What are some major ways that American religion in the late 20th/early 21st century has evolved? Explain why spirituality has emerged as a popular choice of belief and practice for Americans. How do you see this being expressed in our social behavior and in our political development?

A Pew Research Center study on spirituality from 2015 (see the link below) found that fewer Americans are affiliated with established religious groups than in the past. More Americans than ever before are not associated with any religious group, and this is true across racial, ethnic, and socio-economic lines. In addition, the percentage of Americans identifying as Christian is declining (though the number of evangelical Protestants has remained roughly the same). In addition, while still small, the numbers of non-Christians (including Hindus, Muslims, Buddhists, and Jews) are growing. 
Spirituality is a way for the growing number of Americans who do not associate with a specific religion to still feel a sense of the divine. It has infused our culture through practices such as mindfulness and meditation, and it has resulted in people seeking a sense of the divine outside of mainstream religious practice and worship. In addition, it has become less important for political figures to profess a sense of religiosity or to claim ties to an established form of worship (though evangelical voters still find these types of ties important).  
https://www.pewforum.org/2015/05/12/americas-changing-religious-landscape/

How do the poems of Emily Dickinson and Robert Frost touch on themes of death and/or loss?

In Emily Dickinson's poetry, death, even when not explicitly mentioned, is a kind of subtext, an underlying idea existing below the surface thoughts being expressed.
"This is my letter to the world" is doubly poignant because it attests both to Dickinson's isolation, and to her wish to be appreciated and loved by the outside world: "Sweet countrymen, judge tenderly of me!" Yet in this poem, she is anticipating her own death. The finality of the opening statement, that the world "never wrote to me," means that it never will write to her. And in asking that she be "judged tenderly," she can only mean after she is gone. Though it's open to debate, the "unseen hands," to whom Nature's message is committed, are the hands of those future generations, after her death, who will see the beauty in her work that remains hidden from the eyes of the present world.
In "Ample make this bed," Dickinson again does not mention death explicitly, but it is nevertheless more directly dealt with here than in "This is my letter." The bed, obviously, is a grave. But death, to Dickinson, is not something to be feared. Although she speaks again of "judgment," she also refers to it as "excellent and fair." And in spite of the apparent wait for Judgment Day, the second stanza suggests at least the wish that the peace of the grave will be eternal: "Let no sunrise' yellow noise / Interrupt this ground."
One of Dickinson's most famous poems is her most explicit one about death, "Because I could not stop for death." Here again, death is a friend, appearing to her like the suitor she never had, or the one she lost, now coming in his carriage to court her. She reviews those things from life she has lost: the image of the schoolyard and field, saying that centuries have now gone by, but they are like moments to her. There is regret at having left the living world, but a sense that death is better.
Robert Frost's "Stopping by Woods on a Snowy Evening" arguably deals with death also, but only indirectly. The "lovely, dark and deep" woods beckoning to the speaker might represent the world of the dead. When he has his horse move on, saying "I have promises to keep / And miles to go before I sleep," he chooses to continue now with earthly life, instead of relinquishing himself to death. But death is still inviting, warm, and kind. If he did not recognize this, he would not have stopped by the woods to begin with. As with Dickinson, Frost makes a statement about the value of life on earth, and the peace and fulfillment of the grave.
In "The Death of the Hired Man," Frost depicts the end of a man's life as observed by others. Mary and Warren discuss the hired man, Silas, who is exhausted and has reappeared at their homestead, thinking he can still live and work, though he's finished. Death, when it is announced at the poem's end, is a blessing, and Frost seems to be saying this is what it will be for all of us.
Each of these poems by Emily Dickinson and Robert Frost treats death as a thing not to be feared. But there is, by both poets, a recognition of the value of life here. Both poets celebrate life but recognize the inevitability of death.

What are the main procedures/devices that Cortázar uses to destroy the conventions of realist fiction? Make reference to "Continuity of Parks" and "House Taken Over."

Cortázar's short stories are great examples of "hijacked" realist fiction. Both "The Continuity of Parks" and "House Taken Over" incorporate elements of magical realism that cause us to question reality.
In "The Continuity of Parks," time is fluid (one of the most important elements of magical realism). The man in the green velvet armchair is also the hapless husband the hero has set out to kill. Here, the lines between reality and the irrational have been blurred. We know that one can't possibly read about one's impending murder from a book. Yet Cortázar implies that this is possible. What's more, he describes this possibility in a matter-of-fact way.
The narrator shows no alarm that logic has been hijacked by fanciful surrealism. This is another way Cortázar destroys the conventions of realist fiction. What might be considered metaphor in another fictional story is treated as reality in "The Continuity of Parks." Consider the passage below. It is full of metaphors but menacingly "real" within the context of the story.

The dagger warmed itself against his chest, and underneath pounded liberty, ready to spring. A lustful, yearning dialogue raced down the pages like a rivulet of snakes, and one felt it had all been decided from eternity. Even those caresses which writhed about the lover's body, as though wishing to keep him there, to dissuade him from it, sketched abominably the figure of that other body it was necessary to destroy.

In the passage above, lustful infatuation births evil motives and actions (a yearning lust is compared to a "rivulet of snakes"). This cause-and-effect element then leaps from the pages of a fictionalized world into reality. Meanwhile, Cortázar remains tight-lipped about whether irrationality is successful in subverting reality. The conclusion of the story remains open-ended (will the man in the green chair die?), one of the key elements of magical realism.
In "House Taken Over," the conclusion is also open-ended. Cortázar never reveals the source of the noises or the identity of those who have supposedly "taken over the house." The open-ended uncertainty in both stories is another way Cortázar has destroyed the conventions of realist fiction. Unlike realist fiction, magical realism never explains the fantastical elements in a story; instead, they are treated as a normal, intrinsic part of the plot.
In "House Taken Over," the brother and sister eventually find themselves out on the street. The brother has locked the front door and thrown the key down the sewer. It's a perplexing action, since we don't know what or who has driven the siblings out of their home. Just like in "The Continuity of Parks," Cortázar focuses our attention on the emotions of the protagonists. In magical realism, the plausibility of events takes a back seat to strong sentiment. This is unlike realist fiction, where the author/narrator tries to provide plausible reasons for the actions of characters.

What does Holden do to Mrs. Morrow throughout chapter 8?

In chapter 8, Holden meets Mrs. Morrow on the train to New York. He likes her and finds her attractive, so to please her, he tells her a string of lies about her son, Ernest. To us, the readers, he tells the truth about Ernest:

Her son was doubtless the biggest bastard that ever went to Pencey, in the whole crumby history of the school. He was always going down the corridor, after he'd had a shower, snapping his soggy old wet towel at people's asses. That's exactly the kind of a guy he was.

But knowing that parents like to hear good things about their children, he tells her:

He's one of the most popular boys at Pencey.

He also tells her that Ernest should have been class president but was too modest to run.
Holden, who tells her his name is Rudolf Schmidt, has a complex set of reasons for lying to Mrs. Morrow. Although she is much older, he indicates that he is attracted to her, though he denies being "oversexed." He is just "sexy," he says. So in part, he is flirting with her, wanting to make her feel good. He even offers to buy her a cocktail.
On another level, however, Holden is simply being who he is, a person who wants, overly much, to protect other people from unpleasant realities. He means well, at least on one level, but is not particularly mature in his behavior. We see too that he enjoys weaving stories, and, like many adolescents, he is in the process of trying on different identities.

In chapter 8, Holden boards a train heading to New York City and ends up sitting next to a woman named Mrs. Morrow. Mrs. Morrow notices a Pencey Prep sticker on Holden's luggage and asks if he knows her son, Ernest Morrow. Holden says he knows Ernest and introduces himself as Rudolf Schmidt. Holden proceeds to lie to Mrs. Morrow about her son and continues to tell her outrageous lies concerning himself and his situation throughout the trip. Holden tells Mrs. Morrow that her son is a popular, sensitive boy who was too humble to run for class president. Holden takes pleasure in lying to Mrs. Morrow the entire trip and enjoys seeing her smile when he makes up stories about her son's accomplishments and popularity. Holden even tells Mrs. Morrow that he is leaving Pencey Prep early because he is having a small tumor in his head surgically removed. Holden's interaction with Mrs. Morrow characterizes him as a liar and reveals that he is an unreliable narrator.

What efforts did Helen make to speak before her meeting with Miss Sarah Fuller?

In chapter 13, Helen mentions that she had always had the urge to speak and that she used to make noises while keeping one hand on her throat and the other hand on her lips. Helen was always fascinated by anything that made noise and would often feel her pets' throats when they purred or barked. She also recalls enjoying the vibrations emanating from pianos and people's throats while they were singing. Helen would often sit on her mother's lap, place her fingers to her mother's mouth and attempt to replicate her mother's lip movements. She also mentions that she would make unintelligible sounds at times in an attempt to exercise her vocal cords. Helen was aware that other people had a different method of communicating and was encouraged to learn how to speak after hearing the story of Ragnhild Kåta. Fortunately, Miss Sarah Fuller agreed to teach Helen how to speak, and Helen began the arduous process of learning how to talk.

Helen had long had a desire to speak. She communicated by fingerspelling, but longed to use her voice as others did. She knew other people communicated by speaking.  
As a young girl, Helen "used to make noises, keeping one hand on [her] throat while the other hand felt the movements of [her] lips" (Chapter XIII). Though Helen could not hear, she knew others spoke with their mouths by using her sense of touch. She pressed her fingers against the mouths of family members and close friends to feel their lips moving in speech. She also enjoyed the feeling of a cat purring or a dog barking. After Helen lost her hearing and eyesight, she remembered her word for water. She repeated the word "wa-wa" even though she could not hear.
Helen learned about a deaf and blind girl from Norway who learned to speak. This inspired Helen, and she sought assistance from Miss Sarah Fuller in learning how to speak herself.

In chapter 15, what does Holden do for the nuns? Is it true to Holden's personality?

Holden, having made a date with Sally Hayes (whom he thinks of as a phony), sees two nuns with cheap suitcases in a place where is having breakfast. One nun is carrying a straw basket of the type used to collect money for charity. Although the nun says it is not a charity basket, Holden nevertheless wants to donate money to them. He says,

They let me give them ten bucks as a contribution. They kept asking me if I was sure I could afford it and all. I told them I had quite a bit of money with me, but they didn’t seem to believe me. They took it, though, finally.

This is completely in character for Holden. He talks about being careless about money and often forgetting to collect his change after paying a bill, as well as losing money. He attributes this to having a wealthy father. It becomes clear, however, that his wealth, compared to other people's, makes him feel guilty. He says that money makes him feel "blue" or sad.
The nuns' cheap suitcases, as well as the fact they are only eating toast and coffee, when he has had a huge bacon and egg breakfast, makes him want to do something for them. We learn that one of his roommates also had cheap suitcases and kept them under the bed out of shame, so Holden started doing the same with his. He thinks that he would have been willing to trade his suitcases for the roommate's. He wishes too that he had given the nuns more than ten dollars. His money weighs on him, and he would like to use it to help people. Nevertheless, he appreciates his conversation with nuns, telling them he'd "enjoyed talking to them a lot, too. I meant it, too."

In chapter 15 of The Catcher in the Rye, Holden donates $10 to the nuns he talks to at the cafe and attempts to pay for their bill. However, they do not let him. Holden's action absolutely fits with his character, as he enjoys those who are not phony (particularly children). He sees the nuns as innocent, as evidenced by his comment about feeling uncomfortable talking to the nun who happens to be an English teacher about Romeo and Juliet because "that play gets pretty sexy in some parts."
In other parts of the novel, Holden shows charity and kindness toward those who need it. He buys his sister an album, sells his typewriter for $20 even though it cost $90, and helps a little girl at Central Park with her ice skates.
Ultimately, the nuns are merely symbolic of Holden's desire to protect the innocent. His action falls completely within his character.

Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 14

Solve the equation $9x + 1 = 7x - 9$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

9x + 1 =& 7x - 9
&& \text{Given equation}
\\
9x - 7x =& -9 - 1
&& \text{Subtract $(7x+1)$ from each side}
\\
2x =& -10
&& \text{Combine like terms}
\\
\frac{2x}{2} =& - \frac{10}{2}
&& \text{Divide both sides by $2$}
\\
x =& -5
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

9(-5) + 1 =& 7 (-5) - 9
&& \text{Substitute } x = -5
\\
-45 + 1 =& -35 - 9
&& \text{Multiply}
\\
-44 =& -44
&& \text{True}

\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 8

Suppose that a ball is given a push so that it has an initial velocity of $\displaystyle 5 \frac{m}{s}$ down a certain inclined plane, then the distance it has rolled after $t$ seconds is $s = 5t + 3t^2$

a.) Find the velocity after $2s$
b.) How long does it take for the velocity to reach $\displaystyle 35 \frac{m}{s}$



$
\begin{equation}
\begin{aligned}
\text{a.) velocity } &= s'(t) = \frac{ds}{dt}\\
\\
&= 5 \frac{d}{dt} (t) + 3 \frac{d}{dt} (t^2)\\
\\
&= 5 (1) + 3(2t)\\
\\
&= 5 + 6t \frac{m}{s}\\
\end{aligned}
\end{equation}
$

The velocity after $2s$ is $\displaystyle v(2) = 5 + 6(2) = 17 \frac{m}{s}$

b.) if $\displaystyle v = 35 \frac{m}{s}$, solving for $t$


$
\begin{equation}
\begin{aligned}
35 &= 5 + 6t\\
t &= 5 \text{ seconds}
\end{aligned}
\end{equation}
$

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 43

You need to determine the monotony of the function, hence, you need to find where the derivative is positive or negative.
You need to evaluate the first derivative, using the chain rule:
f'(theta) = -2sin theta - 2cos theta*sin theta
You need to solve for theta f'(theta) = 0.
-2sin theta - 2cos theta*sin theta = 0
Factoring out -2 sin theta , yields:
-2sin theta(1 + cos theta) = 0 => -2sin theta = 0 => sin theta = 0 for theta = 0, theta = pi and theta = 2pi
1 + cos theta = 0 => cos theta = -1 for theta = pi
You need to notice that f'(theta)<0 , hence the function decreases, for theta in (0,pi) and f'(theta)>0 , hence, the function increases, for theta in (pi,2pi).
b) The function has a minimum point at theta = pi and it has maximum points at theta = 0 and theta = 2pi.
c) You need to evaluate the inflection points of the function, hence, you need to solve for theta the equation f''(theta) = 0.
f''(theta) =(- 2sin theta - sin 2theta)'
f''(theta) = -2cos theta - 2cos 2theta
f''(theta) = -2cos theta - 2(2cos^2 theta - 1)
f''(theta) = -2cos theta - 4cos^2 theta + 2
You need to solve for theta, f''(theta) = 0 , such that:
-2cos theta - 4cos^2 theta + 2 = 0
2cos^2theta + cos theta - 1 = 0
cos theta = (-1+-sqrt(1+8))/4
cos theta = 1/2 for theta = pi/3 and theta = 5pi/3
or cos theta = -1 for theta = pi
Hence, the function has inflection points at theta = pi/3, theta = pi and theta = 5pi/3.

What types of mood and atmosphere are found in the book Frankenstein?

The mood of Frankenstein is quite ominous and mysterious.  When Walton and his crew find Victor, frozen and starving on the ice, he only has one sled dog still alive, and the captain describes his eyes as possessing a kind of "wildness" and "madness."  This contrasts with Victor's moments of "benevolence and sweetness," though he remains "melancholy and despairing" even in these moments.  What can have happened to this person to create such dissimilar attributes?  His condition cannot be the result of something happy or joyful, and thus the mystery begins: we expect something terrible.
Further, in one of their earliest conversations, Victor tells Walton, 

"You seek for knowledge and wisdom, as I once did; and I ardently hope that the gratification of your wishes may not be a serpent to sting you, as mine has been."

At this point, then, we know that Victor's story is going to be one that contains some tragedy and, likely, some guilt.  He seems to acknowledge the role he has played in getting himself into his current position: he realizes he is here because he sought one thing above all else.  We know this story cannot end well, based on Walton's observations of Victor.  Finally, we also know that Walton also has a terrible thirst for knowledge, and this presents the strong possibility that he could end up in as tragic a position as Victor.  All of this contributes to the ominous and mysterious mood.  

I would say the primary mood/ atmosphere in Mary Shelley's Frankenstein is one of foreboding or dread. Consider, for instance, that we get most of Frankenstein's story after the events of the tale have occurred; in other words, Frankenstein is telling us his story retrospectively, allowing him to reflect on his story as he tells it. Thus, it's easy for him to infuse his tale with a strong feeling of dread and ominous foreboding, as he already knows what happens. Moreover, it's clear from the start that Frankenstein's experiments are a bad idea and will only result in something evil, and the monster's stalking of Frankenstein and those closest to him builds a sense of dread. All in all, the story has a mood of building terror, and we get the sense that we as readers are also being haunted by some monstrosity. That said, it's hard not to sympathize with the monster once we meet him. As such, the mood also involves a sense of melancholy, or even tragedy.

How does Atticus Finch show courage in To Kill A Mockingbird?

In To Kill A Mockingbird, Atticus teaches his children what courage is. In chapter 10, Scout and Jem are surprised when their peaceful, non violent father is called to shoot the rabid dog in the street. Atticus shows courage by making the shot, as he must kill the dog before it can hurt anybody, and only has one shot to do so. He demonstrates courage further by not bragging about his talent, and choosing to live a peaceful life instead of often using his gun.

"I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It's when you know you're licked before you begin anyway and you see it through no matter what. You rarely win, but sometimes you do."

Atticus says this quote at the end of chapter 11, after Mrs. Dubose dies. Atticus makes Jem go to Mrs. Dubose's house and read to her every day, and it is not until afterward that Atticus explains Mrs. Dubose was battling a morphine addiction, and the reading helped her end it. Atticus explains what real courage is in order to teach his children.
Atticus demonstrates this moral courage by accepting Tom Robinson's case and truly fighting for him. Atticus is assigned the case, but people become angry when they see that Atticus does all he can to help Tom get off. According to society, Atticus should not put forth his best effort in the defense, but Atticus does what he knows is right even if it is not popular.
Atticus shows courage when his children are attacked at the end of the novel. He believes Jem has killed Mr. Ewell, but does not want Heck Tate to cover it up.

"Heck," Atticus's back was turned. "If this thing's hushed up it'll be a simple denial to Jem of the way I've tried to raise him. Sometimes I think I'm a total failure as a parent, but I'm all they've got. Before Jem looks at anyone else he looks at me, and I've tried to live so I can look squarely back at him."

Atticus shows a moral courage throughout the novel in what he says, does, and teaches to his children.

Considering the residual racism in Maycomb, Atticus shows courage in taking Tom Robinson's case. He knows that people will be critical of him and his children because of this decision. This is one of the many examples in which Atticus does the right thing even if that means he will face opposition as a result.
While Tom Robinson is being held in Maycomb's jail, Atticus takes it upon himself to guard the jail. He suspects some of the more racist citizens in town might come to attack and/or kill Tom. Even though Mr. Underwood was there to back him up, it certainly was brave of Atticus to sit outside the jail by himself so that he would be there to confront the mob.
In Chapter 23, Atticus explains to Jem why he did not retaliate when Bob Ewell spit on him:

Jem, see if you can stand in Bob Ewell’s shoes a minute. I destroyed his last shred of credibility at that trial, if he had any to begin with. The man had to have some kind of comeback, his kind always does. So if spitting in my face and threatening me saved Mayella Ewell one extra beating, that’s something I’ll gladly take. He had to take it out on somebody and I’d rather it be me than that houseful of children out there. You understand?

This is an example of bravery and restraint. Atticus shows incredible courage and thoughtfulness in taking Mr. Ewell's abuse without reacting. He selflessly reasons that this might save Mayella some abuse.

Calculus: Early Transcendentals, Chapter 9, 9.3, Section 9.3, Problem 14

This is an ordinary differential equation as it involves derivatives in the parameter y only. It is also nonlinear because the equation combines y and the derivative in y in a nonlinear fashion. In particular, there is a y/(1+y) term which is nonlinear in y. Finally it is first order as it involves y and only the first derivative of y and no further higher order derivatives (2nd, 3rd etc). Putting that all together we have that this is a First order nonlinear ordinary differential equation. Now we know what we're dealing with!
To solve differential equations of this type (the method extends to some other types, but let's focus on the type we have here), move terms involving y and its derivatives to the lefthand side, and terms involving x to the righthand side. It is convenient to rewrite y' as dy/dx as this separates this derivate into parts associated with y and x separately ('d' represents 'delta' - meaning, a tiny change in the variable). So, gather terms and write the equation as
(y+1)/y quad dy = xsinx quad dx
I've written the dy and dx slightly apart from the other parts of the equation to emphasise that these are single entities.
Now, the trick is to integrate on both sides. This seems unnatural at first, but note we are doing the same thing to both sides just like with any equation. What we have already is the areas under two separate curves, one in y and one in x, defined by multiplying the function at any point by a minuscule width. This is essentially a set of instructions of how to add up many very small columns under the curve. And the integral sign is the action of getting the areas under the curves, eliminating the tiny widths, using those instructions. So, adding the integral sign we write
int (y+1)/y quad dy = int xsinx quad dx
giving
int 1 + 1/y quad dy = int xsinx quad dx
The integral on the left is a simple one. The integral on the right is less simple, and needs to be done by parts. I will just give the solution to that, which you can work through. So, we have
y + lny = -xcosx + sinx + c
where c is a constant of integration.
This is very nearly a solution, but we can now use the initial condition y(0) =1 to find the value of c . The initial condition tells us that
-0(cos(0)) + sin(0) + c = 1 which gives that
0 + c = 1 implies c = 1
The final solution to the differential equation is then
y + lny = -xcosx + sinx + 1
Note this is an implicit and not explicit solution since y is not fully isolated by itself on the left side of the equation. This, I believe, is the only way to write this equation that involves only the variables y and x.

When did this story take place?

No one knows precisely when The Odyssey was actually written. However, most scholars agree that it was probably composed some time in the eighth century BC. The setting of the poem—although we cannot be absolutely sure—is most likely set during the thirteenth century BC. This is known among historians as the Bronze Age. This was an appropriate historical setting for The Odyssey, as the ancient Greeks regarded it warmly as a golden age, a time of great heroic deeds.
Although the events of the poem are fictitious, archaeological evidence appears to suggest that some kind of war between the Achaeans and the Trojans was fought around this time. Additionally, as the action of The Odyssey takes place not long after the Trojan War has ended, it is safe to assume that this would be the historical era in which the events unfold.
https://www.ancient.eu/Odyssey/

Intermediate Algebra, Chapter 3, 3.4, Section 3.4, Problem 26

Illustrate the compound inequality $3x - y \geq 3$ and $y < 3$

Since the compound inequality is joined by $and$, then we need to find the intersection of the graphs.
To begin, we graph each of the two inequalities $3x - y \geq 3 \text{ and } y < 3$ seperately as shown below






Then, we use heavy shading to identify the intersection of the graphs.



To verify this, we choose a test point on the intersection of the region. Let's say point $(1,-1)$. So, we have

$
\begin{equation}
\begin{aligned}
2x - y &\geq 3 && \text{and} & y &< 3\\
\\
3(1) - (-1) &\geq 3 && \text{and} & -1 &< 3\\
\\
3 + 1 &\geq 3 \\
\\
4 &\geq 3
\end{aligned}
\end{equation}
$


We can see that the ordered pairs we choose inside the intersection of the graph switches both inequalities.

In scene 4, Blanche lays out her objections to Stanley: There's something downright bestial about him! . . . He acts like an animal, has an animal's habits! Eats like one, moves like one, talks like one! There's even something sub-human something not quite to the stage of humanity yet! Yes, something ape-like about him, like one of the pictures I've seen in anthropological studies! Thousands and thousands of years have passed him right by, and there he is Stanley Kowalski survivor of the Stone Age! Bearing the raw meat home from the kill in the jungle! . . . Maybe he'll strike you or maybe he'll grunt and kiss you! Remember that the opening scene—in which Stanley throws a packet of meat to Stella—occurs before Blanche comes on stage (so she can’t be referring to that moment) and then provide an explanation of the multiple ironies of this passage.

The ironic thing about this passage is that Blanche is, in some key ways, more like Stanley than she realizes. She complains that Stanley is motivated by brutal lust: being very blatant with his sexual desires. However, Blanche herself is driven by desires, particularly sexual ones. Remember that she's only living with her sister because she was fired from her teaching job for sleeping with a student.
Blanche did not need to see Stanley throw the meat pack to Stella, because she's already witnessed the way he talks, dresses, and eats. Stanley is not ashamed of his lack of social graces and airs. He takes pride in being "common." And the greatest irony of all is that Blanche is only listing what Stella finds most appealing about Stanley (e.g., his virility, his lack of manners, etc.). Stella did, after all, leave Belle Reve and she chose to live with a man who represents the total opposite of the refined world she came from. As Stanley later states, Stella loved being taken from those "columns."

In this passage, Blanche is largely objecting to Stanley's masculinity and physical aggression—which, together, establish a recurring theme in the play.
Aside from both possessing desire and carnal lust, as was mentioned by other educators, Blanche is not taking Stanley's constant drinking into consideration. She makes no mention of it, even though alcohol exaggerates his masculine tendencies and physicality. This is ironic, because Blanche is criticizing Stanley's behavior which is magnified by drunkenness, while she herself consumes copious amounts of alcohol.
Blanche readily accuses Stanley of inappropriate behavior while hiding important details of her past that would also be deemed inappropriate; for instance, how she had been kicked out of the motel she had been staying at for having multiple sexual encounters with men.
Blanche readily points out Stanley's flaws and is brutally honest about his behavior, wishing Stella to see her husband in a different light; this is ironic because Blanche lives in a fantasy world and actively attempts to escape her own reality.

Ever since she arrived to stay, Blanche has been a regular witness to Stanley's neanderthal behavior. He's a hulking great brute, physically and verbally abusive, always ready to pick a fight with anyone who crosses him. His crude manners appall Blanche, the delicate, refined Southern belle. The two are like chalk and cheese in every conceivable respect, and their mutual hostility and antagonism is there right from the start. Blanche didn't need to see Stanley throw a packet of meat to Stella to know what kind of a primitive throwback he is.
What's ironic in all of this is that Stanley's behavior, like Blanche's, stems from his various desires—to be lord and master in his own place, to be respected, to live up to society's expectations of how a man should behave. It's just that Stanley expresses those desires in a completely different way to the elegant, educated Blanche. Even more ironically, Blanche and Stanley share the most intense desire of all—to secure the sympathy of Stella, who's caught up in the middle of their epic battle of wills.
A further irony in Blanche's litany of complaints against Stanley's ape-like regression is that she's not saying anything that Stella doesn't already know. She seems to overlook the fact that Stella's strongly attracted to Stanley precisely because of his overpowering, thuggish masculinity. Blanche thinks that by telling Stella some home truths about Stanley she'll somehow manage to get her sister to see sense, to realize that she's too good for Stanley and quit this abusive relationship. However, she's sorely mistaken in her assumption; Stella's going nowhere. Despite everything, her bond with Stanley is strong and set to get even stronger with the imminent birth of their child. No amount of colorful insults that portray Stanley as an example of evolution in reverse is going to make the slightest bit of difference.

Intermediate Algebra, Chapter 4, 4.2, Section 4.2, Problem 14

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

x + 2y + 3z =& 1 \\
-x - y + 3z =& 2 \\
-6x + y + z =& -2

\end{aligned}
\end{equation}
$.


$
\begin{equation}
\begin{aligned}

x + 2y + 3z =& 1
&& \text{Equation 1}
\\
-x - y + 3z =& 2
&& \text{Equation 2}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\phantom{x -} y + 6z =& 3
&& \text{Add}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

6x + 12y + 18z =& 6
&& 6 \times \text{Equation 1}
\\
-6x + y + z =& -2
&& \text{Equation 3}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\phantom{6x + } 13y + 19z =& 4
&& \text{Add}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

y + 6z =& 3
&& \text{Equation 4}
\\
13y + 19z =& 4
&& \text{Equation 5}

\end{aligned}
\end{equation}
$


We write the equations in two variables as a system


$
\begin{equation}
\begin{aligned}

-13y - 78z =& -39
&& -13 \times \text{ Equation 4}
\\
13y + 19z =& 4
&&
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\phantom{13y } -59z =& -35
&& \text{Add}
\\
z =& \frac{35}{59}
&& \text{Divide each side by $-59$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

y + 6 \left( \frac{35}{59} \right) =& 3
&& \text{Substitute } z = \frac{35}{59} \text{ in Equation 4}
\\
\\
y + \frac{210}{59} =& 3
&& \text{Multiply}
\\
\\
y =& - \frac{33}{59}
&& \text{Subtract each side by } \frac{210}{59}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

x + 2 \left( - \frac{33}{59} \right) + 3 \left( \frac{35}{59} \right) =& 1
&& \text{Substitute } y = \frac{33}{59} \text{ and } z = \frac{35}{59}
\\
\\
x - \frac{66}{59} + \frac{105}{59} =& 1
&& \text{Multiply}
\\
\\
x + \frac{39}{59} =& 1
&& \text{Combine like terms}
\\
\\
x =& \frac{20}{59}
&& \text{Subtract each side by } \frac{171}{59}

\end{aligned}
\end{equation}
$



The ordered triple is $\displaystyle \left( \frac{20}{59}, - \frac{33}{59}, \frac{35}{59} \right)$.

Calculus of a Single Variable, Chapter 8, 8.6, Section 8.6, Problem 20

Indefinite integral are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
The format of the given integral problem: int 1/(x^2+4x+8)dx resembles one of the formulas from integration table. Recall we have indefinite integration formula for rational function as:
int 1/(ax^2+bx+c) dx = 2/sqrt(4ac-b^2)arctan((2ax+b)/sqrt(4ac-b^2)) +C
By comparing ax^2 +bx +c with x^2+4x+8 , we determine that a=1 , b=4, and c=8 .
Applying indefinite integration formula for rational function, we get:
int 1/(x^2+4x+8)dx =2/sqrt(4(1)(8)-(4)^2)arctan((2(1)x+(4))/sqrt(4(1)(8)-(4)^2)) +C
=2/sqrt(32-16)arctan((2x+4)/sqrt(32-16)) +C
=2/sqrt(16)arctan((2x+4)/sqrt(16)) +C
=2/4 arctan((2x+4)/4) +C
=2/4 arctan(((2)(x+2))/4) +C
=1/2 arctan((x+2)/2) +C

Because of progressivism, how was America different in 1920 from what it had been in 1900?

By 1920 the Volstead Act was a law. This law prohibited alcoholic beverages and was considered at the time to be a victory for Progressives. The law would ultimately fail due to public apathy and a lack of funding for enforcement. Women also gained the right to vote in 1920 with the Nineteenth Amendment. While some states allowed women to vote in 1900, by 1920 women could vote nationwide. Many of the trusts such as Standard Oil that had existed in 1900 were broken into smaller businesses by 1920. Thanks to the Food and Drug Act, consumer goods became safer during this period as well. Patent medicines were a thing of the past by 1920 as companies had to clearly list the ingredients on the labels. Many national parks were in existence in 1920 thanks to the efforts of Theodore Roosevelt's Progressive domestic agenda.

Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 35

Combine the like terms of the polynomial $-m^3 + 2m^3 + 6m^3$

According to the distributive property, for any numbers $a, b,$ and $c, a(b+c)=ab+ac$ and $(b+c)a=ba+ca$. Here, $m^3$ is a factor of both $-m^3$ and $2m^3$
$(-1 + 2)m^3 + 6m^3$

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value.
In this example, subtract the absolute values of $-1$ and $2$ and give the result the same sign as the integer with the greater absolute value.
$(1) m^3 + 6m^3$

Remove the parentheses.
$m^3 + 6m^3$

Again, according to the distributive property, for any numbers $a, b,$ and $c, a(b+c)=ab+ac$ and $(b+c)a=ba+ca$. Here, $m^3$ is a factor of both $m^3$ and $6m^3$
$(1 + 6)m^3$

Add 6 to 1 to get 7.
$(7)m^3$

Remove the parenthesis
Thus, the answer is $7m^3$

What is the difference between American History and World History?

I would say that the difference is, in part, a matter of scope. American History tends to focus on the history of the United States, beginning largely with the colonial era and tracking forwards towards the present. It's largely a national history. World History, on the other hand, is far more encompassing, both geographically as well as temporally.
The thing is, the history of the world is far larger than any one place—it encompasses the full breadth of human history, starting with the earliest cultures to emerge in the Ancient World—cultures like Egypt, Sumeria, the Indus River Valley civilization in India—before tracking forwards. It covers various different geographical regions as they unfold: China, India, the Mediterranean World, the Americas, Western Europe, and so on, stretching across different time periods on both sides of the Common Era.

There is a significant difference between American History and World History. American History is the study of the history of the United States. It focuses on the development of our country from the days we were colonies of Great Britain to current times. The focus is on what happened in and to the United States throughout our history.
World History takes on a much larger view of events because it focuses on the history of many of the countries or the civilizations around the world. It focuses on major world events that have happened throughout history. World History is much longer than American History. While American History can be traced back to around the late 1400s, World History goes back thousands of years prior to the beginning of American History. Therefore, the study of World History usually requires more time to complete. The study of World History may also view events from a different perspective. The study of American History takes on an American perspective while the study of World History takes on the perspective of people in other countries.
There is a significant difference between the study of American History and the study of World History.

What does the water symbolically represent?

In "A Mystery of Heroism" the bucket of water is a very important symbol in two respects. Firstly, it represents heroism. Fred Collins shows extraordinary courage in going off to fetch the bucket of water in the heat of battle. The fighting is intense; Fred could be cut down by a bullet at any moment. Yet his thirst is so great that he's prepared to risk life and limb to go get something to drink.
At the same time, the bucket symbolizes the utter futility of war. Fred's heroics are ultimately in vain; soon after he returns from his courageous mission, the bucket lies empty on the ground. Using the symbol of the bucket of water in such completely different ways allows Crane to express his hostility toward war, while at the same time paying fulsome tribute to the immense bravery of those who serve and fight.

What is the difference between verbal language and non-verbal communication?

Both forms of communication transmit meanings. Both forms of communication include components which are learned. Language is learned, and people in difficult cultures may learn culture-specific gestures, like shrugging to communicate "I don't know." Language is a quintessentially symbolic communication system, but nonverbal communication isn't entirely lacking in symbols. For instance, in my culture, shaking the head from side to side is an arbitrary gesture that stands for the concept "no." That's symbolic communication.
There are many distinctions between these two forms of communication. Here are some, suggested by the work of Charles Hockett.
Structure
Language has structure—all languages have a syntax or grammar; rules of how to put together the units of language into a statement or utterance. Nonverbal communication has no such rules for stringing together units of meaning.
Displacement
With language, we can talk about things that aren't tangible, aren't present in the here and now, and might not even exist. Nonverbal communication is highly restricted. When you come home from school or work, you might be able to communicate that you are sad through nonverbal gestures, but you most likely can't communicate what events earlier that day are responsible for your sadness unless you use sign language. There are nonhuman communication systems that include limited displacement. Specifically, bees can communicate to each other about the location of food by performing a symbolic dance. I think it's difficult to find examples in human nonverbal communication (as opposed to examples that involve human sign language and other types of language that do not employ spoken words).
Productivity
With language, we can combine words to express new meanings. We can say things that nobody has ever said before, like "Gerbils are not willing to sit still and receive instruction for learning to read." Nonverbal communication is extremely limited in this respect. You might be able to communicate something new insofar as, say, nobody before has ever communicated the idea that your Aunt Mildred stinks, but language permits you to say things about Aunt Mildred that may never before have been expressed about any person.
Reflexiveness
You can use language to talk about language (as we are doing here). You can't use nonverbal communication to talk about nonverbal communication.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4544681/

What are twelve major events in chronological order in To Kill a Mockingbird by Harper Lee?

1. Dill arrives in Maycomb to spend the summer with his aunt and befriends Jem and Scout. The children become close friends and the boys are fascinated by the rumors surrounding Boo Radley.
2. Scout has a rough first day at school, which leads to Atticus teaching her an important lesson on perspective.
3. The children embark on a nighttime raid by trespassing into the Radley yard and attempting to get a look at Boo through a window.
4. Atticus tells the children that it is considered a sin to kill a mockingbird while they are playing with their air rifles. Miss Maudie then elaborates on Atticus's comment by telling the children that mockingbirds are defenseless, innocent beings that spread joy.
5. Atticus shoots and kills a rabid dog named Tim Johnson in the middle of the street, which astonishes and impresses his children.
6. Jem and Scout learn about real courage from their experience with Mrs. Dubose, who managed to conquer her morphine addiction before she died.
7. Scout and Jem attend First Purchase African M.E. Church with Calpurnia and gain insight into the African-American community.
8. Atticus prevents the Old Sarum bunch from lynching Tom Robinson before the trial.
9. Tom Robinson is wrongly convicted of assaulting and raping Mayella Ewell. The children lose their childhood innocence by witnessing racial injustice firsthand.
10. Scout attends Aunt Alexandra's missionary circle and Atticus interrupts it to tell them that Tom Robinson has been shot and killed attempting to escape from Enfield Prison Farm.
11: Bob Ewell attacks Jem and Scout and Boo Radley comes to their rescue.
12: Scout walks Boo Radley home and views the neighborhood from his perspective for the first time, which illustrates her maturation and moral development.

Scout, Jem, and Dill try to make Boo Radley come out.
Atticus is appointed the defense attorney for Tom Robinson, a black man accused of rape by Mayella Ewell, a white woman.  His defending Robinson is unpopular with Maycomb’s white population.
Scout gets into fights with schoolmates and her cousin Francis defending her father, even though she doesn’t really understand what the fuss is about.
Boo Radley leaves presents for Scout and Jem, showing that he is not a monster and is really just a shy recluse who wants friends.
There is a fire at Miss Maudie’s house. Boo Radley puts a blanket on Scout’s shoulders.
Scout’s Aunt Alexandra comes to stay with them to support her brother.
The Trial starts.  Atticus demonstrates that no one called for a doctor for Mayella, that her injuries were most likely caused be her father, and that Tom Robinson’s crippled shoulder makes it almost impossible for him to have committed the crime he was accused of.
The trial demonstrates how ugly racism is in Maycomb.  Dill has to leave during the proceedings, unable to stomach the prosecutor Mr. Gilmer’s treatment of Tom Robinson.

“Well, Mr. Finch didn’t act that way to Mayella and old man Ewell when he crossexamined them. The way that man called him ‘boy’ all the time an‘ sneered at him, an’ looked around at the jury every time he answered—” (Ch. 19)

9. Tom Robinson is convicted, but Atticus considers the jury's deliberation a minor moral victory.

... Atticus Finch won’t win, he can’t win, but he’s the only man in these parts who can keep a jury out so long in a case like that. (Ch. 22)

10. Tom Robinson is shot trying to escape prison.
11. Bob Ewell threatens Atticus, spitting in his face.  Atticus dismisses the threat.
12. Boo Radley stops Bob Ewell from hurting Scout and Jem, killing Ewell.  Jem only has a broken arm and Scout is relatively unharmed.

int_0^(1/2) arctanx/x dx Use a power series to approximate the value of the integral with an error of less than 0.0001.

From the Power Series table for trigonometric function, we have:
arctan(x) =sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1)
                     = x -x^3/3 +x^5/5 - x^7/7 + x^9/9-...
Applying it on the integral int_0^(1/2) arctan(x)/x dx where the integrand is f(x)=arctan(x)/x , we get:
int_0^(1/2) arctan(x)/x dx =int_0^1 arctan(x) *1/x dx
                         =int_0^(1/2)sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1) *1/xdx
                         =int_0^(1/2) sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1) *x^(-1)dx
                         =int_0^(1/2) sum_(n=0)^oo (-1)^n x^(2n+1-1)/(2n+1) dx
                         =int_0^(1/2) sum_(n=0)^oo (-1)^n x^(2n)/(2n+1) dx
                         =int_0^(1/2) [1 -x^2/3 +x^4/5 - x^6/7 +x^8/9-...] dx
 Or 
int_0^(1/2) arctan(x)/x dx =int_0^1 arctan(x) *1/x dx
                         =int_0^(1/2) 1/x* [x -x^3/3 +x^5/5 - x^7/7 +x^9/9-...] dx
                          = int_0^(1/2) [x/x -x^3/(3x) +x^5/(5x) - x^7/(7x) +x^9/(9x)-...] dx
                         =int_0^(1/2) [1 -x^2/3 +x^4/5 - x^6/7 +x^8/9-...] dx
To determine the indefinite integral, we integrate each term using Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
int_0^(1/2) [1 -x^2/3+x^4/5 - x^6/7 +x^8/9-...] dx= [x -x^3/(3*3)+x^5/(5*5) - x^7/(7*7) +x^9/(9*9)-...]_0^1
                                                    =[x -x^3/9+x^5/25 - x^7/49 +x^9/81-...]_0^1
Apply definite integral formula: F(x)|a^b =F(b)-F(a) .
F(1/2) or F(0.5)=0.5 -0.5^3/9+0.5^5/25 - 0.5^7/49 +0.5^9/81-...
                             = 1/2 -1/72+1/800-1/6272+1/41472 -...
F(0)= 0 -0^3/9+0^5/25 - 0^7/49+0^9/81-...
         =0-0+0-0+0-...
All the terms are 0 then F(0)=0 .
We can stop on the 5th term  (1/41472 ~~2.4113x10^(-5)) since we only need an error less than 0.0001.
F(1/2)-F(0)= [1/2 -1/72+1/800-1/6272+1/41472]-[0]
                       =1/2 -1/72+1/800-1/6272+1/41472
                        =0.487225785
 Then, the approximated integral value will be:
int_0^(1/2) arctan(x)/x dx~~0.4872

In the story "The Tell-Tale Heart," what is an example of onomatopoeia?

Onomatopoeia is a literary device in which a word is formed to imitate a sound. Examples include "ring," "pow," "snap," and "boom." 
The first example of onomatopoeia in Edgar Allan Poe's short story "The Tell-Tale Heart" is the word "creaked." It describes the sound the lantern made when the narrator lifted the slats to reveal the light.

And then, when my head was well in the room, I undid the lantern cautiously—oh, so cautiously—cautiously (for the hinges creaked)—I undid it just so much that a single thin ray fell upon the vulture eye.

The next example is the word "groan." The old man wakes up startled when the narrator slips and makes a noise with the lantern. After asking who is there and hearing nothing, the narrator describes his groans of terror. The word groan describes the sound that came out of the old man's throat. The quote is below: 

Presently I heard a slight groan, and I knew it was the groan of mortal terror. It was not a groan of pain or of grief—oh, no!—it was the low stifled sound that arises from the bottom of the soul when overcharged with awe. I knew the sound well.

The third example is the word "chirp." In the story, it is describing the sound a cricket makes by rapidly rubbing its legs together. The narrator is speculating as to what the old man is thinking. He supposes he is rationalizing the noise by saying it was the wind, or a mouse, or a cricket: 

He had been saying to himself—"It is nothing but the wind in the chimney—it is only a mouse crossing the floor," or "It is merely a cricket which has made a single chirp."

The next example occurs when the police come over to investigate after the neighbors report the shriek they heard. He is chatting casually with them, and then he becomes uncomfortable and wants them gone. The narrator states: "My head ached, and I fancied a ringing in my ears." The word ringing describes the sound in his ears and is another example of onomatopoeia. 
The sound of the heartbeat itself is not described with onomatopoeia because it isn't really happening. It is all a figment of the narrator's imagination. 

Edgar Allan Poe's use of onomatopoeia is rather subtle in "The Tell-Tale Heart," but it is present in at least three places after the narrator has killed the old man whose eye had disturbed him so terribly.
After killing the old man and dismembering him, the narrator skillfully hides the body parts under the planks of the wooden floor in the old man's room. There are no traces of blood or obvious disturbances on the floor, and when the police come to follow up on a scream heard by a neighbor hours before, the narrator lets them in with confidence.
As the police begin their investigation, the narrator becomes increasingly nervous and swings a chair across the floor; he says, [he] "grated it upon the boards." The guttural sound of the g and the percussive t mimic the harsh sound.
As he begins to imagine the old man's heart "beating," the two syllables of the word with the emphasis on the first, with its dull sound of the b, sounds like a heartbeat.
When the heart begins to beat "louder—louder—louder," the rhythm of the repeated two syllables mimics the "lub dub" of a beating heart.

Which details in Mayella's story change before the end of her testimony in To Kill a Mockingbird?

Mayella's story changes most importantly when Atticus delves into the details of Tom's alleged assault on her. Of course, she has a bruise on her eyes, and the story is that Tom gave her the bruise during his assault, when he supposedly hit her in the face. When she describes his attack, she says "he caught me and choked me and took advantage of me." But she does not mention getting hit in the face, a detail Atticus seizes on almost immediately. When he asks her if she remembers getting hit in the face, she directly contradicts her father's account as well as herself in two sentences, stammering, "No, I don't recollect if he hit me. I mean, yes I do, he hit me." She then says that she can't remember because it all happened so fast.
Atticus reveals that Tom is actually disabled, having an atrophied arm, which would have made it very difficult for him to hit her as she described. She begins to recite new details, some of which are contradictory. In particular, she can't explain why nobody in the house—her six siblings in particular—heard her scream. In short, her story falls apart as Atticus seizes on a contradictory aspect of her testimony. Yet none of it matters in the end, as the jury still convicts Tom for rape.

Mayella isn't too steady as a witness from the time she takes the stand. Even on simple questions, like how long she went to school ("Two year—three year—dunno") and how long her mother has been dead ("Don't know—long time") seem to tax her abilities. When Atticus gets into the actual details of her testimony against Tom Robinson, Mayella is clearly trying to remember the details her father provided, as her accusations become conflicting.
When asked if she had ever asked Tom to do odd jobs for her before, she concedes that she might have. She testifies that Tom choked her, and then Atticus asks if he hit her in the face. This is a detail she wasn't prepped for, and she really struggles with how she should answer. After several false starts, she finally lands on, "No, I don't recollect if he hit me. I mean yes I do, he hit me." Atticus then asks Tom to stand so that Mayella can positively identify him as the man who raped her, and it becomes clear that Tom doesn't have use of his left arm. This would make it pretty difficult for him to have choked her. Mayella then changes her story about her facial injuries, saying that she "ducked and it—it glanced off, that's what it did." Finally Atticus asks Mayella why one of her seven siblings who were always underfoot didn't hear her screams for help. Mayella cannot even formulate a response at this point.
Mayella struggles because she's lying—and she's not educated or quick enough to pull off the discrepancies in her story which are revealed on the witness stand.

Mayella doesn't just contradict her own father's testimony; she changes the details of her own in a number of key respects. For instance, when Atticus asks Mayella if Bob has been a good father to her, her answer is somewhat less than convincing:

He does tollable, 'cept when-

Mayella stutters, knowing that she's about to poke a gigantic hole through her testimony. But Atticus persists with his line of questioning and asks Mayella if her father's ever beaten her. Mayella is indignant in response:

My paw's never touched a hair o' my head in my life...

The fact that she looks rather uncertain when she says this speaks volumes. Not long afterwards, Atticus throws her another curve ball asking her if it was the first time that she'd invited Tom Robinson to come inside the fence. After trying to collect herself, Mayella flatly denies she ever asked him to do so, but it isn't very long before she admits that she may have asked Tom to do some odd jobs for her, and it's difficult to see how he could've done them without being invited to come inside the fence.
Then Atticus asks Mayella if she remembered Tom beating her about the face. Again, Mayella's testimony changes in the blink of an eye:

No, I don’t recollect if he hit me. I mean yes I do, he hit me.

Mayella's whole testimony is full of holes. It's blatantly obvious that the story she tells the court is a tissue of fabrications.

What are some similarities between "The Solitary Reaper" and "Daffodils" by Wordsworth?

In both poems, the narrator seems to have a remarkably emotional experience by observing someone or something in nature. In "Daffodils," the speaker is made to feel happy and "gay" as a result of the beautiful, dancing flowers. In "The Solitary Reaper," the song being sung by the young Highland woman makes him feel an exquisite sort of melancholy as a result of her "plaintive" song. He is so affected by both the sight of the daffodils and the sound of the maiden's singing that it continues to affect him even after he has left their presence. In both cases, the emotional effect on the speaker, as an individual, is of utmost importance, and this is in keeping with the Romantic tradition's focus on the individual and his or her emotions.

In both poems, the speaker is walking in nature when he is stopped by a beautiful scene. In "Daffodils," also called "I Wandered Lonely as a Cloud," he is stunned by the beauty of the sudden sight of thousands upon thousands of daffodils in bloom. They are in front of a lake and swaying in the breeze as if they are dancing. The narrator feels joy as he watches them.
In "The Solitary Reaper," it is sound rather than sight that stops the narrator. He is in the Scottish Highlands and sees a young woman reaping in the fields. The sound of her song fills the air. The notes are more beautiful than the song of the nightingale, and though the narrator can't make out the words, he is transported by the tune's melancholy, plaintive melody.
At the end of both poems, the narrator experiences joy as he later remembers the experience he has had.

Beginning Algebra With Applications, Chapter 3, 3.3, Section 3.3, Problem 142

Evaluate $2(m + 7) \leq 4[3(m- 2)-5(1 + m)]$

$
\begin{equation}
\begin{aligned}
2(m) + 2(7) &\leq 4 [3(m) - 3(2) - 5(1) + (-5)(m)] && \text{Use the Distributive Property to remove the parenthesis}\\
\\
2m + 14 &\leq 4 [3m - 6 - 5 - 5m] && \text{Evaluate}\\
\\
2m + 14 &\leq 4 [ -2m - 11] && \text{Combine like terms inside the bracket}\\
\\
2m + 14 &\leq 4(-2m) - 4(11) && \text{Again, apply Distributive Property}\\
\\
2m + 14 &\leq -8m - 44 && \text{Simplify}\\
\\
2m + 8m &\leq - 44 - 14 && \text{Group terms}\\
\\
10m &\leq -58 && \text{Combine like terms}\\
\\
\frac{10m}{10} &\leq \frac{-58}{10} && \text{Divide each side by 10}\\
\\
m &\leq -\frac{58}{10}\\
\\
m &\leq -\frac{29}{5}
\end{aligned}
\end{equation}
$

How many children visit the factory?

In Roald Dahl's work of fiction, Charlie and the Chocolate Factory, reclusive genius Willy Wonka has kept his business very secretive for many years. In order to stave off spies who might try to steal his recipes, Mr. Wonka shut off his factory from the outside world. One day, Mr. Wonka announces that he has placed golden tickets inside five candy bars, and whoever finds one has the privilege to visit inside the factory. The whole world is in uproar trying to get their hands on one of these tickets and the opportunity to see the inside of such a famous and mysterious candy factory.
As there are only five tickets, only five children are allowed into the Wonka Factory. The children who have found tickets are allowed to bring along a parent or guardian, which makes the total number of visitors ten. The children who find tickets (or have tickets found for them) are Augustus Gloop, Violet Beauregarde, Veruca Salt, Mike Teavee, and Charlie Bucket. 

In the short story A&P by John Updike, what is the difference between the 3 characters Sammy, Queenie, and Lengel?

In the short story "A & P," there are, indeed, differences among the characters Mr. Lengel, Sammy, and Queenie.
Mr. Lengel is the manager of the A & P grocery store. He represents the adult who holds conventional views as he enforces the rules regarding attire and conduct in the store. When Sammy feels that he should act on the girls' behalf after Lengel embarrasses them, he tries to convince Sammy not to quit partly because he is a friend of Sammy's parents. He tells Sammy, "You'll feel this for the rest of your life," implying that he should attend to conventional rules.
Sammy is a nineteen-year-old who works at the grocery store. He has assumed a somewhat cynical attitude about the adult women--the "sheep" and "house slaves" as he calls them--who shop there. He is disgusted with them because they seem to have lost any personal pride. For they come to the grocery store in curlers and shorts that display "varicose veins mapping their legs and nobody, including them, could care less." In contrast to these "house slaves," the sight of the young girls in their swimsuits as they enter the store is welcomed by Sammy as a delightful change, as well as one that is sexually enticing. Unfortunately for Sammy, he becomes romantic in his perception after Lengel accosts them, explaining the store policy: "Poor kids, I began to feel sorry for them, they couldn't help it." This romantic perception leads Sammy to believe that his chivalric act of quitting because of Lengel's having embarrassed them will impress the girls. However, when he goes outside the store after quitting and looks around for "my girls," they are already gone. His act has gone unnoticed, and Sammy cannot decide whether he is heroic or merely foolish.   
Queenie is a somewhat brazen teenager who leads two other girls into the store in violation of the dress code because they wear only their bathing suits. Queenie has the straps of her suit pushed off, and she walks slowly, "putting a little deliberate action into it." She is a self-centered girl who apparently likes the attention that her attractive figure brings her until she feels embarrassed and blushes when Lengel informs them of the store's rules. She and the other girls have no interest in Sammy, and they depart before witnessing his act of chivalry on their behalf. 

What, if any, laws do you think the United States should pass to protect personal information? Why? Should some personal information be more protected than other information? Why?

In an age with breaches of major companies resulting in the unauthorized release of personal information occurring daily, consideration should be given to protect personal information. The problem is that a law cannot protect the personal information that most people freely provide to social media companies, credit reporting agencies, and others with little or no forethought to how the information will be used. Laws that penalize companies with significant fines (e.g., Facebook's recent 5 billion dollar fine by the FTC) do little to deter hackers. Further, a fine is a relatively small penalty for companies earning billions of dollars and does little to prevent consumers from being nonchalant about giving away their personal information.
Think about your average day. If you are like most people, at some point you check your e-mail, use the internet, update your financial accounts, place a retail order, and possibly look at social media. If you eat out, you use a debit or credit card. While driving, you pass through numerous cameras and various other surveillance equipment. Your car may be able to track your driving habits, while your phone continually updates your position in relation to the nearest cell tower. If you make a call, your phone carrier keeps a record of it and it can easily be converted into a history of time, place, location, and who you called. GPS in your car, phone, or other device can pinpoint your location within a few feet. Your employer during the day follows what you do on company computers. Maybe you went on a government website today to pay taxes or to order car tags. You probably don’t think much about how many times you are asked to produce a government-issued identification like your driver's license, passport, or social security number in a day. When you arrive home, if you have smart gadgets, everything from security companies to the entertainment on your smart tv or video games immediately begin to update your electronic activity. Even your fitness watch collects data on you. Where does all of this data go?
So what makes anyone believe additional privacy protection laws are in any way going to protect personal information? No doubt privacy laws need a serious update reflecting the modern reality that we are being virtually surveilled 24/7. Given that it takes very little personal information to be compromised or for a person to steal your identity, all personal data should have equal weight for protection. However, laws cannot protect a person’s private information if we don’t take responsibility to keep it private.
Of course, this is not to suggest that everyone goes off the grid. I am merely proposing that laws only penalize the person or company caught, tried, and convicted. Meanwhile, the consumer may be irreparably damaged by the release of private data, and to that end, any legal reparations fall short of the cost of the damage done to a person. The only real protection for privacy is not to be cavalier in how a person gives private data away.
https://time.com/4673602/terms-service-privacy-security/

https://www.brookings.edu/research/why-protecting-privacy-is-a-losing-game-today-and-how-to-change-the-game/

https://www.futurity.org/privacy-pizza-convenience-1505022/

According to ARMA International, a professional organization for information governance workers, business and government officials have to follow increasingly complex rules to keep the data of their customers and clients safe. Personal data is compromised at alarmingly high rates. For example, according to the ARMA 2008 report "Requirements for Personal Information Protection, Part 1: U.S. Federal Law," more than 79 million records were compromised in 2007 (Identity Theft Resource Center). This report states that the "most overused" personal information is people's Social Security Number. Federal laws such as the 1974 Privacy Act state that privacy is a personal and fundamental right given in the Constitution, so this is incredibly problematic.
Given the high rate at which personal information is compromised and citizens' rights to privacy, the United States should pass additional laws to protect personal information. For example, employers or entities granting loans can access private information in credit reports. In addition, while the federal government grants citizens a right to privacy, states, with the exception of California, do not grant citizens the same rights. Therefore, state laws need to recognize an individual's right to privacy. 
Personal information related to one's health deserves particular protection because, if someone has damaging health information, it can be used against them in prejudicial ways, such as in employment, housing, loans, or education decisions. While The Health Insurance Portability and Accountability Act (HIPAA) passed in 1996, this law does not always protect people's personal health information because people have to access this information with identifiers such as their Social Security Numbers. Therefore, people's health information is stored alongside other personal information. At the very least, patients should be given a new identifier to access their health information, and this data should not be stored with one's Social Security Number.

y = x/2 + 3 , 1

To find the area of this surface, we rotate the function y = x/2 + 3 about the y-axis (not the x-axis) in the range 1<=x<=5 and this way create a finite surface of revolution.
 
A way to approach this problem is to swap the roles of x and y , essentially looking at the page side-on, so that we can use the standard formulae that are usually written in terms of x (ie, that usually refer to the x-axis).
The formula for a surface of revolution A is given by (interchanging the roles of x and y )
A = int_a^b (2pi x) sqrt(1+(frac(dx)(dy))^2)dy
Since we are swapping the roles of x and y , we need the function y = x/2 + 3 written as x in terms of y as opposed to y in terms of x . So we have
x = 2y - 6
To obtain the area required by integration, we are effectively adding together tiny rings (of circumference 2pi x at a point y on the y-axis) where each ring takes up length dy on the y-axis. The distance from the circular edge to circular edge of each ring is sqrt(1+(frac(dx)(dy))^2) dy
This is the arc length of the function x = f(y) in a segment of length dy of the y-axis, which can be thought of as the hypotenuse of a tiny triangle with width dy and height dx .
These distances from edge to edge of the tiny rings are then multiplied by the circumference of the surface at that point, 2pi x , to give the surface area of each ring. The tiny sloped rings are added up to give the full sloped surface area of revolution.
We have for this function, x = 2y -6 , that  (dx)/(dy) = 2
and since the range (in y ) over which to take the integral is 1 <=x <=5 , or equivalently  7/2 <= y <= 11/2  we have a = 7/2 and b = 11/2 .
Therefore, the area required, A, is given by
A = int_((7)/(2))^((11)/(2)) 2pi (2y -6) sqrt(5) dy    = 2sqrt(5)pi int_((7)/(2))^((11)/(2)) 2y - 6 \quad dy
 
= 2sqrt(5)pi y(y - 6)|_((7)/(2))^((11)/(2)) = (sqrt(5))/(2)pi [11(11-6) - 7(7-6)]
So that the surface area of rotation A is given by
A = 24(sqrt(5)) pi
 
http://mathworld.wolfram.com/SurfaceofRevolution.html

In "Two Kinds" what is a good example of a direct characterization and an indirect characterization?

The narrator, Jing-mei, is indirectly characterized by her own descriptions of the feelings she experienced as a child. When she was little, she very much wanted to meet her parents' expectations, to make them proud. She says,

In all of my imaginings I was filled with a sense that I would soon become perfect: My mother and father would adore me. I would be beyond reproach. I would never feel the need to sulk, or to clamor for anything.

However, she also experiences some self-doubt. She says, as the prodigy that she hopes lies somewhere within herself, "If you don't hurry up and get me out of here, I'm disappearing for good . . . And then you'll always be nothing." If she is unable to tap into that inner "prodigy," Jing-mei feels that she will be so insignificant she is literally "nothing." So, when her mother can't find a subject at which she can excel, she begins to grow resentful of her mother.
Soon, though, this self-doubt turns to something resembling empowerment and willfulness. Jing-mei says, using direct characterization now,

The girl staring back at me was angry, powerful. She and I were the same. I had new thoughts, willful thoughts—or rather, thoughts filled with lots of won'ts. I won't let her change me, I promised myself.

Amy Tan uses direct characterization when the narrator describes herself.  Direct characterization occurs when the reader receives description of the character explicitly.  An example of direct characterization is seen when Jing-mei describes her initial excitement at the thought of being a child prodigy:

"I was like the Christ child lifted out of the straw manger, crying with holy indignity. I was Cinderella stepping from her pumpkin carriage with sparkly cartoon music filling the air."

In this quotation, Jing-mei describes herself directly, telling us explicitly what she was like as a child: excited by her own promise.
Tan also uses indirect characterization in shaping Jing-mei.  Indirect characterization reveals a character's traits through actions, speech, or appearance.  When Jing-mei is taking piano lessons from Mr. Chong, she quickly discovers that he does not hear well and is really only able to tell if she is keeping time with the music, not playing the correct notes. She describes how she takes advantage of his inattention to play sloppily.  In describing Jing-mei's actions at her piano lessons, Tan is able to reveal that Jing-mei is intelligent and rather devious.  

Direct characterization occurs when the narrator of a story tells the audience what a character is like. A character in the story may state the direct characterization as well.  In "Two Kinds," Jing-mei is the narrator of the story, and there are several times when she directly describes what her mother is like.  The opening paragraph is a good place to look. 

My mother believed you could be anything you wanted to be in America.

The quote directly tells readers about a basic belief that Suyuan has.  
Indirect characterization occurs when an author shows readers what kind of person a character is through that character’s thoughts, words, and deeds. Indirect characterization requires readers to make inferences about why a character would behave in a particular manner.  
In "Two Kinds," I would describe Jing-mei as stubborn, a description I came up with by looking to examples of indirect characterization. The narrator of this story, Jing-mei, is never explicitly described as stubborn; however, her constant refusal to work toward the child prodigy goal shows that she is.

"Why don't you like me the way I am?" I cried. "I'm not a genius! I can't play the piano. And even if I could, I wouldn't go on TV if you paid me a million dollars!"

 

What is a specific event or quote from Act 1 and the effect of foreshadowing ?

Early on in act one, the conversation between Reverend Parris and his niece, Abigail Williams, reveals that she was dismissed from her employment with the Proctors over half a year ago and that no one has attempted to hire her again since then. He says, "it has troubled me that you are now seven month out of their house, and in all this time no other family has ever called for your service." He is concerned about what Abigail might have done to cause the loss of her position, and he is also concerned that it might have tarnished her reputation in the town.
Further, there are rumors in town that Elizabeth Proctor does not often come to Sunday services because "she will not sit so close to something soiled." Parris's concern, as well as the rumors which seem to circulate regarding Abigail's tarnished virtue, foreshadow the revelation that she has, indeed, had an affair with John Proctor. We later learn that this was the reason Elizabeth Proctor fired her, and the rumors about Abigail's lack of sexual innocence do contain some germ of truth in them.

Throughout Act One, Miller reveals the palpable tension in the community of Salem when the Putnams voice their opinions and John Proctor speaks to Abigail. The audience learns that the Putnams deeply resent Reverend Parris's position, as well as Rebecca Nurse's prosperity. The Putnam's negative feelings towards Reverend Parris and Rebecca Nurse foreshadow their involvement and accusations during the witch trials. Another moment that foreshadows a significant future event takes place when John Proctor has a conversation with Abigail. Abigail Williams expresses her feelings for John, as well as her displeasure towards his sick wife, Elizabeth. Abigail tells John,

"Oh, I marvel how such a strong man may let such a sickly wife be—...She is blackening my name in the village! She is telling lies about me! She is a cold, sniveling woman, and you bend to her! Let her turn you like a—" (Miller, 33).

Abigail's hateful comments towards Elizabeth Proctor foreshadow her accusation. In an attempt to get rid of Elizabeth, Abigail accuses her of witchcraft. Ironically, it is John Proctor who is punished because of Abigail's false accusation.

How is family portrayed in The Lost Boy by Dave Pelzer?

Family is one of the most significant themes of Dave Pelzer’s memoir The Lost Boy. Young David’s relationship with family is profoundly negative at the outset of the book. His mother is a nightmarish figure who subjects him to terrible abuse and frequently drinks herself into a rage. His father is unable or unwilling to stop this abuse, and his brothers are forced to witness and participate in it. Pelzer impersonally refers to his biological family as “The Family” and their house as “The House.” It’s clear that David doesn’t view The Family as his true family or The House as his true home. Once he enters the foster system, his experience of family begins to change and, on the whole, to improve. Caring foster parents like the Catanzes and the Turnboughs show David that a family can (and should be) a positive, supportive thing. Still, David is always aware that these families and homes are temporary and that, along with the many other children he shares each set of foster parents with, he will continue to be moved from home to home, family to family, until he turns eighteen. David ends up leaving his last foster family, the Turnboughs, to strike out on his own as an Army recruit. By the end of the memoir he has finally found a true family of his own with his wife and son, and with it peace.

What are Arendt's definitions of work, labor, and action?

Hannah Arendt devotes the third, fourth, and fifth chapters of The Human Condition respectively to labor, work, and action—the three fundamental human activities.
Labor is the most basic activity necessary for survival. Its salient feature is that it must be repeated endlessly. Examples include agriculture, child-rearing, and cleaning. Because the dish that is washed today must be washed tomorrow and the next day and the next day, labor comes to seem futile and is therefore the least respected form of activity—often the province of slaves in the ancient world.
Work, unlike labor, leaves an end product. The importance of work grows drastically as society becomes more materialist, demanding an ever greater array of physical objects. Work comes closest to labor when the objects it produces are cheap and disposable. It attains its purest form in art, since artworks are valued for themselves, rather than being used for anything else.
Action includes speech and is political in the widest sense. It is the means by which we reveal ourselves to one another and assert ourselves as individuals in the world. It is also the way in which we form relationships with others. Arendt stresses the great risk of acting in the world, one of the most difficult of all human problems, since we can never predict the results of our actions and cannot take back an action once it has been performed. This difficulty is exacerbated as societies become more complex and unpredictable.

The Human Condition was written by Hannah Arendt, a philosopher, to help explain our relationship to the world of others, of things, and of processes. She is especially interested in how human beings have altered their relationship to their environment as civilization has progressed.
To understand human relationships, she defines three principle ways of being in the world that all humans possess. These are defined as labor, work, and action. She does not distinguish between men and women, those of upper versus lower class, or any other established categories.
Labor and work are two types of economic interaction. Labor refers to the type of activity in which the product will be consumed, so the labor is never-ending. Examples of this are child-rearing, farming, and ranching. Labor requires a constant, ongoing relationship to the environment, governed only by the seasons and by time. Labor does not produce a static, fixed, or even necessarily profitable output.
Work, on the hand, results in a product that can be sold, reused, inhabited, built-upon - or otherwise has a separate existence all its own. Work usually refers to the output of goods, although some other activities, such as earning a degree that can be used to make money, are examples of work. Construction of a building is work, because at end there will be a commodity that will be bought and sold and will make someone money.
This distinction is particularly interesting in light of how money is earned in the modern age. Chores, family care, farming, and other "labor" activities are either non-paid or barely paid. Labor is not an activity that will make anyone rich, yet it is the cornerstone of life. Our current economic system, however, does not distinguish between work and labor, and both types of activities are paid jobs.
Labor sustains, whereas work uses up resources in transforming them.
Action can be involved in either labor or work, but principally it is what drives and sustains relationships between individuals. Action refers to anything a person does in which he or she asserts himself or herself as an individual in the world. Action largely defines a person, and Arendt argues that individuality is largely the result of actions and their effect on others.

In Hannah Arendt's book The Human Condition, she is interested in the contrast between what she calls the active life and the contemplative life, and she worries that the debate over the status of each has blinded us to insights about the active life and the way it has changed throughout human history.  She discusses three different categories of active life: work, labor, and action.
Work, Arendt claims, has a clear beginning and end (from the idea for the object and the obtaining of raw material to the finished product) and leaves behind a durable object (e.g., a building or a machine) as opposed to something consumable (e.g., food).  Work involves some sort of interruption to nature to obtain raw materials, such as cutting down a tree for lumber.  She views this interruption as a form of violence, or at the very least, a violation of the natural order.
Labor is seen as action taken in order to survive (e.g., meeting biological needs such as eating) both as an individual and for the survival of the human race as a species.  Unlike work, labor does not have an ending because we must continually meet our biological and reproductive needs in order to survive. The fruits of labor must be consumed, forcing us to create more.
Action is the means by which human beings reveal themselves to one another through speech and physical actions.  This includes both deliberate and unintentional revelations or disclosures, and Arendt argues that what a person reveals in action is more than likely unknown to the person acting (i.e., others know us better than we know ourselves), and that revelation is made known only to the actor when they hear the story of their actions.  Action is the way human beings distinguish themselves from one another and identify who we are as individuals.  Actions in Arendt's view, be it speech or physical action, are always between and directed toward humans, and they are responsible for human relationships.  

Please provide a detailed summary and historical context for the following primary source. Andrew Carnegie Anti-imperialism in the United States http://courses.knox.edu/hist121/18981904.pdf

This primary source is an excerpt written by Scottish-born entrepreneur Andrew Carnegie, who made his fortune in the US and was a key figure in the anti-imperialist movement that gathered steam in the US after the Spanish-American war. These anti-imperialists did not believe that the US should seek to "conquer" foreign lands already inhabited by people not of the same "race"—that is, not white people. The American Anti-Imperialist League was particularly opposed to the American annexation of the Philippines, and many Americans of import, including Mark Twain, wrote critically about this possibility.
In this primary source, Carnegie lays out his reasons for opposition to what he calls "triumphant despotism." He feels that this is opposed to what the Republic stands for and that to attempt to establish "the rule of the foreigner over the people" would lead to "a scattered and disjointed aggregate of widely separated and alien races." Carnegie feels that an attempt to annex and then govern possessions which could never become part of the united Republic would mean abandoning focus on America itself.
He goes on to suggest that there is one type of "possession" which would be permissible—those in which "we establish and reproduce our own race." He gives Australia and Canada as good examples of this. However, he describes "dependencies" as being burdens upon the mother country, with India an example of a burden upon Britain because we "cannot reproduce our own race there."
Carnegie counters the idea that foreign possessions could help with America's exports, stating that the US already produces the largest amount of exports when compared to anywhere else on earth, including Britain, which possessed many colonies and dependencies at this time. While Carnegie feels that it would be potentially to America's benefit to "grow Americans in any part of the world," he does not believe they should undertake "the government of alien races in lands where it is impossible for our own race to be produced."
Carnegie also offers the point of view that the US was currently "impregnable against serious attack" because all colonies currently held were nearby enough to be easily defended. The Philippines, by contrast, represent to him an enormous country composed of "races bitterly hostile to one another" which would be difficult for America to rule. His major issue continues to be that "Americans cannot be grown there," but he also stipulates that it would be unfair to "practice independence and preach subordination." Carnegie concludes by saying that "to be more powerful at home is the surest way to be powerful abroad."
To the modern reader, Carnegie's reasons for opposing American expansion make uncomfortable reading; in his opposition of expansion, he does consider the issues of hypocrisy, but he also makes racist assumptions and behaves as if Britain had not suppressed any existing native populations to claim the US, Australia, and Canada. However, Carnegie represents the spirit of those anti-imperialists who felt the US should concentrate on its own issues, rather than "burden" itself with the governance of races very different to white Americans.

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 60

Determine an equation of the line passing through the points $(-2,2)$ and $(4,2)$.

(a) Write the equation in standard form.

Using the Slope Formula,

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-2}{4-(-2)} = \frac{0}{6} = 0$

Using Point Slope Form, where $m = \displaystyle 0$ and $(x_1,y_1) = (-2,2)$



$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
y - 2 =& 0 [x - (-2)]
&& \text{Substitute } x = -2, y = 2 \text{ and } m = 0
\\
y - 2 =& 0
&& \text{Distributive Property}
\\
y =& 2
&& \text{Standard Form}

\end{aligned}
\end{equation}
$



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

The equation $y = 2$ is also the slope intercept form.

y=lnx , [1,5] Find the arc length of the curve over the given interval.

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

When did the Berlin Wall fall?

The Berlin Wall officially fell on November 9, 1989, having divided the western and eastern parts of the city for twenty-eight years. The ruling Communist party in East Germany, like others in the Eastern Bloc, was under increasing pressure for reform. The official Soviet policy of glasnost, or openness, inevitably trickled down to the USSR's satellite states, influencing their own domestic policies. Initially, the GDR's rulers resisted the Soviet example, but once the genie had been let out of the bottle, there was to be no putting it back.
The pressure for change, both internally and externally, proved irresistible, so the East German authorities relented, allowing people to pass back and forth between East and West Berlin without let or hindrance. Immediately, the Berlin Wall, a hated symbol of Communist oppression, became obsolete. In an almost carnival atmosphere, people from both sides of the divide started taking picks and hammers to the wall, beginning the process of its eventual destruction.

Describe the Enlightenment and the Enlightenment's influence on the American Revolution and French Revolution.

The Enlightenment was an era in Europe in which there was a transition from religious thought and irrationality to the application of reason and investigation to acquire truth. The Enlightenment was inspired by the scientific revolution and the Renaissance.
The colonists directly referenced principles of Enlightenment political philosophy to achieve their severance from England. Thomas Jefferson, who wrote the Declaration of Independence, was heavily directed by John Locke. Locke, the English philosopher in the Seventeenth Century spoke of natural rights that no government can abridge. These rights included life, liberty, and property. Locke, Baron de Montesquieu, and Jean-Jacques Rousseau were all Enlightenment thinkers that advocated for popular sovereignty. The issue of taxation without representation correlates to the notion of popular sovereignty and was paramount to the colonists as a motive for separation from England. The various phases of the French Revolution were also inspired by a variety of Enlightenment thinkers. A detailed description of the French influences can be found on the source I provided below.
http://www.articlemyriad.com/influence-enlightenment-formation-united-states/

https://www.historytoday.com/archive/french-revolution-ideas-and-ideologies

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 15

Determine $\displaystyle \frac{dy}{dx}$ of $\tan \left( \frac{x}{y} \right) = x + y$ by Implicit Differentiation.

$\displaystyle \frac{d}{dx} \left[ \tan \left( \frac{x}{y} \right) \right] = \frac{d}{dx} (x) \frac{d}{dx} (y)$

$
\begin{equation}
\begin{aligned}
\sec^2 \left( \frac{x}{y} \right) \cdot \frac{d}{dx} \left( \frac{x}{y} \right) &= 1 + \frac{dy}{dx}\\
\\
\sec^2 \left( \frac{x}{y} \right) \left[ \frac{(y) \frac{d}{dx}(x)-(x)\frac{d}{dx}(y) } {y^2} \right] &= 1 + \frac{dy}{dx}\\
\\
\sec^2 \left( \frac{x}{y} \right) \left[ \frac{(y)(1) - (x) \frac{dy}{dx}}{y^2} \right] & = 1 + \frac{dy}{dx}\\
\\
\sec^2 \left( \frac{x}{y} \right) \left[ \frac{y - x \frac{dy}{dx}}{y^2}\right] & = 1 + \frac{dy}{dx}\\
\\
\frac{y \sec^2 \left( \frac{x}{y} \right) - x \sec^2 \left( \frac{x}{y} \right) \frac{dy}{dx}}{y^2} &= 1 + \frac{dy}{dx}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
y \sec^2 \left( \frac{x}{y} \right) - xy' \sec^2 \left( \frac{x}{y} \right) &= y^2 + y^2 y'\\
\\
xy' \sec^2 \left( \frac{x}{y} \right) + y^2 y' &= y \sec^2 \left( \frac{x}{y} \right) - y^2\\
\\
y' \left(x \sec^2 \left( \frac{x}{y} \right) + y^2 \right) &= y \sec^2 \left( \frac{x}{y} \right) - y^2\\
\\
\frac{y' \cancel{(x \sec^2 \left( \frac{x}{y} \right) + y^2)}}{\cancel{x \sec^2 \left( \frac{x}{y} \right) + y^2}} &= \frac{y \sec^2 \left( \frac{x}{y} \right)- y^2}{x \sec^2 \left( \frac{x}{y} \right) + y^2}\\
\\
y' & = \frac{y \sec^2 \left( \frac{x}{y} \right)- y^2}{x \sec^2 \left( \frac{x}{y} \right) + y^2}
\end{aligned}
\end{equation}
$

int 12/(1+9x^2) dx Find the indefinite integral

Recall that the indefinite integral is denoted as: 
int f(x) dx =F(x)+C
There properties and basic formulas of integration we can apply to simply certain function.
For the problem int (12)/(1+9x^2)dx
we apply the int cf(x)dx = c int f(x)dx   to become:
12 int 1/(1+9x^2)dx
Then apply the basic inverse trigonometric function formula: 
int (du)/(a^2+u^2) = 1/a arctan(u/a)+C
By comparison with the basic  formula and the given problem, we can let:
a^2 =1 
u^2=9x^2 or (3x)^2
 then du = 3 dx
 To satisfy the given formula, we need to multiply the integral by 3/3 to
be able to match   du = 3 dx .
 
 The integral value will note change since multiplying by 3/3 is the same as multiplying by 1.  Note: 3/3= 1 and 3/3 = 3*(1/3)
 Then 12 int 1/(1+9x^2)dx * 3/3
= 12 int 1/(1+9x^2)dx * 3 * 1/3
= 12 (1/3)int 1*3/(1+9x^2)dx
=4 int (3 dx)/(1+9x^2)
The int (3 dx)/(1+9x^2) is now similar to int (du)/(a^2+u^2) where:
du =3dx , a^2 =1 and u^2 = 9x^2 or (3x)^2
then a=1 and u =3x .
 
Plug-in  a=1 and u = 3x in 1/a arctan(u/a)+C , we get:
4* int (3 dx)/(1+9x^2) = 4* 1/1 arctan((3x)/1)+C
                                  =4 arctan(3x)+C 

On page 36 of The Other Wes Moore, we learn that Wes’s mother slept in the living room to protect the kids from a possible intruder. What other things did she do to protect her children?

Mary tries to protect Wes from himself and the criminal lifestyle into which he's fallen. It's too late for Tony, Wes's older bother, but Mary tenaciously holds on to the belief that Wes's life can still be turned around. In reality, however, Wes is slipping further and further into a life of crime. He's no longer just working as a lookout; now he's a fully-fledged drug dealer, hoping to emulate his brother's lavish lifestyle.
Although Mary can't physically stop Wes from selling drugs, she can still try and protect him from himself. She does this by flushing his stash down the toilet. It's a desperate measure, and ultimately it doesn't change Wes's ways, but it shows the lengths to which Mary's prepared to go to protect her son.

Which Native American tribes were most prevalent in the Pacific Northwest?

The Pacific Northwest Native American tribes lived in a narrow band of land along the coast from southern Alaska to northern California. The northern tribes in this area generally spoke Tlingit and included Haida, Tsimshian, and the Haisla (or the northern Kwakiutl). Further south were the other Kwakiutl, Nuu-chah-nulth, and the Bella Coola. Extending from Vancouver Island south into current-day Oregon were the Coast Salish-Chinook group, including the Makah, Tillamook, Siuslaw, Chinook, and other tribes. The Coast Salish were among the most numerous and powerful of the southern tribes in the Pacific Northwest and made up a group of tribes with different languages and cultures. In what is now northern California lived the Tututni-Tolowa, the Karok, Hupa, Yurok, and Wiyot. The Native American tribes in this region spoke several different languages, and many of the tribes relied on fishing, hunting, and gathering shellfish to survive. 

How do Stephan and Jeremy die?

Jeremy Poldark is Ross and Demelza's second child. In The Twisted Sword he has reached the age of manhood, happily married to Cuby and with a baby on the way. Like so many men of his generation he's become caught up in the Napoleonic Wars currently ravaging the European continent. Jeremy's stationed near Brussels, the capital of modern-day Belgium. He proves himself to be a very brave, skillful soldier and is subsequently promoted to Captain. With exemplary courage, he leads his men into battle, but tragically it proves to be his last. Jeremy is shot twice and dies in the arms of his father.
Stephen Carrington's off on his adventures too. Sadly for him, they end up the same way as Jeremy's. To help solve his perennial financial troubles he captures a ship. It's a prize catch indeed, and Stephen makes an absolute bundle out of it. But his new-found wealth goes to Stephen's swelled head, and he starts acting like a king. As a newly-minted man of substance, he feels himself entitled to better things. He buys a magnificent horse that he feels is an appropriate reflection of his elevated station in life.
Yet as Stephen soon discovers, pride comes before a fall—in this case, quite literally. He tries to impress the comely Harriet Warleggan with his skills as a horseman and foolishly challenges her to see whose horse is best. Unfortunately for Stephen, his horse comes off worst, and he comes off the horse. Thrown from his steed as it fails to negotiate a particularly difficult jump, Stephen breaks his neck. How the mighty have fallen.

Why does Anne say that Margot is more of a proper lady?

Margot has a completely different personality to Anne. She is much less exuberant, for one thing. She also does not seem to share Anne's romantic tendencies when it comes to relationships. Anne makes her sound as if she is quite prim and proper in relation to boys. In that sense, she very much takes after her mother:

I’m pretty sure Margot would never kiss a boy unless there was some talk of an engagement or marriage. Neither Peter nor I have any such plans. I’m sure that Mother never touched a man before she met Father. What would my girlfriends or Jacque say if they knew I’d lain in Peter’s arms with my heart against his chest, my head on his shoulder and his head and face against mine!

Margot comes across as pretty conventional, which is in complete contrast to her sister. Anne follows her heart; she does not really care all that much about what other people think. Margot, however, will not give her heart to someone unless it is a relationship that could lead to engagement or marriage. In this sense, Margot is more of a "proper lady" than Anne. She acts the way that society would expect her to behave. Anne, on the other hand, with her passionately romantic soul, defies convention.

Single Variable Calculus, Chapter 3, 3.9, Section 3.9, Problem 32

Suppose that the radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2cm.
a.) Estimate the maximum error in the calculated area of the disk by using differentials
Area of a circle,
$A = \pi r^2$, where $R = 24$cm and $dr = 0.2cm$

$
\begin{equation}
\begin{aligned}
\frac{dA}{dr} &= \frac{d}{dr}(\pi r^2)\\
\\
dA &= 2 \pi r dr\\
\\
dA &= 2 \pi (24\text{cm})(0.2\text{cm})\\
\\
dA &= 9.6 \pi \text{cm}^2 \qquad \text{Maximum possible error of the area of a circular disk}
\end{aligned}
\end{equation}
$


b.) Find the relative error and the percentage error
For relative error,


$
\begin{equation}
\begin{aligned}
\frac{dA}{A} &= \frac{2 \pi r dr}{\pi r^2}\\
\\
\frac{dA}{A} &= \frac{2dr}{r}\\
\\
\frac{dA}{A} &= \frac{2\left(0.2\cancel{\text{cm}}\right)}{24\cancel{\text{cm}}}\\
\\
\frac{dA}{A} &= 0.0167
\end{aligned}
\end{equation}
$


For percentage error,
$\displaystyle \frac{dA}{A} \times 100\\
0.0167 \times 100 = 1.67 \%
$