Discussion: TDAU Thinkorswim Stock Selections Use the link to address the following in your initial post: Identify which companies you invested in on the TDAU Thinkorswim platform. Explain why you selected those companies. Address whether you feel your portfolio is diversified. Explain your assessment.

It looks like you have to put together a small portfolio of diversified stocks. That's a fun assignment!
First, my advice is based on what I've taught using the Stock Market Game and the Gen I-Revolution online finance games. It looks like the game portal your teacher is using is similar. I typically recommend diversifying with a combination of mutual funds, fixed-income securities like United States Treasury Bills, mid-cap stocks, and large-cap stocks. Non-cyclical stocks are also a good bet. These are basically stocks that aren't overly affected by market fluctuations. They do well whether the economy is buoyant or tanking (within limits). Examples of non-cyclical stocks are food and utilities stocks from companies like General Mills, Proctor and Gamble, Coca Cola, and Duke Energy. Take a look at top performing utilities stocks here.
Compare the list to the top electric utilities stocks of 2016.
Whatever you decide to invest in, remember to check the latest news and updates about the stocks you are interested in. Also, choose utilities or non-cyclical stocks which pay out dividends. It's always a good bet!
Read about cyclical and non-cyclical stocks here.
While we're on the subject of stocks which pay out dividends, here are some larger-cap companies that you may want to include in your portfolio: Apple, Johnson & Johnson, and AT&T. Here are the rest of the ten dividend stocks to buy in September 2016. Each listed stock comes with an explanation of why you should purchase it. Pay close attention to dividend payouts, EPS (Earnings Per Share), and P/E Ratios. Remember to look up the same information for November 2016 for the ten companies before you decide to include them in your play portfolio.
With fixed-income securities, you're lending money to the federal government. At a fixed later date, the U.S. government is supposed to return your principal investment along with a set interest. That's a great investment!
However, one caveat: U.S. Treasury Bills once considered traditionally safe investments are now in danger of becoming less so. To illustrate, the current 10-year yield is at a paltry 1.6%. Even though that's compounded, you may lose purchasing power after ten years. Whatever you do, try to keep up with current events; it's key to good investment. Read the article: The World's Safest Investment Just got More Dangerous.
I hope this helps!

Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 64

Subtract: $(5t^5 - 3t^2 + 2t) - (4t^3 + 2t^2 + 3t)$
Multiply -1 by each term inside the parentheses.
$5t^5 - 3t^2 + 2t - 4t^3 - 2t^2 - 3t$

Since $-3t^2$ and $-2t^2$ are like terms, subtract $2t^2$ from $-3t^2$ to get $-5t^2$
$5t^5 - 5t^2 + 2t - 4t^3 - 3t$

Since $2t$ and $-3t$ are like terms, add $-3t$ to $2t$ to get $-t$.
$5t^5 - 5t^2 - t - 4t^3$

Reorder the polynomial $5t^5 - 5t^2 - t - 4t^3$ alphabetically from left to right, starting with the highest order term.
$5t^3 - 4t^3 - 5t^2 - t$

Who was Hassan in the Kite Runner most like in A Thousand Splendid Suns and The Thorn Birds?

It can be argued that Hassan is most like Mariam in A Thousand Splendid Suns and Dane O'Neill in The Thorn Birds.
Certainly, Hassan's innate incorruptibility, humility, generosity, and loyalty are traits shared by both Dane and Mariam. In The Kite Runner, Hassan retains his loyalty and affection for Amir, despite the latter's betrayals. Years after he is forced out of Baba's home (and after Baba's death), Hassan consents to return to Kabul with Rahim Khan.
There is no hint of anger, bitterness, or malice in Hassan, even as he decides to give up his idyllic life outside Bamiyan for Rahim Khan's sake. Hassan even offers to help Khan tend to his former employer's home. In discussing Amir with Rahim Khan, there is only affection and kindness. When Hassan and Farzana (his wife) reach Kabul, Hassan refuses to stay in any of the rooms in Baba's home. He chooses the hut in the backyard where he was born. When questioned by a bewildered Rahim Khan, Hassan merely replies that it would be a disrespect to Amir for him to take up residence in his former friend's childhood home.
When the tortured Sanaubar, Hassan's mother, finds her way back to Baba's home, Hassan and Farzana nurse her back to health. We must remember that Sanaubar left Baba and Hassan shortly after Hassan's birth. She had rejected Hassan then because of his physical deformity. Despite her past cruelty, Hassan tends to her lovingly and provides her safety and respite in her old age.
Hassan's magnanimity and generosity can be seen in Mariam in A Thousand Splendid Suns. In the story, she opens up her heart to Laila and Aziza, despite her reservations. Mariam acts as a surrogate mother to Laila and a grandmother to Aziza. When Laila decides to flee Rasheed's home, Mariam accompanies her. Both women endure Rasheed's beatings, however, when their plans fall apart. However, the indomitable Mariam courageously comes to Laila's aid when Rasheed threatens to go through with killing the younger woman.
In the throes of unadulterated rage, Rasheed had failed to notice the raised shovel in Mariam's hand. For her part, Mariam had mustered all her strength to bring the shovel down on Rasheed's head. After Rasheed's death, Mariam stays behind to take the blame for his death. Her sacrifice on behalf of Laila, Aziza, and Zalmai is a testament to her depth of character.
In The Thorn Birds, Dane is as close to Hassan's equal as you can get. He is effortlessly sanguine, compassionate, and loyal. Additionally, Dane is inherently ethical, authentic, and sincere. Unlike his father (Ralph de Bricassart), Dane nurses no ambivalence regarding his ambitions: his devotion to the Church and to God is absolute and untarnished by lust for a woman or for anything else the world has to offer.

That's right. I don't want to, ever. Not that I haven't thought about it, or wanted a wife and children. I have. But I can't. Because there isn't enough room to love them and God as well, not the way I want to love God. I've known that for a long time. I don't seem to remember a time when I didn't, and the older I become the greater my love for God grows.

Like Hassan and Mariam, Dane is also unselfish to the very end. His death is precipitated by his gallant behavior in saving two female tourists from drowning. In the last lucid moments before he succumbs to his heart attack, Dane's only thoughts are pure ones.
Hassan's equivalent in The Thorn Birds is Dane, and his equivalent in A Thousand Splendid Suns is Mariam.

What were the political characteristics of the Renaissance period?

     The Renaissance is associated with expansive cultural production and advances in the arts and sciences, however, the political economy that allowed the arts and sciences to flourish was rather regressive from today’s point of view. Here are some characteristics of the political system:
Nation states did not exist. Instead, the Holy Roman Empire covered a vast territory across Europe (from Italy to Northern Germany)
The Holy Roman Empire was headed by the Emperor, who was selected by the Pope
The territory of the Holy Roman Empire was subdivided into smaller territories, cities, and towns that were ruled by monarchs and princes
Absolutism was the form of government (e.g., Louis XIV of France). Absolutism is a form of government in which one ruler enjoys absolute power over his subjects (people).
Cities and towns enjoyed a relatively high degree of freedom and autonomy.
Cities and towns were lively centers of trade, wealth, the arts and sciences.
Wealth was an important indicator of political power; several wealthy and politically influential families emerged during the Renaissance.
 

What is the relationship between genes, chromosomes, and DNA?

Let us start with DNA, and, to keep things more relatable, let us use human DNA.  Human DNA contains about 3 billion base pairs.  That is a really long code.  It would take nearly 100 years to read if you read one base pair per second for 24 hours per day.  To make things more manageable, the DNA is broken up into sections.  In humans, these sections are chromosomes, and humans have 46 total chromosomes.  That means a chromosome is simply a coiled up, long section of DNA.  Each chromosome contains thousands of genes.  A gene is a specific number of base pairs that codes for a trait. As a result, a gene can be defined as either a section of a chromosome, or a gene can be defined as a specific number of DNA base pairs.  
https://www2.le.ac.uk/projects/vgec/schoolsandcolleges/topics/dnageneschromosomes

What does Thomas Paine say will guarantee American success? Why?

Though some people claim that Thomas Paine was not a Christian, the fact remains that in "The American Crisis, Number One," Paine claims that,

God Almighty will not give up a people to military destruction, or leave them unsupportedly to perish.

Here, Paine indicates that the American colonies need not fear defeat at the hands of the British forces. Paine assures his readers that the colonies' cause is a just one that God will support and that they can rely on His intervention on their behalf. 
Additionally, Paine observes that though Britain appears to believe that it can hold the American colonies in a manner he calls "slavery," Britain's declaration that it can "bind us in all cases whatsoever" is sacrilegious because "so unlimited a power can belong only to God." Paine builds his argument that Britain's claims on the colonies must be displeasing to God and implies that British aggression will not be allowed to stand. Paine realizes that the British forces are formidable, and he also realizes that he must convince his readers to stay in the fight by offering a "guarantee" that they will not fight alone.

Thomas Paine played an important role in the American Revolution. He strongly believed that the colonists should fight for their freedom from Great Britain. He shared his thoughts in a few published documents.
Thomas Paine wrote a pamphlet titled Common Sense. In this pamphlet, he explained the reasons why the colonists should be free from Great Britain. Thomas Paine was very much opposed to being ruled by a king. He felt people should elect their leaders and have a say in how the government runs.
In the Crisis Papers, written during the Revolutionary War, Thomas Paine reaffirmed his support for the causes for which the colonists were fighting. He again stated that the colonists should be able to govern themselves and make their own policies.
Thomas Paine believed that if the colonists believed in themselves and in the causes for which they were fighting, success would follow.
https://www.history.com/this-day-in-history/thomas-paine-publishes-american-crisis

https://www.history.com/topics/american-revolution/thomas-paine

Thomas Paine played an instrumental role in the push for the American Revolution or departure of the colonies from the control of the British crown. He is also recognized as one of the Founding Fathers of the United States for his revolutionary and political contributions. He also played an important role in defending the French Revolution through his book Rights of Man.
Two of his most influential titles on the American Revolution include Common Sense and The American Crisis. Common Sense, which was presented as a pamphlet, became very popular during the Revolution. The document communicated the message of republicanism and the need to cut off ties with Britain. The information resonated positively with the rebels and those supporting the cause, and it served to bolster the revolutionary mood.
Paine decried the authority of the monarchy and affirmed the need for separation. These ideas were echoed in his other title The American Crisis, in which he affirms that it is honorable for the rebels to continue the struggle despite the great challenges it presents. Paine suggests that it is fortitude in the face of struggle that will present victory, because the price for freedom cannot be cheap.

Tyranny, like Hell, is not easily conquered; yet we have this consolation with us, that the harder the conflict, the more glorious the triumph.
https://www.ushistory.org/paine/commonsense/

https://www.ushistory.org/paine/crisis/

Thomas Paine was an Englishman who emigrated to North America during the Revolutionary War period. He developed strong opinions about the role of England's form of government, parliamentary monarchy, and its role in colonized America. He published his opinions in pamphlets. In 1776, Thomas Paine authored an influential pamphlet called "Common Sense" a mere six months before the United States declared themselves a nation through The Declaration of Independence.  In it, he advocated for the colonies to develop their own government. Paine suggestion that replacing England's government of the colonies with a local republican form of government would result in a greater success. The new nation would be more successful because they, rather than England, would own the wealth of their considerable natural resources.
https://www.ushistory.org/paine/

How would you characterize the personality of the narrator, based on the General Prologue? Use evidence from the text to support your response.

The narrator in The Canterbury Tales is the lens through which we see every other character, and consequently he is at pains in the General Prologue to portray himself as a truthful person whose descriptions can be relied upon. Accordingly, he states, "whoso shal telle a tale after a man / He moot reherce as ny as evere he can / Everich a word" (whoever tells a story that repeats another person's tale, he must repeat every word as exactly as he can). Part of the reasoning behind the narrator's making this point, however, goes beyond a simple wish to be considered truthful and reliable: the narrator is also keen that any "vilynye," or vulgarity, in the stories he tells be ascribed to his devotion to truth rather than his personality. (See ll. 725-745). Far from being a vulgar person, indeed, the narrator tells us that he is a pious man who respects piety in others. However, one cannot help but infer from the satirical tone of the prologue that, in fact, the narrator protests too much—in distancing himself from any vulgarity in the stories he is about to tell, under the guise of adherence to truth, he has given himself free reign to tell things "so rudeliche and large" as he might wish.
He justifies this sentiment further by referencing, within three lines, both "Crist" and "Plato" to back himself up: "Crist spak hymself ful brode in hooly writ / And wel ye woot no vileynye is it. Eek Plato seith, whoso that kan hym rede, The wordes moote be cosyn to the dede." That is, Christ himself could be vulgar in his speech sometimes, as we see in the bible, and Plato says that words must accurately reflect truth. The narrator, then, while declaring himself only a speaker of truth and a humble, pious man, has also effectively compared himself to Christ and to Plato—and then gone on to declare, ironically, "my wit is short, ye may wel understonde." Chaucer's narrator may declare himself humble and dedicated to truth, but the satire in the prologue indicates to the reader that all may not be as it seems and that the narrator may set considerably more store by his own reputation than he says.
Early in the prologue, this irony is not as evident when the narrator is describing his "devout corage" (devout or pious heart and intentions) and his desire to seek blessed pilgrimage. But because of the way the narrator goes on to describe the present company, the reader is assured, by the end of the prologue, that the narrator is a character slightly ridiculous, if well-meaning, who is willing to think well of everyone and very happy to indulge in repeating "villainy" or bawdy content. A knight is described as courteous, which seems fair enough, but the narrator then goes on to describe his son, "a lovyre and a lusty bacheler," as being "fressh as is the month of May." The nun is "coy" and "dainty," and the monk's desire to leave his cell is glibly explained away by the narrator—"what sholde he studie and make hymselven wood, / Upon a book in cloystre alwey to poure . . . ?" The narrator, seemingly, does not want the reader to feel he is associating with vulgar or impious people, even when his actual descriptions of the company's behavior is in conflict with what he says about their character.
The tone of the General Prologue sets that of what will follow: the narrator declares that he will tell the truth, though it may not be found in what he says directly but in what the reader can infer from the further detail.
https://tigerweb.towson.edu/duncan/chaucer/duallang2.htm

In "A Noiseless Patient Spider" by Walt Whitman, do you think that the narrator is envious or jealous of the spider? Why?

It does seem, perhaps, that the speaker of Walt Whitman's poem "A Noiseless Patient Spider" is somewhat envious of how the spider is able to "tirelessly" and constantly launch filaments that are able to catch onto something.
The controlling metaphor of Walt Whitman's poem is that of the soul being likened to the spider as it is "seeking the spheres to connect them." Much like the spider, the soul casts filament after filament in an effort to find meaning and a sense of the divine. But, the patient spider seems more successful in its venture of launching "filament, filament, filament."
Certainly, the soul's task is more difficult and more complicated. The soul is

Ceaselessly musing, venturing, throwing, seeking the spheres to connect them,Till the bridge you will need be form'd, till the ductile anchor hold,...

In Whitman's poem, much like the spider, man also finds his realm beginning within himself. But, unlike the spider, who engages in the daily spinning of his webs, the soul that reaches out must generate an essential, yet extraordinary anchor that can hold because such casting is not part of man's mundane world; it is, instead, a transcendent experience.

Who wrote the Emancipation Proclamation?

President Abraham Lincoln drafted the Emancipation Proclamation in July 1862. The Proclamation, which did not become law until January 1, 1863, freed all the slaves in the Confederate states. It did not, however, free the slaves living in slave states that had not left the Union, though that freedom would be granted in 1865.
In July 1862, Lincoln showed his entire Cabinet the Proclamation he had written and said he was convinced he must free the slaves. Some of his Cabinet members urged caution. Secretary of State William Seward advised Lincoln to be careful about the timing of the Proclamation, so that it would come from a position of strength, not weakness. He believed that Lincoln should unveil it only after a major Union military victory, so that it wouldn't look like a desperate attempt to win the war.

Why does Jimmy Valentine refer to the young woman as "Polly Simpson"?

Professional safe-cracker Jimmy Valentine has just rocked up at a small town called Elmore. As he's walking down the street to the hotel, he catches sight of a pretty young lady. Immediately, he's smitten. The young lady sees Jimmy looking at her and blushes before walking into the town's bank. After she comes out again, Jimmy starts asking a young boy questions about the lady, as well as about the town of Elmore itself.
He doesn't come right out and ask, "Who is that young lady?" Instead he asks, "Isn't that young lady Polly Simpson?" Jimmy's new in town, and as he knows he's wanted by the police, he's cautious in questioning the young boy. Asking him about a made-up woman called Polly Simpson is a clever trick to try and discover the lady's true identity. It also makes it sound as if Jimmy's more familiar with the town and its people than he actually is. The last thing Jimmy wants to do is to stand out in the boy's mind. That's why he asks the young lad a more indirect question.

What were the main differences and consequences between the first and second Opium Wars? In what sense did either of these wars show that China was under the oppression of the British imperialism?

The main differences between the First and Second Opium Wars are seen in the outcomes of the wars. The Opium Wars began because of trade disputes between Britain and the Qing Empire of China. Chinese goods such as silk and porcelain were in high demand in Britain and the rest of Europe. In addition to spending large sums of silver on Chinese goods, British trade was confined to one port in China, Canton, which allowed Chinese authorities to control trade. The British East India Company started selling opium from India to China in order to offset the trade imbalance and make more money. Many in China soon became addicted to Opium, angering Chinese officials—especially since the British Empire had outlawed opium.
When the Qing outlawed opium and banned the opium trade, the British sent naval and military forces to China. In 1842, after suffering a series of defeats by the British, the Chinese were forced to sign the Treaty of Nanking. Under this treaty, the British were granted special trade rights in China, which granted the British the control of Hong Kong and opened five additional ports to British trade, meaning they were no longer confined to trading solely out of Canton.
The British were not satisfied with these agreements, however, and the Second Opium War began in 1857. During this war, France, Russia, and the United States joined the British in fighting the Chinese in order to gain their own trade rights and secure rights for Christian missionaries they sent to China. In 1860 at the Convention of Peking, Christians were given full civil rights, the city of Tianjin was opened, the No. 1 District of Kowloon was ceded to Britain, and freedom of religion was granted in China. It was also agreed that British ships would be allowed to carry indentured Chinese to the Americas, that China would pay Britain and France each 8 million taels, and that the opium trade would be legalized. As with the First Opium War, European military technology left the Chinese at the mercy of Western demands for free trade and spheres of influence.

Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 73

The expression of this function includes difference, product and two table functions (except the polynomials), sinh^(-1)(z) and sqrt(z).
The difference rule is (u-v)' = u' - v', the product rule is (uv)' = u'v + uv', the chain rule is (u(v(x)))' = u'(v(x))*v'(x).
The derivative of sinh^(-1)(z) is 1/sqrt(1 + z^2), the derivative of sqrt(z) is 1/(2sqrt(z)).
These rules together give us
y' = 2sinh^-1(2x) + 2x ((2x)')/sqrt(1+(2x)^2) - ((4x^2)')/(2sqrt(1+(2x)^2)) =
= 2sinh^-1(2x) + 2x (2)/sqrt(1+4x^2) - (8x)/(2sqrt(1+4x^2)) =
= 2sinh^-1(2x).

Describe the differences between a Federalist and an Anti-Federalist.

The modern USA has a federal, or central, government; but after the ratification of the Constitution in 1788, there were many who were opposed to placing too much power in the hands of a central government, preferring to keep power with the states. This was because they felt that many of the issues with the United Kingdom lay with the fact that the government had too much power. The terms 'anti-federalism' and 'federalism' need not refer exclusively to the United States, as they can be applied in any nation that has county or regional governments as well as a national governmental body, but for the purposes of this question, I will assume you are referring to the Federalists and Anti-Federalists in the US following the American Revolution. 
The Federalists, who wanted a strong and unified national government in order to go about repairing the nation after the damage that had been wrought there by war, were led at their peak by Alexander Hamilton. These people tended to be more educated and more sophisticated, believing that the only way to undo the crippling debt of the young country was to establish a centralized system of banking and a single economic policy for the whole country. Federalism tended to thrive in the larger cities. Federalists supported the Constitution strongly. George Washington was strongly in support of Federalism. 
Anti-Federalists, many of whom were farmers and others who lived in the rural areas which had been most damaged by the war, feared that centralized policies would only lead back to the same issues of underrepresentation and economic disparity that had been suffered under the colonial government. They strongly believed in the free agency of states, whom they felt were best placed to act in the interests of the local people. Anti-Federalists included the likes of Thomas Jefferson and James Monroe. 
https://www.diffen.com/difference/Anti-Federalist_vs_Federalist

In "A Painful Case," do you prefer to sympathize with Mr. Duffy or Mrs. Sinico?

While I feel incredibly sorry for Mrs. Sinico, it is actually Mr. Duffy who I find to be a more sympathetic figure because he must live with his terrible regret. He eventually realizes that the messiness and chaos of a romantic relationship would actually have made both his and Mrs. Sinico's lives worth living. It likely would have prevented her from turning to alcohol to dull her feelings and eventually taking her own life. Such a relationship, though it would have made Mr. Duffy emotionally vulnerable, the thing he seems to fear the most, would have prevented him from becoming an "outcast from life's feast." In the end, Mrs. Sinico at least tried to reach out to another human being; she tried to foster a connection and was rebuffed. Although this would be painful, I would imagine it is far more painful never to have tried to experience this kind of connection with another human, only to realize one's choices have rendered one completely and totally alone in the world. Mr. Duffy is alone, and he has only himself to blame, and this—to me—makes him even more sympathetic than her.

Calculus: Early Transcendentals, Chapter 3, 3.6, Section 3.6, Problem 22

We are given y=log2(exp(-x)*cos(pi*x))=1/ln(2)*ln(exp(-x)*cos(pi*x)). Since the domain of ln(X) is X>0, it means cos(pi*x) cannot equal to zero, we will use this later.
First we use the Chain rule, to the first portion of the answer,
y' = 1/ln(2) * 1/(exp(-x)*cos(pi*x)) * ...
since (ln(f(x)))' = 1/f(x) * f'(x).
The f(x) = exp(-x)*cos(pi*x)
Here use the Product rule, since we have two functions, which are easy to differentiate.
Thus, f'(x) = -exp(-x)*cos(pi*x) + exp(-x)*(-sin(pi*x)*pi)
= -exp(-x) * (cos(pi*x) + sin(pi*x) * pi)
So now y' = 1/ln(2) * 1/(exp(-x)*cos(pi*x)) * -exp(-x) * (cos(pi*x) + sin(pi*x) * pi).
We can immediately cancel the exp(-x). And since cos(pi*x) is never zero, we may divide by it.
Thus, y'(x) = -1/ln(2)*(1 + pi*sin(pi*x)/cos(pi*x))
= -1/ln(2)*(1 + pi*tan(pi*x))

In "A Sound of Thunder," why was the walkway so important to the success of the safari and the future of the world?

In "A Sound of Thunder," the walkway is crucial to the success of the safari and the world because it ensures that nothing in the past is altered. This is important because any change made in the past, no matter how small or big, has consequences for the future.
The importance of the walkway is demonstrated through its description. It hovers six inches above the ground, for example, and does not touch even a blade of grass in the past. The Safari Guide, Mr. Travis, gives clear directions that nobody must ever stray from the walkway:

Don’t go off it. I repeat. Don’t go off. For any reason!

When faced with the dinosaur, however, Eckels has a moment of panic and strays from the walkway. It is only at the end of the story that he realizes that he has stepped on a butterfly, an action which has forever altered the course of time.

What secret did Sam keep for Louis?

Louis' father, hoping to help him make an impression on Serena and carry out a normal swan life, steals a trumpet for his son from a music store. He reasons that since they are all trumpeter swans, a I think the secret you are referring to is related to the origins of Louis' trumpet. Louis is a swan who is mute and makes a connection to a human boy named Sam, who eventually teaches him to read, write, and communicate with humans. This doesn't really help Louis fit into the swan community, though, and when he falls in love with a beautiful swan named Serena, he cannot find a way to make her notice trumpet could be the perfect tool to help Louis find his voice.

I believe the secret you are referring to is related to the origins of Louis's trumpet. Louis is a swan who is mute and makes a connection to a human boy named Sam, who eventually teaches him to read, write, and communicate with humans. This doesn't really help Louis fit into the swan community, though, and when he falls in love with a beautiful swan named Serena, he cannot find a way to make her notice him.
Louis's father, hoping to help him make an impression on Serena and carry out a normal swan life, steals a trumpet for his son from a music store. He reasons that since they are all trumpeter swans, a trumpet could be the perfect tool to help Louis find his voice.
This trumpet only serves to make Louis feel very guilty, though, and he tells Sam the secret of how he got it. Sam then tells him that he could get a job and make money to pay for the trumpet and the damage caused to the music store when his father broke in to steal it.

College Algebra, Chapter 1, 1.6, Section 1.6, Problem 38

Solve the nonlinear inequality $\displaystyle x(2 - 3x) \leq 0$. Express the solution using interval notation and graph the solution set.

We have

$\begin{array}{ccccc}
x \leq 0 & \text{ and } & 2 - 3x & \leq & 0 \\
& & 2 & \leq & 3x \\
& & \frac{2}{3} & \leq & x
\end{array} $

The factors on the left hand side are $x$ and $2 - 3x$. These factors are zero when $x$ is 0 and $\displaystyle \frac{2}{3}$, respectively. The numbers and $\displaystyle \frac{2}{3}$ divide the real line into three intervals.

$\displaystyle (- \infty, 0], \left(0, \frac{2}{3} \right), \left[ \frac{2}{3}, \infty \right)$







From the diagram, the solution of the inequality $x(2 - 3 x) \leq 0$ are

Did most workers in the 1880's in American cities live outside of city limits?

Most workers in the 1880s did not live outside city limits.  This was because of the lack of good transportation for workers which would have allowed them to live outside the cities in which they worked.
In the 1800s, it was not easy to travel long distances to work.  There were streetcars and trolleys, but those forms of mass transit did not generally reach very far and were not widespread.  The average worker needed to live close enough to his or her place of work to be able to walk to and from work every day.  Because they needed to commute by foot, they had to live relatively close to their jobs.  This meant that they could not generally live outside city limits.
Because of a lack of good transportation options, most workers in the 1880s still lived inside city limits.
http://www.digitalhistory.uh.edu/era.cfm?eraid=9

Calculus of a Single Variable, Chapter 9, 9.8, Section 9.8, Problem 9

sum_(n=0)^oo x^(2n)/((2n)!)
To find the radius of convergence of a series sum a_n , apply the Ratio Test.
L = lim_(n->oo) |a_(n+1)/a_n|
L=lim_(n->oo) | (x^(2(n+1))/((2(n+1))!))/((x^(2n))/((2n)!))|
L=lim_(n->oo) | x^(2(n+1))/((2(n+1))!) * ((2n)!)/x^(2n)|
L= lim_(n->oo)| x^(2n+2)/((2n+2)!) * ((2n)!)/x^(2n)|
L= lim_(n->oo)| x^(2n+2)/((2n+2)*(2n+1)*(2n)!) * ((2n)!)/x^(2n)|
L=lim_(n->oo) |x^2/((2n+2)(2n+1))|
L=|x^2| lim_(n->oo)|1/((2n+2)(2n+1))|
L=|x^2| * 0
L =0
Take note that in Ratio Test, the series converges when L < 1.
Since the value of L is zero, which is less than 1, then the series converges for all values of x.
Therefore, the radius of convergence of the given series is R =oo .

How might a speech fail even with adequate audience analysis and preparation?

In writing a public speech, it's important to keep your audience in mind. Part of the preparation for speech writing is in the analysis of potential audience members. This is where the popular "know your audience" mantra comes in. After a thorough analysis, a speech writer would prepare statements, verbal and non-verbal cues, tone, message, and mannerisms based off that analysis. Even with adequate preparation, it's possible a speech will fail in that it won't evoke its intended response.
So, why might that be the case? Let's explore an example to understand this phenomenon.
Suppose a person, Dan, is tasked to give a speech to senior students at a high school in a suburban area (not local). His job is to talk about the importance of education and the value of a college degree in 2016. In his pre-speech analysis, he learns 80% of the students are from Spanish-speaking households, 65% of students would be first-generation college students, and the most unifying groups in the high school are the basketball team and drill team. To prepare his speech, he recognizes the challenges the students may face in their home study habits (maybe their parents can't help with English papers or application essays), the obstacles they may face in applying for college (maybe their family doesn't really understand why a degree is important—after all, they don't have one and it's very expensive to get one), and the motivations that may already exist (they may be working toward a sports scholarship).
So, he writes his speech with all those important things in mind. The day of his talk, he walks in and takes the stage to give his presentation. Even though Dan has a great speech planned, something goes wrong. He starts with his first few slides and the audience is mumbling quietly. Some people are walking out of the room. Others are rolling their eyes. Why might the audience be so restless?
As it turns out, Dan is an older white gentleman dressed in a nice suit and, although he seems nice and professional, the students don't relate with him personally. The majority of the students are young, Hispanic, and from low-income neighborhoods - Dan has none of those characteristics. In fact, no amount of planning could have changed the reception of this speech because Dan was probably not the correct person to give the speech in the first place.

What is social welfare policy?

Social welfare policy refers to policies designed to help the community. These policies mainly affect the needy. One such policy is universal healthcare. Government steps in and and becomes the single payer for the healthcare system, thus giving everyone in society healthcare. The United States provides subsidies to help people pay for healthcare.  
Another example of social welfare policy is subsidized housing. People who make below a certain amount of money can qualify for housing and utilities assistance. This is done in an attempt to provide a sufficient standard of living for everyone in the community. These people also often qualify for nutrition assistance (food stamps) as well as money for the care of children, which in the United States is known as WIC programs.
Social welfare policies can be controversial. Some conservatives see them as governmental overreach that does not encourage people to better themselves. Some liberals, on the other hand, see these programs as necessary for helping people who work in low-paying jobs that society needs in order to function. Social welfare policy is one of the most divisive issues in politics today.

Compare and contrast the tone and style of both Hemingway's "A Clean Well-Lighted Place" and Kincaid's "Girl."

While the two writers couldn't be more different in terms of background and perspective, there are some interesting stylistic commonalities between Hemingway's "A Clean Well-Lighted Place" and Kincaid's "Girl". Both stories have a terse, staccato tone that is matter-of-fact yet also attentive to detail, bringing things to life.
Hemingway's "A Clean Well-Lighted Place" takes place in a café in France and is a beautiful slice of life, exploring loneliness and the existential. The title refers to the importance of having a "place" where one belongs. It's written in simple, unadorned language, yet conveys deep meaning.
Similarly, Kincaid's "Girl" also uses simple language in a short story told as a "to-do list" in one complete, lengthy paragraph. Through the list, Kincaid conveys layers of meaning, offering a host of practicalities about how to get on in the world as a poor, young black woman in the American south.
While the privileged perspective of "A Clean Well-Lighted Place" is very bourgeois, male, and white, the perspective of "Girl" is quite different—it is of a young black woman reflecting on her mother's advice through a "to-do list". Yet both stories share stylistic similarities in their elegant, tightly written simplicity.

Under what conditions does a convex mirror form a real image?

A convex mirror is made by applying a reflective coating on the outside of a piece of a curved surface. The center of curvature of and the focal point of the mirror are thus on one side of the mirror, but the object is on the other side. (Please see the attached reference link for the illustration.) 
When the light rays hit the mirror, they are reflected back in a way that that the angle of reflection (the angle the reflected ray makes with the normal to the surface) is equal to the angle of incidence (the angle the incident ray makes with the normal.) Because the mirror is convex, the reflected rays point away from the focal point of the mirror, or diverge. Therefore, the rays do not intersect, but their extensions do intersect, forming a virtual image. This is true no matter how far away the object is located from the mirror. Again, please see the reference link for the diagram of the image formation by a convex mirror.
As discussed above and can be seen from the diagram, it is impossible to obtain a real image in a convex mirror. The convex mirrors always form virtual images.
 
http://farside.ph.utexas.edu/teaching/316/lectures/node138.html

What are some examples of how humans are the products of their environments?

The most obvious example of how humans are products of their environments concerns the behavior of the Ewell children. Both Mayella and Burris are products of the most despicable individual in Maycomb and grow up in a dirty, crowded shack near the town's dump. Bob Ewell is their alcoholic, abusive father who is portrayed as an ignorant, malevolent man. Influenced by their father, Mayella and Burris are depicted as selfish, disrespectful people, who are unsympathetic toward others. Encouraged by her father, Mayella blatantly lies about Tom Robinson assaulting and raping her—despite the damage her accusation will do to him and his family. Burris Ewell is depicted as a disrespectful, rude child who curses at his teacher and refuses to attend school. Both Mayella and Burris are products of their dirty, unstructured, racist environment.
In contrast, Jem and Scout are raised in an organized, clean home with a supportive, respectful father who is a positive role model in their lives. Similar to their father and Calpurnia, Jem and Scout develop into morally-upright, educated individuals, who sympathize with others and act like respectful citizens. Since Atticus values equality and is not prejudiced, Jem and Scout are some of the few children in Maycomb who do not develop into racist citizens.

Single Variable Calculus, Chapter 5, 5.1, Section 5.1, Problem 4

Estimate the area under the graph of $f(x) = \sqrt{x}$ from $x = 0$ to $x = 4$ using four approximating rectangles at following sample points. Sketch the graph and the rectangles. Also, state that if your estimate is an underestimate or overestimate.

The width of the rectangle is..

$\displaystyle \Delta x = \frac{4 - 0}{4} = 1$

a.) Right endpoints $R_4$


$
\begin{equation}
\begin{aligned}

R_4 =& \sum \limits_{i = 1}^4 f(xi) \Delta x
\\
\\
R_4 =& 1 [f(1) + f(2) + f(3) + f(4)]
\\
\\
R_4 =& 1 [\sqrt{1} + \sqrt{2} + \sqrt{3} + \sqrt{4}]
\\
\\
R_4 =& 6.1463

\end{aligned}
\end{equation}
$








By using a sample point at right endpoints in an increasing function, we can say that this is an overestimate.

b.) Left endpoints $L_4$


$
\begin{equation}
\begin{aligned}

L_4 =& \sum \limits_{i = 1}^4 f(xi) \Delta x
\\
\\
L_4 =& 1 [f(0) + f(1) + f(2) + f(3) ]
\\
\\
L_4 =& [\sqrt{0} + \sqrt{1} + \sqrt{2} + \sqrt{3}]
\\
\\
L_4 =& 4.1463

\end{aligned}
\end{equation}
$








This time, we have an underestimate.

In The Myth of Sisyphus, Camus refers to Sisyphus as "the absurd hero." Discuss a real life person (historical or present) and a fictional character who might also qualify as an absurd hero and explain why each qualifies.

First, let's talk a bit about what Camus means when he refers to Sisyphus as the "absurd hero." What makes Sisyphus absurd is his consciousness; his intelligence got him into trouble with the gods (as he arrogantly scorned them, besting Thanatos and denying Hades his due souls), but his consciousness is also the key to making his eternal torture in the Underworld bearable. The gods can ultimately force Sisyphus to do a certain task (pushing the boulder up the hill each day and watching it roll back down each night), but they cannot control his thoughts. In a futile universe, Sisyphus can convince himself (as we all must) that his task has meaning. As Camus writes, "The struggle itself toward the heights is enough to fill a man's heart. One must imagine Sisyphus happy."
One fictional character who could be called an absurd hero is Jay Gatsby, the titular character of F. Scott Fitzgerald’s The Great Gatsby. Gatsby has worked so hard in order to earn the fortune that he believes will help him win back Daisy. When he could not earn his money legally, he turned to bootlegging (the illegal distribution and sale of alcohol during the Prohibition Era in the U.S.). The American Dream, the idea that anyone can prosper (lawfully) as a result of hard work and determination, is revealed to be false. Gatsby can only prosper when he turns to criminal activity, but this doesn’t seem to bother him at all. He can only focus on his hope, with his "heightened sensitivity to the promises of life." Despite Gatsby’s ability to keep dreaming despite whatever hurdles are thrown into his path, he is "preyed on" by others and his dreams are dirtied by the "foul dust [that] floated in [their] wake." His dream is futile—he cannot beat the system, although he keeps trying. He doesn’t even realize the futility, hoping until the last that "Daisy’ll call."
One real-life person we might call an absurd hero is Al Gore. For a long time, he has been concerned about climate change, and he’s tried very hard to draw attention to the problem and prompt change in the way we treat the environment so we don’t push it past the brink of saving. Despite Gore's data, facts, and statistics and the fact that the brink is edging closer, people continue to ignore his warnings. Nonetheless, he keeps trying. He is absurd because, despite the seeming futility of his speeches, he keeps giving them. He maintains the belief that we might listen and change, even though we don’t make the kind of strides necessary to reverse the damage we’ve already done to the environment or minimize it in the future.

What challenges does Percy Jackson face in chapter 8 of The Lightning Thief?

Percy faces many challenges throughout chapter 8. The first challenge that we see is his struggle to find where he belongs in this new world. He has not yet been claimed by his father, so everyone is watching to see what happens. Percy becomes more bitter about this as time goes on:

"So okay, maybe gods had important things to do. But couldn't they call once in a while, or thunder, or something? Dionysus could make Diet Coke appear out of thin air. Why couldn't my dad, who-ever he was, make a phone appear?"

Often, demigods specialize in a skill that is related to their immortal parent. So he begins exploring different activities such as archery (associated with Apollo) and metal working (associated with Hephaestus). He fails at everything he tries.
Eventually, he finds some success in swordplay, which is its own special challenge. His teacher is Luke, who is the best sword fighter in 300 years. Percy has never lifted a sword before, and first has to spar with Luke. Yet, in the end, he is able to disarm his teacher once, to the surprise of everyone watching. 
The most prominent challenge that Percy faces is the Greek demigod version of "Capture the Flag". He is on the team that consists of the children of Athena, Apollo, and Hermes. Luke, who is also on this team, assigns him to border patrol, which should be a fairly simple task. However, within a few minutes of the game beginning, five members of the Ares cabin come to attack him as revenge for shaming them. All are experienced fighters, and Percy is forced to defend rather than attack until he is pushed back to stand in the creek behind him. He becomes reenergized as soon as he touches the water and is able to stand his ground until his team captures the flag. 
After an incident with a hellhound, Percy is able to overcome his first challenge: he is claimed by his father, Poseidon. With his place now known, the other campers all have a newfound respect for him (although children of Ares aren't particularly happy about it). However, this does not mean his journey has ended. It has only begun.

Prove that 2 + sec(x) cosec(x) = (sin x + cos x)^2 / (sin x cos x).

2+secxcscx=(sinx+cosx)^2/(sinxcosx)
To prove, consider the left side of the equation.
2+secxcscx
Express the secant and cosecant in terms of cosine and sine, respectively.
=2+1/cosx*1/sinx
=2+1/(sinxcosx)
To add, express them as two fractions with same denominators.
=2*(sinxcosx)/(sinxcosx)+1/(sinxcosx)
=(2sinxcosx)/(sinxcosx) + 1/(sinxcosx)
=(2sinxcosx + 1)/(sinxcosx)
Apply the Pythagorean identity sin^2x+cos^2x=1 .
=(2sinxcosx+sin^2+cos^2x)/(sinxcosx)
=(sin^2x+2sinxcosx+cos^2x)/(sinxcosx)
And, factor the numerator.
= ((sinx +cosx)(sinx+cosx))/(sinxcosx)
=(sinx+cosx)^2/(sinxcosx)
Notice that this is the same expression that the right side of the equation have. Thus, this proves that the  2+secxcscx=(sinx+cosx)^2/(sinxcosx)  is an identity.

What can you infer about what Gordimer leaves unstated at the end of her story?

One inference that can be made from the ending of Gordimer's "Once Upon a Time" is that the parents recognize their mistakes.
At the end of the story, Gordimer leaves the family's reactions unstated.  She does not delve into what the mother and father thought as they carried "the bleeding mass" of their son into the house.   One inference that can be made is that the parents realized their folly regarding all of their security measures.  
Throughout the story, Gordimer describes the family as scared of the outside world. They enact security measures such as the gate, the wall, and the barbed wire thicket to keep the outside world away from them. However, when their child is destroyed by these measures, we can infer that the parents would reflect on their actions. They would have to rethink the world they have created. The desire to keep the family safe had the opposite consequence.  It endangered their boy, the love of their lives because as he crawls inside the coiled barbed wire, he "screamed and struggled deeper into its tangle."  
Gordimer shows the parents extracting their son and bringing him inside.  She does not state their thoughts to this painful reality.  We can infer that the parents would have to reconsider their fears of the outside world.  Their fears have essentially killed their son.  This can be an inference based on what is offered at the end of "Once Upon a Time."

What were three hardships that the pilgrims faced aboard the Mayflower?

The Pilgrims faced many hardships aboard the Mayflower. First, the ship was not designed to carry passengers. There was no privacy aboard the ship, and there were chamber pots for toilets. While no one in that time enjoyed indoor plumbing, a chamber pot could be very hard to use when on a ship.
Passengers also had few food choices, as their food had to be non-perishable. Many Pilgrims arrived in the New World already malnourished. There was also the issue of rough seas; the Pilgrims were not a seafaring people and many of them got sick in choppy waters. Seasickness only added to the misery of those aboard the ship. There was also boredom aboard the ship. While the Pilgrims were looking forward to a new life in America, there was some anxiety over what this new life would entail. Given the psychological and physiological stresses of such a long voyage, it is little wonder that many Pilgrims did not survive the first winter.  

Who was Amir in The Kite Runner most like in A Thousand Splendid Suns and The Thorn Birds?

It can be argued that Amir is most like Father Ralph de Bricassart in The Thorn Birds and Jalil in A Thousand Splendid Suns. Let me explain.
All three men make poor choices in their lives, which lead to grief and tragedy. For example, in The Kite Runner, Amir does nothing while his childhood friend suffers a violent sexual assault at Assef's hands. Later, Amir's besmirching of Hassan's character leads to the latter being exiled (albeit reluctantly) from Amir's family home. Amir and Hassan become estranged for the rest of their natural lives. Filled with guilt and regret in later years, Amir tries to make amends for his actions by rescuing Sohrab, Hassan's son. 
In A Thousand Splendid Suns, Jalil best corresponds to Amir. Although Jalil loves Mariam, he is reluctant to recognize her as his daughter during her childhood years. As a result, Mariam is forced to live with the shame of her illegitimacy. Like Amir, Jalil does nothing to protect those who put their trust in him. He (Jalil) allows his wives to decide Mariam's fate after Nana's suicide. Mariam is married off to the wicked Rasheed; she suffers grave physical and emotional abuse at Rasheed's hands for the duration of their marriage. In later years (much like Amir), Jalil tries to make amends for his cowardice. He leaves Mariam an inheritance (in a burlap sack) and writes an emotional letter to her. However, Mariam never gets to see the letter or to collect her inheritance. Like Amir with Hassan, Jalil never gets to reconcile with Mariam.
In The Thorn Birds, Father Ralph de Bricassart is most similar to Amir. Like Amir and Jalil, Father Ralph lives to regret his life choices. He chooses to pursue his ambitions in the Church rather than to recognize Meggie as his wife. Although he consummates his love for Meggie, Father Ralph is reluctant to abdicate his position in the papal hierarchy. He betrays Meggie's love and, as a result, never gets to know Dane as his son. Dane dies without knowing that the priest he admires is his father; ironically, it is Father Ralph who conducts Dane's funeral. 
Hope this helps. Thanks for the question!

In The Ramayana, who are the two key players in the battle?

The two key players in the battle that defines The Ramayana are Lord Rama and the demon-king Ravana of Lanka.
The conflict between Lord Rama and Ravana is one of dharma versus adharma.  "Dharma" means living a life in accordance to the principles of duty, while "adharma" is a life that lacks such structure. The order of Lord Rama's dharma is positioned against Ravana's belief that he and his wishes are the only guiding principles that matter. This battle defines the epic.  Its resolution provides the lasting lessons to The Ramayana.
Lord Rama embodies the principles of living with the honor that comes from duty.  He willingly accepts his exile, no matter how unjust it is. He lives as an ascetic with Devi Sita and Lakshmana.  Whenever there is a threat of injustice, he does not shy away from challenging it because he sees this as his duty as a warrior.  When Ravana abducts Sita, he feels compelled to rescue her because he loves her.  However, he is also motivated because he sees it as his responsibility as a husband. Finally, Lord Rama feels that he has to challenge Ravana because the act itself is unjust and must be confronted. Lord Rama's commitment to dharma is the governing principle of his life.
Ravana believes that his desire represents the structure of the universe. He abducts Devi Sita because he covets her. He wants to add her to his collection of women to further indulge in his sensory-driven life.  His opulent display of wealth accentuates his own narcissism.   Ravana feels that he is the most powerful and most important being in the universe. He demands immediate submission from everyone because of the belief in his own greatness. Ravana does not adhere to any structure larger than himself because he feels that he is the only structure that matters.
When Lord Rama and Ravana confront one another, it is the battle between both sets of ideologies.  The Ramayana addresses how human beings should live their lives.  Do we live our lives in accordance to hedonistic self-gratification or do we recognize a duty to honor a structure larger than ourselves?  This question is answered in the battle between Lord Rama and Ravana.

What was Braverman's struggle and how did he overcome it?

In the story, Braverman struggles with his anger after Millstone hires three men to beat him up. 
We get an idea of how upset he is in chapter 13. In that chapter, Hope is in Braverman's home; she is visiting him in the aftermath of the attack. During their conversation, Braverman admits that, if he had been able to break free, he might have killed any one of the men who held him down. 
Braverman tells Hope that his anger frightens him, and he has begun taking out his anger on his mother and little sisters. He is not proud of the fact that he yells at them, but he feels helpless. It's clear that he is struggling to process his anger in a way that is constructive.
Since Braverman isn't one to let difficulties cripple his motivation, he decides to channel his energy towards getting G.T. Stoop elected. He takes the first step of writing an article for the Mulhoney Messenger, detailing his attack and reaffirming his support for G.T. Stoop. Through his article, Braverman lets Millstone know that he won't be intimidated by the latter's corrupt tactics. 
Braverman also takes the courageous step of confronting Millstone after his speech at a Methodist church picnic. Braverman is joined by fifty-seven teenagers, who turn up to show their support for him.
In all, Braverman overcomes his struggle with anger by channeling his energy towards getting G.T. Stoop elected, rather than submitting to self-pity or other types of destructive behavior.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 9

Determine $\displaystyle \frac{dy}{dx}$ of $x^4(x+y) = y^2(3x-y)$ by Implicit Differentiation.

$\displaystyle \frac{d}{dx} \left[x^4 (x+y) \right] = \frac{d}{dx} \left[y^2 (3x-y) \right]$


$
\begin{equation}
\begin{aligned}
(x^4) \frac{d}{dx} (x + y) + (x+y) \frac{d}{dx} (x^4) & = (y^2) \frac{d}{dx} (3x-y) + (3x-y) \frac{d}{dx} (y^2)\\
\\
(x^4) \left[ \frac{d}{dx} (x) + \frac{d}{dx} (y) \right] + (x+y) \frac{d}{dx} (x^4) &= (y^2) \left[ 3 \frac{d}{dx} (x) - \frac{d}{dx} (y) \right] + (3x-y) \frac{d}{dx} (y^2)\\
\\
(x^4)\left( 1 + \frac{dy}{dx} \right) + (x+y)(4x^3) &= (y^2) \left[ (3)(1) - \frac{dy}{dx} \right] + (3x-y)(2y) \frac{dy}{dx}\\
\\
x^4 + x^4 \frac{dy}{dx} + 4x^4 + 4x^3y &= 3y^2 - y^2 \frac{dy}{dx} + 6xy \frac{dy}{dx} - 2y^2 \frac{dy}{dx}\\
\\
5x^4 + 4x^3y + x^4 \frac{dy}{dx} &= 3y^2 - 3y^2 \frac{dy}{dx} + 6xy \frac{dy}{dx}\\
\\
x^4 \frac{dy}{dx} + 3y^2 \frac{dy}{dx} - 6xy \frac{dy}{dx} &= 3y^2 - 5x^4 - 4x^3y
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
x^4y' + 3y^2y' - 6xyy' &= 3y^2 - 5x^4 - 4x^3y\\
\\
y'(x^4+3y^2 - 6xy) &= 3y^2 - 5x^4 - 4x^3y\\
\\
\frac{y'\cancel{(x^4+3y^2-6xy)}}{\cancel{x^4+3y^2-6xy}} &= \frac{3y^2-5x^4-4x^3y}{x^4+3y^2-6xy}\\
\\
y' &= \frac{3y^2 - 5x^4 - 4x^3y}{x^4 + 3y^2 - 6xy}
\end{aligned}
\end{equation}
$

Describe how a major refurbishment of publicly funded hospital facilities might affect the public sector borrowing requirement.

The question asks how a major refurbishment of publicly funded hospital facilities might affect the public sector borrowing requirement. The assumption here is that the term “major” indicates that the project is too large to fund out of excess hospital operating revenues; i.e. it must be financed somehow. Given that this is a refurbishment (i.e. replacement of depreciated assets), the project may have been anticipated and so funded through a sinking fund. This would be the case if the hospital management had set up such a facility in the past and had funded it consistent with the actual physical depreciation of the assets in question (presumably non-structural fixtures, equipment, etc.). Conversely, the government may be in a position to fund the refurbishment out of its general, budgeted tax revenues.
 Assuming neither of these options are available, we are left with the choice of debt versus equity financing. Equity financing would depend on the specific corporate structure of the ownership of the hospital. In general, facilities wholly owned by the government would not have access to equity (stock issuance) financing. Government financing is generally in the form of bonds (debt). Therefore, the expectation is that the project would increase public borrowing. However, if the hospital is privately owned (on either a for or non-profit basis), the owning entity may have access to equity markets.

A proton is trapped in an infinite square well of width 15.0 nm. The "walls" of the well are at x = 0 and x = 15.0 nm. Assuming that the system is in the n = 2 state, calculate the probability of finding the proton at x = 12.0 ± 0.2 nm. Possibly integral from 11.8 to 12.2 = .027?

Hello!
Yes, this probability is an integral from 12 - 0.2 = 11.8 nm to 12 + 0.2 = 12.2 nm. There are two problems: what is the function to integrate and what is the value of the integral.
It is known that the function to integrate is the probability density, and it is the square of the wave function. Also it is known that the wave function for a particle in an infinite one-dimensional well with the walls x=0 and x=L is
Psi(x) = sqrt(2/L) sin((n pi x)/L),
where n is the state. So we need to integrate
p_d(x) = 2/Lsin^2((n pi x)/L) = 1/L (1-cos((2n pi x)/L)).
It is simple, and the probability is
int_(11.8)^(12.2) 1/L (1-cos((2n pi x)/L)) dx = (x/L - 1/(2n pi) sin((2n pi x)/L))|_(x=11.8)^(12.2)
Recall that n=2 and L=15nm and obtain
p = 0.4/15-1/(4pi)(sin(4pi*12.2/15)-sin(4pi*11.8/15)) approx 0.048.
(that said, your 0.027 is the first term, 0.4/15)
 
 

What is the difference between theme and motif?

Theme and motif are not the same concepts, but they do work together to convey the writer's message. A theme is the central idea or main message that unifies the entire work. It is the main idea the author is trying to convey through his or her writing. The theme is what the author is trying to say. A work may have one or more themes. All other elements of the work contribute to solidify and communicate the overall theme(s).
Motifs are events, actions, symbols, and ideas that recur often throughout the work. They are images or elements that you will see or hear over and over again throughout the work. Motifs help to emphasize the main theme of the work.
For instance, one of the themes of Charlotte’s Web by E.B. White is friendship, or sacrificial friendship. A spider, Charlotte, attempts to save her pig friend, Wilbur, from certain death and is willing to sacrifice her own life to do so. That is the theme, the main idea or central message, of the book. That is main idea the author is trying to communicate. Motifs of the book include recurring elements that contribute to the theme. Spider webs are a recurring element in Charlotte’s Web and help to emphasize the sacrificial love Charlotte has for Wilbur. Charlotte is using her own means of life (the web, which is used for her sustenance) to preserve Wilbur’s life. Words are another motif of the book. Charlotte repeatedly uses words in her attempt to secure Wilbur’s salvation. So, while theme and motif are distinct concepts, motif works to emphasize the main themes of the work.

What is Tolstoy's view on Russian imperialism?

Tolstoy completely opposed Russian imperialism. When Tsar Nicholas II supported European imperialism in China in 1902, Tolstoy referred to his monarch's action as "barbaric." 
Tolstoy admired the Chinese people for taking a stand against the European imperialists, who, he contended, had badly abused and exploited China out of greed. Tolstoy argued that the Chinese people were tranquil and patient, traits he deeply admired. He condemned the Europeans in China as little more than selfish animals, challenging the stereotypes that depicted Europeans as more civilized than Asians.
Tolstoy, who turned to spirituality in his later life, was a firm believer in nonviolence. He called for colonized peoples of the Middle East and Asia to resist imperialism through the use of nonviolent protest and action. Tolstoy wrote encouragingly to Gandhi to resist British domination. Although his stance was radical in his day, people today typically agree with him and condemn the excesses of imperialism. 

In the essay, "Straw Into Gold: The Metamorphosis of the Everyday," Cisneros used an analogy to the fairy tale Rumpelstiltskin to help make her point. In the essay"Cinderella's Stepsisters," Morrison uses a similar technique by discussing how Cinderella'sstepsisters treated her as a basis for a larger argument about how women treat one another. Compare and contrast how Cisneros and Morrison used their analogies. In what ways did they use the technique the same? How did they use them differently?

Cisneros' technique is similar to Morrison's in the sense that both are references to fairy tales, where the main protagonists are women who manage to transcend adversity and misfortune.
In Cisneros' essay, the title references the story of Rumpelstiltskin, where a miller's daughter (with the help of an imp named Rumpelstiltskin) manages to transform straw into gold and eventually marry the king. Cisneros uses the "straw into gold" analogy to highlight how she has blossomed from an awkward child into a successful and empowered woman. Her thesis is that every woman has the potential to succeed, regardless of her current challenges. In this, her analogy is similar to Morrison's, who argues that all women have the power to take hold of opportunities and to realize their ambitions.
In Morrison's essay, the writer references the story of Cinderella and her step-sisters to argue that it is the province of every successful woman to ensure her fellow sisters' self-determination and empowerment; essentially women should refrain from masculine competitiveness and aim to foster the inherent, nurturing tendencies of their feminine nature. Morrison asserts that she is "alarmed by the violence that women do to each other: professional violence, competitive violence, emotional violence...the willingness of women to enslave other women."
Morrison's technique is different from Cisneros' in the sense that Morrison focuses not just on women transcending adversity, but also on feminine violence against their same-sex counterparts. Morrison's essay highlights what women decide to subject their peers to when they are in a position of power, while Cisneros largely concentrates on women transcending traditional norms and societal expectations.
 

y=ln(sinx) , [pi/4 , (3pi)/4] Find the arc length of the graph of the function over the indicated interval.

The arc length of a function of x, f(x), over an interval is determined by the formula below:
L=int_a^bsqrt(1+((dy)/(dx))^2)dx
So using the function given, let us first find (dy)/(dx):
d/(dx)(ln(sin(x)))=(1/(sin(x)))*(cos(x))=(cos(x))/(sin(x))=cot(x)
We can now substitute this into our formula above:
L=int_a^bsqrt(1+((dy)/(dx))^2)dx=int_(pi/4)^((3pi)/4)sqrt(1+(cot(x))^2)dx
Which can then be simplified to:
L=int_(pi/4)^((3pi)/4)sqrt(1+cot^2(x))dx=int_(pi/4)^((3pi)/4)sqrt(csc^2(x))dx=int_(pi/4)^((3pi)/4)csc(x)dx
Then you find the definite integral as you normally would.  (Using the method shown on the link below, you can find the integral of csc(x).)
L=int_(pi/4)^((3pi)/4)csc(x)dx=-ln|csc(x)+cot(x)|_(pi/4)^((3pi)/4)
L=-ln|csc((3pi)/4)+cot((3pi)/4)|-(-ln|csc(pi/4)+cot(pi/4)|)
L=-ln|sqrt(2)+(-1)|-(-ln(sqrt(2)+1|)=-ln|sqrt(2)-1|+ln|sqrt(2)+1|
Here, we will switch the two natural logarithm terms and use the quotient property to combine them into a single log:
L=ln|sqrt(2)+1|-ln|sqrt(2)-1|=ln|(sqrt(2)+1)/(sqrt(2)-1)|
If you rationalize the denominator (by multiplying by the conjugate and simplifying) and use the power property of logs, you are left with:
L=ln|(sqrt(2)+1)^2/1|=ln|(sqrt(2)+1)^2|=2ln|sqrt(2)+1|
So the exact value of the arc length of the graph of the function over the given interval is 2ln|sqrt(2)+1|
which is approximately equal to 1.76.
http://math2.org/math/integrals/more/csc.htm

How did the “agent” jump easily from person to person?

Richard Preston's The Hot Zone is a vivid account of the study of viral hemorrhagic fevers. It begins with outbreaks of the Ebola and Marburg viruses in central Africa and then moves to controlled experiments at USAMRIID, the US Army Medical Research Institute of Infectious Diseases, where military scientists infect rhesus monkeys with these viruses to learn how the diseases progress and whether they can be stopped.
The viruses cause severe vomiting and diarrhea. This is then followed by a weakening of blood vessels throughout the body, which leads to internal and external bleeding in the infected person, who dies of massive blood-loss. The viruses are referred to as "infectious agents" by the scientists in their experiments, and the experiments begin with the commonsense idea that transmission occurs through physical contact with bodily fluids—people or animals exposed to the blood, vomit, or feces of infected persons or animals have a very high risk of contracting the disease.
The breakthrough that occurs at the Reston labs is the discovery that monkeys in separate rooms, who have no contact with one another, are somehow getting infected, which means the viruses must spread by air as well as physical contact. The virus that affects the monkeys is a variant of the Ebola virus, dubbed the "Reston virus," which, fortunately, does not seem to cross the species barrier and affect humans.

What were the short-term and long-term results of the War of 1812?

The War of 1812, while no property changed hands, was very important for America.  It created a new sense of nationalism in the country--America had faced the world's main superpower and managed not to be defeated.  There was an increase in American symbols such as the bald eagle, and America gained a new patriotic song, "The Star-Spangled Banner," though it would not be the national anthem until 1931.  Conversely, the War of 1812 saw the demise of the Federalist Party; this party, mainly made of Northeasterners, wanted that region of the country to secede over the war's unpopularity.  When news of this agenda leaked, those who supported the "Hartford Convention" were branded as un-American and could not be elected.  The Democratic-Republicans were now the main party in America, and under James Monroe, the president who followed Madison, the nation enjoyed the Era of Good Feelings.  Also, during this era Henry Clay, one of the War Hawks of 1812, instituted the American System of a national bank, internal improvements, and heavy tariffs on foreign products.  
Internationally, the War of 1812 led to the British abandoning their forts in the Old Northwest Territory and more Americans moving into the region postwar.  Native tribes in the area, especially the Shawnee, lost their main benefactor in Britain and had to take whatever treaty the United States was willing to give them.  The territory rapidly became populous states within a generation of the war's end.  The British stopped seizing American sailors at sea and trade increased with the new nation.  This led to an increase in American commerce immediately after the war.  Also, after the disastrous Canadian campaign at the onset of the war, Americans quit clamoring to occupy Canada and focused on moving West instead of North.  The national government also increased the size of the army and navy, which had suffered huge budget cuts under Jefferson and Madison--the War of 1812 made the federal government believe that a strong military was essential to American survival.  
Long-term, America gained a new generation of statesmen after this war.  Andrew Jackson made his name at the Battle of New Orleans and would become an international figure.  His campaign nickname of "Old Hickory" also dates from this period as he was said to sleep on the ground alongside his enlisted men.  Not to be outdone, the Whig Party in 1840 brought out William Henry Harrison, hero of the War of 1812's battle of Tippecanoe, in which Tecumseh was defeated.  Harrison had common-man appeal because he was said to have been born in a log cabin, but he was really the governor and most wealthy farmer in Ohio.  Harrison's presidency is nothing of note, as it only lasted one month and led to his Vice-President Tyler completing the term, but it's hard to imagine him becoming famous if not for the War of 1812.

How did the teachings of Moses the raven create problems for the pigs? What do you believe Moses represents?

Moses taught the animals that there was a place called Sugarcandy Mountain, and said that all the animals would go to it after they died and live in paradise. In Sugarcandy Mountain, the animals would find sugar, clover was always in season, and linseed cake grew on the hedges. Moses was a smooth talker and some of the animals believed in the existence of Sugarcandy Mountain. The pigs had to struggle to convince them it did not really exist.
Although the text doesn't say so, the implication is that by focusing on the dream of a wonderful imaginary paradise after death, the animals were diverted from the task of building a better world for themselves in this life. This creates a problem for the pigs, at least at first, as they want everyone to rally around making Animal Farm the best place it can be and not be lost in dreams.
Moses represents the clergy. He is similar to a priest. Oftentimes priests, who did not labor like common workers, were encouraged by the owners and landlords to encourage people to accept miserable and exploited positions on earth with the promise they would be rewarded after death in heaven. Moses, like a human priest, doesn't work and is the special "pet" of Farmer Jones, and his descriptions of Sugarcandy Mountain sound very much like an animal version of heaven. As the book says:

It [Sugarcandy Mountain] was situated somewhere up in the sky, a little distance beyond the clouds, Moses said. ... The animals hated Moses because he told tales and did no work, but some of them believed in Sugarcandy Mountain, and the pigs had to argue very hard to persuade them that there was no such place.

What are some allusions in the novel Shoeless Joe?

W. P. Kinsella's 1982 novel Shoeless Joe contains many allusions to the work of J. D. Salinger. The most obvious is that Shoeless Joe's main character, Ray Kinsella, kidnaps Salinger, who acts as an intermediary between Kinsella and the deceased 1919 Chicago White Sox baseball team.
Additionally, W. P. Kinsella explained that Ray Kinsella was not named for him but for characters in Salinger’s stories. Salinger twice used the name Kinsella in his work. Ray Kinsella appears in the short story "A Young Girl in 1941 with No Waist at All," and Richard Kinsella is Holden Caulfield's friend in Salinger's 1951 masterpiece The Catcher in the Rye, which W. P. Kinsella called "the quintessential book about growing up male in America."
Thematically, Shoeless Joe also alludes to The Catcher in the Rye. Both are about efforts to return to a time of innocence. Ray Kinsella builds the baseball field as a tribute to the past and lost innocence. Holden Caulfield wants to be a "catcher in the rye" who helps children hang onto their innocence.

Calculus of a Single Variable, Chapter 3, 3.3, Section 3.3, Problem 14

You need to determine the intervals on which the function is increasing or decreasing, hence, you need to find out intervals on which the first derivative is positive or negative.
You need to determine the first derivative, using the chain rule, such that:

f'(x) = (cos(x/2))' => f'(x) = -(sin(x/2))*(x/2)'
f'(x) = -(sin(x/2))/2
Now, you need to solve for x the equation f'(x) = 0:
-(sin(x/2))/2 = 0 => (sin(x/2)) = 0
You need to remember that the sine function is equal to 0, in (0,2pi), at x/2 = pi.
x = 2pi
Hence, the derivative is negative for x/2 in (pi,2pi) and it is positive for x/2 in (0,pi).
Hence, the function increases for x in (0,2pi) and it decreases for (2pi,4pi), but, since the behavior of the function is analyzed over (0,2pi), then the function increases over (0,2pi).

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 52

Determine the equation of the tangent line to the curve $y= \sin x + \sin^2 x$ at the point $(0, 0)$.

Solving for the slope


$
\begin{equation}
\begin{aligned}

y' = m =& \frac{d}{dx} (\sin x + \sin^2 x)
\\
\\
m =& \frac{d}{dx} (\sin x) \frac{d}{dx} (\sin x)^2
\\
\\
m =& \cos x + 2 \sin x \cdot \frac{d}{dx} (\sin x)
\\
\\
m =& \cos x + 2 \sin x \cos x
\qquad \qquad \text{Apply Double Angle Formula $(\sin 2x = 2 \sin x \cos x)$}
\\
\\
m =& \cos x + \sin 2 x
\\
\\
m =& \cos (0) + \sin 2(0)
\\
\\
m =& 1 + 0
\\
\\
m =& 1


\end{aligned}
\end{equation}
$



Using the Point Slope Form



$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
\\
\\
y - 0 =& 1 (x - 0)
\\
\\
y =& x
\qquad \qquad \text{Equation of the tangent line at $(0,0)$}

\end{aligned}
\end{equation}
$

Which one of the following is an example of a balanced chemical reaction? A) HCl + KMnO_4 = Cl_2 + MnO_2 + H_2O + KCl B) HCl + KMnO_4 = Cl_2 + MnO_2 + 2H_2O + KCl C) 2HCl + 2KMnO_4 = Cl_2 + MnO_2 + 2H_2O + 2KCl D) 6HCl + 2KMnO_4 = 2Cl_2 + 2MnO_2 + 4H_2O + 2KCl E) 8HCl + 2KMnO_4 = 3Cl_2 + 2MnO_2 + 4H_2O + 2KCl

Hello!
This is actually a math question.
For a chemical equation to be balanced, there must be an equal quantity of atoms of each type on both sides of an equation. Let's start from the first type of atoms involved here, H (hydrogen). It appears only in H Cl at the left (one atom for each molecule) and in H_2O at the right (two atoms for each molecule). Check:
A) 1*1 = 1*2 (false)B) 1*1 = 2*2 (false)C) 2*1 = 2*2 (false)D) 6*1 = 4*2 (false)E) 8*1 = 4*2 (true).
So the only equation which might be balanced is E. Check the remaining types of atoms: Cl, K, Mn, O.
Cl:  8*1 = 3*2 + 2*1 (true),K:    2*1 = 2*1 (true),Mn: 2*1 = 2*1 (true),O:     2*4 = 2*2 + 4*1 (true).
Great, E is a balanced equation and the only such. The answer is E.

What are the specific critical issues, needs, and challenges that may be affecting the organization and its culture in the scenario below? What are the ramifications of a prison lacking a committed and cohesive management team? Scenario: You are an organizational and leadership consultant called in to develop a leadership intervention strategy (LIS) for the state’s largest prison. You learn from several members of the prison management team that they and 30 other management-level staff are actively seeking employment elsewhere. Mass resignations appear imminent. These staff members feel that they are undercompensated, overworked, unfulfilled, and underappreciated. The group consistently complains about the leadership style of the prison warden, John Trevor. He is described as distant, cold, uninvolved, and apathetic. When you meet with John Trevor personally, you are surprised to find a pleasant, unassuming gentleman who is shocked to learn of his team’s displeasure. John feels that his management team is an exemplary group of caring professionals, and he is deeply disquieted about the possibility of these individuals leaving their jobs. John expresses grave concern about the safety and security of the prison, other employees, and inmates should there be a mass exodus of the management team. He is now looking up to you to assess the situation and develop strategies to mitigate these issues. Clearly, significant gaps exist between the prison warden and his management team. These gaps could conceivably lead to safety, cost, and operations issues.

Gaps between management and team members can occur within all businesses and services. The way to narrow the gap is for managers to adopt more effective leadership styles. When managers close the gap between management and team members, managers drive what is called the Service-Profit chain, which is defined as a relationship between management, "employee engagement," "customer engagement/satisfaction," and profit or growth (Lazenby, A., "Managers: Your Key to Bridging the Gap"). While prisons are not typical for-profit businesses, studies show that leadership techniques are key to developing quality prison life, which is the service provided by prisons. Such leadership techniques have a positive impact on employees as well as on inmates, leading to the provision of quality correctional service.One reason why gaps between management and team members occur is because managers are "often promoted because they are outstanding individual contributors" (Lazenby). Since those who are promoted to management level are used to working independently, they must make major transitions to be able to start focusing on developing the skills of their team members rather than on just the development of their own skills. If the prison team members see the prison warden, John Trever, as "cold, uninvolved, and apathetic" when he is actually a very "pleasant, unassuming gentleman," it is most likely because Mr. Trevor has been unable to successfully transition from working independently to developing the skill set of his team members, which is required of him if he is to demonstrate strong leadership skills. To bridge the gap, managers must help team members see their places as contributing members, engage and inspire team members by helping them see the larger goals of the organization, open doors of communication, and build trust (Lazenby).Studies show that when management fails to bridge the gap between the highest level of management, such as the prison warden, and team members, such as the prison managers, in a correctional facility, consequences include low morale, increased burnout rates, increased turnover rates, and even increased suicide rates (Pittaro, M., "Improve Your Facility by Changing Your Leadership Style"). In addition, studies also show that when correctional staff suffers from high levels of stress, they tend to take more "punitive attitudes toward inmates," leading to higher "inmate-upon-officer assaults and inmate-upon-inmate assaults" (Pittaro). Naturally, injuries from such assaults increase medical expenses for prisons and increase safety threats. In addition, states like New York report that correctional officer brutality law suits, for even just one officer, can cost the state as much as $673,000 in settlements ("The State That is Taking on the Prison Guards Union"). The way to overcome such problems is by developing strong "transformational leadership practices" to be exhibited by the highest level of management, such as the prison warden, towards the staff, such as managers and all other staff members, and by the staff towards the inmates (Pittaro). Just as management helps staff members see their roles and goals through strong leadership practices, thereby empowering staff members, staff members can equally help inmates see their roles and goals through mentoring and coaching, thereby equally empowering inmates and creating a genuinely rehabilitative atmosphere.
https://www.themarshallproject.org/2016/04/11/the-state-that-is-taking-on-the-prison-guards-union

How does the structure and tone in "Theme for English B" connect to the theme of racism?

The structure and tone of "Theme for English B" helps to highlight the absurdity of racism and the interconnectedness of black and white life in America. There are six stanzas.
The first stanza is one line, the tag to a quotation, "The instructor said. . . ."
The second stanza contains the words of the professor, "Go home and write / a page tonight. / And let that page come out of you— / Then, it will be true." Then he makes a claim that the page, if it comes out of the speaker, will be true. It is interesting that the professor’s quote is a part of—and begins—the page.
In the third stanza, the speaker tells us that he is black and from the South but is now going to a school up north, where he is the only black person in his class. He descends the hill from school into Harlem and goes to his room at the Y and writes. It is interesting that this stanza ends with a semicolon, almost as if up until now he was relating a story and the words that follow the colon are the "page that [comes out of him]". This is an example of metafiction, in which the narrator calls attention to the writing process and the artificial nature of literary texts. Metafictional techniques come from the modernist tradition of questioning consciousness and reality.
In the fourth stanza, he seems to be addressing the professor. The speaker admits that it is difficult to know what is true at twenty-two years old, but he tries. Here is an example of the questioning of truth and reality metafictional works present. The irregular syntax in the rest of the stanza seem to mirror the unsure young mind of the speaker. It ends, "Me—Who?"
The fifth stanza attempts to answer that question. He likes "to eat, sleep, drink, and be in love." He likes music, "Bessie, bop, or Bach. / I guess being colored doesn’t make me not like / the same things other folks like who are other races." He says to the professor that they are a part of one another and that they learn from one another, though they often wish that wasn’t the case. The speaker says the man is “older—and white— / and somewhat more free.” The fact that the text contains the words of and references his professor points to how interconnected black and white lives are in America and around the world.
Because Hughes’s speaker again mentions race and because we because we know that this is a metafictional work, it is safe to say that Hughes is commenting on the artificialness of societal narratives, particularly the eurocentric ideology that venerates whiteness and demonizes blackness. It’s about how stories profoundly change the way the world thinks, how its systems and governments are structured, how people treat one another within them.
The sixth stanza is one line, which identifies the document: "This is my page for English B." Again we see these pieces of self-referentiality, the literary work pointing to itself, emphasizing this idea of the artificiality of narratives.
The tone throughout is conversational and polite. The speaker is not angry at the professor; there’s no vitriol. They are just two people conversing, though they are different races. This tone further highlights the absurdity of racism.

lim_(x->oo)sinx/(x-pi) Evaluate the limit, using L’Hôpital’s Rule if necessary.

Given to solve,
lim_(x->oo) sinx/(x-pi)
This can be solved by applying the squeeze theorem and is as follows
as we know the limits or boundaries of sin(x) is
-1<=sin(x)<=1
Dividing the above expression with x-pi we get
-1/(x-pi)<=sin(x)/(x-pi)<=1/(x-pi)
now, let us apply the limits that x-> oo we get
lim_(x->oo)(-1/(x-pi))<=lim_(x->oo) sin(x)/(x-pi)<=lim_(x->oo) 1/(x-pi)
but
lim_(x->oo)(-1/(x-pi)) = -1/(oo -pi) = 0
lim_(x->oo)(1/(x-pi))= 1/(oo -pi) = 0
so,
0<=lim_(x->oo) sin(x)/(x-pi)<=0
so ,
lim_(x->oo) sin(x)/(x-pi) = 0

According to Montesquieu in The Spirit of the Laws, who should exercise executive and legislative powers?

Montesquieu's Spirit of the Laws was an important contribution to political theory, particularly in its attempt to adapt political institutions to the needs of each particular culture. Montesquieu was critical of an absolute monarchy in which a single sovereign exercised all power. Instead, he argued for a separation of the executive, legislative, and judicial powers. This concept became a major influence on later democratic political systems, notably the US Constitution. This system would prevent any single person or institution from exercising too much power and would provide a check on abuses.
In particular, Montesquieu admired the English system. England had a monarch as the head of government, but the monarch's rule was not absolute. Legislative authority was vested in a Partliament, and the judiciary was independent as well. Such a system, Montesquieu believed, was best suited to produce well-ordered liberty as an alternative to either despotism or the unchecked rule of the people.

In Montesquieu’s opinion, the best government is a mixed one, with layers that can counterbalance one another. He relates most of his ideas to the British Parliament and governmental system, of which he is a big fan. The executive and legislative powers are both taken control of by opposing parties, and in this way, they keep one another in check while accomplishing important things.
According to Montesquieu, the executive branch should execute laws and steer the direction of the country. As such, it should be filled with nobility and leaders—typically monarchy, since his viewpoint reflects the British system of rule. The legislative branch, on the other hand, should be a representation of the people at large and should act to legislate their will. Legislators would be elected officials who have the citizens' best interests at heart and can write laws that will help the people, which will be eventually executed by the royalty among the executive branch.

Montesquieu loved the idea of a mixed government that included both monarchy and legislature. He believed that the executive powers should rest with the monarch, but that the legislative branch would be a representative branch that carried the beliefs of the people at large.
In order to balance out the powers of monarchy and nobility against the people at large, the executive branch and the legislative branch would be almost opposing forces in order to keep one another in check. In that way, the representative legislative branch would carry out the will of the people who elected them, and would write laws and create a living constitution. The executive branch would consist of nobility who carry out the laws and steer the country overall.

Montesquieu argued for a mixed, or moderate government in which the excesses of the three types of government--government by the people, by the aristocracy, and by a monarch--might be moderated. Putting it as simply as possible (The Spirit of the Laws is a very complex book, with many contradictions) Montesquieu generally thought that legislative branch ought to reflect the will of the people, and be controlled by their representatives. He deeply admired the English "mixed" constitution, under which Parliament also included nobility in the House of Lords, but the important thing was that the body represented the will of the people, particularly property owners. As for the executive, Montesquieu generally understood executive power as exercised by a monarch. Again, he deeply admired the British constitution, in which the king held powers that were limited in practice by his council and by Parliament. The crucial point for Montesquieu was that a mixed government would restrain the abuses that could occur under different types of "pure" government--democracy, aristocracy, and despotic monarchies.
https://oll.libertyfund.org/pages/montesquieu-and-the-separation-of-powers

https://oll.libertyfund.org/titles/montesquieu-complete-works-vol-1-the-spirit-of-laws

Precalculus, Chapter 6, 6.3, Section 6.3, Problem 72

The magnitude of a vector u = a*i + b*j , such that:
|u| = sqrt(a^2+b^2)
Since the problem provides the magnitude |v| = 4sqrt3 , yields:
4sqrt3= sqrt(a^2+b^2)
The direction angle of the vector can be found using the formula, such that:
tan theta = b/a
Since the problem provides the information that the direction angle of the vector v is theta = 0^o , yields:
tan 0^o = b/a => b = 0, a!=0
Replacing 0 for b in equation 4sqrt3= sqrt(a^2+b^2) yields:
4sqrt3= sqrt(a^2+0)=> a = +-4sqrt3
b = 0
Hence, the component form of the vector v can be <4sqrt3,0> or <-4sqrt3,0>.

What are some examples from the text that show how power is used in Fahrenheit 451?

In Bradbury's Fahrenheit 451, the amount of power that a person possesses is based on a combination of two things: individual depth of knowledge about the issues and the person's position of influence. For example, Captain Beatty is knowledgeable because he is a well-read, highly-skilled fireman who has his position as captain to make him powerful. Not only does he have knowledge that other people don't have, but he also has the authority to enforce the government's agenda. When Montag asks what happens to a fireman who happens to take a book from a fire scene, Captain Beatty demonstrates his power by making threats in a polite, professional tone as follows:

We don't get overanxious or mad. We let the fireman keep the book twenty-four hours. If he hasn't burned it by then, we simply come burn it for him (62).

Even though Captain Beatty sounds objective in the above quote, he is threatening Montag. If Montag does not burn the book, Captain Beatty will burn down his house. Needless to say, Beatty can back up any threat he gives because he has the knowledge, authority, and power to do so.
Another way that power is used in the society of Fahrenheit 451 is to control the population's mindset through government-controlled public education. For example, when Montag asks how a girl like Clarisse can escape the clutches of society's system of brainwashing, Captain Beatty responds with the following:

Heredity and environment are funny things. You can't rid yourselves of all the odd ducks in just a few years. The home environment can undo a lot you try to do at school. That's why we've lowered the kindergarten age year after year until now we're almost snatching them from the cradle (60).

By lowering the age that kids start going to school, the government can reach into children's brains earlier to counter anything that they might learn at home.
The Mechanical Hound is another way the government controls people and demonstrates power. A person's chemical makeup can be entered into the Hound's database, which gives it an increased advantage when hunting down criminals. Not only does the Hound's existence represent the power of the government to enforce the law, but it is also used to demonstrate its ability to make examples out of people. For instance, when the Mechanical Hound cannot find Montag during its hunt, the authorities turn it on another man. This keeps people thinking that no one can escape the Hound, and it serves as a way to flex its political and powerful muscles of intimidation. Granger explains the use of the Hound as he and Montag watch the end of the chase as follows:

They're faking. You threw them off at the river. They can't admit it. They know they can hold their audience only so long. The show's got to have a snap ending, quick! . . . So they're sniffing for a scapegoat to end things with a bang. Watch (148).

Granger brings up one more example of power that the government uses to control the populace—the power of mass media, entertainment, and distraction. If no one likes to read, and if reading is illegal, then people turn to television and radio to keep them entertained and happy. If people are happy watching television all day and driving their cars too fast all night, then they won't become upset with political issues. Captain Beatty explains in the following passage:

It didn't come from the Government down. There was no dictum, no declaration, no censorship, to start with, no! Technology, mass exploitation, and minority pressure carried the trick, thank God. Today, thanks to them, you can stay happy all the time. . . People want to be happy, isn't that right? . . . Don't we keep them moving, don't we give them fun? That's all we live for isn't it? For pleasure, for titillation? And you must admit our culture provides plenty of these (58-59).

From what Beatty says, a hedonist culture has taken over the lives and thoughts of everyone in society. As a result, the government only steps in to control the "odd ducks" and largely keeps society moving without much controversy. Still, the government keeps men like Captain Beatty in power to enforce the laws, creates killing machines like the Mechanical Hounds to intimidate and kill criminals, and makes technology and entertainment readily available in order to stay in power and keep control of society.

What characteristics does Walter Mitty wish he had in "The Secret Life of Walter Mitty"?

Walter Mitty would like to be assertive, commanding, courageous, brave, fearless, heroic, and unwavering.
"The Secret Life of Walter Mitty" is a darkly humorous tale of a man who is defeated by authority and audacity, and emasculated by an insensitive wife. Apparently consigned to conducting his domineering wife to town and running silly errands for her, Walter drives along pretending that he is the courageous Commander of a Navy hydroplane until reality interrupts. Then, he is reduced to what has been called the "hen-pecked" husband as his wife scolds the meek Walter and reminds him to buy overshoes and wear his gloves.
Shortly after dropping off his wife at the salon, Mitty drifts into another wishful daydream in which he is again a leader. This time he is a famous surgeon, who assertively fixes a faulty piston so that an operation can continue. In sharp contrast to this heroism and commanding persona, Mitty is reduced again by reality as a lowly parking-lot attendant shouts at him, "Back it up, Mac!" Then, Mitty becomes so nervous that he cannot maneuver the car correctly. Embarrassed, Mitty almost forgets to hand the youth the key; then, the attendant backs up the car with insolent skill that demeans poor Mitty.

"They're so cocky," thought Walter Mitty, walking along Main Street; "they think they know everything."

Mitty recalls how he was mocked by a garage-man who had to come out to take off the winter chains from the car because in his attempts to do so, Mitty had the chains wound around the axle. "...next time...I'll wear my right arm in a sling...." This compensatory plan leads to another daydream in Mitty: This time he is himself and he is on trial for murder. However, his shooting arm was in a sling on the night of the murder. Boldly, nevertheless, Mitty asserts, "I could have killed Gregory Fitzhurst at three hundred feet with my left hand." Chaos breaks out in the courtroom and a beautiful girl hugs Mitty. When the District Attorney strikes her "savagely," the fearless Mitty punches him on the chin, saying, "You miserable cur!"
In reality, the submissive Walter Mitty walks down the street and he remembers the second errand, "Puppy biscuit." A woman laughs as she passes him, saying to her companion, "He said 'puppy biscuit' to himself. Later, Walter Mitty walks to the hotel where is supposed to wait for his wife. In the lobby he sits in a large leather chair that faces the window. After having picked up a copy of a political and general interest magazine of the time named Liberty, a new daydream comes to him. This time he is a captain in World War I and heroically he is going to blow up the ammunition dump of the Germans. Pouring another brandy and "tossing it off" with much machismo, Captain Mitty straps on his huge Webley-Vickers automatic and sets out to destroy the enemy's ammunition. "Cheerio," the heroic Mitty shouts bravely.
This dream is interrupted by his returning wife, who immediately scolds him for sitting where she cannot see him. When she asks him why he hides, Walter Mitty tells her, "I was thinking....Does it ever occur to you that I am sometimes thinking?"

She looked at him. "I'm going to take your temperature when I get you home," she said.

Mitty makes no comment to her demeaning response to him. But, the doors seem to make a derisive sound as they depart the hotel. "Wait a minute," his wife commands him. "She was more than a minute." Walter Mitty lights a cigarette as it begins to rain. He leans against a wall with his shoulders back. "'To hell with the handkerchief,' said Walter Mitty scornfully" as he imagines himself facing a firing squad. All his hope for bravery and assertiveness dashed, Mitty is yet unwavering in his escape.
 
 

What is the significance of Antonio in Twelfth Night?

Antonio plays a small but key function in the plot of Twelfth Night. He is essential to the plot because he is the character who makes Viola suspect that her twin brother Sebastian is probably still alive. Viola is going around disguised as Cesario and in that disguise looks exactly like him. Antonio had developed a deep affection for Sebastian when he found the youth shipwrecked, but Sebastian was alone so Antonio had no clue that he had a twin sister.
Antonio’s role in keeping Sebastian alive also helps propel the action, but his scene with Cesario/Viola is the crucial one. Cesario cannot reveal that “he” is actually Viola because it is too dangerous, and he truthfully denies knowing Antonio, who is in trouble and about to be arrested. Believing that his young friend is denying him, Antonio is deeply wounded. At this point, he speaks bitterly of love’s betrayal:

In nature there’s no blemish but the mind;
None can be call’d deform’d but the unkind:
Virtue is beauty, but the beauteous evil
Are empty trunks o’eflourish’d by the devil.

Meeting next with Orsino, who thinks he acts irrationally, Antonio expands on his complaint against Sebastian, in a substantial monologue. Calling him “most ingrateful,” he reveals that making his presence known in town, where he was in danger of being apprehended on false charges, was all from love:

His life I gave him and did thereto add
My love, without retention or restraint,
All his in dedication

Antonio also helps shape the play’s tone. Because Antonio is a minor character, Shakespeare could easily have given him only brief lines of dialogue with the other, more important characters. Instead he chose to give Antonio a substantial monologue. In addition, this overt profession of love by one man for another in front of many witnesses is different in tone from the typical jesting and bantering. These choices indicate additional, more substantive functions for this character, and thus Antonio brings some gravity to the play. Speaking of love for another man also adds a homoerotic dimension, which has been much commented on, especially in modern times.
Overall, Twelfth Night is a light comedy with a lot of foolishness revolving around mistaken identity, love-sick people chasing each other, and similar stock features of Elizabethan comedy. The dark moments revolve around the torment and false imprisonment of Malvolio. The important moral characteristics of loyalty and honesty are essential parts of Antonio’s nature. While Viola’s disguise protected her, she has definitely been having fun with the liberty that external male appearance allows her. Even though she honestly does not know Antonio, she must confront the pain and anger he expresses.

Antonio in Shakespeare's Twelfth Night first appears in act 2, scene 1. He is a sea captain who assists Viola's twin brother, Sebastian (who she believes perished at sea), once he arrives in Illyria. Antonio is the one who saved Sebastian from dying in a shipwreck, and the pair have developed a fast friendship. Antonio proves to be loyal and devoted to Sebastian by providing him with funds, following after him, and even defending him in a duel. Among scholars, there has been much speculation as to whether Antonio's love is romantic or platonic in nature.
Antonio is a minor character but is significant to the play first for saving Sebastian's life and also in that he is the only character aware that Sebastian has survived and therefore does not mistake him for Cesario (Viola's male disguise) on sight. Antonio's knowledge of Sebastian but not Cesario creates humorous instances of mistaken identity. While Olivia and Orsino mistake Sebastian for Cesario, Antonio is the only character to mistake Cesario for Sebastian.

What is the effect of Plath's choice to write the poem from a mirror's perspective?

It is startling and disorienting to have this poem written from the point of view of a mirror. A person looks into a mirror to receive reassurance or confirmation about their own appearance or reality. We expect that if we see something amiss in our appearance in a mirror, we can quickly fix it. We expect a mirror to provide a reflection of ourselves and nothing more. Beyond its purpose in reflecting us, a mirror seems empty.
It is startling, therefore, to think a mirror could look back at us, see us, and judge us, not merely reflect us. It is disorienting that we might not only see ourselves but that the mirror itself might have a consciousness that could see us clearly and objectively.
A mirror is an object women look into both to see themselves and, in the second stanza, to try to see into their own souls—to see their depths, as in a lake. However, Plath, by personifying the mirror and giving it a personality, a consciousness, and a perspective, seems to be placing the mirror in the role traditionally held by women vis-a-vis men. In other words, men look at women for reassurance and confirmation that they are who they think they are. Men, Plath implies, have no realization that women have a consciousness that sees them just as they are, unvarnished—just as how most people don't assume mirrors have consciousnesses.
But complicating this is the fact the mirror is looked into by a woman. The mirror realizes that it is important to the woman, and it helps her to replace her girlish self-concept with the more terrible concept of looking older.

Plath's poem "Mirror" is written from the perspective of an anthropomorphized mirror, which has "no preconceptions." The effect of writing from the perspective of this inanimate object, which is "not cruel, only truthful," is to create the impression that the narrative is completely objective. Rather than allowing the woman who "bends over" the mirror to describe herself, bringing her own preconceptions and feelings to bear, the mirror can only reflect "faithfully" what it sees.
Offering an insight into the mirror's limitations, furthermore, evokes a sense of pathos in the reader as we see the futility in the woman's search "for what she really is." The mirror is not like "those liars, the candles or the moon," who can alter what the woman sees. Instead, the image of the woman in the mirror is "unmisted by like or dislike."
The emphasis upon the mirror's truthfulness is reiterated throughout the poem: the mirror is faithful, "truthful," "the eye of a little god." The mirror is all-powerful in that it can show everything exactly as it is. Given this, then, the final line of the poem acquires an added power: the old woman who "rises . . . like a terrible fish" cannot be a figment of the woman's imagination or a product of her fear, but simply a truth which the mirror must slowly reveal.