To what extent are characters in Fences in control of their lives and of themselves?

Fences shows us that some aspects of life are in our control, while others are not. Racism is not totally in our control—Troy could not control his life as a baseball player because racism prevented him from playing in the big leagues. Racism keeps Troy at the back of the garbage truck. Although racism holds these characters back, they attempt to overcome it to a certain extent, such as Troy working hard in order to prove to his boss that he can drive the garbage truck.
Troy is in control of his personal life, as he chooses to have an affair. This point is highlighted by the character of Jim Bono. Bono is Troy's best friend, and in many ways, Bono looks up to Troy. However, Bono knows that cheating is wrong. Bono expresses his worry about how the affair will affect his friend's marriage. By remaining loving and faithful to his wife, Bono shows that this is an aspect of life that is under the characters' control.
Gabriel shows us how many things are out of our control. Gabriel was injured in war and now has diminished mental capacity. Gabriel is not in charge of his own life. At times he seems to be ruled by his delusions. We also see how Troy has a power over Gabriel, as Gabriel is not capable of making his own decisions about his care, and so Troy takes this control and determines that Gabriel should go to a mental hospital.

The characters in the play are not in total control over their lives or themselves. Troy tries to defeat the forces of death and mortality, and he regards death as something he can overcome. He builds fences around his property as a way to keep death out, but he dies by the end of the play.
The force of racism is also something that the characters can't control. Troy was not able to play baseball in the major leagues when he was young because he is black, and he fears that his son, Cory, will be unable to play football for the same reasons. Racism affects Troy at work, and he has to petition his boss to be able to drive a garbage truck rather than ride in the back (eventually, he is allowed to do so). Mortality and racism are forces that the characters in the play cannot control, and these forces prevent them from being in control of their own lives.

The characters in Fences are all struggling against forces beyond their control.
Troy arguably has the most control over his life; when the play begins, he is questioning why black employees at his job are not allowed to drive the garbage trucks, but in the next scene, he has been made the first black garbage truck driver in the city. Troy is also clearly the one in control in his home. When it comes to interacting with his son Cory and his wife Rose, Troy's word is law. But Troy struggles to reconcile the bright future he could have had as a baseball player, a future that was denied him because he was black, with the life he ended up living. His life is the result of being unable to control what happened to him.
Because they share his home and rely on him financially, Rose and Cory struggle against a force they cannot control: Troy. Rose must deal with Troy's infidelity and even raise the child that is born out of his affair with Alberta. Cory's desire to play football is crushed by Troy's insistence that he work instead; Troy says he has no future in sports. In addition, Gabriel, Troy's brother, was injured when he fought in World War II, a situation far beyond his control.
Lyons, Troy's oldest son, enjoys a freedom and sense of control that the other characters do not, because he is living out his dream of being a jazz musician. This often means, however, that he struggles to make money, and as a result, he relies on Troy financially. Apart from Lyons, the characters in Fences are forced (often by Troy) to prioritize security and survival over happiness, and in this way, they have limited control over their lives.

What is the name of the inheritance pattern in which both alleles are expressed equally?

When we say "expressed equally," this actually raises a lot of questions about the interaction between the genes, their products, and the effects of those products on the organism. Consider, for example, that a gene could have an error or mutation that causes it to never be transcribed properly at all; in this case, we would not consider the two alleles to be equally expressed. However, what if the gene's product is simply broken or inefficient? In this case we could still say that they are being expressed equally, but they will not be equally visible in terms of their effect on the organism. What is usually meant by "equally expressed" is that both alleles code for products that are created in roughly equal proportion and the effects of both can be recognized in the organism, as compared to organisms that are homozygous for one allele or the other. 
There are two terms that describe an equal expression of alleles; incomplete dominance, and codominance. One of the most common demonstrations of these effects is flower pigmentation.
In codominance, we can think of the allele products as working together to make something new; in the case of flowers, the example would be a red allele and a white allele making a pink flower. Note that they probably aren't combining the red and white pigments to create a pink pigment, but that the red and white pigments are equally distributed so that the cumulative effect is pink.
In incomplete dominance, we can think of both alleles as "fighting" for dominance, but neither one wins; instead they each carve out their own territory where they, and they alone, are dominant, but this is not consistent throughout the organism. In the case of the flowers, this would create a flower with red and white splotches, spots or some other distinct pattern effect.
https://www.ndsu.edu/pubweb/~mcclean/plsc431/mendel/mendel2.htm

College Algebra, Chapter 8, Review Exercises, Section Review Exercises, Problem 16

Determine the center, vertices, foci, eccentricity and lengths of the major and minor axes of the ellipse $\displaystyle 2x^2 + y^2 = 2 + 4(x - y)$. Then sketch its graph.


$
\begin{equation}
\begin{aligned}

2x^2 + y^2 =& 2 + 4x - 4y
&& \text{Distribute } 4
\\
\\
2(x^2 - 2x + \quad ) + (y^2 + 4y + \quad ) =& 2
&& \text{Group terms and factor}
\\
\\
2(x^2 - 2x + 1) + (y^2 + 4y + 4) =& 2 + 2 + 4
&& \text{Complete the square: add } \left( \frac{-2}{2} \right)^2 = 1 \text{ and } \left( \frac{4}{2} \right)^2 = 4 \text{ on the left side, then add 2 and 4 on the right side}
\\
\\
2(x - 1)^2 + (y + 2)^2 =& 8
&& \text{Perfect Square}
\\
\\
\frac{(x - 1)^2}{4} + \frac{(y + 2)^2}{8} =& 1
&& \text{Divide both sides by } 8

\end{aligned}
\end{equation}
$


The shifted ellipse now has the form $\displaystyle \frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1$ with center at $(h,k)$. It is derived from the ellipse $\displaystyle \frac{x^2}{4} + \frac{y^2}{8}$ with center at origin, by shifting it $1$ unit to the right and $2$ units downward. By applying transformations, the endpoints of the vertices of the shifted ellipse are..


$
\begin{equation}
\begin{aligned}

(0, a) \to (0, 2 \sqrt{2}) \to (0+1, 2 \sqrt{2} - 2) =& (1, 2 \sqrt{2} - 2)
\\
\\
(0, -a) \to (0, -2 \sqrt{2}) \to (0+1, -2 \sqrt{2} - 2) =& (1, - 2 \sqrt{2} - 2)
\\
\\
(b, 0) \to (2, 0) \to (2+1, 0 -2) =& (3,-2)
\\
\\
(-b, 0) \to (-2, 0) \to (-2+1, 0 -2) =& (-1,-2)

\end{aligned}
\end{equation}
$



Now, the foci of the unshifted ellipse are determined by $c = \sqrt{a^2 - b^2} = \sqrt{8-4} = 2$. Then by applying transformations, the foci of the shifted ellipse are..


$
\begin{equation}
\begin{aligned}

(0,c) \to (0,2) \to (0 + 1,2-2) =& (1,0)
\\
\\
(0,-c) \to (0,-2) \to (0 + 1,-2-2) =& (1,-4)

\end{aligned}
\end{equation}
$


To sum it up,

eccentricity $\displaystyle \frac{c}{a} \to \frac{\sqrt{2}}{2}$

length of the major axis $2a \to 4 \sqrt{2}$

length of the minor axis $\displaystyle 2b \to 4$

Therefore, the graph is

Explain what DuBois believes is the problem with the 20th-century. What does he mean by "the color-line?"

In W.E.B. DuBois's seminal work, The Souls of Black Folk, the problem of the twentieth-century is, indeed, that of the "color-line."
The phrase "the color-line" first appeared in an article called "The Color Line" written by Frederick Douglass for the North American Review in 1881. It became better-known when DuBois used the phrase to expand its relevance for the issues confronting black Americans in the twentieth-century.
The color-line is a direct reference to the segregation that existed in the United States -- both the legal, de jure, segregation in the South, and the de facto, or "in effect," racism in the North and the West. Segregation made it so that blacks and whites lived in such disparate worlds that their lives generally did not look at all the same. Though black people were very often aware the rights and privileges that were kept from them, particularly since working-class blacks were very often employed in white homes as domestic laborers, many white people were blind -- often willfully -- to the inferior conditions in which black people existed.
The color-line created inequalities in education, housing, and access to employment. It made it nearly impossible for black and white people to have any amity between them. Existentially, it worked to convince black people of their presumed inferiority. 
However, DuBois was concerned not only with the conditions in which black people existed in the United States, but also the lives of darker peoples in other countries, particularly the colonies in Africa, Asia, and Oceania. The subjugation of these peoples was justified by pseudo-scientific racial theories which attempted to give "the color-line" a scientific basis. 

How does Turtle impact Taylor and challenge her to become a good mother? How does she change and grow through this relationship?

Turtle and Taylor have an unusual relationship in Barbara Kingsolver's novel The Bean Trees. Taylor is a free-spirited young woman who's off on a solo adventure. Turtle is the three-year-old that's handed, unexpectedly, to Taylor in a roadside restaurant. For Taylor, the restaurant was just a quick stop, a place to have something to eat, in a town where she knows no one.
How does Turtle impact Taylor and how does Taylor grow though their relationship? Let's go over a few main points.
Turtle compels Taylor to become a mother.
Taylor didn't choose to be a mother. It's only because Turtle has been forced onto her, and she doesn't know what to do, that Taylor becomes a caretaker for the child. Turtle's real mother has abandoned her, and Taylor feels obliged to step in, even though she doesn't know anything about taking care of a child. Here, Taylor first feels the attachment to Turtle:

The most amazing thing was the way that child held on. From the first moment I picked it up out of its nest of wet blanket, it attached itself to me by its little hands like roots sucking on dry dirt. I think it would have been easier to separate me from my hair.

Turtle makes Taylor seek out (and embrace) a community.
Taylor, before meeting Turtle, didn't need a community (or at least she didn't think she did.) She left her own mother and took off on a solo road trip. But when she's forced into a position where she feels like she has to take care of another person, she has to get practical and think about the logistics. She needs an affordable place to live, so she replies to an ad from another young woman who's looking for a housemate. That's how she meets Lou Ann, her friend and confidante who will become like a surrogate family for Taylor and Turtle. 
Turtle helps Taylor see the beauty of the environment.
As a little girl, Turtle loves to play in the dirt, to sing songs about vegetables, and to look at a seed catalogue. Taylor sees the land they're on in a different way after spending so much time with Turtle. Here, Turtle points out the bean trees to Taylor:

Turtle shook her head.
“Bean trees,” she said, as plainly as if she had been thinking about it all day. We looked where she was pointing. Some of the wisteria flowers had gone to seed, and all these wonderful long green pods hung down from the branches. They looked as much like beans as anything you’d ever care to eat.
“Will you look at that,” I said. It was another miracle. The flower trees were turning into bean trees.

Turtle helps Taylor see the importance of female friendship and support.
Taylor needs Lou Ann to help her with childcare. It's because of Turtle that she lets Lou Ann into a more intimate family space; as a result, she reaps the benefits of a family life with her friend and with their respective children. Here, Lou Ann speaks to Taylor:

"Taylor, remember that time you were mad at me because you didn't want us to act like a family? That all we needed was a little dog named Spot? Well, don't get mad, but I told somebody that you and Turtle and Dwayne Ray were my family. Somebody at work said, 'Do you have family at home?' And I said, 'Sure,' without even thinking. I meant you all. Mainly I guess because we've been through hell and high water together. We know each other's good and bad sides, stuff nobody else knows."

After establishing an unconventional family life with Lou Ann, Taylor doesn't need a man to complete the picture, and on top of that, she helps Lou Ann find her own independence after Lou Ann's been abandoned by her husband.
 
 

What is the significance of the title and how is it related to Daru's conflict?

In French, the title of this story is "L'hôte," and this word has two meanings when it is translated into English. Firstly, it means the 'guest' and relates directly to the Arab prisoner who is taken to Daru's school by Balducci and becomes his guest.
Secondly, the title of this story can also be translated as the 'host' and, in this instance, relates directly to Daru, who is forced to host the prisoner when Balducci arrives with him unexpectedly. It is this interpretation of the title which relates to Daru's conflict: he has no desire to host the prisoner and is disgusted by the crime the prisoner committed. Still, he refuses to hand him over to the police, as he explains to Balducci:

"Listen, Balducci," Daru said suddenly, "every bit of this disgusts me, and first of all your fellow here. But I won't hand him over. Fight, yes, if I have to. But not that."

It is only by letting the prisoner make his own choice (to flee or go to jail) that Daru is able to resolve this conflict.

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 4

Determine the integral $\displaystyle \int^{\frac{\pi}{2}}_0 \cos^5 x dx$


$
\begin{equation}
\begin{aligned}

\int^{\frac{\pi}{2}}_0 \cos^5 x dx =& \int^{\frac{\pi}{2}}_0 \cos^4 x \cos x dx
\qquad \text{Apply Trigonometric Identity } \cos^2x = 1 - \sin^2 x
\\
\\
\int^{\frac{\pi}{2}}_0 \cos^5 x dx =& \int^{\frac{\pi}{2}}_0 (1 - sin^2 x)^2 \cos x dx
\\
\\
\int^{\frac{\pi}{2}}_0 \cos^5 x dx =& \int^{\frac{\pi}{2}}_0 (1 - 2 \sin^2 x + \sin^4 x) \cos x dx

\end{aligned}
\end{equation}
$


Let $u = \sin x$, then $du = \cos x dx$, when $x = 0, u = 0$ and when $\displaystyle x = \frac{\pi}{2}, u = 1$. Therefore,


$
\begin{equation}
\begin{aligned}

\int^{\frac{\pi}{2}}_0 (1 - 2 \sin^2 x + \sin^4 x) \cos x dx =& \int^1_0 (1 - 2u^2 + u^4) du
\\
\\
\int^{\frac{\pi}{2}}_0 (1 - 2 \sin^2 x + \sin^4 x) \cos x dx =& u - 2 \cdot \frac{u^{2 + 1}}{2 + 1} + \left. \frac{u^{4 + 1}}{4 + 1} \right|^1_0
\\
\\
\int^{\frac{\pi}{2}}_0 (1 - 2 \sin^2 x + \sin^4 x) \cos x dx =& u - \frac{2u^3}{3} + \frac{u^5}{5} \left. \right|^1_0
\\
\\
\int^{\frac{\pi}{2}}_0 (1 - 2 \sin^2 x + \sin^4 x) \cos x dx =& 1 - \frac{2(1)^3}{3} + \frac{(1)^5}{5} - 0 + \frac{2(0)^3}{3} - \frac{(0)^5}{5}
\\
\\
\int^{\frac{\pi}{2}}_0 (1 - 2 \sin^2 x + \sin^4 x) \cos x dx =& \frac{15 - 10 + 3}{15}
\\
\\
\int^{\frac{\pi}{2}}_0 (1 - 2 \sin^2 x + \sin^4 x) \cos x dx =& \frac{8}{15}


\end{aligned}
\end{equation}
$

Describe the relationship between Emilia and Iago.

As the other educator pointed out, Iago is an overprotective, jealous, and domineering husband. The root of his bad behavior toward his wife Emilia originates from his contempt of her intelligence. In short, Iago doesn't think much of Emilia. She's a tool that he uses to further his ambitious ends.
In act 3, scene 3, Emilia tells Iago that she finally has possession of Desdemona's handkerchief. Recall that Iago had exerted continuous pressure on Emilia to steal the handkerchief in the past. Now that she has it, Emilia thinks that her husband will be pleased with her.
However, he displays nothing but contempt for Emilia. Iago rudely asks her why she's hovering about the place alone. When she hands him the handkerchief, he grabs it with a rude comment: "It is a common thing . . . to have a foolish wife." Iago doesn't thank Emilia. For her part, Emilia is a little irritated by Iago's poor treatment, and she demands, "What will you give me now / For the same handkerchief?"
Iago doesn't humor her with an answer, which upsets her. Now, unlike many past occasions, Emilia openly questions her husband about his intentions. However, Iago rebuffs her, as he always does. At this point, we begin to see Emilia exert her personal agency and begin to push back against Iago's abusive treatment. Emilia's loyalty to Desdemona compels her to do everything she can to protect her mistress.
Matters come to a head when Emilia discovers to her horror (in act 5) that her husband has betrayed Desdemona and accused her mistress of adultery. At this point, Emilia puts aside her characteristic submissiveness and turns on Iago.
She confronts not only Iago but Othello, as well, after the latter murders Desdemona. Emilia's courageous stand rests on her resolve to not "charm" her "tongue" any longer, while her mistress lies "murdered in her bed."
Emilia even tells Iago that she may never go home again, and she characterizes Iago's acts for what they are: evil.

'Twill out, ’twill out.—I peace?
No, I will speak as liberal as the north.
Let heaven and men and devils, let them all,
All, all cry shame against me, yet I’ll speak.

Emilia refuses to keep silent, and her boldness (unfortunately) leads to her death at Iago's hands.

To summarize: Emilia and Iago's relationship is initially unequal in nature. However, Emilia's last act of defending her mistress and the truth demonstrates that she is a better person than her husband. In death, Emilia retains her personhood and conscience.

Iago and Emilia's relationship doesn't appear to be based on love. But then that's probably because Iago is constitutionally incapable of love. Iago is insanely jealous of his wife and has got it into his head that she's been cheating on him with Othello. This isn't an expression of love, however, but of self-regard. Iago is very much a man of his time. The merest hint of infidelity on the part of his wife, however implausible, is a threat to his masculinity. Iago's reputation is everything to him, both as a man and as a soldier, and that reputation is damaged by any suggestion that Emilia's turned him into a cuckold.
Emilia, for her part, is absolutely devoted to her husband. She aims to please, and will do anything for Iago, even if it means being used as a pawn in a wicked plot to destroy Desdemona. Emilia is blissfully unaware of why Iago wants her to go and fetch Desdemona's handkerchief. She hasn't the faintest idea of what her husband proposes to do with it, but it really doesn't matter; all she wants to do is please her man:

I’ll have the work ta'en out And give ’t Iago. What he will do with it Heaven knows, not I. I nothing but to please his fantasy (Act III Scene iii).

In many respects, Iago and Emilia's relationship parallels that between Othello and Desdemona. Both women have the misfortune to be married to unworthy men, who treat them abominably. Yet Emilia and Desdemona respond to their husbands' jealousy, anger, and harsh words with love, kindness and forbearance. There is more than a hint of codependency about these relationships, and Emilia's codependency, like Desdemona's, ultimately leads to tragedy.

What did Kipling mean by "Cold, edged with dear-bought wisdom"?

The line in question comes from "The White Man's Burden," a poem that has gained considerable notoriety for its unabashed justification of Western imperialism. At the same time, one must recognize that, in writing the poem, Kipling was keen to stress the onerous responsibilities entailed by what he saw as the white man's great civilizing mission. It's a thankless task, says Kipling, addressing his audience of white imperialists; don't expect to receive much in the way of gratitude from the natives that you civilize:

Your new-caught sullen peoples, Half devil and half child.

The colonization of these dark and distant lands will not be easy, else it would be a delight and not a burden. Yet Kipling exhorts his audience to stick at it. One may have to endure years of thankless toil, but it'll be worth it in the end. Persistence will ultimately be rewarded with the admiration of one's peers.
Kipling is addressing his observations primarily to the United States government, inviting it to assume the same kind of responsibility for the Philippines—"take up the white man's burden"—as the British and other European colonial powers have done with their overseas territories. As a British citizen, Kipling feels that he speaks from a position of some authority, and is therefore entitled to advise the Americans as to the costs and rewards of the colonial enterprise.
In the final stanza of the poem, Kipling uses especially stirring rhetoric to drive his point home. The "thankless years" refer to the many years of struggle required to build a successful colony. Though undoubtedly a trying and difficult time, those years are valuable in that they provide a vital insight into colonial administration.
This is what Kipling means by "dear-bought wisdom;" European powers such as Great Britain now understand just what colonialism entails, but it took years of hard, practical experience before they were able to attain such knowledge. This "dear-bought wisdom" is "cold-edged," meaning that it is dispassionate, a kind of cold logic that doesn't take the feelings of the indigenous population into account. The rationality of the white man is subtly contrasted here with what Kipling would regard as the barbarism and superstition of the so-called lesser races.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 27

To prove 1/sqrt(1)+1/sqrt(2)+1/sqrt(3)+1/sqrt(4)+........1/sqrt(n)>sqrt(n)
n>=2
For n=2, 1/sqrt(1)+1/sqrt(2)~~1.707
sqrt(2)~~1.414
:. 1/sqrt(1)+1/sqrt(2)>sqrt(2)
Let's assume that for k> 2 , 1/sqrt(1)+1/sqrt(2)+1/sqrt(3)+.....+1/sqrt(k)>sqrt(k)
So, 1/sqrt(1)+1/sqrt(2)+1/sqrt(3)+....+1/sqrt(k)+1/sqrt(k+1)>1/sqrt(k+1)
or let's show that sqrt(k)+1/sqrt(k+1)>sqrt(k+1) ,k>2
Multiply the above inequality by sqrt(k+1)
sqrt(k)sqrt(k+1)+1>(k+1)
Rewriting the above inequality as below; shows that the above is true ,
sqrt(k)sqrt(k+1)+1>sqrt(k)sqrt(k)+1
:. 1/sqrt(1)+1/sqrt(2)+1/sqrt(3)+......+1/sqrt(k)+1/sqrt(k+1)>sqrt(k+1)
By the extended mathematical induction, the inequality is valid for all n,n>=2

Discuss the The Epistle to Dr. Arbuthnot in the light of the pope's remark "To attack vice in the abstract is but fighting with shadows."

In this particular line from the Epistle to Dr. Arbuthnot Pope is attempting to justify the satirizing of named individuals rather than simply condemning, in general terms, the vices of which they're guilty. Throughout his long and illustrious literary career, Pope was never backward when it came to subjecting his enemies—of whom there were many—to the full force of his biting, vituperative wit. In attacking named individuals, Pope believed that he was more effectively dealing with the various aesthetic vices of the age by focusing on their specific manifestations, rather than merely criticizing them generically. An abstract approach to the corruption of art and letters would have taken on the appearance of a philosophical essay or learned disquisition.
What Pope wanted to do in the Epistle to Dr. Arbuthnot, however, was to communicate to a specific audience. He knew that in order to do this he had to name names, as it were, to give the main thrust of his satire added force. The literary world of 18th century England was a very small and intimate one, and Pope knew it inside out. He also knew that his target audience would understand his references to various members of this exclusive clique. So even if, as he often did, he used only initials in his satires on specific individuals, it would be obvious to just about everyone to whom he was referring. The same would also apply to various pseudonymous characters in the Epistle such as "Bufo," "Sporus," and "Codrus."

what are the differences and similarities between Gatsby and Mr. Wilson?

One major difference between the two men is money. Gatsby has lots of it; George Wilson—not so much. George is just an ordinary small businessman, operating a none-too-successful garage in the Valley of Ashes. He has blonde hair like Gatsby, but he doesn't possess any of the great man's charm or charisma. When we're first introduced to him, it only takes a few words to describe him:

He was a blonde, spiritless man, anaemic, and faintly handsome. When he saw us a damp gleam of hope sprang into his light blue eyes.

But, at least, George has a certain rugged honesty about him. He may not be successful, but he's worked hard for every last penny. Gatsby's enormous wealth, on the other hand, has been made off the proceeds of various criminal enterprises.
What ultimately unites the two men, however, is that they are both destroyed by the American Dream. George is arguably the only truly grounded character in the book; he also is the only one who appears to believe in God. But he represents the forgotten class of the Jazz Age, the silent majority who simply put their heads down and worked hard while the East and West Eggers of this world carried on with wild parties, affairs, and riotous living.
For different reasons, neither George Wilson nor Gatsby truly belong to the Eggers' charmed world of wealth and opulence. Nor for that matter does Myrtle, and it's telling that all three of these characters die, with no one taking ultimate responsibility for their deaths. (George would appear to be in an impaired mental state when he kills Gatsby.) In that sense, George and Gatsby (and Myrtle, for that matter) are victims of the prevailing social system and its warped values, their tragic fates symbolizing the recklessness and heedless pursuit of wealth and status marking this period of American history, whose myriad casualties remain all but forgotten.

What did the Babylonians and Israelites have in common?

The Israelites and the Babylonians had more cultural differences than similarities. Their social structures were vastly different, as were their governments and religions. However, there are some similarities worth noting.
First of all, they employed similar technology. Having developed towards the end of the Bronze Age, they both employed the use of metal tools. Pastoralism and the farming of grain was practiced by both civilizations. They also developed sophisticated lunar calendars to plan and keep track of events such as holidays and harvests. Both had a week consisting of seven days (although the Babylonians also employed a five-day week in addition to the seven-day week).
The Babylonians and the Israelites spoke related languages. As part of the Semitic family of languages, Akkadian and Hebrew are closely related in syntax and grammar, meaning they would have sounded somewhat alike. Also, both were highly literate societies for their time, having produced a number of written records, many of which survive to this day.
Both the Israelites and the Babylonians had a written code of laws. The Babylonians are known for Hammurabi's Code, and the Israelites kept most of their laws in the Tanakh. These are some of the earliest known systems of codified law.
Finally, both were patriarchal societies in which men held political power and were in charge of family affairs.
https://www.biblicalarchaeology.org/daily/ancient-cultures/ancient-israel/daily-life-in-ancient-israel/

Babylonians and Israelites were both ancient peoples living in what we would today call the Middle East. Babylon was located in present-day Iraq, and ancient Israel was located in the region that includes present-day Israel/Palestine, Jordan, and Lebanon. Both cultures lost their territories to the Assyrians in the 6th century B.C.Israelites and Babylonians both spoke Semitic languages (Aramaic and Chaldean, respectively) and had similar tools and weapons typical of Late Bronze and Iron Age cultures. The keeping of written records on clay tablets was common in both cultures, and both cultures left lasting literary legacies: the Babylonians with the Epic of Gilgamesh, and the Israelites with most of the books of the Hebrew Bible. Because of Ancient Israel's cultural contact with, and later capture by the Babylonian Empire, both cultures had similar ideas and knowledge regarding astronomy and mathematics.
Because the two cultures flourished during the same periods and also due to their relative geographical proximity, Babylonians and Israelites shared much technologically, scientifically, and culturally, even before Ancient Israel's 6th century B.C. exile to Babylon.To learn more about both cultures, start below:https://www.history.com/topics/history-of-israel
https://www.ancient.eu/babylon/

How is love portrayed in this short story? How is it relevant to readers in modern times?

In this short story, love is portrayed as a risky endeavor, fraught with difficult decisions. In the story, the tension between the couple is palpable.
There is every indication that the man wants his girlfriend to have an abortion. He tells her that it is an "awfully simple operation" and that he has "known lots of people that have done it." The girl, Jig, is not so sure. She questions whether having an abortion will put their relationship back on track. Her companion, however, is focused on what he sees as a "problem": the baby he does not want to have. He repeats his assertion that the operation is a simple one, consistently invalidating the significance of such an operation for his girlfriend.
The strained exchange between the couple highlights the discrepancies between male and female interpretations of love. The story is certainly relevant to modern-day romances. Hemingway's portrait of a relationship in crisis invites us to ponder the true consequences of an abortion on a couple's relationship.  
Hemingway's story poses a very modern question: when a man and a woman differ about how they will address an unwanted pregnancy, what is the right course of action to take? In the story, the man embodies all the traits of Hemingway's quintessential male characters. Hemingway's man is focused on the present; he enjoys sexual escapades and wild, hedonistic nights of pleasure. However, he often miscalculates the consequences of his actions.
Likewise, the male character in "Hills Like White Elephants" not only fails to consider the effects of an abortion on his girlfriend, he also fails to consider how an abortion will impact their lives. Does Jig have an abortion in the story? Hemingway never tells us. However, an important question remains: is abortion always the right answer? The debate rages in our modern world, with both pro-choice and pro-life groups deeply opposed to each other's positions.

According to Guns, Germs, and Steel, explain some of the reasons why fertile crescent enjoyed such success while other regions faltered?

The answer to this question can be found in chapter 8 of Guns, Germs, and Steel, entitled "Apples or Indians." Diamond cites several advantages enjoyed by the Fertile Crescent that led it to become the first region to develop agriculture.
The first is that it "lies within a zone of so-called Mediterranean climate." This is a climate with long, dry summers and warm, wet winters. This makes for plant species that are ideal for domestication, because they put much of their energy into seeds, which are edible.
Another reason is that there were simply a lot of useful plants already native to the area. Diamond writes, "the wild ancestors of many Fertile Crescent crops were already abundant and highly productive," and their potential for domestication must have "been obvious to hunter-gatherers."
The Fertile Crescent also features a number of self-pollinating plants that can be cross-pollinated. This means they create a lot of varieties for potential farmers to select from.
All of these factors, Diamond argues, made the Fertile Crescent a logical site for the development of agriculture. But it also enjoyed some other advantages. First, it was bigger than similar Mediterranean zones around the world. Second, there was enough climatic variation from season to season to encourage the development of more annual plants. Third, it has the highest variation in altitude among other similar regions around the world. Fourth, it has more large domesticable animals than other Mediterranean zones. Finally, Diamond posits that agriculture in the Fertile Crescent may have faced less competition from hunter-gatherers than in other regions.

What rules does Jonas's society have to follow?

There is an extensive list of rules that citizens must obey in order to avoid being released from Jonas's community. Throughout the novel, Jonas is cognizant of these rules at all times, and the anonymous voice over the loudspeaker announces to the citizens when someone has broken a rule. The following is a list of a few of the utopian society's rules throughout the novel The Giver:
Pilots flying fighter jets cannot fly over the community, or they will be released.
Each member of the family must share their dreams with each other every day. 
Citizens are not allowed to hoard food and must eat their meals in designated areas. 
After experiencing puberty, citizens must take pills to suppress the "Stirrings" each day.
Citizens are limited to working in their assigned occupations. 
Citizens are prevented from having independent relationships with each other. 
Nobody is allowed to leave the community unless they are given specific clearance by the Committee of Elders. 
Fighting and lying are prohibited in the community. 
Family units must remain intact with two parents and two children of opposite genders. 
Bikes must be parked neatly in the bikeports and not left lying on the ground. 
Citizens are prohibited from using inflammatory or contradictory language throughout the community.
Each person must complete a certain number of volunteer hours before age 12.
Depending on their age group, citizens must wear assigned outfits and adopt prescribed hairstyles. 
Citizens must attend annual ceremonies.
A person is not allowed to see another person naked. If you do, you have to apologize. 

What are Stephen Kumalo's movements from the beginning of Cry, the Beloved Country to the end? What are the various areas of Johannesburg?

It looks like you need to trace Stephen Kumalo's movements in the novel. I'll provide brief notes about this. Please refer to the novel for further textual evidence regarding Stephen's movements.
1) After receiving a letter from Theophilus Msimangu (a priest), Stephen makes his way to Johannesburg to find his brother, John; his sister, Gertrude; and his son, Absalom. In Johannesburg, he stays with Mrs. Lithebe, a member of Msimangu's church.
2) In Johannesburg, Stephen makes his way to Claremont. There, he stops at Number 11 Hyacinth Street; this is where Gertrude and her son live. Here, Stephen convinces Gertrude to return with him to Ndotsheni. 
3) Still in Johannesburg, Stephen makes his way to John's shop. Here, John provides Stephen with the last known address for Absalom: Doornfontein Textiles Company at 14 Krause St. 
4) Stephen makes his way to the Doornfontein address, but Absalom is not there. The owners of the factory provide Stephen with another address for a Mrs. Ndlela, whom Absalom was supposedly staying with.
5) Stephen makes his way to 105 End Street in Sophiatown, but Mrs. Ndlela tells him that Absalom is now staying with Mrs. Mkize at 79 Twenty-third Avenue in Alexandra.
6) Mrs. Mkize tells Stephen that she does not know where Absalom is. However, she confesses that Absalom knows the taxi driver Hlabeni. When Stephen questions Hlabeni, the latter tells him that Absalom is now in Shanty Town, Orlando.
7) Stephen makes his way to Shanty Town in Orlando. There, a nurse tells him and Msimangu that Absalom used to stay with the Hlatshwayos in one of the houses there. At the Hlatshwayos, the lady of the house tells Stephen that Absalom was sent away to a reformatory.
8) Stephen makes his way to the reformatory, and the school official tells Stephen that Absalom is now living with his pregnant girlfriend in Pimville. However, Stephen does not find Absalom there.
9) Stephen pauses his search for Absalom. He visits the House for the Blind at Ezenzeleni with Msimangu.
10) Stephen is told that Absalom is in prison for killing Arthur Jarvis. So, Stephen makes his way to the prison in Johannesburg and reunites with Absalom.
11) Stephen goes to Pimville to meet with Absalom's pregnant girlfriend. There, he convinces her to marry Absalom and to move in with the Kumalo family.
12) In Chapter 25, Stephen meets James Jarvis (Arthur Jarvis's father) in Springs.
The story ends with Stephen returning to Ndotsheni after he discovers that Absalom will definitely be hanged for Arthur Jarvis's murder.

Calculus of a Single Variable, Chapter 3, 3.3, Section 3.3, Problem 27

Given: f(x)=x^(1/3)+1
Find the critical value(s) by setting the first derivative equal to zero and solving for the x value(s).
f'(x)=(1/3)x^(-2/3)=0
(1)/(3x^(2/3))=0
1=0
1=0 is not a true statement. A critical value cannot be found using the first derivative.
If f'(x)>0 the function increases on the interval.
If f'(x)<0 the function decreases on the interval.
The domain for the function is all real values for x.
Notice that f'(0)=undefined. This means the slope of the function at x=0 does not exist.
Choose an x value less than 0.
f'(-1)=1/3 Since f'(-1)>0 the graph is increasing on the interval (-oo,0).
Choose an x value greater than 0.
f'(1)=1/3 Since f'(1)>0 the graph is increasing on the interval (0, oo).
Since the function does not change direction there will not be a relative extrema.

What is the reaction of the lover when he is rejected by his beloved in the poem "The Last Ride Together" by Browning?

The lover in "The Last Ride Together" knows that his relationship with his beloved is over, but his reaction is to ask for one last ride with her. He knows that he has failed to secure a future with her and says, "Since all, my life seem’d meant for, fails," (line 4) (in other words, everything he wants in life has met with failure), he wants the memory of one last ride with her.  As he waits for her answer, he thinks that "life or death [was] in the balance" (line 16). His beloved relents and goes on a ride with the narrator.
The narrator's reaction to this ride is to live for the day, or carpe diem. He says, "So, one day more am I deified. Who knows but the world may end to-night?" (line 16). In other words, he decides to make the most of every moment because he does not know what the future holds. In several stanzas that follow, he decides that he is better able to live than a solider, a poet, a sculptor, or a musician because he lives in a world in which "the instant [is] made eternity" (line 108). The narrator is content to live in the perfection of the moment with his beloved.  

What does the dialogue between Roger and Mrs.Jones, as well as their actions, reveal about their character traits in "Thank You, Ma'am"?

The dialogue between Roger and Mrs. Jones reveals that they each know something about the other automatically, yet they also have something to learn.
Mrs. Jones, who walks home late at night, is familiar with the danger that she faces by doing so. Consequently, she has her purse weighted down with "everything but a hammer and nails" and is prepared to defend herself against purse snatchers. When Roger tries to steal this purse, she overpowers him, but realizes quickly that he is not really what might be termed a juvenile delinquent. For, Roger is polite when she asks, "Now, ain't you ashamed?" and he replies, "Yes'm."

The woman said, “What did you want to do it for?” The boy said, “I didn’t aim to.” She said, “You a lie!”

Although Mrs. Luella Bates Washington Jones is angry that this boy has tried to steal her purse, she is understanding of the boy. She tells him:

“But you put yourself in contact with me,” said the woman. “If you think that that contact is not going to last awhile, you got another thought coming. When I get through with you, sir, you are going to remember Mrs. Luella Bates Washington Jones."

Clearly, Mrs. Jones realizes that Roger has had no real parenting. So, with a kind but firm heart, she takes Roger home and makes a meal for him. And, with new respect for Mrs. Jones, Roger makes sure that he stands where she can see that he does not try to steal anything out of her purse. "He did not trust the woman not to trust him." Roger wants to earn some respect from Mrs. Jones.
Before he leaves, Roger is given supper and then Mrs. Jones gives him the money for some new shoes, telling him not to try stealing anymore.

“Now, here, take this ten dollars and buy yourself some blue suede shoes."

Roger wants to say more than just "Thank you, m'am," but the door shuts on him. He realizes that Mrs. Jones has been firm, but caring. Mrs. Jones has shown him that if he steals a purse, he takes a valuable possession from a real person.

What is it about Mrs. Sappleton's niece that causes Framton additional distress?

In the story, Mrs. Sappleton's niece, Vera, accompanies her story with acutely expressive facial and bodily expressions. It is these dramatic theatrics that cause Framton additional distress.
After telling Framton the Gothic story of how Mrs. Sappleton's husband and two brothers died, Vera shudders noticeably. Her dramatic action adds to the eerie nature of the story; being of a gullible nature, Framton becomes convinced of the truth of what he's hearing. He begins to see Mrs. Sappleton in a new light and thinks she is deluded. Poor Framton is thoroughly terrified but still remains seated, possibly because of his ingrained social training.
While Mrs. Sappleton continues talking about welcoming her husband and brothers, Vera further distresses Framton by resorting to more dramatics.

Framton shivered slightly and turned towards the niece with a look intended to convey sympathetic comprehension. The child was staring out through the open window with a dazed horror in her eyes. In a chill shock of nameless fear Framton swung round in his seat and looked in the same direction.

When the men do appear, poor Framton is terrified beyond endurance, and he flees the scene altogether. So, Vera uses Framton's trusting and gullible nature against him. By resorting to dramatic expressions, she is able to imbue her story with spine-chilling authenticity, an accomplishment that later causes Framton extreme distress.

Develop a communication strategy to inform clients, staff and other stake holders about the relocation of a community service organization to a nearby suburb. The new location is well served by public transportation, as it is close to a major shopping center, but staff parking will be limited.

A communication strategy that targets employees, customers/clients, and others about the pending relocation of a community service organization is relatively simple, especially in the era of electronic communications (email, for example). A modified version of the same basic bulletin can be applied to each category, and the message targeting employees can be the simplest.
Communicating to staff the planned relocation of the community service organization at which they are employed should be done as soon as practicable, as it may necessitate serious decisions among staff regarding the possible need to relocate residences or, given restrictions on staff parking space availability, changes to the way individual staffers commute to and from work. The message should lay out the facts—the organization is moving to a new location that offers convenient mass transit options that may be needed given limitations on parking spaces. The message should convey a sense of empathy for the staff who will be inconvenienced by the move but qualify that empathy with an emphasis on the positive aspects of the relocation (for example, the new location may be near a shopping mall that offers more lunch options and mass transit). The dates on which preparations for the move and the final relocation of personnel and equipment will be made should be included.
The communication strategy should be modified for customers by excluding staff-specific information, such as the lunch opportunities provided by a location near a shopping mall, but should include information intended to allay any concerns among clients anxious about change. The message should emphasize the benefits to clients of the relocation, such as the mass transit options available. (This is useful for clients without personal transportation and the elderly, who might be nervous about driving to new locations.) The ways in which the new location is better for clientele should be emphasized. Whereas messages to staff can be conveyed via email, messages to clients should be made via postal service. Hard copies of important bulletins are more reliable and personal than blast emails.
Regarding “other stakeholders,” modifications to the basic message may need to be tailored to specific individuals or organizations. This category of recipient should more closely mirror the message sent to clients, as it would be more formal. It should explain the rationale for the relocation and emphasize the benefits while noting that the move might involve inconveniences for some.

A communications strategy is designed to convey your organization's objectives and goals clearly to all stakeholders. The communication strategy usually begins with a statement of purpose--in other words, why you are producing the strategy. In this case, you could write that you want to convey to stakeholders why you are relocating the community service organization. 
You would then likely include an analysis of the current state of your organization, including a SWOT analysis. This involves looking at the strengths, weaknesses, opportunities, and threats to your organization. In this case, you could analyze what your organization is doing well (serving clients), as well as what your organization needs to achieve (which might include making your organization more accessible to clients). Your organization now has the opportunity to move to be more accessible to certain types of clients (such as those who need public transportation). The threat is that clients aren't perhaps coming to your current organization, as it's not well served by transportation. Another threat is that the new location doesn't include sufficient parking for staff.
You can then discuss your organization's objectives, or goals and how the communications department can help achieve those goals. For example, your goal could be to improve the accessibility of the organization to clients. To achieve this goal, the communications staff will reach out to potential clients by posting ads in the nearby shopping mall or through the media, explaining how the organization can help these clients and how accessible the new location will be for clients. The communications strategy should then identify key stakeholders, such as clients, staff, the board of trustees, grant organizations, etc., and discuss how you will reach them. For example, the communications department might want to provide success stories to the grant organizations and board of trustees to encourage them to continue to support the organization. 
The communications strategy should also develop the message it wants to deliver, as well as the method and plans for doing so. For example, if the message is that the new organization is more accessible to clients, who are visiting the nearby shopping mall and using public transportation, the message might include the convenience of the organization and how it can help clients in an efficient way. The message could be delivered through ads in the mall, designed by a publicity firm. Finally, the communications strategy should develop the means to evaluate how effective it has been. How will the organization know it has met its goals? Will it, for example, evaluate success based on the number of new clients that come to the new location in one year?

If the father is A- and mother is A+ then what will the child's blood group be?

The phenotype of type A blood can be produced by the following genotypes-- homozygous AA or heterozygous AO. Since the gene for A is dominant to O, the combination of AO will still result in a person with type A blood. Since we only know the parents blood type is A, if each parent is AA, then the offspring will be type A also. However, if each is type A with the genotype of AO, there is a 1 in 4 chance of producing a child with type O blood. The phenotype of O is produced when two O genes are inherited by the child.
Because the father has Rh negative blood, the only genotype that will produce that phenotype is two Rh negative genes. This is a recessive trait.
The mother has Rh positive blood. This can be produced by either two Rh positive genes, or one Rh positive and one Rh negative gene. Therefore, in this couple, if the father is (--) and the mother is (++), the child will be heterozygous but Rh positive(+-). Or, another possibility is that if the mother is heterozygous (+-) and the father is (--), the offspring will have a 50% chance of being Rh positive (+ ) and a 50% chance of being Rh negative ( -).
If we take into account the blood type and the Rh factor, the offspring of this couple can be type A or O and Rh positive or negative. 
https://www.redcrossblood.org/donate-blood/blood-types.html?icid=rdrt-blood-types&imed=direct&isource=redirect

Explain how weight is affected on other planets and why

Weight is a measure of gravitational force. What this means is that your weight depends on how hard you and a planet are pulling toward each other. If a planet has stronger gravity, it pulls you toward it harder; therefore, you would weigh more. If a different planet pulled weakly, you wouldn't weigh much at all. Newton's Law of Universal Gravitation states that gravity depends on the mass of the objects involved and the distance between them. Mass is a direct proportion. As mass increases, so does gravity. Distance is an inverse proportion. As the distance between any two objects increases, the gravitational attraction between them decreases. This is why we can't feel the sun's much larger gravity. It's way more massive than Earth, so it has a lot more gravity than Earth; however, it is roughly 92,000,000 miles away, and we are right next to Earth. We feel Earth's gravity.
https://www.exploratorium.edu/ronh/weight/

Who is the target audience?

The poem "Bomb" by Gregory Corso is an interesting poem for a variety of reasons. The first reason is that it is a shape poem. The text of the poem is not justified to the left, so the poem takes on the shape of an atomic bomb's mushroom cloud. The first 30 lines are the top of the wide mushroom, and the remaining lines make up the pillar of debris that is shooting up from the ground due to the explosion.
Another reason that this poem is interesting is because it is a satire. Satire is a technique that attempts to expose and/or criticize the corruption or ridiculousness of a person or society. The tools of satire are humor, exaggeration, and irony. A good example of irony in this poem is when the speaker talks about how much he loves the atomic bomb.

O Bomb I love youI want to kiss your clank eat your boom

Corso published this poem in 1958, so this places the poem after the end of World War II and the use of the two atomic bombs against Japan. The date also places the poem in the midst of the Cold War and rising fears of a nuclear holocaust. The world was becoming more and more terrified of atomic bombs, and Corso writes a poem that talks about how much he loves it while mixing in humor about death. Needless to say, the poem was not received well at first.
It is possible that Corso's intended audience was the political movers and shakers as well as the military leaders. That would make sense, because they are the people that have the power to do something about the bombs and rising fears. However, Corso denied that the poem had political significance. He called the poem a "death shot." It is intended to poke fun at people's obsessive focus on the bomb, and potential of death by bomb, when it is way more likely to die in any number of other normal ways. Based on this, it can be surmised that his intended audience is the general public that was living in fear of nuclear war between the United States and the Soviet Union. Corso is attempting to point out that the bomb is a natural progression of mankind's killing tools. The bomb is simply a new tool designed by humans to do the same thing that mankind's tools for war have been doing for hundreds of years.
I cannot hate you Do I hate the mischievous thunderbolt the jawbone of an ass The bumpy club of One Million B.C. the mace the flail the axe Catapult Da Vinci tomahawk Cochise flintlock Kidd dagger Rathbone Ah and the sad desparate gun of Verlaine Pushkin Dillinger Bogart And hath not St. Michael a burning sword St. George a lance David a sling Bomb you are as cruel as man makes you

What is the meaning of Ingsoc in 1984 by George Orwell?

In the novel 1984, INGSOC is an acronym for "English Socialism," which is the political philosophy adopted by Oceania's ruling Socialist Party. Orwell writes that the principles of INGSOC are doublethink, the mutability of the past, the denial of objective reality, and Newspeak. The Party controls every aspect of human life throughout the country and relies on propaganda, economic suppression, fear, and collectivism to oppress its population. The totalitarian regime relies on the tenets of INGSOC to maintain power and control the citizens. Doublethink, which is the ability to accept two contradictory views simultaneously, and the fabrication of history create the impression that Big Brother is omniscient. The Party also alters language using Newspeak, which effects one's capacity to articulate grievances against the government. Essentially, INGSOC is Oceania's Socialist philosophy that relies upon basic principles to control and oppress the population into benefiting the totalitarian regime.

The term Ingsoc is used in George Orwell's novel 1984. It was invented in the novel as one of the many neologisms that comprise "Newspeak," an artificial form of language associated with "doublethink" and designed to brainwash the public. It is not used outside this novel.
Within the framework of the novel, Ingsoc originally stood for "English socialism" but has come to mean the current social and political form of organization in Oceania. The basic structure of this society is sometimes also described as "Oligarchical Collectivism," in which the economy is state-controlled and collectivist but is run by an oligarchy (a small group of people) as opposed to democratic socialism where power is more broadly distributed.
The society is sometimes portrayed as a pyramid with "Big Brother" at the apex, followed by a small number of people belonging to the "Inner Party," a slightly larger group belonging to the "Outer Party," and finally at the bottom of the class hierarchy the masses or "proles" who are basically powerless and do various forms of menial labor.

Calculus of a Single Variable, Chapter 3, 3.3, Section 3.3, Problem 33

Given: f(x)=2x+(1/x)=2x+1x^-1
Find the critical values of x by setting the derivative of the function equal to zero and solving for the x-value(s).
f'(x)=2-1/x^2=0
2=1/x^2
2x^2=1
x^2=1/2
x=+-.707
The critical value is at x=.707, x=-.707 and x=0. The original function f(x) is not defined at 0.
If f'(x)>0, then the function is increasing on that interval.
If f'(x)<0, then the function is decreasing on that interval.
Choose any value for x that is less than -.707.
f'(-1)=1 Since f'(-1)>0, the function is increasing on the interval (-oo, -.707).

Choose any value for x that is in the interval (-.707,0).
f'(-.5)=-2 Since f'(-.5)<0, the function is decreasing on the interval (-.707,0).
Choose any value for x that is in the interval (0, .707).
f'(.5)=-2 Since f'(.5)<0, the function is decreasing on the interval (0, .707).
Choose any value for x that is greater that .707.
f'(1)=1 Since f'(1)>0, the function is increasing on the interval (.707, oo).
Since the sign of the derivative changed from positive to negative, there will be a relative maximum at x=-.707. The relative maximum is the point (-.707, -2.828).
Since the sign of the derivative changed from negative to positive, there will be a relative minimum at x=.707. The relative minimum is the point (.707, 2.828).

What are the similarities between Ralph and Jack's style of leadership in Lord of the Flies by William Golding?

Both boys are very charismatic and use their charisma to persuade others to follow them. The key difference of course is that Ralph uses his charisma for good, whereas Jack abuses his natural gift, using it to establish dictatorial control over the other boys. There's also something very practical about the two rival leaders. After he's indulged in a spot of fun like all of the other boys on the island, Ralph quickly gets down to business, organizing all of the things that need to be done, pulling up his sleeves and getting his hands dirty to set an example.
For his part, Jack understands the importance of establishing a regular food supply, which means going off to hunt pigs at every opportunity. Jack's practicality is tinged with self-interest; he doesn't hunt pigs out of the goodness of his heart to provide food for the other boys. Leading the brutal pig hunts gives him the power and control he so desperately craves.

Both Ralph and Jack choose to lead by example, and they both aggressively stand up to challenges in front of their group members in order to elevate their status as leaders. Also, Ralph and Jack both demand a lot from the members of their tribes. Ralph insists on maintaining a signal fire, building shelters, collecting water, and following the rules. Jack also insists that his tribe hunt pigs and follow his directives without questioning him. Both boys get upset when their members do not follow their instructions. Ralph and Jack also share a misunderstanding of how to lead a group of young boys properly. Ralph does not make individuals accountable for their actions. Jack uses fear to control his tribe. Although Ralph and Jack have drastically different agendas, they both wish to be respected leaders and have high expectations for the members of their tribes.

What were some similarities and differences between Descartes and Spinoza?

Descartes and Spinoza were both rationalist philosophers. This means that they believed that the ultimate truths of philosophy could be established by reason. Rationalism is often contrasted with empiricism, which holds instead that sense experience is the source of truth. To rationalists such as Descartes and Spinoza, however, the senses often deceive us; they can never therefore provide us with the absolute certainty necessary for knowledge of the world around us. For example, that stick that appears bent in the water really is not actually bent, and the moon on the horizon that seems such a short distance away is actually hundreds of thousands of miles away.
Spinoza greatly admired Descartes and used him as a point of departure in his own work. As with the French philosopher, Spinoza constructed an elegant rational structure which purportedly dealt with the most important questions in early modern philosophy. A central element in both Spinoza's and Descartes's respective systems is the relationship between mind and body. Descartes attempted to solve the mind-body problem. In other words, how is it possible for something spiritual—the mind—to interact with a physical entity—the body? For example, we know that mental states are often followed by physical acts. However, if the mind and the body are ontologically distinct substances, then how does this occur?
Descartes attempted to solve the conundrum by seeking to demonstrate that the mind was necessary for the body's survival. As far as interaction between mind and body was concerned, Descartes posited the rather fanciful theory that it took place in the pineal gland, a small gland in the center of the brain.
For Spinoza, there is no mind-body problem. For Spinoza, the mind and the body are not two separate substances, as Descartes believes, but just finite modes or modifications of a single substance, which Spinoza calls God or Nature. Whereas Descartes separates mind and body, Spinoza unites them. Mind is simply substance as conceived under the attribute of thought, whereas body is substance conceived under the attribute of extension. As there is no real separation between mind and body, the problem of their interaction simply does not arise.
As a devout Catholic, Descartes maintained a fairly orthodox position in regards to the question of God. Belief in God was a matter of faith; questions regarding his existence were a matter for theology, not philosophy. Spinoza, on the other hand, was, as a later thinker described him, a "God-intoxicated man." God was an essential part of Spinoza's entire structure of thought. His conception of God was highly unorthodox and earned him the condemnation and opprobrium of many believers. These were not just Christian believers; these were also members of the Jewish community of Amsterdam, into which Spinoza had been born.
Spinoza was what is called a pantheist, meaning that he believed that God and the universe were one and the same. To orthodox believers of religion, this was nothing short of rank heresy; indeed, Spinoza was formally excommunicated by the synagogue of Amsterdam largely on account of his heterodox opinions. In Spinoza's day, most people conceived of God as existing outside of his creation, separate and distinct. By bringing God and his creation together, Spinoza was openly challenging the prevailing theistic assumptions.
On philosophical grounds, Spinoza regarded God or Nature as the one substance, something that did not depend on anything else for its existence. Only God fits this description. Descartes, however, treated mind and body as separate substances. To him, substances were things that had certain attributes. For instance, the mind has the attribute of thought, whereas the body has the attribute of extension, in other words, it occupies space.

What are the main themes in the novel Across a Hundred Mountains?

Fragmentation—of one's identity, one's family, and one's whole way of life—is another important theme of the story. The grinding poverty in which Juana and her family find themselves is the main cause of this fragmentation. This poverty drives Juana's father to seek work in the United States. Inevitably, this has a damaging impact on family life, and these impacts are greatly exacerbated by Juana's own journey north of the border. The loving ties that have bound Juana and her family for so long have been dissolved by the abiding imperative to put food on the table.
In such an environment, religion—the traditional Roman Catholicism of Mexico—acts as a vital integrative force, challenging the fragmentation of family life that is the direct consequence of an economic system that dissolves collective wholes into atomized individuals. Juana may have been separated from her family, but she can never be truly separated from her religious identity. In the midst of all the heartbreak and suffering, religion provides Juana with much-needed solace, fortifying her against the numerous hardships she must endure. In the material world, all is fragmented. But in the realm of the spirit, togetherness prevails, and it is only by drawing deeply upon this vital inner resource that Juana is able to remain in touch with the primal unity to which we all belong.

One of the main themes in the novel Across a Hundred Mountains by Reyna Grande is the strength of family ties. Juana's father, Apá, travels across the Mexican–U.S. border to "el otro lado," or the other side, in search of a better life for his family. He is motivated to look for a better life, and for the American Dream, after his young daughter, Anita, dies in a flood. Though Juana, who is watching Anita during the flood, blames herself for her sister's death, Apá puts the blame on himself. He tells Juana, “It was my fault, Juana. I should’ve worked harder to get us out of there. I should’ve worked more hours, and little by little I could’ve built us a better house closer to town" (page 18). Apá dedicates himself to working to provide for his family, and he travels across the border to help them. Nineteen years later, Juana also decides to cross the border to look for her father, as she feels the tug of family and a deep commitment to them.
Another theme of the book is the way poverty defeats Juana and her family. Juana's mother, Amá, is crushed by the deaths of her children. The author writes:




"María died from a scorpion sting because they didn’t have enough money for a doctor and the healing woman couldn’t save her. Josefina died before leaving her mother’s womb. It was as if she had given up on life, even before she was born. One day she loosened her hold and was stillborn at four months" (page 19).




Amá's life has been incredibly cruel; her family is so devastated by poverty that one of her children died because the family didn't have access to medical care, while the other died in a flood. She lost another child while pregnant, and she is about to lose her husband, who must go north to the United States to find a better life for his family. She eventually turns to alcohol as a result of her sorrows.
Amá tries to find relief in religion, but it is of little solace to her. The author writes of Anita's funeral service:

"Juana looked through the cloud of incense smoke at her mother and father. They were holding on to each other and praying along with the neighbors and her father’s distant relatives. Four years ago, when her other younger sister died from a scorpion sting, Amá and Apá had held on to each other like now, but Juana had been put in between them, so they could share their grief as a family" (page 17).

The cloud of incense smoke obscures Juana's vision rather than helping her cope with the loss. While her parents seek relief in religion, which is another theme of the book, faith alone does not heal their deep wounds that have been caused by their life of privation and poverty.

College Algebra, Chapter 8, 8.3, Section 8.3, Problem 38

Find an equation for the hyperbola with vertices $(0, \pm 6)$ and passes through $(-5,9)$.
The hyperbola $\displaystyle \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$ has vertices on $(0,\pm a)$. So, the value of
$a = 6$. Also, if the hyperbola passes through the point $(-5,9)$. Then the point is a solution for the equation. Thus,

$
\begin{equation}
\begin{aligned}
\frac{(a)^2}{6^2} - \frac{(-5)^2}{b^2} &= 1 && \text{Substitute the given}\\
\\
\frac{81}{36} - \frac{25}{b^2} &= 1 && \text{Add } \frac{25}{b^2}\\
\\
\frac{81}{36} &= \frac{25}{b^2} && \text{Apply cross multiplication}\\
\\
81b^2 &= 900 && \text{Divide both sides by 81}\\
\\
b^2 &= \frac{100}{9} && \text{Take the square root}\\
\\
b &= \frac{10}{3}
\end{aligned}
\end{equation}
$

Therefore, the equation is
$\displaystyle \frac{y^2}{36} - \frac{x^2}{\frac{100}{9}} = 1 \qquad \text{or} \qquad \frac{y^2}{36} - \frac{9x^2}{100} = 1$

College Algebra, Chapter 1, 1.6, Section 1.6, Problem 70

Solve the nonlinear inequality $\displaystyle \frac{1}{x+1} + \frac{1}{x+2} \leq 0 $. Express the solution using interval notation and graph the solution set.

$
\begin{equation}
\begin{aligned}
\frac{1}{x+1} + \frac{1}{x+2} & \leq 0 \\
\\
\frac{(x+2)+(x+1)}{(x+1)(x+2)} & \leq 0 && \text{Multiply the LCD } (x+1)(x+2)\\
\\
\frac{2x+3}{(x+1)(x+2)} & \leq 0 && \text{Simplify the numerator}
\end{aligned}
\end{equation}
$


The factors on the left hand side are $2x+3$, $x+1$ and $x+2$. These factors are zero when $x$ is $\displaystyle \frac{-3}{2}$, -1 and -2 respectively. These numbers divide the real line into intervals
$\displaystyle (-\infty, -2), \left( -2, - \frac{3}{2} \right], \left[ -\frac{3}{2}, -1 \right), (-1, \infty)$




From the diagram, the solution of the inequality $\displaystyle \frac{2x+3}{(x+1)(x+2)} \leq 0$ are
$(-\infty,-2) \bigcup \left[ -\frac{3}{2},-1 \right)$

What is the theme of the first day?

The theme of the first day is the ecclesiastical corruption within the Roman Catholic church and the necessity of turning away from one's sins. Alternatively, one can also say that the theme of the first day is the need to overcome one's moral failings.
The small group enjoys the telling of ten stories on the first day. The first story by Panfilo centers on the corrupt Ciappelletto, who is able to trick a gullible friar into believing that he has lived an exemplary life. On his deathbed, Ciappelleto's inventive tales about his devout life earns him extreme unction, a last rite given only to faithful believers. In this story, Boccaccio satirizes the limitations of a deathbed confession and the arbitrary process of canonization.
The corruption of Church leadership is also the focus of much of the second story. Abraham, a Jew, converts to Christianity after witnessing the depravity of the ecclesiastical order in Rome. Although his actions seem ironic on the surface, he gives a good reason for his decision: despite the clergy's hedonistic lifestyle, the Christian faith continues to flourish. Abraham concludes that the religion must be sustained by God himself and is thus worthy of his loyalty.
The third story is an indirect critique of Catholic doctrine. It proposes that true religion is not limited to any one faith. When Melchizedek, the Jewish money lender, is questioned by Saladin, he proclaims that, just as the loving father cannot decide which of his three sons to bequeath his priceless ring to, neither the Jew, Christian, or Saracen may lay claim to being the only true faith.
In the fourth tale, we are given yet another example of ecclesiastical corruption. As the story goes, an abbot thinks to severely punish a monk for fulfilling his carnal desires with a nubile village girl. However, the wily monk catches the abbot in the same guilty act. He then proceeds to blackmail his superior, and both continue to take turns enjoying sexual pleasure at the expense of the young girl. 
In the fifth tale, we learn how the Marchioness Of Monferrato manages to repel the advances of the King of France. This story highlights the grace and character of a virtuous woman.
The sixth tale gives us yet another example of corruption within the Church. In this story, a friar who works as a religious inquisitor blackmails a wealthy man into parting with his money. He charges the man with being "overheated with wine or excess of mirth" and convinces him to pay up for the sake of his salvation. In the end, the wealthy man has the last laugh: he embarrasses the friar by his clever use of a scriptural verse and manages to free himself from the friar's avaricious grasp.
The seventh and eighth tales also address the sin of avarice or greed. In the seventh tale, Messer Cane della Scala is the Lord of Verona. One day, he decides to hire some entertainers for a performance but neglects to pay them adequately. Bergamino, one of the entertainers, decides to stay behind in the hopes of receiving some compensation for his efforts. Eventually, Bergamino gains an audience with della Scala and by a clever story, is able to get the nobleman to loosen his purse strings. In the eighth tale, Guglielmo is able to convince Messer Ermino de' Grimaldi to change his miserly ways. Both stories reinforce the necessity of forsaking one's sins and making amends for previous infractions.
In the ninth tale, a gentlewoman of Gascony manages to persuade the King of Cyprus to take action on her behalf. After being assaulted by a gang of never-do-wells, she takes her case to the king. However, she is warned that the king is so cowardly that she would never receive justice for her suffering. Undeterred, she approaches the king and censures him gently for his lack of courage. Embarrassed by her words, the king not only avenges the lady, but he also becomes a "very rigorous prosecutor of all who committed aught against the honour of his crown." This tale highlights the nature of cowardice, which some experts maintain is one component of the sin of sloth.
The tenth and last tale of the first day highlights the need to guard against presumption. Master Alberto manages to shame Malgherida for basing her judgment of him on her preconceived notions about older men. In all, the need to overcome one's moral failings, whether one is a member of the clergy or an average citizen, is the theme of the first day.
 

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 32

$\displaystyle \lim_{h \to 0} \frac{\sqrt[4]{16 + h} - 2}{h}$ represents the derivative of some function $f$ at some number $a$. State such an $f$ and $a$ in this case.

Recall the limit equation for the derivatives

$\lim\limits_{h \to 0} \displaystyle \frac{f(a + h) - f(a)}{h}$

We can see that the left side equation on the numerator is a square root base 4, So $f(x) = \sqrt[4]{x}$ and $a = 16$ as stated in the limit equation for derivatives.

To check if $a = 16$,

$f(a) = \sqrt[4]{a}$

$f(16) = \sqrt[4]{16} = 2$ just like the value of $f(a)$


Therefore,


$f(x) = \sqrt[4]{x}$ and $a = 16$

X is a normally distributed random variable with mean 57 and standard deviation 17. What is the probability that X is between 40 and 74?

Hello!
Actually, the probability density of the normally distributed random variable is known. The probability in question is the integral of this probability density over the given interval.
Because this integral is not an elementary function, it is common to use approximate computations, and a z-table is the most used tool. Such a table is for the standard normal distribution. To use it, we need to transform our data.
The general formula is L' = (L-mu)/sigma, U' = (U-mu)/sigma, where L is the lower value (40 in our case), U is the upper value (74),  mu is the mean (57) and sigma is the standard deviation (17). L' and U' are the equivalent endpoints for the standard normal distribution which may be used with a z-table.
Our case is somewhat special (very well-known), because
L-mu = 40-57 = -17 = -sigma, and  U-mu = 74-57 = 17 = sigma,
the limits are one standard deviation across the mean. The corresponding probability is about 68%, as we know from the mnemonic "68-95-99.7 Rule".
So the answer is about 0.68.
http://www.oswego.edu/~srp/stats/6895997.htm

Paper has few errors regarding typos, spelling, punctuation, and grammar (no fragment sentences and/or run on sentences). Paper uses language in creative and sophisticated ways,incorporating the author's voice throughout the paper.

To write a paper about Meeting at the Crossroads that addresses the concerns in this question, it's important to consider the meaning of the authors.  How did they get their data, what were their conclusions, and how did they present the information?
Lyn Mikel Brown and Carol Gilligan designed a study to examine how girls become women and how it affects their ability to relate their own experiences. The results of that study are what Meeting at the Crossroads is based on. They argued that girls become less competent at articulating their experiences as they lose individual freedom. Individual freedom is lost when girls are encouraged to act socially appropriate and conform to standards as they get older. 
It's important to be able to clearly express Brown and Gilligan's ideas, as well as to incorporate direct quotes from the text. For example, saying that the researchers paid close attention to how the girls expressed ideas nonverbally is a way of expressing your own understanding of the experiment. Saying that "It was the adult women in their lives that provided the models for silencing themselves and behaving like ‘good little girls' is a way of quoting Brown and Gilligan's conclusion directly—and directly incorporates the voice of the author. 
To use creative and sophisticated language, vary your sentence length and composition. Make some sentences short. Other sentences should be longer and contain more ideas and details. It makes your writing more dynamic and interesting.
To avoid typographical and grammatical errors, consider using an online grammar checker before you submit your work. There is no substitution for reading it through yourself, either. Reading it out loud is an especially effective way to find errors.
Sentences fragments are incomplete sentences. Each of your sentences should be a complete sentence. A run-on sentence is one in which two sentences are joined together in an incorrect way without the right punctuation.
If you cite direct quotes from the authors to support your own conclusions, edit your work for errors, and use attractive language, you will fulfill the requirements set forth in this question.

How could Wigglesworth's work have been both comforting and frightening?

The poet-minister Michael Wigglesworth became well known for his Puritan poem titled "The Day of Doom," which depicts Judgement Day as God sentences all men to Hell. Part of what makes Wigglesworth's poetry so damning is his complete refusal to show mercy to anyone. The poet spends line after line listing many different kinds of people whom he would expect to see in Hell. One particular passage reads:

Blasphemers lewd, and Swearers shrewd,
Scoffers at Purity,
That hated God, contemn'd his Rod,
and lov'd Security:
Sabbath-polluters, Saints persecuters,
Presumptous men and Proud,
Who never lov'd those that reprov'd;
all stand amongst this Crowd

Basically, Wigglesworth doesn't leave much room for anyone to escape eternal damnation. Of course, these ideas would be terrifying to many, particularly those who would prefer to believe in a merciful and forgiving God.
Much of his work focused on taking a similar path, with poems such as "Vanity of Vanities" and "To A Christian Reader" taking morbid and unsentimental approaches to physical life. The prior poem, for example, seems to suggest vanity to be a sin, particularly because he believes that Death is far more powerful than beauty. Basically, his poetry is very much of the proverbial fire and brimstone that makes much religious imagery graphic and frightening.
As to how his poetry is comforting, it would be plausible that like-minded Puritans would agree with Wiggleworth's damnatino of sinners, taking happiness and comfort that their way of life, the right way of life (they believe), will possibly spare them in the domain of the Lord.
https://biography.yourdictionary.com/michael-wigglesworth

What happens after the sniper puts his cap on his rifle in "The Sniper" by Liam O'Flaherty?

"The Sniper," a short story, describes a conflict between two unnamed snipers during the Irish Civil War in 1922. The main character is the Republican sniper, who has been camped out on a rooftop for hours, covering the street below him. He takes the risk of lighting a cigarette, knowing this will give away his position to anyone watching. The fire from the match is seen by another sniper, who manages to hit the Republican sniper in the arm, pinning him down behind cover on the rooftop. He is faced with a few choices. If he waits for daylight, he may succumb to his injury, or lose the advantage of darkness to cover his position. If he attempts to escape, he will be seen immediately, and probably killed. His injury also renders him unable to use his rifle. He still has a revolver with him, so he decides (unannounced to the reader) to trick the enemy sniper into revealing himself, so the Republican sniper can kill his enemy with the revolver.
To do this, the Republican sniper places his hat on top of his rifle, and raises the cap into view, so it will look as if he is attempting to peer out from behind cover. The enemy sniper takes the bait and shoots at the cap, hitting it, and the Republican sniper pretends to die, even dropping his (useless) rifle off the roof, in order to mislead his opponent. The trick works; the enemy sniper believes the Republican is dead, and stands up, revealing himself. The Republican sniper then kills him with the revolver, leading to the story's tragic ending; on inspecting the dead sniper's body, the Republican discovers the sniper was his own brother.

What was the role of women in the English colonies?

Women in the English colonies had three primary objectives: to maintain their households for their husbands, to productively submit themselves to men, and to operate as the spiritual backbone of their home.
Girls were expected to assume the tasks of adult women when they turned 13 years old, and women were largely expected to marry by the age of 20. By doing so, they found some sort of legal identity through the representation of their husband. Otherwise, women had few legal rights; they could not vote or hold public office.
Thus, most of their work took place within and around the home; these tasks included churning, spinning, weaving, mending and cleaning clothes, making candles, dyeing cloth, gardening, tending to livestock, raising children, and preparing meals.
Acting outside of the appropriate gender roles could result in women being shunned by the rest of society or punished. With little to no formal education (outside of sometimes being taught to read the Bible) and the watchful eye of religious establishments, women had little choice but to stay strictly in line with tradition.

Single Variable Calculus, Chapter 4, 4.5, Section 4.5, Problem 38

Use the guidelines of curve sketching to sketch the curve. $\displaystyle y = \frac{\sin x}{2 + \cos x}$

The guidelines of Curve Sketching
A. Domain.
The domain is $(-\infty, \infty)$

B. Intercepts.
Solving for $y$-intercept, when $x = 0$
$\displaystyle y = \frac{\sin 0}{2 + \cos 0} = 0$
Solving for $x$-intercept, when $y = 0$
$\displaystyle 0 = \frac{\sin x}{2 + \cos x}$

C. Symmetry.
Since $f(-x) = -f(x)$, the function is symmetric to origin.

D. Asymptotes.
Since the domain is $(-\infty,\infty)$, we can say that the function has no vertical asymptote.

E. Intervals of Increase or Decrease.

$
\begin{equation}
\begin{aligned}
\text{if } f(x) &= \frac{\sin x}{2 + \cos x} \quad \text{, then by using Quotient Rule}\\
\\
f'(x) &= \frac{(2 + \cos x)(\cos x)-(\sin x)(-\sin x)}{(2+\cos x)^2} = \frac{2\cos x + \cos^2 x + \sin^2 x}{(2 + \cos x)^2}\\
\\
f'(x) &= \frac{2 \cos x + 1}{(2 + \cos x)^2} \quad \text{; recall that } \sin^2x + \cos^2 x = 1
\end{aligned}
\end{equation}
$

when $f'(x) = 0$,
The critical numbers are, $\displaystyle x = \pm \frac{2\pi}{3} + 2 \pi n \quad$ where $n$ is any integer


F. Local Maximum and Minimum Values.
Since $f'(x)$ changes from positive to negative at $\displaystyle x = \frac{2\pi(3n+1)}{3}, \quad f \left( \frac{2\pi(3n +1)}{3} \right) = \frac{\sqrt{3}}{3}$ is a local maxima. On the other hand, since $f'(x)$ changes from negative to positive at $\displaystyle x = \frac{2\pi}{3} (3n + 2), \quad f \left( \frac{2\pi(3n+2)}{3} \right) = -\frac{\sqrt{3}}{3}$ is a local minima.

G. Concavity and Points of Inflection.

$
\begin{equation}
\begin{aligned}
\text{if } f'(x) &= \frac{2 \cos x + 1}{(2 + \cos x)^2} \quad \text{, then by using Quotient Rule and Chain Rule}\\
\\
f''(x) &= \frac{(2 + \cos x)^2 (-2\sin x)- (2 \cos x +1) \left(2 (2 + \cos x)(-\sin x) \right)}{\left[ (2 + \cos x)^2 \right]^2}
\end{aligned}
\end{equation}
$

Which can be simplified as...
$\displaystyle f''(x) = \frac{2 \sin x(\cos x -1)}{(2+ \cos x)^3}$
So, $f''(x) < 0 \text{ on interval } \left( \pi (2 n - 1) , 2\pi n\right)$
H. Sketch the Graph.

What is the expected lifetime for a star with twice the mass of the sun?

The Main-Sequence Lifetime of stars charts the approximate lifetime of stars.  The chart is based on the mass and luminosity of the star.  There is a correlation between mass and luminosity as well.  The sun is given one solar mass and one solar luminosity.  The expected lifetime for the sun is about 10 billion years.  A star with twice the mass would be ten times as bright, but live only 2 billion years (or about 1/5 as long).
Stars with more mass do not last as long because they burn fuel at a faster rate.  A star with twice the mass of the sun would burn its fuel about ten times faster.  The timeframes are estimates and based largely on the luminosity, which is an indicator of fuel consumption.  The lifetime could vary by a few billion years. 
http://cseligman.com/text/stars/mldiagram.htm

https://www.coursehero.com/file/p7d143f/A-star-with-twice-the-mass-of-the-sun-will-have-a-luminosity-11-times-greater-A/

In Kazuo Ishiguro's The Remains of the Day, is there a difference between Stevens' idea of dignity and that of greatness?

Stevens’ ideas of dignity and greatness are connected, both qualities relying on each other, yet distinct in their presentation. Stevens discusses at length what it is that makes a great butler. He summarizes it using his father’s words: Dignity in keeping with the position. No matter what, a butler must keep his dignity strong, letting no emotion or personal opinion be visible to his employer. The stereotypical British “stiff upper lip” or restraint is synonymous with Stevens’ opinion of dignity. Therefore, dignity leads to greatness.
Greatness is the quality that Stevens attempts to show in two characters: Stevens himself and Lord Darlington. Having defined greatness, Stevens tries to show himself in this light. During many times of awkwardness or tragedy, Stevens shows restraint, though at times his feelings are obvious, such as the death of his father. However, he never admits to the trouble, merely saying that he is tired.
As for Lord Darlington, Stevens wants to present his employer by the best interpretation of his actions before World War II, in which Lord Darlington was a Nazi sympathizer. Stevens views his employer’s actions as coming from the best of intentions and an honorable heart, but afterward he is considered a traitor. However, Stevens’ own greatness is tied to that of Lord Darlington. When it is clear that Lord Darlington is not a great man, Stevens’ own dignity is shattered, evidence that he has wasted his life serving a man who is less than honorable. While he has tried to convince the reader throughout the novel that both he and Lord Darlington have some measure of greatness by their dignity, he at last comes to admit that neither one does, both having pledged their support to someone who is not what he seemed to be. Stevens doubts that he can lay claim to either one of these qualities, dignity or greatness,  since Lord Darlington has been discredited in each.

f(x)=2/x n=3,c=1 Find the n'th Taylor Polynomial centered at c

Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of f^n(x) centered at x=c. The general formula for Taylor series is:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...
To determine the Taylor polynomial of degree n=3 from the given function f(x)=2/x centered at x=1 , we may apply the definition of Taylor series.
To determine the list f^n(x) up to n=3 , we may apply Law of Exponent: 1/x^n = x^-n  and  Power rule for derivative: d/(dx) x^n= n *x^(n-1) .
f(x) = 2/x or 2x^(-1)
f'(x) = d/(dx) 2/x
            = d/(dx) 2x^(-1)
           = 2*d/(dx) x^(-1)
           =2*(-1 *x^(-1-1))
           =-2x^(-2) or -2/x^2
f^2(x)= d/(dx) -2x^(-2)
            =-2 *d/(dx) x^(-2)
           =-2 *(-2x^(-2-1))
           =4x^(-3) or 4/x^3
f^3(x)= d/(dx) 4x^(-3)
           =4 *d/(dx) x^(-3)
          =4 *(-3x^(-3-1))
          =-12x^(-4) or -12/x^4
Plug-in x=1 , we get:
f(2)=2/1 =2
f'(2)=-2/1^2 = -2
f^2(2)=4/1^3 =4
f^3(2)=-12/1^4 = -12
Applying the formula for Taylor series, we get:
sum_(n=0)^3 (f^n(1))/(n!) (x-1)^n
=f(1)+f'(1)(x-1) +(f^2(1))/(2!)(x-1)^2 +(f^3(1))/(3!)(x-1)^3
=2+(-2)(x-1) +4/(2!)(x-1)^2 +(-12)/(3!)(x-1)^3
=2-2(x-1) +4/2(x-1)^2 -12/6(x-1)^3
=2-2(x-1) +2(x-1)^2 -2(x-1)^3
The Taylor polynomial of degree n=3  for the given function f(x)=2/x centered at x=1 will be:
P_3(x)=2-2(x-1) +2(x-1)^2 -2(x-1)^3

How was the Etruscan culture different from other Eastern Mediterranean cultures?

Because Greek culture (as an Eastern Mediterranean culture) was closely connected to the Etruscan culture, you may also wish to compare the architecture of the respective temples. 
Etruscan architects often placed columns at the front of the building. The columns would create a porch area at the entrance to the temple. In contrast, Greek architects placed columns and steps all around the temple, making the front and back of the building indistinguishable. Unlike Greek temples, Etruscan temples also often had three cellas, which housed three Etruscan gods: Uni, Tinia, and Menrva.
More information and differences between Greek and Etruscan temples can be found here.
Source: Gardner's Art through the Ages: Backpack Edition, Book A: Antiquity by Fred S. Kleiner

The Etruscan culture differed from that of other Eastern Mediterranean cultures in terms of language, women's roles, and art. 
In terms of language, the Etruscans used the Greek alphabet; however, Etruscan words bore no similarities to Greek words and were unrelated to other Indo-European languages.
In regard to women's roles, it was said that Etruscan women were sexually uninhibited and highly promiscuous creatures. Unlike Greek women, Etruscan women enjoyed the same rights as men and often indulged in lustful extra-marital relationships. It was said that Roman women participated in the social sphere much as Etruscan women did. However, unlike Estruscan women, Roman women did not engage in the ecclesiastical or political spheres. Etruscan women were said to be feminists long before the word came into existence.
As for the Greeks, it was said that they were appalled by the Etruscans' lax rules regarding male and female public discourse. Etruscan wives attended public banquets side by side with their husbands. The Greeks considered it uncouth for men and women to dine together. In fact, the only Greek women who openly dined with men were prostitutes. Also, while Etruscan women were featured nude in paintings, the Greeks and Romans considered female nudity in art vulgar. So, Etruscan social mores differed from those in other Eastern Mediterranean countries. While Greek fathers decided the fate of their children, Etruscan families often raised illegitimate children side by side with legal siblings.
Sources: 
1) Aztec Treasure House by Evan Connell.
2) Encyclopedia of Women in the Ancient World by Joyce E. Salisbury
https://diotimawcc.wordpress.com/

https://www.ancient.eu/Etruscan_Language/

Why is it reasonable to describe a large ecosystem like a biome as being in equilibrium, but not a very small ecosystem like a rotting log?

An ecosystem is an interdependent system comprised of living, nonliving, and dead components. Nonliving elements, such as light from the sun and carbon, are essential for plants ability to synthesize carbohydrate energy. As organisms die, their nutrients are utilized by other members of the ecosystem community. Fungus, in particular, is a decomposer that aids in breaking down dead matter.
A log is part of a dead tree. It can be home to organisms such as moss, fungi, mold, and bacteria. However, it does not contain the nonliving elements that are essential to create a full cycle of energy exchange between living, nonliving, and dead materials. Without sunlight, moss is unable to photosynthesize the energy it needs to thrive. Without oxygen, bacteria cannot metabolize the carbohydrates found in the chlorophyll of a dead plant. Although a log can be a member of an ecosystem community, it does not contain all of the components necessary to be its own ecosystem.
 
https://en.wikipedia.org/wiki/Ecosystem

What is the main message in "The Veldt"?

As in so much of his fiction, Bradbury warns us against allowing technology to get the upper hand in our lives.
In this story, the Hadley parents initially believe they are doing the best possible thing in buying the state-of-the-art HappyLife home, an expensive nursery with televised walls which does everything for them.
What they do not realize until too late is that a technology that does everything for a family will soon come to control the family. Lydia feels anxious and displaced with nothing to do. The children, Wendy and Peter, soon come to see the nursery as a better and more indulgent parent to them than their own parents. They come to hate their real parents as an impediment to their happiness.
As the story illustrates, the old-fashioned virtues of a simple home and parents who actually raise and discipline their children are far healthier than relying on technology to make life easier. In the end, in fact, technology does not make life easier but instead leads to death.

One could argue that Bradbury's main message in the short story "The Veldt" is that over-reliance on technology can negatively affect humanity. In the short story, the completely automated HappyLife Home does everything for the Hadley family, and the children have virtually no responsibilities. George and Lydia rely on their automated smart home to complete every task, and their children realize that the parents are irrelevant. Wendy and Peter become consumed with their nursery, which displays three-dimensional realistic landscapes that reflect their thoughts and feelings. Wendy and Peter view their technologically advanced nursery as more important than their parents, and their negative feelings toward George and Lydia are reflected on the nursery screens as the African veldt. When the psychologist David McClean visits the Hadley home, he encourages George and Lydia to close the nursery for a while and says,

You’ve let this room and this house replace you and your wife in your children’s affections. This room is their mother and father, far more important in their lives than their real parents.

After their parents lock the nursery, Wendy and Peter throw tantrums and become increasingly hostile toward them. Eventually, George and Lydia find themselves locked in the nursery, which displays the African veldt that comes to life and leads to their death. Overall, Bradbury's short story explores the negative effects of over-reliance on technology by illustrating how technology can destroy a family and ruin the most meaningful relationships between parents and their children.

Arguably, the main message of "The Veldt" is that people should not be over-reliant on technology, and this is shown clearly by the story's main events.
When the Hadleys install the HappyLife Home, they believe that they are doing something good for their children. As George says:

But nothing’s too good for our children.

However, as the story progresses, we see that the HappyLife Home has a number of negative aspects. For a start, Lydia feels that the HappyLife Home threatens her role as a mother since she is no longer required to carry out her maternal tasks, like feeding and clothing her children. The new nursery takes care of everything, leaving her feeling without purpose.
In addition, the story's violent conclusion, in which the Hadleys are attacked by lions, demonstrates that the HappyLife Home is indeed the stuff of nightmares.
Through these events, Bradbury warns his readers that while technology may appear to offer a solution to every problem, we must proceed with extreme caution before accepting it into our lives.

College Algebra, Chapter 8, 8.1, Section 8.1, Problem 20

Determine the focus, directions and focal diameter of the parabola $\displaystyle x - 7y^2 = 0$. Then, sketch its graph.



The equation $\displaystyle x - 7y^2 = 0; y^2 = \frac{x}{7}$ is a parabola that opens to the right. The parabola has the form $y^2 = 4px$. So


$
\begin{equation}
\begin{aligned}

4p =& \frac{1}{7}
\\
\\
p =& \frac{1}{28}

\end{aligned}
\end{equation}
$


So, the focus is at $\displaystyle (p,0) = \left(\frac{1}{28},0 \right)$ and directrix $\displaystyle x = -p = \frac{-1}{28}$. Also, $\displaystyle 2p = 2 \left( \frac{1}{28} \right) = \frac{1}{14}$, thus the endpoints of the latus rectum are at $\displaystyle \left( \frac{1}{28}, \frac{1}{14} \right)$ and $\displaystyle \left( \frac{1}{28}, \frac{-1}{14} \right)$. The focal diameter is $\displaystyle 4p = 4 \left( \frac{1}{28} \right) = \frac{1}{7} $ units. Therefore, the graph is

Because of the differences in political, social, and economic institutions established during the initial period of colonization, why were the British colonies in North America better suited for self–government than their Spanish counterparts?

The early British (and Dutch, too) colonies were better suited for self-government because they were mostly comprised of proprietary (owned by businesses or individuals; such as New Amsterdam, later New York) colonies and religious colonies, peopled by Europeans seeking a place to practice to their religious beliefs and customs without monarchial interference (e.g., Plymouth, Massachusetts Bay, or Maryland). The third type of colony in the "New World" was the royal colony. These colonies were under direct supervision and governance of a European monarchy. The Spanish colonies were royal colonies and therefore were not granted self-governance. In the case of religious colonies, the British crown was happy to be free of those who did not conform to the religious dictates of the crown. In the case of proprietary colonies, as long as they made money for the owner individual or business, they were more or less able to govern themselves. Proprietary colonies were often more likely to be tolerant and inclusive—commerce and profit were the primary concerns.

How do William Wordsworth's poems "Daffodils" and "Solitary Reaper" establish him as a poet of nature?

Wordsworth is the poet of nature because, for him, nature isn't just a thing of beauty. Rather, in his works, nature achieves sublimity. He takes it to spiritual and divine heights, acknowledging nature's ability to affect him in these ways.
In "Daffodils," the speaker certainly does appreciate nature's beauty, saying that he "gazed—and gazed—but little thought / What wealth the show to me had brought," speaking of the dancing and "jocund" daffodils that so arrested his attention. It is only later that he realizes the power the memory of those flowers has to impart "bliss" and fill his heart with "pleasure." They have affected his soul, and even just the memory is powerful enough to alter his state of mind and sense of well-being.
In "The Solitary Reaper," the beautiful song of the young woman in nature is enough to fill the vale in which she labors. The speaker says that her voice is even more beautiful than the nightingale or the cuckoo, and her song seems to enhance the natural world around her, emphasizing her connection to nature. Working alone in this natural and innocent setting, girl and song and nature seem to be one, and the music she creates stays with him long after he leaves. He carries it "in [his] heart" now, just like he carries the memory of the daffodils. He has been irrevocably affected for the better.

In both poems ("Daffodils" is often called "I Wandered Lonely as a Cloud"), Wordsworth shows how nature can touch the human soul. He loves nature and explains how long its positive benefits can last. In "I Wandered Lonely as a Cloud," the poet comes across a field of daffodils dancing in the wind before a lake. This simple scene from nature fills him with joy. The sight of the daffodils is "wealth" to him as he gazes at them, transfixed.
"The Solitary Reaper" is slightly different, in that Wordsworth likens a human to a wild creature of nature. Walking in the Scottish Highlands, he is arrested by the beautiful, mournful song a woman sings as she reaps. He compares her song to a nightingale's and a cuckoo's. He says it is even more beautiful. 
In both cases, the poet ends by noting that the natural beauty he saw or heard enters his soul and stays with him. In "The Solitary Reaper," he writes:

The music in my heart I bore, 
Long after it was heard no more.

 
In "I Wandered Lonely as a Cloud," he comments: 
 


For oft, when on my couch I lie 
In vacant or in pensive mood, 
They flash upon that inward eye 
Which is the bliss of solitude; 
And then my heart with pleasure fills, 
And dances with the daffodils.