Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 29

How fast is the area of the triangle increasing when the angle between the sides of fixed length is $\displaystyle \frac{\pi}{s}$
Given: Length of the sides of the triangle

$
\begin{equation}
\begin{aligned}
L_1 &= 4m\\
L_2 &= 5m
\end{aligned}
\end{equation}
$

The rate of change of the angle between them, $\displaystyle\theta = 0.06 \frac{\text{rad}}{x}$
Required: rate of change of the area of the triangle when the angle between the length is $\displaystyle \frac{\pi}{3}$




We use the formula $\displaystyle A = \frac{1}{2} L_1 L_2 \sin \theta$, for area given two sides and an included angle.

$
\begin{equation}
\begin{aligned}
A &= \frac{1}{2} L_1 L_2 \sin \theta\\
\\
\frac{dA}{dt} &= \frac{1}{2} L_1 L_2 \cos \theta \left( \frac{d \theta}{dt}\right) && \Longleftarrow \text{ derivative with respect to time}\\
\\
\frac{dA}{dt} &= \frac{1}{2} (4)(5) \cos \left( \frac{\pi}{3}\right) (0.06) && \Longleftarrow \text{ we use radian mode to be consistent with measurements}\\
\\

\end{aligned}
\end{equation}\\
\boxed{\displaystyle \frac{dA}{dt} = 0.3 \frac{m^2}{s}}
$

Did Napoleon’s rise to power represent a continuation of or an end to revolutionary ideals?

This is a very good question, as the debate around this issue has been raging among historians for quite some time. In terms of military expansion and conquest, Napoleon was very much a child of the Revolution. The French revolutionaries sought to extend the Revolution beyond the boundaries of France to bring the benefits of liberty to the poor, benighted masses of other countries groaning under the lash of monarchical oppression. However, what started out as a war of liberation soon turned into a war of conquest, and this formed the basis of Napoleon's inheritance. However, it should be acknowledged that Napoleon was no ideologue; he was a pragmatic opportunist who believed that military conquest would add to his personal glory and strengthen his grip on power.
Much the same could be said about Napoleon's attitude toward the centralized state he inherited from the revolutionaries. The revolutionaries believed that a strong, centralized state was necessary to build the new nation. Gone was the loose and often bewildering patchwork of ancient regions and provinces; it was to be replaced by a single, unified nation. That was the theory, at any rate. In any case, Napoleon realized that a centralized structure of government was better able to maintain and consolidate his hold on power.
To some extent, Napoleon represented a synthesis of the ancien regime and the Revolution. At heart he was a revolutionary, but, in practice, he acted more like a king, culminating in his crowning as Emperor in 1804. In time, he came to regard the inheritance of the Revolution largely as a means to an end: a strong, stable France with himself as its undisputed master.

How does Katherine Mansfield use literary features such as language, structure, and imagery to generate significance when talking about the aloe plant, her dog, and her husband?

Some of the imagery used to describe the husband (Stanley) reveals much about his character. When the family awakens after their first night in the house, Stanley is doing exercises in front of his wife and is described as "glowing" and "squatting like a frog" as he does his exercises. His body (which he quite admires) is described as "firm" and "obedient." This imagery strongly suggests that Stanley is somewhat vain, but he reveals very soon thereafter that he is also more than a little insecure. He worries that he will one day become fat, like some men of his age already are. 
As for the aloe plant, the imagery used to describe it emphasizes that it is strange and unusual to Keziah, underscoring (like the wallpaper decorated with parrots) the strange new surroundings the family has moved into. The plant is described as "fat" and "swelling" and as having "cruel leaves." The encounter with the aloe plant, which is contrasted with the other familiar plants elsewhere in the garden, is at the center of the narrative—indeed, "Prelude" was initially intended to be part of a novel entitled Aloe. 
As for the dog, his name is Snooker. In the words of one literary critic, he is described as "endur[ing] treatment that oscillates between care and cruelty." The dog is ugly, and it smells bad. The boys are always concocting some bizarre chemical mixture to give him for reasons that are not exactly clear. He is himself somewhat wild and has to be restrained when the boys kill a duck at the pond. Like the aloe, the dog is on the edge of wildness and civilization.
https://books.google.com/books?id=JdJrkah327EC&printsec=frontcover&dq=Katherine+Mansfield+and+Literary+Modernism&hl=en&sa=X&ved=0ahUKEwi7_NqViYHYAhXK34MKHYTHDVUQ6AEIKTAA

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 39

You need to use the substitution theta^2= t , such that:
theta^2 = t => 2theta d theta= dt => theta d theta= (dt)/2
Replacing the variable, yields:
int_(sqrt(pi/2))^(sqrt pi) theta^3(cos(theta^2)d theta = int_(t_1)^(t_2) t*cos t*(dt)/2
You need to use the integration by parts such that:
int udv = uv - int vdu
u = t => du = dt
dv = cos t => v = sin t
int t*cos t = t*sin t - int sin t dt
int t*cos t = t*sin t + cos t + C
Replacing back the variable, yields:
int_(sqrt(pi/2))^(sqrt pi) theta^3(cos(theta^2)d theta = (theta^2*sin (theta^2) + cos (theta^2))|_(sqrt(pi/2))^(sqrt pi)
Using the fundamental theorem of integration, yields:
int_(sqrt(pi/2))^(sqrt pi) theta^3(cos(theta^2)d theta = (pi*sin (pi) + cos (pi) - (pi/2)*sin(pi/2) - cos(pi/2))
int_(sqrt(pi/2))^(sqrt pi) theta^3(cos(theta^2)d theta = -1 - pi/2
Hence, evaluating the integral, using substitution, then integration by parts, yields int_(sqrt(pi/2))^(sqrt pi) theta^3(cos(theta^2)d theta = (1/2)(-1 - pi/2).

How did refrigeration impact agriculture and society?

The refrigerator was invented in 1805 by an American engineer and businessman, Oliver Evans. However, it wasn't until 1913 that the first domestic refrigerator was created by Fred W. Wolf.
The refrigerator became accessible to most people during the early twentieth century and contributed immensely to industrial and agricultural development. Before the invention of the refrigerator, most farmers experienced losses, since farm products could get spoiled before being delivered to the market. Fresh-product farmers had to find a ready market for their products, or they would end up making losses. The refrigerator made it easy for farmers to transport their farm products to industries and other towns. The refrigerator also contributed to the growth of fresh-product industries such as milk and fresh meat processing.
The refrigerator further contributed to family life by helping people preserve foods for long periods. In some ways, it helped reduce food-related problems, since perishable foods could be stored for a long time.

In 1805, inventor Oliver Evans invented a refrigerator system. It was not until later, however, that refrigeration was widely used. Other inventors and scientists continued to develop and build upon his invention.
Fred W. Wolf created the first refrigerator for domestic use in 1913. In the following years, an electric refrigerator was invented. In-home refrigeration changed the way people ate. Food could be kept much longer without spoiling. In the warm summer months, food could be kept cool. Previously, food would spoil from the heat unless it was in an icebox or cellar.
In agriculture, refrigeration was used for the storage and transport of goods. Fruits and vegetables could be transported longer distances because of refrigeration. Time constraints were loosened for transporting produce across the country. This also meant that fresh fruits and vegetables could be enjoyed throughout the year.

How do you factor ab(a+b)+bc(b+c)+ca(c+a)+3abc?

In order to factor this expression, first open all parenthesis by distributing the term in front of the parenthesis. The given expression will then become
a^2b + ab^2 + b^2c +bc^2 + ac^2 + a^2c + 3abc .
We need to group these terms in a way so that we could find some common factors. Now there are 7 terms in the expression, which is not a very convenient number. However, the coefficient 3 in front of the abc term gives us a clue that this term should be broken up into 3: abc + abc + abc.
Now we have 9 terms, which we can group into three groups of three so that each group has a common factor:
a^2b + a^2c + abc = a(ab + ac + bc)
ab^2 + b^2c + abc = b(ab + bc + ac)
bc^2 + ac^2 + abc = c(bc + ac + ab)
Note that the expressions in parenthesis are the same, so the three groups of terms have a common trinomial factor! It can be factored out, and the entire sum of nine (originally, seven) terms becomes
(a + b+c)(ab + ac + bc) .
The given expression can be factored as (a + b + c)(ab + ac + bc)
 

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 74

Solve $b^2 x^2 - 5bx + 4 = 0 (b \neq 0)$ for $x$.


$
\begin{equation}
\begin{aligned}

b^2 x^2 - 5bx + 4 =& 0
&& \text{Given}
\\
\\
b^2 x^2 - 5bx =& -4
&& \text{Subtract 4}
\\
\\
x^2 - \frac{5x}{b} =& \frac{-4}{b^2}
&& \text{Divide both sides by } b^2
\\
\\
x^2 - \frac{5x}{b} + \frac{25}{4b^2} =& \frac{-4}{b^2} + \frac{25}{4b^2}
&& \text{Complete the square: add } \left( \frac{\displaystyle \frac{-5}{b}}{2} \right)^2 = \frac{25}{4b^2}
\\
\\
\left( x - \frac{5}{2b} \right)^2 =& \frac{-4}{b^2} + \frac{25}{4b^2}
&& \text{Perfect square}
\\
\\
x - \frac{5}{2b} =& \pm \sqrt{\frac{-16 + 25}{4b^2}}
&& \text{Take the square root, then simplify the right side of the equation by using LCD}
\\
\\
x =& \frac{5}{2b} \pm \sqrt{\frac{9}{4b^2}}
&& \text{Add } \frac{5}{2b}, \text{ simplify the right side of the equation}
\\
\\
x =& \frac{5 + 3}{2b} \text{ and } x = \frac{5 - 3}{2b}
&& \text{Solve for } x
\\
\\
x =& \frac{4}{b} \text{ and } x = \frac{1}{b}
&& \text{Simplify}



\end{aligned}
\end{equation}
$

How was the money of the author deposited into the bank?

The author deposited his money with help from the bank accountant and clerk.
As the story progresses, we understand how nervous the author is. He enters a bank to deposit a sum of fifty-six dollars, but his anxiety gets the better of him. The author first asks to speak to the manager, and the latter assents.
Because of the author's air of secrecy, the manager assumes that the former is some sort of private detective. Of course, the author has to disabuse the manager of this notion. Still maintaining his secretive air, the author then tells the manager that he would like to deposit some money. At this point, the manager assumes that the author is a man of wealth who must manage his large deposits discreetly.
When the author admits that he is only depositing fifty-six dollars, the manager unceremoniously refers him to the accountant. For his part, the accountant hands the author's money to a clerk. Then, he orders the author to write the deposited sum on a slip and attach his signature to his deposit. After he completes these actions, the accountant announces that the fifty-six dollars has been deposited.

In the book Coming of Age in Mississippi, why didn't more southern blacks join the movement?

There were many reasons why more Southern blacks didn't join the civil rights movement. For many, fear was the overriding motive. Violence, arson, and terror were all commonly used against those campaigning for civil rights. And as the so-called forces of law and order were dedicated to upholding white supremacy, anyone on the wrong end of such criminal acts would've found themselves unprotected.
Moody also blames the leaders of the civil rights movement for the lack of support from certain sections of the African-American community. She criticizes them for an undue focus on issues such as segregation instead of more everyday concerns such as poor housing and lack of employment opportunities. Moody believes that the civil rights leadership, in failing to engage with the question of substantive economic rights, has shown itself to be hopelessly out of touch with the concerns of most ordinary African-Americans. Little wonder, then, that so many of them choose not to join in the struggle.

Coming of Age in Mississippi is a memoir, written by Anne Moody, that tells the story of her life growing up in rural Mississippi. This novel explains the struggles that many African Americans faced in the Deep South and describes how Moody came to participate in the civil rights movement. The fourth section of the book tells the story of "the movement" in Mississippi. Moody participated in several sit-ins, where she experienced violent treatment at the hands of protesters and the police.


In her memoir, Moody talks about her frustration that more southern blacks did not join the civil rights movement. African Americans in the South refused to support the civil rights movement for a variety of reasons. Many were simply afraid that their participation would lead to violent reprisals for them and their families. Others felt that the cause was hopeless and that nothing would change how they were treated by whites in the Deep South. Moody talks about this conflict in her memoir.

In chapter 21, Holden makes a comment comparing how adults sleep to how children sleep. How does this relate to what we know about Holden's character?

In Chapter 21, Holden happens upon his little sister, Phoebe, sleeping peacefully in his brother D.B.'s room. After watching her, he decides that children always look very peaceful when they sleep, unlike adults. It makes sense that Holden would say this. He is a character who is quite thoughtful and critical about everything. He tends to see things in a more cynical light than other people his age, and it shows in his observations of others. In life, he experiences a feeling of discontent with everything; this contributes to his views on the adult pursuasion and his judgemental attitude toward virtually everyone else that he runs into.
Adults, he thinks, are very "phony" in general. In fact, he sees a lot of what happens in the world as their fault. We know that he has experienced some trauma in his past which makes him a troubled person and an unreliable narrator. It also gives him a unique perspective on certain situations. Where someone else might look upon Phoebe sleeping in a positive light, he marvels at how different she looks than an adult would. This negative spin that he puts on everything that he witnesses speaks to his internal anger and critical nature. 

How does Shakespeare make Act II, scene viii, from the Merchant of Venice such a dramatic moment?

This scene depicts a conversation between two of Antonio's friends, Salanio and Salarino - gentlemen we met in Act 1, when they were with him.
The two are discussing our protagonist, Antonio, and his enemy, Shylock. The mere mention of these two names in the same conversation already creates drama since the two despise one another so much. What makes this particular conversation even more dramatic is that Shakespeare has the two characters talk about Shylock's excessively exaggerated reaction to his daughter Jessica's elopement with a Christian, Lorenzo, and how this incident could affect Antonio.
Shakespeare has the two characters repeat Shylock's cries as he went about the streets of Venice searching for Jessica. The men mock him but are, at the same time, afraid of how this event will impact on Antonio, who had come to Bassanio's defense when he negated a claim that Jessica and Lorenzo were on Bassanio's ship en route to Belmont. Salanio and Salarino obviously know how spiteful and vengeful Shylock is and fears that he may want to punish Antonio for protecting Bassanio. They hope that he does not give Shylock a means to get back at him and that he has to ensure that he repays the Jew's debt.
It is, however, clear from what Salarino says that Antonio may, indeed, be in some danger, for he had been informed by a Frenchman that a richly laden Venetian ship had suffered some disaster in the English channel, losing its entire cargo. Salanio tells him to inform Antonio of this travesty in such a way that the news may not come as too great a shock.
Shakespeare reminds the audience of Antonio's vulnerable state by having Salarino recount how he witnessed him taking leave of his closest friend and confidante, Bassanio, and how heartbroken the merchant was. Added to this, Salarino also emphasizes Antonio's magnanimity when he told Bassanio not to worry about the contract he had made with Shylock for it would be taken care of.
Salanio, obviously concerned about Antonio's well-being, then suggests that the two of them should seek Antonio out and give him some cheer. At this point of the play, the audience is aware of Shylock's malice and would probably share the two gentlemen's sentiment to a greater or lesser degree.  
This scene sets the audience up for greater drama which is about to unfold since it foreshadows events later, when Antonio loses all his ships and forfeits on the bond. Shylock then has him arrested and demands recompense in the form of a pound of Antonio's flesh. 

Compare and contrast the images, tone and theme of the poems "How Do I Love Thee? Let Me Count The Ways" by Elizabeth Browning and "Do Not Go Gentle into that Good Night" by Dylan Thomas.

Thematically, both poems are about love, but Browning's "How do I Love Thee?" concerns a person's romantic love for another person, while Thomas focuses on a son's love for his father. We know that that the narrator of "Do Not Go Gentle" is a son, because he says in the last stanza "and you, my father." In "How do I Love Thee?" we often assume the speaker is a woman, because the poem was written by a woman, but since no gender is given, we can understand it as a beloved of any gender addressing the loved one. 
Both poems convey deep attachment to the person addressed and each addresses the beloved person directly, but "How do I love thee?" has a gentler tone, while the tone of Thomas's poem is relentlessly fierce. In Thomas's poem, the narrator demands that his elderly father fight for his life as long as possible, repeating over and over again "do not go gentle into that good night." By "that good night," the narrator means death. The imagery that he uses is violent and raw: 

Old age should burn and rave at close of day

He repeatedly says that his father should 

Rage, rage against the dying of the light.

Words like "burn" and "rave" and "rage" are angry, high-energy words, words that make us think of getting fired up and fighting back. Thomas uses other fierce, high-energy images to further emphasize his point: He talks about "wild men," who "caught and sang the sun in flight." Wild men, of course, are fierce and active, and verbs like "caught" and "sang" are active, vital, high-energy words as well. One must be fierce too to catch something as powerful and burning as the sun. The sun "in flight" brings to mind the image of fast-paced motion. 
Thomas turns the blindness we associate with old age into fierce, bright, high-energy imagery with words like "blinding," which means bright, "blaze," which makes us think of fire, and "meteors," which shoot rapidly across the sky:

men...who see with blinding sightBlind eyes could blaze like meteors... 

He also tells his father to "Curse, bless, me now with your fierce tears, I pray."
The tone, with its repeated images of rage, fire and light, is meant to inspire his father to rally all his energy and force to fight off death.
Browning's narrator also conveys deep passion towards the beloved. The narrator communicates this by writing: "I love thee [you] to the depth and breadth and height my soul can reach." In other words, if we imagine the love stretching out in all directions, the narrator loves the beloved totally, with every ounce of strength, in an all-encompassing way. The passion is also reinforced by repetition of the phrase "I love thee" over and over: one line does not convey all the love: instead, the love has multiple dimensions.
At the same time, the poem has a gentler, quieter tone than Thomas's poem and does not use the same fierce images. Browning uses more domestic images, such as in these lines: 

I love thee to the level of every day'sMost quiet need, by sun and candlelight.

Words such as "level," "every day," "quiet," and "candlelight" are not fierce and wild but simple, gentle, and calm. The love is free and pure and the "passion put to use," as if it is channeled constructively rather than burning wildly. It is the ever-present quality of this love, always there in ordinary, everyday life, that conveys its depth.
Unlike Thomas, this narrator doesn't fight against the possibility of death or tell the beloved to fight death. Here, death is not an end, "a dying of the light." Instead, the narrator in Browning's poem believes their love will continue beyond the grave, saying: "I shall but love thee better after death." 

What is the view point of the author in "The Most Dangerous Game?"

Richard Connell's short story "The Most Dangerous Game," was published in 1924. The short story is written in the 3rd person, limited, which means that the thoughts and feelings of one of the characters are visible to the author. For a fictional work to be third person omniscient, the author has to have knowledge of all the character's thoughts and feelings.  
Here is an example from the text: 

"Rainsford's second thought was even more terrible. It sent a shudder of cold horror through his whole being. Why had the general smiled? Why had he turned back?" 

This quote shows that Rainsford's thoughts are perceived by the author. The other characters, Ivan, Whitney, and General Zaroff, are revealed only through dialogue and physical description. Their thoughts and feelings are not revealed by the narrator.   
 

 

Its third person, ( Omniscient ) .
 

Single Variable Calculus, Chapter 5, 5.5, Section 5.5, Problem 36

Find the definite integral $\displaystyle \int^7_0 \sqrt{4 + 3x} dx$

Let $u = 4 + 3x$, then $du = 3 dx$, so $\displaystyle dx = \frac{du}{3}$. When $x = 0, u = 4$ and when $x = 7, u = 25$. Thus,


$
\begin{equation}
\begin{aligned}

\int^7_0 \sqrt{4 + 3 x} dx =& \int^7_0 \sqrt{u} \frac{du}{3}
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& \frac{1}{3} \int^7_0 u^{\frac{1}{2}} du
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& \frac{1}{3} \left[ \frac{u^{ \frac{1}{2}+1}}{\displaystyle \frac{1}{2} + 1} \right]^7_0
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& \frac{1}{3} \left[ \frac{u^{\frac{3}{2}}}{\displaystyle \frac{3}{2}} \right]^7_0
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& \frac{1}{3} \left[ \frac{2u^{\frac{3}{2}}}{3} \right]^7_0
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& \frac{2u^{\frac{3}{2}}}{9} \left|^7_0 \right.
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& \frac{2 (25)^{\frac{3}{2}}}{9} - \frac{2(4)^{\frac{3}{2}}}{9}
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =&\frac{250 - 16}{9}
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& \frac{234}{9}
\\
\\
\int^7_0 \sqrt{4 + 3 x} dx =& 26
\end{aligned}
\end{equation}
$

What are some problems and solutions in The Bronze Bow by Elizabeth George Speare?

Throughout the novel, Daniel struggles to control his anger with the occupying Roman forces and Leah battles her inner demons. Thacia tries her best to positively influence Daniel, but Daniel is too stubborn to let go of his vow to fight against the Romans. As the novel progresses, Daniel begins to listen to Jesus preach and Daniel's relationship with his sister improves. When Daniel tells Leah about Jesus' messages, Leah comes out of her shell and thrives. Daniel's relationship with Thacia also begins to grow, and Daniel starts to have feelings for her. However, Daniel's hate and bitterness ruin each of his relationships. Daniel cannot accept Jesus' tolerant disposition towards the Romans and holds onto his hate. He threatens Marcus, the Roman soldier who has been speaking to Leah, which negatively affects Leah's well-being. Daniel also rejects Thacia's love because of his vow to fight the Romans. It is only when Daniel destroys each of his relationships and loses hope that he decides to follow Jesus. At the end of the novel, Jesus heals Leah and Daniel accepts Jesus' message of love. Daniel then marries Thacia and invites Marcus into his home.

After he learns of the laundry scheme, what does the warden tell the children will happen if they get into any more trouble in Al Capone Does My Shirts?

In the book, Piper (the warden's daughter) has hatched a money-making scheme using the prison's laundry service. Moose doesn't really want to get involved with the specifics of the scheme, but Piper forces him to talk up the laundry-service to their classmates. Moose tells tall tales about living at Alcatraz, prompting his classmates to want to have some of their clothing laundered by the supposedly infamous convicts at the prison.
Piper makes the laundry scheme work by stuffing her classmates' clothing in other families' laundry bags.
In time, however, the warden gets wind of the scheme when Mrs. Del Peabody (Del Junior's mother) writes a scathing letter of complaint to him. When he discovers the kids made money from the scheme, he demands they put the money on his desk. After they do so, he accuses them of acting out of "greed," "silliness," and "incredibly poor judgment." For their part, Moose and Theresa aren't guilty of actual participation in the scheme, but the warden includes them in his threat to have their fathers fired (without severance pay) if they ever participate in such a scheme again.
Meanwhile, Piper (the warden's daughter) remains silent about her culpability in the laundry scheme. When the warden demands the children hand over their profits, Piper makes no move to hand over her money. Subsequently, the warden lectures Annie for disappointing her mother, and he accuses Jimmy of not considering how hard things will be if his father loses his job at Alcatraz. Next, the warden lectures Moose about getting involved in such a dishonest project.
As a last word, the warden warns the children that, if they break any more rules or even give the impression that they have done so, they and their families will be asked to leave Alcatraz.

The warden tells the children that, although they aren't the first kids to break the rules on the island, they will be the last. He accuses them of being greedy and having poor judgment. He says that if the children get into any more trouble, their fathers will be dismissed without severance pay. That means they will be fired, as the fathers work at the prison, and won't receive any money to support their families while they look for other jobs. The warden makes all the children feel worried and guilty about the potential for their fathers to be fired during the Great Depression, when it is unlikely their fathers will be able to find more work to support their families. The warden also tells the children he will be speaking to their parents about their laundry scheme and they must return the money they took to their classmates.

What cultural issues does Foucault shed light on in this book.

In Discipline and Punish, Foucault challenges the idea that the move from physical punishment to reforming a person through surveillance and psychological means—what Foucault calls discipline—is an "advance" from barbarism to a more civilized approach to treating criminality. Both are displays of power, Foucault contends, but what we today see as the extreme cruelty of physical punishment was, in former times, kinder than modern discipline. We have gone from punishing the body to controlling the soul. 
Foucault looks first at how criminals were dealt with in the Renaissance, pointing out that they were often tortured or killed so that the power of the king could be inscribed or shown on their bodies. Punishment, including execution, was a public spectacle, a display of power. However, while their bodies were physically punished in harsh ways, criminals' souls were largely left alone.
Foucault then turns to discipline and describes it as revealing the movement of power from the body of a king to the invisible power of the state. Now, criminals are both hidden away and subjected to endless surveillance. Foucault cites Jeremy Bentham's concept of the panopticon, a prison in which the prisoner was under constant surveillance, as the model for the new concept of discipline. Outward punishment was now no longer enough: the mind and soul of the prisoner also had to be kept in subjection. As Foucault put it:

It is the fact of being constantly seen. . . that maintains the disciplined individual in his subjection.

The important point is that Foucault reverses the idea dear to our culture that we have become more humane in how we treat criminals. By constantly observing the criminal and forcing him—and, in fact, all of us—to internalize the values of the state, we have become less free than we used to be.

Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 24

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

& -3x + y = -5 \\
& x + 2y = 0

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

We solve for $y$ in equation 1


$
\begin{equation}
\begin{aligned}

-3x + y =& -5
&& \text{Given equation}
\\
y =& 3x - 5
&& \text{Add each side by $3x$}

\end{aligned}
\end{equation}
$


Since equation 1 is solved for $y$, we substitute $3x - 5$ for $y$ in equation 2.


$
\begin{equation}
\begin{aligned}

x + 2(3x - 5) =& 0
&& \text{Substitute $y = 3x - 5$}
\\
x + 6x - 10 =& 0
&& \text{Distributive Property}
\\
7x - 10 =& 0
&& \text{Combine like terms}
\\
7x =& 10
&& \text{Add each side by $10$}
\\
x =& \frac{10}{7}
&& \text{Divide each side by $7$}

\end{aligned}
\end{equation}
$


We found $x$. Now we solve for $y$ in equation 1.


$
\begin{equation}
\begin{aligned}

y =& 3 \left( \frac{10}{7} \right) - 5
&& \text{Substitute } x = \frac{10}{7}
\\
\\
y =& \frac{30}{7} - 5
&& \text{Multiply}
\\
\\
y =& \frac{30-35}{7}
&& \text{Get the LCD}
\\
\\
y =& - \frac{5}{7}
&&

\end{aligned}
\end{equation}
$

Who is the narrator of thr novel?

The narrator of To Kill A Mockingbird is Scout Finch. She is the daughter of Atticus, and the brother of Jem, and the novel begins when she is almost six years old. Her real name, used only by a couple of characters in the novel, is Jean Louise. The story is told when Scout is much older, and so it takes on the character of a reminiscence: a woman remembering the maturation process of her childhood as much as the very traumatic events that surrounded the trial of Tom Robinson. What is especially powerful about the novel is that its themes of racial injustice appear particularly insidious when viewed through the eyes of a young girl, who has not yet absorbed the prejudices of her community. In addition to the trial, Scout's relationships with her father and brother, her friends, and with the mysterious Boo Radley, are at the center of the novel.

What impact might a narrow span of control have on a manager?

A "narrow span of control" typically refers to the number of subordinates, or people to manage, that a manager has. Having a narrow span of control, or fewer subordinates, allows a manager to be more involved in the day to day work of his or her subordinates. This is beneficial when the work involved is complex. Managers are able to be more available and involved because they aren't supervising as many people. The disadvantage to a narrow span of control would be that there are a larger number of managers within the organization. This can make it more difficult to make changes, as there are a larger number of people that need to be involved in each decision. There are also more levels of management in organizations with a narrow span of control, so it can be more difficult to reach upper levels of management.

The impact of the "narrow span of control" on a manager really depends on the level of the manager in the organization and what industry and size of an organization the manager is working. The span of control refers to how many employees a manager can control efficiently and effectively on a daily basis.
To answer the above question, we have to discuss the two types of organizations.  
 1. Centralized organizations 
 2. Decentralized organizations
In a centralized organization, many of the decisions are made from the top managers and the lower level managers carry out the top manager's requests. 
In the decentralized organization, the decisions do not come from the top managers but utilize the managers that are closest or have more expertise in the department in order to take appropriate action to solve the problems. 
An example of a centralized organization is the U.S. Army. The top managers make the decisions whether to make any changes within departments and the lower level managers carry out the directives. 
An example of a decentralized organization is Johnson & Johnson. Johnson & Johnson believe that a decentralized organization creates more innovation compared to a centralized organization due to the freedom employees have in solving problems.
In answering the question above, the impact of a narrow span of control can be costly because there is a need for more managers to supervise more employees, the level of hierarchy can lead to slow decision-making processes within the organization, and the communication with other managers can be more complex leading to more miscommunications within the organization. 

It depends on what's meant by "narrow span of control," but I can certainly think of examples that might be helpful in answering this question. When we use the term "manager," we are presupposing this individual supervises and has some degree of control over at least one other individual. The thing to remember is that every manager has their own manager, and so their ability to manage is either aided or hindered by the expectations of those above them. If the culture at the organization is lenient and casual, the manager might not find support in her ability to enforce an expectation of punctuality. If the head of the organization doesn't demonstrate the expectation that employees are to arrive and leave at a designated time, then a mid-level manager has a narrow span of control when it comes to insisting that her employees are on time.

What were some political causes of the Mexican War of Independence?

The major reasons behind the Mexican War of Independence have their roots in the social struggle for freedom from Spanish rule. However, there were some important underlying political catalysts for the war as well. To understand the political causes of the revolution in Mexico, it is important to consider the political situation in Spain in the early 19th Century.
In 1808, Joseph Bonaparte was installed as the King of Spain by his brother Napoleon not long after the French invasion. He was very much unliked by the majority of the Spanish populace. His mere presence as king instigated a revolt against his rule known as the Peninsular War. Spanish nationalists fought to return Spain to Spanish rule and expel the French from political control of their country.
The Mexican elite were also divided over loyalty to the new monarch in Spain and the old system of Spanish kings. Supporters of Spanish rule were successful in ousting the viceroy of Mexico and installing Pedro Garibay, a retired Spanish general, to the position. All this led to a very uncertain political situation in Mexico.
While Spain was consumed by its struggle in Europe and Mexican political control was itself very uncertain, Mexican proponents of independence sensed that this would be an opportune time make their bid for liberty. On September 16, 1810, Miguel Hidalgo made his famous cry for freedom that officially began the Mexican War for Independence.
http://coursesite.uhcl.edu/HSH/Whitec/xhist/MexIndWar.htm

College Algebra, Chapter 2, 2.1, Section 2.1, Problem 36

Draw the parallelogram with vertices $A(1,2), B(5,2), C(3,6)$ and $D(7,6)$ on a coordinate plane. Find the area of the parallelogram.




Recall that the area of the parallelogram is $A = L \times W$ and we know that $AC = BD$ and $AB = CD$
By using distance formula,

$
\begin{equation}
\begin{aligned}
d_{AC} = d_{BD} &= \sqrt{(3-1)^2 + (6-2)^2}\\
\\
&= \sqrt{2^2 + 4^2}\\
\\
&= \sqrt{4+16}\\
\\
&= \sqrt{20} \text{ units}\\
\\
d_{AB} = d_{CD} &= \sqrt{(5-1)^2 + (2-2)^2}\\
\\
&= \sqrt{4^2 + 0^2}\\
\\
&= \sqrt{4^2}\\
\\
&= 4 \text{ units}
\end{aligned}
\end{equation}
$


Therefore, the area of the parallelogram is $A = d_{AC} \cdot d_{AB} = (\sqrt{20})(4)$
$= 8 \sqrt{5}$ square units

What did Magwitch say that he characterizes as “low?”

The incident referred to here takes place in chapter 40 of the book, when Pip is meeting secretly with Magwitch, whom he has described as his "uncle" to the watchman. Magwitch explains that his real name is Magwitch, and that he was brought up to be "a warmint, dear boy." Pip deduces from what Magwitch says that he has been a criminal and was tried in London.
After he has eaten, Magwitch begins effusively describing how Pip, being "his gentleman," should have "horses to ride, and horses to drive," and appropriate footwear and clothes. He then produces "a great thick pocket-book" and throws it onto the table. He declares that he has returned to England in order to "see my gentleman spend his money like a gentleman." His fervor rises to such a pitch that he stands up and declares, "blast you all!," encompassing the judge who sentenced him as well as the colonist "stirring up the dust." He then says that Pip will be "a better gentleman" than all of these put together.
Pip is embarrassed and upset, in "a frenzy of fear and dislike." At this point, Magwitch apologizes for having said something "low." He then describes himself as having been "low" for many years, and Pip acknowledges this but says he doesn't want to think too much about it. This suggests that the "lowness" he is referring to is his own criminality. The comment he makes about the judge and the colonists was low because it reflects the behavior and attitudes of a criminal, who dislikes the ruling classes and disagrees with the general setup of society, particularly as regards the law. It also may refer to the fact that his money has come as a result of criminal activities. Pip does not seem upset at the fact that Magwitch is discussing money—as, obviously, in these circumstances, they must—but rather at the fact that he leaps to his feet and addresses the room with surly and inappropriate comments about judges and others, suggesting a resentment at the way his "warmint" lifestyle has been treated. In promising to be "low" no longer, Magwitch is saying that he will no longer behave in that way and will try to ensure that Pip can be a real gentleman with the help of the money.

Magwitch is telling Pip of the enormous wealth that he can come to expect from him in addition to the substantial sum he's already received. Magwitch has made it big in Australia, becoming a very wealthy and successful sheep farmer and stock breeder. He wants to continue to shower his good fortune upon Pip, funding his lifestyle as a young gentleman about town. He's so excited at revealing himself to be Pip's benefactor that he takes out his pocketbook and some papers and throws them down on the table. These items contain the details of the substantial wealth that Magwitch wishes to pass on to Pip.
But Magwitch suddenly remembers where he is. He's in the company of a young gentleman and such enthusiasm over one's wealth is considered somewhat vulgar, or "low" in polite society. Magwitch fulsomely apologizes to Pip; he was clearly forgetting his manners. But as someone who's spent most of his life as a convict, Magwitch can be forgiven for his brief relapse.

True or False? Fiji was conquered primarily through germs which spread, wiping out entire villages.

Fiji was initially annexed by the British in 1874. However, in 1875 three Fijians visited Sydney and caught measles there. On their return to Fiji, the British administration chose not to quarantine the three, despite having a very good knowledge of the effects a new disease could have on a population that had not encountered it before. As a result, Fiji was afflicted with a measles epidemic that killed more than 40,000, roughly two thirds of the total indigenous population. Whether the British deliberately introduced measles in order to control the native Fijians is uncertain, although it was claimed by some at the time. Regardless of whether it was a deliberate act of what could be called germ warfare or gross negligence, the measles epidemic did immediately follow the British annexation of Fiji and devastated all the islands.

The “Account Balances.xls” data set has information on the account balances of customers at a bank’s four locations. We want to test the null hypothesis that the mean account balances are equal in the four towns. Part (a) Using an α of 0.05, carry out a one-way ANOVA using Excel. You must submit your actual Excel file with the output as part of the assignment. Part (b) Do you reject the null hypothesis or not? Indicate on which part of the Excel output you base your decision. Part (c) Assuming that an acquaintance of yours has never heard of ANOVA, explain to her what the outcome in part (b) means in non-statistical terms.

(a) I do not have a current copy of Excel. The following are instructions that should get the Anova output:
(1) Enter the data in columns A,B,C, and D.(2) On the toolbar select Data -> Data analysis(3) Select Anova -> single factor(4) Enter the range A4:D23 (as it appears in your spreadsheet)(5) Select grouped by columns(6) Select or enter 0.05 for the alpha level(7) Check output range and type in E2
You should get the following information:
F=2.352657462p=0.0792776228Factor:df=3SS=2551767.07MS=850589.022Errordf=72SS=26031162.9MS=361543.929SXP=601.285231
(b) Do not reject the null hypothesis. p > alpha . (.07>.05; the probability that you could have a group such as this by chance is greater than your level of confidence.)
Compare p to the alpha level. When p <= alpha we reject the null hypothesis. 
(c) Our basic assumption is that the average values for each city (means) are the same. We assume that the spread of the data is the same for each city (variances.) The Anova test returns the probability that we could get samples from a group of cities that looks like the samples we got if the averages really were the same.
If that probability (p) is low  (lower than some expectation that we had before running the test) then we conclude the averages of at least two of the cities must be different (reject the null hypothesis.)
http://mathworld.wolfram.com/ANOVA.html

Why were poems and stories that reflected events of the day needed early in the 20th Century? What purpose did they serve?

An interesting question. People have always written about current events, but, arguably, the First World War, combined with the rise of Modernism, meant that the poetry and literature of the First World War era reflected day-to-day events with greater realism than anything that had come before. Even a comparison between poetry from early in the War, such as Rupert Brooke's idealistic "The Soldier," and the vivid realism of poems like Sassoon's "Suicide In The Trenches" gives an indication of the change. But what was the purpose of these apparently demoralizing poems showing the reality of war?
For Sassoon and Owen, they wrote as a means of showing truth to those at home who received only a false idea of what was really going on, filtered through a lens of propaganda. Their poems brought home, back to those who had not experienced the war, what was really happening: the incompetency of the generals, the suffering of those who returned home missing limbs, and the truth of how many would not return home at all. After the war, many who had fought in it went on to write longer memoirs of their time fighting, like Sassoon's Memoirs of a Fox Hunting Man and Graves's Goodbye to All That. On a personal level, writing these works helped them to process what they had seen. On a wider scale, people read these works because the world was changing so enormously that fictionalized accounts and poetry about that changing world was one way both to normalize it and to come to grips with it. Poetry and literature can be for the purposes of escapism, but it can also serve an important purpose in presenting a mirror of the world to those who have to live in it, through which they can understand themselves better.

What personal belongings do George and Lydia find in the nursery? Why are they there? How do they work as a literary device And which one(s) in the story "The Veldt?"

The short story "The Veldt" by Ray Bradbury tells of a family that invests in a high-technology intelligent home. The parents quickly become disillusioned with the house, but the children thrive on it. The nursery in particular is impressive to them because it can construct realistic scenes from anywhere in the world. For some reason (which a psychologist later explains), the children select the landscape of an African veldt, complete with animals such as antelopes, vultures, and predatory lions.

On their first visit to the veldt in the nursery, the parents, George and Lydia, become terrified by the lions. When George reenters the nursery, the children have changed the scene to a more peaceful forest setting. On the ground, George finds something.


"An old wallet of mine," he said. He showed it to her. The smell of hot grass was on it...and the smell of a lion. It was wet from being in the lion's mouth, there were tooth marks on it, and there was dried blood on both sides. He closed the door and locked it, tight.


As becomes evident later, this wallet is there because the children have placed it there. Later, George and the psychologist he has brought in find a bloody scarf of Lydia's on the veldt. These are examples of the literary device of foreshadowing, or setting up what is to transpire later. Foreshadowing takes various forms to hint to readers what will happen in the future. In this story, the children have become so enamored of the nursery that they have come to see it as more real than the outer world. The personal belongings that the parents find foreshadow that the children eventually will set up their parents to be killed by the lions.

The parents first find the father's, George Hadley's,  wallet in the nursery. It has been chewed by the lions, has the lions' saliva on it and is bloody. Later, they find the mother's bloody scarf on the nursery floor. Finding these items frightens the parents, who can't figure out how they got there. The parents are so unnerved by this, along with children's fixation with Veldtland, that they decide to shut down the nursery, which badly upsets the children. The two bloody items represent examples of the literary device of foreshadowing, suggesting to the reader before it happens that George and Lydia will be killed and eaten by the supposedly imaginary lions in the nursery. 

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 13

a.) Determine the average rate of change of the area of a circle with respect to its radius $r$ as $r$ changes from
$(i) 2 \text{ to } 3 \qquad (ii) 2 \text{ to } 2.5 \qquad (iii) 2 \text{ to } 2.1$

b.) Find the instantaneous rate of change when $r=2$
c.) Show that the rate of change of the area of a circle with respect to its radius (at any $r$) is equal to the circimference of the circle.

Recall that the Area of the circle is $A = \pi r^2$ where $r$ is radius. where $r$ is radius
$(i)$ $r$ from 2 to 3
$\displaystyle \text{Average rate} = \frac{A(3) - A(2)}{3-2} = 5 \pi = 15.7080 \frac{\text{unit area}}{\text{unit radius}}$

$(ii)$ $r$ from 2 to 2.5
$\displaystyle \text{Average rate} = \frac{A(2.5) - A(2)}{2.5-2} = \frac{9}{2} \pi = 14.1372 \frac{\text{unit area}}{\text{unit radius}}$

$(iii)$ $r$ from 2 to 2.1
$\displaystyle \text{Average rate} = \frac{A(2.1) - A(2)}{2.1-2} = \frac{41}{10} \pi = 12.8805 \frac{\text{unit area}}{\text{unit radius}}$


$
\begin{equation}
\begin{aligned}
\text{b.) } \frac{dA}{dr} &= \pi \frac{d}{dr} (r^2)\\
\\
\frac{dA}{dr} &= \pi(2r)\\
\\
\frac{dA}{dr} &= 2\pi r
\end{aligned}
\end{equation}
$


when $r = 2$
$\displaystyle \frac{dA}{dr} = 2\pi(2)$
$\displaystyle \frac{dA}{dr} = 4\pi \frac{\text{unit area}}{\text{unit radius}}$

c.) Recall that the circumference of the circle is equal to $c = 2 \pi r$ and the area of the circle $A=\pi r^2$ has rate of change of $A'(r) = \pi \frac{d}{dr}(r^2) = \pi (2r)$. We have,
$A'(r) = 2 \pi r$ which equals the circumference of the circle.

int x^2sinx dx Find the indefinite integral

Recall that indefinite integral follows int f(x) dx = F(x) +C where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration.
 For the given  integral problem: int x^2 sin(x) dx , we may apply integration by parts: int u *dv = uv - int v *du.
Let:
u = x^2  then du =2x dx  
dv= sin(x) dx then v = -cos(x)
Note: From the table of integrals, we have int sin(u) du = -cos(u) +C .
Applying the formula for integration by parts, we have:
int x^2 sin(x) dx= x^2*(-cos(x)) - int ( -cos(x))* 2x dx
                              = -x^2cos(x)- (-2) int x*cos(x) dx
                              =-x^2cos(x)+2 int x *cos(x) dx
Apply another set of integration by parts on int x *cos(x) dx .
Let: u =x then du =dx
       dv =cos(x) dx then v =sin(x)
Note: From the table of integrals, we have int cos(u) du =sin(u) +C .
int x *cos(x) dx = x*sin(x) -int sin(x) dx
                              = xsin(x) -(-cos(x))  
                              = xsin(x) + cos(x)
Applyingint x *cos(x) dx =xsin(x) + cos(x) , we get the complete indefinite integral as:
int x^2 sin(x) dx=-x^2cos(x)+2 int x *cos(x) dx
                              =-x^2cos(x)+2 [xsin(x) + cos(x)]+C
                               =-x^2cos(x)+2xsin(x) +2cos(x) +C
 

How did framers put limits on democracy?

The framers limited democracy in the US by developing a government structure that isn't a pure democracy. Instead, the framers developed a democratic republic. In a democratic republic, elected officials make governing decisions rather than the masses. In creating this type of government, the framers hoped to streamline the government's decision-making process and create a system that would be less negatively affected by low voter turn-out and tensions between the classes. 
Another way in which the framers limited democracy was by incorporating a central government. By including a central government, the framers made it so the states had to work together rather than compete with one another for commerce and power. The central government is divided into three branches that each have checks and balances on one another's power. These checks and balances make sure that the representatives do not develop too much power. It also protects the minority from the majority votes by making sure that those in power are governed by the laws of the land. 

What reactions and responses are there for the deaths in The Outsiders?

I believe the question is asking about responses or reactions a reader might typically have to the deaths in that occur in the novel.  
I think one typical reaction is anger.  Several central and loved characters die in the book, and being angry over the deaths is understandable.  I remember reading The Outsiders for the very first time, and I remember being very upset at Johnny's death.  I had grown to really like his quiet strength.  I also really appreciated how he and Ponyboy were essentially two halves that completed each other.  To know that Ponyboy would have to live without Johnny made me mad.  Plus, I was upset that Hinton could kill him off from something that happened when he was trying to save people.  I just never thought that Johnny deserved to die, so I was angry that he, of all characters, dies. 
Sorrow and sadness are two other reactions that I think readers typically might experience regarding the deaths in the story.  It's sad to have to say goodbye to characters like Johnny and Dally.  We've grown to really love them and appreciate them and their idiosyncrasies.  
Perhaps one last emotion is relief, joy, or satisfaction.  I think any of those emotions might be felt when the reader learns that Johnny killed Bob.  We know that he is the leader of the "enemy."  We also know that he is the guy that previously beat Johnny to within an inch of his life.  Readers might feel some satisfaction that Johnny was able to get his revenge.  Or maybe we feel relief and happiness that Johnny no longer has to be afraid of that guy.  

Compare and Contrast Macbeth and Banquo in Act One, Scene Three. (Include context.)

Both Macbeth and Banquo are bewildered by the weird sisters. The witches proclaim that Macbeth is Thane of Glamis and Cawdor, and will eventually be king. Banquo asks Macbeth why this news startles him. Banquo asks the witches to tell his future. They say that he will not be king, but his sons will. Given Macbeth's first reaction, it seems that Banquo is initially more comfortable with the prophecies than Macbeth is.
Seeing proof of what the witches had said, Macbeth becomes ambitious. Banquo, on the other hand, collects his thoughts and becomes skeptical. Here, we clearly see how Macbeth gives in to his ambition while Banquo takes a step back and employs a healthy (intelligent) skepticism:

And oftentimes, to win us our harm,
The instruments of darkness tell us truths,
Win us with honest trifles, to betray's
In deepest consequence. (I.iii.133-46)

After hearing Banquo's warning, and considering how "foul and fair" the day has been, Macbeth is skeptical as well. So, both men share a healthy skepticism. But Banquo inevitably accepts the notion that if the future matches the witches' prophecies, so be it. Macbeth becomes more obsessed with the prophecies and his future. Macbeth's ambition and his wife's influence will feed this obsession.
In this particular scene, Macbeth is skeptical but intrigued to the point of being obsessed. Banquo is skeptical and careful in thinking about the encounter.

Which character matures the most throughout The Prince and the Pauper? What are examples of that change?

I would have to say that Edward, Prince of Wales, matures the most throughout the novel.
Edward had good manners throughout the book due to his training as a prince. He deepens and matures through his experiences. These start the moment he meets Tom. Edward responds sympathetically to Tom’s account of his life, and when he hears Tom gets beaten, tells him “BEATINGS!—and thou so frail and little. Hark ye: before the night come, she shall hie her to the Tower. The King my father"—
Tom interrupts, saying, "In sooth, you forget, sir, her low degree. The Tower is for the great alone."
Edward has a better formal education, but Tom understands the way of the world and that there are major differences in how the rich and noble experience the world compared to how the poor experience it.
Edward's experiences once he seems to be poor fundamentally change him for the better. Twain summarizes these changes in the novel’s conclusion. Edward acts more ethically toward individuals and works to make things better for his people as a whole. He matures by moving from sympathy to active ethical action.

What are some examples of the government and laws in the new England colonies.

In the colonies, male land owners could participate in their government by electing people to the Colonial Legislature. However, a governor with higher authority was appointed solely by the king.  Thus, although some people could influence who was elected, colonial government was not truly democratic.  The monarchy of England was limited by the fact that the Atlantic Ocean stood between England and the colonies. 
The government in the New England colonies of the United States evolved between the time that England chartered the settlement of North America in the 1600s and the Declaration of Independence in 1776.  When each colony was chartered, they were established under the authority of the king of England.  At this time, England's form of government was parliamentary monarchy.  In 1620, The Mayflower arrived on land that was outside of the king's approved charter.  The pilgrims were required to produce a new document, now referred to as the Mayflower Compact, to establish their settlement in Massachusetts under the rule of England. Because this document was a collaboration between the pilgrims, it is often viewed as a precedent to more autonomous self-government.  In 1774, the Continental Congress was developed by the colonies to work towards unification and to represent the colonies to the government of England.  
 
There were many laws imposed by England that were perceived as unfair by the pilgrims.  The Stamp Act of 1756 created a tax imposed on legal documents and newspapers.  Because one was required to buy a stamp each time one of these documents was issued, the king's government would easily become aware of property transfers or publication of information that could undermine their authority.  The Tea Act of 1773 established a monopoly for British East India Tea Company to be the sole merchant of tea in the colonies.  At this time, tea was the typical daily drink in most households.  Any increase in price would negatively impact the quality of life for many.  These two examples of laws show how the monarch's authority could impact the daily lives and livelihoods of those living in the colonies.
 
 
 
 
http://memory.loc.gov/ammem/amlaw/lwjclink.html

https://avalon.law.yale.edu/17th_century/mayflower.asp

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 24

To determine the time of death in homicide investigations, Newton's Law of Cooling is used. The normal body temperature is $98.6^{\circ} F$.
Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of
Cooling is approximately $k = 0.1497$, assuming that the time is measured in hours. Suppose that the temperature of the surroundings is $60^{\circ} F$.

(a) Determine a function $T(t)$ that models the temperature $t$ hours after death.

(b) How long ago was the time of death, if the temperature of the body is now $72^{\circ} F$?



Recall the formula for Newton's Law of Cooling is

$T(t) = Ts + D_0 e^{-kt}$

where

$T(t)$ = temperature of the object at time $t$

$T(s)$ = surrounding temperature

$D_0$ = initial temperature difference between the object and its surroundings

$k$ = positive constant, depending on the object

$t$ = time

a.) If the temperature of the object and the surrounding is $98.6^{\circ} F$ and $60^{\circ} F$ respectively, then

$D_0 = 98.6 - 60 = 38.6^{\circ} F$

Thus, the model is

$T(t) = 60 + 38.6 e^{-0.1947 t}$

b.) If $T(t) = 72$, then


$
\begin{equation}
\begin{aligned}

72 =& 60 + 38.6 e^{-0.1947 t}
&& \text{Subtract each side by } 60
\\
\\
12 =& 38.6 e^{-0.1947 t}
&& \text{Divide each side by } 38.6
\\
\\
\frac{12}{38.6} =& e^{-0.1947 t}
&& \text{Take $\ln$ of each side}
\\
\\
\ln \left( \frac{12}{38.6} \right) =& -0.1947 t
&& \text{Divide each side by } -0.1947
\\
\\
t =& - \frac{\displaystyle \ln \left( \frac{12}{38.6} \right)}{0.1947}
&& \text{Solve for } t
\\
\\
t =& 6 \text{ hours}

\end{aligned}
\end{equation}
$



It shows that the body has been dead after 6 hours.

Who is the antagonist in the short story, "Tears, Idle Tears"?

In my opinion, the mother is the antagonist in the story. The point is supported by the fact that the mother is opposed to her son’s uncontrollable emotions. She is worried that her son would not fit in school because he cries constantly. The mother tries to control the boy’s behavior by taking away some privileges, but her efforts are futile. She takes to belittling and reprimanding the boy after her attempts to stop the boy from crying fail. The mother does not seem interested in trying to understand why her son cries often and uncontrollably. She is more concerned with the social effects of her son’s public outbursts, and she leaves him behind to avoid the embarrassment. She cares for her son, but she is unable to handle his outbursts.

Calculus of a Single Variable, Chapter 5, 5.1, Section 5.1, Problem 84

Locate any extrema and points of inflection for the graph of y=x^2ln(x/4) :
The domain for the function is x>0.
Extrema can only occur at critical points, or where the first derivative is zero or fails to exist.
y'=2xln(x/4)+x^2((1/4)/(x/4))
y'=2xln(x/4)+x This is continuous and differentiable for all x in the domain so we set it equal to zero:
2xln(x/4)+x=0 ==> ln(x/4)=-1/2
x/4=e^(-1/2) ==> x=4e^(-1/2)~~2.43
For 0Any inflection points can only occur if the second derivative is zero:
y''=2ln(x/4)+(2x)(1/4)/(x/4)+1
y''=2ln(x/4)+3
2ln(x/4)+3=0 ==> ln(x/4)=-3/2 ==> x=4e^(-3/2)~~.89 so there is an inflection point at x=4e^(-3/2) as the concavity changes from concave down to concave up.
The graph:

What were the long-lasting consequences of Reservation of Separate Amenities Act?

The policy of apartheid, or the separation of whites and blacks, had long been in practical effect in South Africa before the Reservation of Separate Amenities Act became law on October 9, 1953, but this act legalized various aspects of egregious racial segregation that already existed. The long-term effect of this law was the legalization of mixed standards for whites and non-whites concerning the use of public amenities.
According to the Reservation of Separate Amenities Act, public facilities for whites of European descent and black Africans were to be segregated. These facilities included methods of transportation such as trains, buses, ambulances, taxis, and hearses. They also included buildings such as town halls, church halls, theaters, cinemas, schools, restaurants, and cafes. Races were also to have separate elevators, parks, and benches. An amendment to the act was later added that segregated seashores and beaches. Unlike the Jim Crow laws in the United States, the act made no provision that facilities had to be separate but equal. It was legally acceptable for white amenities to be better than black amenities, and this was in fact what overwhelmingly came to be the case.
In the long term, the Reservation of Separate Amenities Act gave the white minority in South Africa the ability to legally enforce the appropriation and use of superior facilities for themselves and to force black people to accept inferior conditions. This act remained law for several decades until it was repealed by the South African Parliament in 1990.
https://sahistory.org.za/dated-event/reservation-separate-amenities-act-no-49-commences

https://www.sahistory.org.za/dated-event/south-african-parliament-repeals-separate-amenities-act-1953

https://www.smithsonianmag.com/history/what-did-apartheid-south-africa-look-180956945/

The Reservation of Separate Amenities Act was a piece of legislation passed by the Apartheid government in South Africa. It stipulated that public facilities could either be for the use of white people only or for the use of black people only. It meant that certain facilities, such as public toilets, swimming pools, park benches, and schools, were for the exclusive use of the white population, while separate (typically inferior) facilities were designated for use by black people.
As with every piece of Apartheid legislation, this Act was designed to keep black people and white people apart. In doing this—preventing ordinary white people from engaging with ordinary black people (apart from those who worked as their servants) on a daily basis—the Apartheid government ensured the longevity of the racist ideology which formed the backbone of Apartheid.
The Act was passed in 1953 and was only repealed in 1990, meaning that it was in place for the majority of the Apartheid regime.
In terms of long-lasting effects, it is interesting to note that this act has no relevance upon South African society today. Everybody uses whichever public facilities they need to. The effects of other acts, such as the Group Areas Act, which dictated where white and black people could respectively live and work, can still be seen today, with certain areas still inhabited predominantly by certain races.
https://www.history.com/topics/africa/apartheid

The Reservation of Separate Amenities Act created legal segregation in South Africa. This law allowed for segregation in public facilities including restaurants, schools, transportation, and theaters. This law stated that segregation could occur even if the facilities were not equal in quality.
The long-term impact of this law and others that made up the apartheid system was that the races were kept apart, and the white minority remained in control of the government. It also created a great deal of tension between white South Africans and non-white South Africans.
Eventually, there was a great deal of international pressure placed on the South African government to end the system of apartheid. Several countries imposed sanctions on South Africa. Travel, trade, and international sporting competitions were reduced or banned.
This pressure eventually worked as the Reservation of Separate Amenities Act ended in 1990, and apartheid ended in 1994.
https://omalley.nelsonmandela.org/omalley/index.php/site/q/03lv01538/04lv01828/05lv01829/06lv01857.htm

https://www.history.com/topics/africa/apartheid

Does Walt Whitman's poem "O Captain! My Captain!" teach anything or have any controlling ideas about loss?

A useful way to think about poetry is that poems make observations about the human experience. "O Captain! My Captain!" was inspired by the death of Abraham Lincoln, a man Walt Whitman greatly admired; in fact, the poem is an elegy, a formal poem of mourning.
Because Whitman does not name Lincoln as the subject of the poem, it can be read as a work that captures the emotions surrounding the death of a greatly admired or respected leader. The speaker exhorts his captain to rise from the deck where he has fallen dead; he wants the captain to be able to enjoy the rewards of the successful journey they took together and join the people who are gathered to celebrate. He implores the captain to rise and receive the adulation of the crowds gathered in his honor. At the end of the poem, the speaker sorrowfully observes that his captain cannot answer and has not lived to share in the triumph.
Whitman's controlling idea is the tragedy inherent in the death of a leader who doesn't survive to witness his legacy. Though in this case he means, particularly, the president who has led the reunification of the United States in the Civil War, the poem's lament is generally for anyone who does not live to see the fruits of his or her labor.

What's a possible thesis statement for an essay themed on conformity and rebellion?

Thematically speaking, a thesis that focuses on conformity and rebellion is very possible to do from the story "Two Kinds."  The thing to remember about writing a thesis statement is that it is largely a statement of opinion.  It is possible for you to write a thesis statement like the following:
"The story 'Two Kinds' shows the themes of conformity and rebellion."  
The above statement is a statement of opinion about the story.  In the body of your essay, you will need to prove to your readers where those themes are illustrated.  Broadly speaking, Jing-mei is rebelling against her mother's wishes instead of conforming to them.  
The previous thesis statement is manageable, but it is also really boring.  I would recommend doing a thesis statement that is a two-part statement.  That kind of thesis allows you to write about two sides of an issue.  For example:
"Although conforming to Suyuan's wishes would have been difficult for Jing-mei, rebelling against her mother was a much more difficult action."  
That thesis now allows you to focus on the themes of conformity and rebellion while also discussing the impacts that each action would have on the characters.   

What is meant by: "They were not simple folk, you see, though they were happy. But we do not say the words of cheer anymore. All smiles have become archaic." Is the author foreshadowing here, by implying there was one incident that changed the view of Omelas? Or has this always been a view of Omelas that no one was willing to admit? How does this section of the story relate to the theme and argument of the story?

In describing the citizens of Omelas, the narrator says,

They were not simple folk, you see, though they were happy. But we do not say the words of cheer anymore. All smiles have become archaic.

The narrator is concerned that we understand how nuanced the people of Omelas are. They aren't some simply happy folk who are thoughtless and ignorant. No, they are essentially everything that we are, complex and developed, except that they are happy. The narrator seems to suggest that we are not as happy as they are, that they exist somewhere in our past and that their happiness has been lost to us. The action of smiling, for example, does not occur nearly as often as it did then. Thus, there does seem to be a bit of foreshadowing; she reveals that this community does not last—that, eventually and inevitably, it turns into us. Perhaps this confirms the story's theme that happiness cannot exist without sadness and upset. Maybe it even suggests that humanity eventually prevails. If Omelas eventually turns into us, then this must mean that the abused child was brought up out of the closet. Otherwise, it alone would feel misery, and everyone else would be free to feel only happiness.

Analyze "Pied Beauty" by Gerard Manley Hopkins. Explore the central theme and the poet's stance toward God.

"Pied Beauty" is a short poem, only two stanzas long. In its use of language, it displays several features characteristic of Hopkins's work: the newly-coined terms compounded with hyphens ("rose-moles," "fresh-firecoal," "chestnut-falls") and the unique typography ("áll trádes"). Hopkins's spontaneous use of these coinages creates a sense that he, as a poet, is overwhelmed by the "dappled things" which are the subject of the poem: their "glory" is God's creation, and pre-existing language is insufficient to describe it.
The core theme of the poem, as with many of Hopkins's poems, is God's creation and its beauty. Hopkins was fascinated with nature and how it reflected the hand of God on earth. The final line of this poem addresses the reader directly, an exhortation: "Praise him." This line seems to summarize the point the poet has been making in the preceding lines, as he enumerates all the many things "counter, original, spare, strange" which God has created. Hopkins deliberately chooses to praise God for "dappled" things to emphasize the fact that there is "pied beauty" in everything—beauty does not require regularity or convention. Instead, there is beauty to be found in the "couple-colour" of skies and in things that are "fickle, freckled." Hopkins's stance towards God is that we should see all parts of nature as evidence of God's handiwork, because he is the creator of everything and should be praised for the great originality of his creation.

How did Thomas Jefferson oppose Alexander Hamilton?

Thomas Jefferson and Alexander Hamilton were both influential in shaping the American political system and early government. They first worked together during Washington's presidency: Jefferson served as Washington's Secretary of State, and Hamilton served as his Secretary of the Treasury. Although they worked together in Washington's cabinet, the two men differed in their visions for the future of America and the role of the government.
Hamilton felt that the federal government should have significant power over state and local governments because he did not trust popular will, fearing it would lead to tyranny of the majority. Jefferson, on the other hand, distrusted a powerful federal government, believing that state governments and governors should mostly be left to make their own laws and policies. In addition, Hamilton felt that commerce and manufacturing should be the economic focus of the new nation, whereas Jefferson believed that America's future lay in becoming an agrarian nation of independent, land-owning farmers. These economic differences were manifested in the debate over Hamilton's financial plans in 1791. Hamilton proposed a plan to Congress that included tariffs (taxes on imports) to help protect and encourage American manufacturing and a national bank that would assume the states' debts and oversee public credit. Jefferson fiercely opposed Hamilton's plan, believing it gave too much power to the federal government at the expense of the state governments. Despite this opposition, Hamilton's Bank of the United States was created in 1792. By the time Washington left office in 1796, the differences between Hamilton and Jefferson started to form the nation's first political parties, with Hamilton and John Adams leading the Federalists and Jefferson leading the Democratic-Republicans, or simply Republicans.
http://www.let.rug.nl/usa/outlines/history-2005/the-formation-of-a-national-government/hamilton-vs-jefferson.php

What is the Ceremony of Twelve, and why is this the most important ceremony in The Giver?

The Ceremony of Twelve is the most important ceremony in Jonas's community because it is when the adolescent children are given their permanent Assignments, which are their individually selected occupations. It is the last ceremony each year and is considered a rite of passage to becoming an adult.
The Committee of Elders carefully monitors each adolescent leading up to the Ceremony of Twelve as the children volunteer for different occupations. The elders then choose the best Assignment for each child based on their personalities, interests, and abilities. Leading up to the ceremony, Jonas is nervous about what his Assignment will be.
He is initially skipped when the Chief Elder begins presenting each adolescent their future occupation. After each child receives their Assignment, the Chief Elder informs the community that Jonas has been selected to be the community's next Receiver of Memory, which is the most prestigious and important job in the entire community.

The Ceremony of Twelve takes place each year in December; at this time the Elders select the position that each Twelve will hold in the community. Since this is the final ceremony, it represents a rite of passage into adulthood and is, therefore, the most important ceremony performed for members of the community.
No other ceremonies are performed after the Ceremony of Twelve. Also, this is the occasion on which differences are acknowledged. The Elder tells the soon-to-be Twelves:

"You Elevens have spent all your years till now learning to fit in, ....But, today we honor your differences. They have determined your futures. (Ch.7)

The new Twelves are called one-by-one according to their birth order; then they are given their Assignments, their roles in the community which they will perform for the rest of their lives. The Twelves are assigned roles in the community that the Elders have chosen for them, based upon their observations of each child. After this ceremony age is no longer important, and birthdays are no longer celebrated.

What plan do the men make? What does Rudolf need to do to make it work?

When the men hear that the king is quite sick, they decide to break into the castle and rescue him. Here is the plan:
Johann opens the front door to the new castle at 2:00 in the morning. Sapt and his men run into the castle and hold the men who are sleeping there. When Duke Michael hears Antoinette’s cry for help and runs out of his room, Sapt will catch him and take the key from him. Sapt lets down the drawbridge. When Rupert and De Gautet hear the noise and cross the drawbridge, Rudolf will kill them. In order to do that, Rudolf needs to hide himself in the river by the bridge and wait for them to pass the bridge. Then Rudolf, Sapt, and their men rush to the king’s room and kill Detchard and Bersonin before they have time to kill the king.

How does the narration change with chapters 16-19

Dr. Livesey takes over as the narrator of Treasure Island from chapters 16 to 18. Before and after this, it's Jim Hawkins who tells us what's happening in the story. The change of narrator allows Stevenson to fill us in on details and events that are important to the story, but which Jim's not able to witness. It also heightens the suspense; we notice Jim's absence since he's been the narrator for the first fifteen chapters, and now all of a sudden he's gone.
As an adult, the good doctor can also give us a more mature perspective on things. Jim's a perfectly reliable narrator, but he's still just a young lad and so naturally he'll have a different take on events. And up until this point in the story, those events have moved along at a rollicking pace. Dr. Livesey's narration adds a sense of plausibility to all the excitement we've witnessed. All the same, Livesey's observations are rather similar to Jim's so there's no significant break in continuity when he picks up the story.

How does Nick act during the conference in Andrew Clements' Frindle?

In chapter 9 of Andrew Clements' Frindle, Mrs. Chatham, the school principal, visits the Allens' home to have a conference with Nick Allen and his parents. Just as he usually does, Nick tries to distract the adults around him and redirect the conversation by asking what he thinks is a "first-class thought-grenade." However, Mrs. Chatham is not fooled and very easily redirects the conversation to the topic of disrespecting authority.Mrs. Chatham visits the Allen family because, in her mind, as well as in Mrs. Granger's mind, the children are disrespecting authority by refusing to stop calling a pen a frindle. As Mrs. Chatham explains, Mrs. Granger forbidding the children from using the word is just like forbidding them to use the word ain't: "There have to be standards" (p. 48). Since Mrs. Granger thinks there should be language standards, she is keeping kids who use the word frindle in detention and treating the usage of the word as an act of rebellion. When Mr. Chatham brings up the point about preventing kids from using the word ain't, Nick tries to redirect the conversation by pointing out that the word ain't actually has been added to the dictionary:

You know that big dictionary in Mrs. Granger's room? The word ain't is right there in the book. I looked it up, and there it was. I don't see why I can't use a word if it's in the dictionary. Mrs. Granger even said that her big dictionary was the law. (p. 48)

Nick bringing up the usage of the word ain't is a bit off-topic since the main topic concerns Nick's usage of a word that he completely made up, a word not in the dictionary. However, despite his efforts to distract the conversation, Mrs. Chatham gets the conversation back on track by saying that neither the usage of the word ain't or frindle are the real problem; the real problem is the lack of respect for authority kids at Nick's school are showing because of Nick's influence.

College Algebra, Chapter 7, 7.4, Section 7.4, Problem 20

Determine the determinant of the matrix $\displaystyle \left[ \begin{array}{ccc}
1 & 2 & 5 \\
-2 & -3 & 2 \\
3 & 5 & 3
\end{array} \right]$. State whether the matrix has an inverse, but don't calculate the inverse.

Let

$ A = \displaystyle \left[ \begin{array}{ccc}
1 & 2 & 5 \\
-2 & -3 & 2 \\
3 & 5 & 3
\end{array} \right]$

$\displaystyle \det (A) = \left[ \begin{array}{ccc}
1 & 2 & 5 \\
-2 & -3 & 2 \\
3 & 5 & 3
\end{array} \right] = 1 \left| \begin{array}{cc}
-3 & 2 \\
5 & 3
\end{array} \right| -2 \left| \begin{array}{cc}
-2 & 2 \\
3 & 3
\end{array} \right| + 5 \left| \begin{array}{cc}
-2 & -3 \\
3 & 5
\end{array} \right| = 1 (-3 \cdot 3 - 2 \cdot 5) - 2 (-2 \cdot 3 - 2 \cdot 3) + 5 (-2 \cdot 5 - (-3) \cdot 3)$

$\det (A) = -19 + 24 - 5$

$\det (A) = 0$

Since the determinant of $A$ is zero, $A$ cannot have an inverse, by the invertibility criterion.

Why do plants in waterlogged soil have to resort to anaerobic respiration?

Respiration is a complex series of reactions which occur in all living cells to release energy from food. Oxygen is generally required for respiration as this releases more energy per glucose molecule. This type of respiration is referred to as aerobic respiration. 
Plants in waterlogged soil do not have adequate oxygen for aerobic respiration and yet they have to release energy from food in order to survive. So, they resort to the second form of respiration referred to as anaerobic respiration. 
Anaerobic respiration is a form of respiration that does not utilize oxygen. This form of respiration (anaerobic) involves incomplete oxidation of carbohydrate into some carbonic compounds such as ethyl alcohol and carbon dioxide. The amount of energy released is much less when compared to aerobic respiration but this still makes it possible for them to obtain the energy they require to survive.
https://www.bbc.co.uk/bitesize/guides/zwvx8mn/revision/2

What is the role of money and gold in the life of Silas in the book Silas Marner?

Gold and money are the substitutes for love and companionship in the life of Silas Marner.
Silas was once a relatively happy man. He was well-known in his town of Lantern Yard, had a strong standing in his church, was engaged to be married, and enjoyed his life fully

His life, before he came to Raveloe, had been filled with the movement, the mental activity, and the close fellowship, which, in that day as in this, marked the life of an artisan early incorporated in a narrow religious sect.

Then, tragedy struck. Silas was framed by his so-called best friend, William Dane, and accused of robbery. The sadness that accompanied the accusation was made worse when Dane also takes Marner's fiancée from him, prompting Silas to leave town a broken man.
Once in Raveloe, he discovers that the grief of the events of Lantern Yard were superficially soothed by working long hours and collecting the fruits of his labor. To Silas, money was not as important in Lantern Yard. He used it for the typical comforts of any citizen who works for a living. Since none of the daily happenings that filled his life existed anymore, however, money and gold became the substitutes of love and companionship that he really missed so much.
Chapter 2 tells us as much when it asks the question of what the guineas really meant to Silas.

It was pleasant to him to feel them in his palm, and look at their bright faces, which were all his own: it was another element of life, like the weaving and the satisfaction of hunger, subsisting quite aloof from the life of belief and love from which he had been cut off.

This is the evidence that money and gold were essentially substitutes of joy in the new life of Silas, one which was lonely and lacked the velocity of his life in Lantern Yard.

For twenty years, mysterious money had stood to him as the symbol of earthly good, and the immediate object of toil. He had seemed to love it little in the years when every penny had its purpose for him; for he loved the purpose then.

Hence, the former "purpose" that propelled Silas to live day by day is no longer there, and he needs a way to make up for the emptiness he feels in his life.
Finally, notice how money and gold also seem to move Silas away from his gloomy depression—or at least that is what he thinks. In a metaphorical way, Eliot explains that the money and gold shine in the darkness. This is an allusion to the state of mind of Silas, and of the false sense of joy that these material possessions bring him. 

Silas walked homeward across the fields in the twilight, he drew out the money and thought it was brighter in the gathering gloom.

Where did most immigrants to the "American Colonies" come from during the 1600s & early 1700s?

The vast majority of immigrants to the original thirteen colonies in the early 1600s came from England. Initially, these were primarily Puritans fleeing religious persecution, as well as some risk-tolerant merchants who wanted to set up commercial colonies. The former settled in what became the Massachusetts Bay Colony and then spread out over New England, while the latter started to settle in Virginia, and soon spread to the Carolinas.
Joining the English settlers in the 1600s were the Dutch, who settled what later became New York and New Jersey, when the British seized that land through military conquest in the mid-1600s. Originally, however, the fertile farming land settled by the Dutch in the Hudson River Valley was named New Amsterdam. Aside from the English and Dutch, Scottish and Irish laborers also came to the colonies in the late 1600s and early 1700s, often as indentured servants. Some of the more affluent Scottish settlers were Presbyterians (essentially Scottish Puritans), who had also fled religious persecution in their home country. Finally, in lesser numbers, there arrived French Protestants, called Huguenots, who had fled religious persecution in France. This latter group should not be confused with the French Catholics (Jesuits), who first settled in Quebec (Canada) in the late 1500s.

College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 24

Sketch the graph of the equation $y = -\sqrt{1-x^2}$ by making a table and plotting points.

We have,

$
\begin{equation}
\begin{aligned}
1 - x^2 &\geq 0\\
\\
(1-x)(1+x) &\geq 0
\end{aligned}
\end{equation}
$

The factors on the left hand side is $1-x$ and $1+x$. These factors are zero when $x$ is $1$ and $-1$, respectively. These numbers divide the number line into intervals,
$(-\infty, -1], [-1,1], [1,\infty)$
By testing some points on the interval,



Thus, the domain is $[-1,1]$

Let


$
\begin{array}{|c|c|}
\hline\\
x & y = - \sqrt{1-x^2}\\
\hline\\
-1 & 0\\
\\
-0.75 & -0.661\\
\\
-0.5 & -0.866\\
\\
-0.25 & -0.968\\
\\
0 & -1\\
\\
0.25 & -0.968\\
\\
0.5 & -0.866\\
\\
0.75 & -0.661\\
\\
1 & 0\\
\\
\hline

\end{array}
$

Calculus of a Single Variable, Chapter 3, 3.3, Section 3.3, Problem 48

You need to determine the relative extrema of the function, hence, you need to find the solutions to the equation f'(x) = 0.
You need to evaluate the derivative of the function, using the quotient rule:
f'(x) = (sin ' x * (1 + cos^2 x) - sin x*(1 + cos^2 x)')/((1 + cos^2 x)^2)
f'(x) = (cos x* (1 + cos^2 x) + sin x*(2sin x*cos x))/((1 + cos^2 x)^2)
f'(x) = (cos x* (1 + cos^2 x) + 2sin^2 x*cos x)/((1 + cos^2 x)^2)
Replace 1 - cos^2 x for sin^2 x, such that:
f'(x) = (cos x* (1 + cos^2 x)+ 2(1 - cos^2 x)*cos x)/((1 + cos^2 x)^2)
f'(x) = (cos x + cos^3 x + 2cos x- 2cos^3 x)/((1 + cos^2 x)^2)
f'(x) = (3cos x- cos^3 x)/((1 + cos^2 x)^2)
You need to solve for x the equation f'(x) = 0:
(3cos x- cos^3 x)/((1 + cos^2 x)^2) = 0
3cos x- cos^3 x = 0
Factoring out cos x :
cos x*(3 - cos^2 x) = 0 => cos x = 0 or 3 - cos^2 x = 0
The function cosine cancels on (0,2pi) at x = pi/2 and x = 3pi/2.
Solving for x the equation 3 - cos^2 x = 0 , yields:
3 - cos^2 x = 0 => 3 = cos^2 x => cos x = +-sqrt 3 impossible since cos x in [-1,1].
The function f'(x) is negative on intervals (pi/2, pi) and (pi,3pi/2) , and positive on (0,pi/2), (3pi/2,2pi) , hence, the function increases on (0,pi/2) U(3pi/2,2pi) , and it decreases on (pi/2, pi)U (pi,3pi/2). The function has relative extrema at (pi/2,f(pi/2)) and (3pi/2,f(3pi/2)).

Suppose that you want to test the claim that the mean wingspan of the Eurasian eagle-owl is 64 inches or more. You collect a sample of 54 Eurasian eagle-owls and find that the mean wingspan in the sample is 62 inches. The standard deviation is 8 inches. Using a level of significance α of 0.05, test the claim using the p-value.

We are asked to test the claim that the average wing span is greater than or equal to 64 inches. We have a sample of size 54 with a mean of 62 inches. The population standard deviation is 8 inches. We are asked to test at the 95% confidence level.
H_0: mu=64 This is the null hypothesis and the claim.
H_1: mu < 64 This is the alternative hypothesis.
Since the alternative hypothesis is one-tailed, we find the critical value z such that the area to the left is .05. From a standard normal table or technology we find the critical value to be -1.645 and the critical region to be z<-1.645. (Some texts will use 1.64 or 1.65 here.)
We compute the test value: z= (62-64)/(8/sqrt(54))~~-1.837
Using a standard normal table or technology we get p~~0.033 (My calculator gives p~~0.0330962301 )
Since p=.033<.05 we reject the null hypothesis.
There is sufficient evidence to reject the claim that the average wing span is 64 or more inches.
http://mathworld.wolfram.com/HypothesisTesting.html

Why does Hannah decided not to tell the women any more about what to expect in the camp?

In the book The Devil's Arithmetic, the young Hannah Stern is taken back in time, and realizes pretty quickly that she is now living through the Holocaust. Because she's Jewish and has family members who survived the Holocaust, she knows all about what happened during this period of tragedy. 
When she and other guests at a Jewish wedding are forced by Nazis onto an overcrowded train, going to an unknown destination, Hannah knows that they are being taken to a concentration camp. At first, she tries to tell others about the terrible things she knows will probably happen at the concentration camp, to give them some sort of warning. However, she soon realizes that this is only scaring people even more, and doing more harm than good. 

Calculus: Early Transcendentals, Chapter 4, 4.4, Section 4.4, Problem 62

Replacing oo for x in limit equation yields the nedetermination oo^o . You need to use the following technique, such that:
f(x) = (e^x + x)^(1/x)
You need to take logarithms both sides, such that:
ln f(x) = ln ((e^x + x)^(1/x))
Using the property of logarithms yields:
ln f(x) = (1/x)*ln ((e^x + x))
ln f(x) = (ln ((e^x + x)))/x
You need to evaluate the limit:
lim_(x->oo) ln f(x) = lim_(x->oo) (ln ((e^x + x)))/x = oo/oo
You need to use L'Hospital theorem:
lim_(x->oo) (ln ((e^x + x)))/x = lim_(x->oo) ((ln ((e^x + x)))')/(x')
lim_(x->oo) ((ln ((e^x + x)))')/(x')= lim_(x->oo) (((e^x + x)')/(e^x + x))/1
lim_(x->oo) ((e^x + x)')/(e^x + x) = lim_(x->oo) (e^x + 1)/(e^x + x)
You need to factor out e^x such that:
lim_(x->oo) (e^x + 1)/(e^x + x) = lim_(x->oo) (e^x(1 + 1/(e^x)))/(e^x(1 + x/(e^x)))
lim_(x->oo) (e^x(1 + 1/(e^x)))/(e^x(1 + x/(e^x))) = lim_(x->oo) (1 + 1/(e^x)))/((1 + x/(e^x)))
Since lim_(x->oo)1/(e^x) = 0 and lim_(x->oo) x/(e^x) = 0 yields:
lim_(x->oo) (1 + 1/(e^x)))/((1 + x/(e^x))) = 1
Hence, lim_(x->oo) ln f(x) = 1, such that lim_(x->oo) f(x) = e^1
Hence, evaluating the given limit, using l'Hospital rule and logarithm technique yields lim_(x->oo) (e^x + x)^(1/x) = e.

Is Joe Leaphorn the murderer?

Joe Leaphorn is a Navajo Tribal Police Lieutenant, who as well as being familiar with Navajo culture from his own heritage also holds a master's degree in anthropology from Arizona State University, something that enables him to understand the cultural patterns of both Navajo and Zuni as well as those of the bilagáana (white people). He is unusual as the protagonist of detective fiction in being a Native American and balancing his scientific and academic training with Navajo values concerning the land and community.
Leaphorn uses a combination of skill in tracking and in observing and assessing people to solve crimes. Far from being a murderer, he is a detective employed as a member of the Navajo police force. He blends compassion with a strong sense of justice, tracking down the real killer, Dr. Chester Reynolds, an embittered Anglo archaeologist.
https://www.nytimes.com/1989/05/14/magazine/navajo-cops-on-the-case.html

Please identify which party controls each part of the elected branches in the US government today.

In the United States, we have a system of separation of powers.  We have a legislative branch that is composed of two houses, the House of Representatives and the Senate.  We have an executive branch that is run by a president who is elected separately from the Congress.  This allows us to have the situation that we have today where different political parties control different parts of the government.
The US presidency is controlled right now by the Democratic Party.  Barack Obama is a Democrat.  When the presidential election occurs in November, the Democratic Party will retain control of the presidency if Hillary Clinton wins the election.
Both houses of the Congress are controlled by the Republican Party.  Their hold is stronger in the House than in the Senate.  It is possible that the control of one or both houses will change after the November elections.  Most observers think that it is much more likely that the Democrats could take control of the Senate and much less likely that they could take over the House.
For the time being, then, the Democratic Party is in control of the Presidency and the Republicans have both houses of Congress.

How do Zeus and Aphrodite feature in The Women of Trachis?

Zeus and Aphrodite are presented as devious and manipulative. A common refrain in Greek drama and literature is the way in which the gods control the mortals to satisfy their own whims. Humans are often presented as the helpless playthings of the gods, jerked around by the immortals like puppets on a string. And so it proves to be in The Women of Trachis.
Although Hercules may be Zeus's son, and thus bound for great glory, he is no less prone to manipulation by the father of the gods. Zeus is a jealous god, and we can be sure that he won't take kindly to Hercules's impiety in demanding that Hyllus marry Iole. Hercules goes to his death knowing that it is the will of the gods. Hyllus is much less accepting of his father's fate and laments the cruel, unforgiving nature of the immortals.
As for Aphrodite, she is blamed by the Chorus for the tragedy of Deianira's death. Aphrodite enjoys making people fall in love with each other for no other reason than the satisfaction of her own personal whims. In keeping with her manipulative attitude towards love, it was Aphrodite who filled Hercules with love for Iole, which in due course led to Deianira's fateful decision to give Hercules what turned out to be a poisoned robe that almost devoured his flesh.

Zeus and Aphrodite are gods of the Olympian pantheon, with Zeus being the king of the gods and Aphrodite the goddess of love. Neither of these two gods actually appears in the play as a character, but they have effects on the main characters and are mentioned in speeches.
Hercules was the son of Zeus and a mortal woman, Alcmene. It is his half-divine nature that gives him his extraordinary strength. He also inherits his father's wandering eye. Just as Zeus is unfaithful to Hera with myriad mortal women and young men, so too is the plot of The Women of Trachis set in motion by Hercules's infidelity to Deianira with Iole. Although Hera is not mentioned in the play, it is her enmity that has, in the past, led to many of Hercules's problems, although Hercules's impulsiveness and self-indulgence are always inciting factors. At the end of the play, Hyllus, the son of Hercules and Deianira, seems to blame Zeus for his father's suffering and death.
Aphrodite does not appear as directly, but she is the goddess of love, and the messenger blames love for Hercules's delayed return, as his desire for Iole caused him to kill Eurytus. After the messenger reveals this, the chorus says, "Great is the power of Aphrodite's triumph!" and describes several examples of her power. Hercules's love for Iole and Deianira's desire to reclaim her husband's love are, along with the malice of the centaur, the causes of Hercules's downfall. 

How can I compare and contrast the writers' use of style, structure and linguistic features to convey the context, identities, feelings, and purpose? I need to compare the excerpt about country dancing from Oranges Are Not the Only Fruit with the poem "Not Waving But Drowning."

These two texts are very different. The genre of the first text is a novel or autobiography, and the context is the narrator's experience in a dancing class. The second text is a poem about a man who drowns and the narrator's feeling of drowning. The structures are also very different, as the first text tells a story related to dance class, while the second text narrates a man's experience of drowning. 
The style of narration of each text is also different. The first text is narrated from the point of view of a young person experiencing the events in the tale; for example, the narrator says, "We flapped along twisting each others' fingers off and promising untold horrors as soon as the lesson was over." The narrator explains how the children in the dance class torture each other when they are forced to dance together. The poem is similar to the first text in that it is also narrated in the first person; however, it is not clear who the "I" in the poem is. While the narrator in the first text is not identified, it is clear that he or she is a child who has to endure dance lessons. The narrator of the poem is unidentified. He or she witnesses a man drowning and then says, at the end of the poem, "I was much too far out all my life/And not waving but drowning." The reader understand the narrator's feelings but knows little about him or her.
In the first text, the narrator captures the humiliation and torture of childhood dance lessons with a few very descriptive sentences. The first sentence, "Country dancing was thirty-three rickety kids in black plimsolls and green knickers trying to keep up with Miss who always danced with Sir anyway and never looked at anybody else" conveys the haphazard, embarrassing, and tortured nature of the dance class right away. Using an economy of words, the narrator explains why he or she hates the class. The text uses humor and imagined dialogue, such as, "'What me Miss? No Miss. Oh Miss. I never did.' But I did, I always did," to explain how the narrator explains away his or her antics to the teacher. The addition of "I always did" makes the text darkly funny, as does the description of the different tortures awaiting the girls and boys.
The second text uses a metaphorical image--a man drowning while others think he is waving--to describe the narrator's sense of desperation. The poem starts with a literal drowning and moves to a metaphorical drowning to explain the narrator's emotions. Both texts convey a sense of the narrator's desperation, but the first, a story that is darkly funny, leaves a different sense in the reader's mind than the second text, which is a more metaphorical explanation of the narrator's emotions. The more spare form of the poem presents an image in the reader's mind of a person drowning, and the style of each text affects the reader in different ways. The first text is funnier, while the second text is starker. 

What are the benefits of "The Hitchhiking Game" for each participant? At what point is the game no longer fun? Why?

"The Hitchhiking Game" explores the idea of personas in relationships through the perspectives of a young couple simply referred to as "the girl" and "the young man." While both characters begin the game amused and optimistic, they reach a limit for it at different points in the story.
The Girl
At the beginning of the story, the girl is self-conscious and represses the sexual aspect of her personality, both by society's expectations and her own. The hitchhiking game offers her the benefit of escaping and expressing the repressed aspects of her personality in a seemingly low-risk scenario. She is able to adopt the persona of the type of woman she believes the young man is attracted to and, in doing so, is given the benefit of working out many of her insecurities and overcoming her inhibitions.
The game stops being fun for the girl towards the end of the story when the young man spontaneously takes her to a hotel. He begins treating her as a sexual object, rudely ordering her around and making hurtful remarks. She pleads with him to remember she is still the woman he fell in love with and her personality hasn't really changed, even if she has been playing a different role. At this point, she realizes her lover is attracted to her persona of innocence, while she herself is a multi-dimensional person. In this sense, the hitchhiking game benefits the girl by allowing her to express herself as a whole person. It also provides a stinging revelation about the conditionality of her partner's love for her.
The Young Man
The young man reaches his tolerance for the hitchhiking game much sooner than the girl does. He is almost immediately put off by what he perceives as her overtly sexual behavior. He does find himself more physically attracted to her, however, and enjoys the game on a superficial level in the very beginning. He acknowledges, if only to himself, that although he has had many casual encounters with other women, he never respected them. He is fond of the girl because he perceives her as a somewhat one-dimensional symbol of purity and innocence. Her innocence is what he values most, and when she abandons it in favor of the persona of a seductress, she loses value in his eyes. The game ceases to be fun for him when he realizes how enthusiastically the girl has taken to this new role, dashing his perception of her as being different from the other women he has known.
Both the girl and young man benefit from the hitchhiking game in their respective ways. The climax of the story involves an emotional outburst in which the girl begs the young man to see her for who she is. In return, he is forced to acknowledge, somewhat grudgingly, that he has placed her on an impossible pedestal. The game is no longer fun for either of them, but it does give the young couple deeper insight into themselves and their relationship.