Did Conrad’s brief but intense experience in Africa in 1890 open his eyes to Europe’s crimes, or did he visit and return with the same blinders worn by others during his time? Your answer should include mention of Belgium’s role in the so-called Congo Free Republic.

It is safe to say that Conrad was horrified by what he witnessed in Congo. While Heart of Darkness has been criticized by Chinua Achebe as racist because Conrad depicts the Congolese as subhuman or savage, the real source of Conrad’s disgust was the whites he encountered in the Congo Free State under Belgian King Leopold II’s repressive and exploitative regime. The Congo was ruled by Leopold essentially as his private property, and, while he was able to gain control of Congo by promising the European powers that he would bring civilization and Christian values to the jungle, his purpose was to extract as much money from the country (in the form of raw materials) as he could. This took the form of ivory at first, but after the invention of the pneumatic tire, the prime commodity was rubber. Leopold formally confiscated all the land in the Congo and imposed a tax on locals in the form of rubber, essentially converting the entire country into a forced labor camp. What Conrad took from his Congo experience was that the colonizers were nothing more than looters. No doubt this is why after signing up to work in the Congo for three years, he quit after only one.

Discuss the origins of the major social-reform movements in the early nineteenth century. In what ways did they influence American society and politics?

Social reform movements largely stemmed from the Second Great Awakening. This movement led to increased evangelism and people believing that God commanded them to change what was wrong with society. One social change movement that came from this period was the temperance movement. Factory owners wanted their workers to work efficiently and soberly. Women also did not want their husbands buying alcohol with their entire paycheck and/or being abusive drunks. While the movement did not catch on nationally because the United States made too much money on excise taxes, some localities did decide to go dry.
The Second Great Awakening also helped to drive the abolitionist movement. People thought that if they were equal before God then it should be wrong for people to own other people. They also viewed slavery as something that created laziness, something that displeased God. Many abolitionists were also prominent in the church such as Henry Ward Beecher. Likewise, Southerners who were influenced by the Second Great Awakening believed that God condoned slavery by placing it in the Bible. Some also claimed that they were doing their slaves a favor by converting them to Christianity.
Not all social movements came from the Second Great Awakening. The women's rights movement came from the Market Revolution. Women were starting to work in factories outside the home and many thought that they should receive more rights in marriage and suffrage. The women's rights movement was often tied to the abolitionist movement as well as both sides often used the same speakers to champion their causes.

The reform movements of the antebellum period emerged in the context of two enormously important developments: the Second Great Awakening and the Market Revolution. The Second Great Awakening was a national religious revival that featured an emphasis on evangelism and an individual's relationship with the divine. Many people took their religious faith as a mandate to improve the world, and some even believed that reforming society's ills was the way to bring about God's kingdom on earth. This belief in free will and human redemption motivated a number of reform movements, ranging from temperance to prison reform to, of course, abolition. Each was motivated by a religious conviction that sin and injustice could not be tolerated in a society, and that it was the duty of Christians to eliminate these evils.
But reform movements also took place in the context of the major social changes associated with the emergence of capitalism in the United States. Known as the Market Revolution, this development led to rapid change, including economic instability, mass communication, and the transformation of traditional occupations to mechanized and more disciplined work. This was related to reform movements in many ways. Many business owners embraced temperance, for example, as a means of maintaining a disciplined workforce. But the expansion of slavery, which was also a direct consequence of the Market Revolution's demand for more cotton, also galvanized abolitionists to agitate for its end.
The abolition movement in particular had a profound effect on politics, at least in the sense that it tended to contribute to Southern concerns that the North threatened the institution of slavery. On the local level, reformers promoted normalized public education, temperance laws, prison reform, and many other improvements.
http://www.americanyawp.com/text/08-the-market-revolution/

The origins of the reform movements of the early 1800s can be traced back to the Second Great Awakening and the formation of new religious groups. The Second Great Awakening led to an increase of religious study and religious practice. It also encouraged missionary work and the focus on improving society. New religious groups tried to create the perfect society. These groups focused less on the industrial growth of the country and more on the community as a whole. They believed in cooperation among people instead of competition between individuals.
The reforms movements impacted society in many ways. There were efforts to improve the American educational system by training teachers and having a longer school year. There was a growing anti-slavery movement in the United States, and some people wanted to reduce or eliminate the availability of alcohol. Women’s rights also became a focus of the reform movement, along with improving the treatment of people who were mentally ill and who were in prison. These activities impacted politics as some northern states adopted laws banning slavery and eliminating alcohol. Anti-slavery political parties formed such as the Free Soil Party and the Republican Party. Anti-slavery societies such as the American Anti-Slavery Society worked to enact laws ending slavery. The American Colonization Society worked to free slaves and to relocate them to Liberia. Eventually, political parties had to pay attention to the demands women were making for equal treatment and for equal rights, including the right to vote.
https://ohiohistorycentral.org/w/American_Anti-Slavery_Society?rec=832

https://www.thoughtco.com/free-soil-party-1773320

The social reform movements of the early 19th century arose in part from the Second Great Awakening. This movement emphasized good work and a more enthusiastic experience of religion. It strengthened religions such as Baptism and Methodism, was in part a reaction to the rationality of Enlightenment, and grew out of the Romantic movement and its emphasis on emotion over reason. 
The social reform movements of the early 19th century included temperance, reform of prisons, women's rights, and abolitionism. The abolitionist movement in particular influenced American society as it grew in force in the antebellum period. After the Second Great Awakening, the moral imperative abolitionists felt to end slavery intensified, and there was a movement away from gradualism (the eventual end of slavery) to a sense that slavery had to end immediately. The fervor that abolitionists felt intensified the question of slavery in the country (particularly when new states were added to the union and had to decide between being slave or free states) and pushed the country toward the brink of war. 

How does Jing-Mei's attitude toward her mother change in the final chapter of The Joy Luck Club by Amy Tan?

In the final chapter of The Joy Luck Club, the main character, Jing-mei, chooses to embrace and take on her mother's Chinese identity. Jing-mei is attempting to write her mother's story. She is battling a cultural gap throughout the story, as she was raised in the US and her mother was raised in China. Jing-mei describes her dislike for her mother's Chinese culture growing up. As a teenager, Jing-mei leaned into assimilation and resisted her mother's Chinese teachings. She didn't understand her mother's way of life and preferred to spend her time with her white friends. As an adult, Jing-mei begins to want to learn more about her heritage and her mother's life. Throughout the novel, Jing-mei attempts to reconcile this gap and gain a closer understanding of her mother. She does just that when she travels to China and meets her half-sisters. Here she narrows the gap and brings the two worlds together.
In the final chapter she states,

The minute our train leaves the Hong Kong border and enters Shenzhen, China, I feel different. I can feel the skin on my forehead tingling, my blood rushing through a new course, my bones aching with a familiar old pain. And I think, My mother was right.

In this final chapter, Jing-mei embraces her mother and the Chinese identity she represents. The character says,

But today I realize I've never really known what it means to be Chinese.

The story ends with Jing-mei embracing her sisters and understanding for the first time how much she is like her mother.

In the final chapter of the novel, Jing Mei comes to accept her mother's premise about being Chinese. As she prepares to meet her half-sisters, she finds that she can finally revel in being both Chinese and American.

So, there was no doubt in her mind, whether I agreed or not: Once you are born Chinese, you cannot help but feel and think Chinese. "Someday you will see," said my mother. "It is in your blood, waiting to be let go."

Jing Mei's attitude towards her mother begins to change when she hears the true story of how Suyuan had to leave her twin girls behind decades earlier. After fleeing Kweilin, Suyuan had tried to get to Chungking, where her husband was stationed. However, her physical suffering eventually made traveling on foot all but impossible.
Suyuan was suffering from dysentery pains; additionally, she was hungry, exhausted, and thirsty. In the end, to make sure that her babies survived, she had had to leave them behind. Suyuan was to have a rude awakening when she got to Chungking, however; her husband had died two weeks earlier. Bereft of both her babies and husband, she had vowed not to rest until she found her daughters again.
In continuing her mother's quest, Jing Mei comes to see how much Suyuan had loved each of her daughters. When she sees her half-sisters at the airport, she sees her mother's image in their faces. Just as she did everything she could to preserve her twin daughters' lives, Suyuan also taught Jing Mei how to value her Chinese heritage. Jing Mei's attitude towards her mother begins to change to one of respect and deep appreciation after she realizes how much her mother had sacrificed for her and her sisters when she was alive.

IN THE FEDERALIST PAPERS 10 How did the 20th century developments of Primary Elections and Expansion of Suffrage move the United States from a less democratic System to a more democratic system?

The development of the primary election and the expansion of suffrage moved the United States toward a more democratic society. Before primary elections were held, party leaders chose the candidates of the party who were running for office. This limited the involvement of citizens in determining who their leaders would be. For example, the state legislatures used to choose United State Senators. This changed with the passage of the 17th amendment. With the direct primary, anybody could run for an office. Party members would then choose their candidate.
The expansion of suffrage meant more people were voting. When more people are involved in the process of choosing their leaders, it allows for the expansion of democracy. In 1920, women got the right to vote. As a result, there was an expansion of the democratic process by allowing women to vote.
When more people are involved in democratic progress, this reduces the likelihood that factions will control the government and taint our public administrations.
https://avalon.law.yale.edu/18th_century/fed10.asp

Explain how Woody ended up in Japan.

The other educator answer here does a good job of explaining what Woody does while he is in Japan and what it means to him personally. Instead of repeating this, let us look at some of the historical background of why Woody would be in Japan as part of an occupying American force.
After the surrender of Japan in August of 1945, the United States led the Allied effort to rebuild the shattered nation. This was also the case in Europe, where it was thought that the broken Axis powers would be susceptible to Soviet influence if their economies were not quickly rebuilt. Under the terms of the peace treaty, Japan's government was also to be restructured and its military dismantled. To achieve this, several divisions of US military personnel would spend the next six years occupying Japan.
Woody was one of the 5,000 Japanese American GIs to participate in the occupation. Many served as interpreters. Woody was still a member of the army after being drafted during the war. Unlike Woody's experience during the war, he serves in an integrated unit alongside non-Japanese American soldiers. It was thought that having Japanese Americans in these units would help build connections between the occupiers and the occupied. For many Nisei like Woody, this served as their first direct experience with their ancestral homeland.

Woody is in Japan as part of the American occupying forces. While stationed there, he makes the decision to go visit his family. This takes place almost a year after the atomic bomb was dropped on Hiroshima. At first, Woody is somewhat reluctant to visit. After all, he's part of what the Japanese consider to be an enemy force. Nonetheless, he goes ahead with the visit and is soon very glad that he did. His family welcome him with open arms and are genuinely pleased to see him.
Woody is thoroughly Westernized, a loyal American citizen, completely comfortable in his own identity. Yet his visit to his Japanese family is very important as it enables him to reconnect to his heritage and gain a greater understanding of the pride of the Wakatsukis, that "ancient, inextinguishable dignity."

How did the Cold War affect Africa?

As both the United States and the Soviet Union were nuclear powers, direct confrontation between the two superpowers was impossible, not to say unthinkable. So both sides used proxies in the developing world to help advance their respective geopolitical objectives. The continent of Africa, like Asia, became a Cold War battleground. The economic weakness of Africa made it especially vulnerable to overtures from both Americans and Russians alike as they sought to gain a strategic foothold in the continent. The main area of interest for successive American governments was North Africa, due to its proximity to the Middle-East and the vital oil supply routes so important to the US economy. Yet the Soviets checked US interests in Egypt, for example, using the Arab nationalism of Nasser as a way of gaining influence in the region.
The Soviets' approach to Egypt was indicative of a wider strategy. The USSR set itself up as an ally of subject African peoples in their struggle against Western colonialism. Communism—in theory, at least—was a natural partner with anti-colonialism on account of its liberationist ideology. The growing desire of many Africans to throw off the yoke of colonial oppression could comfortably be reconciled with Marxist rhetoric about emancipation of the workers from capitalist domination and control. The Soviets aggressively exploited this rhetoric to the full in their dealings with a number of African governments, rebels, and independence movements.
Yet aside from the high-flown revolutionary slogans, the Soviet Union was also motivated by economic interests in its dealings with Africa. Angola, for instance, became an especially volatile theater of conflict in the Cold War, opening a new front in the struggle between East and West. As the country was rich in oil it inevitably attracted the attention of both sides. The United States supported rebel movements such as UNITA against the Marxist MPLA, which was backed by the Soviets. The ensuing Angolan Civil War lasted a staggering 27 years before the MPLA finally prevailed. But the conflict took an incredible toll of death and destruction on the country, undoubtedly exacerbated by the constant flow of arms and cash supplied by both the Americans and the Soviets.
There's often a fine line between assistance and exploitation, especially in the conduct of an overtly ideological conflict like the Cold War. Whatever the respective motivations of the United States and the Soviet Union may have been, there's little doubt that self-interest played a major part, and that both sides saw in a continent moving away from its colonial past a great opportunity to open up virgin territory and make their mark.

Africa was impacted by the Cold War. Much like other parts of the world, the communists and "non-communists" tried to get control over lands in Africa. There were some nations that sided with the Soviet Union, while some sided with the United States. There were wars fought in countries such as Angola, Mozambique, and the Democratic Republic of the Congo. These wars killed many African people.
One example of the Cold War can be seen in Egypt. When Egyptian president Nasser could not get money for the building of the Suez Canal, he seized the canal from British and French investors. This eventually led to a conflict with Israel, France, and Great Britain against Egypt, which was supported by the Soviet Union. The Soviet Union threatened to use nuclear weapons against Europe unless the invasion ended. The United States suggested to the Soviet Union that this was not a good idea and also suggested that the Soviet Union stay out of the conflict. Eventually, the United States pressured Great Britain, France, and Israel to end the conflict. Once the conflict ended, the Soviet Union still supported Egypt, leading to future tensions between the Soviet Union and the United States.
https://nassirhassan.wordpress.com/tag/the-effect-of-the-cold-war-on-third-world-countries/

https://www.aljazeera.com/indepth/features/2016/02/east-west-cold-war-legacy-africa-160214113015863.html

https://www.history.com/topics/cold-war/suez-crisis

What is GDP?

Gross domestic product, or GDP, is an economic term referring to the sum total monetary value of all goods produced in a particular country, as well as the value of any services performed there. Essentially, this is a way of measuring economic activity within a period of time to track growth or decline. The value of the gross domestic product is not only dependent upon the consumption of finished goods, but also investment, the value of exported goods, and government spending. 
The value of a gross domestic product is often used in reference to a nation's development and growth, as well as the quality of life for people in that nation.
Some people disapprove of the gross domestic product as an indicator of economic activity because it does not account for any unofficial, or "black market," goods and services produced by a nation.
https://www.britannica.com/topic/gross-domestic-product

https://www.investopedia.com/terms/g/gdp.asp

how and why Fahrenheit 451 invites the reader to identify with situations, characters and/or ideas (look below the surface of the text here). Explore three specific discussion points of identification. What are they? Why are they important?

Early in the novel, Bradbury encourages us to identify with Clarisse. Unlike most people in this society, this young woman walks outside at night in the moonlight. Montag is taken with her and how different she is from everyone else he knows. Bradbury uses lyrical language and metaphor to show how Clarisse stands apart from the average person. Hers is a softer, more old-fashioned approach to life. It reminds Montag of a candle:

Her face, turned to him now, was fragile milk crystal with a soft and constant light in it. It was not the hysterical light of electricity but-what? But the strangely comfortable and rare and gently flattering light of the candle.

It is important that the reader identifies with Clarisse, because she highlights how much the average person in this society has moved from the simple things in life that have meaning, such as staying in touch with nature. We understand how Montag's discontent grows after his encounter with Clarisse. She is a first inkling that he is deeply unhappy. 
At a midpoint in the novel, we are meant to identify with Montag and his growing frustration with his wife Mildred's obsession with watching mindless television. In one scene, he shuts off her view screens and tries to get her to interact with him. This is important, because it highlights how isolated and desperate Montag feels. He tries to connect with Mildred, but it is impossible. 
We are also meant to identify with Faber. When he and Montag meet at the beginning of part II, and Faber gets over his fear of talking to Montag; he begins to confide in him and show his true character. Like Clarisse, he lives life on a deeper level. 

"I don't talk things, sir," said Faber. "I talk the meaning of things. I sit here and know I'm alive."

The encounter with Faber is important because it encourages Montag to seek a more satisfying life, particularly through books, than his sterile existence. 
 

Discuss five reasons why Ghana is regarded as a developing country.

Although sources cannot agree on an appropriate definition for “developing country,” most define a developing country as one that has low indicators/ratings of economic development. Some of these indicators include per capita income, life expectancy, and literacy rates. Below I will describe why Ghana is considered a developing country.
Per Capita Income
A country’s gross domestic product (GDP) describes the market value of all goods and services made within a country. The GDP per capita is the aforementioned definition divided by the number of people living in the country. Sources posit that the average GDP per capita for developed countries is $12,000. The GDP per capita for Ghana, however, was $1,641 in 2017.
Life Expectancy
Life expectancy describes the average lifespan of the residents of the country. The average life expectancy in developed countries is between seventy-six and eighty-two years old. The life expectancy in Ghana is only about sixty-three years old. This low expectancy can be influenced by a number of factors, including war, poor health conditions, and the possibility of famine.
Literacy Rates
Literacy rates describe how many of a country's residents can read and write. For developed countries, the average literacy rate is anywhere from 95–99%. In Ghana, however, the literacy rate is 77%, meaning that almost a quarter of the country’s residents cannot read or write. The low literacy rate could be an indication of problems within the education system in Ghana, including lack of access to education and lack of appropriate educational resources.
Poverty
The poverty ratio is the number of people whose income falls below a defined poverty line. In 2017, the poverty rate in the United States was 12.3%. The poverty rate in Ghana at that same time was 23.4%. This statistic may speak to the poor availability of jobs and low quality of life available in the country.
Fertility Rates
A fertility rate describes the expected number of children born per woman in her child-bearing years. The fertility rate of the United States is 1.2%, while the fertility rate of Ghana is 3.9%. This number is elevated in developing countries, a factor that is usually attributed to limited access to contraceptives and insufficient sex education.
https://data.worldbank.org/country/ghana

https://www.statista.com/statistics/274507/life-expectancy-in-industrial-and-developing-countries/

First, Ghana has a low Gross Domestic Product (GDP) per capita. It is ranked 139th out of 191 nations in a recent report. The World Bank states that its per capita income is $2,200. This means the average person in Ghana lives on less than $200.00 per month.
Second, the country depends too heavily on agriculture. Cocoa is important and more than half of Ghana's fertile land is devoted to growing it. The value of the country's exports fluctuates wildly along with the price of cocoa beans.
Next, Ghana's literacy rate is low. In this area, the country ranks between Sudan and Cambodia.
Fourth, Ghana has a high population growth rate at 2.17%. This growth puts a strain on the country's limited resources.
Finally, there is too much corruption in Ghana. This impedes economic growth because the benefits of an expanding economy are not shared fairly.
http://worldpopulationreview.com/countries/literacy-rate-by-country/

https://www.transparency.org/cpi2018

https://www.worldometers.info/gdp/gdp-per-capita/

Ghana is a West African country that is found along the gulf of Guinea and the Atlantic Ocean. It neighbors the Ivory Coast, Burkina Faso and Togo. It has a population of over 25 million and covers an area of about 238,533 square kilometers. The following are some reasons why Ghana is regarded as a developing country:
Low per capita income
Developing countries have lower per capita income compared to developed countries. According to the World Factbook, Ghana is currently ranked at position 172 out of 230 countries, with a GDP per capita of about $4,400. Some developed countries such as Norway have a GDP that is 16 times Ghana’s per capita income.
Low average life expectancy
Low-income countries generally have lower average life expectancies than high-income countries. According to the World Health Organization, Ghana currently has a life expectancy of about 62.4 years. This, when compared to countries in the developed world—such as the United States at 79.3 years, the United Kingdom at 81.2 years, Sweden at 82.4 years and Germany at 81 years—is quite low. Ghana’s life expectancy is, however, slightly higher than that of the very poor countries of the world, such as war-torn Somalia at 55 years.
High levels of poverty
Developing countries have a large percentage of their populations living in abject poverty. However, Ghana has made huge strides in this aspect by being the only country in sub-Saharan African to meet the Millennium Development Goal of halving cases of extreme poverty in the country by the year 2015. Presently, about 24.3% of Ghanaians live below the poverty line, as compared to 31.9% in the year 2005. Poverty is attributed to social and political inequalities in the country.
High population growth
Most developing countries have high population growth rates due to high birth rates. Ghana currently has a growth rate of about 2.19% compared to Norway’s 1.19%, Australia’s 1.09% and Japan’s –0.13%.
Over-reliance on agriculture as the main economic activity
Ghana’s agricultural sector contributes about 40% to its GDP. It is also thought that the sector employs over 40% of its citizens. Agriculture, in spite of being the backbone of the Ghanaian economy, has experienced slumps due to adverse weather conditions and government budgetary red tape.

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 60

Find an equation of the circle with endpoints of a diameter at $P(-1,3)$ and $Q(7, -5)$.

Recall that the diameter is twice the radius so by getting the distance between the points using distance formula,


$
\begin{equation}
\begin{aligned}

d_{PQ} =& \sqrt{(-5 -3)^2 + (7 - (-1))^2}
\\
\\
d_{PQ} =& \sqrt{(-8)^2 + (8)^2}
\\
\\
d_{PQ} =& \sqrt{64 + 64}
\\
\\
d_{PQ} =& 8 \sqrt{2} \text{ units}

\end{aligned}
\end{equation}
$


Therefore, the radius is..

$\displaystyle r = \frac{d_{PQ}}{2} = \frac{8 \sqrt{2}}{2} = 4 \sqrt{2} $ units

Also, recall that the general equation for the circle with circle $(h,k)$ and
radius $r$ is..


$
\begin{equation}
\begin{aligned}

(x - h)^2 + (y - k)^2 =& r^2
&& \text{Model}
\\
\\
(x - h)^2 + (y - k)^2 =& (4 \sqrt{2})^2
&& \text{Substitute the given}
\\
\\
(x - h)^2 + (y - k)^2 =& 32
&&

\end{aligned}
\end{equation}
$


To get the center $(h,k)$, we get the midpoint of the endpoints of the diameter $PQ$

$\displaystyle h = \frac{-1 + 7}{2} = 3 \text{ and } k = \frac{3 - 5}{2} = -1$

Thus, the equation of the circles..


$
\begin{equation}
\begin{aligned}

(x - 3)^2 + (y - (-1))^2 =& 32
\\
\\
(x - 3)^2 + (y + 1)^2 =& 32


\end{aligned}
\end{equation}
$

Calculus: Early Transcendentals, Chapter 5, 5.2, Section 5.2, Problem 10

You need to use the midpoint rule to approximate the interval. First, you need to find Delta x, such that:
Delta x = (b-a)/n
The problem provides b=pi/2 , a=0 and n = 4, such that:
Delta x = (pi/2-0)/4 = pi/8
Hence, the following 4 intervals of length pi/8 are: [0,pi/8], [pi/8,pi/4], [pi/4,(3pi)/8], [(3pi)/8,pi/2].
Now, you may evaluate the integral such that:
int_0^pi/2 cos^4 x dx = Delta x(f((0+pi/8)/2) + f((pi/8+pi/4)/2) + f((pi/4+(3pi)/8)/2) + f(((3pi)/8+pi/2)/2))
int_0^pi/2 cos^4 x dx = pi/8(f(pi/16) + f(3pi/16) + f(5pi/16) + f(7pi/16))
int_0^pi/2 cos^4 x dx = pi/8(cos^4(pi/16) + cos^4 (3pi/16)+ cos^4(5pi/16) + cos^4(7pi/16)))
cos(pi/8) = cos((pi/4)/2) => cos^2((pi/4)/2) = (1 + cos(pi/4))/2 => cos^4((pi/4)/2) = ((1 + cos(pi/4))^2)/4
cos^4((pi/4)/2) = ((1 + sqrt2/2)^2)/4
cos^4((pi/4)/2) = ((2 + sqrt2)^2)/16
cos(pi/16) = cos((pi/8)/2) => cos^2((pi/8)/2) = (1 + sqrt((1 + sqrt2/2)/2))/2
cos^4(pi/16) =(0.9619)^2 = 0.6637
cos(3pi/16) = -cos(pi/16) => cos^4(3pi/16) = cos^4(pi/16) = 0.6637
cos(5pi/16) = -cos(pi/16) => cos^4(3pi/16) = cos^4(pi/16) = 0.6637
cos(7pi/16) = -cos(3pi/16) = -(-cos(pi/16) ) => cos^4(7pi/16) = cos^4(pi/16) = 0.6637
int_0^pi/2 cos^4 x dx = pi/8( 0.6637 + 0.6637 + 0.6637 + 0.6637)
int_0^pi/2 cos^4 x dx = 4*pi/8(0.6637)
int_0^pi/2 cos^4 x dx = pi/2*(0.6637)
int_0^pi/2 cos^4 x dx = 0.3318*pi
Hence, approximating the definite integral, using the midpoint rule, yields int_0^pi/2 cos^4 x dx = 0.3318*pi.

f(x) = 2arcsin(x-1) Find the derivative of the function

The derivative of function f with respect to x is denoted as f'(x) .
To take the derivative of the given function: f(x) =2arcsin(x-1) ,
we can apply the basic property: d/(dx) [c*f(x)] = c * d/(dx) [f(x)] .
  then f'(x) = 2 d/(dx) (arcsin (x-1))
  To solve for the d/(dx) (arcsin(x-1)) , we consider the derivative formula of an inverse trigonometric function.
 For the derivative of inverse "sine" function, we follow:
d/(dx) (arcsin (u)) = ((du)/(dx))/sqrt(1-u^2)
 
To apply the formula with the given function, we let u= x-1 then (du)/(dx) = 1 .
d/(dx) (arcsin(x-1))= 1/sqrt(1-(x-1)^2)
 Then f'(x)=2 d/(dx) (arcsin (x-1)) becomes:
f'(x) =2 * 1/sqrt(1-(x-1)^2)
f'(x) =2 /sqrt(1-(x-1)^2)
 
To further simplify, we can evaluate the exponent inside the radical:
f'(x) =2/sqrt(1-(x^2-2x+1))
Note: (x-1)^2= (x-1)(x-1)
Applying FOIL or distributive property:
(x-1)(x-1)= x*x + x*(-1) + (-1)*x + (-1)(-1)
                       =x^2 –x –x+1
                       =x^2 -2x+1
 
Simplify the expression inside radical:
f'(x) =2/sqrt(1-x^2+2x -1)
f'(x)=2/sqrt(-x^2+2x) or f'(x)=2/sqrt(2x-x^2)
 
 

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 21

int(xe^(2x))/(1+2x)^2dx
If f(x) and g(x) are differentiable functions, then
intf(x)g'(x)=f(x)g(x)-intf'(x)g(x)dx
If we rewrite f(x)=u and g'(x)=v, then
intuvdx=uintvdx-int(u'intvdx)dx
Using the above method of integration by parts,
Let u=xe^(2x)
u'=xd/dx(e^(2x))+e^(2x)d/dx(x)
u'=x(2e^(2x))+e^(2x)
u'=e^(2x)(2x+1)
v=1/(1+2x)^2
intvdx=int(1/(1+2x)^2)dx
Let's integrate by the use of substitution method,
Let t=1+2x
dt=2dx
int(1/(1+2x)^2)dx=intdt/(2t^2)
=1/2(t^(-2+1)/(-2+1))
=-1/(2t)
substitute back t=1+2x,
=-1/(2(1+2x))
int(xe^(2x))/(1+2x)^2dx=xe^(2x)int(1/(1+2x)^2)dx-int(d/dx(xe^(2x))int(1/(1+2x)^2)dx)dx)
=xe^(2x)(-1/(2(1+2x)))-inte^(2x)(1+2x)(-1/(2(1+2x)))dx
=(-xe^(2x))/(2(1+2x))+inte^(2x)/2dx
=(-xe^(2x))/(2(1+2x))+(1/2)e^(2x)/2
=e^(2x)/4-(xe^(2x))/(2(1+2x))
Add a constant C to the solution,
int(xe^(2x))/(1+2x)^2dx=e^(2x)/4-(xe^(2x))/(2(1+2x))+C

(0, 2) , y'=x/(4y) Find an equation of the graph that passes through the point and has the given slope.

We need to find the equation of the graph that passes through the point (0,2). The slope of the tangent line to the graph of y(x) is the derivative y' and it is given by the equation
y' = x/(4y) .
This equation can be solved by the method of separating variables. First, rewrite
(dy)/(dx) = x/(4y) .
Now, multiply by 4y and dx:
4ydy = xdx
Now both sides can be integrated:
4y^2/2 = x^2/2 + C . Here, C is an arbitrary constant.
From here,
4y^2 = x^2 + 2C
Since the graph of the equation has to pass through the point (0, 2), we can find C:
4*2^2 = 0 + 2C
C = 8.
So the equation of the graph is
4y^2 = x^2 + 16 , which can also be written as
y^2/4 - x^2/16 = 1 . This is a hyperbola that opens up and down, with the vertices at the points (0, 2) and (0, -2).
y^2/4 = x^2/16 + 1
y^2 = x^2/4 + 4
y = +-sqrt(x^2/4 + 4)

Beginning Algebra With Applications, Chapter 6, 6.2, Section 6.2, Problem 64

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

1.25x - 0.01y =& 1.5 \\
0.24x - 0.02y =& -1.52

\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}

0.24x - 0.02y =& -1.52
\qquad \text{Solve equation 2 for } y
\\
\\
-0.02y =& -0.24x - 1.52
\\
\\
y =& \frac{-0.24x - 1.52}{-0.02}
\\
\\
y =& 12x+76

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

1.25x - 0.01y =& 1.5
\qquad \text{Substitute } 12x+76 \text{ for $y$ in equation 1}
\\
\\
1.25x-0.01 (12x+76) =& 1.5
\\
\\
1.25x - 0.12x - 0.76 =& 1.5
\\
\\
1.13x =& 1.5+0.76
\\
\\
1.13x =& 2.26
\\
\\
x =& 2

\end{aligned}
\end{equation}
$


Substitute the value of $x$ in equation 2


$
\begin{equation}
\begin{aligned}

y =& 12(2) + 76
\\
\\
y =& 24+76
\\
\\
y =& 100

\end{aligned}
\end{equation}
$


The solution is $(2,100)$.

In "Charles," why did Laurie’s parents take so long to find out the truth about Charles?

Laurie's parents never make an effort to ascertain the real truth about their son's fictional classmate, Charles. Their complacency stems from their belief that he is telling the truth. Laurie probably realizes that his parents are taken in by his story and that they won't try to establish the truth since there is no reason for them to do so. After all, he is not the one misbehaving. Although his parents are aghast at what Laurie tells them about Charles, they do not make any inquiries, and they wait until the PTA meeting to address the issue. Their apathy gives Charles more opportunity to persist in being disruptive and disrespectful.
For his part, Laurie obviously believes that speaking about Charles absolves him from guilt since he is, indirectly, admitting to his own wrongdoing. His repeated reports about Charles's behavior encourage him to say even more. He is testing the waters and attempting to see how far he can test his parents' patience. His reports indicate that Charles is getting worse, and Laurie clearly wants to see how far he can go before his parents become indignant enough that their child is being exposed to such horrendous behavior.

There are two reasons Laurie's parents took a long time to find out the truth about Charles.
First, they never suspected that Laurie was hiding the truth from them. Both parents believed Laurie's stories about Charles, simply because Laurie never showed any guilt about his embellished narrative. Laurie's stories about Charles also provided a rationale for his shocking overnight transformation. In all, Laurie's parents were probably relieved that their son could provide a reasonable explanation for his puzzling behavior.
Second, Laurie's parents made little effort to verify Laurie's veracity; such was the trust they placed in their young son. Neither parent could envision Laurie as anything but Charles' unwilling victim. In fact, Laurie's mother discovered the truth only after she attended the P.T.A. meeting. She had hoped to see Charles' mother there. However, as the text reveals, she was shockingly disappointed.
So, Laurie's parents took a long time to discover the truth because they trusted Laurie's version of events completely and they failed to confirm their authenticity.

There are several textual clues that can be used to support inferences as to why it took so long for Laurie's parents to discover the truth, but there is no direct statement made in the story that explains it.
The opening paragraph describes Laurie as a sweet-voiced nursery school tot who has turned into a swaggering, belt wearing boy who forgets to say goodbye to his mother. One could infer that one of the reasons the parents are slow to figure out the truth is because they are having difficulty letting go of the image of their sweet young son. They close their eyes to the changes going on in Laurie that go beyond his physical appearance.
The author gives several clues throughout the story that show that Laurie's behavior is similar to Charles's. He shouts raucously on two occasions: once on his first day home from kindergarten, and once the first day Charles has to stay after school. He speaks insolently to his father, saying "Hi pop, ya old dust mop" and telling a joke "Look up, look down, look at my thumb, gee you're dumb." He also spills his baby sister's milk. 
But because of the invention of Charles, the parents don't suspect Laurie, they simply think that Charles has been a bad influence on their son. 
It is interesting that there is no communication between adults in this situation until the PTA meeting at the conclusion of the story. The teacher doesn't call Laurie's parents to tell of his unruly behavior in school. Laurie's parents don't talk to the teacher or other school personnel about their concerns about Charles. Laurie's mother is desperate to meet Charles's mother at the PTA meeting, but she doesn't make any efforts to try to get in touch with her prior to that meeting. 
The invention of Charles appears to be the perfect ruse for Laurie to deflect the truth and consequences for his bad behavior.
 

In Julius Caesar, was Brutus responsible for his own downfall?

Brutus was responsible for his own downfall because he was naïve and did not listen to advice. 
The main reason that Brutus was responsible for his own downfall was that he did not listen to Cassius.  He never took anyone else’s advice on issues such as how best to assassinate Caesar or how to run the military campaign against Antony and Octavius.  Instead, he wanted to remain optimistic.  Since he did not, they failed.  He was naïve, and he paid the price. 
An example of this is when Brutus explains to Cassius that they should not kill Antony, because it will hurt their reputation with the Roman people. 

BRUTUS
Our course will seem too bloody, Caius Cassius,To cut the head off and then hack the limbs,Like wrath in death and envy afterwards;For Antony is but a limb of Caesar:Let us be sacrificers, but not butchers, Caius. (Act 2, Scene 1) 

Brutus believed that Antony’s only power was in his relationship to Caesar.  He underestimated Antony, but Cassius was concerned that Antony might cause trouble.  Cassius turned out to be right. 
To Brutus, image was more important than practicality.  Even though Cassius had been involved in the conspiracy longer than he had, he did not allow Cassius to have any sway over him and continually overruled his decisions in front of the other members of the group.  In addition to this decision, his decision to allow Antony to speak at Caesar’s funeral was especially disastrous, resulting in an uprising of public sentiment against the conspirators. 
Even when they have their own armies and are fighting the triumvirate, Brutus makes the same mistakes.  He argues with Cassius about going to Philippi, and overrules Cassius when he doesn’t want to go.  Philippi turns out to be a nightmare for them, and they both end up committing suicide there.  Antony and Octavius win and go on to rule Rome.

What are some points on writing a critical paper on The Canterville Ghost?

This prompt is wide open because you can write a critical analysis paper about this story from many, many different angles. On one hand, that is good. On the other hand, it can be very frustrating and overwhelming to have zero guidance on a particular assignment. If the critical analysis is entirely up to you, I recommend an analysis of themes or characters. Often, those two subjects will blend together in a natural way; you will use characters to illustrate and explain themes, or you will discuss themes that are focused around particular characters.
A possible analysis for this story could be an examination of the cultural differences that the story displays between the British upper class and the Americans. Wilde presents the Otis family as very different from Lord Canterville. While the British might be willing to accept the ghost and the dismal weather, the Otis family is not willing to accept either of those things.
Another thematic angle is the theme of forgiveness or atonement. Sir Simon is quite guilty of killing his wife and of being a bad person in life. He continues to act this way in death as well. However, he is tired. He desperately wants to gain his eternal rest, but he is prevented from being able to cross over. He needs help, and that is why Virginia Otis is such an important part of this story. She is the "golden girl" whose prayers and presence can get Sir Simon to his eternal resting place. Your analysis could even tie this theme to the previous theme. Virginia Otis is the only member of the Otis family that is willing to accept the ghost as he is. In this way, she is very British. However, she is also quite American because she is willing to do something about the ghost, and she hopes for a better future. She is a bridge for Sir Simon, but she is also a bridge between two cultures, as evidenced by her marriage to the Duke of Cheshire.

What is Gatsby's view of materialism in The Great Gatsby?

Gatsby views material wealth as largely a means to an end, whether it's winning Daisy's heart or being accepted by the old money elite of East Egg. In such a shallow, superficial world, opulent displays of wealth are a surefire way to impress people. Gatsby makes the fatal mistake, however, of thinking that appearance is everything; that what matters is what people think you are, rather than what you actually are.
And so the vast wealth he's accrued ultimately avails him nothing. Not only does Daisy refuse to leave Tom, but the East Eggers will never accept him as one of their own. They'll gladly go to his lavish parties, eat his food, and drink his champagne, but to them he'll always be a vulgar parvenu, an upstart who's trying to buy his way into high society. Daisy may cry over Gatsby's impressive collection of shirts, but that doesn't mean she's about to ditch Tom to be with Jay. Good breeding and background still matter in this world, after all, and no amount of wealth, no matter how phenomenal, is ever going to change that.

What does Kazuo Ishiguro try to tell us through his novel Never Let Me Go ? What is it all about?

The novel points a dystopian future where human beings are cloned to provide a supply of organs for transplant. This practice, while based in science and a plausible topic for a work of speculative fiction, is also a rich metaphor that may be at the root of the author's purpose in telling the story. The clones, who don't have parents and who are wards of the state, who are in fact possessions of the state, could be seen to represent the poor or underprivileged classes of Great Britain. They are treated not only a ssecond-class citizens, but as subhuman. The belief that they are not truly human, and that their expressions of emotion or creativity are simply glitches and not evidence of their having a soul, could be seen to parallel the notion, not unheard of in modern Britain, that the lower classes are intellectually and socially inferior to the upper classes. This reinforcement of social hierarchy is a theme that also occurs in other novels by Ishiguro.
It is also not inappropriate to suggest that the novel offers a commentary on the breakdown of the medical industry in Great Britain, which once had one of the finest healthcare systems in the world. Its transition from socialized to partly privatized has been disastrous, and the novel could be exploring what it would mean for the rich to be the recipients of the best medical care while the poor are exploited by this system.

Based upon information in the text and through informed speculation, what does Miss Brill look like in Katherine Mansfield's story "Miss Brill"?

Miss Brill is probably a woman who is slightly past middle age because she seems rather old-fashioned, wearing a necklet that she has owned for some time. She also ranks other people that she sees as either "young" or "old."
In the story that is told from the perspective of Miss Brill, the reader notes when Miss Brill goes to the park to listen to the Sunday concert that she observes: "The young ones, the laughing ones who were moving together, they would begin...." Later, Miss Brill alludes to the very "old invalid gentleman" to whom she reads the newspaper four times a week. This activity suggests that Miss Brill is older because usually young people do not want to read to really old people, nor do they have the time. Also, her association with this man suggests her connection to an era that is now obsolete. Further, when the old gentleman asks if she is an actress because of the way that she reads, Miss Brill smooths the newspaper as if it were a manuscript of a play and says with kindness, "Yes, I have been an actress for a long time." This remark may have the hidden meaning that for years she has pretended to be someone she is not because she has not married or has no children. She may even have called herself an actress because she has accomplished little that is significant in life.
After a while, as Miss Brill listens to the music and hears something "so beautiful--so moving..." her eyes fill with tears in her sentimentality, an emotion usually more reflective of a woman who is, at least, middle-aged. Also, she thinks to herself:

Yes, we understand, we understand, she thought--though what they understood she didn't know.

Then, when the "boy and girl" sit down where the "old couple" had been, the middle-aged Miss Brill notices that they are infatuated with each other. In her romantic mind, she thinks, "They were beautifully dressed; they were in love. The hero and heroine, of course...." as she sings along, soundlessly to the music being played.
Miss Brill then hears the girl tell her boyfriend, "No, not now....Not here, I can't." The boy asks her why not. "Because of that stupid old thing at the end there?" the boy asks. "Why doesn't she keep her silly old mug at home!" And, the two laugh at the little fur of which she has always been so proud.Hurt by the young couple's remarks and giggles, Miss Brill returns to her "room like a cupboard" without stopping as she usually does for a "tiny present" for herself at the bakery. Once in her room, she sits for some time without moving. Finally, she puts away her obsolete little fur in the little box and she thinks that "she heard something crying." Such sentimentality is usually indicative of an older person who was young in another era. 

How can the story "Two Kinds" be misunderstood?

There are, of course, many ways to misunderstand any short story, and in this regard, “Two Kinds” is no exception. But the story does end with the narrator experiencing an epiphany, and it is an epiphany that clarifies a misunderstanding that she has long had. Because of that, this answer will focus on the narrator’s own misunderstanding, and how it might relate to the reader’s own.
As the title suggests, the short story sets up a series of oppositions. The main one is introduced by the mother, who tells her daughter that there are only two kinds of daughters:

"Those who are obedient and those who follow their own mind! Only one kind of daughter can live in this house. Obedient daughter!"


But in the final moment, we realize that this is not the case. Looking at the sheet music, the narrator experiences an epiphany:

And for the first time, or so it seemed, I noticed the piece on the right-hand side. It was called "Perfectly Contented." I tried to play this one as well. It had a lighter melody but with the same flowing rhythm and turned out to be quite easy. "Pleading Child" was shorter but slower; "Perfectly Contented" was longer but faster. And after I had played them both a few times, I realized they were two halves of the same song.

The narrator realizes that the mother was wrong; the binary relationship between the two kinds of daughter can be deconstructed, and that they actually coexist inside one another. This moment also helps the narrator realize why her mother kept the piano for her: although she did not become a piano-playing prodigy, her mother still saw her as a success. As the narrator explains, “after that, every time I saw it in my parents' living room, standing in front of the bay window, it made me feel proud, as if it were a shiny trophy that I had won back.”
These two intersecting epiphanies corrects the narrator’s—and potentially the reader’s—misunderstanding: although the mother is disappointed with the daughter’s performance and behavior, she is not disappointed in the daughter as a piano player or a person.

Describe the reasons for the changes in Lincoln’s thinking with the progression of the Civil War. It initially focused on preserving the Union and then became more of a war to end slavery. Why do you think this was the case?

Lincoln's goal was first and foremost to preserve the Union.  He did not want to come out too strong against slavery because this would cause the border states—Missouri, Kentucky, Maryland, and Delaware—to secede and join the Confederacy.  Lincoln realized that if Maryland joined the Confederacy, Washington, DC, would be surrounded, and the war would be over.  As the war progressed, Lincoln initially thought it acceptable if armies in the field freed the slaves of secessionists and claimed the newly freed people as "contraband" in war.  Lincoln issued his Emancipation Proclamation on January 1, 1863 in order to demonstrate that he was in control over the "states in rebellion," as this law did not cover slaves living in loyal states.  Lincoln hoped that such a move would scare hardened slaveowners back into the Unionist fold, but he had no such luck.  Another reason for this decree was that it gave the war a higher cause— now Britain and France would hopefully not agitate for mediation between the two warring factions.  Lincoln finally relented and put African Americans into active combat roles at the behest of Frederick Douglass, who thought that this was the only way for African American to achieve any semblance of equality after the war.  Lincoln did not believe that the former slaves would get a fair chance in the United States after the war, so he wanted to create a colony in the Western Hemisphere for them similar to Liberia.  Frederick Douglass and other black leaders talked him out of this.  The valor of black soldiers in battles such as The Crater and Fort Wagner also demonstrated to Lincoln that black soldiers were just as capable as white soldiers.  After the war, Lincoln saw that freeing all the slaves was the right thing to do, and it would also galvanize his party's abolitionist core to go along with him on other parts of his large domestic agenda to get the nation together.  Lincoln was a man of his time, and he did not quickly embrace civil rights. However, he was starting to become more accepting right before his untimely assassination. 

What is Patrick Maloney referring to when he says "I know it’s kind of a bad time to be telling you"?

Mary Maloney seems to adore her husband. She caters to his every need, from preparing his dinner to giving him his needed time after work to unwind before she tries to engage in conversation with him. She tries to anticipate his needs, making him his favorite strong drink when he comes in from work. And she adores him:

She loved to luxuriate in the presence of this man, and to feel—almost as a sunbather feels the sun—that warm male glow that came out of him to her when they were alone together. She loved him for the way he sat loosely in a chair, for the way he came in a door, or moved slowly across the room with long strides.

And she is six months pregnant.
On this particular night, she senses that something is amiss. Finally, he admits that he has to tell her something and that he hopes she won't be too upset.

And he told her. It didn't take long, four or five minutes at most, and she sat very still through it all, watching him with a kind of dazed horror as he went further and further away from her with each word.

Her husband is leaving her—and doing so while she is less than three months away from delivering their first child. At this point,he stops and mentions that "it's kind of a bad time" to deliver this news.
These words ring hollow to a woman who has devoted her every hour to taking care of her husband's needs. It would always be a bad time to hear that one's husband is leaving, but to leave a pregnant wife without just cause and then to casually throw out that it might be poor timing is a bit much for this wife to take.
Of course, all that leads to her moment of revenge.

Readers are never sure of exactly what Patrick tells Mary, but we do know that it is quite upsetting to her. It is generally assumed that Patrick tells Mary that he wants a divorce or that he is leaving her. Either way, readers can be fairly certain that the marriage is over.
His comment about it being a bad time sends the message that he actually believes that there might be a good time to share this kind of news with his wife; however, that is not exactly what he means by "bad time." 
Mary is pregnant, and she is going to have the baby in the next few months.  

Her skin—for this was her sixth month with child—had acquired a wonderful translucent quality, the mouth was soft, and the eyes, with their new placid look, seemed larger and darker than before.

Patrick's comment is referring to her pregnancy and their nearly arrived child. Patrick is not only leaving Mary. His absence not only affects Mary, but his actions now leave a child without a father figure. Yes, Patrick's timing is absolutely terrible.  

Why were the American colonies unhappy with the British government?

The American colonists had a number of grievances against the British government, although they were all related in some way to the issue of autonomy, or the ability of Americans to run their own affairs. Most colonists were committed to the connection between America and Great Britain, but still valued a certain degree of independence in the day-to-day running of their affairs. Over time, British policy on America contributed to a growing sense among the colonists that they were not being respected or treated fairly by the mother country in a number of key areas.
The catalyst for much of the colonists' dissatisfaction was the French and Indian War. Having prevailed in the conflict, the British felt that it was necessary for them to keep their troops stationed on American soil. For the most part, the colonists were strongly against this measure, not least because they'd have to pay for it. At that time, standing or permanent armies were quite rare. Soldiers tended to be recruited on an ad hoc basis, only called up when there was a war to be fought. Once the ensuing conflict was over, they would be demobilized until they were needed again. Having a permanent army, however, was seen as dangerous, as it could so easily be used by the authorities as an instrument of repression, and that was what the American colonists feared.
As a result of the recent war, the British had incurred substantial debts and so needed to find a way to pay them off. Once again, they looked to the American colonists to make up the shortfall. Legislation such as the notorious Stamp Act of 1765 and the Townsend Acts of 1767 was deeply unpopular as it placed an excessive burden of taxation on the colonists. Worse still, from the American point of view, was the fact that they had no influence over these laws due to their lack of political representation in the Westminster parliament.
Under such conditions, it's not surprising that colonists resorted to more direct methods of action such as the famous Boston Tea Party, where chests of imported tea were dumped in Boston harbor in protest against the imposition of tea duty. As a direct result of the disturbances, the British government passed the draconian Coercive Acts in 1774, which drove the two sides further apart and brought the prospect of armed conflict ever closer.

What would be a good written introduction for the topic of gun violence?

To write an introduction of this topic, you could start by sharing some statistics on gun violence. You could focus on your country specifically. For example, according to the Gun Violence Archive, there were over 61,000 incidents involving a firearm in the US in 2017. Using the charts on this website, you could compare and contrast the number of gun violence incidents over the last decade. (See the first reference link provided).
Alternatively, you could compare and contrast the number of gun violence incidents among different countries. See the report in the second reference link for some statistics.
Another option is to focus on a specific incident of gun violence. You could use an example which happened in or around your home city, or something which made the national news. You could talk about what happened in this particular incident, who was involved, and if any people were injured. You could also discuss the incident's aftermath, such as how many people were injured, or if the perpetrators were prosecuted.
Once you have included one or more of these ideas, you can then move on to the main body of your essay.
http://www.smallarmssurvey.org/fileadmin/docs/U-Reports/SAS-Report-GVD2017.pdf

Who are the main characters in Markus Zusak's The Book Thief and what are their goals and conflicts?

Two main characters are Liesel and Max, who both desire to belong and be free.
The protagonist of The Book Thief is Liesel. Her first goal is to get parents. Because her father is gone and her mother seems to be a Communist, Liesel and her brother are sent to live with the Hubermanns as foster parents, but her brother dies on the train. Liesel’s second goal is to learn how to read, as she finds refuge in words and books. She learns how to read by stealing books, which is the origin of her nickname Book Thief.

She hadn’t learned to speak too well, or even to read, as she had rarely frequented school. The reason for that she would find out in due course (Chapter 1).

Liesel finds belonging with the Hubermanns. She has a family at last. In Hans’s loving arms, Liesel learns how to read. Liesel’s other conflict is the individual vs. society conflict of World War II, especially since she has befriended a Jew hiding in her basement.
The individual vs. society conflict of World War II also affects Max, the Jew hiding in Liesel's basement. Max’s conflict is that he is fighting for his life. He is Jewish, and therefore outlawed. The Hubermanns are sheltering him in their basement, and he tries to keep a positive outlook. Max feels the conflict with Hitler is personal, which is why he imagines himself in fisticuffs with Hitler.

“Come on, Führer,” he said, and this time, when Adolf Hitler set upon his Jewish counterpart, Max stepped aside and plunged him into the corner. He punched him seven times, aiming on each occasion for only one thing.
The mustache (Chapter 34).

Max fulfilled his wish to live life on his own terms by going outside at night during air raids, and by leaving even though it was at great risk to himself. Even when caught, Max was still himself. Max was a survivor. He lived because he was creative and positive.

What is an analysis of Austen's Persuasion?

Austen never fully revised Persuasion, her last completed novel, so it is shorter than the four novels she published in her lifetime. If the earlier Pride and Prejudice was "light, bright, and sparkling" (as Jane Austen herself wrote in her letters), Persuasion has a somber, autumnal quality. As it opens, the heroine, Anne Elliot, believes she threw away her one chance of happiness seven years before. At that time, she had refused to marry the man she was in love with, Captain Wentworth, because his financial prospects were uncertain.
Wentworth returns, rich and successful. Anne, marginalized because she is a dependent single woman in a family absorbed in shallow pursuits, is aware she is still in love with him. 
Anne is a woman who has learned to serve others, from her self-absorbed married sister to her vain father, who judges everyone by their looks. When, against Anne's will, the family moves to Bath to economize, Anne spends time generously visiting an impoverished, invalid schoolmate, the widowed Mrs. Smith.
While Anne and Wentworth find their way back together, this is a mature love, based on a knowledge that life can be painful and fraught with disappointment. The novel also illustrates the quiet toll that being treated as a person of no importance can take on a single woman. Yet it is also a story of virtue rewarded, for Anne, with a depth of character molded by a life of serving others, has more compassion and sensitivity than most of those around her. She wins one of the most virile and socially adept of Austen's heroes. The novel shows there are second chances. It also questions a marriage market in which women are taught love must be subordinated to economic security. 

Based on the Preface, Introduction and Chapters 1-4 of Ian Haney López's Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class: How are minorities blamed for problems in society? How and why do many whites see themselves as victims?

In the introduction to the book, Lopez presents its central thesis, that "politicians backed by concentrated wealth manipulate racial appeals to win elections and also to win support for regressive policies" that benefit the very wealthy. This is part of his overarching concern, that despite the victories of the civil rights movement and changes in attitudes, deeply-held racist beliefs still structure American society. In short, ordinary white people have been persuaded to vote against their economic interests by politicians who make veiled racist appeals (i.e."dog whistles") and cynically play on their prejudices. Lopez (and many historians) use the Reagan Administration to illustrate this phenomenon. In Chapter Three, he shows that Jimmy Carter, a liberal, had tacitly defended white attempts to resist de facto integration (in schools and neighborhoods in particular), but the Reagan campaign in 1980 took this strategy to new depths. Lopez shows that Reagan coupled his policy proposals with "aggressive race-baiting." A man Lopez describes as a "key operative" (Lee Atwater, who would become one of Reagan's campaign directors in the 1984 election) famously described this strategy:

By 1968, you can't say [racial slurs]...Backfires. So you say stuff like forced busing, states' rights, and all that stuff. You're getting abstract, you're talking about cutting taxes, and all these things you're talking about are totally economic things and a byproduct of them is, blacks get hurt worse than whites.

Reagan, Lopez shows, used racially-coded language to rally white support for regressive policies like massive tax cuts and deregulation. This set him apart from politicians like George Wallace and Richard Nixon, who had used very similar language, but actually advocated relatively moderate political agendas. Reagan used rhetoric about so-called "welfare queens" who lived extravagantly while exploiting welfare programs to argue that hard-working whites were actually victims. Their paychecks were going to support the lifestyles of supposedly lazy people that whites would invariably imagine as minorities. He described a "strapping young buck," a heavily racially coded phrase, buying a steak with food stamps while "you were waiting in line to buy hamburger." Reagan had risen to prominence in California by advocating for "law and order," evoking images of Black Panthers and other radicals.
Lopez cites polling data that show Americans overwhelmingly support social welfare policies when presented in the abstract, but reject them at the polls. This, he argues, demonstrates the efficacy of the "dog whistle" appeals made by conservative politicians who seek to wreck these policies. The power of these appeals is such that many politicians have even embedded them in the appeals for "color-blind" justice once advocated by Martin Luther King. In this telling, explained in the fourth chapter, "reverse racism" has victimized hard-working whites and favored people of color.
https://books.google.com/books?id=20QSDAAAQBAJ&printsec=frontcover&dq=lopez+dog+whistle+politics&hl=en&sa=X&ved=0ahUKEwiClLvV6tveAhXpc98KHdjyAQgQ6AEIKjAA

Haney Lopez speaks about how the Republican party uses what he calls a "dog whistle," or a coded message to a target audience (page 4) to appeal to the shrinking portion of the electorate made up of white people. The "dog whistle" contains a thinly veiled reference to race and uses fear to blame nonwhite people for issues such as welfare fraud and illegal immigration; denies allegations that the GOP is pandering to whites; and denies nonwhites' claims of racial discrimination. In other words, while blaming race for many of society's problems, this form of dog whistling involves Republicans denying that they are doing so. The coded messages teach their audience that minorities are the cause of many of society's ills and that whites are the victims.
The first two chapters of this book trace the rise of the GOP as what the author calls "the white man's party" with Nixon and the turn to the party's use of what the author calls "strategic racism" to win votes. Chapter 3 discusses Reagan's use of "dog whistle" politics to dismantle the government's commitment to social welfare and the middle class, and Chapter 4 discusses the way in which "dog whistle" politics falsely promote colorblindness. 

College Algebra, Chapter 1, 1.5, Section 1.5, Problem 86

Suppose that the two television monitor has the same height. One has a conventional screen, which is $5 in$ wider than it is high. The other has wider, which is $1.8$ times as wide as it is high. The diagonal measure of the wider screen is $14 in$ more than the diagonal measure of the smaller. What is the height of the screens?

If we let $TV_1$ be the smaller and $TV_2$ has the wider screen, then


$
\begin{equation}
\begin{aligned}

& \text{Given on } TV_1
&& \text{Given on } TV_2
\\
\\
& w_1 = 5 + h
&& w_2 = (1.8) h
\\
\\
& d_1
&& d_2 = 14 + d_1

\end{aligned}
\end{equation}
$















By Pythagorean Theorem,


$
\begin{equation}
\begin{aligned}

d_1^2 =& (5 + h)^2 + h^2
\\
\\
d_1^2 =& 25 + 10h + h^2 + h^2
\\
\\
d_1^2 =& 25 + 10h + 2h^2
\\
\\
d_1 =& \sqrt{2h^2 + 10h + 25}
\\
\\
(14 + d_1)^2 =& (1.8h)^2 + h^2
\\
\\
196 + 28d_1 + d_1^2 =& 3.24h^2 + h^2
\\
\\
196 + 28d_1 + d_1^2 =& 4.24 h^2 \qquad \text{Equation 1}


\end{aligned}
\end{equation}
$


Substitute $d_1$ and $d_1^2$ in Equation 1


$
\begin{equation}
\begin{aligned}

196 + 28 \sqrt{2h^2 + 10h + 25} + 25 10h + 2h^2 =& 4.24h^2
&& \text{Combine like terms}
\\
\\
28 \sqrt{2h^2 + 10h + 25} =& 2.24 h^2 - 10h - 221
&& \text{Square both sides}
\\
\\
784(2h^2 + 10h + 25) =& 5.0176 h^4 - 44.8h^3 - 990.08h^2 + 4520h + 48841
&&
\\
\\
1568h^2 + 7840 h + 19600 =& 5.0176 h^4 - 44.8h^3 - 990.08h^2 + 4520h + 48841
&&
\\
\\
5.0176h^4 - 44.8h^3 - 2558.08h^2 - 3320 h + 29241 =& 0
&&


\end{aligned}
\end{equation}
$








Based from the graph the height that crosses the $x$-axis is at $h \approx 27.90 in$

In “Could Have Danced All Night,” the entire poem seems to use positive language, until we read the last line "planted painfully like a flag". The poem talks about dancing and wanting the other person, but the last line makes me think he is in pain and unable to dance because he is stuck. Why was the character expressing "pain" and "being planted" instead of being free and pain-free?

Ian Iqbal Rashid's poem "Could Have Danced All Night" tells of the speaker's dream to be held "knowingly" in the arms of a man. While the language of the poem's first segment (the section to which the question is posed) is positive, the final lines denote a negative tone. The idea that the speaker finally finds himself dancing in the arms of a man, something he has dreamed of, is inherently positive—that is, until readers come to the final lines:

Tonight I would dance with you across an alien landscape.
We might fly. ("I'm positive.")
But this night finds our legs rooted, knotted,
planted painfully like a flag. ("I've tested positive.")

It is here where the poem's tone changes. Instead of being happy that he has seen his dream come true, the speaker is sad because he has tested positive. This, most likely, is a reference to having tested positive for HIV/AIDS. The speaker wanted to dance all night, living life within his dream of being in another man's arms, yet he feels rooted to the ground, unable to dance, because he has tested positive for HIV/AIDS. Without the positive test, he could have flown (figuratively). Now, with the positive test, he is unable to dance freely (figuratively).
The initial statement "I'm positive" could refer to the idea that the speaker is positive that he could fly freely with his partner. He is positive that their relationship possesses a positive connotation in life. But the reiteration with the addition of "tested" changes the meaning completely.
In the end, the positive test has changed the speaker's life forever. The poem continues with the speaker addressing the fact that the man he had been dancing with leaves, most likely the result of the test. The speaker is, therefore, rooted to the ground while his partner leaves. It is the speaker's diagnosis, not the other man's. This diagnosis, then, leaves the man rooted to the ground, "painfully like a flag."
The flag could refer to the idea of homosexuality and flag-waving. Because times have changed, many gay people proudly wave or display the rainbow flag. The fact that the flag is "painfully" planted could refer to the idea that although the speaker has "come out" as a homosexual, he possesses the stereotypical curse of homosexuality (AIDS/HIV). Therefore, while the planting of the flag should be a positive and hopeful event, the positive test makes his "coming out" painful.

Who is Baba in The Kite Runner most like in A Thousand Splendid Suns and The Thorn Birds?

In a previous answer, I argued that Baba was most like Fiona (Fee Cleary) in The Thorn Birds.
In this answer, I would like to present some evidence that Baba also shares some important similarities with Mary Carson in The Thorn Birds. First, both have a rather irreverent view of religion. They are also stubbornly independent, self-assured, and dominant. In her youth, Mary left Ireland and leveraged her beautiful face and figure to snag a wealthy husband in Australia. It is a point of pride for her that Michael Carson doted on her until the day he died. It's clear that Mary has always had an iron will and an indefatigable focus on her priorities.
In terms of religious preferences, Mary is Roman Catholic, while Baba is Muslim. Neither, however, has any illusions about priests or religious leaders. Here's what Mary Carson says about them:

"I must confess, Father, that this past year has been very pleasant," she said. "You're a far more satisfactory shepherd than old Father Kelly was, God rot his soul."
"I, too, think that there are more important things than lovers, but being a receptacle for God isn't one of them."
"Stuff and nonsense! You're here because of human failings—your own and the bishop's."

Mary is predominantly obsessed with preserving her power and influence in the society in which she lives. After her husband dies, she remains a widow, refusing to let either new suitors or priests decide her destiny in life. Baba is similarly independent in nature. Like Mary, he stubbornly refuses to bow to the spiritual authority of priests or holy men.

"Do you want to know what your father thinks about sin?"
"Then, I'll tell you," Baba said, "but first understand this, and understand it now, Amir: You'll never learn anything of value from those bearded idiots."
"You mean Mullah Fatiullah Khan?"
"I mean all of them. Piss on the beards of all those self-righteous monkeys."

Both Baba and Mary are pragmatic, shrewd individuals. They choose not to deny the lusts that beguile them, and they freely acknowledge the baser instincts of their nature. Mary openly lusts after Father de Bricassart, privately comparing him to an Adonis. Meanwhile, Baba has an affair with Sanaubar (his servant's wife). Both Baba and Mary are accustomed to getting what they want.
So, when Mary's overtures are consistently rebuffed by Father Ralph, she becomes bitter. Her bitterness grows into malice when she realizes that her beloved priest is drawn to Meggie Cleary. In the end, Mary uses her expansive wealth as a vehicle to torment Father Ralph for the rest of his life. She essentially betrays the man she claims to have loved and lusted after.
For his part, Baba also betrays those he claims to have loved: Sanaubar, Ali, and Hassan. After his affair with Sanaubar (which results in Hassan's birth), he neglects to recognize his illlegitimate son. Later, out of pride and social pressure, Baba lets Ali and Hassan leave his employ.
Similar to Baba and Mary, Jalil in A Thousand Splendid Suns also betrays the one who loves him. Sure, there are plenty of similarities between Baba (in The Kite Runner) and Nana in A Thousand Splendid Suns. Both have affairs that result in great suffering in their lives. However, Baba doesn't die in bitterness; Nana does. In that vein, Nana is similar to Mary Carson, who also dies with bitter malice in her heart. Before her death, she promises Father Ralph that she will make him sell himself like any "painted whore."
Back to Jalil. For his part, Jalil is one of Herat's wealthiest men. Despite his wealth, however, he succumbs to societal pressure and chooses not to recognize Mariam as his daughter. After Nana's death, Jalil gives in to his wives and chooses not to welcome Mariam into his household. Jalil's decision results in great suffering for Mariam, who ends up being married to the despicable Rasheed.
Having said the above, it is evident that Baba shares as many important similarities with Mary Carson and Jalil as he does with Fiona Cleary and Nana.

In 1984, is Winston shown as more of a rebel or a hero?

While Winston demonstrates both rebellious and heroic qualities, one could argue that Winston is portrayed as more of a rebel than a hero. Throughout the novel, Winston's hatred toward Big Brother motivates him to commit numerous thoughtcrimes, such as writing his rebellious feelings in his journal and attempting to join the Brotherhood. While Winston realizes that it is only a matter of time before he is arrested by the Thought Police, he continues engaging in rebellious behavior by carrying on his affair with Julia and attempting to become a member of the underground resistance. While Winston's actions and passion are admirable and even heroic to the audience, his sacrifices are in vain, and he cannot contend with Big Brother's authority and influence. The fact that Winston ends up becoming a loyal supporter of Big Brother after being tortured and brainwashed in the ominous Room 101 is the main reason why one could classify Winston as more of a rebel than a hero. Winston's efforts against the Party have virtually no effect on Big Brother's omnipotent rule, and he is simply an afterthought in Oceania's society. Winston's insignificance and his inability to undermine the Party are the reason he is not a hero. At most, Winston is a disgruntled Party member who attempts to live an independent life away from Big Brother, and he engages in several rebellious acts.

What is Macbeth?

Macbeth is one of the most famous plays by one of the world’s most legendary authors, William Shakespeare.  William Shakespeare, who wrote in the late 16th century and early 17th century, revolutionized the theater by writing linguistically intricate plays that dealt seriously with human emotion across a wide range of characters. Macbeth is no exception!  
Macbeth is a Shakespearean tragedy. The strict definition of a tragedy is a serious literary work that portrays the downfall of a heroic, albeit flawed, individual. Tragedies often end in the death of their protagonists; in this case, Macbeth’s attempts are foiled by MacDuff. Though Shakespeare fans quibble about  his best works, Macbeth is widely seen as an exemplar of the tragic form, alongside Hamlet, Othello, and Romeo and Juliet.
In a nutshell, Macbeth portrays a man whose desperate ambition leads him to his downfall. After three witches prophesy that Macbeth will rise in power until he becomes king, Macbeth, goaded by his cruel and avaricious wife, first murders King Duncan. His guilt and paranoia cause him leave a bloody legacy during his short kingship,  including his former ally and friend, Banquo, as well as the innocent wife and children of MacDuff, another Scottish thane. Ultimately, Macbeth is foiled by his misreading of the witches’ further prophecies. He believes himself to be invincible but dies at the hands of MacDuff. Through Macbeth's death, law and order are restored to Scotland.
Though I’ve given you a synopsis, the question “What is Macbeth?” can definitely lead you into deeper analysis. I’ve given you a link to the Folger Shakespeare library’s commentary on Macbeth, which will give you many more details about this fascinating literary masterpiece.
 
 
 
https://www.folger.edu/macbeth

Macbeth is a play by Shakespeare about a general and a trio of witches.

Precalculus, Chapter 5, 5.3, Section 5.3, Problem 37

csc(x)+cot(x)=1
1/sin(x)+cos(x)/sin(x)=1
1+cos(x)=sin(x)
1+cos(x)-sin(x)=0
1+cos(x)-cos(pi/2-x)=0
1+2sin((x+pi/2-x)/2)sin((pi/2-x-x)/2)=0
1+2sin(pi/4)sin(pi/4-x)=0
1+2(1/sqrt(2))cos(pi/2-(pi/4-x))=0
1+sqrt(2)cos(pi/4+x)=0
cos(pi/4+x)=-1/sqrt(2)
General solutions for cos(pi/4+x)=-1/sqrt(2) are
pi/4+x=(3pi)/4+2pin , pi/4+x=(5pi)/4+2pin
solving above,
x=((3pi)/4-pi/4+2pin) , x=((5pi)/4-pi/4+2pin)
x=pi/2+2pin , pi+2pin
solutions for the range 0<=x<=2pi are,
x=pi/2 , pi
since the equation is undefined for pi
Solution is pi/2

What are some compare and contrast essay topics?

One could compare and contrast two characters in a text. What motivates them? Are they static (fundamentally unchanged in the text) or dynamic (undergoing some significant change in the text)? What insights can be gained by contrasting them? Are they foils, illuminating some aspect of the other character via contrast? Or are they more similar? Why would the author make them similar in certain ways?
One could also compare and contrast two settings within a text. Is there a city setting and a country setting, for example? Often, city settings are places that symbolize restriction and rules whereas there is typically more freedom in a country setting. Or, perhaps some of the story takes place in a character's home country and then some of the story takes place in a country that is foreign to him or her? Often, foreign settings give us a unique opportunity to see that character out of his or her comfort zone, to get a better sense of who they are now that they do not have the comfort of the familiar.
You might also compare and contrast the effects of point of view on different texts, or even within the same text. Is the narrator a participant in the story, or merely an observer? Does the narrator know all characters' thoughts and feelings, only one character's, or none at all?  What effects do these differences have on their respective texts?

What are some thematic concerns in the General Prologue?

Chaucer's Canterbury Tales was the work that put English on the literary map as a language capable of producing great literature. Before the 'Tales, most great works had been written in Greek, Latin, French, and Italian.
The General Prologue is the first "chapter" in the Tales. In the Prologue Chaucer tells the reader about the pilgrims journey and introduces each of the characters. Thematically, Chaucer gets the reader ready for the characters' tales that follow by describing the various characters' personalities, and in some cases, their moral weaknesses.
Some characters, like the Pardoner, Friar, and Monk, advance the theme of corruption in the church. Characters like the Doctor advance the theme of greed. But there are good characters too, like the Parson and the Plowman, who Chaucer uses to present of theme of simple human goodness based on humility and faith. 
Much of Chaucer's message is delivered with a verbally ironic tone, as he seems to be describing characters in a positive way even when they turn out to be morally corrupt. We are left to wonder if the narrator is just not that bright, or if he just doesn't want to be directly critical of his fellow travelers. 

Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 44

Determine the domain and the range of the graph below. Identify any functions.



Based from the graph, the domain is $[-4, 4]$ and the range is $[0, 2]$.
The given relation defines a function because each $x$-values corresponds to exactly one $y$-value.

In what passages in James Joyce's "Araby" can one see how dialectical materialism corresponds with Bakhtinian theories of polyphony and carnivalesque?

"Araby" is a story about a boy’s first brush with desire. He has a crush on a girl. When she notices him and speaks to him, she asks if he is going to Araby, the local bazaar; the boy, seeking to impress her, says he is and promises to bring her something from the fair. His desperation to get to the fair has less to do with getting a present and everything to do with proving his devotion and maturity. He wants to be an adult, and love this girl like an adult. When he gets to the fair, it is not what he had expected; he is so put off by the manner of the one shopkeeper who is still open that he decides to buy nothing.
It might seem odd to try to pin grandiose terms like “dialectical materialism” and “dialogism” to such a slim slice of life, but it can be useful to think about the story in these ways to understand what forces are at play. Dialectical materialism—the assertion that thought or consciousness is the product of labor—underpins the boy's deterministic expectations. The girl is defined by her visible attributes, to which the boy is terrifically sensitive (even while she is talking to him, at the longed-for moment of acknowledgment, he is noticing how she looks, “The light from the lamp opposite our door caught the white curve of her neck, lit up her hair that rested there and, falling, lit up the hand upon the railing. It fell over one side of her dress and caught the white border of a petticoat, just visible as she stood at ease.” The bargain he happily makes with himself is simple: he will go to Araby on her behalf; he will “bring [her] something,” a present she has not asked for but which he thinks will be sufficient to secure another conversation with her, during which he can relive for her the experience of Araby and develop their relationship further. To crudely characterize this exchange in “dialectical materialistic” terms, by performing the “labor” of visiting the bazaar, he will in effect “produce” the opportunity to talk to the girl again, and own for himself her image that tantalizes him so.
Of course, this formulation is spoiled by his real experience getting to the bazaar. First, he is made late by his uncle, who does not return home until the bazaar is nearly closed; then, after rushing to it and arriving just before closing time, he is put off again by the manner of the shopkeeper, as shown below:

Observing me the young lady came over and asked me did I wish to buy anything. The tone of her voice was not encouraging; she seemed to have spoken to me out of a sense of duty. I looked humbly at the great jars that stood like eastern guards at either side of the dark entrance to the stall and murmured:
“No, thank you.”

Bakhtin’s idea of polyphony, or dialogism, can be seen as opposed to dialectical materialism in that, instead of labor as the determining element in understanding reality, language is paramount, in particular the way different forms of speech or discourse interact. In this case, part of his reaction to “the young lady” is that she is flirting with the two boys in a way that is not only inaccessible to him, but is counter, perhaps, to the way he thinks boys should talk to girls. Certainly her casual exchange is at odds with how he would like to talk to the girl he likes. Another Bakhtinian touch is his sensitivity to her change in tone when she addresses him: she is not flirting with him; she is speaking “out of a sense of duty.”
The end of the story, in which he says “Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger,” can be interpreted as a realization of the delusional nature of his desire for the girl and his mission in coming to the bazaar. It’s not just that he sees that she is perhaps not what he wanted, or that he is not brave enough to do what he thinks will get her; it’s that his suppositions about how the world works have been undermined. He realizes that his way of thinking about the world is only one insignificant piece of a much larger conversation, one in which he has yet to learn how to participate.

How do the four stages of human diseases contribute to natural selection?

I think you're referring to the transfer of disease from animals to humans, a subject that Jared Diamond discusses in his 1997 Pulitzer Prize-winning book Guns, Germs, and Steel: The Fates of Human Societies.
To quote Diamond:

Given our proximity to the animals we love, we must be getting constantly bombarded by their microbes. Those invaders get winnowed by natural selection, and only a few of them succeed in establishing themselves as human diseases. A quick survey of current diseases lets us trace out four stages in the evolution of a specialized human disease from an animal precursor.

Let's review those four stages and how they contribute to natural selection. In the book, Diamond illustrates some of this information in "Table 11.1: Deadly Gifts from Our Animal Friends."
Stage 1: A human picks up a disease directly from a pets or another animal.
These include cat-scratch fever (from cats) and brucellosis (from cattle.) These are not spread from human to human, nor from animal to animal.
Stage 2: A former animal pathogen evolves to the point where it does get transmitted directly between people. Causes epidemics.
The epidemic dies when everyone becomes immune, or when everyone who's infected dies. The author uses laughing sickness (a fatal illness) in New Guinea as an example.
Stage 3: Former animal pathogens that established themselves in humans that have not yet died out.
May become "killers of humanity," to borrow Diamond's phrase. Lyme Disease is a good example.
Stage 4: Major, well-known epidemic diseases that are limited to humans.
These diseases are the winners, so to speak, in the process of evolution: they've survived when other epidemics and diseases have died out, as mentioned above.
Diamond uses the example of typhus, which was initially spread between rats via rat fleas. Those fleas could also infect humans. But typhus microbes "discovered" that human body lice was a better way to transmit the disease. And the microbes have continued adapting:

Now that Americans have mostly deloused themselves, typhus has discovered a new route into us: by infecting eastern North American flying squirrels and then transferring to people whose attics harbor flying squirrels.

This is natural selection at work. According to Diamond, "diseases represent evolution in progress," and "microbes adapt by natural selection to new hosts and vectors." Those microbes that figure out how to survive are the ones that are able to propagate. The typhus microbes that exist today are a product of natural selection, which is why it's still possible to hear about someone being diagnosed with typhus—and not, say, laughing sickness.

Single Variable Calculus, Chapter 5, Review Exercises, Section Review Exercises, Problem 14

Find the intergral $\displaystyle \int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du$, if it exists.

$
\begin{equation}
\begin{aligned}
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \int^1_0 \left[ (\sqrt[4]{u} )^2 + 2 \sqrt[4]{u} + 1 \right] du \\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \int^1_0 \left( \sqrt{u} + 2 \sqrt[4]{u} + 1 \right) du \\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \int^1_0 u^{\frac{1}{2}} + 2 u^{\frac{1}{4}} + 1 du\\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \left[ \frac{u^{\frac{1}{2} + 1}}{\frac{1}{2}+ 1} + 2 \left( \frac{u^{\frac{1}{4}+1}}{\frac{1}{4}+1} \right) + u \right]^1_0\\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \left[ \frac{u^{\frac{3}{2}}}{\frac{3}{2}} + 2 \left( \frac{u^{\frac{5}{4}}}{\frac{5}{4}} \right) + u \right]^1_0\\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \left[ \frac{2u^{\frac{3}{2}}}{3} + \frac{8u^{\frac{5}{4}}}{5} + u \right]^1_0\\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \frac{2(1)^{\frac{3}{2}}}{3} + \frac{8(1)^{\frac{5}{4}}}{5} + 1 - \frac{2(0)^{\frac{3}{2}}}{3} - \frac{(0)^{\frac{5}{4}}}{5} - 0 \\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \frac{2}{3} + \frac{8}{5} + 1 \\
\\
\int^1_0 \left( \sqrt[4]{u} + 1 \right)^2 du &= \frac{49}{15}
\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 5, 5.5, Section 5.5, Problem 44

Find the definite integral $\displaystyle \int^{\frac{\pi}{2}}_0 \cos x \sin (\sin x) dx$

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



$
\begin{equation}
\begin{aligned}

\int^{\frac{\pi}{2}}_0 \cos x \sin (\sin x) dx =& \int^{\frac{\pi}{2}}_0 \sin(\sin x) \cos x dx
\\
\\
\int^{\frac{\pi}{2}}_0 \cos x \sin (\sin x) dx =& \int^{\frac{\pi}{2}}_0 \sin u du
\\
\\
\int^{\frac{\pi}{2}}_0 \cos x \sin (\sin x) dx =& \left. - \cos u \right|^{\frac{\pi}{2}}_0
\\
\\
\int^{\frac{\pi}{2}}_0 \cos x \sin (\sin x) dx =& - \cos (1) - (- \cos 0)
\\
\\
\int^{\frac{\pi}{2}}_0 \cos x \sin (\sin x) dx =& - \cos(1) + 1
\\
\\
\int^{\frac{\pi}{2}}_0 \cos x \sin (\sin x) dx =& 0.4597

\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 2

a.) Express $\displaystyle \frac{dA}{dt}$ in terms of $\displaystyle \frac{dr}{dt}$
b.) At what rate is the area of the spill increasing when the radius is 30m?

a.) Given: $A$, area of the circle

$\qquad r$, radius

Required: $\displaystyle \frac{dA}{dt}$ in terms of $\displaystyle \frac{dr}{dt}$

Solution: Let $A = \pi r^2$ be the area of circle where $r$ = radius

$\displaystyle \frac{dA}{dt} = \frac{dA}{dr} \left( \frac{dr}{dt} \right) = 2 \pi r \left( \frac{dr}{dt} \right)$

$\fbox{$\large \frac{dA}{dt} = 2 \pi r \left( \frac{dr}{dt} \right)$}$

b.) Given: $\displaystyle \frac{dr}{dt} = 1 m/s$

Required: $\displaystyle \frac{dA}{dt} = ?$ when $r = 30 m$

Solution: $\displaystyle \frac{dA}{dt} = 2 \pi (3)(1)$

$\fbox{$\large \frac{dA}{dt} = 60 \pi m^2/s$}$

Compare Canada and the United States.

Canada and the United States share many common cultural features. This is not surprising, as these North American neighbors developed as countries after breaking ties with England. However, their governmental systems are markedly different.
Canada’s independence came roughly a century after the United States’ independence, though England did not officially recognize Canada's independence until 1931. Unlike the United States, Canada did not break all ties with England (you will find a portrait of Queen Elizabeth on the Canadian dollar bill).
While the United States' government is led by a President elected by the people, Canada’s Prime Minister does not have to be elected—he or she can be appointed by a Governor General representing the English monarchy. The United States elects a President every four years, but there is no term limit for the Canadian Prime Minister.
The three branches of the United States' government (executive, legislative, and judicial) were designed to balance each other out and to prevent any one group from becoming too powerful. In Canada, the Prime Minister has ultimate authority and can override any decisions made by the Parliament.
https://classroom.synonym.com/differences-canada-americas-political-system-11085.html

https://www.indexmundi.com/factbook/compare/united-states.canada

What is an example of a theme in The Crucible, and what are some examples that show how Arthur Miller develops that theme?

Another theme in The Crucible is hunger for power. Both Reverend Parris and Thomas Putnam are exemplary of this. Reverend Parris is described in the exposition of the play as a man who "felt insulted if someone rose to shut the door without first asking his permission." He frets over the possible loss of his position, where he holds great power over a fanatically religious community. Before becoming a clergyman, Parris was a merchant in the Barbados, where he obtained his "Negro slave," Tituba.
While Reverend Parris represents the hunger for power within the religious community, Thomas Putnam represents the hunger for power among landowners. Though there is no animus between Parris and Putnam, Putnam wants his brother-in-law, James Bayley, to be the minister of Salem. Putnam is described as "the eldest son of the richest man in the village." He also considers himself smarter than everyone around him, which makes him doubly offended that the community overlooks his candidate for the ministry. Putnam also tries to break his father's will, due to it leaving "a disproportionate amount to a stepbrother." Putnam was a vindictive man before the witch trials began, but he later uses the panic and persecution of other villagers to his benefit to seize the land of those who are accused, tried, and killed in the witch hunts.

A single theme evident in The Crucible observes that in a climate of mass hysteria, the rights of individuals are sacrificed.  Though the theocratic law of Puritan Salem operated on the tenet that the accused were assumed guilty until proven innocent, the magistrates accepted spectral evidence as hard proof that the accused were practicing witchcraft.  Once spectral sight was entered into evidence, there was no recourse for the accused.  The accused were not allowed legal representation, seen in Act III when Judge Danforth proclaims, "the pure in heart need no lawyers," and when Hale implores Danforth to let the accused have lawyers, Danforth derides him by saying, "Mr. Hale, believe me; for a man of such terrible learning you are most bewildered."  The mass hysteria gripping Salem and the desperation of the theocratic authority to maintain its power and legitimacy combined to deprive the accused people of Salem their rights, and in some cases, their lives.

What is the difference between electronegativity and core charge? Please keep it simple and provide examples. From what I understand, electronegativity means that ANY electrons can be attracted, while core charge only refers to the valence electrons.

This is a great question, and you are on the right track because you realize that the difference is about context. Let me help clarify some of the details.
The short version is that core charge is something that we can calculate rather simply from the particles in an atom as long as we know how many valence and core electrons we have. It is a whole number. Electronegativity is found by experiment and, like most measured values, it is not a whole number. Many tables report electronegativity to two decimal places. Electronegativity is probably confusing because you potentially have not yet learned the context in which it applies. You will be expected to learn how electronegativity varies with position in the periodic table, and core charge can help you understand and remember this.
Core charge and how to find it
Core charge is defined as the charge of an atom’s nucleus minus the charge of the core electrons. I do not know how you were taught to find the number of core electrons. The easiest way I know is to take your element’s atomic number and subtract the number of valence electrons in a neutral atom. The valence electrons, as you probably know, are the s and p electrons in the atom‘s outermost shell, and they can be obtained by counting main-group (A group) elements across the row from left to right up to and including your element. When counting valence electrons, skip over the B group elements (the transition metals).
For example, consider magnesium (Mg). I have included a link to my favorite interactive periodic table, Ptable, so you can easily check the Periodic Table for all my examples. Magnesium has the atomic number 12. We know it has 12 protons, and neutral magnesium has 12 electrons. Magnesium is the second element from the left in its row, so it has two valence electrons. All of the rest of its electrons are core electrons, so it has 12 - 2 = 10 core electrons.
Now consider oxygen (O), on the right side of the table. Its atomic number is 8, so 8 electrons make up neutral oxygen. Counting from the left, we count two, then skip over the transition metals and count three, four, five, six valence electrons. Again, core electrons will be total electrons minus valence electrons or 8 - 6 = 2 core electrons.
Core charge is the atomic number Z (which is the charge on the nucleus) minus the number of core electrons. I think from your question that you understand that this represents the net charge that is attracting the valence electrons. Since we already subtracted valence electrons from atomic number to get the number of core electrons, when we take atomic number and subtract the number of core electrons, we get back the number of valence electrons in the neutral atom.
core charge = Z - (core electrons) but core electrons = Z - (valence electrons)
so
core charge = Z - (Z - (valence electrons))
= (valence electrons)
Remember here that core charge is always positive and is equal to the number of valence electrons in the neutral atom.
Core charge is useful for understanding periodic properties, especially atomic radius, since the increasing core charge going from left to right across the periodic table explains why the valence electrons are more strongly attracted and hence closer to the nucleus, making the radius smaller as you go from left to right.
Electronegativity explained
Now let us discuss electronegativity. The reason electronegativity is hard to understand at this point is that you are probably studying periodic trends and have not yet learned anything about the context in which it is used. Later, you will talk about the bonding that holds atoms together. All chemical bonding involves the attraction of positive and negative charges. One of the types of bonding involves two atom cores that are both attracted to the same pair of electrons. Both atoms are attracted to the electrons, and the electrons are attracted to both atoms. As a result, the whole thing holds together. This kind of bonding is called covalent bonding, with “co” suggesting sharing and “valent” indicating that it is valence electrons that are shared.
In covalent bonding, unless the two bonded atoms are the same element, they will pull unequally on the shared pair of electrons, so the shared electrons will be closer to one atom core than to the other. This affects the properties of the bond and the molecule that it is in. Electronegativity is the relative ability of atom cores of different elements to attract a shared pair of electrons in one of these bonds.
For now, you are probably expected to know that electronegativity involves an atom’s ability to attract electrons and how it varies with position in the periodic table. Electronegativity is greatest at the upper right (excluding noble gases, which do not usually form bonds). Fluorine is the most electronegative element. Oxygen, nitrogen, chlorine, and bromine are also highly electronegative.
Electronegativity is greatest at the right side of the periodic table because core charges are greatest in these elements. Electronegativity is also related to atomic radius. Remember, is it ultimately about the attraction of positive and negative charges, which depends both on how strong the charges are and on how close together they are. The elements with small atomic radii have their cores closer to a shared pair of electrons, so they are able to attract them more strongly.
All of the periodic properties are related, and you will understand and remember them better if you try to see the connections. Core charge affects atomic radius, and both core charge and atomic radius play a role in electronegativity (and in first ionization energy).
https://ptable.com/