What is the best way to get stronger Pokemon in Pokemon Go?

The trick to playing Pokemon Go and getting strong Pokemon is focusing on leveling up your character.






 






Don't worry about powering up Pokemon until you are a higher level; you'll gain levels quickly—and you'll catch higher level Pokemon later.




 






So if the best way to get strong Pokemon is to level up your character, what is the best way to level up your character?
 
The best way to power level is to save all your Pidgeys, Weedles, Ratatas, etc. and then evolve them all at once when you have a lucky egg running.  A lucky egg doubles all XP you get for 30 minutes.




 






You get your first lucky egg at level 9, or you can buy one with real money.




 






I have done this three times now.  I saved a bunch of simple Pokemon and then evolved a ton of Pidgeys, Weedles, and Zubats. I went from level 11 to 14, and later from 17 to 19. With my final egg I leveled up from 20 to almost 21.




 






Now that I am at a higher level, I find Pokemon that are also at higher levels.  For example, when I was a lower-level character I had a Flareon and I invested a ton of Eevee candies/stardust into that Flareon, making it as strong as possible—about 800 cp.  But then two days later, after I power leveled and gained 5 levels, I caught an Eevee that was around 550 cp, evolved it, and without powering it up at all I got a 1200 cp Vaporeon. 
 
Don't make the same mistake I did.  Wait until you are a higher level before using your candies and dust to level up your Pokemon.

Discuss the final usage of fire and the natural setting. Why is it significant that the Creature determines to immolate himself? Why is it appropriate that he will do this when he reaches the North Pole?

One of the first elements the Creature understands in his recollection is fire. At first, he finds the heat of a fire pleasant; when he puts his hand into it, he recalls the feeling of confusion that something could be capable of causing such disparate sensations. Later, when he has approached the cottage dwellers and been rejected, fire takes on another meaning. He immolates the cottage out of a sense of fury at what has happened to him. At the same time, revenge is "kindled" in his heart towards his creator.
After the Creature has returned to his creator, fire appears again; this time, the "fire of love" expresses his desire for a mate. Fire, then, has signified almost every emotion the Creature has strongly felt in his short life. It is fitting, then, that the creature seeks the opposite extremity—the "furthest corner of the globe"—to commit himself to fire and remove all trace of his being from the earth. He is determined to escape humanity as far as possible so that nobody else will ever attempt to replicate a creature such as him. He declares his desire to "exult in the agony" of flames, experiencing the simultaneous pain and joy he first felt when he put his hand into the fire.

List descriptive details that help you visualize the marketplace in which the astrologer conducts his business, in the story "An Astrologer's Day"

The marketplace and its vendors is described in fairly vivid detail in "An Astrologer's Day" by R. K. Narayan. India is often described by first time visitors as a place of many colors, smells and textures, especially the outdoor markets where vendors of food, crafts and clothing sell their wares. The astrologer wears a "saffron-colored turban" wrapped around his head and "this color scheme never failed." He says customers are drawn to him "as bees are attracted to cosmos or dahlia stalks." Before we even see the marketplace we see that it will be a place of visual splendor, based upon the description of the astrologer's preparations.
The place itself is a bustle of activity. The astrologer's location in the market is "under the boughs of a spreading tamarind tree." One visual detail that seems important and which makes it possible to imagine how it looks is the fact there there is no municipal lighting, so vendors must provide their own lights. So the market place is not consistently lit and this adds to its unique visual appeal:

One or two had hissing gaslights, some had naked flares struck on poles, some were lit up by old cycle lamps, and one or two, like the astrologer's, managed without lights of their own. It was a bewildering criss-cross of light rays and moving shadows.

This passage is followed by a description of the astrologer's way of doing business: it is discovered he knows almost nothing about astrology, and simply speaks as the mood takes him, so the random quality of light and shadow seems appropriate here.
 
 
 

Precalculus, Chapter 1, 1.2, Section 1.2, Problem 64

Find the intercepts of the equation $y = x^4 - 1$ and test for symmetry.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

y =& x^4 - 1
&& \text{Given equation}
\\
0 =& x^4 - 1
&& \text{To find the $x$-intercept, we let } y = 0
\\
1 =& x^4
&&
\\
\pm 1 =& x
&&

\end{aligned}
\end{equation}
$



The $x$-intercepts are $(-1,0)$ and $(1,0)$

$y$-intercepts:


$
\begin{equation}
\begin{aligned}

y =& x^4 - 1
&& \text{Given equation}
\\
y =& (0)^4 - 1
&& \text{To find the $y$-intercept, we let } x = 0
\\
y =& -1
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,-1)$

Test for symmetry

$x$-axis:


$
\begin{equation}
\begin{aligned}

y =& x^4 - 1
&& \text{Given equation}
\\
-y =& x^4 - 1
&& \text{To test for $x$-axis symmetry, replace $y$ by $-y$ and see if the equation is still the same}

\end{aligned}
\end{equation}
$


The equation changes so it is not symmetric to the $x$-axis

$y$-axis:


$
\begin{equation}
\begin{aligned}

y =& x^4 - 1
&& \text{Given equation}
\\
y =& (-x)^4 - 1
&& \text{To test for $y$-axis symmetry, replace$ x$ by $-x$ and see if the equation is still the same}
\\
y =& x^4 - 1
&&

\end{aligned}
\end{equation}
$


The equation is still the same so it is symmetric to the $y$-axis

Origin:


$
\begin{equation}
\begin{aligned}

y =& x^4 - 1
&& \text{Given equation}
\\
-y =& (-x)^4 - 1
&& \text{To test for origin symmetry, replace both $x$ by $-x$ and y by $-y$ and see if the equation is still the same}
\\
-y =& x^4 - 1
&&

\end{aligned}
\end{equation}
$


The equation changes so it is not symmetric to the origin.

Therefore, the equation $y = x^4 - 1$ has an intercepts $(-1,0), (1,0)$ and $(0,-1)$ and it is symmetric to the $y$-axis.

How is the theme of hatred evident in the text?

Being a story about the Holocaust, at its core, The Boy in the Striped Pajamas explores the deep and essential question of peoples’ behaviors during desperate and horrific times. In such moments, do people choose goodness and compassion, or do they choose to blindly follow authority and show cruelty? While the characters of Bruno and Shmuel exemplify innocence and kindness, the characters of Father and the Lieutenant show a cruelty toward the Jews that can only be based on hatred.
When Bruno moves from his house in Berlin to live at “Out-With,” he begins to recognize the injustice firsthand when he sees the Jewish boys and men living on the opposite side of the fence. When Bruno asks his Father who the people are, his father answers, "Those people . . . well, they're not people at all, Bruno . . . at least not as we understand the term." This quote is one example of the theme of hatred in the novel. We see how this understanding and definition of the Jews as “not people” led the Nazis to unspeakable crimes against them.

Calculus of a Single Variable, Chapter 9, 9.4, Section 9.4, Problem 8

The direct comparison test is applicable when suma_n and sumb_n are both positive series for all n such that a_n<=b_n
If sumb_n converges , then suma_n converges,
If suma_n diverges , then sumb_n diverges
Given the series is sum_(n=1)^oo1/sqrt(n^3+1)
Let a_n=1/sqrt(n^3+1) and b_n=1/sqrt(n^3)=1/n^(3/2)
1/sqrt(n^3)>1/sqrt(n^3+1)>0 for n>=1
The series sum_(n=1)^oo1/n^(3/2) is a p-series with p=3/2
The p-series sum_(n=1)^oo1/n^p converges if p>1 and diverges if 0As per the p-series test the series sum_(n=1)^oo1/sqrt(n^3) converges, so the series sum_(n=1)^oo1/sqrt(n^3+1) as well, converges by the direct comparison test.

The subtitle of The Cherry Orchard is "A Comedy in Four Acts"; Anton Chekhov famously disagreed with the play's first director, Konstantin Stanislavsky, about whether the play was a comedy or a tragedy. Which is it?

It is often referred to as a comedy, no doubt due to the subtitle and Chekhov's insistence on calling it a farce, but to me the tragic elements overwhelm the comic. This family, though terribly flawed, falls victim to its illusions. Although the cherry orchard in prior years was made possible by slave labor, it still seems unfortunate that it must be cut down, and tragic that the family members can't get out of fantasyland long enough to make decisions that might help them to save themselves.
It is sad and ironic that in trying to cling to the past, represented by the cherry orchard, they lose both the estate and the orchard itself, which is cut down anyway. They lose their status, they lose their home, and they go out into the world ill-equipped to adapt to new realities. If this is comedy, it is dark comedy; if it is farce, it is tragic farce.

What is the climax of the story "Little Things Are Big"?

The climax of this story occurs when the narrator decides not to help the woman with her children or her luggage.
The entire story has been building up to this point, with the narrator grappling with an internal conflict between his culture and upbringing, which dictated that he should be offering his assistance to this stranger, and his common sense, which told him that because he was Puerto Rican and had black skin, any offer to help may be perceived as a threat.
The excitement of this great short story reaches a crescendo at this moment, because the audience has, by this point, become emotionally involved in this story and wants to know whether courtesy will emerge victorious over racist rigidity.

In the story, “Little Things are Big,” the climax is the point when the narrator is faced with the dilemma of a choice between offering his help to a white lady and walking past her leaving her in her predicament.
It is quite late after midnight. In the train, there is a young lady with three small children including a baby on her right arm and a big suitcase in her left hand. Both the narrator and the lady with children will get off at Atlantic Avenue. He knows he must help her to get off the train, and he seems to be willing to do so.
But there is a problem - he is black and she is a white lady. He ruminates over the possible ways the lady might react if he offers to help her. He thinks,

What would she say? What would be the first reaction of this white American woman? Would she say: 'Yes, of course you may help me,' or would she think I was trying to get too familiar or would she think worse? What do I do if she screamed when I went to offer my help?

This is the moment when the story has reached its point of highest tension. The reader is dying to know what the narrator finally chooses to do.
He “pushes by her” and moves on “leaving the children and the suitcase and the woman with the baby in her arms.” He does so with hesitation and a guilty conscience though.

The climax of the story "Little Things Are Big" is when the narrator, Jesús Colón, decides not to help the white woman who is getting off the New York City subway, even though she has a baby, two other children, and a suitcase because he is afraid of the way that she might perceive his offer of help. Even though, as Colón writes, "courtesy is a characteristic of the Puerto Rican," he decides not to help this woman because he is a what he describes as a Negro and a Puerto Rican. He fears that she might have preconceptions about what people who look like him are like, especially in an empty subway station late at night. He doesn't know whether she'll accept his help or scream for help. As a result, he decides to do nothing at that moment, and he feels that racism has caused him to act in a way that is uncharitable. However, he makes up his mind that in the future, he is going to offer help, no matter how it is perceived.

I'm writing an essay for the book Into the Wild. The question I need to answer is "How does the allure of high-risk activities control young people of a certain mind"?

The first step in answering the question is to note that it conflates two different issues, sensation-seeking behavior and risk. One good approach to answering the question is to parse its assumptions and note the difference between sensation-seeking and risk.
The human brain does not fully develop until the mid-twenties. A combination of lack of impulse control and lack of experience can mean young people will take actions without understanding risks or will act in ways that give immediate pleasure without thought of long term consequences. For example, young people might try vaping or engage in other unhealthy lifestyle choices such as extreme dieting. The fact that these might have impacts on their health when they are in their 50s reflects the way in which 30 or 50 years seems an unimaginably long time scale to young people. Even realizing the dangers such as reckless driving or binge drinking require the ability to vividly imagine the future and to be aware that statistics apply to everyone. Someone who is older and has seen people die on car accidents has a much greater sense of the reality of the consequences of risky behavior.
A related issue is "sensation seeking behavior." Thrill-seekers are not motivated by risk itself but seek exciting experiences. An unintended consequence of this can be risk. For example, extreme skiers seek out peak (literally!) experiences. Many are highly skilled and seek to minimize risk through carefully maintaining equipment, training, monitoring snow conditions, and carrying emergency rescue gear. Wilderness adventure, extreme sports, or other forms of sensation-seeking must be combined with skill and discipline to be done safely. Unfortunately, some people, such as Chris McCandless, have the desire to seek extreme experiences but not the skills or discipline to survive them. One problem is a culture of instant gratification stoked by media in which young people are bombarded with images on Instagram and YouTube showing people effortlessly doing extreme activities but not emphasizing the years of conditioning and training needed to do them successfully.

Before developing a feasible thesis statement for this question, you might want to interpret some of the terms and phrases in the question and run your ideas by your teacher for approval. For example, "young people of a certain mind" is vague, which means you may have an opportunity to define the term according to your own ideas. For example, if your teacher accepts "young people like Chris McCandless, who have a seemingly insatiable impulse for adventure" as an interpretation, you are in a position to create an interesting argument for your essay. Other possible definitions that might interest you include "young people who seek an escape from their day-to-day lives" or even "young people who are running away from something painful".
Once you have determined what the phrase means to you, you can get to work developing your thesis and your outline. If your teacher approves your interest in exploring the connection between high-risk activities and escapism, for example, you may want to argue that young people are vulnerable to the romanticized notions of adventure that are linked with many high-risk activities. In order to support your argument, you would look for quotes in Krakauer's book that contain information about the romance of adventure and the danger that can come from taking such fantasies too seriously. Make sure your topic sentences all link back to your thesis statement, and write your introduction last; that way, you know exactly what you are introducing and your chances of creating a compelling hook increase with this certainty.

I would first look at other risk-takers, primarily Krakauer himself, that Krakauer discusses in his book, along with his explanations of their reasons for risk-taking. I might also explore another risk-taker extraordinaire, Alex Honnold, star of the documentary Free Solo. The question is, how does McCandless's reasons for risk-taking line up against theirs? Just thinking about Honnold, I might explore why he takes the risk he does versus why McCandless takes his risk.
As a starting point, I would list comparisons and contrasts. For example, Honnold and McCandless both appear to want to test themselves against an ultimate challenge. However, in contrast to Honnold, who seems to want to prove something to the world, McCandless seems to have been primarily pursuing an inward journey of spiritual purification. Is this kind of link between risk and spiritual growth a common practice? What spiritual figures might he be compared to? Perhaps Francis of Asissi, who also subjected his body to severe rigors for spiritual reasons.
A possible thesis might be that "Certain kinds of young people let high-risk activities take control of them as a way of testing and proving their mettle in facing danger. While this is true of Chris McCandless, he pursued risk-taking primarily as a form of spiritual challenge."
Of course, you will need to finesse this to suit the requirements of your paper, but since Krakauer puts great emphasis on the connection between McCandless's risk-taking and his spiritual journey, this seems an important angle to explore.

The writing prompt that is given is fairly vague, which isn't necessarily a bad thing. First, decide how to define "young people of a certain mind." What exactly is the certain mind that causes a person to pursue high-risk activities? Next, define which direction the paper is going to go with "high-risk activities." This will be key for your response, because Chris McCandless isn't an adrenaline junkie in pursuit of big wave surfing, skydiving, or bungee jumping. Instead, McCandless's high-risk activity is his pursuit of extreme isolation for long periods of time in incredibly rugged and harsh environments. Further develop this idea by pointing out that plenty of people enjoy this hobby or lifestyle quite frequently. McCandless took it to a completely different level by incorporating severe minimalism into his solitude. He would often go into the wilderness with poor gear or even not having the gear that he should. This is ultimately what got him killed, in my opinion. McCandless's mindset was heavily influenced by men like Jack London, who wrote quite romantically about the rugged wilderness. That influence, combined with youth's general "I'm indestructible" attitude, is perhaps what drove McCandless (and others like him) to pursue his extreme rugged individualism.

How would you explain the four chief elements of Canada's political culture: community, freedom, equality, and attitude toward and expectation of government?

Canada has stated policies that frame Canadian residents' political culture, but residents' actual experience may diverge from the framed political culture. To make the point using the element of community, Canada's Department of Multiculturalism and Citizenship was adopted in 1991 and dismantled in 1993 because of residents' criticism of weaknesses in its defining points, such as in assisting Canadians to "enhance and share their cultures" (Marc Leman).Community: Canada's political cultural element of community is explained as a sense of membership in a collected body of residents and citizens. Canada has a long history of regionalism to take into account. This underpins French-English divisiveness, including differences along economic and geographic lines. Current community issues for Canada include multiculturalism, diversity and ethnic distinctiveness.Freedom: The political cultural element of freedom is explained through Canadians' belief in majority rule, parliamentary system, democratic process, and political compromise when in the absence of a majority. Freedoms relate to institutions and the law, to private and community rights, and to public expression of ideas. Equality: The political cultural element of equality is explained as Canadians' belief in the power of one vote, in honoring a regular electoral process, and in being governed by popular sovereignty (the people hold the voice of power). Political equality is a less contentious equality than the equality of groups. Quebec's policy of interculturalism illustrates this. The policy of interculturalism acknowledges and accepts "culturally diverse groups (cultural communities) without, however, implying any intrinsic equality among them" (Marc Leman). Attitude toward government: The political cultural element of attitude toward government is explained as Canadians' acceptance and support of government. Canadians look to government as the authority that binds and protects Canada's residents. Alienation toward federal government, founded in regionalism, does exist in some regions such as Western Canada and is historically based.Expectation of government: The political cultural element of expectation of government is explained as the expectation of active government intervention to protect and direct society while ensuring solutions to social problems such as health care and education, and economic problems such as inflation and market crashes. RESOURCES
Marc Leman, "Canadian Multiculturalism."
Open Textbook, Canada, "Chapter 17. Government and Politics." Introduction to Sociology.
David Zussman, "Political Culture." The Canadian Encyclopedia.
http://publications.gc.ca/Collection-R/LoPBdP/CIR/936-e.htm

https://opentextbc.ca/introductiontosociology/chapter/chapter17-government-and-politics/

According to Chapter 3, "Canadian Political Culture" by Stephen Brooks, in James Bickerton's book Canadian Politics (5th edition), the four crucial dimensions of Canadian politics are community, freedom, equality, and attitude towards the state (page 46). With regard to community, the author states that the "search for national identity unites successive generations of Canadians" (page 46). He believes that Canadians' constant search for a national identity helps to define the country. Canadians define their national identity based on a political culture rather than in an ethnic or racial way. He believes that this political culture has resulted in a modus vivendi that exists most of the time between anglophone and francophone Canadians.
Canadians' conception of freedom is different than that of Americans, in that they believe that it requires more frequent government interference with the market and with individual liberties. Canadians have a more positive conception of freedom, which requires the government to act, than a negative conception of freedom (as Americans do), which requires the government not to get involved in people's lives. Canadians also support equality to a greater extent than Americans do, including a publicly funded healthcare system. Canadians support government intervention to make their society more egalitarian. Canadians value equality of results, while Americans tend to value equality of opportunity. Finally, as mentioned earlier, Canadians tend to expect more government intervention and help than Americans do. The Canadian government is more active in wealth redistribution than the American government is, and it also provides more social services and collects a higher percentage of people's income as taxes than does the government in the U.S. 

What are some key terms from 1984?

Let us take each question in turn:
1). Comrade Ogilvy is a character invented by Winston Smith as part of his job at the Ministry of Truth. He has been created to replace Comrade Withers, a real person who was once a comrade of Big Brother. He was declared an enemy of the Party and vaporized. Now he is an "unperson" and must be written out of history as if he never existed.
2). The Junior Anti-Sex League is a youth organization within the Party. Its members are extremely loyal, fanatical, and totally dedicated to the cause of IngSoc (English Socialism). As their name implies, they are also committed to the eventual eradication of all sexual relations by the regime. In the future, it is hoped that all procreation will take place entirely by means of artificial insemination.
Julia is a member of the League, which is one of the reasons that Winston is initially distrustful of her, believing her to be a Party zealot.
3). The Golden Country is a place that Winston visits in his dreams. It is a beautiful place, where everything is carefree and the sun is always shining. He often dreams of Julia being there. The Golden Country is important to Winston for two reasons. First, it provides him with a means of escape from the grim, sordid reality of life in Oceania; second, it holds out the hope of a better world, one from which the Party has been expunged. To some extent, it also represents an idealized past, civilization as it was before the Party took over.
4). Thoughtcrime. Oceania is such a repressive society that not just wrong actions but even wrong thoughts are considered treacherous. Thoughtcrime is monitored by the Thought Police, the secret police force used by the state to root out seditious thinking. Each individual is carefully monitored by way of telescreens, which minutely scrutinize body language to find anything vaguely suspicious.
5). The Four Ministries will be described as follows: the Ministry of Truth is where Winston works. This is the propaganda arm of the state which peddles the Party line; the Ministry of Love brutally seeks to promote and enforce the unconditional love of Big Brother through brainwashing and other nefarious means; the Ministry of Peace, which despite its title, is actually concerned with the conduct of perpetual war against either Eastasia or Eurasia; and finally, the Ministry of Plenty, which is concerned with the organization of Oceania's planned economy. Like all the other ministries' names, the Ministry of Plenty is a complete misnomer, as the country's economy suffers from acute shortages, leading to widespread hardship and grinding poverty.
6). Doublethink is an officially prescribed mode of thought whereby people are required to hold mutually contradictory opinions at the same time. Examples include "Peace is war," "freedom is slavery," and "ignorance is strength." The purpose of doublethink is to maintain the Party's control over public opinion. The Party is always right; thus, there can be no true contradictions in its ideology. It also needs to change its line at a moment's notice. Hence, believing two contradictory opinions at once is absolutely necessary.
7). A Memory Hole is a chute in the Ministry of Truth used to send old photos, texts, and newspaper clippings down into a large furnace. This is a simple method for rewriting history and keeping up with the perpetually changing Party propaganda line.
8). Facecrime. This is an example of Newspeak (see point 10) and is related to point 4. Using telescreens, the Thought Police can closely monitor facial expressions and other forms of body language to determine if someone is guilty of treacherous thoughts.
9). Parsons is a fanatically loyal Party member. As such, he is despised by Winston, despite his outward friendliness. He and his family are almost model citizens, so it comes as something of a shock when Parsons's daughter turns him in to the Thought Police. Apparently, he said "down with Big Brother!" in his sleep. Even Party zealots can unconsciously resist Big Brother, it would seem.
10). Newspeak is a kind of official jargon and is the only approved language in Oceania. The language perfectly reflects the official ideology, as it is often meaningless, contradictory and highly simplistic. Newspeak is particularly fond of syllabic abbreviations, such as "IngSoc" (English Socialism), and compound words such as "Doublethink," (see above)  and "Goodsex," which is the only prescribed form of sexual intercourse. "Goodsex" refers to sexual activity between a man and a woman for the purposes of procreation.
The whole purpose of Newspeak is to keep its level of expressiveness and meaning as restricted as possible in order to ensure that the Party may manipulate and control it more effectively for its own ends.
11). The Chestnut Tree Cafe is a place where people go after they have been tortured by the Ministry of Love for crimes against the Party. Despite having all the trappings of a normal cafe, it is a grim, depressing place, perfect for un-persons. It is like purgatory in that it is not the final resting place but the penultimate one. In this case, it is the penultimate place where each individual goes before being totally destroyed. Winston and Julia end up there after they have been tortured. However, there is no longer any love between them. In fact, there is nothing there at all.
12). O'Brien is a high-ranking government official, an elite member of the Inner Party. He poses as a member of The Brotherhood, an undergound resistance movement, in order to trap Winston and Julia. He later presides over Winston's brutal torture sessions.
13). Emmanuel Goldstein is the alleged head of The Brotherhood, a subversive, counterrevolutionary group dedicated to overthrowing the Party. We are never actually sure that he exists; it is entirely possible he is just an invention of the Party used to try and smoke out potential subversives. Winston is certainly convinced of his existence, and his conviction is strengthened when he and Julia go to visit O' Brien in his flat. O'Brien says he will give Winston some books written by Goldstein that set out in great detail how to overthrow the Party and what kind of system can be put in its place.
14). Syme, though a minor character, is very important due to the insight he provides into life in Oceania and how the system works. He is a colleague of Winston, someone who works in the Records Department. His role involves the compilation of the 11th edition of a Newspeak Dictionary. Although fiercely loyal to the regime, Syme is correctly predicted by Winston to be vaporized. He is simply way too intelligent and vocal to thrive under the existing regime.
15). Winston's Diary is incredibly important to him because it is the only place where he can truly be free. In a brutal, totalitarian society in which thoughts, deeds, and actions are constantly controlled and monitored, the diary provides Winston with a much-needed sanctuary where he can step back from the madness, lies, and sheer sense of hopelessness surrounding him and cling, however tenuously, to a sense of who he really is. The diary is the only thing that Winston possesses which can give him any sense of identity in a society in which the faintest trace of individuality is ruthlessly crushed.

Intermediate Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 74

Evaluate $ak + bt = 6r$ for $k$


$
\begin{equation}
\begin{aligned}
ak + bt - bt &= 6r - bt
&& \text{Subtract $bt$ from each side}\\
\\
ak &= 6r - bt
&& \text{Evaluate}\\
\\
\frac{ak}{a} &= \frac{6r - bt}{a}
&& \text{Divide each side by } a\\
\\
k &= \frac{6r - bt }{a}
&& \text{Simplify}
\end{aligned}
\end{equation}
$

Why is it significant that Four nicks Tris's ear during the knife-throwing exercise?

When Tris accuses Four of nicking her ear on purpose, he cryptically retorts, "You know, I’m getting a little tired of waiting for you to catch on!” Although Four does not directly address Tris's complaint, we can deduce his motives from his interactions with her. From the beginning of the initiation program, Tris's unique characteristics quickly draw Four's interest and scrutiny. During a knife-throwing exercise, Tris stands up for Al. Although she does not know it, her actions betray her divergence. It is very likely that Four is first alerted to her unique qualities at this point.
Later, Four’s suspicions are confirmed when he observes Tris’s reactions during a fear simulation practice. Since he knows that Eric hunts divergents, Four also understands the danger Tris is under. In nicking her ear, Four does two things. First, he satisfies Eric's sadistic desire to see Tris punished. Second, he demonstrates his supposed impartiality to Tris and deflects attention away from his growing interest in her. In doing so, Four ensures that Tris is shielded from Eric's scrutiny for some time.

Calculus of a Single Variable, Chapter 3, 3.5, Section 3.5, Problem 17c

You need to evaluate the limit, hence, you need to replace oo for x in equation:
lim_(x->oo) (5 - 2x^(3/2))/(3x -4) = (5 - oo)/(3oo - 4) = -(oo)/oo
Since the result is indeterminate, you need to force x^(3/2) and x factors out at numerator and denominator:
lim_(x->oo) (x^(3/2))(5/(x^(3/2)) - 2)/(x(3 - 4/x)
Since lim_(x->oo) 5/(x^(3/2)) = 0 and lim_(x->oo)4/x = 0, yields:
lim_(x->oo) (x^(3/2 - 1))(-2/3) = -2/3*lim_(x->oo) (x^(1/2)) = -2/3*oo = -oo
Hence, evaluating the given limit yields lim_(x->oo) (5 - 2x^(3/2))/(3x -4) = -oo.

What technology allowed for European exploration to increase?

The use of a compass and maps became standard on late medieval European ships. Some of these ships, such as small, very flexible caravels, carried a combination of square and triangular sails that allowed them to sail against the wind. When Portuguese ships appeared in the Indian Ocean, they proved sturdier than most Indian and Arabian ships, and they carried considerably more guns; this gave them a decisive advantage in a number of key naval battles.
The British and the Dutch had even better artillery than the Portuguese and Spanish. Moreover, the Dutch introduced a very capacious ships called fluyts (flyboats), which needed less human labor than previous ships.
In America, the Spanish used steel swords, rudimentary small firearms, and guns as well as horses and metallic protective armor to conquer the Central and South American Aztec and Inca empires.
European mariners of the Age of Discovery used globes and various astronomical instruments to find the coordinates of their ships in the open ocean. It was much easier to find latitudes than to find longitudes. In the eighteenth century, English artisans invented precise chronometers that finally made it possible to find longitudes accurately.
In the second half of the nineteenth century, new industrial technologies made possible the second big wave of European exploration and colonial conquest. These technologies included repeat rifles, railroads, telegraph lines, quinine for treating malaria, iron- and steel-hulled steamships, and machine guns.

Calculus and Its Applications, Chapter 1, 1.2, Section 1.2, Problem 2

Determine if the statement
$
\displaystyle
\lim_{x \to 2}
f(x) = 9
$,
then
$
\displaystyle
\lim_{x \to 2}
\sqrt{f(x)} = 3
$.
is either true or false.


The statement is true because according to the limit principles,
$
\displaystyle
\lim_{x \to a} [f(x)]^n
=
\left[ \lim_{x \to a} f(x) \right]^n
=
L^n$
and
$\displaystyle
\lim_{x \to a} \sqrt[n]{f(x)}
=
\sqrt[n]{\lim_{x \to a} f(x)}
=
\sqrt[n]{L}
$


Considering that $n$ is a postive integer and $L \geq 0$. In this case, $n = 2$
$\displaystyle \lim_{x \to 2} f(x) = 9$ and $\displaystyle \lim_{x \to 2} \sqrt{f(x)} = \sqrt{ \lim_{x \to 2} f(x)} = \sqrt{9} = 3$

How does Eliot portray the different states of mind between Godfrey and Nancy Lammeter in Silas Marner?

Godfrey's state of mind is openly described by showing all of Godfrey's fears, tribulations, and past history. Nancy, on the other hand, has a frigid personality that makes her almost impossible to read. Therefore, Eliot uses those personality traits to indirectly and directly describe the mindsets of both characters.
Godfrey is always in fear. He has followed the ways of his wayward brother, Dunstan, who fathered a child with an opium fiend and is consistently out of money. His state of mind is easy to describe because Eliot fully explains what makes Godfrey such a weakling.

Godfrey Cass was looking forward to this New Year's Eve with a foolish reckless longing, that made him half deaf to his importunate companion, Anxiety.
"Dunsey will be coming home soon: there will be a great blow-up, and how will you bribe his spite to silence?" said Anxiety.
"Oh, he won't come home before New Year's Eve, perhaps," said Godfrey; "and I shall sit by Nancy then, and dance with her, and get a kind look from her in spite of herself."

This excerpt is very telling. Anxiety rules Godfrey's days. His brother dominates him. He knows he is not worthy of Nancy. He also knows he has disappointed his father (if he ever finds out about his actions), and thinks he has basically ruined his life to a point. His brother consistently follows and preys upon Godfrey's vulnerabilities. For this reason, Godfrey manages to survive mentally from all the pressures he is under.
Nancy, on the other hand, has a cold personality that combines coquettish, prudish and sanctimonious natures together. It is hard to read Nancy, perhaps because she is definitely not the sophisticated creature that she attempts to be. Nonetheless, Nancy's mindset is the exact opposite of Godfrey's. She is not reactive or emotionally hungry. She is calm, appears way more collected than everyone else, and her icy temperament is a huge contrast to Godfrey's nature

The modest calm of Nancy's speech and manners told clearly of a mind free from all disavowed devices.

In all, Eliot demonstrates the clear differences in the states of mind of Nancy and Godfrey. Eliot is also able to identify the causes behind such mindsets. Godfrey's vulnerable personality tends to take on the wild nature of his brother, making him fail at any of his original good intentions of doing well.
Nancy, calm, proud, and much more sure of having everyone's approval, is used to being always accepted and admired; as a result, she really does not have to do much to impress herself or others. This is why her mind is "free from all disavowed devices," while Godfrey is in a consistent state of fear.

How did Flannery O'Connor's life and beliefs influence her writing in "A Good Man is Hard to Find"?

Flannery O'Connor was a devout Roman Catholic who was diagnosed with lupus in 1952. As a result, she moved back to her family farm in Georgia for the last twelve years of her life.
We can see the influence of her faith in the story. O'Connor's Catholicism caused her to understand that the world is an evil and fallen place, as exhibited in the behavior of the Misfit and his men, and also to a lesser extent in the grandmother, a silly, manipulative, racist woman who causes the murder of her family. However, O'Connor's faith also led her to believe that, although all human beings are grotesque and fallen, all of us are children of God and able to receive God's grace and salvation. The grandmother experiences the grace of God, for example, when she can perceive the Misfit who is about to murder her as her "son." For a brief instant, even the Misfit seems to feel God's spirit as the grandmother connects with him on a deep level right before he shoots her.
We can see the influence of O'Connor's life in the southern and 1950s setting of the story. She too must have often felt grotesque with her illness and also saw an imperfect set of people in her home town on which she could model her characters and then embellish them with her own touches.

Author Flannery O'Connor's life and beliefs heavily influenced her writing in "A Good Man is Hard to Find." O'Connor was a prominent Catholic writer and she openly acknowledged the significant role her beliefs played in her works. In her essay, "The Church and the Fiction Writer," the author explains that life for the Catholic author is viewed through a lens of the "central Christian mystery." She also believed that a writer's beliefs should lead to a broader world view rather than a narrower one. The influence of these predispositions can be found throughout "A Good Man is Hard to Find," which is arguably her most famous work.
O'Connor's Personal Life
O'Connor grew up in a Roman Catholic family in Savannah, Georgia before relocating to Milledgeville. The author's upbringing heavily influenced her works, most of which are set in the rural American South. "A Good Man is Hard to Find" takes place during a rural family road trip to Florida. The grandmother wishes to visit family members who live in east Tennessee. The combination of influences from O'Connor's early life in the Deep South and her religious upbringing and faith are perhaps most obvious in this short story.
Major Themes and Influences
Throughout this short story, which has been widely recognized as a dark comedy with a strong moral message, themes of redemption and virtue are prevalent. The grandmother and all major characters in the story except for The Misfit are shallow and often selfish. Throughout her life and her final journey with her family, the grandmother has focused on superficial concerns and seems incapable of viewing those around her for who and what they really are. After a car accident, the grandmother and her family find themselves stranded in the woods, but they are not alone for long. The Misfit, an escaped convict traveling with his cronies, soon finds them and leads the family off one by one to be shot. In the grandmother's final conversation with The Misfit, O'Connor takes the opportunity to explore many of the thematic elements that were central to her faith and life.
Although the grandmother has lived a shallow life up until her encounter with The Misfit, she is defined not by the poor quality of her life but the mercy she shows just prior to her death. She is able to recognize the convict as "her son," hinting at O'Connor's belief that all humans are children of God. O'Connor strongly believed that she had a responsibility to explore the paradoxes of life through her writing. Like her general body of work, this short story centers around her Christian beliefs and communicates the message that love can look in the face of evil and smile, as the grandmother finds herself smiling into the sky after being shot by The Misfit.
https://www.britannica.com/biography/Flannery-OConnor

Write a summary of Chapter 1 of the novel The Boy in the Striped Pajamas.

Bruno, the nine-year-old son of a Nazi commander, arrives home after a day at school to find the house being packed up. At first, he's concerned he's being sent away, but quickly notices that his mother's things are also being packed. He asks his mother about this change, and she confirms that the family is embarking on a "great adventure." Bruno learns that they are moving for his father's work. The Fury, as Bruno calls him, sees a lot of potential in his father, and is sending them someplace important to conduct a key job. Bruno doesn't understand his father's job and has little perspective for what this means.
Bruno is upset as he learns more about the move. Realizing he will be traveling far away and not returning to school causes a great deal of stress. He will have to say goodbye to his friends, Karl, Daniel, and Martin. His mother tries to reassure him but eventually tells Bruno that they don't have a choice.
Bruno reflects on everything he loves about their house: the five stories, the long banister, and the proximity to Grandfather and Grandmother. He wonders if they'll move along with the family. He can hear his parents argue, and it becomes clear that his mother does not want to move any more than Bruno does. He eventually returns to his room and helps the maid pack his things.

At the beginning of Chapter 1, Bruno, a nine-year-old boy living in Berlin, comes home to find his family's maid, Maria, packing up all of his belongings. Bruno's mother then walks into his room and explains why Maria is packing his things. He follows his mother downstairs where she tells him that they are moving because his father's job has forced them to relocate. Bruno then begins to think about what his father does for a living and realizes that he doesn't really know what he does. Bruno then thinks about his friends and how much he will miss them. Bruno is upset about the news and slides down the long banister as he reminisces about his house. He mentions that he will miss the banister as well as living close to his grandparents. Bruno then overhears his mother and father arguing in his father's office. Dejected, Bruno walks into his room to help Maria pack his things.

How does A Brave New World by Aldous Huxley connect to modern life psychologically?

A Brave New World critiques the psychological implications of modern society's reliance on technology. In the World State, human truths, such as love and friendship, are repressed because individuality is not valued by the state. In fact, individuality is not only undervalued, it is almost completely eradicated as a form of social control. This social control is maintained through state-controlled technology, such as the "feelies," a meaningless form of entertainment meant to distract the citizens of the World State, and "soma," a drug which induces a state of oblivious contentment. From a psychological perspective, Huxley is critiquing the superficiality of consumerist culture. In a society where production and consumption are valued more than "human truths," humans are psychologically degraded to the commodities which they consume. Huxley is advancing the notion that this degradation results in a society of mindless, soulless, and purposeless individuals with no real psychologies at all, and the character John represents an attempt to regain human psychology, as represented through his discovery of the works of Shakespeare. 

In what sense are the US and China “rivals” today? When can “rivalry” be a good/bad thing?

The rivalry between the United States and China stems from the recent emergence of China as a great power on the world stage. Following the Cold War and the dissolution of the Soviet Union, the United States emerged as the sole superpower in the world. Superpower, in this context, means a nation or state with the ability to exert incredible levels of influence over the rest of the world, and project power, both hard (military) and soft (economic and cultural) around the world. The United States clearly fits this criteria, with its ability to wage wars simultaneously around the globe and its relatively strong control of the United Nations, as well as its leadership role among its allies in military organizations such as NATO and economic organizations such as G7. Recently, with developments leaning closer to nationalism rather than globalism, the United States has been said to be diminishing its role in soft power (though hard power, unarguably, is growing), though this tends to be greatly exaggerated, as the United States is still heavily invested in the world outside its borders.
China has been steadily growing in population, industrial output, technology, infrastructure, and military power for the past five decades. This has led to the state becoming a great power (level below a superpower, meaning they can project both hard and soft power globally, but would not be able to maintain the simultaneity of dealing with two or more separate global military situations, having less economic power than the superpowers, and are not as far-reaching in their capabilities as a superpower, though this line blurs as geopolitics develops today). China is steadily increasing its influence over the military and economic affairs of the East Asian region, which is seen as a threat to the United States considering that, in a zero-sum game, they are losing influence over such affairs in the region. China also is increasing its global investments, a role the United States both filled previously and currently fills, but again, in a zero-sum game, someone else gaining means one is losing influence. The United States invests globally, but China's recent developments have been in Africa and South America, two key emerging markets. Between its large military, strong economy, and increasing global hard and soft power, China is positioning to emerge as a second superpower, a scenario the United States has not been in since the dissolution of the Soviet Union.
This upsetting in the balance of power and restoration of a two-superpower world creates a rivalry between the United States and China. This is not the same, however, as a new Cold War. Though there is a great deal of espionage between the two nations, and noticeable proxy-"wars"(not shooting wars, but tense situations, namely Taiwan and the Koreas), the amount of trade and cultural exchange between the countries makes this situation markedly different from the Cold War. Rivalry can exist without a Cold War, however, and China's growing economy and influence certainly makes them a global rival to the United States. This rivalry, so long as it leads to good things such as a technological boon and rapid economic development (which is currently does, to a large extent), and not bad things such as the threat of war and poor/illegal trading practices (which it also currently does, considering the Koreas and Chinese labor and trade practices as well as American protectionism), can be a good thing. It is currently leaning more towards good than bad, but is a delicate balance that is easy to shake.

The sense that US and China are rivals stems in part from the growth in China's military, as it seeks to expand its power in Asia and across the globe. In addition, the US has been wary of Chinese trading practices, which they criticize for dumping products into the American market. China has become a major donor of aid to nations in Africa. While this aid may seem benevolent, some in the American press have criticized it as providing support for dictatorial regimes and for securing jobs for Chinese workers to build infrastructure projects abroad. In addition, some have criticized Chinese aid as entirely self-interested, allowing the Chinese to access raw materials abroad.
The US-China rivalry can lead to negative consequences, including military buildups and potential confrontations as China attempts to vie with the US for world power. However, the rivalry can also be positive, as it can put pressure on the United States to work with China in a strategic way. As China is a power that can no longer be ignored, the US needs to engage China in security and trade talks that are aimed at creating a more democratic country in China. Chinese aid abroad can also stimulate the United States to increase its own aid to developing nations in Africa and elsewhere.

College Algebra, Chapter 3, 3.6, Section 3.6, Problem 48

Find $f \circ g \circ h$ if $f(x) = \sqrt{x}$, $\displaystyle g(x) = \frac{x}{x-1}$ and $h(x) = \sqrt[3]{x}$

$
\begin{equation}
\begin{aligned}
(f \circ g \circ h) (x) &= f(g(h(x))) && \text{Definition of } f \circ g \circ h\\
\\
(f \circ g \circ h) (x) &= f \left( g\left(\sqrt[3]{x}\right)\right) && \text{Defintiion of } h\\
\\
(f \circ g \circ h) (x) &= f \left( \frac{\sqrt[3]{x}}{\sqrt[3]{x}-1} \right) && \text{Definition of } g\\
\\
(f \circ g \circ h) (x) &= \sqrt{\frac{\sqrt[3]{x}}{\sqrt[3]{x}-1}} && \text{Definition of } f
\end{aligned}
\end{equation}
$

Where did most enslaved Americans live in North America?

In 1860, the state of Virginia had the largest number of enslaved Americans, at 490,850, followed by the states of Georgia, Mississippi, and Alabama, each of which had more than 400,000 slaves. These were all states with a strong base of cotton-growing, a labor-intensive form of farming that relied on slave labor to enrich the plantation owners.
The explosion of cotton growth after the invention of the cotton gin by Eli Whitney in 1793 dismayed those Americans who had hoped that the institution of slavery would gradually wither away, especially after the relatively new country of the United States failed to abolish it. It would take the Civil War to finally sweep away an institution many had objected to since the founding of the United States.

How is the dramatic purpose of the ghost in Act 1 of Shakespeare's Hamlet to show the strong relationship between Hamlet and his father before he was murdered?

Let's go step by step. Reading through and considering the situations of each scene in Act 1 slowly explains to us the relationship between Hamlet and his father.
Firstly, we learn that the ghost of the dead King of Denmark has begun appearing to guards at night time. Each time, the guards try to speak to it and understand what it is and why it appears. But the ghost does not speak and does not respond to them. Horatio, a friend of Hamlet, says that they should inform Hamlet about this, for the ghost that refuses to speak to them shall surely speak to him. This is really the first indication we have as to the nature of the father-son relationship. Horatio, who knew the king well and who also knows Hamlet well, implies that the ghost of the King would not be silent upon seeing his son, indicating that Hamlet and his father had a strong bond before the King's death.
And then consider the entry of Hamlet in Act I, Scene II, when his mother Gertrude immediately criticizes Hamlet for continuing to mourn his father's death. His mother asks him to stop wearing black clothes, a sign of mourning, saying that he cannot continue to think of his father all his life... and that it's common for people to die.
Hamlet explains to his mother the extent of his grief and mourning, which is far deeper than what his dark clothes, weepy eyes and sighs show. This is the most significant moment when we realize that Hamlet's love and attachment for his father was very strong and deep, much deeper than what his mother or uncle had felt, as they have visibly moved on with their lives by getting married and advise Hamlet to do the same. But Hamlet is in deep grief over his father's death and also over the unexpected and quick marriage of his mother to his uncle. 
Hamlet goes on to meet Horatio and others in Scene II and speaks highly of his father, saying that he will not come across a man like his father again. 
And in Act I, Scene IV, the ghost of the King comes again and motions for Hamlet to follow him. The ghost then proceeds and speaks to Hamlet, telling him that he is the ghost of the King and asks him to revenge him, to which Hamlet immediately accepts. Then the ghost goes on to tell him that he was murdered by his uncle, asks him to take revenge and asks Hamlet to remember him. Hamlet is naturally devastated and vows to avenge his father and says that he will remember only his father.
So Hamlet's father only spoke to Hamlet and not only did he do so, but he revealed the secret of his death and also entrusted Hamlet to avenge his death. We understand from this scene that not only did Hamlet love his father very much, but that his father loved Hamlet a lot, too. The King clearly felt that only Hamlet was worthy and capable of the task of avenging his death and reached out to him as a ghost and not to anyone else. 
From all of these scenes, we understand that Hamlet and his father shared a most strong and deep bond of love and trust.

What kind of supernatural elements are used in gothic literature?

Gothic literature delves deeply into mysticism, monstrosity, and hauntings. The literary canon for this genre contains a rather staggering array of what can be identified as "supernatural" phenomena. Below are just a few.
Ghosts and hauntings. Typically in settings of large, cavernous, austere castles and estates, the characters of Gothic literature are assailed by ghosts and hauntings of many kinds. Jane Eyre is haunted by her dead uncle's spirit in the "red room" of her aunt's home. The children of Henry James's "Turn of the Screw" are plagued by the ghosts of two former staff members, with deadly outcomes. 
Monsters. Mary Shelley's Frankenstein revolves around an unnaturally animated (and yet curiously human) monster who is grotesque in appearance. Bram Stoker's Dracula, and its original inspiration Carmilla by Sheridan Le Fanu, feature narratives pushed and pulled by the drama surrounding vampires. In The Strange Case of Dr. Jekyll and Mr. Hyde, Jekyll possesses a violent alter ego, Hyde, which can only be kept at bay by a serum.
Inexplicable happenings. Other works of Gothic literature still employ supernatural elements; they simply do not fall into such explicit categories as "ghost" or "monster." For example, in Oscar Wilde's The Picture of Dorian Gray, Dorian Gray's soul and behavior become supernaturally intertwined with a painting of him. The painting mysteriously changes as the character commits more vain and terrible actions in real life. The painting grows older, uglier, and more unseemly, yet the character never seems to age.
These supernatural elements are, in many ways, literary sketches of "evil" human behaviors and impulses. The origins of these ghosts, monsters, and strange happenings are essentially projections of cruelty, vanity, mental illness, and unresolved past trauma. Even more examples of the supernatural as a literary element in Gothic works exist beyond those mentioned here.

Why does the miller ask Beetle if she has gone daft?

Jane, the wicked midwife, is shouting at poor Beetle again. Having lost another one of her few remaining teeth and having also broken her ankle, the old crone is in a foul mood, and she throws copper pots and cooking spoons about the cottage. She takes out her growing anger on poor Beetle—except for the fact that she is no longer called Beetle, says Beetle; her name is now Alyce. On hearing this, Jane splutters with contempt. The very idea of a young waif found on a dung-heap having such a delightful name is simply way too ridiculous for words. As the nasty old midwife continues throwing pots at her, Alyce figures it is best to go outside.
Outside, in the summer morning, Alyce comes across the cat that she likes to pat and stroke. Now that she has finally plucked up the courage to say her new name out loud, Alyce wants everyone and everything to hear about it, even the cat. As the cat playfully rubs up against her, Alyce tells the cat that she wants to know what her name is. Alyce then goes through a list of common cat names, hoping that the cat will respond to one of them. A passing miller walks by and hears Alyce talking to the cat. That is why he thinks she may have gone "daft" or, in other words, a little mad.

What purpose does the opening of the story serve?

The opening of "Once Upon A Time" is unusual because it begins with the author's refusal to write a children's story. She says that she wants to preserve the freedom to write whatever stories she chooses, not the stories that other people expect. In addition, the beginning of the story is also unusual because it comes into her mind when she hears some strange noises in the night and cannot get back to sleep.
The purpose of these two opening points is to inform the reader that this story is not going to be a traditional fairy tale, as we might expect from the story's title. In fact, the narrator is telling the reader that she intends to create the very opposite of what is expected of her. She is, therefore, setting out her intention to create a different kind of fairy tale, one which does not follow the traditional conventions. As we see from the story's character and events, this is exactly what happens. Gordimer writes a story that is sinister and unnerving, the very opposite of a Disney-style fairy tale.
The opening of the story, therefore, foreshadows her unconventional and resistant approach to telling a children's story.

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 1

The graph of $f$ is given. Estimate the value of each derivative then sketch the graph of $f'$.








a.) $f'(-3)$

Referring to the graph, the approximate value of $f'(-3)$ is $1.5$

b.) $f'(-2)$

Referring to the graph, the value of $f'(-2)$ is $1$

c.) $f'(-1)$

Referring to the graph, the value of $f'(-1)$ is

d.) $f'(0)$

Referring to the graph, the value of $f'(0)$ is $-4$

e.) $f'(1)$

Referring to the graph, the value of $f'(1)$ is

f.) $f'(2)$

Referring to the graph, the approximate value of $f'(2)$ is $1$

g.) $f'(3)$

Referring to the graph, the approximate value of $f'(3)$ is $1.5$

College Algebra, Chapter 7, 7.4, Section 7.4, Problem 34

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

6x + 12y =& 33
\\
4x + 7y =& 20

\end{aligned}
\end{equation} \right.$ using Cramer's Rule.

For this system we have


$
\begin{equation}
\begin{aligned}

|D| =& \left| \begin{array}{cc}
6 & 12 \\
4 & 7
\end{array} \right| = 6 \cdot 7 - 12 \cdot 4 = -6
\\
\\
|D_{x}| =& \left| \begin{array}{cc}
33 & 12 \\
20 & 7
\end{array} \right| = 33 \cdot 7 - 12 \cdot 20 = -9
\\
\\
|D_{y}| =& \left| \begin{array}{cc}
6 & 33 \\
4 & 20
\end{array} \right| = 6 \cdot 20 - 33 \cdot 4 = -12

\end{aligned}
\end{equation}
$


The solution is


$
\begin{equation}
\begin{aligned}

x =& \frac{|D_x|}{|D|} = \frac{-9}{-6} = \frac{3}{2}
\\
\\
y =& \frac{|D_y|}{|D|} = \frac{-12}{-6} = 2

\end{aligned}
\end{equation}
$

Precalculus, Chapter 9, 9.3, Section 9.3, Problem 55

The given geometric series is:
sum_(n=1)^7 4^(n-1)
Take note that if the geometric series has a form:
sum_(n=1)^n a_1 * r^(n-1)
its finite sum is:
S_n=a_1*(1-r^n)/(1-r)
Rewriting the given sigma notation in exact form as above, it becomes:
sum_(n=1)^7 4^(n-1)=sum_(n=1) 1 * 4^(n-1)
From here, it can be seen that the values of the first term and the common ratio are a1=1 and r=4.
Plugging in the values of a1 and r to the formula of Sn, the sum of the first seven terms of the geometric sequence is:
S_7=1*(1-4^7)/(1-4) = 5461

Therefore, sum_(n=1)^7 4^(n-1) = 5461 .

What were the causes of the Civil War? Which cause do you think was the most significant? Could this conflict have been avoided?

Simply put, slavery was at the center of the Civil War. While there were other issues at play (the tradition of states' rights, for example), it would be difficult to argue against the claim that by seceding, southerners were attempting to protect the continued survival of slavery into the future. After all, slavery's legal status was explicitly enshrined within the Confederacy's Constitution (as seen in Article 1, Section 9). But the full scope of that problem is far more complicated than a one word answer (“slavery”) would suggest.

Of the three questions asked, it's the third that's perhaps most significant: could this conflict had been avoided? Here we start to think about the larger context which gives rise to secession, and explains more deeply why the Civil War happened at all. The thing to keep in mind here is that secession was not a spur of the moment decision. In fact, an argument could be made that the Civil War culminated from a chain of events which could be traced at least as far back as 1848, with the end of the Mexican War, when the United States acquired territories west to California.

The decade that would follow would be one of heated tension and turmoil, even violence, surrounding slavery's legality in the territories. For both abolitionists and pro-slavery advocates, the stakes were high. Ever since 1787's Northwest Ordinance, there had been the precedence that US territories, upon reaching the minimum population requirements, could formally apply for statehood in the Union. Both abolitionists and slaveholders saw that that the future of slavery would be determined by the territories. Should abolitionists halt the spread of slavery into the territories, one day those territories would become states. Then the Free States would outnumber the Slave States, and could potentially have the majority required to end slavery through Congressional legislation. Likewise, should slavery be established in the territories, the institution would become more secure than ever.

Things would deteriorate quickly when California, thanks to the Gold Rush, reached the population threshold to formally apply for statehood in 1849. In California, slavery was made illegal. In response, Congress became gripped by debate and argument, with South Carolina Senator John C. Calhoun threatening secession as early as 1850, whereas Henry Clay of Kentucky and his allies championed the Great Compromise. While Clay's solution passed and California formally joined the United States in 1850, the tensions surrounding slavery would only grow worse from this point forward: from the Great Compromise to the Kansas-Nebraska Act, the Dred Scott Decision and the Lincoln-Douglas Debates, all the way to John Brown's 1859 raid at Harper's Ferry. In the end, the final straw came when Abraham Lincoln was elected President, and South Carolina responded by seceding.

Was the Civil War inevitable? That question is almost impossible to answer. What's more important is the recognition that it is difficult (and historically problematic) to separate the act of secession itself from the context that gave rise to it. Secession did not happen in a vacuum; it was the last act in a decade long drama as the question over slavery continually escalated, carrying over from one crisis to the next.

Though both Southern and Northern revisionists tended for many decades after the Civil War to explain its causes in terms of tariffs, states' rights in the abstract, and cultural differences, the direct cause of the war was, in fact, the issue of slavery and Southern fear of the North's interference with the "peculiar institution."
The election of Lincoln as President in 1860 was the immediate catalyst for the secession, first of South Carolina, and then of most of the other states south of the Mason-Dixon line. Lincoln and the Republican party had built their platform around the principle that slavery must not be extended into the territories of the United States. This was, in itself, an anti-slavery position. Revisionists generally asserted that, because Lincoln, himself, and many in his party, did not wish to abolish slavery where it already existed, the cause of the war had nothing to do with slavery. But this argument is a non sequitur. As stated, the planned exclusion of it from the territories was itself a position against slavery. In his speeches, during his debates with Stephen Douglas in 1858 and later, Lincoln had stated again and again that slavery was morally wrong. Moreover, the Southern leadership believed that stopping the spread of slavery would reduce the price of slaves and eventually destroy the institution. In addition, they sensed that even if Lincoln personally didn't wish to abolish slavery where it was already being practiced, others in his administration, in Congress, and among the Northern population in general were in favor of abolition, and that the more compromising position of Lincoln was just a cover for a more radical purpose.
As the secession process took place, the states which had already seceded sent "commissioners" to the other Southern states to urge their legislatures to vote for secession as well. The speeches made by the commissioners focused on the wish to preserve slavery and on their fear that abolition would destroy society and the dominance of the white race. If states' rights were the issue, it was the states' right specifically to preserve slavery that the seceding states wished to defend, not rights in the abstract, or protectionism against tariffs, as was often claimed.
The fact that most Southerners who served did not own slaves, as well as the fact that most Northern soldiers and many leading officers did not wish equality for black people, have often been advanced as reasons that slavery was not at the root of the war. But this argument is a kind of changing-the-subject affair. It confuses cause and effect and ignores what started the war in the first place. Even if Southerners believed they were fighting for the "land" and for "honor," the subtext of their defense of their home states was that they didn't want African Americans to be liberated and to mix freely in society with white people. The Jim Crow laws established after the war prove that this was their thinking.
One cannot see how, in the context of the developments taking place in the world at that time, the conflict could have been avoided. Americans in 1776 had known that a basic contradiction lay at the heart of the newly formed nation. The founders, even those who practiced slavery themselves, knew it was wrong. In the nineteenth-century, technology and the spread of democratic ideals, as well as the ban on the slave trade that went into effect in 1808, were making the oppression of people and the exploitation of labor something shameful and obsolete. Sooner or later an explosion would have to occur, as it did in April, 1861.

What does bias mean in history?

Bias in this context refers to the absence of objectivity. In historical practice, bias exists on two levels. The first is our own bias as historians. Whenever we try to understand historical events, we bring our own assumptions and beliefs, and these are shaped by our own times. Sometimes called "presentism" by historians, it is not good history, because it can tend to hold historical actors accountable to the standards of our time, as opposed to their own. We can see another level of bias when we read primary sources, which are the lifeblood of history. On the one hand, we depend on first-hand accounts and sources to make sense of the past. On the other hand, we have to remember that these accounts were generated by human beings, and that these humans brought their own biases to bear on the subject. For example, if we want to learn more about Native Americans, the writings and first-hand accounts of Europeans who came in contact with them are essential. But they are very problematic sources, because Europeans made assumptions about their own superiority, and in any case didn't really understand the culture of the people they were describing. Biases, both on the part of the historian and within the sources themselves, are unavoidable, and historians have to take them into account to do intellectually rigorous work.

How does the horse feel about wearing riding gear?

After an idyllic existence as a foal, the time has come for Black Beauty to make the difficult transition to adulthood. At the start of chapter 3, Black Beauty has reached the age of four. Squire Gordon comes down to the field to take a good look at the horse. After a close examination, he concludes that the time is right for Black Beauty to be broken in. This means he needs to be taught how to wear a saddle and bridle.
Black Beauty's used to wearing a halter and a headstall, but a bit and a bridle are a whole different matter. Having a bit in his mouth is a horrible experience for the young horse; it's not very nice having a piece of cold hard steel the width of a man's finger shoved into your mouth. Even worse, the bit's secured by uncomfortable straps that fit tightly around the nose, chin, and throat. But Black Beauty soon gets used to it. He knows that his mother and the other horses have to wear a bit and bridle; and the master was ever so careful when putting them on, making the whole experience much easier for the young horse with a combination of gentle patting, soft words, and oats.
The master's also very gentle when he puts the saddle on, which is generally a much more pleasant experience for Black Beauty. Again, it's amazing what some oats and a little TLC can do. One morning, the horse's master rides him around the meadow on the soft grass. It feels more than a little strange at first, but Black Beauty soon feels incredibly proud to carry his master, and each day he becomes more and more accustomed to it.

What is the summary of After the First Death by Robert Cormier?

Robert Cormier's After the First Death is a young adult suspense novel written in 1979 that revolves around a school bus that is hijacked by ruthless terrorists. The bus is headed to summer camp and is being driven by a young high school student named Kate.
The four hijacking terrorists, whose names are Miro, Antibbe, Artkin, and Stroll, ruthlessly announce that they kill a child for each time the police attempt to intervene. When Miro, one of the youngest of the terrorists is told to murder Kate, he hesitates. Meanwhile, the children are given candy laced with a sleeping drug in order to keep them calm and quiet. One of the children accidentally overdoses from this drug and dies, and the killing of Kate is postponed so she is able to help take care of the now-panicking children.
Kate, thinking like the star of an action film, decides to attempt to drive the bus off a bridge. Her plan is unsuccessful due to the bus stalling, and Kate begins to panic.
Once the terrorists' leader Sedeete is kidnapped, Ben, a young boy whose father is the general of an anti-terrorism squad, is sent to provide proof that the Sedeete is alive. Ben is tortured by the terrorists. Miro and Kate escape the bus, and Miro eventually kills Kate when he thinks she is attempting to deceive him.
Eventually, Ben is ashamed and scarred for the ordeal and commits suicide. His father goes insane and imagines talking to him in an insane asylum.

int_0^(1/4) xln(x+1) dx Use a power series to approximate the value of the integral with an error of less than 0.0001.

From the basic list of power series, we have:
ln(x) =sum_(n=0)^oo (-1)^(n) (x-1)^(n+1)/(n+1)
         = (x-1)-(x-1)^2/2+(x-1)^3/3 -(x-1)^4/4 +...
We replace "x " with "x+1 " to setup:
ln(1+x) =sum_(n=0)^oo (-1)^n ((x+1)-1)^(n+1)/(n+1)
               =sum_(n=0)^oo (-1)^n x^(n+1)/(n+1)
               =x-x^2/2+x^3/3 -x^4/4+...
Note: ((x+1)-1) = (x+1-1) = x
Then,
x ln(1+x) =sum_(n=0)^oo (-1)^n x^(n+1)/(n+1) *x
                   =sum_(n=0)^oo (-1)^n x^(n+2)/(n+1)
 
Note: x^(n+1) * x = x^(n+1+1) =x^(n+2)
Applying the summation formula, we get:
x ln(1+x)= x*[x-x^2/2+x^3/3 -x^4/4+...]
                  or
                  = x^2 -x^3/2+x^4/3-x^5/4 +...
Then the integral becomes:
int_0^(1/4) xln(x+1) = int_0^(1/4) [x^2 -x^3/2+x^4/3-x^5/4 +...]dx
To determine the indefinite integral, we integrate each term using the Power Rule for integration: int x^n dx= x^(n+1)/(n+1) .
int_0^(1/4) [x^2 -x^3/2+x^4/3-x^5/4 +...]dx
= [x^3/3 -x^4/(2*4)+x^5/(3*5)-x^6/(4*6) +...]_0^(1/4)
= [x^3/3 -x^4/7+x^5/15-x^6/24 +...]_0^(1/4)
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
F(1/4) or F(0.25) =0.25^3/3 -0.25^4/7+0.25^5/15-0.25^6/24 +...
                                =1/192-1/1792+1/15360 -1/98304+...
F(0)=0^3/3 -0^4/7+0^5/15-0^6/24 +...
          = 0-0+0-0+...
All the terms are 0 then F(0) =0 .
We may stop at 4th term (1/98304~~0.00001017) since we only need an error less than 0.0001 .
F(1/4)-F(0) = [1/192-1/1792+1/15360 -1/98304]-[0]
                       = 0.00470522926
Thus, the approximated integral value:
int_0^(1/4) xln(x+1) dx ~~0.0047

What observations help us determine whether a chemical reaction has taken place?

There are several observations that can be made to determine if a chemical reaction has occurred. The first is a change in temperature. Heat can be absorbed (endothermic reaction) or released (exothermic reaction) which results in a temperature change. This can be noted with a thermometer. Reactions can also have a color change. A change in color represents a chemical reaction. Another observation is if there is a smell or odor after the reaction takes place. When a reaction takes place, gases can sometimes be removed from the system. This can be observed by the formation of bubbles. Another observation is the formation of a precipitate. This is a solid that forms out of solution. When a solute is dissolved in a solution, a chemical reaction took place. Lastly, if there is a change in pH a chemical reaction took place. This will need to be tested with pH strips.

What brought on the Great Depression, and why was Hoover not able to address the crisis?

Following World War I, a series of three presidential administrations promoted the economic theory known as laissez-faire (which translates to English as “let do”) capitalism. This philosophy encourages the government to stay out of the economy and maintains that the lack of interference will promote growth within the private market. However, the increasing distance between regulatory power and a whirlwind economy had serious consequences that Americans had to face collectively during the Great Depression.
The lack of oversight between the federal government and the banking industry was the primary driver of the stock market crash of 1929. Americans were buying many expensive items on unlimited credit and purchasing stocks “on the margin,” creating a bubble within the stock market that burst in October in 1929. The domino effect caused by the stock market crash led to the Great Depression. People pulled all of their money from their bank accounts in mass numbers in a practice that came to be known as “bank runs.” Without the ability to lend, banks closed in mass numbers, and local economies were decimated. Americans lost their jobs and their homes across the country.
Instead of reversing course and advocating government intervention to solve the crisis, President Hoover continued to promote the laissez-faire theory, which contributed to the economy getting progressively worse. Instead of investing in work programs for the American public, Hoover provided large banks and corporations with the expectation that this money would filter back into the American economy. However, these funds typically stayed within those organizations, and little was done to lift the country out of the economic crisis. Hoover eventually did promote legislation intended to reverse the course, but it was too little, too late.
https://hoover.archives.gov/exhibits/great-depression

In what ways do the two women's emotional and psychological struggles, in relation to the experience of the shelter, aggravate the racial conflict between them? How did it help to build a bond between them?

The bond develops between Twyla (the black girl) and Roberta (the white girl) as a result of how they are treated by the other orphans. Both of the girls' mothers are still alive, therefore they "[aren't] real orphans with beautiful dead parents in the sky." Both, particularly Twyla, whose mother "danced all night," retain the glimmer of hope that someone will come get them.
In addition, both Twyla and Roberta failed subjects in school. Roberta also has the kind habit of leaving "whole pieces of things on her plate" for Twyla, who is undernourished, to eat.
The bond develops out of loneliness, things shared in common, and their isolation from the other orphans and their teachers. This is particularly interesting in light of the prejudice that both girls have learned. Twyla's mother forewarned her that white people "smelled funny." Meanwhile, Roberta's mother expresses her disapproval of black people by "[looking] down at [Twyla] and then looked down at Mary too" before refusing Mary's handshake, then walking quickly to the back of the line in front of the chapel. This mistrust has been instilled in them, but it becomes irrelevant at the orphanage, where they have no other recourse for companionship. When Roberta later, during young adulthood, dismisses Twyla for her ignorance about Jimi Hendrix, as though trying to embarrass her, Twyla is able to use their shared memory of abandonment to remind her that they are the same.
Another shared memory that becomes muddled in both of their minds is that of the abuse of Maggie, "a sandy-colored," mute, bow-legged old woman who worked in the kitchen. Her vulnerability and childlike appearance, including the "chin-straps of her baby boy hat," made her a target of the older orphans. Roberta and Twyla imagine themselves as Maggie's abusers, though they never were. For Roberta, the old woman's mental instability reminds her of her mother's mental illness and her fear that she would face the same fate. For Twyla, Maggie's deaf-mute state reminds her of her mother, who danced all night, who heard nothing but party music, who "would [not] hear you if you cried in the night." Maggie's small, awkward body reminds the girls of their own vulnerability and of the fact that they, like Maggie, were not wanted by anyone. Maybe they could end up like her, too.
Roberta, due to her whiteness, is able to achieve an upper-class status that eludes Twyla. However, that sense of vulnerability, of not being wanted, revisits them through the memory of Maggie. In an attempt to free herself from it, and knowing the currency of her whiteness, Roberta tries to make herself less vulnerable through a rejection of Twyla. She first does this in the 1960s at the Howard Johnson's where Twyla works as a waitress. She does it again, probably in the 1970s, when protesting against busing. In a moment of peril, the narrator reaches for Roberta, who, at the orphanage, had been there to pull her up, "to kick and scratch" during a fight; but, in this instance, "no receiving hand was there."

To what extent does Franz Kafka's life experience influence the novel "The Metamorphosis." Provide in-depth detail.

Franz Kafka’s life experiences had a direct influence on his novella The Metamorphosis. The hypochondriac author tells a story of a man/creature in decline, a fate that Kafka experienced himself, albeit less fantastically.
As a Jewish man living in Austria, Kafka experienced the rejection and isolation that anti-semitism brought on his community. In the story, Gregor experiences a similar sense of loneliness after his transformation into a giant insect. The harsh treatment that others inflict upon him are indicative of Kafka’s experiences, as those outside of his religious and ethnic community would behave in a manner sometimes similar to those who come in contact with Gregor.
Kafka’s experiences with his own family seem to have a strong influence on the story as well. His overbearing father caused Kafka to develop a sense of anxious isolation, as Gregor likewise experiences in the story. Another similarity is the fact the Kafka lived with his parents after graduating from college. This sense of dependence is mirrored in the story, as Gregor becomes incapable of caring for himself.
Gregor becomes further isolated as the family enjoys meals and music without his company. His appearance causes his mother to cry and faint, his father to swat and throw apples at him, and his sister to gradually resent him. Drawing on a family that was cold and distant, a failed marriage engagement, and a notable lack of self-esteem, Kafka tells a story that transfers at least some of his own feelings onto his character in The Metamorphosis. Gregor is lonely and gradually resentful of his circumstances, as Kafka no doubt experienced.
The author’s stressful life experiences and the stories produced by that tension gave us the term “Kafkaesque,” meaning full of anxiety and uncertainty. These isolating emotions are on full display in Gregor’s story as he is rejected by those he loves most.

There are many parallels, or similarities, between the real life of Franz Kafka and the fictional life of Gregor Samsa, the protagonist of “The Metamorphosis.” For one, Kafka had a domineering and critical father in real life, paralleled by Gregor’s hostile and cruel father in “The Metamorphosis.” Kafka’s mother was dominated by his grumpy father, just like Gregor’s parents in the novel. Kafka felt intimidated by his emotionally distant father in the novel and felt weak and unsuccessful because of him, as Kafka felt toward his father. Gregor’s father seemed to consider money and social position of great importance as did Kafka’s father. Kafka’s father even directed his rage toward his son Franz, as did Mr. Samsa in “The Metamorphosis,” for example, when he angrily threw an apple at Gregor. Unlike Gregor, Franz Kafka had 3 sisters (and 2 younger brothers who died in infancy); however, Kafka took his role as big brother seriously and was closer to his youngest sister, Ottla, than other members of his family. Similarly, Gregor was closest to his younger sister Grete in “The Metamorphosis,” at least until she became rather uncaring and hostile toward him later in the novel, just as Mr. Samsa, their father, did. Franz Kafka even chose to live with his family for most of his adult life, as did Gregor Samsa in the novel.
The real-life Kafka also seemed unhappy and mentally and physically delicate, as did the character of Gregor. In “The Metamorphosis,” Gregor Samsa was a traveling salesman (at least until his transformation into a vermin). The real-life Franz Kafka worked in the field of insurance. Like Gregor, however, Kafka hated his work but took it very seriously, working hard to do what was required of him as an employee. The general alienation (or disconnection from society, including his family) and anxiety that Gregor demonstrated so much in “The Metamorphosis” were also feelings that Franz Kafka felt on a fairly continual basis. In real life, Kafka often felt isolated from society and did not understand the strange world in which he lived, which is mirrored by Gregor’s character in “The Metamorphosis.”

Further Reading:
https://www.biography.com/people/franz-kafka-9359401
https://www.britannica.com/biography/Franz-Kafka
http://www.kafka-online.info/franz-kafka-biography.htm

Like Gregor Samsa, who lives with his parents, Kafka was deeply shaped by his immediate family. He lived in the same neighborhood as his parents for almost his entire life. He had a complicated relationship with them, especially with his father, who, like many in middle-class European society, did not approve of his son's literary aspirations. Kafka's father was a successful businessman and hoped that his son would follow what he deemed a more practical pursuit. Gregor's father in "The Metamorphosis" is also a problematic figure. His family depends on his income as a salesman to maintain their lifestyle, but when he transforms into a bug, his family quickly loses interest in him. They are not willing to support him in the same way he had provided for them, and his parents treat him with a combination of neglect and outright cruelty.
The bleak tone of "The Metamorphosis" and much of Kafka's body of work surely must have been influenced by the sad state of his personal health. He suffered from chronic illness throughout his life and died of tuberculosis. So the physical decline experienced by Gregor Samsa, while absurd, may have been an allusion to the illnesses endured by Kafka himself.
https://www.biography.com/writer/franz-kafka

Calculus of a Single Variable, Chapter 6, 6.2, Section 6.2, Problem 50

Formula for compounding n times per year: A=P(1+r/n)^(nt)
Formula for compounding continuously: A=Pe^(rt)
A=Final Amount
P=Initial Amount
r=rate of investment expressed as a percent
n=number of compoundings per year
t=time in years

a) r=5% n=1 (annually)
A=P(1+r/n)^(nt)
2000=1000(1+.05/1)^(1*t)
2=1.05^t
ln(2)=tln(1.05)
ln(2)/ln(1.05)=t
14.21=t
Final Answer: 14.21 years

b) r=5% n=12 (monthly)
A=P(1+r/n)^(nt)
2000=1000(1+.05/12)^(12*t)
2=(1.00416)^(12t)
ln(2)=12tln(1.00416)
ln(2)/[12ln(1.00416)]=t
13.89=t
Final Answer: 13.89 years

c) r=5% n=365 (daily)
A=P(1+r/n)^(nt)
2000=1000(1+.05/365)^(365*t)
2=(1.000136)^(365t)
ln(2)=365tln(1.00136)
ln(2)/[365ln(1.00136)]=t
13.86=t
Final Answer: 13.86 years

d)A=Pe^(rt)
2000=1000e^(.05*t)
2=e^(.05t)
ln(2)=.05tlne
ln(2)/[.05lne]=t
13.86=t
Final Answer: 13.86 years

Do you think that the narrator is to blame for Doodle's death in "The Scarlet Ibis?"

It is hard to blame the narrator ("Brother") completely because he is just a kid himself. He openly admits his responsibility in tormenting Doodle and pushing him too far, though, so the narrator is largely to blame.
Brother says Doodle was "a disappointment" from the beginning. Brother wanted a more physically able companion. As a result, he resents Doodle. Brother torments Doodle by showing him the casket that was meant for him.
Brother teaching Doodle to walk seems like a generous gesture to his parents, but Brother reveals he only taught Doodle to walk out of shame.

They did not know that I did it for myself, that pride, whose slave I was, spoke to me louder than all their voices, and that Doodle walked only because I was ashamed of having a crippled brother.

At the end of the story, when Doodle has "failed," Brother leaves him, literally and symbolically. Brother runs away faster and faster, knowing Doodle will push himself but inevitably be unable to keep up. As Brother runs away, he feels a "streak of cruelty." He runs faster and pushes Doodle to run himself ragged. He puts Doodle through physical and emotional strain and this becomes too much for Doodle's body to handle.

Calculus: Early Transcendentals, Chapter 4, 4.8, Section 4.8, Problem 26

cos(x^2-x) = x^4
Set the left side equal to zero.
0=x^4-cos(x^2-x)
To solve using Newton's method, apply the formula:
x_(n+1)=x_n - (f(x_n))/(f'(x_n))
Let the function of the given equation be:
f(x) =x^4-cos(x^2-x)
And its derivative is:
f'(x) = 4x^3 + (2x-1)sin(x^2-x)
Plug-in f(x) and f'(x) to the formula of Newton's method.
x_(n+1) = x_n - ((x_n)^4-cos((x_n)^2-x_n))/(4(x_n)^3+(2x_n-1)sin((x_n)^2-x_n))
To get the initial value of x, refer to the graph of f(x). (See figure.)
Notice that when f(x) =0, the values of x are near -0.8 and 1. Use these two values of x to solve for the roots of the function to eight decimal places.
For the first root, let the initial value be -0.8.
x_1=-0.8
x_2= x_1 - ((x_1)^4-cos((x_1)^2-x_1))/(4(x_1)^3+(2x_1-1)sin((x_1)^2-x_1))=-0.7396478896
x_3= x_2 - ((x_2)^4-cos((x_2)^2-x_2))/(4(x_2)^3+(2x_2-1)sin((x_2)^2-x_2))=-0.7348883415
x_4= x_3 - ((x_3)^4-cos((x_3)^2-x_3))/(4(x_3)^3+(2x_3-1)sin((x_3)^2-x_3))=-0.7348591049
x_5= x_4 - ((x_4)^4-cos((x_4)^2-x_4))/(4(x_4)^3+(2x_4-1)sin((x_4)^2-x_4))=-0.7348591038
Notice that the two approximates have the same eight decimal places. So we stop the iteration here. Thus, one of the roots of f(x) is x=-0.73485910 .
For the second root, let the initial value be 1.
x_1=1
x_2= x_1 - ((x_1)^4-cos((x_1)^2-x_1))/(4(x_1)^3+(2x_1-1)sin((x_1)^2-x_1))=1
Notice that the second root is an integer. It has an exact value which is x=1.

Therefore, the solution of the equation cos(x^2-x) =x^4 is x={-0.73485910, 1}.

What are the advantages and disadvantages of using Big Five Trait Taxonomy to assess personality in a specific population?

The Big Five personality traits (also called the five-factor model and the OCEAN model) refers to a taxonomy for personality traits. This taxonomy is based on the theory that uses common language descriptions to categorize individuals into five broad categories that describe psyche and personality.
The five personality traits that comprise this taxonomy include: openness to experience, conscientiousness, extraversion, agreeableness, and neuroticism.
This theory contends that family life and how an individual was raised in childhood will affect where one falls in this taxonomy. Openness to experience, conscientiousness, extraversion, and neuroticism are all associated with a stable life for an individual during childhood.
An advantage of this taxonomy is using it to better understand others and oneself. Acknowledging the validity behind these traits and associated classification can help explain motivations and causes for specific decisions. With a better understanding of others as well as oneself, an individual can work to put himself or herself in better situations that are more likely to produce positive outcomes.
A disadvantage of the system occurs when an individual lends too much credence to the theory and uses it to explain every decision someone makes. Humans are complex beings whose decisions are made based on a number of complicated factors. Assigning preconceived notions to an outcome of a decision strictly due to their classification within the taxonomy is a fallacy and unscientific way to evaluate oneself and others.

The Big Five Trait Taxonomy is a contemporary conceptualization of personality across five different dimensions. These dimensions include Openness to Experience, Conscientiousness, Extroversion, Agreeableness, and Neuroticism (it may help to remember them by the mnemonic O.C.E.A.N.).
Let's start by going over the advantages.
First, the Big Five Taxonomy measures personality along scales and not through categories. This means that the taxonomy does not simply describe whether or not a person exhibits a trait. It also describes the degree with which a person possesses it, making it easier to track a person's personality as they age or compare different populations. This sets it apart from personality tests like the Myers-Briggs, which places people into personality categories. The issue with this approach is that fails to account for nuanced situations in which a person straddles the boundary between one personality trait and its counterpart.
Second, the Big Five personality test is easy to take and widely accessible. To take the test, one does not need to go to a special facility or proctor. One can find it online, and with just 50 items, it takes most people between three and eight minutes to complete. This makes it more possible for personality psychologists to distribute tests throughout entire populations and collect data from large sample sizes.
The Big Five theory of personality certainly has disadvantages, however.
One of the most frequently made criticisms is that it focuses on traits chosen with an inherent Western bias, neglecting to account for cultural differences. A behavior that typically indicates high neuroticism in the US, for instance, may not garner the same interpretation in Japan.
A second weakness is one shared by many personality measures, and it is that the Big Five Taxonomy relies on self-report data. The test-taker, whether consciously or not, may answer questions in a way that produces the results he or she desires.
Finally, the Big Five Taxonomy defines personality under an implicit assumption that personality is static. In reality, a person's behavior and personality can undergo significant changes from one day to another. For example, a person may experience positive social events that sway him or her towards a high degree of extroversion that he or she may not exhibit the following week. A country might witness a major tragedy that pushes its population towards unusually high neuroticism in the aftermath.
While the Big Five theory of personality has its fair share of disadvantages, it is still widely used among personality psychologists. If you are interested in seeing it in action, you can take the assessment yourself here.

The Big Five Trait Taxonomy is a model of personality. This inventory is the result of decades worth of research into the fundamental components of personality. Five dimensions comprise this theoretical framework including openness, conscientiousness, extroversion/introversion, agreeableness, and neuroticism. It is important to note that these dimensions rely on a spectrum of degree, meaning that a person typically possesses a range of these characteristics rather than either-or. This inventory is often used to predict the success of relationships based on each individual's personality dimensions.
The primary disadvantage of this model is similar to any self-reporting psychological assessment, which is the possible likelihood that the results will be skewed. Consider someone taking the Big Five inventory to predict the success of their relationship. It is not uncommon for someone in this scenario to rely on confirmation bias, which is the result they are hoping to see, rather than objectivity. Another disadvantage might be language barriers. A specific population may misinterpret inventory items based on their cultural understanding. Furthermore, the dimensions themselves may not be traits that certain cultures value, making it difficult to understand the results.
A possible advantage to the Big Five inventory is the potential for its intended outcome, which is to understand oneself better. Given that a specific population understands and values the measured dimensions, it can be an excellent tool for self-awareness. Moreover, this self-awareness can certainly contribute to better functioning relationships and perhaps a better functioning society.
https://www.psychologytoday.com/us/basics/big-5-personality-traits

https://www.psychologytoday.com/us/blog/science-choice/201504/what-is-confirmation-bias

In two single-spaced pages (please answer all the parts), use critical tools to analyze cultural texts: In this case, you have to make an argument not just about why Charlie Brown’s endless struggle against Lucy and her football is funny, but what the significance of the humor is. Is this cartoon about gender politics and sexism, and if so, how do you read Lucy’s character and her motives? Is it a nihilistic warning against ambition and the inevitability of our disappointment or a sympathetic portrayal of an indomitable underdog? Consider one of the theorists of humor we’ve discussed already (Arendt/Brecht, Freud, Critchley, Carpio, or Bergson) and make a concise, detailed argument about what Charlie Brown’s struggle is, why it is important, and why it is important to address it in the form of a joke. For this assignment, closely analyze the plot and language of one of Peanuts cartoons.

Peanuts creator Charles M. Schulz prided himself on putting Charlie Brown through the wringer. In fact, a September 2015 article in The Atlantic claims that when Schulz was asked if his final strip would include Charlie Brown finally kicking the elusive football, Schulz reportedly said "'Oh, no! Definitely not! . . . That would be a terrible disservice to him after nearly half a century.'" This in itself suggests that Peanuts is, as a whole, "a nihilistic warning against ambition and the inevitability of our disappointment"; the overwhelming majority of strips focus on the disappointment of children and their too jaded, perhaps too wise, views on the nature of existence. However, because of Charlie Brown's perpetual attempt to try and try again—to give others the benefit of the doubt despite knowing that he will be disappointed—the strip is also "a sympathetic portrayal of an indomitable underdog." This is what makes it so endearing, even nearly three quarters of a century after its first publication.The specific comic in focus presents good old Chuck's perpetual struggle, but as is often the case, Schulz has presented it in a slightly different way. When it comes to the "football gag," as it is often referred to, the beginning and the ending are always the same. The middle is where Schulz will switch things up a bit. This is where Lucy's different strategies come into play. In this particular strip, she has chosen to sucker Chuck in by playing on his sympathies toward her. She accuses him of threefold mistrust, claiming he mistrusts her as an athlete, a person, and, finally, a woman. She then connects herself to his mother via gender, which is what finally gets Charlie Brown to fall for her trick, yet again. However, despite her ploy, this cartoon seems to be less about sexism and more about sympathy. As the above mentioned Atlantic article states:

Peanuts was deceptive. It looked like kid stuff, but it wasn’t. The strip’s cozy suburban conviviality, its warm fuzziness, actually conveyed some uncomfortable truths about the loneliness of social existence.

Charlie Brown wants so desperately to connect to those around him that he is always willing to give people the benefit of the doubt, regardless of gender, race, or age; he simply will not learn from past experiences because he wants the world to be a much better place that it is. Perhaps this is why the comic and characters are so timeless. Deep down, most of us have the desire to connect, even when our attempts are either rebuffed or deliberately foiled. Like good old Charlie Brown, we keep falling flat on our back because even the chance of contact makes it all worth it.
https://www.theatlantic.com/magazine/archive/2015/11/the-exemplary-narcissism-of-snoopy/407827/

How does the schoolmaster Kantorek refer to his former students in All Quiet on the Western Front? Why do Paul and Kropp scoff at the term Kantorek uses?

The schoolmaster Kantorek refers to his former students as "Iron Youth."
Paul and Kropp scoff at the term Kantorek uses because it is incongruent with what the young soldiers have become. The word "iron" conjures up images of strength and durability, while the word "youth" conjures up images of innocence and life. Yet, Paul, Kropp, and the other soldiers are no longer the innocent, trusting youth they once were. Many of them have been physically and emotionally shattered by their war experience. The brutal violence of war has dulled their faith and enthusiasm for pretentious labels.
Paul maintains that it was men of the older generation like Kantorek who taught him and his peers that "duty to one's country is the greatest thing." To Paul, the older generation were "very free with all these expressions" of duty and patriotism. However, they were never the ones who had to sacrifice  life and limb to fulfill the dictates of their philosophy. In other words, Paul and Kropp think that the older generation has betrayed them.


They surpassed us only in phrases and in cleverness. The first bombardment showed us our mistake, and under it the world as they had taught it to us broke in pieces. While they continued to write and talk, we saw the wounded and dying. While they taught that duty to one's country is the greatest thing, we already knew that death-throes are stronger.

The horrific experiences of war have essentially made the young soldiers old before their time. They no longer stand upon the threshold of life, as Kantorek would have maintained. Instead, adrift on a sea of confusion and pain, they are bereft of any hope for a better future. Both Paul and Kropp are powerless as they watch their fellow soldier, Kemmerich, die. They can do nothing for him; all the patriotic catchphrases are impotent in the face of youthful death.
While the older men have "wives, children, occupations, and interests... a background...so strong that the war cannot obliterate it," young men like Paul and Kropp have nothing to hold on to. So, the idea that they are "Iron Youth" is ludicrous to them because it is incongruent with what war has reduced them to.