Outline and discuss the distinction between a private and a public company highlighting the advantages or disadvantages of either.

The distinction between public and private corporations is one of ownership and control. A privately-owned business is just that: a company owned and operated by an individual or group of individuals who individually or collectively make all major decisions pertaining to the company’s direction and strategy. They are beholden to nobody but themselves and, in the case of businesses employing unionized labor, whatever union is involved (e.g., United Steel Workers, International Brotherhood of Teamsters, Service Employees International Union, etc.).
A publicly-held or traded corporation is owned by its shareholders. The more shares of stock an individual or group of individuals hold in a particular publicly-traded company, the more influence they wield in discussions of the company’s future direction, whether to invest profits in recapitalization vice issuing monetarily greater dividends, and other major decisions. Publicly-traded corporations fall under a federal regulatory structure that does not apply to privately-owned businesses, such as the Securities and Exchange Commission’s watchdog mission of monitoring publicly-held companies for indications of “insider trading.”
The advantage to privately-owned companies is the absence of a large group of mostly anonymous people involved in major corporate decisions and in the ability of ownership to retain control of all profits. Contrast this with the requirement of publicly-traded corporate officers to issue profits in the form of dividends to shareholders. A disadvantage to privately-held companies, on the other hand, is their more limited avenues from which to raise money for new product development, physical plant expansion, and other routine but expensive endeavors. Publicly-held companies have the option of selling more shares of stock as a means of raising capital while continuing to have the option of applying for loans through banks and other financial institutions. Additionally, as noted above, privately-owned companies are not subject to the level of scrutiny imposed upon publicly-traded corporations.
There are advantages and disadvantages to both forms of corporation. Privately-owned companies often find it difficult to expand beyond a certain level without the kind of cash that can only be raised through public sales of shares in the company. Publicly-held companies, on the other hand, have far more cumbersome decision-making processes by virtue of the vastly greater number of “owners” involved.

Single Variable Calculus, Chapter 2, 2.4, Section 2.4, Problem 26

Show that the statement $\displaystyle\lim\limits_{x \to 0} x^3 = 0$ is correct using the $\varepsilon$, $\delta$ definition of limit.

Based from the defintion,


$
\begin{equation}
\begin{aligned}

\phantom{x} \text{if } & 0 < |x - a| < \delta
\qquad \text{ then } \qquad
|f(x) - L| < \varepsilon\\

\phantom{x} \text{if } & 0 < |x-0| < \delta
\qquad \text{ then } \qquad
|x^3-0| < \varepsilon\\

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
& \text{That is,}\\
& \phantom{x} & \text{ if } 0 < |x| < \delta \qquad \text{ then } \qquad |x^3| < \varepsilon\\
\end{aligned}
\end{equation}
$

Or, taking the cube root of both sides of the inequality $|x^3| < \varepsilon$ , we get...
$\quad \text{if } 0 < |x| < \delta \quad \text{ then } \quad |x| < \sqrt[3]{\varepsilon}$

The statement suggests that we should choose $\displaystyle \delta = \sqrt[3]{\varepsilon}$

By proving that the assumed value of $\delta = \sqrt[3]{\varepsilon}$ will fit the definition...



$
\begin{equation}
\begin{aligned}
\text{if } 0 < |x| < \delta \text{ then, }\\
& \phantom{x} &
|x^3| < \delta^3 = (\sqrt[3]{\varepsilon})^3 = \varepsilon

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

& \text{Thus, }\\
& \phantom{x} \quad\text{if } 0 < |x| < \delta \qquad \text{ then } \qquad |x^3| < \varepsilon\\
& \text{Therefore, by the definition of a limit}\\
& \phantom{x} \qquad \lim\limits_{x \to 0}x^3 = 0

\end{aligned}
\end{equation}
$

3) In each case explain (using appropriate graphs for support) what happens to prove and output in the market for wheat bread; assuming that wheat bread is a normal good, rye bread is a substitute in consumption, wheat is an input in making wheat bread and rye is an input in making rye bread. A: There is an increase in incomeB: There is an decrease in the price of ryeC: There is an increase in the price of wheatD: There is an improvement in the production technology for bread. Continuing with the previous problem, explain (using appropriate graphs for support) what happens to price and output when: A: There is an increase in income and an increase in the price of wheatB: There is an increase in income and an improvement in the production technology for bread.C: There is a decrease in the price of rye and an increase in the price of wheatD: There is a decrease in the price of rye and an improvement in the production technology for bread. In each case (using appropriate graphs for support) describe the distortions that occur in a competitive market when the government imposes:a price ceilinga price floor

Part 3(A): As wheat bread is a normal good, an increase in income will result in an increase in demand. 
3(B): A substitute good is a good that can serve as a replacement for another good. In this case, rye bread can replace wheat bread, so if the price of rye went down, demand for wheat bread would decrease (as more people would choose to buy the cheaper rye bread). Rye bread is cheaper because the input, rye, has decreased in price. 
3(C): Similarly for part B, if the price of wheat increased, the cost of wheat bread would increase. Therefore demand would decrease, as more people would choose to purchase cheaper rye bread instead. 
3(D): An improvement in bread-making technology should increase efficiency of production for both kinds of bread, meaning that both wheat and rye bread should decrease in price, and demand should increase. 
 
4(A): If there is both an increase in income and an increase in the price of wheat (meaning an increase in price of wheat bread), demand will depend on which increase is relatively higher. As this is not stated, it's unclear whether or not demand would increase, decrease, or stay the same. 
4(B): If there is an increase in income and improved bread-making technology, demand should increase greatly. Higher income increases demand for normal goods, and improved technology should decrease the cost of wheat bread, so there are two factors both working to increase demand here. 
4(C):A decrease in the price of rye and an increase in the price of wheat would lead to greatly decreased demand for wheat bread. This is because cheaper rye means cheaper rye bread than usual, and more costly wheat means more costly wheat bread than usual. This should lead to very large numbers of people choosing to buy rye bread instead of wheat bread. 
4(D): A decrease in the price of rye and improved bread-making technologies should decrease prices for both breads (due to the improved technology), but rye bread will be relatively cheaper than wheat bread. This will increase demand for both breads, but demand for rye bread will be especially high. 

How did the ancient Romans create a huge and long-lasting empire, when the ancient Greeks were never able to unify for very long?

The most important factor was geography. Greece is extremely mountainous, making land travel between different regions quite difficult. Although Greece had been inhabited in the neolithic age, Greek culture as we think of it began in a period know as Early Helladic III, starting in roughly 2200 BC as Greek-speaking peoples gradually moved into the area that became Greece. These Bronze Age towns grew in a pattern that was determined by geography. Usually there was an urban center, often a fortified acropolis, consisting of civic, religious, and domestic structures surrounded by farmlands and a harbor. These functioned as city-states (polis; plural poleis). External trade and communication was usually by sea, and cities were as likely to trade with islands, Asia Minor, Sicily, or Egypt as with each other. Because city states could not expand in their own regions (due to the surrounding mountains), they planted colonies in places like Italy, North Africa, and the east coast of the Mediterranean. Colonies usually remained loyal to their parent cities. Because of this early history, ancient Greece simply did not exist as a nation. The city states might share a language in common and form alliances, but they did not, until the Hellenistic period, consider themselves part of a common political unit and thus did not form empires, as they did not individually have the population or wealth necessary to do so.
Rome, on the other hand, existed as a unified state, gradually expanding through Italy and then the Mediterranean.

Is the Awakening by Kate Chopin a feminist text? Why or why not? Use evidence from the talks and The Awakening to support your opinion. Ted Talks: https://www.ted.com/talks/chimamanda_ngozi_adichie_we_should_all_be_feminists https://www.ted.com/talks/roxane_gay_confessions_of_a_bad_feminist

The Awakening is most certainly a feminist novel, or at least a "protofeminist" novel since the book predates both the word and concept of feminism.  It presents a society, the Creoles, who live in New Orleans and summer in Grand Isle, in which, as Chimamanda Ngozi Adichie says in her TEDtalk, "men are more important than women."  It is not what Edna wants that matters; it is what her husband, Leonce, wants that is important.  When she is inattentive after he wakes her up in the middle of the night, he accuses her of neglecting her children.  When she rejects his sexual advances, he acts like a petulant child.  She is supposed to put his desires before her own, always.
Adichie says that "We have evolved, but it seems to me that our ideas of gender have not evolved."  Physical strength is no longer paramount in Edna's society, yet men are still very much in control.  They work outside the home and find entertainment outside the home; it is Leonce who can decide when he wants to leave and when he will return—Edna cannot do the same, nor can she weigh in on his decisions.  
When the waiters at restaurants in Nigeria ignore her and only pay attention to the man she is with, Adichie says, "I feel invisible; I feel upset."  Similarly, when no one understands Edna, when her husband fails to comprehend why she is so dissatisfied with their life together, she gets angry, very angry—just like Adichie when she points out the "grave injustice" of "Gender as it functions today."  Edna smashes a vase and flings her wedding band across the room.  She cannot even quite put into words what it is that she wants, but it sounds a lot like freedom.  She does not have the same freedom her husband, or Robert does—Robert can pick up and move to Mexico at a moment's notice.  Edna's desire for equal freedom makes her a feminist, and Chopin's depiction of Edna's ultimate unwillingness to compromise on this desire renders the novel a feminist one.

What was John Stuart Mill's purpose for writing "The Subjection of Women"?

John Stuart Mill's purpose behind writing The Subjection of Women was to promote the advancement and happiness of humankind as a whole. Mill was advocating for women to be given the opportunity to reach their full potential—and for society to allow women to contribute as meaningful participants. In chapter 1, Mill himself states:

That the principle which regulates the existing social relations between the two sexes—the legal subordination of one sex to the other—is wrong itself, and now one of the chief hindrances to human improvement; and that it ought to be replaced by a principle of perfect equality, admitting no power or privilege on the one side, nor disability on the other.

This statement in his first chapter shows that he felt the current (for his time in the Victorian era) social practices of having men rule over women and make all of the decisions in society was outdated. Throughout the rest of The Subjection of Women, Mill discusses various ways in which the world as a whole would be a happier, better place if the genders were viewed as equals. He argues that all individuals should be eligible for a moral and intellectual education. Once that education was received, that individual should be able to participate in the society's functions, regardless of gender.

Who is Mr. Keesing in Anne Frank: The Diary of a Young Girl?

Mr. Keesing, a school teacher who Anne describes as an "old fogey." Although a math teacher, he assigns her extra homework in the form of writing essays because she talks too much in class. She writes her first three-page essay about herself as a chatterbox, saying it is both a female and an inherited trait, as her mother chatters all the time too. The essay writing does nothing to stop Anne's chattering in class, so Mr. Keesing assigns her a second and then a third essay. By the third one she is tapped out, so she writes a poem instead, which amuses the class and Mr. Keesing. The episode illustrates the carefree nature of Anne's life as a school girl as late as 1942. More subtly, her first essay about chattering shows the influence of the sexual and racial (genetic) ideas permeating the times: women as a gender have certain characteristics (chattering) and these traits are passed on. Anne writes innocently, but the idea of inherited "racial traits" helped justify the genocide against the Jews that Anne and her family got tragically caught up in. 

Mr. Keesing was Anne Frank's teacher before she and her family went into hiding in the Annex.  Mr. Keesing thought that Anne talked too much in class.  He assigned a composition for her to write as punishment.  This composition was to be called 'Quack, Quack, Quack, Says Mrs. Natterbeak.'
Anne decided to put a great deal of effort into creating this composition.  She decided that she wanted to write it as poetry.  She sought help from a friend, who had skill in writing poetry.  In the end, the poem was a funny one about a family with a duck as a mother and a swan as a father.  In the poem, "the baby ducklings were bitten to death by Father because they chattered too much"  (The Diary of Anne Frank). This was supposed to symbolize Mr. Keesing punishing Anne for talking too much in class.
When Mr. Keesing read Anne's composition, he was amused.  He was not at all offended, and saw it as a joke.  After this, he let Anne talk in class without assigning her any extra work for it.  He also referenced her poem on occasion.

College Algebra, Chapter 4, 4.6, Section 4.6, Problem 78

Graph the rational function $\displaystyle y = \frac{x^4 - 3x^3 + x^2 - 3x + 3}{x^2 - 3x}$ and find all vertical asymptotes, $x$ and $y$ intercepts, and local extrema. Then use long division to find a polynomial that has the same end behavior that has the same end behavior as the rational function, and graph both functions in a sufficiently large viewing rectangle to verify that the end behaviors of the polynomial and the rational function are the same.







Based from the graph, the vertical asymptotes are the lines $x = 0$ and $x = 3$. Also, the $x$ intercept of the function are approximately $0.75$ and $2.85$ but the $y$ intercept does not exist. The estimated local maximum $5$ occurs when $x$ is approximately $2.6$. Also, the local minima $3$ and $14.9$ occurs when $x$ is approximately $-0.75$ and $3.25$ respectively.

Then, by using Long Division,







Thus, $\displaystyle y = \frac{x^4 - 3x^3 + x^2 - 3x + 3}{x^2 - 3x} = x^2 + 1 + \frac{3}{x^2 - 3x}$


Therefore, the polynomial $f(x) = x^2 + 1$ has the same end behavior with the given rational function. Then, their graph is

McDougal Littell Algebra 2, Chapter 5, 5.2, Section 5.2, Problem 19

All you have to do is put in the problem in a calculator and graph:
y = x^2 + 10x + 25

the graph has a zero at -5, therefore this is the p and the q
intercept form is:
y = a (x - p) (x - q)
plug in the number:
y = a ( x - -5) (x - - 5)
y = a (x + 5) (x + 5)
now we have to solve for a. for this we can use any point on the graph. As you can see, the graph crosses the point (-3 , 4) so we can use this coordinate to substitute as x and y
4 = a (-3 + 5) (-3 + 5)
4 = a (2) (2)
4 = 4a
1 = a
so the intercept form is:
y = 1 (x + 5) (x + 5)

What trade goods did Vasco da Gama find?

Vasco da Gama was a Portuguese nobleman who sailed from Lisbon, the capital city of Portugal, in 1497. He was chosen by Portugal's King Manuel I to find a maritime route to to India. Portugal required access to India so that they could participate in the spice trade of the Far East. A land route was not possible due to the Muslim occupation of the Arabian Peninsula.
Da Gama traveled south along the coast of Africa before rounding the Cape of Good Hope and heading back north along the eastern coast. After multiple stops in Africa, da Gama finally reached Calicut, India, in 1498.
At many of da Gama's stops, his attempts at trade were not welcomed. The goods he brought to trade were not of significant enough value. Despite this, da Gama was able to return to Portugal with peppercorns, ginger, cloves, nutmeg, and cinnamon. The journey back to Portugal was difficult, and many lives were lost to scurvy. Da Gama was hailed as a hero upon his return, and an attempt to replicate his journey was made immediately under Pedro Alvares Cabral. Following Cabral's voyage, da Gama returned to India in 1502 and secured an alliance with the ruler of Cochin.
http://www.bbc.co.uk/history/british/tudors/vasco_da_gama_01.shtml

Da Gama set out from Portugal and sailed around the southern tip of Africa, the Cape of Good Hope. Da Gama reached Calicut, India, where he traded with local Hindus whom he mistook for Christians. He loaded his ships with valuable spices, but Muslim traders in the area forced him to barter the spices for sailing provisions in order to get back home. These spices were unique to the Asian market—peppercorns and cinnamon among many others—as Calicut was a major trading port for the entire region. The spices fetched a large price back in Portugal and made da Gama a hero even though he lost considerable numbers of men due to scurvy. Da Gama made a second voyage on which he attacked Muslims living in Calicut and made Portugal a major trading partner in the region. Da Gama would finish his career as an explorer while serving as a viceroy in India.
https://www.livescience.com/39078-vasco-da-gama.html

Single Variable Calculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 9

Describe how the graphs of the following functions can be obtained from the graph of $f$. Suppose that the graph of $f$ is given.



$
\begin{equation}
\begin{aligned}

\text{a) } y=& f(x) + 8\\
& \text{ shift the graph 8 units upward}\\
\text{b) } y=& f(x+8)\\
& \text{ shift the graph 8 units to the left}\\
\text{c) } y=& 1+2f(x)\\
& \text{ stretch the graph vertically by a factor of 2, then shift it 1 unit upward}\\
\text{d) } y=& f(x-2) - 2\\
& \text{ shift the graph 2 units to the right and 2 units downward}\\
\text{e) } y=& -f(x)\\
& \text{ reflect the graph about the $x$-axis}\\
\text{f) } y=& 3-f(x)\\
& \text{ reflect the graph about the line $x$-axis, then shift it 3 units upward.}



\end{aligned}
\end{equation}
$

Who is George Washington?

George Washington was a large plantation owner in Virginia who later became one of the most famous generals of the American Revolution and the first president of the United States.
Washington's military exploits are legendary, namely because he kept his army from being destroyed during the Revolutionary War. Washington is famous for winning the Battle of Trenton where his army crossed the Delaware River and surprised a Hessian army. He also worked with the French navy to corner the British General Cornwallis at the Battle of Yorktown. Washington also kept the needs of his men in mind as general as he constantly asked the Continental Congress for funds in order to outfit his army.
Washington served two terms as president of the United States. He set several precedents. He insisted on his title being "Mr. President." He stepped aside after two terms. He assembled a cabinet of accomplished statesmen such as Alexander Hamilton and Thomas Jefferson even though these two men did not get along. In his Farewell Address, Washington gave the nation two final pieces of advice: stay away from foreign entanglements and stay away from political parties. Washington's greatest legacy as president came when he left office after two terms and went back home to Mount Vernon.

How does the poem "The White Man's Burden" relate to British imperialism in India?

"The White Man's Burden" is a poem by Rudyard Kipling published in 1899. British imperialism around the world, including India, was already in full swing by then, so we can't say that Kipling caused British imperialism.But if you read the poem, there's something very jarring about it, at least to a modern cosmopolitan reader: It is unabashedly, even proudly, racist and imperialist. It was written in response to the US invasion of the Philippines, and the story it tells is not of a powerful country conquering and oppressing a weak one, but of a superior, advanced culture trying their very best to civilize and improve an inferior, primitive one, and being constantly thwarted by the primitive savages. It isn't exactly rejoicing in imperialism, but the downsides it talks about are all about how hard it is being the White imperialist, constantly misjudged for his altruistic actions. The desires of the people being conquered are conveniently ignored.Thus, we can think of "The White Man's Burden" as a kind of apologia for imperialism, and particularly focused at American and British readers. That word is sometimes translated "apology", but "apology" sounds like you're saying sorry for something you agree is bad; an apologia is a defense of why it is not bad, even though so many people seem to think so. We can't really know what Kipling himself believed (perhaps it was intended as satire?), but if the poem is read literally, it is a staunch defense of imperialism as the necessary burden of White men to bring civilization to the primitive masses, whether they want it or not.This was of course a narrative that the British used heavily, in an attempt to justify their imperialism in India, Africa, and around the world. "It's for their own good" makes the violence and exploitation much easier to swallow than it would have been if they'd admitted it was mainly for the gain of the rich and powerful in Britain. And they had just enough examples of actual improvements in standard of living (accomplished in the most violent way possible, of course) to back up their argument; yes, there was in fact real economic development in India under the British Raj. Defenders of imperialism conveniently ignored of course that there could have been much more development had they engaged in fair and equal trade rather than imperialist exploitation---but there was in fact some development, which gave them some measure of excuse or deniability, and many in Britain clung to these excuses and spread them widely. Kipling's poem is part of that attempt to give an ethical and altruistic veneer to a project that was at its core violent and exploitative.This soon backfired, however, as "the White Man's Burden" actually became a satirical slogan against imperialism in the US and Britain (and is sometimes still used that way today). It was used as an example of how weak and inhumane the justifications for imperialism truly were.
http://historymatters.gmu.edu/d/5478

http://www.bbc.co.uk/history/british/empire_seapower/east_india_01.shtml

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

How fast is the area of the square increasing when the radius is 30m?

Given: $\displaystyle \frac{dx}{dt} = 6 cm/s$

Required: $\displaystyle \frac{dA}{dt}$ when $\displaystyle \frac{dr}{dt}$

Solution: Let $A = x^2$ be the area of square where $x$ = side of the square

$\displaystyle \frac{dA}{dt} = \frac{dA}{dx} \left( \frac{dx}{dt} \right) = 2 x \frac{dx}{dt} $

$\displaystyle \frac{dA}{dt} = 2x \frac{dx}{dt}$

To get the value of $x$, we use the given area to get $x$


$
\begin{equation}
\begin{aligned}

A =& x^2
\\
\\
x =& \sqrt{A} ; A = 16
\\
\\
\frac{dA}{dt} =& 2 (4)(6)
\\
\\
\end{aligned}
\end{equation}
$


$\fbox{$\large \frac{dA}{dt} = 48 cm^2 /s $}$

How much do the lovers say their love has grown?

It's Act II Scene VI, and Romeo and Juliet, the star-crossed lovers, are finally to be married by Friar Lawrence in his cell. The good friar sees the forthcoming marriage as a golden opportunity to put an end to the seemingly never-ending war between the Montangues and the Capulets.
But more than anything else, this will be a love match, and the love between Romeo and Juliet has grown so much that neither is able to express it in words. Romeo tries his best, but can't, and so asks his bride to try and articulate how they both feel:

"Ah, Juliet, if the measure of thy joy
Be heaped like mine, and that thy skill be more
To blazon it, then sweeten with thy breath
This neighbor air, and let rich music’s tongue
Unfold the imagined happiness that both
Receive in either by this dear encounter."

But Juliet is no more equal to the challenge than Romeo:


"Conceit, more rich in matter than in words,
Brags of his substance, not of ornament.
They are but beggars that can count their worth.
But my true love is grown to such excess
I cannot sum up sum of half my wealth."



What she means is that the enormous love that Romeo and Juliet share is richer than any word could possibly suggest. One's true worth cannot be counted; anyone who claims to be able to do so is poor. Juliet's love for Romeo has made her so rich that she cannot even begin to count half the wealth such love has brought.

What was Italy's role in WW1?

Before World War I broke out in 1914, Italy had been allied with Germany and Austria-Hungary, so, at first, it seemed likely that Italy would join the Triple Alliance. Mussolini, then the editor of a socialist newspaper, was eager to keep Italy out of the war, as he saw the war as an effort by capitalist bosses to use the proletariat as cannon fodder. By 1915, though, Mussolini's views had changed, as he saw the war as what he called "a great drama." At first, many socialists in Italy sided with Mussolini in staying out of the war, but, like him, they began to gravitate towards intervention (even as he was kicked out of the Socialist Party in Italy).
The Italian government began to see the war as a way to gain more territory. In the Treaty of London of 1915, Britain agreed to grant Italy territory in the Adriatic if they became involved in the war, so Italy joined in April of 1915, entering the war on the side of the Triple Entente—Britain, France, and Russia. Britain and its allies wanted Italy to help start a southern end of the Western Front to further weaken the Triple Alliance. 
From 1915 to 1917, Italy made very little progress into Austrian territory, and Italian troops were defeated soundly at the battle of Caporetto in October of 1917, resulting in the deaths of 300,000 soldiers. Over 600,000 Italian soldiers died in the war, and the government was in debt as a result of the fighting. In addition, the Italians got very little of what they had wanted at the treaty negotiations in Versailles in 1919, giving rise to a sense of wounded pride and a current of nationalism in Italy after the war.

Briefly describe the significance of the trial scene.

The trial scene takes place in Act four, Scene one, and is significant because it marks the resolution of the second major plot complication of the play. The play's climax also takes place during the trial scene and is the moment when Portia saves Antonio's life. The remaining scenes of the play following the trial scene in Act four, Scene one, constitute the dénouement. During the trial scene, the Duke of Venice initially attempts to prevent Shylock from retrieving a pound of Antonio's flesh and refuses to continue with the proceedings without consulting Bellario of Padua. Both Nerissa and Portia arrive at the court disguised as men and Portia pretends to be a lawyer named Balthasar acting on Bellario's behalf. Portia then attempts to persuade Shylock to act mercifully by sparing Antonio's life but he remains obstinate and determined to kill him. Shylock even refuses to accept three times the original bond and Portia initially seems to be in his favor. However, Portia offers a strict interpretation of the law that prevents Shylock from extracting a drop of Antonio's blood and anything other than the exact amount of flesh. Portia then mentions that Shylock is guilty of threatening the life of a Venetian citizen and says that the court will confiscate his wealth. Overall, Portia successfully saves Antonio's life and Shylock ends up leaving the court a broke, embittered man at the end of the trial scene in Act four, Scene one.

Describe Doug's character or personality.

On the whole, Doug Swieteck is an amazingly good kid. He has every opportunity to turn into a real jerk of a kid. It's what he sees and knows from home because his home life is terrible. His father is abusive as well as his brother. Doug's mom feels sympathy for him, but she is too weak of a person to stand up to her husband and actually defend Doug. Add to that the fact that Doug is forced to move away from the few friends that he has and has to start over again. He could absolutely be a negative, bitter, antisocial teenager; however, he's patient, kind, friendly, and hardworking. These traits are what allow Doug to obtain and keep a job at Spicer's Deli. Those traits are also why Doug is earning tips for doing his job and doing it well.
Another good indicator of Doug's work ethic and all around intelligence is the fact that he learns to read as an 8th grader. That shows he's willing to improve himself as well as humble himself to get help. He picks up reading quickly as a result of his natural talent and determination. Doug is also willing to help those in need. He works tirelessly to help Lil practice her lines, and he even humbles himself to take her part when she gets sick. This means that he has to dress up like a girl; therefore, I see Doug as quite brave as well.

Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 22

Solve the system $\begin{equation}
\begin{aligned}

& -3x - 5y = -17 \\
& y = 4x + 8

\end{aligned}
\end{equation}
$ by substitution. If the system is inconsistent or has dependent equations.

Since equation 2 is solved for $y$, we substitute $4x + 8$ for $y$ in equation 1.



$
\begin{equation}
\begin{aligned}

-3x - 5(4x + 8) =& -17
&& \text{Substitute $y = 4x + 8$}
\\
-3x - 20x - 40 =& -17
&& \text{Distributive Property}
\\
-23x - 40 =& -17
&& \text{Combine like terms}
\\
-23x =& 23
&& \text{Add each side by $40$}
\\
x =& -1
&& \text{Divide each side by $-23$}

\end{aligned}
\end{equation}
$


We found $x$. Now we solve for $y$ in equation 2.


$
\begin{equation}
\begin{aligned}

y =& 4(-1) + 8
&& \text{Substitute $x = -1$}
\\
y =& -4 + 8
&& \text{Multiply}
\\
y =& 4
&& \text{Add}

\end{aligned}
\end{equation}
$

Why do Squeaky and Gretchen smile genuinely at each other after the race?

Squeaky and Gretchen smile at each other after the race because they now respect each other. Before the race, both think little of the other.
For example, Squeaky initially thinks Gretchen is vain and arrogant. Additionally, Mary Louise (formerly a close friend of Squeaky's) now socializes with Gretchen and engages in spiteful gossip against her. Rosie, the other girl who befriended Gretchen, is also on shaky ground with Squeaky because Rosie is unkind to Raymond, Squeaky's brother. When they meet on the day of the race, the girls treat each other warily, keeping each other at arms length:

Gretchen smiles, but it’s not a smile, and I’m thinking that girls never really smile at each other because they don’t know how and don’t want to know how and there’s probably no one to teach us how, cause grown-up girls don’t know either.

Squeaky and Gretchen view each other as competition. Neither thinks the other deserves to win. By the end of the race, however, both girls view each other with newfound respect and regard. Squeaky notices that Gretchen isn't just another pretty girl: she really worked hard to win.

And I lean down to catch my breath and here comes Gretchen walking back, for she’s overshot the finish line too, huffing and puffing with her hands on her hips taking it slow, breathing in steady time like a real pro and I sort of like her a little for the first time.

For her part, Gretchen now realizes Squeaky really does run well. Both girls smile to demonstrate their new regard for each other.

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 4

Suppose that
$\displaystyle \lim_{x \to a} f(x) = 0 \quad \lim_{x \to a} \quad \lim_{x \to a} h(x) = 1$
$\displaystyle \lim_{x \to a} p(x) = \infty \quad \lim_{x \to a} q(x) = \infty$

Which of the following limits are indeterminate form? Evaluate the limit if possible, for those that are not an indefinite form.

a.) $\displaystyle \lim_{x \to a} [f(x)]^{g(x)}$
b.) $\displaystyle \lim_{x \to a} [f(x)]^{p(x)}$
c.) $\displaystyle \lim_{x \to a} [h(x)]^{p(x)}$
d.) $\displaystyle \lim_{x \to a} [p(x)]^{f(x)}$
e.) $\displaystyle \lim_{x \to a} [p(x)]^{q(x)}$
f.) $\displaystyle \lim_{x \to a} \sqrt[q(x)]{p(x)}$


$
\begin{equation}
\begin{aligned}
\text{a. ) } \lim_{x \to a} [f(x)]^{g(x)} &= \lim_{x \to a} [f(x)]^{\lim\limits_{x \to a}g(x)}\\
\\
&= 0^0 && \Longleftarrow \text{(Indeterminate)}\\
\\
\text{b. ) } \lim_{x \to a} [f(x)]^{p(x)} &= \lim_{x \to a} [f(x)]^{\lim\limits_{x \to a} p(x)}\\
\\
&= 0^{\infty}\\
\\
&= 0\\
\\
\text{c. ) } \lim_{x \to a} [h(x)]^{p(x)} &= \lim_{x \to a} [h(x)]^{\lim\limits_{x \to a} p(x)}\\
\\
&= 1^{\infty} && \Longleftarrow \text{(Indeterminate)}\\
\\
\text{d. ) } \lim_{x \to a} [p(x)]^{f(x)} &= \lim_{x \to a} [p(x)]^{\lim\limits_{x \to a} f(x)}\\
\\
&= \infty^0 && \Longleftarrow \text{(Indeterminate)}\\
\\
\text{e. ) } \lim_{x \to a} [p(x)]^{q(x)} &= \lim_{x \to a}[p(x)]^{\lim\limits_{x \to a} q(x)}\\
\\
&= \infty^{\infty}\\
\\
&= \infty\\
\\
\text{e. ) } \lim_{x \to a} \sqrt[q(x)]{p(x)} &= \lim_{x \to a} [p(x)]^{\frac{1}{q(x)}}\\
\\
&= \lim_{x \to a} [p(x)]^{\frac{1}{\lim\limits_{x \to a}q(x)}}\\
\\
&= \infty \frac{1}{\infty}\\
\\
&= \infty^0 && \Longleftarrow \text{(Indeterminate)}
\end{aligned}
\end{equation}
$

Why was Charlotte the only one to defend Zachariah against the Captian?

Zachariah and Charlotte are both exceptional among the Seahawk crew- one being a Black man and the other a girl. Zachariah stresses the importance of their getting to know each other and looking out for one another on ship because their respective differences put them at risk for mistreatment. Of all the people on board, Zachariah is really the only one who treats Charlotte with respect. Sure, the Captain speaks to her, but only in a way that builds up his own identity as a dominant force on board.
When Zachariah is about to be whipped as punishment for the crew's mutiny, Charlotte stands up for him as a friend. She is the only one to do so, however, perhaps because the other crew are thankful it is not them being whipped. As the only Black man on board, Zachariah is scapegoated because his life as regarded as less valuable than those of the white crew members. As a high-society girl, Charlotte has grown up with the institution of racial oppression, but she has no familiarity with it in a ship setting. I think that the foreignness of the ship's social structure makes her more free in challenging the Captain because she does not yet know what it means to violate those unspoken rules. 

What is the symbolic significance of the war imagery in "My Oedipus Complex"?

The the war imagery in Frank O’Connor’s “My Oedipus Complex,” symbolizes the metaphorical war between Larry, the story’s young narrator, and his father. The two are caught in a bitter battle over the attention of Larry’s mother. The story begins with Larry telling the reader how his father, a serviceman in World War I, will soon be returning home. The first war imagery we see relates to the various war souvenirs that Larry’s father brings home on his visits. We learn that his father has returned with “model tanks and Gurkha knives with handles made of bullet cases, and German helmets and cap badges and button sticks, and all sorts of military equipment.” While Larry is interested in his father, who seems quite magical when visiting, it is when his father returns home for good that the real battle begins.
When describing Larry and his father’s struggle, O’Connor writes, “Father and I were enemies, open and avowed. We conducted a series of skirmishes against one another, he trying to steal my time with Mother and I his.” O'Connor deftly uses war imagery, like the words “enemies” and “skirmishes,” to enhance the father/son conflict in his story. Furthermore, this usage contains a twist of irony because, during the real war, when his father was abroad fighting, Larry says he experienced the “most peaceful period” of his life. In fact, he enjoyed the accoutrements of war. He found the treasures and his father’s occasional presence in his military uniform quite interesting. However after his father’s return, which should have been a happy time for Larry, Larry finds himself at war with his dad. The tension between father and son results in a battle in the household, one which Larry, the ever-committed soldier, claims he will “never give up.” Of course, at the story’s end, Larry and his father reconcile, but O’Connor’s deft and clever use of war imagery does much to illuminate the father son struggle in “My Oedipus Complex.”

In 1984, what are the three sacred principles of Ingsoc?

The three sacred principles of Ingsoc are Newspeak, doublethink, the mutability of the past. Newspeak is the official language of Oceania and the totalitarian regime's attempt to alter human thought and completely eradicate political dissent. Each year, the Newspeak dictionary becomes smaller and smaller as government agents delete adjectives and incendiary words while they combine opposite words that can be used to describe contradicting thoughts.
The illogical Newspeak words directly connect to the second principle of doublethink, which is the ability to believe two contradicting ideas simultaneously and accept whatever information the Party declares. The Party attempts to control reality via the practice of doublethink. Essentially, the Party can make false, contradictory claims and the public with fully accept, believe, and embrace the information by practicing doublethink.
The third principle is the mutability of the past, which is the government's ability to continually alter historical documents that favor their current policies. One of the Party's slogans reads,

Who controls the past . . . controls the future: who controls the present controls the past. (Orwell, 44)

Winston Smith works in the Ministry of Truth, where he alters and fabricates historical documents to coincide with the Party's current policies. These three principles allow the Party to control, manipulate, and oppress the population of Oceania.

The three main principles of Ingsoc (English Socialism) are expressed in the slogans WAR IS PEACE, FREEDOM IS SLAVERY, and IGNORANCE IS STRENGTH. The significance of these principles, and the reasons for the slogans expressing them, become increasingly apparent to Winston as the story of 1984 progresses.
The Party's reasoning (if one can call it that) is that the population can be controlled and manipulated by destroying its power to think and understand reality. In dictatorial regimes, such as the Communist and Fascist countries of Orwell's own time, the rulers always attempted to obliterate the concept of objective truth. Truth, to them, becomes not what people objectively observe as occurring, but instead whatever the government or the "Party" says it is. Orwell's novel is a projection into the future of what was already happening in the nightmare world of the 1930's and 40's. The statements that "War is Peace," and "Freedom is Slavery," since they are direct self-contradictions and make no sense, are intended to negate the concept of logic. They are also examples of doublethink, the ability to hold two contradictory ideas in the mind and believe both of them simultaneously, as the Party desires people to do, including its own members.
In 1984, the scene in which, in the middle of a rally, the speaker suddenly declares that Oceania is at war with Eastasia and has always been at war with it and is in alliance with Eurasia and has always been—the direct opposite of the truth—demonstrates the Party's manipulation of facts ad absurdum. To the Party, truth is whatever it declares truth to be, and people are expected to believe it in spite of what their own senses and memories tell them, just as they are expected to believe that opposites such as freedom and slavery are the same thing. This is the 1984-version of "alternative facts" being presented as reality.
The third slogan, "Ignorance is Strength," is not as much of a direct self-contradiction as the first two, but it nevertheless demonstrates the same principle—that it is desirable for people not to have knowledge. If people are kept in a state of ignorance (which the Party considers strength), then they can be manipulated and controlled to whatever degree the Party wishes. As O'Brien reveals during Winston's interrogation and torture, the Party's sole motivation is power. In other words, the old ideas about creating an egalitarian society and freedom for the working class are a sham, and this is obvious when one considers the principles embedded in Ingsoc.

int sec^6(4x)tan(4x) dx Find the indefinite integral

Given to solve,
int sec^6 (4x)tan(4x) dx
let u = 4x , du = 4dx
so,
int sec^6 (4x)tan(4x) dx
= int sec^6 (u)tan(u) (du)/4
= (1/4) int sec^6 (u)tan(u) du
let secu = v
so, dv = (sec u)(tan u) du
so ,
(1/4) int sec^6 (u)tan(u) du
= (1/4) int sec^5 (u) tan(u) *sec(u) du
=(1/4) int (v)^5 dv
= (1/4) v^6/6
= (v^6)/24
= ((sec (u) )^6)/24
=((sec (4x) )^6)/24 +c

Calculus of a Single Variable, Chapter 8, 8.7, Section 8.7, Problem 31

Given to solve ,
lim_(x->oo) cosx/x
by applying the squeeze theorem we can solve the limits
and it is as follows,
as we know the boundaries of the cos(x) as
-1<=cos(x)<=1
now dividing the above expression with x , we get
-1/x<=cos(x)/x<=1/x
now applying the limits of x-> oo for the above expression, we get
lim_(x->oo) (-1/x)<=lim_(x->oo) cos(x)/x<=lim_(x->oo) (1/x)
now upon x-> oo we get
lim_(x->oo) (-1/x) =(-1/oo) =0
and
lim_(x->oo) (1/x) = (1/oo)=0
so,
lim_(x->oo) (-1/x)<=lim_(x->oo) cos(x)/x<=lim_(x->oo) (1/x)
=>0<=lim_(x->oo) cos(x)/x<=0
=>lim_(x->oo) cos(x)/x =0

Single Variable Calculus, Chapter 4, 4.8, Section 4.8, Problem 14

Use Newton's Method to approximate the root of $2.2x^5 - 4.4x^3 + 1.3x^2 - 0.9x - 4.0 = 0$ in the interval $[-2, -1]$ correct to six decimal places.







We apply Newton's Method with


$
\begin{equation}
\begin{aligned}

f(x) =& 2.2x^5 - 4.4x^3 + 1.3x^2 -0.9x - 4 \text{ and }
\\
\\
f'(x) =& 2.2 \frac{d}{dx} (x^5) - 4.4 \frac{d}{dx} (x^3) + 1.3 \frac{d}{dx} (x^2) - 0.9 \frac{d}{dx} (x) - \frac{d}{dx} (4)
\\
\\
f'(x) =& (2.2)(5x^4) - (4.4)(3x^2) + (1.3)(2x ) - 0.9(1) - 0
\\
\\
f'(x) =& 11x^4 - 13.2x^2 + 2.6x - 0.9

\end{aligned}
\end{equation}
$


Based from the graph, we choose $x = 1.4$

Using Approximation Formula


$
\begin{equation}
\begin{aligned}

x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)}
\\
\\
x_2 =& x_1 - \frac{2.2x_1^5 - 4.4x_1^3 + 1.3x_1^2 - 0.9x_1 - 4}{11x_1^4 - 13.2x_1^2 + 2.6x_1 - 0.9}
\\
\\
x_2 =& -1.4 - \frac{2.2(-1.4)^5 - 4.4(-1.4)^3 + 1.3(-1.4)^2 - 0.9(-1.4) - 4}{11(-1.4)^4 - 13.2(-1.4)^2 + 2.6(-1.4) - 0.9}
\\
\\
x_2 \approx & -1.4
\\
\\
\\
\\
x_3 =& -1.404176 - \frac{f(-1.404176)}{f'(-1.404176)}
\\
\\
x_3 \approx & -1.404118
\\
\\
x_4 =& -1.404118 - \frac{f(-1.404118)}{f'(-1.404118)}
\\
\\
x_4 \approx & -1.404118


\end{aligned}
\end{equation}
$


Since $x_3$ and $x_4$ agree to six decimal decimal places, therefore $x \approx -1.404118$

How is geography structured and described in the novel Lost City Radio?

In Lost City Radio, the city is the epicenter of the country, surrounded by the mysterious and eerie jungle, which death and destruction have laid to waste. At the beginning of the novel, Victor is a refugee from the jungle, who the residents of his village, now renamed 1797, have sent to Norma in the city. They write her a letter, stating that they "have pooled our monies together, and sent him to the city" (page 5). They have done so because "we want a better life for Victor" (page 5). 
The city is where people go for hope, while the jungle is a mass of renamed villages whose histories have been erased. The towns in the jungle bear numbers related to their geography. Odd-numbered towns are near water, and those with high numbers are way up in the mountains. Alarcon writes, "Norma hated the numbers. Before, every town had a name; an unwieldy, millenarian name inherited from God-knows-which extinct people, names with hard consonants that sounded like stone grinding on stone" (page 5). The government's erasure of the old town names is a symbol, eerie in tone, of their attempt to eradicate the past. In the past, villages had solid foundations on maps; Alarcon compares the sound of the villages' old names, in a simile, to the sound of stone grinding on stone to convey how solid the old villages were. Now, given simply numbers, the towns seem ephemeral and without history.
The city is the center of the lost jungle, the place to which refugees come streaming for a better life. Norma's radio show, during which people call in looking for lost friends and family, is described in the following way: "And Norma listened, and then repeated the names in her mellifluous voice, and the board would light up with calls, lonely red lights, people longing to be found" (page 9). The red lights are symbolic of people from the jungle who stream and call into the city looking for hope. 

Throughout the course of the play there is reasoning that Iago fits the description of "motiveless malignity," however, are there reasons for why Iago is not motivelessly malignant?

Iago states in act 1, scene 1 that he is jealous Othello made Cassio his lieutenant. Iago believes he has had more battle experience and is therefore better qualified for the position than Cassio. He accuses Cassio of getting all his military knowledge from reading—what Iago calls "bookish theoric"—whereas Iago implies he himself is battle-hardened and presumably wiser about military matters:

One Michael Cassio, a Florentine,A fellow almost damned in a fair wife,That never set a squadron in the field,Nor the division of a battle knowsMore than a spinster—unless the bookish theoric,... mere prattle, without practiceIs all his soldiership. But he, sir, had the election.

In act 1, scene 3, Iago asserts he has heard rumors that Othello is sleeping with his wife, Emilia. Although he says he does not know whether it is true, his reaction fits into his pattern of expressing twisted views of women, considering them all sexually unfaithful. When he says the Moor, Othello, has done his "offices" "'twixt his sheets," he means he has heard Othello has slept with Emilia. Iago states:

I hate the Moor,And it is thought abroad, that 'twixt my sheets'Has done my office.

While I believe Iago does suffer from what Coleridge called motiveless malignancy—that is, he appears to have a hatred of Othello disproportionate to anything Othello has done to him—Iago does, in fact, provide rationales for his actions. He states he resents the unfairness of Cassio being promoted over him and fears that Othello is sleeping with his wife. Whether we believe what he says is the question.

Bruno Bettleheim argued that fairy tales played an important role in children’s development. How far would you agree with Bettleheim, and are his theories as relevant to fairy tales on film?

In his book The Uses of Enchantment, Bettleheim argued that children should be exposed to the harsh realities revealed in fairy tales rather than kept away from them. Bettleheim argued that children have many fears and understand that life isn't perfect. They know bad events can occur. Fairy tales, by displacing fear and anxiety into the realm of fantasy, can help children to deal with the real fears they experience in their young lives.
I agree with Bettleheim up to a point. I wouldn't expose children to a steady diet of, say, the fairy tales recorded by the Grimm brothers, but I also wouldn't surround children with a steady diet of saccharine stories that all have happy endings, as that would not be a realistic exposure to life. It's also important, I believe, to remember that life for most children now is not as harsh as it was when the fairy tales were being told, and so children today could be exposed to an unnecessary degree of anxiety if they read too many fairy tales. For example, far fewer children lose their parents to early death than in the old days. Hunger and abandonment are also both far less likely than they used to be in, say, the eighteenth century. Children may need to deal with these fears, but they don't need to be immersed in this kind of literature.
Many have criticized filmed versions of fairy tales, especially those produced by Disney, for softening  and putting happy endings on stories, such as "The Little Mermaid," that were harsher in the original version. That practice makes filmed fairy tales less relevant to Bettleheim's theories.

How can Freud’s concept of Oedipus complex be used to describe John the Savage?

Freud's Oedipus complex states that young boys unconsciously want to kill their fathers so they can have their mothers to themselves. Young boys want to have sex with their mothers, according to Freud. This leads them to experience a good deal of unconscious guilt.
John is unlike the other people in the World State because he was raised by his mother, Linda, on the Indian Reservation. He has a troubled relationship with his mother.
In his earliest memory, he has her all to himself in bed:

It was very hot. They had eaten a lot of tortillas and sweet corn. Linda said, “Come and lie down, Baby.” They lay down together in the big bed. “Sing,” and Linda sang. Sang “Streptocock-Gee to Banbury-T” and “Bye Baby Banting, soon you’ll need decanting.”

But soon, although his father is not on the scene, he has to compete for her attention with other men who also want her sexually—and he loses her to them, just as a young boy loses his mother to his father:

There was a loud noise, and he woke with a start. A man [Popé] was saying something to Linda, and Linda was laughing. She had pulled the blanket up to her chin, but the man pulled it down again.

John is banished so that Popé can have sex with his mother. Popé's phallic masculinity is symbolized by his hair:

His hair was like two black ropes

We are told John hates Popé and the other men who visit his mother:

He hated Popé. He hated them all—all the men who came to see Linda.

When he discovers Shakespeare, John is immediately drawn to Hamlet, a text Freud pointed to as playing out a repressed version of the Oedipal conflict. John especially focuses on Hamlet's Oedipal relationship with his mother. John instantly perceives Linda in Hamlet's accusations about his own mother:

In the rank sweat of an enseamed bed,
Stew’d in corruption, honeying and making love
Over the nasty sty.

Both John and Hamlet want to make love to their mothers and both are jealous and filled with guilt over their unconscious desires. In the Freudian reading of the play, Hamlet wants to kill his uncle Claudius not because Claudius killed his father, but because Claudius is doing what Hamlet secretly wishes he could do: sleeping with his mother.
In John's case, after seeing Pope in bed with his hand on his mother's breast and his braid draped across her throat, the jealous John tries, unsuccessfully to kill his rival by stabbing him.
We can see John's desire to be whipped as a way to alleviate his unconscious guilt, just as we can see his self-flagellation after he moves to the World State as yet another manifestation of his intense guilt.
Lenina, the woman John falls in love with in the World State, is very much like his mother, and therefore represents another facet of his Oedipal desire. Because of his very confused relationship with his mother, who is both loving and rejecting towards him, John lashes out at Lenina. He becomes very frightened when Lenina unzips and steps out of her unitard suit and approaches him sexually: he both desires her and yet has to guard against the desire as he had to guard against his desire for his mother. He projects the anger he felt towards his mother for sleeping with other men against Lenina, calling her a whore and a strumpet:

The Savage caught her [Lenina] by the wrists, tore her hands from his shoulders, thrust her roughly away at arm’s length.
“Ow, you’re hurting me, you’re. oh!” She was suddenly silent. Terror had made her forget the pain. Opening her eyes, she had seen his face-no, not his face, a ferocious stranger’s, pale, distorted, twitching with some insane, inexplicable fury. Aghast, “But what is it, John?” she whispered. He did not answer, but only stared into her face with those mad eyes. The hands that held her wrists were trembling. He breathed deeply and irregularly. Faint almost to imperceptibility, but appalling, she suddenly heard the gneding of his teeth. “What is it?” she almost screamed.
And as though awakened by her cry he caught her by the shoulders and shook her. “Whore!” he shouted “Whore! Impudent strumpet!”

While Huxley critiques the sterility and lack of deep relationship in the World State, he also shows what an Oedipal mess families can be.

Provide three examples of allusions that King uses to support his reasoning. How does this type of evidence strengthen his argument?

Dr. King uses an allusion when he refers to the Reverend Reinhold Niebuhr, an American theologian and professor as well as a leading intellectual during the mid-20th century. Niebuhr wrote several influential books, one in particular that addressed the morality of the individual versus the immorality of society. He is also credited with writing the Serenity Prayer. Dr. King writes,

History is the long and tragic story of the fact that privileged groups seldom give up their privileges voluntarily. Individuals may see the moral light and voluntarily give up their unjust posture; but, as Reinhold Niebuhr has reminded us, groups are more immoral than individuals.

This reference to such an eminent person—one who has actually been called the greatest Protestant theologian in the last two centuries—strengthens Dr. King's argument and credibility with his intended audience, a group of white, Southern religious leaders. Not only is he familiar with Niebuhr's work, but he is also influenced by it, as they likely have been as well.
Dr. King employs another allusion when he refers to the common drug, thalidomide. He says that black Americans are often told to wait, as though waiting will eventually result in there being a good time, so to speak, for them to demand their rights. However,

This 'wait' has almost always meant 'never.' It has been a tranquilizing thalidomide, relieving the emotional stress for a moment, only to give birth to an ill-formed infant of frustration.

Thalidomide was a drug used to treat anxiety and other kinds of tension as well as morning sickness in gestating women. Sadly, thalidomide causes terrible birth defects and many thousands of infants were born with malformed limbs, among other problems, as a result of their mothers' ingestion of the drug while pregnant. Many of these infants could not survive. Here, Dr. King continues to show his own intellectual capacity and the extent of his knowledge, referencing what would have been a very well known issue of the time, something sure to grab the attention of his audience and give them pause, make them think about how the black community has been placated only to have even bigger problems later.
Dr. King employs another set of allusions when he writes that

You express a great deal of anxiety over our willingness to break laws [...]. Since we so diligently urge people to obey the Supreme Court's decision of 1954 outlawing segregation in the public schools, it is rather strange and paradoxical to find us consciously breaking laws. One may well ask, "How can you advocate breaking some laws and obeying others?" The answer is found in the fact that there are two types of laws: there are just laws, and there are unjust laws. I would agree with St. Augustine that "An unjust law is no law at all."

Here, he alludes to the Supreme Court ruling in favor of desegregation, Brown v. Board of Education. The highest court in the land has ruled that desegregation of schools must take place but a black person still cannot sit at the same coffee counter as a white person? He also alludes to St. Augustine, another important touchstone for the religious community. In making these references, Dr. King both establishes his knowledge of the law as well as his knowledge of what is right. The idea that one does not have to obey an unjust law is not his own but is grounded in religious authority and sacred texts.

An allusion is a reference or connection to something else. Using an allusion connects what a person is writing or speaking about to a different event, place, person, or thing, and this helps put their topic into a specific context for the reader or listener, helping the audience connect, intellectually and/or emotionally, to what is being said or done. The type of allusion used might have to do with the audience. To an audience of children, you might make an allusion to an experience they are familiar with, like learning to ride a bike or being forced to go to bed early. To an audience of religious leaders like Dr. King's, he makes allusions to religious and historical people and events he expects them to know about and have strong connections to.
Dr. King uses allusion in his letter to compare what he is doing to important historical people and events, putting his own work into an important historical context. Three examples are as follows:
1) "...just as Apostle Paul left his little village of Tarsus and carried the gospel of Jesus Christ to practically every hamlet and city of the Greco-Roman world, I too am compelled to carry the gospel of freedom beyond my particular hometown."
2) "Isn't this like condemning Jesus because His unique God-consciousness and never-ceasing devotion to His will precipitated the evil act of crucifixion?"
3) "It was 'illegal' to aid and comfort a Jew in Hitler's Germany."
In all these cases, Dr. King is referencing important historical people and events he expects his audience of Southern preachers to understand and have certain associations with. He uses references to Christian heroes and recent terrible events to appeal to his audiences' knowledge of and emotions about these people and events. In doing so, he compares himself and the people he is working with to people he knows his audience will be sympathetic with, appealing to their morals. He also places himself in an important historical context, elevating what he is doing as important work.

Allusion is used many times throughout Dr. King's letter. Here, I will point out just three:
1. "just as the Apostle Paul left his village of Tarsus and carried the gospel of Jesus Christ to the far corners of the Greco Roman world"
2. "Just as Socrates felt that it was necessary to create a tension in the mind so that individuals could rise from the bondage of myths and half truths to the unfettered realm of creative analysis and objective appraisal"
3. "It was "illegal" to aid and comfort a Jew in Hitler's Germany."
In all three cases, Dr. Martin Luther King Jr. uses allusion to cast his struggle in the terms of historical significance. By drawing comparison to events that most people are familiar with, he makes the argument that what he is doing is monumental, something to be written down in history books for generations to come.
Let us also remember his audience: the letter begins by addressing "My Dear Fellow Clergymen." Dr. King was a Baptist minister, and his allusion to the Apostle Paul invokes the sacred oaths that he and his readers have all taken. He reminds them of their collective similarity in a time of drastic segregation, and he calls forth their allegiance to justice and truth.
Finally, Dr. King was a realist. He understood that his task in writing this letter was to induce sympathy in the unsympathetic and to make his cause and struggle a common one. His allusions to Socrates and Hitler's Germany remind us of a lesson history repeatedly teaches us: to exist as a responsible member of society is to question its traditions.

How did Scott recover from his addictions?

Scott used to work as a nurse before his license was revoked due to addiction issues. He'd become hooked on painkillers and other opioids. Not only has Scott's addiction cost him his job, it's also cost him his car and home. So like so many others in Milwaukee, he's found himself out on the streets with no place to go. At a homeless shelter, he meets Teddy, a man with disabilities, and together they move into a trailer, where Scott uses his nursing skills to help Teddy with his partial paralysis. He also helps out with the chores.
Life at the trailer park is tough for Scott. His addictions get worse, and he starts shooting black tar heroin. His life is in a downward spiral. Things deteriorate further when he and Teddy are subsequently evicted from the trailer park for allowing two drug addicts, who themselves have already been evicted, to stay with them. Scott ends up moving from place to place, in and out of rehab. After finding a place in a homeless shelter, Scott finally manages to stay clean. He works there as a custodian for a year before being given subsidized housing. This is the life raft that Scott sorely needed. With an affordable place to live, he's able to stay off drugs, find meaningful work, and strive for independence.

College Algebra, Chapter 2, 2.4, Section 2.4, Problem 76

According to the manager of a furniture factory, it costs $\$2200$ to manufacture 100 chairs in one day and $\$ 4800$ to produce 300 chairs in one day.

a.) Assume that the relationships are linear, find an equation that expresses this relationship. Then graph the equation.

b.) What is the slope of the line in part (a) and what does it represent?

c.) What is the $y$-intercept of this line, and what does it represent?

a.) By using two point form, the slope of the points $(100, 2200)$ and $(300, 4800)$ is..

$\displaystyle m = \frac{4800 - 2200}{300 - 100} = \frac{2600}{200} = 13$

By using two point form,


$
\begin{equation}
\begin{aligned}

y =& mx + b
&&
\\
\\
y =& 13 x + b
&& \text{Substitute the value of the slope}
\\
\\
2200 =& 13(100) + b
&& \text{Solve for } b
\\
\\
b =& 900

\end{aligned}
\end{equation}
$


Thus, the equation is..

$y = 13x + 900$







b.) The slope of the line is 13, it represents the cost per chair produced.

c.) The $y$-intercept is 900, it represents the cost outside production, regardless of the number of chairs produced. Maybe for maintenance cost or rental cost.

College Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 62

Suppose that $f(x) = 8 - 3x$. (a) Determine the average rate of change of $f$ between $x = 0$ and $x = 2$ and the average rate of change of $f$ between $x = 15$ and $x = 50$ (b) Were the two average rates of change that you found in part(a) the same? Explain why or why not.

Recall that the formula for averate rate is...
$\displaystyle \frac{f(b) - f(a)}{b - a}$
Thus,

$
\begin{equation}
\begin{aligned}
\text{a.) } \frac{f(2) - f(0)}{2 - 0} &= \frac{8-3(2) - [8-3(0)]}{2}\\
\\
&= \frac{8-6-8}{2}\\
\\
&= -3
\\
\\
\\
\frac{f(50) - f(15)}{50-15} &= \frac{8-3(50) - [ 8 - 3 (15) ] }{35}\\
\\
&= \frac{8-150-8+45}{35}\\
\\
&= \frac{-105}{35}\\
\\
&= -3
\end{aligned}
\end{equation}
$

b.) The average rates are the same in part(a). This shows that the distance covered between the two pair of points have equal slopes.

Why was a form of writing important to civilizations?

We may not think very much about how people know what they know, but when we stop and do think about this, it is easy to see what a difference writing has made. Writing was a quantum leap for civilization.  It saved people from having to reinvent the wheel, it allowed people to share ideas, facts, and great beauty through time and space, and it even aided commerce.   
Imagine, if you will, a world without writing in which someone discovered an antibiotic a thousand years ago.  There are bound to be rumors through the years about a discovery like this, but without the knowledge being written down, millions of people who could have been saved will die.  We would all have to wait around for someone else to stumble upon this antibiotic again.  There is no history of much of anything without writing.  We would stumble around making the same mistakes over and over again, a sort of dreadful Fifty First Dates scenario in which we didn't know which tribes were historically our enemies and which were our friends or in which we did not know that those weeds we keep finding are actually edible and can save us from starvation.  And whatever lessons we glean, with writing, we can transmit them to others and transmit them to the future, too.
Without writing, we would have little of the riches we have now in our lives.  Philosophy has come down to us in writing.  Our works of literature have come to us in writing.  Beowulf probably emerged from an oral tradition, but had someone not written it down, it seems quite unlikely that we would be able to study and enjoy it today.  Our appreciation for the heavens is thanks to ancient astronomers who wrote down what they knew.  Music is handed down through the ages through writing now.  We can look at scores of music that are hundreds of years old and play them.  Mathematics is a form of writing, too, one that comes to us via Indian and Arabic cultures.  Most of the religions in the world are based upon one or more holy texts that encouraged and solidified membership in their respective religious communities.  And say what you will about the divisive aspect of religion, there is no question that its development has made substantial contributions to civilization, at the very least, creating community and building some of the most magnificent architecture ever built.
Writing helped commerce. People could create tallies, keep track of their inventories and profits, and take orders once we had writing. (Perhaps the first writing in commerce was a customer complaint!) Writing helped trade to expand, which spread civilization, as people went further afield and shared ideas.  While I'm not sure that I would consider Amazon to be the quintessence of civilization, the fact is that it could not exist at all without writing. 
There are probably hundreds more ways in which writing helped us to build civilization. It created a truly paradigmatic shift in the affairs of human beings.  But certainly, at the very least, it saved us from having to invent or discover things over and over again, it allowed beauty and wisdom to be broadcast through time and space, and it was crucial in the development of trade and commerce. 
 
http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=ab33

In the novel The Bronze Bow, how does Samson celebrate Daniel's return to the mountain? Why does this bother Daniel?

In Chapter 8, Daniel returns to the mountain after suffering a serious injury inflicted by a Roman soldier. Samson is patiently waiting for Daniel when he spots him struggling to climb a steep hill. Samson walks down the mountain and carries Daniel back to the cave. Samson does not allow Daniel to stand on his feet for three days so that he can rest. Speare describes Samson as a "vast shadow" that shelters Daniel. Samson goes out his way to bring Daniel water mixed with wine and takes the choicest bits of meat to feed him. Samson's attitude towards Daniel demonstrates his loyalty to him, and the rest of Rosh's men seem relieved that Daniel is back. Although Speare does not directly comment on Daniel's feelings concerning Samson's special treatment, one can imagine that Daniel does not like the attention. Daniel is a self-reliant, independent individual. He does not enjoy being the center of attention and does not appreciate the fact that he receives special treatment.

How have developing countries and poor people responded to globalization?

Societies in developing countries have been divided in their response to globalization. Poor farmers from the global South have rejected some aspects of globalization, such as the export of heavily subsidized American and European food to Africa and Latin America, as this export has in many cases harmed local agriculture. There has been much anger in Africa and India about the attempts of Monsanto and other transnational companies to encourage African and Indian farmers to buy their genetically modified wheat and cotton seeds.
At the same time, global mobility has allowed millions of migrant workers from Asia, Africa, and Latin America to find better paying jobs in the West. They have been able to send money to their relatives at home, where these remittances have energized local economies. Western companies seeking cheap labor have transferred their production facilities to Mexico, China, Vietnam, Bangladesh, India, and many other places in the developing world. As a result, hundreds of millions of people in the developing world now have better paying manufacturing jobs; on the other hand, the United States and European countries have lost many industrial jobs.
Similarly, because jobs requiring special training or education encourage migration, highly educated people tend to leave their countries for the West. Researchers speak about the global brain drain created when scientists, nurses, engineers, programmers, and other highly educated people move to the West from the developing world.
Thus, the impact of globalization on the developing world has been mixed.

What are some cultural rights of passage (For example, Bar Mitzvah, Quinceanera, etc.), and what images or pictures do you automatically think of when someone refers to culture?

Cultural rights of passages are coming of age ceremonies. A teenager transitioning into adulthood may partake in a rights of passage ceremony, reflecting his or her culture. Culture is the specific customs and beliefs of a certain group of people and can include music, arts and style of clothing.
As you mentioned in your question, a Bar Mitzvah and Quinceaneara, are a few of these ceremonies. In Jewish culture, a Bar (Male) or Bat (Female) Mitzvah is a religious ceremony for a Jewish boy or girl who reaches the age of 13 and can now observe religious doctrine and partake in worship service. A Bar or Bat Mitzvah may be celebrated with a lavish party. In Latin American culture, a Quinceaneara celebrates a young woman's 15th birthday and acknowledges her transitioning from a child to a young adult. With similarities to a Bat/Bar Mitzvah, a Quinceaneara is celebrated with a luxurious party.
A few additional examples of rites of passage include a Debutante ball and Sweet Sixteen.

The cultural rites of passage that first come to mind for me are the two you listed, both of which can be classified as coming of age ceremonies. Bar Mitzvah (a Jewish boy who reaches the age of thirteen) and Bat Mitzvah (a Jewish girl who reaches the age of twelve) are terms that signify one has reached the age of obligation to serve the commandments of Jewish law, and this can also refer to a large celebration that coincides with this milestone.
In many regions, including South America, a girl who reaches the age of fifteen is called a quinceañera, a term which combines the words quince (which is the number fifteen) and años (which means years). A large birthday celebration often accompanies this milestone, and the party itself is also referred to as a quinceañera. Equivalents to a coming of age ceremony in American culture may include a "Sweet Sixteen" party, which is thrown to celebrate the pivotal birthday in which a teenager is eligible for a driver's license, and a debutante ball, in which members of the upper class are formally presented to society in a lavish celebration.
Religious rites of passage such as circumcision, or the surgical removal of foreskin, and christening, which occurs when water is sprinkled as a sign of admission to the Christian Church, occur in infancy and extend across cultures. Circumcision is common in Judaism, Islam, and various Christian denominations, and christening is common in Catholicism and Christianity, though in other branches of Christianity the practice of believer's baptism is utilized instead, and occurs following a profession of faith at a mature age. Other important Catholic rites of passage include Confirmation, First Eucharist, and First Confession, and marriage is an important religious rite of passage in almost every culture.
A few things that come to mind regarding your second question: I associate hijabs with Muslim culture, I associate dashikis with African culture, and I associate the Confederate flag with rural areas in the southern United States, even though I know many people with roots in these cultures who don't dress or associate themselves with those items—therefore, these associations likely may be misinterpretations. The most vivid cultural image I can recall is Holy Week in Spain, filled with religious imagery, extravagant processions and ceremonial dress, while my husband most associates Spanish culture with bullfighting. My Spanish culture association is primarily influenced by time spent traveling, and my husband's is most influenced by popular culture. I think media can affect (and often, simplify) the immediate associations we make, and I would suggest that life experience plays an equally important role. Combining media representations of subject matter with actual relationships is an excellent way to maintain a well-balanced outlook on any subject.
https://www.globalcitizen.org/en/content/13-amazing-coming-of-age-traditions-from-around-th/

https://www.tripsavvy.com/semana-santa-in-spain-1644106

Single Variable Calculus, Chapter 5, Review Exercises, Section Review Exercises, Problem 34

Determine the derivative of the function $\displaystyle F(x) = \int^1_x \sqrt{t + \sin t} dt$ using the properties of integral.
Using the properties of integral
$\displaystyle \int^a_b f(x) dx = - \int^b_a f(x) dx$

Then,
$\displaystyle F(x) = \int^1_x \sqrt{t + \sin t} d t = - \int^x_1 \sqrt{1 + \sin t} dt$
Since $F(t) = - \sqrt{t + \sin t}$, using the first fundamental theorem of calculus
$\displaystyle g(x) = \int^x_a f(t) dt$, then
$F'(x) = -\sqrt{x+\sin x}$

Calculus of a Single Variable, Chapter 8, 8.1, Section 8.1, Problem 56

y'=1/(xsqrt(4x^2-9))
y=int1/(xsqrt(4x^2-9))dx
Apply integral substitution: x=3/2sec(u)
dx=3/2sec(u)tan(u)du
y=int1/(3/2sec(u)sqrt(4(3/2sec(u))^2-9))(3/2sec(u)tan(u))du
y=inttan(u)/sqrt(4(9/4sec^2(u))-9)du
y=inttan(u)/sqrt(9sec^2(u)-9)du
y=inttan(u)/(sqrt(9)sqrt(sec^2(u)-1))du
Now use the identity:sec^2(x)=1+tan^2(x)
y=inttan(u)/(3sqrt(1+tan^2(u)-1))du
y=inttan(u)/(3sqrt(tan^2(u)))du
y=inttan(u)/(3tan(u))du assuming tan(u) >=0
y=int1/3du
take the constant out,
y=1/3intdu
y=1/3u
Substitute back u=arcsec((2x)/3)
and add a constant C to the solution,
y=1/3arcsec((2x)/3)+C

(Lines 509-518) Why was the general bored by the hunt last night?

After Rainsford spends a sleepless night in General Zaroff's chateau, he joins the general for lunch the next day. When the general arrives for lunch, he inquires about Rainsford's health and says that he is worried. The general explains to Rainsford that he is becoming bored with hunting again because his prey is not challenging enough. General Zaroff tells Rainsford that the previous night's hunt was not exhilarating or fun because the man he was chasing lost his mind. The general says that the sailor made a straight trail through the forest and could not navigate the island, which resulted in a boring hunt. General Zaroff believes that the sailors have dull minds and finds it more annoying than satisfying to hunt someone who cannot challenge his abilities. After listening to the general lament about his boring hunting experience the previous night, Rainsford asks to leave the island. Unfortunately, General Zaroff dismisses his request and ends up hunting Rainsford for the next three days.

The narrator tells us that he never had any troubles until he began drinking alcohol, yet there is evidence in the story that alcohol isn't the only thing to blame for his sociopathic actions. Describe other things we learn about the author that likely contribute to his slide into violence and insanity.

While it's true that the narrator of Edgar Allan Poe's "The Black Cat" initially blames alcoholism for his change in behavior and evil acts, as the story progresses, he adds other details that suggest alcoholism is not to blame for every heinous act he commits.
The narrator describes his love for the cat named Pluto, and the closeness of his relationship with the cat. One night, when he arrives at home drunk, the cat avoids him. This angers him enough to cruelly cut the cat's eye out. The narrator has this to say shortly before he hangs the cat:

Who has not, a hundred times, found himself doing wrong, doing some evil thing for no other reason than because he knows he should not? Are not we humans at all times pushed, ever driven5 in some unknown way to break the law just because we understand it to be the law?

There is no evidence that he is drunk at the time this act is plotted or committed. What he says next certainly calls into question his sanity, regardless of alcohol abuse:

I hung it from one of the wood beams above my head. I hung it there until it was dead. I hung it there with tears in my eyes, I hung it because I knew it had loved me, because I felt it had given me no reason to hurt it, because I knew that my doing so was a wrong so great, a sin so deadly that it would place my soul forever outside the reach of the love of God!

So basically, he cruelly maims and then kills a cat who, by his own admission, never did anything but love him. After the death of the cat, the narrator's house burns, and he again responds in a way that calls his mental state into question:

I thought of the cat as I watched it burn, the cat whose dead body I had left hanging in the cellar. It seemed almost that the cat had in some mysterious way caused the house to burn so that it could make me pay for my evil act, so that it could take revenge upon me.

I think everyone would agree that it's outside the bounds of sanity to blame a house fire on a dead cat's revenge. It's paranoid and delusional, actually. When he finds another cat and continues his psychotic behavior, he blames his alcoholism and mentions that he is intoxicated when he attacks the next cat. But throughout the rest of the story, there is an intermingling of alcoholism and madness.

I would recommend examining the story's second paragraph for information that could clue readers into the idea that the narrator was not exactly a mentally and emotionally stable individual before he began drinking excessively. The narrator describes himself as a docile individual, and he admits that his submissive nature made him the target of the more alpha male personality type.

My tenderness of heart was even so conspicuous as to make me the jest of my companions.

When a reader reads that information, he/she might suspect something. Teasing happens to kids all across the board; however, the narrator doesn't tell us how severe the jesting was. It's possible that the narrator was targeted and bullied by just about everybody. The narrator says "jest," but it could be verbal abuse. That would then perhaps lay the seeds for his future violent tendencies. He couldn't protect himself then, but with alcohol, he is less inhibited to act out on his pent up aggression.

I suffered myself to use intemperate language to my wife. At length, I even offered her personal violence.

We have to be careful here as the story is told from the standpoint of an unreliable narrator. This means, as the term implies, that we cannot take at face value anything he says. Bearing that in mind, we can still piece together some of the bits of information he provides to construct a relatively plausible, coherent account of what led up to his seemingly inexplicable acts.
In addition to the narrator's drinking problem, we also learn that he was quite a shy, passive child. He admits to being teased by other children for this, though to what extent we cannot know. However, it's often the case that children who are bullied develop a sense of loving companionship with animals. Such children find a degree of acceptance from animals which they simply can't find among other people.
The downside to these relationships is that they encourage children to remain in a fantasy world, arresting their emotional and psychological development. Without offering anything by way of a formal diagnosis, that's what appears to have happened here. The narrator, though biologically speaking a fully-grown man, still remains psychologically trapped in childhood. As such, he finds it difficult to cope with life in the adult world.
Alcohol has replaced animals as an emotional crutch, so much so that the narrator no longer sees their warm companionship as offering a safe retreat from a hostile world. Indeed, his animals, along with his wife, are now a part of that world. As he has no further need for them, he becomes hostile towards them. And so he vents upon them his alcoholic rages, which ultimately derive from a general inability to cope in a world which he doesn't understand and which in turn doesn't understand him.

In Gods Go Begging, how do war and prison impact the characters and affect their ability to experience their lives? Use quotes from the text to analyze the metaphors and symbols, the tone and/or feeling of each scene, demonstrating its connection to your claims and arguments.

In the novel, the devastating effects of war and prison negatively impact the main characters. In my answer, I will discuss two characters from the novel: Jesse Pasadoble and Anvil Harp.
Jesse Pasadoble is a San Francisco public defense attorney who has to wrestle with some personal demons. As a Vietnam Vet, he consistently experiences the symptoms of PTSD (post traumatic stress disorder), which means that he struggles with disturbing flashbacks and frightening dreams on a frequent basis. Jesse also has difficulty connecting emotionally with his long-suffering girlfriend, Carolina. It is obvious that memories from a decades-old war still haunt Jesse, and are impacting his ability to forge deep connections with others.
For example, Jesse thinks that Carolina is beautiful but "excessively demanding." Carolina "wants a normal, healthy, loving relationship" with Jesse, but he is uncomfortable with a relationship on that basis. Jesse had always left previous girlfriends when "sexual demands gave way to emotional demands." Here's a quote that perfectly explains Jesse's struggle:

How could he ever explain this to Carolina...to anyone? The painful memories had evolved into a cold, quizzical passacaglia, eternal notes in basso profundo and in unbreakable code. Someday he would solve the riddle of it. Someday, he would live one sweet, mortal moment without the constant accompaniment of percussive anger and a grinding bass line of grief.

The tone of the above passage is somber and melancholy in nature. Jesse uses musical metaphors to characterize the pervasive consistency of his tormenting symptoms: "The painful memories had evolved into a cold, quizzical passacaglia, eternal notes in basso profundo and in unbreakable code." In music, a passacaglia is a solemn dance that originated from Spain in the 17th century. What's unique about a passacaglia is that it often contains what is called an ostinato, which is a musical motif that repeats itself throughout the passacaglia. The ostinato is usually performed in bass. From the passage, basso profundo is the lowest range sub-type of the bass voice; the basso profundo is strong, bold, and powerful in nature.
The passage above effectively uses auditory imagery to describe Jesse's torment; his terrifying dreams and flashbacks are continual, pervasive, and entrenched. Note the bold and heavy descriptors: "basso profundo," "passacaglia," "grinding bass line of grief," and "percussive anger." 
Now, we discuss the negative impact of prison in the novel. In the story, Anvil Harp is in prison for the murder of Princess Sabine's purported husband. Anvil admits to Jesse that he had always adored Princess Sabine, but he was unlucky in love. Sabine had turned down every single one of his marriage proposals. Later, the wrenching discovery that Sabine had bedded his twelve-year-old brother sent Anvil into a depression. Although he never held Sabine's unnatural desires against her, Anvil had been devastated by the knowledge that Sabine enjoyed preying on pre-adolescent boys. 
Anvil knows that he must resign himself to serving out the rest of his sentence, and he is philosophical about it. In fact, he doesn't regret killing Princess Sabine's husband. Like others who have been incarcerated, Anvil knows that he cannot erase the past; it will continue to haunt him for as long as he lives. Here is how Jesse describes men in prison:

Jesse Pasadoble knew that those men lying down up there were all stuck on cruise control, going from place to place without any discernible motion. They moved from county jail to state prison to federal prison and even to death row in the same insensible condition: half-alive and half-asleep, moving only in the fourth dimension.

In the passage above, the tone is one of despondency. The prisoners languish in prison; they are "stuck on cruise control" and have ceased to approach life with any vestige of hope. They are neither dead nor alive, operating only in the "fourth dimension." Here, the author uses the "fourth dimension" as a metaphor to characterize the hopeless condition of the prisoners. The experience of being incarcerated is devastating to the men and far removed from the scope of any normal human experience.
 

What is a summary of the Declaration of Independence?

The Declaration of Independence is one of the most important documents in American history. It set out, for the first time, the reasons why the American colonies should break away from Britain and declare their independence.
The Declaration starts off with what's called a preamble. This is kind of like a mission statement, a way of letting everybody know what the signatories to the document are doing and why. It's a statement of intent and a justification for what's about to follow.
Then we move on the first section proper. Here, Jefferson famously justifies independence on broad philosophical grounds:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.–That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, –That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.

We are all endowed by God with natural rights. We also have the right to remove any government that doesn't respect those rights and replace it with one that does.
There then follows a long list of grievances against King George III. Among other things, he has persistently undermined attempts by the American colonists to set up legislative institutions. He has also levied taxes without the colonists' consent. Even worse, he has undermined the nation's security by, among other outrageous acts, confiscating American ships and hiring foreign mercenaries.
Finally, the American colonists have made repeated attempts to reach an amicable settlement with the British, but they have all been ignored and treated with contempt. There's nothing for it. We have no alternative but to declare our independence from Britain once and for all. In doing so, we have established a new nation. That nation is to be called the United States of America.
https://billofrightsinstitute.org/founding-documents/declaration-of-independence/

What is the central theme in The Palace Thief?

The central theme in Ethan Canin’s A Palace Thief is that of moral corruption, and he builds it around two major characters: Mr. Hundert and his student, Sedgewick Bell. The author shows the extent certain individuals go in employing unscrupulous techniques to selfishly obtain what they want. Even though Sedgewick is unruly, he seems to be under pressure from his authoritative father to excel. It is out of Hundert’s empathy and intimidation by Sedgewick's powerful father that a cycle of cheating and moral entrapment begins. Sedgewick cheats his way to good grades in tests, and at one point, does so with the aid of Mr. Hundert who is hoodwinked by his impressive ‘improvement’.
The epitome of Sedgewick’s cheating is perhaps during the ‘Mr. Julius Caesar’ competition. He boldly peeks at answers before a filled auditorium. Unfortunately, Mr. Hundert, out to safeguard his job, heeds to the headmaster’s advise to ignore the incident. Many years later, Hundert presides over a rematch of the competition only this time, Sedgewick is a powerful entrepreneur and the audience full of high ranking academics and corporate luminaries. History repeats itself; Sedgewick cheats, and Hundert fails the moral test by not calling him out.

The title story of The Palace Thief, Ethan Canin’s collection of four novellas, explores several themes. Mr. Hundert, the protagonist, is a teacher of ancient history at an elite Virginia private school. The story’s key theme centers around his attempts to live by his principles and subsequent guilt over his moral failings.
The key relationship of the story that demonstrates is that of Mr. Hundert and his student Sedgewick Bell, the son of a prominent U.S. senator. Hundert reflects on his career, haunted by his dealings with this pupil. A theme this relationship illustrates is the role of a teacher. Hundert sees himself as not just an academic leader but also a moral guide, seeking to mold the characters of the young men he teaches. This role is questioned by Bell’s father who challenges Hundert, saying, “You will not mold him. I will mold him. You will merely teach him” (164).
Hundert’s relationship with his problem student also magnifies the theme of comprising principles in the face of power. The teacher recounts a series of moral failings with Sedgewick Bell: raising his grade undeservedly, overlooking his cheating in an academic contest, and again failing to report the man’s cheating years later in another academic contest. Hundert regrets that he has lost all opportunity to mold his student’s moral character because of his own moral corruption. 

The central theme in The Palace Thief is moral corruption.  The theme is furthered by the characters of both Sedgewick Bell and Hundert.
Sedgewick Bell is morally corrupt from the beginning.  As a student in Hundert's class, Sedgewick Bell continually lies and cheats.  He is never punished (or even reprimanded) for this moral corruption even when Sedgewick Bell wins the Tournament of Roman History through cheating.  Of course, Sedgewick Bell grows up to be a corrupt businessman.  As the head of a large corporation now, Sedgewick Bell asks for yet another Tournament of Roman History and wins again by cheating.  Sedgewick Bell is never exposed as the liar and cheater he truly is.
Hundert's moral corruption appears through his cowardice at not exposing Sedgewick Bell.  Hundert, Sedgewick Bell's original teacher, knows exactly what kind of a liar and a cheater Sedgewick Bell is.  Hundert is told by his superiors to keep Sedgewick Bell's corruption quiet due to his father's position as a senator.  Hundert could have exposed Sedgewick Bell in either tournament; however, Hundert does not.  His cowardice costs Hundert his self-respect as well as the position of headmaster.

Hundert was once manipulated by a powerful senator into making allowances for his ne’er-do well son, whom Hundert knows to have cheated and whose dishonesty he has never exposed.

The only exit from moral corruption can be seen in Hundert's retirement where he warns others of corruption within the system.

The following excerpt from "The Tragic Hero: From Oedipus to Batman" implies that the character Macbeth is similar to the character Oedipus in Oedipus the King by Sophocles: Earlier in the story, he gets in a fight with a man riding a chariot, which ends in the man's death. Oedipus doesn't know it, but the stranger he kills is King Laius of Thebes. What Oedipus also doesn't know is that King Laius is his father. You see, Oedipus was abandoned as a baby and grew up in a different city, never knowing his parents. In fact, once he makes it to Thebes, the people are so thankful the Sphinx is gone that they decide to make him king, so he marries Queen Jocasta, who just happens to be his mother. In your response, argue that Macbeth's tragic hero status is actually different from Oedipus's.

As the other answers indicate, Oedipus killed his father unknowingly, while Macbeth knew exactly what he was doing in his premeditated murder of Duncan. Oedipus was, in fact, trying to flee the prophecy when he left Corinth and met his father on the road to Thebes. Macbeth almost backs out of his murderous plan, but at his wife's urging plunges forward.
However, what these different beginnings lead to is the key difference in the two men's tragic trajectories: Oedipus moves from pride and blindness to humility and virtue. Macbeth moves in the opposite direction, from decency, courage, and conscience to become a hardened tyrant filled with bitterness and despair. Oedipus, through tragedy, moves from vice to virtue. Macbeth, in contrast, moves from virtue to vice. Macbeth creates tragedy through a consciously evil act and multiplies it until he is dehumanized and without insight. Oedipus blinds himself but gains humanity and insight.
Oedipus as tragic hero teaches us we should cultivate humility because we can't control our fates. Macbeth as tragic hero teaches us that violating moral law to satisfy our ambitions—i.e., knowingly doing evil—destroys both us and the people around us.

Macbeth's status is a tragic hero is very different from that of Oedipus. For a start, Oedipus did not plan to kill his father. It happened as a result of a fight between the two men. In contrast, Macbeth plotted to kill King Duncan because he wanted to take his throne. Macbeth's desire for power far outweighed any respect and love that he felt toward Duncan.
In addition, while Oedipus is made king by the people, Macbeth takes the throne before the true heir, Malcolm, has the chance to do so. In fact, as soon as Duncan is dead, Macbeth travels to Scone to be invested, leaving the reader in no doubt of his ambition.
Finally, we can see further differences between these two men when we look at their wives. Lady Macbeth, for example, contributes to Macbeth's downfall because she drives his ambition and chastises him when he loses the courage to kill Duncan. Without her, there is a chance that Macbeth might never have killed Duncan. In contrast, we see no such malice or cunning in Queen Jocasta. Her only crime is marrying her own son. However, she did not know his true identity at the time of their marriage.

When Oedipus murders King Laius, his biological father, he does so unknowingly.  Further, Laius had actually been aggressive toward Oedipus when they ran into each other on the road.  Oedipus only thought that he was killing some stranger, a nobody, who had treated him violently first (remember, too, that Oedipus grew up as the prince of Corinth, so he's used to respectful treatment, and Laius, as the king of Thebes, was used to being treated deferentially as well -- so, lots of pride in that interaction). 
On the other hand, when Macbeth kills King Duncan, he does so with his eyes wide open, in full knowledge of who he's killing and why.  He kills his kinsman, his king, his guest, and his friend, all in one, and he does so in order to usurp the king's power and position.  Oedipus does not; he's not trying to achieve power, he's just trying to get some answers.  This is just one reason that Oedipus seems to be a much more sympathetic tragic hero: he only wants the truth -- a truth which has been withheld from him for his whole life.  Macbeth doesn't pursue truth; he pursues power, and this makes him a lot less sympathetic of a tragic hero.

Do you think we will ever see a one world government? What would be the benefits of a New World Order and what would be the risks? What would you like to see occur and why?

It is not possible to predict whether we will ever see a world government. Predictions about global political changes are sufficiently unreliable and shade into science fiction or fantasy. Instead, at best, it is possible to extrapolate events in the next few decades based on current trends.
The period immediately after World War II was one in which there seemed to be a trend toward global governance. The United Nations was founded in 1945, the European Union gradually evolved from 1951 until its formal foundation in 1993, the World Trade Organization in was founded in 1995, and the International Criminal Court in 2002. The twenty-first century, however, has seen a dramatic rise in nativism and revanchism, and a rolling back of international cooperation, with Brexit and the United States's withdrawing from the Paris Climate Accord and undermining NAFTA and other trade treaties. This suggests that nationalism and fissiparous nation-states may remain common for at least another century.
On the positive side, global government would mean an end to wars between nations and wasteful competition. It would be an economic boon, removing many barriers to movement of goods and people. On the other hand, the benefits of a global government would depend on the nature of the government and its policies. A global authoritarian government, or one that did not respect the rights of women and minorities would be quite harmful. Also, even if there were an overarching global government, there would still need to be local and regional structures in place to deal with such issues as building permits, fire departments, water and sewer systems, road building, and other local issues. Whether some form of world government would be good or bad depends on the nature of such a government and its relationship to more localized forms of governance. Without knowing those details, it is impossible to judge the value of such a system.
Personally, I think increased international cooperation is a good idea in principle, but implementation details would be quite complex.

int_0^1 sinx/x dx Use a power series to approximate the value of the integral with an error of less than 0.0001.

From the Power Series table for trigonometric function, we have:
sin(x) =sum_(n=0)^oo (-1)^n x^(2n+1)/((2n+1)!)
             = x -x^3/(3!) +x^5/(5!) - x^7/(7!) +...
Applying it on the integral int_0^1 sin(x)/x dx where the integrand is f(x)=sin(x)/x, we get:
int_0^1 sin(x)/x dx = int_0^1 sin(x)*1/x dx
                 =int_0^1 sum_(n=0)^oo (-1)^n x^(2n+1)/((2n+1)!) *1/xdx
                   =int_0^1sum_(n=0)^oo (-1)^n x^(2n+1)/((2n+1)!) *x^(-1)dx
                    =int_0^1sum_(n=0)^oo (-1)^n x^(2n+1-1)/((2n+1)!) dx
                    =int_0^1sum_(n=0)^oo (-1)^n x^(2n)/((2n+1)!) dx
                   =int_0^1 [1 -x^2/(3!) +x^4/(5!) - x^6/(7!) +...] dx
 Or 
int_0^1 sin(x)/x dx =int_0^1 sin(x)/x dx
                   =int_0^1 1/x* [x -x^3/(3!) +x^5/(5!) - x^7/(7!) +...] dx
                    = int_0^1 [x/x -x^3/(3!x) +x^5/(5!x) - x^7/(7!x) +...] dx
                    =int_0^1 [1 -x^2/(3!) +x^4/(5!) - x^6/(7!) +...] dx
To determine the indefinite integral, we integrate each term using Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
int_0^1 [1 -x^2/3! +x^4/5! - x^6/7! +...] dx= [x -x^3/(3!*3) +x^5/(5!*5) - x^7/(7!*7) +...]_0^1
           = [x -x^3/(1*2*3*3) +x^5/(1*2*3*4*5*5) - x^7/(1*2*3*4*5*6*7*7) +...]_0^1
           = [x -x^3/(6*3) +x^5/(120*5) - x^7/(5040*7) +...]_0^1
           = [x -x^3/18 +x^5/600- x^7/35280+...]_0^1
Apply definite integral formula: F(x)|a^b =F(b)-F(a) .
F(1)= 1-1^3/18 +1^5/600- 1^7/35280+...
         =1-1/18 +1/600- 1/35280+...
F(0)= 0-0^3/18 +0^5/600- 0^7/35280+...
         =0-0+0-0+...
All the terms are 0 then F(0)=0 .
We can stop on the 4th term  (1/35280 ~~2.8345x10^(-5)) since we only need an error less than 0.0001.
F(1)-F(0)= [1-1/18 +1/600- 1/35280]- [0]
                     =1-1/18 +1/600- 1/35280
                      = 0.9460827664
 Then, the approximated integral value will be:
int_0^1 sin(x)/x dx~~0.9461