Since they have liberalized their markets (to, by some measures, the freest markets in the world), Hong Kong has seen high economic growth, but also much higher inequality and volatility. Overall Hong Kong is better off, but some people have benefited much more than others, and many people may actually be worse off.
https://www.cia.gov/library/publications/the-world-factbook/geos/hk.html

https://www.globalpolicy.org/component/content/article/218/46552.html

https://www.imf.org/external/np/exr/ib/2008/053008.htm

Discuss the poetry of Thomas Hardy in light of interest in both "chance" and in the indifference of nature. What seems to be his attitude toward war and violence?

One of Thomas Hardy's best-known poems is "Hap," in which the speaker expresses the view that an indifferent universe, one governed by chance, is worse than one ruled by a hostile God. If there were a "vengeful god," he says, "Then would I bear it, clench myself, and die." The theme of randomness and the way it governs the human condition is stated in Hardy's novels as well. Another famous poem is "The Man he Killed," in which a soldier observes that it is mere chance that has made the man he's struck down an enemy, and in the absence of war, the man could have been a friend:

"Yes; Quaint and curious war is!
You shoot a fellow down
You'd treat where any bar is,
Or help to half a crown."

Hardy describes the insanity of war not only here, but perhaps even more effectively in "Channel Firing," written on the eve of World War I. The poem is a dialogue between dead men and God, when the dead are "awakened" in their crypts in a country church by the horrible sound of gunnery practice on the naval vessels in the Channel. At first, they believe the sound is that of the Last Trumpet on Judgment Day, but they are then told by God that man, in his foolishness, is simply planning another round of war and destruction. The dead go back to their rest, saying,

"I wonder,
Will the world ever saner be,"
Said one, "Than when he sent us under,
In our indifferent century!"

Hardy closes the poem with an eerie stanza pointing out that man's reckless behavior is unending, stretching through the millennia:

Again the guns disturbed the hour,
Roaring their readiness to avenge,
As far inland as Stourton Tower,
And Camelot, and star-lit Stonehenge

Why does Phineas say there is no war in 1943

Throughout the novel, the boys attending Devon School prepare to enter World War II following graduation. Despite the constant news covering the war and enthusiasm surrounding America's involvement, Finny purposely denies the existence of a world war. Finny had been by far the best athlete in the school before Gene shook him from a tree and broke his leg. Tragically, Finny never regained his old athleticism and would not be able to enlist in the armed forces like the other boys. Not being able to enlist in the Army torments Finny throughout the novel, and he begins denying the existence of the war. Despite the overwhelming evidence to the contrary, Finny insists that the war is simply a hoax concocted and propagated by wealthy old men. Finny's purposeful denial is his way of psychologically protecting himself. Devastated that he will not be able to participate in the war, Finny finds it easier to pretend that the war does not exist. After Finny breaks his leg for the second time, he admits to Gene in the infirmary why he denied the existence of the war. Finny tells Gene,

I’ll hate it everywhere if I’m not in this war! Why do you think I kept saying there wasn’t any war all winter? I was going to keep on saying it until two seconds after I got a letter from Ottawa or Chungking or some place saying, "Yes, you can enlist with us" (Knowles, 103).

How are the Powerball numbers drawn?

Powerball and other lotteries are often described as a tax on people who are bad at math. In other words, because the state lotteries are used as a source of revenue, on the average you will lose a fixed percentage of money if you buy several tickets. The larger the number of tickets you buy, the more accurately the money you personally lose over time (a figure you can obtain by tracking the cost of tickets and subtracting any winnings and the taxes on those winnings) will track the percentage taken out from the lottery pool to fund state projects.
The actual mechanism which selects Powerball winning numbers is the Halogen machine, manufactured by Smartplay International of Edgewater Park, New Jersey. The numbered balls are mixed in a chamber by a turntable. Randomly selected balls are chosen and sent up through a clear acrylic tube to a display. The machine can be adjusted to draw balls at different intervals and to select different numbers of balls. 

Why can it be said that Hobbes is the founder of modern political liberalism? "For these words of good, evil, and contemptible are ever used with relation to the person that useth them: there being nothing simply and absolutely so; nor any common rule of good and evil to be taken from the nature of the objects themselves." Discuss in detail the ethical and political thought of Thomas Hobbes.

This quote relates to Hobbes's belief in Mechanism, a view that everything in the universe is explained by the interactions of material objects. Mechanism related to the idea of materialism, which is that there is only one substance in existence in the world. The theories of Mechanism and materialism, which Hobbes helped to explain and expound, were opposed to the philosophy of dualism, which stated that there were two distinct substances of things in the world. An example of dualism is Descartes's idea of the separation of the mind and the body.
Hobbes believed that all human actions and emotions originate in bodily actions,  which are referred to as endeavors. In turn, all these bodily actions can be traced to universal laws that govern the mechanical workings of the universe. Therefore, there is a strong and direct connection between the social and psychological world and the physical world, in Hobbes's view. In the passage above, Hobbes expresses his view that there is nothing that is inherently good or evil; instead, the world is objectively neutral, and it is people who give things in the world their subjective quality. Therefore, Hobbes was a relativist in terms of ethics.
Hobbes can be seen as a founder of modern liberal theory (though others think of him as a totalitarian) because he believed that man is born into a state of nature in which he enjoys a certain degree of liberty. People give up this liberty to enter into a social contract with a ruler, but they have the right to reject the ruler if the ruler violates the protections the ruler must adhere to. Hobbes's belief in humans' right to a certain degree of liberty marks him in some ways as a liberal. 

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 62

Determine the $\displaystyle \lim_{x \to 1} (2-x)^{ \tan \left( \pi x/ 2\right) }$. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.

If we let $\displaystyle y = (2-x)^{ \tan \left( \pi x/ 2\right) }$, then

$\displaystyle \ln y= \tan \left( \frac{\pi x}{2} \right) [ \ln (2-x)]$
So,
$\displaystyle \lim_{x \to 1} \ln y = \lim_{x \to 1} \tan \left( \frac{\pi x}{2} \right) [\ln (2-x)]$
$\displaystyle \lim_{x \to 1} \tan \left( \frac{\pi x}{2} \right) [\ln (2-x)] = \lim_{x \to 1} \frac{\ln(2-x)}{\cot \left( \frac{\pi x}{2} \right)}$

By applying L'Hospital's Rule...

$
\begin{equation}
\begin{aligned}
\lim_{x \to 1} \frac{\ln(2-x)}{\cot \left( \frac{\pi x}{2} \right)} &= \lim_{x \to 1} \frac{\frac{-1}{2-x}}{-\csc^2 \left( \frac{\pi x}{2} \right) \cdot \frac{\pi}{2}}\\
\\
&= \lim_{x \to 1} \frac{2}{\pi(2-x) \csc^2 \left( \frac{\pi x}{2} \right)}\\
\\
&= \frac{2}{\pi} \lim_{x \to 1} \frac{1}{(2-x)\left( \frac{1}{\sin^2\left( \frac{\pi x}{2} \right)} \right)}\\
\\
&= \frac{2 }{\pi} \lim_{x \to 1} \frac{\sin^2 \left( \frac{\pi x}{2} \right)}{(2 -x)}\\
\\
&= \frac{2}{\pi} \cdot \frac{\sin^2\left( \frac{\pi(1)}{2} \right)}{2-1}\\
\\
&= \frac{2}{\pi} \cdot \frac{\left( \sin \frac{\pi}{2} \right)^2}{1}\\
\\
&= \frac{2}{\pi} \cdot \frac{1}{1}\\
\\
&= \frac{2}{\pi}
\end{aligned}
\end{equation}
$

Thus, $\displaystyle \lim_{x \to 1} \ln y = \lim_{x \to 1} \tan \left(\frac{\pi x}{2} \right) [\ln(2-x)] = \frac{2}{\pi}$
Therefore, we have

$\displaystyle \lim_{x \to 1} (2 -x)^{\tan \left( \pi x/2 \right)} = \lim_{x \to 1} e^{\ln y} = e^{2/\pi}$

Why does Monsieur Loisel go to so much trouble to get an invitation to the party at the Ministry?

In "The Necklace," Madame Loisel is a woman who is unhappy with her position in life and desires more than she has. Feeling that she is entitled to every "delicacy and luxury" instead of her meager possessions, Madame Loisel longs to be the object of others' envy. Her husband, Monsieur Loisel, brings home an invitation to a fancy party hoping it will bring happiness to his wife. However, instead of the excitement he hopes for, Monsieur Loisel only manages to upset his wife. He explains that he had "tremendous trouble" in obtaining the invitation, because invitations were not given to many clerks. He goes through the trouble because he realizes his wife does not often go out, and he hopes to please her. Instead of being happy or excited, Madame Loisel tosses the invitation aside and instructs her husband to give the invitation to someone with a wife who has something suitable to wear.

What events saved Jamestown from destruction?

Jamestown, as with other early European colonies, suffered greatly at its inception. Disease, starvation, droughts, lack of agricultural skills, and intermittent Indian attacks made the colonists' existence precarious. Captain John Smith proved a decisive leader and was adept at trade, which kept the colony afloat in its early years. However, from its founding in 1607 through 1610, the colony was at risk, as attacks by Indians intensified, and starvation drove some to cannibalism. The colony would continue to suffer from food shortages and Indian attacks, although peace was established for several years through the marriage of colonist John Rolfe to Pocahontas, daughter of local Indian chief, Powhatan. 
If the population continued to drop, how could the population replenish itself? Although children were born at the colony, what really kept it afloat in its early years was its financial backer, The Virginia Company. The company was determined to make a profit and continuously resupplied the colony with material and people until its charter was revoked in 1624, when Jamestown became a crown colony. By this time, the colony had secured enough of a foothold that it expanded and eventually became self-sufficient.
There was no singular event that saved Jamestown. Yes, the actions of the colonists kept the colony from collapsing, particularly after 1610 when starvation and attacks by local Indians reduced the population sharply. But it was also the work of The Virginia Company to make sure that the colony survived through replenishing the population. And this latter point is often missed. To become a colonist was a huge gamble. The vast majority would never return and they were more than likely putting their lives at risk. However, people continued to take that risk. In the end, it was the work of colonists in Jamestown, as well as those willing to become colonists, that ensured the colony's survival.
https://www.smithsonianmag.com/history/starving-settlers-in-jamestown-colony-resorted-to-cannibalism-46000815/

y = x/ln(x) Locate any relative extrema and points of inflection.

Find the extrema and points of inflection for the graph of y=x/(lnx) :
Extrema can only occur at critical points, or where the first derivative is zero or fails to exist.
Note that the domain for the function is x>0, x ne 1 .
y'=(lnx-1)/(lnx)^2 This function is defined for all x in the domain so we set it equal to zero. Note that a fraction is zero if the numerator, but not the denominator, is equal to zero.
lnx-1=0 ==> lnx=1 ==> x=e . For 1e it is positive, so the only extrema is a minimum at x=e.
Any inflection point can only occur if the second derivative is equal to zero.
y''=((ln^2x)/x+(2lnx)/x)/(ln^4x) or
y''=(2+lnx)/(xln^3x) Which is negative for x<1, and positive for x>1. The graph is concave down on 01, but x=1 is undefined so there are no inflection points.
The graph:

In "The Cold Equations," what details open Marilyn's eyes to the harshness of life on the space frontier?

As she converses with the EDS pilot, Marilyn learns that there are few colonies and exploration parties on the space frontier. Additionally, these are scattered in remote locations across the wide expanse. In Woden itself, there are only sixteen men living there. Everyone living on colonies has to acclimate to strange environments and to work against all odds to prepare the way for newcomers.The unpredictable weather also makes life harsh on the space frontier.
For example, a tornado materialized seemingly overnight out of the Western Sea; it wrecked extensive damage at Camp One on Woden. Half of the prefabricated buildings were destroyed, including the one that housed all the medical supplies, and six men were killed. The inhabitants of Camp One found themselves powerless against the "blind and mindless force" of nature.

Since most of the space frontier represents uncharted territory, there is very little margin for error. Because the medical supplies were destroyed, the remaining survivors need a fresh delivery of kala serum. Six men on Woden have already been stricken with the kala fever, and their lives depend upon a prompt delivery by the EDS. Since EDSs (or Emergency Dispatch Ships) can only carry a limited amount of fuel, the fuel is always rationed with care. The computers must consider "the course coordinates, the mass of the EDS, and the mass of pilot and cargo." No extra weight can be admitted onto the ship once these calculations have been made.
Any extra weight (such as an extra person like Marilyn) will doom the lives of all those on board. Additionally, the lives of the six men on Woden who have been stricken with the kala fever will be forfeit. These details open Marilyn's eyes to the harshness of life on the space frontier.


Additional fuel would be used during the hours of deceleration to compensate for the added mass of the stowaway, infinitesimal increments of fuel that would not be missed until the ship had almost reached its destination. Then, at some distance above the ground that might be as near as a thousand feet or as far as tens of thousands of feet, depending upon the mass of ship and cargo and the preceding period of deceleration, the unmissed increments of fuel would make their absence known; the EDS would expend its last drops of fuel with a sputter and go into whistling free fall. Ship and pilot and stowaway would merge together upon impact as a wreckage of metal and plastic, flesh and blood, driven deep into the soil.


 
 

What was a major result of the plague on the medieval social system?

The Black Death cut a vast swathe across the European continent, claiming the lives of almost 60 percent of the population. As one can imagine, this had a devastating impact on society. Most people at that time lived off the land, and huge tracts of the countryside became depopulated in the wake of the plague. Among other things, this meant that landowners found it hard to find enough peasants to bring in the harvest. Whole villages emptied, not just as a result of death and disease but also from economic migration.
The decline of the countryside, combined with the growth of towns and cities, severely undermined the power of the nobles. In turn, this gave kings, princes, and other rulers much greater power and authority than they'd previously enjoyed. Prior to the Black Death, kings often found themselves entangled in bitter conflicts with their nobles. But the great plague that wrought such devastation on Europe changed all that, leading to the demise of feudalism and the rise of absolute monarchies.

In "Strangers," how does Toni Morrison address the concept of "otherness" and "outsiders," and how might this idea of otherness manifest in the marginalization of groups and individuals in society?

"Strangers," an essay by Toni Morrison, addresses the concepts of "otherness" and "outsiders" with a personal anecdote.
The anecdote begins with Morrison seeing a woman fishing in her neighbor's garden. Morrison explains that her first feelings towards the woman are welcoming. The woman is using a homemade fishing pole and wearing "a man's hat, a well-worn colorless sweater, and a black dress." Upon viewing the stranger's attire, "a feeling of pleasantness washes over [Morrison]." As she talks to the woman, she does not question the woman's claims about herself: Morrison accepts them as factual. The woman says that her name is "Mother Something," that she lives in a "nearby village," and that she has permission from Morrison's neighbor to fish catfish and eel out of that particular pond as often as she likes. Morrison says that the woman seems "witty and full of the wisdom that older woman seem to have a lock on." She expects to see more of the stranger, to even invite her into her own home to become better acquainted.
Unfortunately, she does not see the woman again, and soon discovers that the stranger lied about herself. She was not given permission to fish in the pond—Morrison's neighbor does not know who the woman is. No one else in their community seems to know who the woman is either; no one has even heard of "Mother Something." Soon, Morrison's pleasant, welcoming feelings turn into feelings of "annoyance" and "bitterness." Morrison is annoyed because the woman had used notions of "female camaraderie" to deceive her; she is bitter because the interaction illuminated the shame of otherness for her.
To understand the shame of otherness Morrison identifies in her essay, it helps to compare the anecdote to Jean Paul Sartre's concept of the "Other." Sartre theorized that people perceive others as if peeping through a key hole in a door. In such scenarios, the complex person being viewed is interpreted as an objectified body. When Morrison first spotted the woman, she held preconceived notions about who the stranger should be, and these notions influenced her gaze. When she viewed the stranger's clothing, Morrison interpreted the woman as an object that molded to those preconceived notions of the stranger's identity.
Sartre explains that there is a certain shame that comes when held in the "gaze" of another. A person might understand another person as one dimensional, judging the other to be defined by one or two attributes that they noted while "peeping." For example, one might judge another person as "shy" when gazing upon them in a moment of displayed insecurity. How one exists in the mind of others cannot be changed, which brings about a feeling of shame.
Morrison felt bitter because she had held this stranger—this "Other"—in her gaze. Her gaze limited the woman's personal identity, and she realized bitterly that the woman had done the same to her. In other words, Morrison is bitter—not because of guilt for her own objectification of the stranger, but because she felt the shame of objectification herself.
As the anecdote in "Stranger" illustrates, the Other is interpreted through "images, language, and experience." Morrison explains how images and language manifests as a control dynamic:

These two godlings, language and image, feed and form experience. My instant embrace of an outrageously dressed fisherwoman was due in part to an image upon which my image of her was based. I immediately sentimentalized and appropriated her. I owned her and wanted to (and I suspect she glimpsed it). I had forgotten the power of embedded images and stylish language to seduce, reveal, control. Forgot too their capacity to help us pursue the human project—which is to block the dehumanization of others.

Examples of Morrison's experience can also be identified in the images, language, and experience that are communicated in visual mediums; these representations also have a tendency to marginalize the "Other."
Consider, for example, portrayals of the poor in popular media. The poor are often described as dangerous, criminally minded, child abusers, and alcoholics: generally lacking "wholesome values" altogether. If, however, poor characters don't have these identity-limiting stock characteristics, then the plot usually turns to elevate them to a higher class through some miraculous means of material gain.
Consider, for instance, the films Good Will Hunting and Pretty Woman. In both films, the characters are represented through the gaze of a person from a more privileged class. Viewers experience the "gaze" of the wealthier characters, perceiving impoverished characters from this privileged perspective, which alters the point of view, images perceived, and dialogue exchanged. The "gaze" determines that the poor characters in both films possess attributes that make them "worth helping," and so they are rewarded.
In these instances, there are several techniques utilized through visual storytelling and dialogue to illustrate that, while these characters are poor, they are still "valuable." First, film viewers are shown that these poor characters do not deserve their circumstances. Misfortune has dealt them an unjust hand. It is no fault of their own. Second, the audience is shown that these types of characters are "valuable" people. Will is "wicked smart," and therefore deserves the education that will allow him to contribute to society. Vivian has kept at least some part of herself withheld and chaste (she reserves the intimacy of a kiss from the men she has serviced), and therefore possess a higher "moral value" than other prostitutes in the film; the emotional intimacy she withholds in the form of a kiss qualifies her to be rescued by her "white knight" from her life of sexual bondage.
Ultimately, the media's attempt to represent the plight of the poor limits the complexity of our understanding of the poor. These representations marginalize the poor into acceptable versions of strangers that we can understand and control, just like Morrison experienced in her interaction with the woman in "Strangers."

In Toni Morrison's essay, "Strangers," the author explores the notion of strangers, folks we do not know, and their impact on our psyche. She uses an example of a fisherwoman as a stranger who intrigues her by her dress and her witty conversation. After the meeting, Morrison looks forward to meeting the stranger again. However, that meeting never takes place, and the author feels both betrayed and disturbed by this experience (para 4) as she has envisioned many more interesting visits with this woman. Morrison created her own image of this stranger, and the stranger failed to live up to her expectations.
Morrison goes on to postulate that we tend to mold strangers into our image of them. These images, combined with language, "saying, listening, reading" (para 5), form the basis of our experience. It is through this reasoning that Morrison explores the notion of otherness. That is, our created images can blur our vision and shape others into what they may or may not prove to be in reality. This complex idea can result in dehumanizing individuals resulting in their marginalization from the rest of society.

Toni Morrison’s essay “Strangers” was written as an introduction to the book A Kind of Rapture by Robert Bergman. Morrison’s piece explores the judgments we all form about strangers before getting to know them. The assignment topic of otherness and marginalization will give you plenty to discuss about this text.
In planning your essay, first decide what your claim will be on theme of otherness and marginalization. Because this essay needs to be five to seven pages in length, determine an organizing principle around which to build your essay. For example, you may want to examine the three elements of language, image, and experience that Morrison says are the ways humans “access” each other.
Phrase your thesis in one or two sentences in the introduction, being as clear and specific as possible. In your introduction, be sure to include the author’s name and title of the text you are analyzing. It is also a good idea to preview the main points you will discuss. Try beginning your introduction with an idea that shows the importance of the topic. For example, you may want to speak about the idea of otherness, connecting this theme to a broader context and illustrating why this issue is significant.
The part of the prompt asking how the idea of otherness is manifested in the marginalization of people in society seems to be open to your own interpretation, rather than strictly analyzing just the “Strangers” text. This would be a good opportunity to incorporate your other sources to support your argument. I recommend using specific examples from historic or current events that illustrate how different groups have been marginalized. Another possibility of an outside primary source would be to discuss the line that Morrison references from Jean-Paul Sartre’s No Exit: “Hell is other people,” an idea that directly ties in to the topic of otherness.

Theme is clear and distinguishable to the reader. Example given to support theme ideas in the reading.

Meeting at the Crossroads by Lyn Mikel Brown and Carol Gilligan has a clear theme, namely, how girls moving from childhood into adolescence become increasingly less free in their actions and communication due to social pressure. What is most important here is that they are primarily concerned with how their peers and the media affect girls' behavior. While some feminists focus on the patriarchal elements being present in overt political structures, Brown and Gilligan argue that the forces involved are more ubiquitous and diffuse.
In writing a paper about a single theme in the book, one might to choose "likability." One of the major motivations in the ways the girls censor themselves is the desire to be liked or popular. This can mean refraining from self-assertion, expressing ideas tentatively, "playing dumb," and otherwise internalizing a need to be "nice" in a manner that not only suppresses girls' own feelings and ideas but also makes them appear weaker, more passive, and less competent. 
The authors use close observation and case studies of a small number of girls at a private girls' school to study this effect. This means that the girls are in a classroom environment dedicated to fostering women's excellence and are not directly competing with or for boys. Instead, they are internalizing and policing a patriarchal ideology themselves. 
One of the most telling examples is the parable of the moles and the porcupine, which serves as a symbolic way of measuring how Jessie negotiates the tension between independent thinking and outspokenness and the need to be "nice" to be socially accepted. 
Sonia's example shows a case where family support can lend strength to a young girl and help her form a strong and independent identity. Nonetheless, we see that Sonia's freedom at home and independence of thought can lead her into awkward relationships with the other girls and social conflicts. She advocates for the need to be assertive, but she laments the way other girls may disapprove of displaying rational thinking and assertive action when it does not conform to the oppressive standard of "niceness." Perhaps the most tragic example is that of Liza, whose attempts at social conformity are partially responsible for her descent into anorexia. 
One way to conclude this sort of thematic analysis might be to look at the present, where women in politics and business are still described as facing a "likability/competence trade-off." The pressure for girls to appear "nice" or "likable" forces them to appear less competent and vice versa. Thus, we can argue that this work by Brown and Gilligan illuminates a theme of how the ideology of female "niceness" impedes not only the social lives of girls, but also women's careers.
https://hbr.org/2013/04/for-women-leaders-likability-a

Calculus of a Single Variable, Chapter 2, 2.2, Section 2.2, Problem 65

The original equation will intersect a point on the tangent line.
Set both equations equal to each other.
k/x = -3/4 x +3
We have 2 unknowns and 1 equation.
Take the derivative of f(x) in order to find another relationship between k and x.
f(x)=k/x
f(x)=kx^(-1)
f'(x) = -kx^-2
f'(x)=-k/x^2
Substitute the slope -3/4 into f'(x) .
-3/4=-k/x^2
Cross multiply.
3x^2=4k
k=(3x^2) /4
Substitute k back to the original equation to solve for x.
k/x = -3/4 x +3
k* 1/x = -3/4 x +3
((3x^2)) /4 * 1/x = -3/4 x +3
3/4 x= -3/4 x+3
6/4 x = 3
3/2 x = 3
3x = 6
x=2
Substitute the x value back to .
k=(3(2)^2) /4 = (3*4) /4
The answer is: k=3

Why does Paul get kicked off the Lake Windsor Middle School soccer team?

Essentially, Paul gets kicked off the Lake Windsor Middle School soccer team because his disability prevents him from being covered under the school's accident insurance plan.
Insurers often won't cover disabled students without charging higher premiums for such players. Meanwhile, other insurers may decline to insure a school sports team altogether, if any number of students on the team have egregious disabilities.
To explain, many schools must purchase sports insurance today, and some even purchase catastrophic accident insurance. Both pay for injuries sustained during the playing of a sport; however, the second pays for medicals costs above a certain amount, usually in the millions of dollars.
So, why is sports insurance necessary? The answer is that sports insurance protects schools from expensive lawsuits, in the event that a student is injured. Injured students may sustain economic and non-economic damages, such as physical injuries, permanent impairment, and emotional suffering. To recuperate their costs, they may sue the school.
In Paul's case, Lake Windsor Middle School simply does not want to risk being declined for insurance. Depending on the disability, sports insurers may decline to insure a student or even the entire team. In their opinion, Paul's disability (visual impairment) is a liability, potentially exposing him to more injuries than the typical student.
So, despite Paul's ability to play (and play well), his supposed visual handicap status on the IEP (which Paul's mom filled out) is a significant mark against him.

Paul is visually impaired and, as such, is on an IEP at Lake Windsor Middle School. One day, Paul gets all excited because he thinks that Coach Walski's called him over to tell him how impressed he was with his goalkeeping abilities. Unfortunately, the coach has some bad news for Paul—he's not allowed to play soccer for the school; he's no longer eligible. The problem is that every child on the program has to be insured; it's a legal requirement. As Paul has such a serious visual impairment, there's no way that the insurance company would provide coverage. And just one child without insurance coverage would be enough to end the program altogether. Paul's devastated at the news. As far as he's concerned, he can see well enough to be a good goalie. But it's no use; the rules are the rules and nothing can be done to change them. So Paul's off the team.

College Algebra, Chapter 8, Review Exercises, Section Review Exercises, Problem 32

Identify the type of curve which is represented by the equation $\displaystyle \frac{x^2}{12} + \frac{y^2}{144} = \frac{y}{12}$.
Find the foci and vertices(if any), and sketch the graph

$
\begin{equation}
\begin{aligned}
12x^2 + y^2 &= 12 y && \text{Multiply by } 144\\
\\
12x^2 + y^2 - 12y &= 0 && \text{Subtract }12y \\
\\
12x^2 + y^2 - 12y + 36 &= 36 && \text{Complete the square: Add } \left( \frac{-12}{2} \right)^2 = 36\\
\\
12x^2 + (y - 6)^2 &= 36 && \text{Perfect square}\\
\\
\frac{x^2}{3} + \frac{(y-6)^2}{36} &= 1 && \text{Divide by } 36
\end{aligned}
\end{equation}
$

Since the equation is a sum of the squares, then it is an ellipse. The shifted ellipse has the form $\displaystyle \frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$
with center at $(h,k)$ and vertical major axis. It is derived from the ellipse $\displaystyle \frac{x^2}{3} + \frac{y^2}{36} = 1$ with center at origin by
shifting it $6$ units upward. Thus, by applying transformation

$
\begin{equation}
\begin{aligned}
\text{center } & (h,k) && \rightarrow && (0,6)\\
\\
\text{vertices:major axis } & (0,a)&& \rightarrow && (0,6) && \rightarrow && (0,6+6) && = && (0,12)\\
\\
& (0,-a)&& \rightarrow && (0,-6) && \rightarrow && (0,-6+6) && = && (0,0)\\
\\
\text{minor axis } & (b,0)&& \rightarrow && (\sqrt{3},0) && \rightarrow && (\sqrt{3},0+6) && = && (\sqrt{3},6)\\
\\
& (-b,0)&& \rightarrow && (-\sqrt{3},0) && \rightarrow && (-\sqrt{3},0+6) && = && (\sqrt{3},6)
\end{aligned}
\end{equation}
$

The foci of the unshifted ellipse are determined by $c = \sqrt{a^2 - b^2} = \sqrt{3c - 3} = \sqrt{33}$
Thus, by applying transformation

$
\begin{equation}
\begin{aligned}
\text{minor axis } & (0,c)&& \rightarrow && (0,\sqrt{33}) && \rightarrow && (0,\sqrt{33}+6) && = && (0,6+\sqrt{33})\\
\\
& (0,-c)&& \rightarrow && (0,-\sqrt{33}) && \rightarrow && (0,\sqrt{33}+6) && = && (0,6-\sqrt{33})
\end{aligned}
\end{equation}
$

Therefore, the graph is

What are the different approaches to the study of political science?

Political science studies political processes, institutions, and behavior to attempt to understand the political environment both in the present and historically. An approach to political science should be capable of describing what exists, explaining why it exists, and predicting what might exist in the future. Historically, however not all approaches have always done all three of these things.
For instance, Plato's approach to political science is called a Normative approach. Plato skipped the describing and explaining steps in order to spend his energy dreaming of what he thought a perfect world would be like. Many other political philosophers, including Rousseau and More, also used this approach.
As the desire to describe and explain emerged, approaches which relied on analyzing the state, its institutions, and its laws became popular. These approaches consider past and present to analyze what has been in order to determine what could be. These approaches are considered Traditional ways of looking at political science.
These traditional approaches had gaps as well, however, and the modern age has brought more kinds of questioning into the mix, by expanding its study to include more than just political institutions themselves. Modern approaches seek to understand the people who participate with the political system and the environments they live in in order to see how these things affect the system as a whole.

In order to properly understand the different approaches to the study of political science, we have to first break the topic down into two general categories: modern and traditional. And then each of those has its own subcategories.
Let's first explain the difference between modern and traditional. Then we'll break these down into more specific categories.
Traditional approaches to political science focus on the study of the government. How does the government function? How is it organized? What would an ideal state look like? These are questions that this approach would address. This traditional approach is idealistic and more concerned with history than science.
There are four kinds of traditional approaches:

Philosophical. This is the oldest approach, with roots in the philosophies of Plato and Aristotle. It's idealistic and concerned with ethics, with what is good and bad in a state or society. This approach focuses on the establishment of an ideal government with a standard set of values and social norms.

Historical. As the name suggests, this approach is based on the idea that we can only understand the present political situation by considering the past. Machiavelli is a famous proponent of this way of thinking, as he believes that history and politics are intricately and inextricably linked.

Legal. This approach is based on the idea that the government is meant to create and enforce laws. The legal process and how justice is served are key concerns of this approach. Examples of thinkers who embodied this approach include Cicero and Jeremy Bentham.

Institutional. This approach is concerned with the formal branches and structures of government: political parties, legislature, the judicial system, and so on. In this approach, the organization of political institutions is of critical importance. Like the philosophical approach, it has roots in the philosophy and teachings of Aristotle.
Now, onto modern approaches.
Modern approaches to political science are, in part, a reaction to the traditional approaches discussed above. Contemporary thinkers introduced these approaches to fill in the gaps left by the traditional approaches in use for so many years.
What are those gaps? Well, traditional approaches are focused on history and formal structures. Modern approaches, in contrast, embrace a multidisciplinary way of thinking, and they embrace science more than history. They're not just focused on empirical data, but on what we can extrapolate from that data.
There are two key subcategories under the general category of modern approaches:

Behavioralism. Initiated by David Easton, this approach is all about predicting what will happen based on what has already happened (i.e., using empirical data to draw conclusions, as I mentioned above.) The idea is that we can observe and make generalizations about political behavior and that those generalizations can help us figure out what to expect in future political situations.

Post-Behavioralism. Modern approaches are a reaction to traditional approaches, and post-behavioralism, in turn, is a reaction and a reform (and, in some ways, a continuation) to behavioralism. The post-behavorialist approach is based on the notion that behavioralists were too focused on methods and techniques and that not every problem can be neatly solved. Not every future situation can be predicted by generalizations and stereotypes, post-behavioralists argue.

Calculus of a Single Variable, Chapter 9, 9.7, Section 9.7, Problem 14

Maclaurin series is a special case of Taylor series that is centered at a=0 . The expansion of the function about 0 follows the formula:
f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n
or
f(x)= f(0)+(f'(0)x)/(1!)+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +...
To determine the Maclaurin polynomial of degree n=5 for the given function f(x)=e^(-x) , we may apply the formula for Maclaurin series..
To list f^n(x) , we may apply derivative formula for exponential function: d/(dx) e^u = e^u * (du)/(dx) .
Let u =-x then (du)/(dx)= -1
Applying the values on the derivative formula for exponential function, we get:
d/(dx) e^(-x) = e^(-x) *(-1)
= -e^(-x)
Applying d/(dx) e^(-x)= -e^(-x) for each f^n(x) , we get:
f'(x) = d/(dx) e^(-x)
=-e^(-x)
f^2(x) = d/(dx) (- e^(-x))
=-1 *d/(dx) e^(-x)
=-1 *(-e^(-x))
=e^(-x)
f^3(x) = d/(dx) e^(-x)
=-e^(-x)
f^4(x) = d/(dx) (- e^(-x))
=-1 *d/(dx) e^(-x)
=-1 *(-e^(-x))
=e^(-x)
f^5(x) = d/(dx) e^(-x)
=-e^(-x)
Plug-in x=0 , we get:
f(0) =e^(-0) =1
f'(0) =-e^(-0)=-1
f^2(0) =e^(-0)=1
f^3(0) =-e^(-0)=-1
f^4(0) =e^(-0)=1
f^5(0) =-e^(-0)=-1
Note: e^(-0)=e^0 =1 .
Plug-in the values on the formula for Maclaurin series, we get:
f(x)=sum_(n=0)^5 (f^n(0))/(n!) x^n
= 1+(-1)/(1!)x+1/(2!)x^2+(-1)/(3!)x^3+1/(4!)x^4+(-1)/(5!)x^5
= 1-1/1x+1/2x^2-1/6x^3+1/24x^4-1/120x^5
= 1-x+x^2/2-x^3/6+x^4/24 -x^5/120
The Maclaurin polynomial of degree n=5 for the given function f(x)=e^(-x) will be:
P_5(x)=1-x+x^2/2-x^3/6+x^4/24 -x^5/120

What does the heron symbolize in "Night Calls" by Lisa Fugard?

Symbolism can be very subjective and tricky to discern, and there might not be a single answer that suffices to express the symbolic subtext of a work of literature. In any case, here are my own thoughts concerning this question.
"Night Calls" is a story that is very much about death and loss, with the protagonist and her father having had their lives reshaped by the protagonists's mother's death. But in the aftermath of that tragedy, the heron was brought to the sanctuary, and the father was tasked with rehabilitating it. In many respects, the heron is what keeps her father at the sanctuary.
Symbolically, the heron ties together themes of life and death as well as past and future. The heron is one of the last of its species, but they hope that, if it finds a mate, then the species might be preserved. In its early years at the sanctuary, it was a beacon for tourism, but by the time that the story takes place, public interest in the bird has long since waned. It is also interesting that it ties together themes of beauty and ugliness—with the bird, at one point, described as:

a large gray bird, with ugly hooked feet, a long slithery neck that gave me nightmares, and a red crest that was raised during the courtship ritual.

In this sense, I would suggest that the heron represents the paradoxes and tensions which make up and often define life and death and the ways that these tensions are often intertwined with one another. This is also reflected in the story's ending: the heron dies while life for the father and daughter goes on.

The heron symbolizes both hope and the transient nature of life.
In the story, Marlene's mother dies in a car accident before Marlene turns eight. The loss is devastating to Marlene, as her mother had been both her beloved parent and tutor. At the time, Marlene's father had wanted to leave the sanctuary altogether; it was too painful to continue living there.
However, in due time, a red-crested night heron is brought to the sanctuary; the National Parks Board wants the heron to be kept at Modder River until a mate can be found for it. So, Marlene is sent to boarding school, while her father tends to the heron's welfare. During school vacations, Marlene returns to the Modder River Wildlife Sanctuary to visit her father. As the warden of the sanctuary, Marlene's father is responsible for all the animals there. Marlene notices that, as time progresses, her father becomes almost enthusiastic about life. Here, the heron symbolizes hope to Marlene and her father; it represents healing and a new beginning.
During the holidays, Marlene's father shares with her the latest news about the heron. He even shows her the South African 37-cent stamp bearing the heron's image. For a time, the bird becomes the chief attraction at the wildlife sanctuary. Visitors come, and Marlene's father chats with them about the bird. Eventually, however, public interest evaporates, as the prospect of finding a mate for the heron diminishes.
In the end, Marlene's father decides to release the heron back to the wild; however, he neglects to tell the truth to Marlene and instead, explains that a hyena had probably gotten the best of the heron. Marlene never lets on that she had witnessed him taking the heron down to the river one night. It remains a cherished secret between them. Each evening, both father and daughter privately savor listening to the heron's night calls.
Yet, as fate will have it, the heron dies, presumably because it was attacked by a wild animal. With the death of the heron, the night calls stop, reinforcing the notion of the heron as a symbol of ephemeral (transient) life. For a time, the heron gives hope to Marlene's father, and he finds a purpose in caring for it. However, in returning it to the wild, he also delivers the heron to the whims of nature.
Its fate mirrors that of his wife's fate; both the heron and his wife are subject to events beyond their power to control. So, the heron symbolizes initial hope and new beginnings for Marlene and her father, but it also represents the transient nature of life when it succumbs to nature's demands.
 
 
 
 

Which aspects of the prioress would Chaucer most likely find disagreeable?

In order to understand Chaucer's attitude toward Prioress Madame Eglentyne as he depicts her in the General Prologue to The Canterbury Tales (ca. 1380-1392 CE), we need to understand the Tales is both an example of satire and the frame narrative. The frame is the pilgrims' journey to visit the tomb of Thomas Becket in Canterbury. More importantly, the poem is also an example of Medieval Estates Satire; that is, satire aimed at the three estates, roughly equivalent to social classes: 1) the Church and clergy; 2) the nobility (those who fought to protect society); and 3), everyone else, which included the peasantry and, later, the middle classes.
As your question implies, Chaucer finds the representatives of the First Estate—beginning with the Prioress—to be less-than-perfect representatives of their class. Chaucer's opening description of the Prioress begins his damnation of her by faint praise:

Ther was also a Nonne, a Prioresse
That of hir smylyng was ful symple and coy;
. . . And she was cleped Madame Eglentyne.
(There was also a nun, a prioresse, who smiled simply and quietly, and her name was Madame Eglentyne)

This begins Chaucer's description of a woman, the head of a convent, who seems to be part of the Second Estate, the nobility, rather than the Church. Rather than taking a name typical of nuns, the Prioress has a name one associates with women of the nobility, and her title—Madame—is not appropriate for a Prioress.
Madame Eglentyne also speaks French, although Chaucer makes it clear she speaks dialectal French (French as it is learned and spoken in England) rather than the preferred French of Paris, poking fun at Madame Eglentyne's pretensions to nobility. By this time, when English had become the language of common speech, speaking French was an affectation, not a necessity. Chaucer's portrait is of a church representative who seems to be confused as to which estate she represents.
In addition to having impeccable table manners, Madame Eglentyne travels with lap dogs:

Of smal houndes hadde she that she fedde
With roasted flessh, or milk and wastrel-breed.
But soore wepte she if oon of hem were deed,
Or if men smoot it with yerd smerte (ll 146-148).
(She had lap dogs that she fed with roasted meat or milk and white bread. And would cry bitterly if one should die or if a man struck one with a stick.)

Chaucer points out that the Prioress is soft-hearted when it comes to her dogs, the implication being that she lavishes inappropriate attention on the dogs to the exclusion of people, who should be her real concern as a Prioress. The fact that she cannot stand to see one of them hurt is yet another example of her refined sensibility, an attribute we would associate with a woman of the noble class.  
Although Chaucer couches his satire in seeming praise of Madame Eglentyne's table manners, personal grooming, speech, and sensibilities, we have the portrait of an important representative of the clergy who is much closer to the nobility than to the church. She is, like the Friar and the Monk, a fraud.

What is the meaning of "The Reapers" by Jean Toomer? Does it shed any additional light on the symbolism of the tractor in A Gathering of Old Men and its connection to the larger ideas of the novel?

Here, you have a three-part assignment that asks you to understand Toomer's work in light of his background.
The key biographical fact you want to discuss is Toomer's mixed race heritage and the way that has led to much of his work exploring the question of racial identity. Many of his works focus on the intersection of various cultures. For example, Candy, although white, regards Mathu almost as a father-figure, and the "Salt and Pepper" team also exemplify racial interdependence. 
In the poem, the initial quatrain focuses on black men sharpening scythes, while the conclusion of the poem focuses on the death of the rat. In the poem, the rat's death is obviously an accident. No one intended to kill it; it merely got in the way. The black men are just laborers doing their jobs. They don't own the fields and are not the ones who organized the harvest. What your instructor wants you to think about, given the juxtaposition of this and the novel, is how mechanization is an oppressive force that works together with racial injustice.
Chapter 9 of A Gathering of Old Men recounts a story in which a black man's mules prove more efficient than a Cajun's tractor. It is a power mower in the poem that kills the rat, something that would not happen with manual scythes.

Compare and contrast the common theme in Everyman to Chaucer's "The Pardoner's Tale."

Unlike Everyman, the characters in “The Pardoner’s Tale” and the Pardoner himself do not come to any sort of internal revelation that results in a significant change in their perceptions and actions.
The Pardoner starts out as a greedy, selfish church official, and he ends up as a greedy, selfish church official. He even publicly proclaims his own greed early in his tale:

I preach for nothing but for greed of gain.

He then goes on to tell a tale of greed and bloodthirsty violence. The characters in this tale learn nothing from their faults—in fact, they all die miserably as a result of their faults. Then, amazingly, he tries to lure the traveling pilgrims into paying him for his forgiveness:

If there be be one among you that is willing
to have my absolution for a shilling

While Everyman is sincere in his desire for redemption, the Pardoner has no such inclination. He is thoroughly cynical, and even wants to draw others into his sinful activities. He is held up by Chaucer as an example of all that is wrong with some aspects of the Medieval church—hypocrisy, greed, and deceitfulness.

Covetousness is both the root and stuff of all I preach.

The medieval morality play Everyman and Chaucer's "The Pardoner's Tale" have some similarities with regard to theme, but also have distinctions. Both plays focus on the inevitability of death and the futility of riches to help one in the afterlife. In the opening of Everyman, Everyman is enjoying his life and his riches, taking no thought of God or eternity. He learns he must give an account to his Maker and begins a quest to find someone to go with him to help him plead his case. He repents and embraces the teachings of the church, and he finds joy in Heaven. In "The Pardoner's Tale," the three rioters are drinking in a tavern and go on a quest to find and kill Death. On their way, they find treasure and end up killing each other because of greed. 
Both stories emphasize the truth that death faces all men. In the first lines of Everyman delivered by the Messenger, the Messenger states that the play will show life is not man's to keep and that man must live his life remembering that the end will come. In "The Pardoner's Tale," Death is personified, and the three rioters who seek to kill death are obviously bound to fail, as they do. 
Both stories also emphasize the futility of riches. Everyman learns that Goods will not follow him to heaven and will not plead for him before his Maker. The three rioters find that money, far from helping them in their quest to slay Death, actually brings their deaths upon them.
The two stories emphasize different points, though. Everyman seeks to explain how to get to Heaven, and Everyman learns what he must do to clear his account in God's eyes. It is meant to be a teaching tool for the Church to proclaim its doctrine of salvation. On the other hand, the Pardoner takes pains to explain that the moral of his story is that "the love of money is the root of all evil." The Pardoner is trying to sell pardons from the Pope, and if he can convince his listeners that their money is poison, that will result in more collections for him. 
The stories have similar themes, but their different purposes lead to different emphases. 

What commentary can be made about the ending of "The Last Leaf"?

As in other stories, in "The Last Leaf" O. Henry exploits the romantic wish that people are inherently good and unselfish and possessive of an innate dignity. And, as is also characteristic of O. Henry, in this story the narrative is constructed on the basis of some contradiction.
The contradiction in "The Last Leaf" exists in the character of Mr. Behrman, an older man who is "a failure in art." For forty years he has painted, and for forty years he has always been going to paint a masterpiece, yet the canvas stands empty in his little basement apartment. Every once and a while he receives a commission to paint for an advertisement or for some commercial enterprise. In addition, he earns some money as a model for young artists in Greenwich Village who cannot afford a professional model. 
Therefore, for Behrman to become the hero who is the cause of Johnsy's change of heart about dying, there is, indeed, a contradiction. This contradiction exists in his heroic and loving act of going out into the wet, cold winter night, climbing a ladder, and painting an ivy leaf upon a brick wall so that Johnsy will not fulfill her promise of dying when all the leaves fall from the vine.Behrman, an old curmudgeon who complains about just going upstairs and modeling for Sue, and who has procrastinated for forty years on painting his "masterpiece," braves the icy cold and unselfishly risks his own health because he loves Johnsy. Truly, then, Old Behrman becomes heroic in his final act, and does, indeed, contradict his unmotivated nature as he paints his "masterpiece," at last. 

sum_(n=1)^oo (2^n+1)/(5^n+1) Use the Limit Comparison Test to determine the convergence or divergence of the series.

Limit comparison test is applicable when suma_n and sumb_n are series with positive terms. If lim_(n->oo)a_n/b_n=L where L is a finite number and L>0 ,then either both series converge or both diverge.
Given series is sum_(n=1)^oo(2^n+1)/(5^n+1)
Let the comparison series be sum_(n=1)^oo2^n/5^n=sum_(n=1)^oo(2/5)^n
The comparison series sum_(n=1)^oo(2/5)^n is a geometric series with ratio r=2/5<1
A geometric series converges, if 0<|r|<1
So, the comparison series which is a geometric series converges.
Now let's use the Limit comparison test with:
a_n=(2^n+1)/(5^n+1)   and b_n=2^n/5^n
a_n/b_n=((2^n+1)/(5^n+1))/(2^n/5^n)
a_n/b^n=(2^n+1)/(5^n+1)(5^n/2^n)
a_n/b^n=((2^n+1)/2^n)(5^n/(5^n+1))
a_n/b^n=(1+1/2^n)(1/(1+1/5^n))
lim_(n->oo)a_n/b_n=lim_(n->oo)(1+1/2^n)(1/(1+1/5^n))
=1>0
Since the comparison series sum_(n=1)^oo2^n/5^n converges,the series sum_(n=1)^oo(2^n+1)/(5^n+1) as well ,converges as per the limit comparison test.

Calculus and Its Applications, Chapter 1, Test, Section Test, Problem 40

If $f(x) = x^2 - x$ and $g(x) = 2x^3$. Find $f(f \circ g)(x)$ and $(g \circ f)(x)$

$
\begin{equation}
\begin{aligned}
(f \circ g)(x) = f(g(x)) &= f(2x^3) \\
\\
&= (2x^3)^2 - (2x^3) \\
\\
&= 4x^6 - 2x^3\\
\\
(g \circ f)(x) = g(f(x)) &= g(x^2 - x) \\
\\
&= 2(x^2 - x)^3
\end{aligned}
\end{equation}
$

What are some suggestions for change for first responders in post-incident injury that would reduce strain and stress?

Presumably, the question refers to injuries sustained by the first responder in the performance of his or her duties, and not the injuries sustained by the patient. First-responders, including local police, firefighters, ambulance crews and Emergency Medical Technicians (EMTs), are all employed in professions in which injury or death is a daily risk. All of these professions are inherently stressful, and, depending upon the scenario, involve varying levels of activity at the scene of the event. In other words, the event to which the first responder is responding could involve anything from a routine traffic accident to the detonation of a car or dirty bomb resulting in a large number of casualties. Obviously, the first example would involve minimal stress and little to no risk of injury to the first responder. The mass casualty scenario, in stark contrast, would involve considerable risk to the first responder, especially if secondary explosions occurred or the incident involved a live shooter armed with automatic or semi-automatic weaponry.
If a first responder is injured in the performance of his or her duties and, again, the injury occurs in the midst of a major event, such as a terrorist attack or fire, then the short-term risks are primarily physical and would be treated by physicians. The longer-term issues, depending upon the nature of the physical injuries (e.g. loss of limb or simple fracture) and of the incident in question, will affect the psychological state of the first responder to greater or lesser degrees.
For this answer, we will assume the injury is serious and sustained in a major incident. The level of risk associated with major incidents and the stress that is a regular part of the job of first responders requires regular counseling sessions to detect signs of post-traumatic stress disorder (PTSD), which can take months to materialize and even longer to become outwardly visible. PTSD is, however, potentially debilitating and, even at less extreme levels, can seriously impede the individual's ability to perform his or her responsibilities. The importance of mandatory psychological screening and occasional follow-ups cannot be overstated. Unlike physical injuries, mental impairment or conditions like depression or anxiety are, unfortunately, perceived as signs of weakness. The stigma associated with mental health problems has historically precluded their being adequately addressed. The conditions under which first responders function, however, demands a fundamental transformation in how issues like PTSD are perceived and handled.
If one recommendation could be offered, then, with respect to first responders dealing with post-incident injuries, it is the need for psychological counseling, even if the first responder insists that he or she does not need such care.

What is an interloper? Who are the interlopers in the story? Is there more than one kind of interloper?

According to the American Heritage College Dictionary, an interloper is a trespasser, a person who intrudes in a place or situation. An interloper is also a meddler in the affairs of others.
In Saki's short story entitled "The Interlopers," Ulrich von Gradwitz patrols the dark forest one night in search of his enemy. He considers Georg Znaeym an interloper, a trespasser and "game-snatcher" on his "narrow strip of precipitous woodland" that has been reclaimed from the illegal possession of the Znaeym family "in a famous lawsuit." There is strong animosity between the two men, but when they suddenly confront each other as they each come around the trunk of a huge beech tree, they hesitate in a civilized moment before firing their rifles at each other. In that instant, lightning strikes the tree, and the men are pinioned beneath a tangle of branches.
Although not fatally injured, the two men are exasperated that they are trapped together. Each curses the other and adds insults, describing what his men will do to the other when they arrive. After some time, though, the two men reconcile with one another because they realize the folly of their animosity. Graciously, one tells the other than when his men come, he will have them aid the other. However, in another twist of fortune, there are new interlopers. In the "chattering laugh of a man unstrung with hideous fear," Ulrich von Gradwitz tells Znaeym that these new interlopers are wolves.

Calculus of a Single Variable, Chapter 8, 8.4, Section 8.4, Problem 61

Arc length of curve can be denoted as "S ". We can determine it by using integral formula on a closed interval [a,b] as: S = int_a^b ds
where:
ds = sqrt(1+ ((dy)/(dx))^2 )dx if y=f(x)
or
ds = sqrt(1+((dx)/(dy))^2) dy if x=h(y)
a = lower boundary of the closed interval
b =upper boundary of the closed interval

From the given problem: y =ln(x), [1,5] , we determine that the boundary values are:
a= 1 and b=5
Note that y= ln(x) follows y=f(x) then the formula we will follow can be expressed as S =int_a^bsqrt(1+ ((dy)/(dx))^2 )dx
For the derivative of y or (dy)/(dx) , we apply the derivative formula for logarithm:
d/(dx)y= d/(dx) ln(x)
(dy)/(dx)= 1/x
Then ((dy)/(dx))^2= (1/x)^2 or 1/x^2 .
Plug-in the values on integral formula for arc length of a curve, we get:
S =int_1^5sqrt(1+1/x^2 )dx
Let 1 = x^2/x^2 then we get:
S=int_1^5sqrt(x^2/x+1/x^2 )dx
=int_1^5sqrt((x^2+1)/x^2 )dx
=int_1^5sqrt(x^2+1)/sqrt(x^2 )dx
=int_1^5sqrt(x^2+1)/sqrt(x^2 )dx
=int_1^5sqrt(x^2+1)/xdx
From the integration table, we follow the formula for rational function with roots:
int sqrt(x^2+a^2)/x dx = sqrt(x^2+a^2)-a*ln|(a+sqrt(x^2+a^2))/x| .
Applying the integral formula with a^2=1 then a=1, we get:
int_1^5sqrt(x^2+1)/xdx = [sqrt(x^2+1)-1*ln|(1+sqrt(x^2+1))/x|]|_1^5
= [sqrt(x^2+1)-ln|(1+sqrt(x^2+1))/x|]|_1^5
Apply the definite integral formula: F(x)|_a^b= F(b)-F(a) .
[sqrt(x^2+1)-ln|(1+sqrt(x^2+1))/x|]|_1^5
=[sqrt(5^2+1)-ln|(1+sqrt(5^2+1))/5|]-[sqrt(1^2+1)-ln|(1+sqrt(1^2+1))/1|]
=[sqrt(25+1)-ln|(1+sqrt(25+1))/5|]-[sqrt(1+1)-ln|(1+sqrt(1+1))/1|]
=[sqrt(26)-ln|(1+sqrt(26))/5|]-[sqrt(2)-ln|1+sqrt(2)|]
=sqrt(26)-ln|(1+sqrt(26))/5| -sqrt(2)+ln|1+sqrt(2)|
Apply logarithm property: ln(x)-ln(y) = ln(x/y) .
S =sqrt(26)-sqrt(2)+ln|1+sqrt(2)|-ln|(1+sqrt(26))/5|
S =sqrt(26)-sqrt(2)+ln|(1+sqrt(2))/(((1+sqrt(26))/5))|
S =sqrt(26)-sqrt(2)+ln|(5*(1+sqrt(2)))/(1+sqrt(26))|
S =sqrt(26)-sqrt(2)+ln|(5+5sqrt(2))/(1+sqrt(26))|
S~~4.37