How would you design an experiment to demonstrate the first law of reflection of light?

The first law of reflection says simply that the angle of the incident ray and the reflected ray are always the same, theta_I = theta_R .To show this experimentally, we need three things: a laser, to give us well-defined incident rays of light, a mirror, to reflect off of, and some form of sensors or detectors that allow us to measure the angles.Then, we point the laser at the mirror at various known angles, theta_I , and measure the angle of the light that comes off the mirror, theta_R . We can't actually see the rays, but we can measure where the light hits our detectors and extrapolate what the rays must have been, thereby determining the angle. (We could also put this whole apparatus in a cloud chamber and almost actually see the rays — what's really happening is we've essentially set up millions of detectors right in a row.)If the first law of reflection is right (and it is), the reflected ray and the incident ray should have the exact same angle, within the margin of error of our experimental setup. In fact, this law is so thoroughly empirically supported that if we don't get that result, we can basically be sure there is something wrong with our experimental setup, and have no reason to actually doubt the first law of reflection.
https://www.physicsclassroom.com/Class/refln/u13l1c.cfm

What does Dr. Reynolds do for a living?

In Tony Hillerman's 1973 novel Dance Hall of the Dead, Joe Leaphorn and Jim Chee of the Navajo Tribal Police investigate the disappearance of two young boys, one a Navajo and the other a Zuni. Interwoven into the story is factual information about Zuni and Navajo history, as well as traditions and non-Native intrusions into them.  
Dr. Chester Reynolds is an anthropology professor who has identified Folsom and Paleo-Indian cultural sites. He is advising his graduate assistant, Ted Isaacs, who is leading an archaeological dig at one of the sites. Dr. Reynolds, however, has been "salting" the excavation sites with artifacts, unknown to Isaacs. Dr. Reynolds eventually resorts to a double murder, killing both George Bowlegs and Ernesto Cata to cover up his malfeasance at the dig sites.
Ultimately, Dr. Reynolds becomes a missing person case, though it is strongly implied that he has been killed because of his capital crimes as well as his cultural desecration.

"Nora left me three days ago and I've had a lot of time to think." How would I write a monologue with this statement?

What a wonderful idea for an assignment. We are left to wonder what happens to everyone after the door slams.
Torvald is not a particularly well-developed character, so it will require a lot of introspection to figure out what makes him tick and to identify what his logical next steps would be.
Torvald is a very conventional person and a bit of an ostrich. He wanted to believe his life with Nora was moving along according to plan, and it seems that he willingly overlooked the signs that something was amiss.
Several key questions to consider:
Will Torvald's behavior actually change? Does he truly want Nora back? If so, his monologue could largely consist of possible plans to get her back.
Is Torvald willing to accept responsibility, or will he continue to blame Nora? If he is still undecided, his speech could include more of his interior states as he ponders how things got to this point.
Also, what play might this speech be part of? Is it in one more act added onto the existing play? The first act of a new play? To what broader action might this one character's speech be connected?
In addition, remember to take clues from his lines in the play. Torvald speaks of his having "cherished" Nora, so we must ask if he believes this. But he also speaks of how things look "in the eyes of the world"—would that remain a more important concern than repairing his marriage?
Finally, it might be fun to take things in a different direction. Maybe Torvald wants a complete break with this tainted past. Thousands of Norwegians went to the New World in the nineteenth century—maybe Torvald would like start a new life in, say, Minnesota.
Lucas Hnath is among those who wondered what happened, and in 2017 he wrote a play following up with Nora and company fifteen years later. It is called simply A Doll's House, Part 2.

This monologue seems to center on Torvald and might include his reflections on whether he made the right decisions in his marriage to Nora. He treated her like a silly dependent, and he put her in the position in which she had to borrow money to help him. Later, he became angry at her for hiding her debt from him.
In this monologue, Torvald can reflect on whether he should have treated Nora in a more equal way. If he had treated her more like an adult than like a child, they could have spoken openly about their financial problems. She would not have had to go behind his back to borrow money. If she had borrowed money, it could have been a decision they made jointly. Do you think Torvald regrets his actions, or do you think he is steadfast in his decision to have treated Nora as a kind of pet? In this monologue, Torvald can wrestle with these decisions and with the ideas he has about marriage. He might decide that he has changed his views, or he might decide that he made the right choices. He might also have regrets but decide that he acted the right way.

I assume that you are being asked to write a monologue in which the character speaks to himself, alone, and not to another person (both because of the way your question is phrased and because we can assume that Nora has not returned). Therefore, you will want to present his honest and true feelings; if he's talking to himself, then he has no one to impress or to whom he has to prove anything.
Consider that Nora has done something that was so radical at the time that Ibsen actually had to write an alternate ending (in which Nora did not leave her family) when the play was first performed. How do you think Torvald would respond to her completely unique behavior? Would he be contrite and sorry, recognizing the validity of her accusations? Would he take responsibility for treating her like a doll, as she says? Or would he be angry that he's tried so hard to provide for Nora and their family and that she is acting selfishly? Would he be furious that he's done what "good husbands" do and been met with such opposition in his wife? I would suggest rereading the section of the play where Nora stands up to him in order to find some evidence to support your opinion regarding his response.
Once you've come to some conclusion about what you think his response would be, as well as located some evidence for that conclusion, you are ready to begin writing! You might even want to refer back to things either Nora or Torvald said during their confrontation, just to really make it convincing.

What is a summary of the Industrial Revolution in Great Britain, including key events, causes, effects, and key players?

The Industrial Revolution began in Great Britain in the mid/late 1700s. To summarize, the world essentially transitioned from a rural, agrarian society to a more urban one. Manufacturing and other industries began to evolve, which brought on a variety of changes for Great Britain and for the world as a whole.
One cause of the Industrial Revolution in Great Britain was the amount of natural resources the country had. Coal and iron were prevalent. Moreover, these resources provided the energy for the machines that became the backbone of the revolution. One effect of the Industrial Revolution was the urbanization of the country. With more manufacturing centers being built, more people moved into towns and away from agrarian life. This resulted in exponential population growth and the development of cities.
One key player in Great Britain was James Hargreaves. He was able to create a machine that held multiple spools of thread. This was important for the textile industry, which experienced huge growth during the Industrial Revolution.
Another key player was Henry Bessemer in the 1850s. He developed a way to produce steel by using iron ore more efficiently. Steel became the lifeblood of the Industrial Revolution throughout the world.
https://www.history.com/topics/industrial-revolution/industrial-revolution

The Industrial Revolution began in Great Britain towards the end of the 18th century, when specialized machinery allowed companies to mass-produce goods. Previously, manufacturing was done by hand and was often accomplished by family-run businesses using basic tools at home. Along with new manufacturing techniques and machinery, the Industrial Revolution also led to the development of new strategies for transportation and finance.
Key Events
Changes in the textile industry served as a catalyst for Britain's Industrial Revolution. While textiles and garments had previously been handcrafted in the homes of artisans, machines made it possible to produce massive quantities of goods at a far more efficient pace. The spinning jenny produced multiple spools of thread at the same time, while the power loom allowed manufacturers to weave cloth at a much faster rate. The invention of the steam engine was another key event that made it possible to remove water from mines and transport goods more efficiently.
Causes and Effects of the Industrial Revolution
The Agricultural Revolution was one of the primary causes of the Industrial Revolution. With the increased production of food, it became cheaper than ever for Great Britain to feed its growing population. Families in turn spent their excess money on manufactured products, which led to a greater demand for goods produced at low prices and in high quantities. Industrial machinery made it possible to produce items that were once considered luxuries at a cost the average worker could afford.
The Industrial Revolution had both positive and negative effects on the quality of life in Britain. The demand for workers led to the mass integration of children into the workforce, and a significant number of factory workers were under the age of 15. Child laborers were often subjected to harsh hours and grueling working conditions. The abuse of workers in the Industrial Revolution laid the groundwork for modern child labor laws and union regulations designed to protect workers.
Key Players
Charles Wheatstone and William Cooke were two major players in the Industrial Revolution as the co-inventors of the telegraph. The electrical telegraph was used to aid communications across long distances, making it easier for businesses, governments, and individuals to communicate efficiently. An American named Robert Fulton built the first commercial steamboat during the height of the Industrial Revolution, allowing for faster transportation of cargo across the Atlantic Ocean. George Stephenson was another prominent figure of the Industrial Revolution, and he was commonly known as the "Father of Railways." His was the first commercial railway and locomotive system to be adopted across the world.
https://www.history.co.uk/biographies/george-stephenson

https://www.history.com/topics/industrial-revolution

By the year 1000, the Mediterranean world was quite different from the Classical world. How and why did this happen?

Perhaps the most dramatic factor that changed the Mediterranean by the year 1000 CE was the rise of Christianity and Islam. The diverse religious beliefs of antiquity were largely replaced by two major monotheistic religions with orthodoxy of belief (rather than just token offerings) enforced by the government. Consequently, vast areas became united in their beliefs. Two factors accounting for the success of these religions in the Mediterranean were (1) their promise of an idyllic afterlife for their followers and (2) their usefulness in supporting imperial ideology.
Next, the capital of the Roman Empire shifted east from Rome to Constantinople, signaling an increasing division, both religious and linguistic, between the Greek east and Latin west. Part of this division grew due to barbarian invasions and conquests of territory that had been subject to Roman rule in antiquity.
Finally, in the chaos following the fall of the western Roman Empire, many smaller states arose that were organized along feudal lines.

How does "In Another Country" reflect a modernist point of view?

Hemingway's short story about men at an Italian hospital during World War I reflects a modernist point of view in three different ways. First, modernists attempted to portray the modern world in both form and content. To show the fragmentation of this new world, they often omitted traditional elements of fiction such as expositions, conflicts, and resolutions. Rather than spending any time establishing the character of the narrator, Hemingway simply places him in Milan during World War I. He doesn't even tell us the man's name or anything about him other than he may have played football and that he is learning Italian. Hemingway called this the "iceberg principle," reflecting his attitude that a good story would say less, but in its suggestiveness would say much more.
This lack of exposition is followed by a complete lack of true conflict or resolution. In traditional short stories the conflict generally leads to an inevitable resolution, such as a completion of a great deed, a death, a birth, or a wedding. The best we get from Hemingway is the irony that the major escaped death in a war which claimed millions yet his wife died after only a short illness.
Hemingway is also thoroughly modern in his style. He brings a simplicity and succinctness to his stories much like a newspaper reporter who attempts to hone down his story to a series of simple facts without any editorial comments. Newspaper writers are often limited by the number of words they can submit so they strive to say as much as possible in just a few words. Hemingway's stories, and "In Another Country" is no exception, are virtually devoid of descriptive adjectives or long paragraphs describing setting or character. He hoped to pack as much meaning as possible into direct, declarative sentences. He succeeds in the story's opening sentence: "In the fall the war was always there, but we did not go to it any more." This simple statement suggests several things. It states facts but also portends a feeling of despair as the "war" and its experiences hover over the narrator's story.
Finally, Hemingway, like the great English war poets of the time, casts doubt on mankind's use of war as a way to bring men bravery and glory. In previous wars, literature tended to celebrate the heroes (think of the "Iliad," "Song of Roland," "The Charge of the Light Brigade"). Instead, World War I is bereft of heroes in Hemingway's modernist outlook. The major, who had been badly injured in the war, scoffs at the idea of bravery:

The major, who had been a great fencer, did not believe in bravery, and spent much time while we sat at the machines correcting my grammar.

The major seems obsessed with grammar because it is a way for him to control the world. Grammar makes sense and has rules, unlike the war which is arbitrary and confusing.

Calculus of a Single Variable, Chapter 7, 7.5, Section 7.5, Problem 5

Hooke's law states that a force is needed to stretch or compress a spring by a distance of x. The force is proportional to the distance x. is written as F = kx
where:
F = force
k = proportionality constant or spring constant
x= length displacement from its natural length
Applying the given variable force: F= 5 to compress a 15 -inch spring a total of 3 inches, we get:
F=kx
5=k*3
k=5/3
Plug-in k =5/3 on Hooke's law, we get:
F = (5/3)x
Works is done when a force is applied to move an object to a new position, It can be defined with formula: W = F*Deltax where:
F = force or ability to do work.
Deltax = displacement as
With variable force function: F (x)= (5/3)x , we set-up the integral application for work as:
W = int_a^b F(x) dx
W = int_0^7 (5/3)xdx
Apply basic integration property: int c*f(x)dx= c int f(x)dx.
W = (5/3)int_0^7 xdx

Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1).
W = (5/3) * x^(1+1)/(1+1)|_0^7
W = (5/3) * x^2/2|_0^7
W = (5x^2)/6|_0^7
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
W = (5(7)^2)/6 -(5(0)^2)/6
W =245/6 - 0
W=245/6 or 40.83 inch-lbs

How does one conduct a SWOT analysis of a company like Apple, Google, Redbox, or Netflix? What steps has the company taken in the strategy-making process? At which level was each decision made?

Though Netflix experienced dramatic increases in stock value in September 2014, stock since then has fallen because increase in customer base has slowed. A slow increase in customer base can be attributed to higher subscription fees and competitors in the online streaming business such as Amazon. Netflix's recent declines in stock make business analysts start to wonder how successful Netflix will be in the future, and Netflix's future rate of success might be predicted through a SWOT analysis (Ingram, M., "Netflix Flies Too Close to the Sun, Stock Prices Melt," Fortune).A SWOT analysis is a means of identifying the Strengths, Weaknesses, Opportunities, and Threats of a business in order to develop business strategies and make decisions. A SWOT analysis can help a business see possible "solutions to problems," determine what if any "change is possible," and develop new plans ("SWOT Analysis: Strengths, Weaknesses, Opportunities, and Threats," Community Tool Box, University of Kansas).Strengths:Most of the company's growth is dependent on its streaming market as opposed to the DVD rental system via mail developed in 1999.  In his article titled "Netflix: A Short SWOT Analysis," researcher Michael Napoli informs us that one area of strength is that the company has put in a great deal of effort into making streaming convenient, including making streaming available on multiple devices connected to the internet such as computers, smart phones, androids, and smart televisions. The company is also continually increasing the amount of streaming content available and even beginning to produce its own TV series and films. The company is confident its streaming customer base will continue to grow.Weaknesses:Napoli further informs us that one weakness concerns the membership losses for its "DVD-by-mail rental operation" ("Netflix"). When the company launched its streaming business in 2007, DVD rentals and streaming were offered in combined subscription packages. Starting in 2011, Netflix separated the streaming and DVD rental membership plans, making subscribers pay for two separate plans if they wanted both. As a result, DVD rental membership declined drastically and is expected to continue to decline. While the company's streaming membership rates are still high enough to compensate for losses in DVD rental membership, the company could suffer losses if DVD membership continues to fall "at a faster rate than previously expected" (Napoli). A second weakness is that expanding internationally is causing some problems, especially because new higher European taxes are causing profit loss (Napoli). Netflix reported its greatest contribution profit loss came from the oversees steaming market, with a total loss of 17.1%, as opposed to 32.9% a gain in profit in the domestic streaming market (Netflix, "Financial Statements").Opportunities:Despite higher taxes in Europe, Napoli informs us that Netflix is still pursuing growth oversees through its streaming market ("Netflix"). Expansion oversees still looks like the greatest opportunity for growth. As of 2016, Netflix reported gaining 30,024 international streaming memberships by the end of December 2015, resulting in a total of $1,953,435 earned (Netflix, "Financial Statements"). In addition, producing original content continues to be a great opportunity for growth (Napoli).Threats:Netflix's greatest threat is competitors in the streaming market such as Amazon Prime being offered by Amazon (Napoli). Netflix further reports that their competitors are "liner networks, pay-per-view content, DVD wtching, video gaming, web browsing, magazine reading, video piracy, and much more" (Netflix, "Netflix's View: Internet TV is replacing linear TV"). Netflix expects all of these avenues of entertainment to improve over the years, creating greater competition.

What does the first stanza describe in "Because I Could Not Stop for Death" by Emily Dickinson?

The first stanza in Emily Dickinson’s poem “Because I Could Not Stop for Death—” describes an encounter between the speaker and Death, with Death personified as a carriage driver who stops his carriage in order to pick up the speaker and take her on a ride to Eternity. This encounter is striking for its lighthearted tone; the speaker seems to be going on an everyday ride and the character of Death is described as a gentleman with “kindly” intentions, which is most at odds with the stereotype of Death as the much-feared Grim Reaper. The iambic meter is also at odds with the meaning of the poem. The iambic rhythm (da DUM da DUM da DUM) creates a lively momentum to the lines, and yet the meaning of the lines emphasizes the exact opposite: that the momentum of life has stopped because Death has stepped in to stop it. Dickinson’s use of dashes and capital letters also attempt to break up the inevitable rhythm.
Unlike the driver, Death, who is in control, the speaker has no control. However, she does not resent this. She is not resistant to her fate at all; there is no anxiety or fear. The striving of life is over, and the speaker accepts that immediately; she is content to simply settle in for the ride, especially since the character of Death seems to be so very courteous. The release from life is not fraught with any tortured last moments. The passivity of the speaker suggests a life that may have been spent following its own rhythms (da DUM da DUM da DUM) without thinking too much about where this rhythm of life was taking her. Did the speaker ever take the time to consider life’s meaning, or was she always too busy to deal with such questions? No matter, because Death steps in and takes control.
The fourth line in the first stanza indicates another character as well, “Immortality,” suggesting the hope that the speaker’s last stop will not be the grave but will be an afterlife, “Eternity.” Only at the end of the poem do we learn that the action in the first stanza, the speaker being taken by Death, actually occurred many centuries ago. The gentle cessation of the striving rhythms of life have left a powerful mark on the speaker, who remembers the vivid details of this day, despite the fact that she has been dead for centuries.

The first stanza of "Because I Could Not Stop for Death" describes the gentleman caller who appears in order to take the speaker with him in his carriage. This caller is Death personified.
As readers of this poem peruse the stanzas, they realize the gentleman caller is Death. He appears to the speaker in the form of a man, but the mention of the carriage containing only the speaker, driver, and Immortality indicates the driver's role: he is transporting the speaker from her earthly house to the "House" that seems but a "swelling of the ground" with a scarcely visible roof. In other words, Death is carrying the speaker through her life to its end, the grave. As they ride, the speaker views her youth as the children playing at recess in school. She then views the "Fields of Gazing Grain" that represent her maturity into womanhood. Finally, they pass "the Setting Sun" as she reaches the end of her life.
In the final stanza, the speaker addresses her audience from the grave as she recalls her realization that her caller was transporting her "toward Eternity."

How did the French Revolution inspire the people of the world?

The French Revolution initially caused great enthusiasm among educated European contemporaries because it offered an example of people’s self-affirmation against the despotism of an autocratic government, promoted civil equality irrespective of social status, abrogated feudal privileges, and proclaimed individual human rights by adopting the Declaration of the Rights of Man and of the Citizen.
Many people were dismayed when the same revolution later resorted to violence and terror against both its real and perceived opponents. Feminists, such as Olympe de Gouge and Mary Wollstonecraft, denounced the revolution’s failure to give equal civil rights to the female part of the French population.
Nevertheless, revolutionary France with its civic fervor, patriotism, egalitarianism, abolition of slavery, sense of global historical mission, and successful armed national self-assertion against the forces of the reactionary European powers remained a source of inspiration to revolutionaries and radicals across the world. Many of them sought to wrest independence for their own countries from the West or to liberate their countries from European colonial domination.
Lenin, for example, often declared the Russian Bolsheviks and their Red Army to be the rightful and legitimate successors of the French revolutionary Jacobins with their favorite slogan “Peace to the cabins, war on the palaces;” Lenin’s forces were fighting against the Whites and against British and French interventionist armies.
Sun Yat-sen, the first president of the Republic of China, acknowledged that the history of the French Revolution made a strong impression on him during his student years when he was gradually turning against the Manchu domination of China. Ho Chi Minh’s Declaration of Independence of the Democratic Republic of Vietnam (1945) contains references to both the American Declaration of Independence and the French Declaration of the Rights of Man and of the Citizen.

Beginning Algebra With Applications, Chapter 8, 8.2, Section 8.2, Problem 132

Find the positive integer values of $k$ for which the polynomial $y^2 + 5y + k$ are factorable over the integers



$
\begin{array}{c|c}
\text{Factors whose sum is 5} & k \\
\hline\\
1,4 & 4 \\
2,3 & 6
\end{array}
$

The positive integer values of $k$ are $4$ and $6$. So the polynomials are $y^2+5y+4$ and $y^2+5y+6$.

What makes Kevin so angry his eyes blaze?

The answer to this question can be found in chapter 4. Freak and Max are still getting to know each other at this point, so they don't know all of the other person's idiosyncrasies, likes, dislikes, preconceived notions, etc. The chapter starts with Freak telling Max about King Arthur and the knights, and the more Freak talks, the more Max realizes that Freak is a genius level kid. The other thing that impresses Max is how passionately Freak shares his knowledge.

This is the first time for me, hearing Freak really talk, and right away I know one thing: When he’s talking, you can’t take your eyes off of him. His hands are moving, and it’s like he’s really seeing it, this story about an old king.

Freak starts telling Max about the knights and how the knights were essentially the predecessors to modern day robots. Max makes the mistake of saying that he thought robots weren't real and only existed in the movies. Freak can barely contain himself.

". . . which is sort of how they program robots right now.”
I go, “I thought there weren’t any real robots. Just in the movies.”
Boy does that make his eyes blaze. Like whoa! talk about laser beams! He’s like fuming, so upset he can hardly talk.

Freak is a smart kid, and he's passionate about a lot of things. Science, technology, and robots rank high on his list of passions, and he's a bit angered and dumbfounded at Max's completely erroneous thoughts on robots. Freak gets control of himself and then tells Max about how very real and very cool robots are.

What life lessons are we taught in the poem "If"?

There are several life lessons taught in Rudyard Kipling's famous poem "If." For, this poem, addressed to Kipling's son, is a paean to the stoicism characteristic of the British of the Victorian Age, and to uprightness.
Stanza 1
In this first stanza, Kipling initially stresses that one must "keep" one's head; that is, remain rational while others are becoming irrational and placing blame upon others rather than accepting responsibility:

If you can keep you head when all about youAre losing theirs and blaming it on you...

Kipling also stresses self-discipline: "trust yourself when all men doubt you." "..wait and not be tired by waiting...."And, he emphasizes manly rectitude: " Or being lied about, don't deal in lies."
Stanza 2
Kipling emphasizes that it is important to dream and have an imagination, but control of one's imagination is necessary, as well, for one must be realistic:

If you can dream--and not make dreams your master...

One must also be strong and willing to take risks and lose, then turn and start again after watching the

...things you gave your life to, broken, and bend down to pick them up and "build'em up with worn-out tools.

Stanza 3
In this stanza Kipling emphasizes fortitude and the ability to begin anew when necessary. A man must be able to suffer losses and start over:

If you can force your heart and nerve and sinewTo serve your turn long after they are gone,And so hold on when there is nothing in youExcept the Will which says to them: "Hold on!"

Stanza 4
This stanza emphasizes and extols the virtues of moral uprightness.  Kipling praises the virtue of humility--"the common touch"--and making the most of time--

...fill the unforgiving minute...with sixty seconds worth of distance won,

Then, he can conquer anything and be a true man.
 

y = x^(coshx) , (1, 1) Find an equation of the tangent line to the graph of the function at the given point

Given
y = x^(coshx) , (1, 1) to find the tangent line equation.
let
y=f(x)
so,
f(x) =x^(coshx)
so let's find f'(x) = (x^(coshx))'
on applying the exponent rule we get,
a^b = e^(b ln(a))
so ,
x^(coshx) = e^(coshx lnx)
so,
f'(x)= ( e^(coshx lnx))'
=d/dx ( e^(coshx lnx))
let u=coshx ln x
so ,
d/dx ( e^(coshx lnx)) = d/ (du) e^u * d/dx (coshx lnx)
= e^u * d/dx (coshx lnx)
=e^u * (sinhx lnx +coshx/x)
=e^(coshx ln x) * (sinhx lnx +coshx/x)
=> x^coshx * (sinhx lnx +coshx/x)
now let us find f'(x) value at (1,1) which is slope
f'(1) = x^cosh(1) (sinh(1) ln(1)+cosh(1)) = x^cosh(1) (0+cosh(1))
 = x^cosh(1) (cosh(1))
now , the slope of the tangent line is x^cosh(1) (cosh(1))
we have the solope and the points so the equation of the tangent line is
y-y1 = slope(x-x1)
y-1=slope(x-1)
y= slope(x-1) +1
 =x^cosh(1) (cosh(1)) (x-1)+1
but x^cosh(1) = e^(cosh(1)ln(1)) = e^0 =1
so,
 
=1 (cosh(1)) (x-1)+1
= xcoshx -coshx +1
so ,
y=xcoshx -coshx +1 is the tangent equation

Beginning Algebra With Applications, Chapter 8, 8.2, Section 8.2, Problem 118

State whether or not the trinomial has a factor of $(x+y)$.

a. $2x^2 - 2xy - 4y^2$


$
\begin{equation}
\begin{aligned}

2x^2 - 2xy - 4y^2 =& 2 \left(x^2 -xy-2y^2 \right)
&& \text{Factor out } 2
\\
=& 2 (x-2y)(x+y)
&& \text{Factor } x^2 - xy -2y^2

\end{aligned}
\end{equation}
$


The trinomial $2x^2 - 2xy - 4y^2$ has a factor of $(x+y)$.

b. $2x^2 y - 4xy - 4y$

$2x^2 y - 4xy - 4y = 2y(x^2 - 2x - 2) \qquad$ Factor out $2y$

The trinomial $2x^2y - 4xy - 4y$ is not a factor of $(x+y)$.

How did America change after WWI?

One very important change America experienced after World War I was in the presidency. President Woodrow Wilson, the last president of the progressive era, ended his presidency in failure. He tried repeatedly to get the United States to join the League of Nations; he failed and his efforts to reach that goal led to his physical collapse. Warren G.
Harding, Wilson's successor in the White House, was different from Wilson in all respects. In his campaign for the presidency, Harding promised a "return to normalcy." After his electoral triumph, he sought to undo the achievements of the progressive movement. For instance, he lowered taxes on affluent Americans. Harding served for only two years before dying in office, but his brief tenure marked a complete break from previous domestic and foreign policies.
Households changed in the 1920s as modern conveniences and entertainment became widely available. The washing machine, flush toilet, and electricity became much more common. Heads of household received large raises during this decade, so their families could enjoy many of the new products on the market. Families gathered around the radio to listen to newscasts or sporting events. Calvin Coolidge, Harding's successor, became the first president to speak to the nation on the radio.
Automobiles changed the culture of the country. Americans could commute to work or drive to one of the new movie cinemas. The Model T became affordable for middle-class Americans.
Airplanes had been used extensively in World War I, and their use accelerated after it ended. Airports were built. Finally, Charles Lindbergh electrified the nation when he flew non-stop to Paris from New York.

World War I impacted and changed the United States in a number of notable ways that can be added to the answers below. For starters, it signaled the entry of the country to the world stage. For much of the previous generation, the United States had tried not to involve itself in the affairs of other countries. Although the United States had begun meddling in imperialism abroad, it tended to keep its nose out of the business of other countries when not directly concerned.
This war changed that. It was the first time that the United States got involved in world events on such a level. While many Americans went to war to counter the threat of Germany, its post-war mission was to create a world-order safe for democracy. After the war, the country briefly returned to its isolationist stance, but it would not be long before the United States became a world player again.
At home, World War I changed much of the domestic landscape. For one thing, it spurred the Great Migration. African Americans from the rural South began moving to the urban North and Midwest in large numbers to fill job vacancies left by soldiers overseas. When the war ended, many stayed, signaling a huge demographic shift. This resulted in a lasting change in African American culture and politics that still reverberates today.

The United States changed significantly after World War I ended. Prior to the war, the United States pursued an expansionist foreign policy and a domestic policy that worked to correct the problems that existed in the country. The United States had expanded its influence in Asia, the Caribbean, and South America. When Germany interfered with the American right to trade after World War I began, the United States joined the war in 1917 against Germany and the Central Powers. Through the actions of people associated with the Progressive Movement, attempts were made to eliminate child labor, clean up politics, control the actions of big businesses, help working class people, and protect the environment.
After World War I ended, the people of the United States didn’t want the country to be so involved in world affairs, and the American people began to look inward. The people also didn’t want the government to be so actively involved in the economy and in dealing with social issues. The United States passed strict immigration laws when the Emergency Quota Act and the National Origins Act were passed. The Dawes Act was passed to help deal with the issue of Germany’s payment of reparations. The Washington Naval Conference was held, leading to agreements to reduce weapons that various countries possessed. The Kellogg-Briand Pact outlawed war, although it was a non-binding agreement. The government began to pursue a laissez-faire policy toward economic issues and the actions of businesses. Companies were given more latitude to run their businesses, and there was less government involvement in the economy. Taxes were cut with the belief that the prosperity of businesses would trickle down to the average American.
The terms the Roaring 20s and the Magic Decade are used to describe this decade. Americans wanted to enjoy life and not be so concerned about world affairs and problems facing the country.

WWI opened doors for radical change in the United States, such as advocacy for progressive policy regarding women's suffrage and an economic boom and gave way to the "roaring 20s." At the same time, however, the migration of African-Americans from the South to occupy the jobs of those from the North who joined the military lead to pushback from conservative groups like the Ku Klux Klan, making social issues more tumultuous than they had been since the Civil War.

The period after World War I is called the Roaring Twenties in American history. It is a period that is marked by a sharp uptick in the American economy, especially with respect to manufacturing and investment.  The United States became a consumer driven economy. There was an attitude that prosperity was boundless. Americans began to use consumer credit to drive their purchases. In general, the Republican presidential administrations took a laissez-faire approach to big business and the economy.
The decade was also a period of tremendous cultural conflict. The fear of communism and increase of immigrants during the decade led to a strong nativist sentiment. This xenophobia saw enrollment in the Ku Klux Klan escalate to historic levels.
There was also a conflict between the secular portion of the population and a growing Christian fundamentalist movement. This is evidenced by the sensationalism of the Scopes Trial and the introduction of the Prohibition Amendment. The period was also one in which women and African-Americans fought for political, social, and economic equality.
https://www.history.com/topics/roaring-twenties

What does the egg symbolize?

The egg symbolizes the frustrated dreams of the narrator's parents, but also the general inscrutability of life. The parents are "ambitious"—they feel an urge to somehow be more than what they are, which leads them first to become chicken farmers and then, later, restaurant owners. But in each endeavor they are frustrated—it is as if they cannot understand how to be successful, or as if success eludes them somehow. Anderson sees the chicken, in particular, as symbolic of a kind of "con" at the center of the American dream: raising chickens may seem like a good idea, and many books have been written about it, but "do not be lead astray by it," the narrator warns. "It is not for you." The chicken farm fails because chickens themselves are creatures that die easily and whose products (eggs) simply serve to start the same process over again. The father's sudden desire to make his restaurant successful by entertaining customers is akin to the egg-laying process, in that his "act" of squeezing an egg into a bottle is likely to fail and, even if it does work, will only lead to more customers and more awkward performances. The father, in his desperation for success and his need for acceptance, finally breaks the egg trying to force it into the bottle, grows furious, and starts throwing eggs at his audience (usually it is the audience that throws eggs at poor performers). The father has, ironically enough, laid his own egg!

In Sherwood Anderson's 1920 short story "The Egg," the egg symbolizes a family's hopes and dreams. An egg represents a potential new life, and Anderson observes that hopes and dreams can come to fruition, be dashed, or be imperfectly realized.
The narrator's family struggles along as chicken farmers for a decade before giving it up to embark on a new dream. The father keeps "grotesques," malformed chicks, in jars in hopes of making money by showing them to other people. He opens a restaurant, and his attention turns to making eggs for diners, who fail to materialize. Again, the dream that the egg symbolizes fails to deliver the successful business he has envisioned.
Ultimately, the father tries to captivate his customers by performing tricks with eggs, such as standing them on end or forcing them through the neck of a bottle. In the end, he is defeated, and the narrator observes that the egg has triumphed over his family instead of fulfilling their aspirations.

How are social groups, issues, and ideas represented in the film “The Book Thief”?

The idea of knowledge as a defense against ignorance and prejudice.
In the movie, knowledge is represented as a defense against hatred and intolerance. At the beginning of the story, we learn that Liesel Meminger is illiterate. When asked by her teacher to write her name on the blackboard, Liesel can only manage three Xs. It is Hans Hubermann, Liesel's adopted father, who teaches her how to read. The movie represents knowledge as a means of developing self-awareness and preserving self-identity. As Max Vandenburg argues, the procurement of knowledge reinforces our humanity:

Write. In my religion we're taught that every living thing, every leaf, every bird, is only alive because it contains the secret word for life. That's the only difference between us and a lump of clay. A word. Words are life, Liesel.

In the movie, Liesel's stories are encapsulated in the words of her journal. Her words inspire subsequent generations even after her death.
Social groups as an arm of totalitarian government, a vehicle for sanctioned violence, and a means of perpetrating destructive ideologies.
In the movie, Liesel and Rudy are members of Hitler Youth, the juvenile wing of the Nazi Party. One of the scenes shows a Nazi official presiding over the burning of books. In attendance are members of the German military, local citizenry, and Hitler Youth. The official gives an impassioned speech in German, and the locals express their support through enthusiastic shouts. The camera pans in on Liesel and Hans; both appear to be troubled by the Nazi exercise in totalitarian intimidation. 
Franz is seen taunting Liesel and Rudy; he threatens them and warns them against disobeying explicit orders to participate in the book burning. Meanwhile, the local citizenry sing patriotic Nazi songs as the books burn. The movie represents social groups like Hitler Youth as a means of securing the future of oppressive political structures. During WWII, the Nazis indoctrinated the members of Hitler Youth in Nazism and anti-religious ideologies. Members of Hitler Youth were encouraged to spy on their peers and to participate in violent acts against subversives (those who refuse to bow down to the dictates of Nazism). In the movie, Franz threatens to report Leisel and Rudy for being "up to something."
Issues of discrimination and persecution of minority groups as a horror and a stain upon a nation's honor.
In the movie, German soldiers routinely perpetrate horrific violence on defenseless Jews. The Jews are represented as the persecuted scapegoats of the Nazi regime. As the movie progresses, we learn that Leisel's adopted parents are sheltering Max Vandenburg, a Jewish fugitive. In WWI, Max's father saved Hans's life, so Hans feels obligated to Max. Rudy, suspecting that something is up, demands to know who Liesel's family is sheltering. Liesel's response is that she will put her adopted parents and herself in danger if she tells him the truth.
Eventually, Leisel does admit the truth to Rudy (he assures her of his loyalty), but their conversation is overheard by Franz. Franz tries to grab Leisel's journal, but Rudy throws it into the river. Enraged by this act of insubordination, Franz attacks Rudy. In the movie, youth violence testifies to the horrors endured by Jews and those who tried to help them during WWII. The movie represents the issue of religious discrimination as a dire threat to civilization.
The idea of death as an imminent fate for all, regardless of religion, race, or nationality.
Death speaks at the beginning of the movie; he assures us that, sooner or later, we will meet him, regardless of who we are. He tells us that death comes to all and that no one lives forever. In his characteristic bland tone, he informs us that panicking when death comes calling is a useless reaction. The movie represents death as a natural human experience. 
It also highlights death as the great equalizer on the field of battle. As Death watches the unfolding of WWII, he proclaims: "I met so many young men over the years who have thought they were running at their enemy, when the truth was, they were running to me." So, death is no respecter of persons, regardless of whether one fights to defeat evil or whether one fights on the side of evil.
 

Precalculus, Chapter 7, 7.3, Section 7.3, Problem 20

EQ1: 2x-y=0
EQ2: x-y=7
To solve this system of equations, let's apply substitution method. Let's isolate the x in the second equation.
x - y=7
x=7+y
Then, plug-in this to the first equation.
2x - y=0
2(7+y)-y = 0
And solve for y.
14+2y-y=0
14+y=0
y=-14
Now that the value of y is known, solve for x. Let's plug-in y=-14 to the second equation.
x -y=7
x-(-14)=7
x+14=7
x=7-14
x=-7

To check, plug-in x=-7 and y=-14 to one of the original equations. Let's use the first equation.
2x-y=0
2(-7) - (-14)=0
-14 + 14=0
0=0 (True)

Therefore, the solution is (-7,-14).

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 21

Suppose that $f(x) + x^2 [f(x)]^3 = 10$ and $f(1) = 2$, find $f'(1)$
$\displaystyle \frac{d}{dx} [ f(x) ] + \frac{d}{dx} \left( x^2 [f(x)]^3 \right) = \frac{d}{dx}(10)$

$
\begin{equation}
\begin{aligned}
\frac{d}{dx} [f(x)] + \left[ (x^2) \frac{d}{dx} [f(x)]^3 + [f(x)]^3 \frac{d}{dx} (x^2) \right] &= \frac{d}{dx} (10)\\
\\
f'(x) + (x^2) (3) [f(x)]^2 \frac{d}{dx} [f(x)] + [f(x)]^3 (2x) &= 0\\
\\
f'(x) + 3x^2 [f(x)]^2 f'(x) + 2x [f(x)]^3 &= 0\\
\\
\end{aligned}
\end{equation}
$

when $x = 1$,

$
\begin{equation}
\begin{aligned}
f'(1) + 3(1)^2 [f(1)]^2 f'(1) + 2(1) [f(1)]^3 &= 0\\
\\
f'(1) + 3(2)^2 f'(1) + 2(2)^3 &= 0\\
\\
f'(1) + 12f'(1) + 16 &= 0\\
\\
13f'(1) + 16 &= 0\\
\\
13'f(1) &= -16\\
\\
\frac{\cancel{13}f'(1)}{\cancel{13}} &= \frac{-16}{13}\\
\\
f'(1) &= \frac{-16}{13}
\end{aligned}
\end{equation}
$

What happens if our Sun suddenly becomes a black hole? I already know that the mass of the Sun is too small for it to become a black hole; I'm asking for a hypothetical scenario.

First, it is unlikely that our sun would become a black hole as it is not sufficiently massive. Instead, it is likely to expand into a red giant and then gradually fade away to become a white dwarf star, gradually decreasing in mass and energy. A star massive enough to become a black hole would radiate so much energy and heat that anything as close as earth's orbit would be uninhabitable.
The way in which a star evolves into a black hole is generally by first becoming a supernova. If one bent the laws of physics to imagine this happening to our sun, the catastrophic release of energy would vaporize the earth, and so no living beings would be around to observe the process. Next, if sufficient mass is left over after a supernova, the core of the star gradually shrinks until it becomes a black hole. Although no energy passes the event horizon of the black hole itself, material nearby can be very hot and energetic and emit large amounts of radiation, including x-rays.
To imagine some sort of science fiction universe in which the sun was instantaneously replaced by a black hole without going through the supernova phase, one would still end up with something that would eject streams of high energy particles and radiation, meaning that all living beings on earth would die with minutes or even seconds.
If, for example, there were a technological civilization on a planet orbiting a nearby star such as Alpha Centauri, several years after the sun became a black hole, their scientific instruments would observe that the sun would no longer resemble a star, but rather a turbulent gas and dust accretion disc with a black hole at the center. If they looked at stars in the same region of the sky, they would notice the phenomenon of gravitational lens effects, in which light would be bent by the gravity of the black hole.
https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-a-black-hole-58.html

What is the central theme in Death in Venice?

The central theme of Death in Venice is the destructive power of obsessive love. On a trip to Venice, Aschenbach becomes more and more attracted to a fourteen-year-old boy named Tadzio who he sees at his hotel.
Aschenbach is glad when a luggage mixup sends him back to the hotel. Although he becomes aware of a cholera epidemic in Venice, he doesn't care as long as he can be near the boy. He begins to stalk him. Despite Aschenbach's deep obsessive love, he and the boy never speak to each other. Instead, they exchange looks.
Because of his obsession, Acshenbach loses his sense of identity. While he had formerly been repulsed by an older man made up to look younger, he adopts the same strategy in an attempt to be attractive to Tadzio. He also risks his life staying in Venice to be near the boy, and eventually dies of cholera as a result.
The novel raises the question: to what extent should we sacrifice ourselves for an obsession? Is Acshenbach's quest for the purity and beauty, represented by the young boy, noble or is it degrading? The trajectory of the plot critiques the power of illusion and obsession by showing how it destroys Aschenbach, but at the same time leaves us perhaps with an admiration for his dedication to an ideal.

Why does Dee take pictures of the house?

Maggie and her mother use family heirlooms for their practical purposes as well as the for the connection they feel to their ancestors. Dee (Wangero), on the other hand, wants some of these items for purely aesthetic purposes. Dee might actually think she is paying homage to her ancestors in this way, but her intent to display these items as cultural artifacts seems quite superficial. When she asks for the butter churn, she intends to use it as a centerpiece rather than as a tool for making butter. And, of course, Dee wants the quilts for display purposes as well. She wants to display her family's heritage like an explorer who has returned with items from a more "primitive" culture, showing these items like trophies. There is something superficial and even mocking in this gesture.
When Dee emerges from the car and starts taking pictures, she is doing the same thing. She wants to document her family's quaint, primitive way of life to show the pictures to her more "modernized" friends. Dee is not wrong for being progressive, but she clearly misses the point of the real value of something like a family quilt or their way of life. The quilt represents family connection. The different pieces are sown together. Maggie would use the quilt as a bed cover, every day, literally and figuratively connecting her to her ancestors. Dee doesn't get this. She would rather take a picture of it.

In the poem "The Last Ride Together" by Robert Browning, what do stanzas 6-8 mean?

Robert Browning's poem “The Last Ride Together” is the monologue of a dejected lover as he contemplates the end of a relationship. The title of the poem comes from the setting in which the poem takes place—on a final ride that the speaker and his ex-lover share. Stanzas six, seven, and eight (lines 56-88) strongly develop the character of the speaker and reveal the speaker's attitudes about the end of his relationship. These three stanzas are explained below. Stanza VI
What hand and brain went ever pair’d?What heart alike conceived and dared?What act proved all its thought had been?What will but felt the fleshly screen?  We ride and I see her bosom heave.        There’s many a crown for who can reach.Ten lines, a statesman’s life in each!The flag stuck on a heap of bones,A soldier’s doing! what atones?They scratch his name on the Abbey-stones.        My riding is better, by their leave.
In the sixth stanza, the speaker becomes philosophical about the end of his relationship, considering the nature of love, reality vs. dream, and the nature of failure. The speaker considers that all men fail. In mentioning statesmen and soldiers in this stanza, the speaker justifies his failure, explaining that all men—even those held in high regard—do fail. 

Stanza VIIWhat does it all mean, poet? Well,Your brains beat into rhythm, you tellWhat we felt only; you express’dYou hold things beautiful the best,          And pace them in rhyme so, side by side.’Tis something, nay ’tis much: but then,Have you yourself what’s best for men?Are you—poor, sick, old ere your time—Nearer one whit your own sublime        Than we who never have turn’d a rhyme?Sing, riding’s a joy! For me, I ride.
In this stanza, the speaker continues his philosophical musings with false optimism. The speaker compares himself to a poet, who has only words, whereas the speaker at least has his final ride. The speaker's long thoughts on the poet (an entire stanza) serve as a distraction from his loss, while at the very end, he consoles himself, saying, "For me, I ride," as he accepts the reality that this is the final ride with his lover.Stanza VIIIAnd you, great sculptor—so, you gaveA score of years to Art, her slave,And that’s your Venus, whence we turn        To yonder girl that fords the burn!  You acquiesce, and shall I repine?What, man of music, you grown grayWith notes and nothing else to say,Is this your sole praise from a friend,       ‘Greatly his opera’s strains intend,Put in music we know how fashions end!’  I gave my youth: but we ride, in fine.
Stanza eight is a continuation of the speaker's justification in the seventh stanza. In the seventh stanza, the speaker compared his relationship to the labors of a poet, and decided he preferred the in-the-flesh experience of love over the intangible beauty of poetry. In the eighth stanza, that line of thought is continued, but this time the speaker compares his ended relationship to the work of sculptors and musicians, which he claims is also intangible. Although the speaker appreciates the labors of both of these artists, he still decides that he prefers the love he had, even though it is at its end. Again, the stanza ends with his decision, "I gave my youth: but we ride, in fine."
https://www.bartleby.com/42/665.html

Intermediate Algebra, Chapter 3, 3.6, Section 3.6, Problem 38

a.) Solve the equation $x - 4y = 8$ for $y$ in terms of $x$, and rewrite the equation using function notation $f(x)$.


$
\begin{equation}
\begin{aligned}

x - 4y =& 8
&& \text{Given equation}
\\
\\
-4y =& -x + 8
&& \text{Subtract each side by $x$}
\\
\\
y =& \frac{1}{4}x - \frac{8}{4}
&& \text{Divide each side by $-4$}
\\
\\
y =& \frac{1}{4}x - 2


\end{aligned}
\end{equation}
$


So,

$\displaystyle f(x) = \frac{1}{4} x - 2 \qquad y = f(x)$

b.) Find $f(3)$.


$
\begin{equation}
\begin{aligned}

f(3) =& \frac{1}{4} (3) - 2
\qquad \text{Let } x = 3
\\
\\
=& \frac{3}{4} - 2
\\
\\
=& - \frac{5}{4}

\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 9, 9.6, Section 9.6, Problem 48

To determine the convergence or divergence of a series sum a_n using Root test, we evaluate a limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
For the given series sum_(n=1)^oo (ln(n)/n)^n , we have a_n =(ln(n)/n)^n .
Applying the Root test, we set-up the limit as:
lim_(n-gtoo) |(ln(n)/n)^n|^(1/n) =lim_(n-gtoo) ((ln(n)/n)^n)^(1/n)
Apply Law of Exponent: (x^n)^m = x^(n*m) .

lim_(n-gtoo) ((ln(n)/n)^n)^(1/n)=lim_(n-gtoo) (ln(n)/n)^(n*1/n)
=lim_(n-gtoo) (ln(n)/n)^(n/n)
=lim_(n-gtoo) (ln(n)/n)^1
=lim_(n-gtoo) (ln(n)/n)
Evaluate the limit using direct substitution: n = oo .
lim_(n-gtoo) (ln(n)/n) = oo/oo
When the limit value is indeterminate (oo/oo) , we may apply L'Hospital's Rule:
lim_(x-gta) (f(x))/(g(x)) =lim_(x-gta) (f'(x))/(g'(x)) .
Let: f(n) = ln(n) then
g(n) = n then g'(n) =1 .
Then, the limit becomes:
lim_(n-gtoo) (ln(n)/n)=lim_(n-gtoo) ((1/n))/1
=lim_(n-gtoo) 1/n
= 1/oo
=0
The limit value L=0 satisfies the condition: L lt1 since 0lt1.
Therefore, the series sum_(n=1)^oo (ln(n)/n)^n is absolutely convergent.

What is the relationship between Europe and Africa in Joseph Conrad's Heart of Darkness?

It's clear that the relationship between the continents, as depicted by Conrad, is a dysfunctional one. The Europeans are carrying out an extended project of exploitation and theft of both labour and resources from Africa. Though the process is a systematic one, it is also inefficient. When Marlow arrives at the colonial outpost, he sees a chaotic situation where equipment is lying about unused and men are being mistreated and are sick and dying.
The mystery surrounding Kurtz is emblematic of this warped dynamic. The madness into which Kurtz has been plunged, the megalomania of setting himself up as a god over the "natives," is a kind of parable of the larger scenario of one people (the Europeans) abusing and robbing another (the Africans, and what would later be referred to as "third-world" people in general). Interestingly, none of this is stated with any real explicitness by Conrad. It would be several decades before George Orwell, for instance, in essays such as "Shooting an Elephant" and "Marrakesh" would spell out these facts directly, without the ambiguity and irony that mark Conrad's Heart of Darkness and other works of fiction from the period around 1900.

Europe represents the colonizer, while Africa represents the colonized. European nations such as Belgium, France, England, Italy, Spain, Portugal, and Germany had been a part of aggressively invading and colonizing parts of Africa throughout the 19th century. From a white supremacist perspective, Europe may be seen in the novel as the "progressive" and "enlightened" continent, and Africa is the "backwards" continent. However, it should be clear that if any nations are "backwards", it is certainly the invading nations of Europe that brought slavery, genocide, and brutal resource extraction and land theft to Africa and Africans. Conrad seems to want to emphasize the brutality of the Europeans and how that stands in stark contrast to the racist tropes of Africans as the "savages" or "brutes". It is hopefully clear in the novel to readers that the nations of Europe and the individual Europeans bring the brutality of human nature into Africa.

The Europeans are clearly in Africa to extract natural resources as cheaply and efficiently as possible. They are exploiters, plainly. Not only do they exploit the African population, using slave labor (Marlowe encounters many of these slaves, sick and dying, in the “grove of death” sequence from the book), but they decimate the wildlife in their greed for ivory.
On the other hand, Africa is not a hospitable place for the Europeans. Conrad suggests that there is something about the jungle that undermines the European ideals of rationality or efficiency. This is shown in part by the haphazard way the company is run; when riverboat captain Marlowe shows up on station, his boat is sunk; repairs are difficult because it is impossible to get the metal plates and rivets together in the same place to patch the bottom. But the true effect of the jungle is seen in Kurtz, whose mental state has been impaired by his experience upriver. It seems that Africa holds a mysterious truth that European civilization cannot counteract or subdue.

The relationship between Europe and Africa is central to Joseph Conrad's Heart of Darkness. Essentially, Conrad shows that the relationship between the two continents is based on the exploitation of resources. More specifically, Conrad illustrates how European colonial powers venture into the territory of African countries in order to harvest raw materials and resources and enslave native populations. Thus, in exploring the relationship between Europe and Africa, Conrad is also exploring the ways in which a colonial power exploits other countries for material and/or economic gain. That said, it's important to point out that Conrad suggests colonial excursions don't always work out well for European powers, as he also shows how the evil nature of colonialism corrupts those involved with it. Indeed, several characters (such as Kurtz) end the novel as broken shells and hollow individuals. As such, if Conrad shows how European cultures oppress African natives through colonialism, he also shows how this endeavor irreversibly corrupts the Europeans involved with it.

Single Variable Calculus, Chapter 4, 4.3, Section 4.3, Problem 16

Using the first and second derivative tests. Find the local maximum and minimum values of $\displaystyle f(x) = \frac{x}{x^2 + 4}$. State which method do you prefer.

$
\begin{equation}
\begin{aligned}
\text{if } f(x) &= \frac{x}{x^2 + 4} \quad \text{, then by using Quotient Rule}\\
\\
f'(x) &= \frac{(x^2+4) (1) - x (2x) }{(x^2+4)^2} = \frac{-x^2+4}{(x^2+4)^2}\\
\\
f''(x) &= \frac{(x^2+4)^2 ( -2x) - (-x^2+4)\left(2(x^2+4)(2x) \right)}{\left[ (x^2+4)^2 \right]^2}\\
\\
f''(x) &= \frac{2x^3-24x}{(x^2+4)^3}
\end{aligned}
\end{equation}
$


By using first derivative test, we set $f'(x) = 0$, then.

$
\begin{equation}
\begin{aligned}
f'(x) = 0 &= -x^2 +4\\
x^2 &= 4\\
\text{Solving for critical numbers, }\\
x &= \pm 2
\end{aligned}
\end{equation}
$

If we divide the interval by:

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f'(x) & f \\
\hline\\
x < - 2 & - & \text{decreasing on } ( - \infty, -2)\\
\hline\\
-2 < x < 2 & + & \text{increasing on } (-2,2)\\
\hline\\
x > 2 & - & \text{decreasing on } (2, -\infty)\\
\hline
\end{array}
$

Since the function changes from positive to negative at $x=2$. It means that the local maximum is at $x = 2$. On the other hand, since the function changes from negative to positive at $x = -2$. It means that the local minimum is at $x = -2$

By using Second Derivative Test, we evaluate $f''(x)$ at these critical numbers:

$
\begin{equation}
\begin{aligned}
\text{so when } y &= 2, \\
f''(2) &= \frac{2(2)^3 - 24(2)}{(2^2+4)^3} = \frac{-1}{16} < 0\\
\\
\text{when } y &= -2, \\
f''(2) &= \frac{2(-2)^3 - 24(-2)}{((-2)^2+4)^3} = \frac{-1}{16} < 0
\end{aligned}
\end{equation}
$


We see that $f(2) < 0$, therefore, 2 is a local maximum. Also, $f(-2) > 0$, hence, -2 is a local minimum.
It's more easy to use the Second Derivative Test compare to the first one.

What were the tragic flaws of Cassius and Brutus in Act 5?

In Act V, Cassius's tragic flaw is that he too readily accepts defeat. When his servant, Pindarus, informs Cassius that "Mark Antony is in your tents, my lord Fly, therefore, noble Cassius, fly far off," Pindarus is mistaken. Mark Antony, Cassius's enemy, has not defeated Brutus, but Cassius too readily believes Antony has won and says, "My life is run his compass," meaning that his life has completed its circuit. He then bids his servant, Pindarus, to kill him and promises Pindarus his freedom if he does so. As he's dying, Cassius says, "Caesar, thou art revenged, Even with the sword that kill'd thee." In other words, Cassius believes his death is Caesar's revenge on him, as he asks Pindarus to kill him with the same sword that was used to kill Caesar.
Brutus, for his part, tempts fate by facing his opponents yet again, and this is his tragic flaw. After finding Cassius's dead body, Brutus urges on his troops, saying, "Romans, yet ere night We shall try fortune in a second fight." In other words, Brutus is "trying fortune" or testing fate by returning to the battlefield. In taking on Antony yet again, Brutus fails and is forced to retreat. Brutus then rushes upon his sword, held by his servant, Strato, and says, "Caesar, now be still: I kill'd not thee with half so good a will." In other words, Brutus is happier to die than he was to kill Caesar. Brutus's rushed return to the battlefield has resulted in his death.

y = 100e^(-2x) Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

We are asked to determine if the function y=100e^(-2x) has an inverse function by finding if the function is strictly monotonic on its entire domain using the derivative. The domain is all real numbers.
y'=-200e^(-2x) and y'<0 for all real x so the function is strictly monotonic (in this case strictly decreasing) and therefore has an inverse function.
The graph:

What is the meaning of "bars of rage" mentioned in the second stanza?

Maya Angelou’s poem “Caged Bird” reflects the anguish of a divided society, as she compares the free bird, who can do anything he pleases, with the caged bird, who can only dream of happiness as he sits in his prison.
The free bird “leaps / on the back of the wind” as he travels in infinite space. He has the freedom to go anywhere and to do anything. His possibilities are endless, so he “names the sky his own.” He thinks of traveling with the breeze and of the “fat worms” of opportunity he has only to pluck from the grass. Staying under the warmth of the sun, he will always have chances to achieve his dreams.
In contrast, the caged bird sits in his cage, knowing the free bird flies and that he cannot follow. He “stalks / down his narrow cage” because he is angry at his helplessness. He has no opportunity to see beyond “his bars of rage.” Angelou attributes the anger to the bars of the cage, but it is really that of the caged bird. His rage follows because he feels trapped and sees no way out of his situation. His wings are clipped, so he can only sing about the freedom he so desperately desires. He knows he should be out there flying in freedom instead of standing “on the grave of dreams.” He has given up his goals and dreams, and only “his shadow shouts” now.
Angelou depicts the situation that Black Americans face in society; however, her poem can also reflect all types of oppression. By juxtaposing the free and caged birds, she clearly depicts the unfairness and cruelty of oppression. She pleads with her audience to understand and to correct the wrongs.

The poem "Caged Bird" by Maya Angelou is filled with symbolism that conjures feelings of freedom and confinement.  The juxtaposition of the stanzas creates a stark contrast between the "free bird" and the "caged bird."  After the initial stanza's description of the way in which a free bird "floats downstream" effortlessly "on the back of the wind," the second stanza presents the perspective of the caged bird:

But a bird that stalks down his narrow cage can seldom see through his bars of rage his wings are clipped and   his feet are tied so he opens his throat to sing.

Here the "bars of rage" are symbolic of the bird's confinement.  Whereas the free bird was lifted and supported on the wind, the caged bird is trapped, but not necessarily by an outside force.  The bird "can seldom see through / his bars of rage," which suggests that the cage is the bird's own creation.  They are "his" bars of rage, that he cannot see through.  In this way the bars are a metaphor for the anger that traps the bird and keeps it from being free.  This anger could be due to an outside force, such as sexism, racism, or another type of oppression, but the poem itself lets us understand that no matter what outside forces are acting upon the bird, the bars around it are of the bird's own making.

In Beowulf, how does culture contribute to the creation of a hero?

One of the basic ways in which culture can be considered a creator of a hero is by manifestation. Lines 175–179 describe the people as worshipping at shrines and “vow[ing] offerings” (lines 175–176) in hopes that a “killer of souls” (line 177) will come to help them. It is not made clear how long the people did this, but the reader is aware of at least 12 years passing between the fall of Heorot to Grendel and the arrival of Beowulf. In a time before the internet, news traveled much, much slower, and therefore Beowulf in Geatland was not aware of this trouble for some time.
A more complex way in which culture contributes to the creation of a hero is through the specific focus of warrior culture. Beowulf essentially comes ashore and tells the watchman that he and his men are there because he can help Hrothgar defeat Grendel. When Hrothgar and Beowulf meet face-to-face the first time, Hrothgar tells him he has heard tales of him and his “strength of thirty in the grip of each hand” (lines 380–381). During the time that this story takes place, strength and tales of heroes were valued. Think along the lines of how the Greeks would have felt about Hercules and Odysseus. Beowulf appears to be heavily influenced by Germanic heroic poetry, which showed the relationship between a warrior and the lord he served. This shows not only the behavior of the characters within the story but also outside forces such as focus on heroes and strength in reality.
Another way is through obligation. Though it is admittedly difficult to keep track of who’s a distant relative, who’s a herald, and who’s an enemy, there was a long standing friendship between Hrothgar and Beowulf’s father, and this is partially why Beowulf feels a sense of duty to the king. This would have been a value taught to him from an early age. Then we have Grendel’s mother, who seeks revenge for her son’s death and takes back their “trophy” (line 1302) of his severed arm. Part of being a warrior, other than battle skill, was seeking trophies and being rewarded by your lord, which goes back to the Germanic heroic poetry influence.
All quoted material in this answer comes from the Norton Anthology of English Literature, The Major Authors, 9th Ed.

What is ironic about Julius Caesars death in relation to preceding events?

I assume you are referring to the death scene of Julius Caesar in the eponymous play by Shakespeare. In this play, in Act 3, Scene 1, Caesar remarks to the Soothsayer at the opening of the scene that "the Ides of March are come," it having been prophesied that this day would bring doom for Caesar. In response, the Soothsayer cautions that they are not yet gone. This draws the audience's attention to the significance of what happens next.
Artemidorus appeals to Caesar to read "this schedule," which the audience knows contains information about the planned attack on Caesar. He implores Caesar to read it, but unfortunately the approach he takes is unsuccessful. He prevails upon Caesar to read his letter first because it "touches Caesar nearer," but this only has the effect of Caesar setting the letter aside. He says, "what touches us ourself shall be last served," an expression of humility. The great dramatic irony here is that, had Caesar read the letter, perhaps, had Artemidorus made his appeal on different grounds, then Caesar would have been forewarned of what was about to occur, and might have avoided death. Caesar has willingly rejected information that could have saved him.

What is an example of a delusion in the book Brain on Fire?

Susannah Cahalan suffered from a rare brain disease that included delusions and hallucinations; she wrote about the experience in her book Brain on Fire. Cahalan's disease was called anti-NMDA receptor encephalitis. The disease begins with symptoms similar to the flu and then progresses into delusions and hallucination episodes. These are followed by an unresponsive period, during which the patient starts to have seizures and has difficulty breathing.
One of the hallucinations that Cahalan has in Brain on Fire involves a moment where she is watching a newswoman talk about her on the television. During this time, Cahalan calls for a nurse to come to her room, but she hears one of her roommates in the hospital laughing. The woman speaks in Spanish, but Cahalan believes she can understand what the woman is saying, and she believes the woman is going to record her talking. Then she is going to send the recording into the Post. The roommate tells Cahalan that the nurses can't be trusted and Cahalan becomes frightened. She runs outside of her room after pulling out the EEG electrodes connected to her body. Two nurses have to pull her down and contain her until help comes. This episode is entirely a hallucination that Cahalan has while in the hospital.

Why is freedom important?

Freedom is generally defined as the right and ability to act, speak, and think however one wants without fear of restraint or harm.
Most societies offer varying degrees of freedom. Some societies, such as totalitarian dictatorships, for example, offer hardly any freedom at all. The United States promotes itself as a beacon of freedom. Yet, even in this nation, there are limitations on freedom. Sometimes, these limitations exist to protect citizens or to maintain a level of public decency. For example, one is not allowed to use profanity on national radio or television due to obscenity standards imposed by the Federal Communications Commission (FCC). 
It is also important to note that, in some societies, not all citizens are given the same level of freedom. Discrimination based on race, class, religion, ethnicity, and sometimes class, can disallow the expression of freedoms. In some countries, one's political views can also limit their freedom, especially if they happen to disagree with the regime in power. 
Working to ensure the freedom of everyone—regardless of one's identity, economic status, or political views—is important in the interest of generating new ideas and in allowing people to live authentic lives. Freedom allows for a more prosperous society, as well as a morally richer one.

Give the climax from the story "A Rose for Emily." Support your answer with examples from the story.

"A Rose for Emily" is not told in chronological order, so the climax of the story isn't placed on the page where most readers would expect it to be.  The climax of the story is the final lines of the story.  

Then we noticed that in the second pillow was the indentation of a head. One of us lifted something from it, and leaning forward, that faint and invisible dust dry and acrid in the nostrils, we saw a long strand of iron-gray hair.

It's at this moment when most of my students all of a sudden say something like, "Wait. What? Oh that's so messed up!"  Faulkner chooses to end his story with its ultimate climax.  Readers figure out exactly what all of those other small details were leading up to.  Readers are told in section four that Emily buys enough arsenic to kill an elephant, but she refuses to say why she needs the poison.  We are told that shortly after buying the poison, Homer disappears and is never seen again.  In section two, readers are told that the awful smell developed shortly after Homer's disappearance.  In a different part of the story, we are told that Emily didn't willingly give up her father's dead body, so we know that she has a history of keeping a dead body in her house.  All of those pieces of information serve as foreshadowing and rising action.  They all lead up to the climactic moment when readers are told that Emily kept Homer's body in her bed for years and slept next to it. 

How can Such a Long Journey from Rohinton Mistry be read as postcolonial literature?

One reason that Rohinton Mistry's novel is postcolonial derives from the author's position. He was born in India five years after independence. Mistry's heritage is Parsi, an ethnic and religious minority that suffered discrimination under British colonial rule. In the new nation of India, with a dominant Hindu majority, Parsi status did not significantly improve, leading to widespread flight. Mistry himself left for Canada.
Such a Long Journey gives a portrait of a Parsi family that remained in India and is now suffering the consequences after 25 years of independence. The protagonist, Gustad Noble, maintains a positive view of their situation despite reversals of fortune that have left them barely clinging to the middle class. His involvement with a humanitarian activist is connected to the plight of Bengalis, another minority in India, who have become refuges from the war with East Pakistan (on the verge of becoming Bangladesh).
The deep, reprehensible corruption that afflicts this noble cause unexpectedly intrudes into Noble's life. He is forced to question his assumptions about a man whose friendship he trusted: Major Bilimoris. The political dynamics of Mistry's questioning of the postcolonial status quo elevates the novel from a personally-oriented melodrama to a social critique. Not only Bilimoris but officials up through the nation's prime minister are implicated in the refugee assistance scam.
While the major pays for these schemes with his life, the higher-placed conspirators escape prosecution. Noble's family is torn apart and then put back together, somewhat the worse for wear—much like the Indian nation.

Postcolonial literature emphasizes "the view from below" or the point of view of the oppressed. Often it is written by people from countries with a long history of being oppressed by European colonial occupiers who came in and exploited the land and its people. However, more broadly, it can represent any view that depicts the lives of the oppressed. It counters the official, often rosy narrative of the dominant group with a different version of the story.
Mistry's novel, which takes place in India in the 1970s, fits the description of post-colonial because it tells its story from the point of view of oppressed Indians and outlines in detail the extreme poverty that existed in India. While it is not attacking an outside colonial power, it is criticizing a system that treats lower-class people with humiliation, imprisonment in a work camp, and torture. A character refers to a real-life political leader, Bal Thackery, as one who "worships Hitler and Mussolini." This depiction of a politician struck such a nerve in the ruling elite that the book was banned in 2010 from the University of Mumbai's reading list. Like other post-colonial literature, it brings to light aspects of society that the "official" version would rather keep quiet and explores the effects of poverty, cruelty, and injustice.

What environmental issue relates to the use of nail polish removers or to the chemical acetone?

Nail polish removers consist of solvents such as acetone to enable the removal of nail polish. Acetone can be manufactured and is also found naturally. It is considered a volatile organic compound.
Acetone typically enters the environment through the atmosphere, and from there it can move into the hydrosphere (water) and lithosphere (soil) through precipitation (rainfall, snow, etc.). It can also find its way to groundwater through spills or landfill leachate. It is somewhat toxic to aquatic life and can cause membrane damage. It can also result in a reduction in the size and germination of various plants.
Acetone has a short half-life (22 days) in the air. It gets degraded by sunlight and does not bioaccumulate in plants, animals, or human beings. The maximum limit for acetone in drinking water is 6.3 mg/L in Massachusetts.
Low amounts of acetone in our body can be broken down by the liver. However, exposure to higher concentrations of acetone can cause eye irritation, issues with the respiratory system, headache, confusion, nausea, and vomiting. It is not a known carcinogen. In fact, it has been stated that common consumer's usage of nail polish removers is not expected to cause any adverse health effects.
Hope this helps.

In Maniac Magee, why doesn't Maniac feel he can go to Mars Bar's house?

Maniac doesn’t want to go to Mars Bar’s house because he has been moving from home to home, but he realizes he belongs with the Beales. 
Maniac Magee has been homeless since he ran away from his foster parents (his aunt and uncle), except for a couple of brief stints with people who took him in.  He lived with the Beales, and then in the buffalo pen at the zoo, and then with Grayson, the old groundskeeper until he died.  After Grayson died, Maniac resumed sleeping in the buffalo pen.  This is where Mars Bar found him. 
Mars Bar tells Maniac about saving Russel from the trestle.  Maniac explains that he wasn’t able to save the boy because he was reminded of how his parents died.  The boys understand each other better after this.  Although Mars Bar and Maniac have not always seen eye to eye, this conversation helps.  Mars Bar tells Maniac that sleeping with the buffalo has not been good for him.

"Magee!"
"Yeah?"
"I had to ask you something. Now I gotta tell you something."
"What's that?"
"You smell like a buffalo."
Ears of a hundred different shapes prickled at the long, loud laughter of the boys. (Ch. 45)

Maniac may seem to not know or care what other people think of him, but he has been having a very hard time finding a home.  At this point, he just isn’t ready to go to Mars Bar’s house.  Smelling like a buffalo is a good excuse.

Having made a full circle of the zoo, they were back at the pen of the American bison. Maniac said, "I can't."
"Why not?” said Mars Bar. "My house not good enough? My mother?"
Maniac struggled for words. "I didn't say I didn't want to. I don't know...things happen… I can't..." (Ch. 45)

Luckily, Amanda Beale knows where to find Maniac, and tells him to come home.  The Beales are Maniac’s real family at this point.  He allowed himself to be run off from there because of the troubling race relations between the East and West End.  However, by this point, he is ready to return “home” for good.

How is Romeo and Juliet's love presented in Act 2, Scene 2, line 33?

That's a tough question, because line 33 is part of a sentence that extends from earlier lines and into later lines.  Using only line 33 is hard because it is being taken out of the overall context.  Line 33 is the following:

Of mortals that fall back to gaze on him

Too many questions surround that line.  Why are mortals falling?  Who is the "him" in the line?  
 
Let's look at the entire sentence instead.  


O, speak again, bright angel! For thou art
As glorious to this night, being o'er my head,
As is a wingèd messenger of heaven
Unto the white, upturnèd, wondering eyes
Of mortals that fall back to gaze on him
When he bestrides the lazy-puffing clouds
And sails upon the bosom of the air.



Act 2, Scene 2 is the famous balcony scene, and the above lines take place before Romeo and Juliet start talking to each other.  Romeo is looking up at Juliet, and she doesn't know he is there.  You can decide if that is creepy or not.  
 
Line 33, and its surrounding sentence, is being spoken by Romeo about Juliet.  He is comparing her and her beauty to an angel of heaven.  He looks upon her with amazement and wonder, which is how he imagines that he would be looking at an actual angel of God sailing through the sky. 
 
Understanding the line in that context causes me to see their love for each other presented in a specific way.  Their love is being presented as cosmic, godly, angelic, glorious, and/or heavenly.  Line 33 shows that Romeo isn't quite certain that mere mortals are supposed to have these kinds of feelings, yet he is witnessing something (Juliet) that appears to be straight from heaven.   

Are the parents good in the story "The Veldt?"

The parents in Bradbury's "The Veldt" are good, well-meaning people who love their children. However, they have made some mistakes. First, they believed they could buy their way to a happy family life by purchasing the expensive Happylife Home. It does everything for them, including parenting their children. Mrs. Hadley feels displaced because the home has taken over her function as housewife and mother. She has little to nothing to do.
Perhaps the worst mistake the parents have made is building the expensive nursery for the children with its walls of screens that display everything the children want to see. As the story opens, the parents are beginning to realize that the nursery has replaced them as parents. They are beginning to realize that the technology they bought to serve them is beginning to own them and their children.
Because the Hadleys are fundamentally good people, they don't want to face that their children might have turned to evil and might deliberately have planned to have the lions murder and eat them. Because of this, the parents leave themselves open to being killed. Although they should have been firmer about turning off the nursery, their hearts were in the right place.

Calculus of a Single Variable, Chapter 5, 5.5, Section 5.5, Problem 63

For the given problem: y = x^(2/x) , we apply the natural logarithm on both sides:
ln(y) =ln(x^(2/x))
Apply the natural logarithm property: ln(x^n) = n*ln(x) .
ln(y) = (2/x) *ln(x)
Apply chain rule on the left side since y is is function of x.
d/dx(ln(y))= 1/y *y'

Apply product rule: d/(dx) (u*v) = u'*v + v' *u on the right side:
Let u=2/x then u' = -2/x^2
v =ln(x) then v' = 1/x
d/(dx) ((2/x) *ln(x)) =d/(dx) ((2/x)) *ln(x) +(2/x) *d/(dx) (ln(x))
= (-2/x^2)*ln(x) + (2/x)(1/x)
=(-2)/(x^2ln(x))+ 2/x^2
= (-2ln(x)+2)/x^2

The derivative of ln(y) = (2/x) *ln(x) becomes :
1/y*y'=(-2ln(x)+2)/x^2
Isolate y' by multiplying both sides by (y):
y* (1/y*y')= ((-2ln(x)+2)/x^2)*y
y' =((-2ln(x)+2)*y)/x^2
Plug-in y = x^(2/x) on the right side:
y' =((-2ln(x)+2)*x^(2/x))/x^2

Or y' =((-2ln(x)+2)*x^(2/x))*x^(-2)
y' =(-2ln(x)+2)*x^(2/x-2)
y' =(-2ln(x)+2)*x^((2-2x)/x)
y' =-2x^((2-2x)/x)ln(x)+2x^((2-2x)/x)
y = -2x^((2-2x)/x) (lnx-1)

According to Pavic, what did the Khazars do as a result of the Khazar polemic?

According to legend—on which the Dictionary of the Khazars is based—the Khazars were a Turkic tribe who purportedly vanished during the tenth century AD. In the story, the ruler of the Khazars invites a rabbi, a monk, and a dervish to interpret a portentous dream. The three holy men stage a polemic, or debate, between them, hoping that their individual interpretation of the dream will be the one to prevail. The religion of the debate's winner—Christian, Jewish, or Muslim—will be the one that the Khazars will adopt.
However, Pavic, in his creative reconstruction of the lost dictionary of the Khazars, does not tell us who actually wins the debate, or which religion the Khazars chose to adopt as a consequence. All we know is that the Khazars chose en masse to convert to one religion, and that they soon vanished from history not long afterwards.

What were the main characteristics of Native Americans’ lives prior to the arrival of European settlers?

There were millions of Native American people in the Americas before contact with Europeans, and their lifestyles and cultures were very diverse, influenced by their respective environments, as well as contacts with other peoples. A few generalizations can be made about most Native American, however. First, most (but not all) did not believe in private property in the European sense (i.e., that it could be held by an individual in perpetuity). This aspect of Native culture led to clashes with Europeans, particularly the English. Additionally, most Native peoples from Mesoamerica to modern New England (and east of the Mississippi River Valley) were to one degree or another settled agriculturalists, cultivating corn, beans, squash, pumpkins, and other crops. They were not, contrary to contemporary popular culture, nomadic peoples. Indeed, it was only with the arrival of the horse from Europe that many of the Plains Indians that most associate with Native culture today began to embrace a lifestyle that revolved around hunting buffalo. Many, including Mesoamerican and Mississippian peoples, lived in and around large urban areas constructed of earthen mounds or stone. No Native societies featured what Europeans recognized as written languages, and some predominately hunter-gatherer societies were quite egalitarian, but many had formal structures of government and bureaucracies that rivaled those of Europe.
https://www.history.com/topics/native-american-history/native-american-cultures

Native American culture was diverse across the Americas and tribal characteristics were mostly dependent upon climate and region. In Eastern North America many tribes practiced a mix of small-plot farming and seasonal hunting. They would also maintain permanent villages and semi-permanent hunting camps which were typically small communities connected by marriage. In the Great Plains and Western North America peoples were much more mobile and dependent mainly on the movement of the buffalo herds for their survival. Trade was also a key characteristic of native life which would maintain complex systems stretching across the continent.
In Central and South America larger permanent cities were established and agriculture was a much more prominent resource to the peoples. Trade would also be prominent as well as cultural and religious warfare between cities and regions.
In all of the Americas a special connection to the natural world was also present which would influence the beliefs of peoples and their place in the world.

(x-h)^2+y^2=r^2 , h>r Find the volume of the torus generated by revolving the region bounded by the graph of the circle about the y-axis.

Volume of a shape bounded by curve y=f(x) and x-axis between a leq x leq b revolving about y-axis is given by
V_y=2pi int_a^b xy dx
In order to use the above formula we first need to write y as a function of x.
(x-h)^2+y^2=r^2
y=+-sqrt(r^2-(x-h)^2)
The positive part describes upper half of the circle (blue) while the negative part (red) describes the lower semicircle. 

In the graph above r=2 and h=5.   
Since the both halves have equal ares the resulting volumes will also be equal for each half. Therefore, we can calculate volume of whole torus as two times the semi-torus (solid obtained by revolving a semicircle).
Bounds of integration will be points where the semicircle touches the x-axis.
4pi int_(h-r)^(h+r)x sqrt(r^2-(x-h)^2)dx=
Substitute x-h=r sin t => x=r sin t+h => dx=r cos t dt, t_l=-pi/2, t_u=pi/2
t_l and t_u denote new lower and upper bounds of integration.
4pi r int_(-pi/2)^(pi/2)(r sin t+h)sqrt(r^2-r^2 sin^2 t)cos t dt=
4pi r int_(-pi/2)^(pi/2)(r sin t+h)r sqrt(1-sin^2 t)cos t dt=
Use the fact that sqrt(1-sin^2 t)=cos t.
4pi r^2 int_(-pi/2)^(pi/2)(r sin t+h)cos^2 t dt=
4pi r^3 int_(-pi/2)^(pi/2) cos^2 t sin t dt+4pi r^2h int_(-pi/2)^(pi/2)cos^2 t dt=
Let us calculate each integral separately
I_1=4pi r^3 int_(-pi/2)^(pi/2) cos^2 t sin t dt=
Substitute u=cos t => du=sin t dt, u_l=0, u_u=0.
4pir^3 int_0^0 u^3/3 du=0
I_2=4pi r^2h int_(-pi/2)^(pi/2)cos^2 t dt=  
Rewrite the integral using the following formula cos^2 theta=(1+cos2theta)/2.
2pi r^2h int_(-pi/2)^(pi/2)(1+cos 2t)dt=2pi r^2h(t+1/2sin2t)|_(-pi/2)^(pi/2)=
2pi r^2 h(pi/2+0+pi/2-0)=2pi^2r^2 h
The volume of the torus generated by revolving the given region about y-axis is 2pi^2r^2h.  
The image below shows the torus generated by revolving region bounded by circle (x-5)^2+y^2=2^2  i.e. r=2, h=5 about y-axis. The part generated by revolving y=sqrt(r^2-(x-h)^2) is colored blue while the negative part is colored red.

What effect did Reconstruction have on blacks? Were they better off after Reconstruction than they were before the Civil War?

Your question asks whether African-Americans were better off AFTER Reconstruction than they were before the Civil War. Most unfortunately, the answer to this question is neither straightforward nor obvious. Although it is true that, after Reconstruction, slavery no longer existed in the United States, the fact remains that for most black people, this was the only difference in their status when the Reconstruction initiative was abandoned--and, in many cases, it made no material difference at all. It could even be argued that for the black people who were now working the same jobs in the same places, with the same lack of respect, it was worse to have had a taste of freedom and then to have had promise after promise broken by the US government. Before the Civil War, black people dreamed of a time when they would no longer be enslaved. What happened under Reconstruction seemed to suggest to many that this time could never come.
Immediately after the Civil War, the world changed for blacks in the American South. They were free, but provisions for freed slaves were scarce. Eventually, provision was made of "forty acres and a mule," and many blacks did succeed in establishing farms and beginning to sustain themselves. This, however, was not to last. The white landowners, who originally had been stripped of their lands, began to petition for their return. As feeling changed (and a recession set in) in the North, even those who had previously been in favor of emancipation started to lose interest in the plight of the black man. Racist feelings in the South reached fever pitch, with whites feeling that the white North cared more about Southern blacks than about Southern whites--something they could not stand. In response to huge outbreaks of lynchings and other racial violence, policy was changed so that those who petitioned for the return of their lands could take them back. The black people who had been given lands had their lands taken away from them again, and they became laborers, paid a low wage. As before, they were unequal.
At the height of Reconstruction, black men were elected to the Senate, with black voters turning out for them in droves. This threatened whites in both North and South to the extent that laws that had been passed were repealed, and the legally-elected black senators thrown out and even violently attacked. No longer able to label their black laborers property, whites turned to another means of oppression: segregation. Many black people felt that this was evidence of the Constitution's meaninglessness in the hands of whites: every citizen was created equal, unless he or she were black.
Yes, it is true that blacks after Reconstruction were no longer owned by other human beings. Nominally, they were free. But to state that this categorically made their lives better than they had been before the war is to overstate the case. Blacks would have to wait a long time before the civil rights they had been promised would ever materialize.

Reconstruction had a major impact on African-Americans. African-Americans were better off as a result of Reconstruction, even if some of the improvements were temporary. Before the Civil War, most African-Americans in the South were slaves. They had no rights and no freedoms. This changed after the Civil War.
After the Civil War, the Freedmen’s Bureau was created to help the former slaves adjust to being freed. They received food, clothes, and medical care. They also received funds to build their own schools. The 14th Amendment was ratified that said that all people born in the United States were citizens and had the rights of citizens. These rights couldn’t be taken away without due process of law. The 15th Amendment gave African-American males the right to vote. Some African-American males got elected to office. African-Americans received rights that they didn’t have before the Civil War.
Even though many of these rights were restricted or taken away after Reconstruction ended, African-Americans were still free. Having freedom is far better than being a slave. African-Americans were being educated, something that didn’t happen during slavery. They were free to move from place to place with a pass. This also didn’t occur while they were slaves. Even though they had to struggle for about another 100 years before they regained some of the freedoms they lost after Reconstruction ended, such as equal access to public places, they were better off as free people than as slaves.
https://www.ushistory.org/us/35b.asp

Intermediate Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 42

Evaluate the inequality $\displaystyle \frac{5}{3} ( x - 2) + \frac{2}{5} (x + 1) > 1$. Express the solution set in interval form.


$
\begin{equation}
\begin{aligned}
\frac{5}{3}x - \frac{10}{3} + \frac{2}{5} x + \frac{2}{5} &> 1
&& \text{Apply Distributive Property}\\
\\
\frac{31}{15} x - \frac{44}{15} &> 1
&& \text{Combine like terms then get the LCD}\\
\\
\frac{31}{15} x &> \frac{59}{15}
&& \text{Simplify}\\
\\
x &> \frac{59}{15}\left( \frac{15}{31} \right)
&& \text{Multiply each side by the reciprocal of $\displaystyle \frac{31}{15}$ to solve for } x\\
\\
x &> \frac{59}{31}
\end{aligned}
\end{equation}
$

Thus, the solution set in interval form is $\left( \frac{59}{31}, \infty \right)$

Are animals capable of empathy?

This is an area currently being studied by many psychologists, as it may help them understand the basis for human emotions. One cautionary note I would offer is that such studies can assess the behavior of animals but not internal states. In other words, a scientist can observe a vole comforting its mate by licking or monkeys grooming the loser in a leadership contest but cannot actually get inside animals' heads to see how they are thinking or whether animals have "cognitive empathy," which is grounded in understanding the feelings of others.
Animals do appear to experience "emotion contagion," feeling pain in response to the pain of other animals, and will also help other animals who are injured or in distress. Rats given a choice between freeing a jailed fellow rat and a delicious treat, in a 2010 study, would help the fellow rat. Other experiments and observations have yielded evidence of many forms of behavior which people would see as grounded in empathy; however, the mental processes behind those behaviors cannot at this point be fully known.

What were the most significant aspects of Alexander’s legacy (in terms of kingship and military command) immediately after his death for the Macedonians? How did this change in the 50 or so years after his death?

First, before the rise of King Philip II of Macedon (380–336 BC), Macedonia was a fairly minor kingdom that was regarded as backward and insignificant by its neighbors. The rise of Philip and Alexander turned Macedonia into a well-known multinational empire through the conquest of the great realms of Egypt and Persia, the unification of Greece, and even the extension of power to India. This conquest brought great wealth and power to the Macedonians. It also gave rise to a cosmopolitan Hellenistic culture that was predominantly Greek but borrowed freely from Persian and Egyptian traditions.
Perhaps one of the most important effects on Macedonian soldiers was the institution known as cleruchy (based on an earlier form of Athenian colonialism), in which soldiers were offered plots of fertile farmland, especially in Egypt, in return for their service. This did two things: first, it gave soldiers an incentive to be loyal and stay in the army in order to become wealthy landowners on retirement. Second, it established a cosmopolitan Hellenized class of landowners throughout the areas Alexander conquered.
Alexander was an innovative commander who inspired loyalty not only in Macedonians, but also in recently conquered barbarians. They were able to enlist in his armies, something that became a tradition in his successor states. Next, his army had a far larger proportion of cavalry than previous Greek armies, something that again changed military strategy, as did his use of the Macedonian phalanx. He copied many of the administrative and logistical innovations of the Persians in running his empire.
After his death, there was no clear succession plan, and the territories he conquered were split into three empires, the Seleucid in the east, the Ptolemaic in Egypt, and the Antigonid in Greece. Although these states eventually collapsed, the cultures and administrative innovations of Alexander continued on. Perhaps the most important innovation for the average Macedonian was the Hellenization of their world and the sense of being part of a cosmopolitan Greek culture.