Identify the form of energy that is converted into thermal energy by your body.

Different names are sometimes used for the different forms of energy, so I’m going to include some explanation to make sure there’s no confusion.
Thermal energy is the energy of motion of the atoms and molecules that make up a substance or a living organism. Temperature is related to thermal energy and is proportional to the average kinetic energy (energy of motion) of the atoms and molecules. One of the reasons our bodies need energy is to convert it to thermal energy, so as to maintain a constant body temperature. This is part of homeostasis, maintaining constant conditions so that the processes of life can function consistently.
We obtain energy one way: by eating food. Energy in food is stored in the chemical bonds within molecules of the foodstuff. The energy stored in food is released in a process that breaks higher-energy chemical bonds and replaces them with lower-energy bonds. The difference in energy is often called chemical potential energy.
Potential energy is a general term for energy that is, in principle, available for conversion to other forms. Gravitational potential energy is the energy stored in an object at some height above the ground, while latent heat, or phase potential energy, is potential energy that a substance has by virtue of the way its atoms or molecules are arranged as a solid, liquid, or gas. Similarly, chemical energy, or chemical potential energy, is the energy that is available when bonds are broken and new ones are formed.
Since all energy used by our cells is derived from breaking and reforming bonds in molecules which originate in our food, the source of thermal energy in our bodies must be chemical potential energy.

What role did anti-Semitism play in the development of Nazi policy towards the Jews between 1933 and 1945?

Anti-Semitism was at the very heart of Nazi policy towards the Jews. Simply put, the Nazis hated the Jews, believing them to be racially inferior and responsible for most of Germany's problems. As with all others on the extreme Right, the Nazis further believed that a small cabal of powerful, wealthy Jews was secretly running the world for their own benefit. Anti-Semitic propaganda portrayed them as malevolent string-pullers working behind the scenes to bring war and economic depression to the world. It was upon such delusional, hate-filled fantasies that Nazi policies towards the Jews were ultimately based.
On the domestic front, the Nazis set about the process of gradually stripping German Jews of their civil rights. Nazi ideology had always maintained that the Jews weren't real Germans; they weren't pure Aryans; they constituted an alien race that simply didn't belong in the new Germany. They must therefore be deprived of their rights as citizens. Jews were systematically excluded from every walk of life, from the civil service to the professions, from the arts to industry. Before long, it became almost impossible for any Jew to make a half-decent living, and many left the country to seek a new life elsewhere.
The regime sought to place its hatred of Jews on a legal footing, devising a detailed set of racial laws—the Nuremberg Laws—which defined who was and who wasn't a Jew. At the same time, outbreaks of lawlessness against the Jews were still all too common, such as the notorious Krystallnacht, or Night of Broken Glass, in which almost a hundred Jews were murdered, and countless synagogues and Jewish-owned businesses were destroyed by Nazi thugs. Tens of thousands of Jews were also rounded up and sent to concentration camps.
Some historians have seen the events of Krystallnacht as the informal beginning of what would eventually become the Holocaust, the systematic murder of at least six million Jews by the Nazi regime. The tragic events of that night showed clearly that the Nazis' hatred of the Jews wasn't just political rhetoric; they were prepared to put that hatred into practice by physically exterminating people they didn't like. The Holocaust took that warped principle to its ultimate conclusion, using Germany's territorial expansion during World War II as an opportunity to attempt to wipe out the entire Jewish population of occupied Europe.

Intermediate Algebra, Chapter 4, Review Exercises, Section Review Exercises, Problem 26

Use row operations to solve the system $
\begin{equation}
\begin{aligned}

2x + 5y =& -4 \\
4x - y =& 14

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

Augmented Matrix

$\displaystyle \left[
\begin{array}{cc|c}
2 & 5 & -4 \\
4 & -1 & 14
\end{array}
\right]$

$\displaystyle \frac{1}{2} R_1$

$\displaystyle \left[
\begin{array}{ccc}
1 & \displaystyle \frac{5}{2} & -2 \\
4 & -1 & 14
\end{array}
\right]$

$\displaystyle R_2 - 4R_1 \to R_2$

$\displaystyle \left[
\begin{array}{ccc}
1 & \displaystyle \frac{5}{2} & -2 \\
0 & -11 & 22
\end{array}
\right]$

$\displaystyle - \frac{1}{11} R_2$

$\displaystyle \left[
\begin{array}{ccc}
1 & \displaystyle \frac{5}{2} & -2 \\
0 & 1 & -2
\end{array}
\right]$

This augmented matrix leads to the system of equations.


$
\begin{equation}
\begin{aligned}

x + \frac{5}{2}y =& -2
\\
\\
y =& -2

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

x + \frac{5}{2} (-2) =& -2
&& \text{Substitute $y = -2$ in equation 1}
\\
x - 5 =& -2
&& \text{Multiply}
\\
x =& 3
&& \text{Add each side by $5$}

\end{aligned}
\end{equation}
$


The solution set of the system $\{ (3,-2) \}$.

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 30

If $\displaystyle f(x) = \sqrt{3x + 1}$, find $f'(a)$.

Using the definition of the derivative


$
\begin{equation}
\begin{aligned}

f'(a) &= \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}
&& \\
\\
f'(a) &= \lim_{h \to 0} \frac{\sqrt{3(a + h) + 1} - \sqrt{3a + 1}}{h}
&& \text{Substitute $f(a + h)$ and $f(a)$}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\sqrt{3a + 3h + 1} - \sqrt{3a + 1}}{h} \cdot \frac{\sqrt{3a + 3h + 1} + \sqrt{3a + 1}}{\sqrt{3a + 3h + 1} + \sqrt{3a + 1}} && \text{Multiply both numerator and denominator by $(\sqrt{3a + 3h + 1} + \sqrt{3a + 1})$}\\
\\
f'(a) &= \lim_{h \to 0} \frac{3a + 3h + 1 -(3a +1)}{(h)(\sqrt{3a + 3h + 1} + \sqrt{3a + 1})}
&& \text{Simplify the equation}\\
\\
f'(a) &= \lim_{h \to 0} \frac{\cancel{3a} + 3h + \cancel{1} - \cancel{3a} - \cancel{1}}{(h)(\sqrt{3a + 3h + 1} + \sqrt{3a + 1})}
&& \text{Combine like terms}\\
\\
f'(a) &= \lim_{h \to 0} \frac{3 \cancel{h}}{\cancel{(h)}(\sqrt{3a + 3h + 1} + \sqrt{3a + 1})}
&& \text{Cancel out like terms}\\
\\
f'(a) &= \lim_{h \to 0} \frac{3}{\sqrt{3a + 3h + 1} + \sqrt{3a + 1}} = \frac{3}{\sqrt{3a + 3(0) + 1} + \sqrt{3a + 1}} = \frac{3}{\sqrt{3a + 1} + \sqrt{3a + 1}}
&& \text{Evaluate the limit}

\end{aligned}
\end{equation}
$


$\qquad\fbox{$f'(a) = \displaystyle \frac{3}{2\sqrt{3a + 1}}$} $

How did Larson use Burnham and Holmes to offer a commentary on two very different views on creativity and invention?

Larson, writing about the 1890s Chicago World's Fair, uses Daniel Burnham and Henry Holmes to symbolize the two directions in which technology would go in the twentieth century.
Daniel Burnham, the architect who, with several others, masterminded the magnificent Chicago World's Fair, which showcased how far the world had come technologically in a hundred years, foreshadows the glorious achievements of twentieth century technology, such as moon shots and polio vaccines. He represents all the creative potential for good in modern invention.
Henry Holmes, coexisting side by side with Burnham in the same city, represents man's capacity to use modern technology and invention for evil. A sociopath and serial killer, Burnham, with his ingenious gas chambers and ovens meant to hide the evidence of his misdeeds, chillingly foreshadows the evil technology would be used for in the twentieth century.
By juxtaposing the stories of two men who represent extremes in the use and misuse of invention, Larson highlights that technology is a complicated force that can't be simply applauded or condemned, but must be handled with care.

Daniel Burnham and Henry Holmes were both brilliant in some ways, but Burnham used his brilliance to create, while Holmes used it to destroy. Burnham was the architect who created the magnificent World's Columbian Exposition of 1893--a formidable feat, given the hurdles he faced to get it built. The results were so opulent that "some [visitors] wept at its beauty" (page 6). The fair also introduced visitors to new experiences, including the sights of Egypt and the taste of Cracker Jacks. One exhibition hall had more volume than the U.S. Capitol, St. Paul's Cathedral, and several other large structures combined.
Dr. Henry Holmes (an alias), on the other hand, used the fair to showcase his capacity for malevolence. He constructed a hotel not far from the magnificent fair grounds that housed airtight vaults that were used as gas chambers. He also built a crematorium in the basement of his hotel. Holmes killed many young women who attended or worked at the fair, and he eventually admitted to killing 27 people (including three children). However, he may have actually killed more, as he dedicated his brilliance to causing death.
Larson alternates the chapters about Burnham with chapters about Holmes to contrast how Burnham worked to invent things that would bring joy to people, while Holmes used his considerable force and intelligence to create new ways to kill. The contrast between Burnham and Holmes is that Burnham used the new technology of his age to create, while Holmes, a devil-like character, used it to destroy.

What, according to Kipling, is the "white man's burden"?

According to Kipling, the white man's burden is the need for white, "civilized" nations to travel abroad and impart their values and culture to other nations. The poem, therefore, is a defense of imperialism. This is made clear in the first stanza of the poem when Kipling talks about white men sending their sons abroad to serve their "captives' need."
For Kipling, this burden is a necessary one because people living abroad are in urgent need of civilization. He calls them "half devil and half child," for example, and suggests that they are "wild." Moreover, they suffer from "famine" and "sickness" and, therefore, are in need of the white man's help.
Although this task is a necessary one, Kipling argues that it is a "burden" because people will not appreciate it. He talks about "ungrudged praise," for instance, and "thankless years." However, Kipling believes that imperialism is so necessary that it is worth suffering the judgment and criticism of white peers and colonized citizens alike. It is, in his view, the only way to civilize foreign nations and to increase their cultural and economic worth.

According to Kipling, the "white man's burden" is a call for predominately white nations to send their best and brightest white males to uncivilized lands to spread Western civilization and culture to the "sullen peoples." Kipling presents the concepts of imperialism as a just and honorable goal to civilize the apparent uncivil natives around the world. Kipling challenges civilized nations with Western ideals to humbly embark on a journey of imperial conquest, which apparently benefits the foreign people living in uncivilized territories. Kipling describes the duties of the "white man's burden" by encouraging imperialist nations to promote peace, educate the natives, and feed the starving. Kipling mentions that the white men should toil as they build infrastructure in the foreign lands and cautions them against becoming lazy. He also informs the imperialists that their work will be difficult and encourages them to persevere even if they do not receive praise from the natives they are civilizing.

"The white man's burden," according to Kipling, is the civilization of the supposedly uncivilized peoples of the English colonies. Each stanza highlights a different component of the "burden."
In the first stanza, the "burden" is traveling to a foreign land to serve the native peoples. The second stanza emphasizes the need to educate the foreigners with Western philosophy, which will ultimately "work another's gain." According to the third stanza, the "burden" is to fight "heathen" evils like famine, even in the face of discouragement. The "burden" is of servility in the fourth stanza and of thankless labor in the subsequent stanza. (Apparently, the natives will not realize what exceptional aid it is they are receiving.) The final stanzas conclude with the clarion call to take up the burden, regardless of the hardship.
Since its publication, Kipling's poem has received a great deal of criticism, owing to its assumptions that white (Western) culture supersedes all others and that said cultures are ignorant and subsequently indebted to whites for their intervention. The same year (1899), H. T. Johnson responded with the poem "The Black Man's Burden."
http://historymatters.gmu.edu/d/5476/

Since no sane person would really open that door, how does this consideration prompt allegorical readings of the story?

Connie going through the door is symbolic on a number of levels. Doors, windows, and thresholds are common metaphorical symbols in coming-of-age stories such as this one. On one level, these structures represent the leaving of one particular phase of life and crossing over into another. Sometimes that phase can be from death to rebirth (usually symbolic), or from innocence to knowledge. The movement from innocence to knowledge is also seen in the loss of virginity, and given Connie's earlier sexual experimentation, it can be said that her sexual curiosity outweighs her fear and repulsion in her decision to open and go through the door. But since the story does hint at being symbolic and allegorical, then Arnold Friend may not be a literal lover who appears but a representation of that first sexual experience that Connie is drawn to, yet apprehensive of.
Arnold Friend represents secrets and realities of adult life that Connie finds frightening yet alluring. The story is dedicated to Bob Dylan, and we can surmise that the figure of Arnold Friend is something of a composite of all the fantasies and wishful thinking that Connie superimposes on young men in her life based upon the popular music she listens to, and Dylan's musings about love and rebellion were surely in the rotation that she listened to on the radio. Opening the door represents opening the conscious mind to experiences and ideas, and the popular music of the period was known to be aligned with the modes of consciousness exploration that became popular in the late 1960s when the story was published. Those modes also included meditation, hallucinogenic drugs, and the occult arts (such as astrology, tarot, etc.), as well as practices found in Eastern religions such as Buddhism. Consciousness exploration was a subject of the music by many popular bands of the day like the Beatles, Jefferson Airplane, and the Moody Blues (who made one album entitled "On the Threshold of a Dream"), and these ideas were picked up by the youth culture of the time via that music.

Why does Dracula want to move to England? What do you make of his collection of English books, maps, etc., and his desire to speak like an English gentleman? Why might Dracula’s move to England and his collection of English texts be viewed as preparations for war to Victorian readers?

Dracula wants to move to England because it was, at the time, the center of the world's most powerful empire. Britain was the most admired and feared superpower in the world, and its culture was envied and emulated. For someone as ambitious as Count Dracula, it would be the natural place to move. It would also be natural for someone with his large ego to want to be that most admired of figures, a learned and cultured English gentleman. Further, ships went all over the world to and from England's ports, which would help him with his plans for spreading vampirism.
Victorian readers might have perceived Dracula's move to England as preparation for war for two reasons. First, we as readers are explicitly told through Harker's and Seward's journals that Dracula is coming to England to create an army of vampires and wage war. From Harker's journal we read the following:

This was the being I was helping to transfer to London, where, perhaps, for centuries to come he might, amongst its  teeming millions, satiate his lust for blood, and create a new and ever-widening circle of semi-demons to batten on the helpless. 

We further learn from Dr. Seward's diary: 

So he [Dracula] came to London to invade a new land. He was beaten, and when all hope of success was lost, and his existence in danger, he fled back over the sea to his home; just as formerly he had fled back over the Danube from Turkey Land.

This idea of vampires from an exotic land invading played on people's fear at the time of the seemingly strange, unnatural foreigner invading. Britain was at the height of empire at this period but also increasingly beginning to worry about being headed for decline. Also, like France and the United States, England feared being swamped by non-Nordic immigrants. For example, as Latour argues persuasively in his The Pasteurization of France, France took Lister's ideas of bacteria seriously because the country was worried that white French people would be wiped out by the periodic disease epidemics that hit and the nation then swamped by darker-skinned foreigners. And a quick glance at the racist Tom Buchanan's sentiments in The Great Gatsby shows that fears of the non-Nordic foreigner invading were still prevalent in the 1920s. In Dracula, we see the same anxieties in English culture. Count Dracula is fought by doctors as a disease.
These fears of pollution and invasion morphed into fears of sexual union with the foreigner. As we know from Dracula, the bite of the vampire, with its sexual implications, is what pollutes the blood of pure English women and turns them into something alien and fearful. 
The average Slovaks who live near Dracula's castle are described as exotic. Harker writes:

The strangest figures we saw were the Slovaks, who were more barbarian than the rest, with their big cow-boy hats, great baggy dirty-white trousers, white linen shirts, and enormous heavy leather belts, nearly a foot wide, all studded over with brass nails. They wore high boots, with their trousers tucked into them, and had long black hair and heavy black moustaches. They are very picturesque, but do not look prepossessing. On the stage they would be set down at once as some old Oriental band of brigands. They are, however, I am told, very harmless and rather wanting in natural self-assertion.

Even such "harmless" people, because they are different, can hide a malevolent invader like Dracula. It is easy to see, therefore, how Dracula's move to England would play on Victorian anxieties.

What should Johnny be charged with in The Outsiders?

If Johnny were to be arrested, he would likely be charged with justifiable homicide or manslaughter. Ponyboy was an innocent victim of the attack by the Socs, and Johnny's impulsive decision to defend Ponyboy with the use of his knife could be defended or excused by his desire to protect an innocent person from more harm. If Johnny's move to stab Bob is deemed an overreaction, perhaps brought on by Johnny's anxiety or his deep-seeded fear rather than malicious intent, then it is possible he would be charged with voluntary manslaughter. Because Johnny acted out of strong emotion, his murder of Bob could be understood as a crime of passion, which typically carries a lesser punishment than straight-up murder in the first degree. Johnny's charges would also be complicated by the fact that he fled the scene of the crime, which can carry felony charges.

In the novel The Outsiders, Johnny Cade is a sympathetic character who lives a difficult life and is led to stab Bob Sheldon in order to save Ponyboy's life. Unfortunately, Johnny Cade kills Bob Sheldon and immediately flees the scene. Johnny ends up traveling to Windrixville where he hides out in an abandoned church on Jay Mountain with Ponyboy.
Johnny should be charged with manslaughter for accidentally killing Bob Sheldon. Manslaughter is defined as an unlawful killing that doesn’t involve malice aforethought and typically carries a less severe punishment than first- or second-degree murder. Since Johnny Cade is a minor, he should also be charged with running away, which is something Ponyboy fears will result in him being taken away from Darry. Johnny Cade should also be charged with evading arrest and trespassing.

What is the take-home message in The Last Lecture by Randy Pausch?

The "take home message" of The Last Lecture is that our dreams must play an active role in the lives we lead.
Pausch is confronted with a challenging reality as he decides to deliver his "last lecture."  He knows that he has only months to live.  He also knows that the summation he gives should not be about dying as much as how to live life even in the face of a defined end.  This understanding determines his message:

Whatever my accomplishments, all of the things I loved were rooted in the dreams and goals I had as a child…and in the ways I had managed to fulfill almost all of them. My uniqueness, I realized, came in the specifics of all the dreams—from incredibly meaningful to decidedly quirky—that defined my forty-six years of life. Sitting there, I knew that despite the cancer, I truly believed I was a lucky man because I had lived out these dreams.

Randy's "take home message" is that individuals should live their lives in accordance to their dreams.  He believes that a dream worth dreaming drives a life worth living.  
Randy employs several key moments to communicate this message. One such moment is when he recalls painting the walls of his room.  When he paints the quadratic formula and the elevator, it is clear that Randy's aspiration will fuel his hard work. His dream of utilizing math at an early age as well as the dream of smashing boundaries through the image of the elevator helped to fuel Randy's purpose in life.
Another detail that reveals the importance of dreams in Randy's life is when he was able to meet "Captain Kirk." Randy talks about how he "imagined a world where I actually got to be Captain Kirk."  It fuels his desire to build his landscape of virtual reality and share it with William Shatner, the actor who played Kirk on the television series.  Randy's dream fueled his work as an engineer. Randy's dream also played a role in how he faces death. This is seen when he received an autographed photo of Shatner playing Kirk with the line "I don't believe in the no-win scenario."  Randy's dream and "infatuation" with Star Trek kept him "in good stead" because it fueled his life's work and assisted him with how he would confront cancer.
Finally, Randy's dream of "making it" to the National Football League (NFL) was another instance where one's aspirations provides the blueprint for how to live life. Randy wanted to be a football player, a dream that never came true.  However, in this key detail, Randy's message is that there are instances where we can derive much from not accomplishing our dreams.  When Coach Graham treats Randy in a rough manner, he realizes that Coach won't "give up" on him.  Coach Graham taught Randy the value of hard work and that our work ethic must match our dreams.  He gave Randy "a feedback loop for life." Randy's experience with Coach Graham taught him the "head fake," where we learn a life lesson "well into the process" of doing something.  This provides the inspiration for Randy's last lecture.  It becomes a head fake for his kids, an instruction manual on what to do and how to live even when their father is absent.

Dr. King's Interconnected World: https://nyti.ms/2DyHR5eF.B.I. Director Wants to Move Forward: https://nyti.ms/2pgDKI8If This is America: https://nyti.ms/2p8OMyU These are the links. I am suppose to read the links and answer the following question for my History/social studies homework please help. Please provide a summary for each of the three links.

I will summarize the main points of the three articles you have provided. This should allow you to apply the main points to your community. In the first article about Dr. Martin Luther King, Jr., the author is trying to convey how issues are really connected to each other. For example, the author believes that the battles that environmentalists were fighting were similar to the fight for equality for all people. The author is also trying to show that many of the concerns that King had fifty years ago still exist today. King was fighting against economic inequality and racial antagonism. The author believes those issues are alive and well today. The author believes that King may have been ahead of his time by saying that we need to fight these issues. The fact that the author believes these issues exist today is proof of his point.
In the article about the FBI, the authors are saying that the President is making the job of the director of the organization more difficult. When the President makes negative comments about the organization, the FBI agents begin to wonder if their director really will support them. The director, Christopher Wary, has tried to steer clear of any political action. However, if the President continues to attack the integrity of the FBI, the FBI agents will want to know where their director really stands. This could create a showdown between the FBI director and the President.
The third article is based on a Rudyard Kipling poem titled “If.” The article is a condemnation of President Trump’s first year in office. The author argues that the President is ruining the United States with his words, actions, and policies. The author believes the President must be stopped. He believes that this will not be an easy task. However, according to the author, it is a task that must be undertaken.
https://www.nytimes.com/2017/12/22/opinion/america-trump-united-nations.html?smid=pl-share

https://www.nytimes.com/2017/12/22/opinion/martin-luther-king-christmas.html?smid=pl-share

https://www.nytimes.com/2017/12/22/us/politics/fbi-director-president-trump.html?smid=pl-share

Why does John have so much trouble dealing with the children and the Head Nurse?

John is experiencing a good deal of grief about his mother dying and can't understand why children are being allowed to intrude on the experience.
They pop up around Linda's bed as John sits with her. They make rude comments about her, because they have never seen anyone fat or old or with bad teeth.
John doesn't know about the death-conditioning children in the World State undergo to make dying seem pleasant and natural to them. He gets angry at them for clustering around Linda's bed. He even lifts one child up and slaps him, sending him off "howling."
This noise attracts the Head Nurse, who asks what is going on. John says to her:

"Well then, keep them away from this bed." The Savage’s voice was trembling with indignation. "What are these filthy little brats doing here at all?"

The nurse, however, is far more concerned that the children be properly conditioned than with Linda being allowed to die in peace or John's grief. Rather than speak to the children, she threatens to have John thrown out. Essentially, John has difficulties because he doesn't understand the norms of this culture.

How do the Cratchits react to their Christmas feast, and what does their celebration show Scrooge in Dickens' A Christmas Carol?

The Cratchit family is grateful for their feast even though it is meager, and Scrooge realizes that you do not need much to be happy as long as you have people you love.
The Cratchit family reminds Scrooge what it means to be deliberately happy.  The Cratchits are happy because they want to be.  The enjoy each other’s company.  They make the most of small luxuries.  They love each other, and because they do not have much they savor what they have.
Scrooge, who is a stingy miser who spends his nights eating alone and usually just has gruel because it is cheap, is astonished when he sees how excited the Cratchits are about their Christmas feast.  They are making much of little.

And now two smaller Cratchits, boy and girl, came tearing in, screaming that outside the baker's they had smelt the goose, and known it for their own; and basking in luxurious thoughts of sage and onion … (Ch. 3)

The Cratchits all enjoy their goose, and their gravy, apple-sauce and potatoes.  The goose was cooked at the baker’s because they didn’t have a way to cook it.  They were too poor.  When they were praising the goose, the fact that it was cheap was one of the things they were most proud of.  The pudding was also a source of admiration for all.

Everybody had something to say about it, but nobody said or thought it was at all a small pudding for a large family. It would have been flat heresy to do so. Any Cratchit would have blushed to hint at such a thing. (Ch. 3)

The Cratchits would never complain that there wasn’t enough to eat or the dinner was not fine enough. When Scrooge is toasted as the “Founder of the Feast,” Mrs. Cratchit objects at first, calling him “odious.”   Bob tells her to think of the children and she agrees to toast.
The celebration the Cratchits have tells Scrooge that family is more important than money, and you should savor what you do have.  Holidays are about more than spending and presents.  Holidays are about being with the ones you love and enjoying time with them.

Calculus of a Single Variable, Chapter 8, 8.6, Section 8.6, Problem 59

int (sin sqrt theta)/sqrt theta d theta
To solve, apply u-substitution method.

u=sqrt theta
u= theta ^(1/2)
du = 1/2 theta^(-1/2) d theta
du = 1/(2theta^(1/2))d theta
du =1/(2 sqrt theta) d theta
2du =1/sqrt theta d theta

Expressing the integral in terms of u, it becomes:
= int sin (sqrt theta) * 1/sqrt theta d theta
= int sin (u) * 2du
= 2 int sin (u) du
Then, apply the integral formula int sin (x) dx = -cos(x) + C .
= 2*(-cos (u)) + C
= -2cos(u) + C
And, substitute back u = sqrt theta .
= -2cos( sqrt theta) + C

Therefore, int (sin sqrt theta)/sqrt theta d theta= -2cos( sqrt theta) + C .

How has life in Ember changed since the seven-minute power outage?

The seven-minute power outage is significant enough that it causes the community to come together and discuss what to do going forward about the increasing lack of power. However, the lack of actual effort toward finding a permanent solution makes the people of Ember angry—that's the change that occurs after the power outage.
Power outages are a fact of life in Ember, but when one lasts for seven minutes, it's not business-as-usual. It's twice as long as any outage that came before and puts people in a silent panic. Unlike the past outages where people would talk about the time without power, no one seems inclined to discuss the seven-minute outage. DuPrau writes:

It was strange how people didn’t talk much about the blackout. Power failures usually aroused lively discussion, with clumps of people collecting on corners and saying to each other, "Where were you when it happened?" and "What’s the matter with the electricians, we should kick them out and get new ones," and that sort of thing. This time, it was just the opposite.

When everyone gathers to hear the mayor, the crowd is restless and seems almost on the verge of a riot. They can't hear him through the speaker and he doesn't offer any real solutions. At one point, Lina is even afraid that she'll be trampled. The people have reason to be upset: the mayor is keeping supplies back from the shortages for himself and others while not actively looking for a solution to benefit everyone.

Before that people have already experienced blackouts during daytime every once in a while. They have heard of rumors of power shortage, but most people are not too concerned about that and still believe that they can somehow cope with it and carry on with their normal lives. The seven-minute power outage causes great panic among the citizens of Ember, as it’s not only the longest one in history but also more than twice as long as any other outage before. It’s clear that the situation has been getting worse rapidly. People become more aware of the severity of the power shortage issue facing Ember and begin to fear that one day Ember may run out of power. Some people start to actively search for solutions.

What did Frederick Douglass accomplish that gave him prominence in American history?

Frederick Douglass rose to prominence as a leading African-American voice in the nineteenth century abolitionist movement. Born into slavery, he escaped as a young man and met William Lloyd Garrison, a leader in the movement, in the 1840s. Douglass was by all accounts a very talented orator, and his thunderous speeches against slavery made him a celebrity in the North. His widely-read autobiography added to his fame, and by the time of the Civil War, he was a frequent correspondent with President Abraham Lincoln, who he constantly lobbied to issue the Emancipation Proclamation, to allow African-American men to fight to preserve the Union, and to push the Thirteenth Amendment through Congress. After the war, Douglass was an advocate for the rights of freedmen in the South, both during and after Reconstruction. He spoke publicly for the rights of African-Americans even as they were severely circumscribed under emerging Jim Crow regimes. In short, Douglass was a lifelong activist for the rights of African-Americans, both under slavery and after it came to an end. 
https://www.history.com/topics/black-history/frederick-douglass

What were the positive and negative effects of industrialization and change during the period from 1877 to 1900?

With the end of Reconstruction in 1877, the United States entered what would come to be called the Age of Industrialization. There were many changes during this period. Many are considered positive, while others were clearly negative changes.
Some positive effects of industrialization include the spread of transportation and communications across the country. During this period, railroad construction boomed. Resources and workers were constantly being moved from one place to another with the aid of rail. With the completion of the transcontinental railroad in 1869, industry grew exponentially. By 1880 there were about 40,000 active locomotives in the country, more than half of which carried passengers. This led to a period of mobility unlike anything ever seen before.
The process of industrialization also ushered in an overall increase in the standard of living for many Americans. More jobs outside of the agricultural sector led to more disposable income for many families. With the mass production of goods that the assembly line brought, more was available at affordable prices for the typical consumer as well.
Cities also grew at a rapid pace during this period. As workers clustered around factories, cities grew. By the end of the nineteenth century, more people lived in cities than ever had previously. This has been one of the most enduring effects of industrialization. In fact, many cities in the United States today started out as humble mill towns and grew to great sizes during industrialization.
There were many negative effects of industrialization as well. Working conditions for most were appalling, uncomfortable, and often dangerous. Until the widespread rise of workers' unions in the twentieth century and the passage of labor laws, a factory worker had few if any benefits and protections. Pay was generally very low, and mill workers often worked as many as ninety hours in a week.
Until the passage of the Fair Labor Standards Act in 1938, child labor was common. Children would often work long hours in factories for very little pay. As a result, they received no formal education and consequently no opportunity for upward mobility.
Slums and tenements also developed around the factories. Poor housing and sanitation, as well as pollution from the factories, meant that health problems were common in many urban areas. Many of these neighborhoods did not have access to clean drinking water or health services. As a result, outbreaks of otherwise preventable diseases were common.
The period of industrialization had many positive and negative effects. The sad outcome, however, is that these effects were not evenly distributed. Captains of industry, such as Cornelius Vanderbilt and John Rockefeller, became incredibly wealthy. However, the average worker experienced very poor conditions and saw little of the wealth that they helped to create. In fact, in 1900 the richest 1% of Americans had 51% percent of the nation's wealth, and the poorest 44% had just 1.1%. This is perhaps why Mark Twain dubbed this period the Gilded Age; America showed an outward appearance of wealth, while many on the inside never experienced it.
https://time.com/5122375/american-inequality-gilded-age/

Precalculus, Chapter 9, 9.5, Section 9.5, Problem 51

In order to solve this problem we can use the following equation of the binomial theorem:
(a+b)^n =sum_(k=1)^n ((n!)/((n-k)! *k!)) * a^(n-k) * b^k
where:
a= first term
b= last term
n = exponent (power in original equation)
k = term required - 1
This will be clearer by solving the above example:
Our example is as follows:
(10x - 3y)^12
In this example we are looking for the 10th term, therefore:
a = 10x
b=3y
n =12
k = 10 - 1 = 9 (the 10th term we are looking for so we subtract one from it)
Because we are looking for the 10th term the following equation will be used:
t_(k+1) =(n!)/((n-k)! *k!) * a^(n-k) * b^k
t_(9+1) = (12!)/((12-9)!(9)!) (10x)^(12-9) * (3y)^9
t_10 = 220 (1000x^3)(19683y^9)
t_10 = 4330260000 x^3 y^9
So if we expand our binomial, and if we are looking for the 10th term, our answer is 4330260000x^3y^9

I need assistance identifying the farthest observations from the mean in the attached histogram image?

Hello!
Although the range is from 1 to 6, the mean and the distances from the mean are computed using the vertical values (those below 0.2). They are relative frequencies (probabilities) of the corresponding outcomes. Note that the horizontal values could be even non-numeric (for example, if the die would be marked with letters, not digits).
The mean is the arithmetic mean of the values. We cannot compute it because there are no enough marks on the vertical axis. But we can determine what observations (outcomes) are the farthest from the mean: they are the observations with the maximum frequency and with the minimum frequency.
At the given graph, they are 5 (the outcome with the highest bar) and 6 (the outcome with the lowest bar). The relative frequencies of other outcomes are closer to the mean.
The answer: 5 and 6.
 
https://www.mathsisfun.com/data/relative-frequency.html

Why was Potter arrested?

Muff Potter has been accused of the murder of Dr. Robinson. One night, he went along with the doctor and Injun Joe on a grave-robbing expedition at the local cemetery. The men got into an argument, and Injun Joe stabbed Dr. Robinson to death. During the melee, Muff got knocked out, and when he came to, Injun Joe was long gone, leaving him as the only plausible suspect for the doctor's murder.
Fortunately for Muff, Tom and Huck witnessed everything. At first, they're reluctant to come forward and tell the sheriff what happened. They're scared of what Injun Joe might do to them if they spill the beans. But eventually, they realize that Muff's heading for the gallows if they don't confess what they saw that terrible night. So they take the witness stand in the trial of Muff Potter and pin the blame on Injun Joe, who makes a sudden, daring escape, diving through the courthouse window.

Muff Potter is arrested because he is believed to have murdered Doctor Robinson. In reality, it was Injun Joe who killed the doctor. Early on in the novel, Potter, Joe, and Robinson appear to be working together to rob graves in the local cemetery. An argument breaks out, Potter is knocked unconscious, and Joe kills Robinson with a knife. After these events, Potter is framed for murdering Robinson and subsequently arrested. Though many other events take place in the novel, this grisly act of murder functions as the plot's centerpiece and contributes to most of the drama. Luckily, since Tom Sawyer (along with Huck Finn) witnesses the murder in the cemetery, he is able to clear Potter's name before he is unjustly condemned for a murder he didn't commit.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 14

You need to use mathematical induction to prove the formula for every positive integer n, hence, you need to perform the two steps of the method, such that:
Step 1: Basis: Show that the statement P(n) hold for n = 1, such that:
1 = 1/2*(3*1-1) => 1 =2/2 => 1=1
Step 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds:
P(k): 1 + 4 + 7 + .. + (3k-2) = (k(3k-1))/2 holds
P(k+1): 1 + 4 + 7 + .. + (3k-2) + (3k+1) = ((k+1)(3k+2))/2
You need to use induction hypothesis that P(k) holds, hence, you need to re-write the left side, such that:
(k(3k-1))/2 + (3k+1) = ((k+1)(3k+2))/2
3k^2 - k + 6k + 2 = 3k^2 + 2k + 3k + 2
You need to add the like terms, such that:
3k^2 + 5k + 2 = 3k^2 + 5k + 2
Notice that P(k+1) holds.
Hence, since both the basis and the inductive step have been verified, by mathematical induction, the statement P(n): 1 + 4 + 7 + .. + (3n-2) = (n(3n-1))/2 holds for all positive integers n.

What special quality of the birds and wildflowers does the speaker comment on?

In this poem, the speaker personifies both the wild flowers and the birds, watching them and comparing them favorably to "what man has made of man." While "sad thoughts" have come to the speaker while sitting pensively at rest in the grove, the special quality he identifies in the wild flowers and the birds is that they do not seem to experience such waves of melancholy while out in nature. On the contrary, the speaker observes the various flowers in the grove and comes to the conclusion that every one "enjoys the air it breathes." For the flowers, it seems to the speaker, life is intended to be pleasurable, and they appear to be enjoying their quiet existence.
Likewise, the speaker attributes the human quality of thought to the birds, although he concedes that he is not able to "measure" those thoughts as such. Still, watching the way they move—he chooses the active verbs "hopped" and "played," which we often associate with children and a carefree nature—the speaker believes that the birds, too, take "pleasure" in everything they do.
The observation of these behaviors in the wild flowers and birds of the grove fills the speaker with the conviction that nature was intended to engender pleasure in those who experienced it. As such, the contrast between their "thoughts" and his own feelings is a dispiriting one, and drives the speaker to "lament" what man has created of himself. Unable now to simply enjoy nature as the birds and flowers do, he suggests that man has developed himself into something different to what nature intended, and has become less happy as a consequence.

What did the Socs do when they jumped Ponyboy after he left the movie?

In the opening scene of the novel, Ponyboy is walking home alone from the movies when a Corvair pulls up beside him, and five Socs get out. Ponyboy quickly scans the ground for a pop bottle to fend off the Socs, but there is nothing in sight he can use to defend himself. When the Socs approach Ponyboy, they sarcastically tell Ponyboy that they are going to do him a favor by cutting off his long, greasy hair. One of the Socs then pulls out a knife, and Ponyboy begins backing up until he accidentally walks into another Soc standing behind him. The Socs proceed to throw Ponyboy to the ground and pin down his arms and legs while one of them sits on his chest. When Ponyboy struggles to free his arms and legs, the Soc member on his chest punches him a few times in the face before holding a blade next to his throat. Ponyboy then panics, and the Socs attempt to shove a handkerchief in his mouth. Fortunately, Pony is able to bite one of the Soc's hands before they take off running as the Greasers come to his rescue. While Ponyboy is laying on the ground, the Greasers arrive at the scene and comfort him after his traumatic experience.

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 20

sum_(n=1)^oo1/sqrt(n+2)
The integral test is applicable if f is positive , continuous and decreasing function on infinite interval [k,oo) where k>=1 and a_n=f(x) . Then the series sum_(n=1)^ooa_n converges or diverges if and only if the improper integral int_1^oof(x)dx converges or diverges.
For the given series a_n=1/sqrt(n+2)
Consider f(x)=1/sqrt(x+2)
Refer to the attached graph of the function. From the graph we observe that the function is positive and continuous for x>=1
Let's determine whether the function is decreasing by finding the derivative f'(x)
f'(x)=(-1/2)(x+2)^(-1/2-1)
f'(x)=-1/2(x+2)^(-3/2)
f'(x)=-1/(2(x+2)^(3/2))
f'(x)<0 which implies that the function is decreasing.
We can apply the integral test,since the function satisfies the conditions for the integral test.
Now let's determine whether the improper integral int_1^oo1/sqrt(x+2)dx converges or diverges.
int_1^oo1/sqrt(x+2)dx=lim_(b->oo)int_1^b1/sqrt(x+2)dx
Let's first evaluate the indefinite integral int1/sqrt(x+2)dx
Apply integral substitution:u=x+2
=>du=dx
int1/sqrt(x+2)dx=int1/sqrt(u)du
Apply the power rule,
=(u^(-1/2+1)/(-1/2+1))
=2u^(1/2)
=2sqrt(u)
Substitute back u=x+2
=2sqrt(x+2)+C where C is a constant
int_1^oo1/sqrt(x+2)=lim_(b->oo)[2sqrt(x+2)]_1^b
=lim_(b->oo)[2sqrt(b+2)-2sqrt(1+2)]
=2lim_(b->oo)sqrt(b+2)-2sqrt(3)
=2(oo)-2sqrt(3)
=oo-2sqrt(3)
=oo
Since the integral int_1^oo1/sqrt(x+2)dx diverges, we conclude from the integral test that the series also diverges.

Why does Robert Walton sympathize with a complete stranger?

Robert Walton is naturally drawn toward Victor Frankenstein. He is intelligent, curious, and passionate. Unfortunately for him, he is starved of company and intellectual stimulation during his journey to the frozen north. He yearns for a companion as compassionate and intelligent as he. As a result, the arrival of Victor into his life is like a breath of fresh air. Robert also has a profound sense of humanity. When he first sees Victor, he presents a truly pitiful sight—emaciated, cold, and exhausted. It is not surprising, given Robert's character, that he forges such a strong bond with Frankenstein. It is almost as if Victor is a kindred spirit. Robert's natural sympathy makes him the ideal listener for the terrible tale that Frankenstein is about to tell.

How does the simile of lines 36 to 45 in book 13 of the Odyssey relate to the story as a whole?

And as a man longs for supper, for whom all day long a yoke of wine-dark oxen has drawn the jointed plough through fallow land, and gladly for him does the light of the sun sink, that he may busy him with his supper, and his knees grow weary as he goes; even so gladly for Odysseus did the light of the sun sink.

This simile can be related to the story of Odysseus as a whole in that Odysseus spends the entirety of his journey longing for the end of it; he is glad when it feels like the end of his journey is near. However, there are definitely limits to the similarity—a man ploughing a field is doing a deliberate piece of creative work for a definite gain (the harvest), whereas Odysseus has been buffeted hither and thither by fate, has lost everything—his crew, his money, all the prizes he won during the Trojan War—and has nothing to show for it; there is no “harvest” for him. He is limping home, exhausted, after twenty years of being away. Ten years were spent in a war, and ten years were spent just being lost—the victim of one catastrophe after another. He is more like someone who, having been lost, sees a light in a window at the edge of the forest and knows that help is near and that his trials are nearly over.
Arguably, the fact that Alcinous loads him down with gifts (because the Phaecians are so moved by his tale of woe) is sort of like Odysseus finally reaping a reward for all the toil he has undergone to get this close to home—they restore to him the greater part of what he lost through his various disasters, give him a good ship, and point him back toward Ithaca. The farmer who senses that the end of his labor is near is like Odysseus; Odysses is finally, after all this time, in sight of home, and he knows that he will soon be able to rest. Perhaps the “harvest” is in fact his homecoming (and, in addition to his home itself, his wife and his son). When Odysseus set out at the beginning of his “day” ten years ago, he knew the journey home meant work, but he thought it would be straight journey from Troy to Ithaca. Instead, he zigged and zagged across the Aegean for a decade, and each time he got close to home, he was turned away again in the opposite direction. This is similar to the way a team of oxen must turn at the end of each row to properly plough a field. Now he knows he is on the final furrow, and when he crosses it, he is finished; there will not be any more turning. The thought fills him with hope, and, simultaneously, he is exhausted because the prospect of rest after all this time is almost too much to bear. He just has to finish this last leg of his journey before he can reap the harvest of home, family, and rest.

What is a summary of chapter 7 from Harry Potter and the Sorcerer's Stone?

Professor McGonagall welcomed the first-year students and guided them to the sorting ceremony, where each student would be sorted into one of Hogwarts' four houses, namely, Gryffindor, Hufflepuff, Ravenclaw, and Slytherin. She told them about the importance of this ceremony and mentioned the House Cup. The ceremony was held in the Great Hall, a splendid dining hall, with all the school's students and teachers at present. After singing a greeting song, the sorting hat started to shout out the name of the house each student was assigned to as McGonagall called the students to put on the hat one at a time in alphabetical order. Hermione and Neville were both put in Gryffindor, and Malfoy was put in Slytherin. When it was Harry's turn, the sorting hat hesitated for a while, hearing Harry asking not to be put in Slytherin, then put him in Gryffindor. Lastly, Ron joined his new friends and his brothers at the Gryffindor table. After the sorting ceremony, Dumbledore welcomed the students with a short speech and treated them to a feast created by magic. The students chatted with each other while enjoying their dinner. Harry also talked to the ghost Nearly Headless Nick, and saw Professor Quirrell and Professor Snape for the first time. Dumbledore concluded the feast with another speech, telling the new students about the school rules. Then they sang the school song and the ceremony was dismissed. Harry and his friends followed Percy into Gryffindor’s dormitory. Harry was so tired that he fell asleep almost immediately. He had a strange dream but forgot about it the next morning.

Calculus of a Single Variable, Chapter 7, 7.5, Section 7.5, Problem 10

Hooke's law is written as F = kx
where:
F = force
k = proportionality constant or spring constant
x = length displacement from its natural length
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b

From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:

2 inches = 1/6 ft

1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]

k =7.5*72
k =540

To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs

Briefly explain how nuclear fission is used to generate electricity. Be sure to use the terms "steam" and "turbine."

In general a process that releases heat can be harnessed to generate electricity. The heat is transferred to water, turning the water to steam. The expansion of water to steam is used to turn a turbine. The turbine turns a generator: a rotating coil of wire in a magnetic field, which induces an electric current according to Faraday's Law of Induction.
Back to the process that releases heat. Some electrical generation plants are heated by burning fossil fuels, but nuclear reactions can be used as well.
The most common fuel to use is uranium, specifically uranium that has been enriched in the uranium-235 isotope (most uranium is uranium-238). When a moving neutron strikes the nucleus of an atom of uranium-235, it forms unstable uranium-236. "Unstable" means the uranium-236 nucleus rapidly splits into two smaller nuclei. This splitting is fission. In the process, three more neutrons are released, along with a quantity of nuclear binding energy.
The released energy heats the water that bathes the reactor fuel, and the heat is transferred to pressurized water in a heat exchanger. This hot, pressurized water is vaporized to steam and used to turn the turbine. The heat exchanger is necessary because the water that cycles through the reactor itself is radioactive.
The neutrons that are released can be absorbed by other uranium-235 nuclei, causing them to undergo fission, releasing more energy and three neutrons apiece. This is a chain reaction. Various means are used to control the speed of the neutrons in order to maintain a steady rate of fission, rather than a catastrophic increase in which the number of reacting nuclei increases by a factor of three at each step! In addition, control rods are available to be lowered into the reactor, where they slow down or stop the chain reaction by absorbing the neutrons.

Calculus: Early Transcendentals, Chapter 2, 2.2, Section 2.2, Problem 1

The equation lim_(x->2) f(x) = 5 means that for the values of x approaching to 2, the values of the function f (x) are being 5. As we go the closer to the x values of 2, the closer the resulting f (x) values are supposed to get to 5.
Yes,It is possible for the limit to equal 5 even though f (2) = 3. The function f (x) = [[(1 - x^2)]] , the limit as x approaches 0 is 0, but f (0) = 1. so now we can create a relation as the function
f (x) = 5- 2 [[(1- (x-2)^2)]]
and for this function, the limit as x approaches 2 is 5, but f (2) = 3

Pretend you are a court reporter and write your impression of Atticus, Mayella, Tom and Mr.Ewell.

A court reporter might write profiles of the following characters using these characteristics as guidelines:
Atticus Finch: A man of charisma and great respect for the law, Atticus holds himself with authority and kindness. His voice is calm and not at all forceful, and he often waits for silence before expressing himself.
Mayella Ewell: A young woman always looking over her shoulder, Mayella has the face of someone older than her years. She looks tired and suspicious, holding her body stiffly as if she is uncomfortable being looked at. Mayella's eyes are active, jumpy, and full of pain.
Tom Robinson: A confused man dressed in clean but torn clothing, Tom speaks softly and looks everyone in the eye when he addresses them. When he is not speaking, he looks down at the floor with a sad look on his face.
Mr. Ewell: A worn-out man, unkempt and sullen, Bob Ewell sits in a slouch as if to communicate disdain for the court and for the law in general. He hasn't bothered to shave or wash his hands, and he often makes noises under his breath when he hears something he doesn't like. He sneers at anyone who dares to look at him.

int e^(cos6x)sin(6x) dx Evaluate the integral if improper determine whether convergent or divergent. (I think is integration by parts)

Hello!
This indefinite integral is simple if we note that  sin(6x) dx = -1/6 d(cos(6x)).  Formally, perform the variable substitution  u = cos(6x),  then du = -6sin(6x)  and the integral becomes
int e^u (-1/6) du = -1/6 e^u + C = -1/6 e^cos(6x) + C,
where C is an arbitrary constant.
 
You haven't shown the limits of integration, but the function under integral is continuous and bounded on the whole axis, therefore this integral is not improper at any finite interval.
If we consider it at any infinite interval (to +oo or to -oo, or both), then it diverges because the expression  -1/6 e^cos(6A)  is periodic and has no limit when A -> oo.
 

Overall, which alliance system was the strongest in World War I? Why?

There were two alliance systems in World War I—the Triple Alliance and the Triple Entente.  The Triple Alliance, formed in 1882, was made up of Germany, Italy, and Austria-Hungary.  The Triple Entente, formed in 1907, was made of France, Russia, and Great Britain.  Both from a military and a loyalty standpoint, the Triple Entente would prove to be more powerful.  Italy left the Triple Alliance in World War I in order to join the Allied powers and to take some land from the Austro-Hungarian Empire.  The Ottoman Empire joined the Triple Alliance in 1914 in order to claim land in southern Russia and to avenge the Russo-Turkish War of 1878.  Germany was the strongest member of the Triple Alliance, and it suffered most of the losses of the Central Powers during World War I.  The Austro-Hungarian Empire was quite weak by 1914, as the different ethnic groups in it were trying to separate and form their own states.
Britain was the largest imperial power in the world in 1914 and had the largest navy—any alliance containing Britain would already be at an economic and military advantage.  France and Russia were great powers in their own right, though Russia would have to leave the war in 1917 due to a revolution.  The greatest strength of the Triple Entente was that Britain and France were able to coordinate attacks along the Western front and that they were able to convince the United States to join the war in 1917.    

Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 5

y=e^x,y=x^2-1 , x=-1 , x=1
Refer the attached image. Graph of e^x is plotted in red color and y=x^2-1 is plotted in blue color.
From the graph ,the region of y=e^x lies above the region of y=x^2-1,
Area of the region enclosed by the given curves A=int_(-1)^1((e^x-(x^2-1))dx
A=int_(-1)^1(e^x-x^2+1)dx
A=[e^x-x^3/3+x]_(-1)^1
A=(e^1-1^3/3+1)-(e^-1-(-1)^3/3-1)
A=(e-1/3+1)-(1/e+1/3-1)
A=e+2/3-1/e+2/3
A=e-1/e+4/3
A~~3.68374

What effect did western imperialism have on Japan?

Western imperialism, most notably Commodore Perry's opening of Japanese ports in 1853, forced Japan to confront the modern age. They knew that unfair treaties had been imposed by the West on the Chinese and that China's refusal to modernize made it vulnerable to European control. In response, the Japanese, led by the samurai, took a different strategy.
They set out on an ambitious and rapid modernization campaign. They imitated Western models of state organization, established a parliament, industrialized, built a modern transportation infrastructure, and updated and modernized their army and navy. At the same time, they maintained Japanese traditions, such as the institution of the Emperor, as well as the Buddhist and Shinto religious faiths.
The Japanese decided that to stay safe, they needed an empire like the Western powers. They saw this as a defensive move. They aggressively went to war against other countries in Asia, including Korea, Manchuria, and China, in order to secure themselves by becoming the dominant power in the region. Because they were strong and modern, they were able to dominate Asia until their defeat in World War II.

Who is the President in 2055?

Ray Bradbury's futuristic short story "A Sound of Thunder," tells the tale of a man named Eckels who has paid a significant sum of money to take a time machine to the Cretaceous period to hunt a Tyrannosaurus Rex. The story is set in the year 2055. Eckels leaves the path during his safari, which causes a significant shift in historical events, even changing who was elected to the presidency in the year 2055. 
In the beginning of the story, a man whose last name is Keith is elected president in 2055. Readers learn this information from a conversation Eckels has with a person from Time Safaris, Inc. 

"Makes you think if the election had gone badly yesterday, I might be here now running away from the results. Thank God Keith won. He'll make a fine President of the United States."

At the end of the story, readers learn how Eckels's fumble in stepping off the path has cost humanity. The man who is described as anti-everything, Deutscher, has become the president in the year 2055, rather than Keith. Eckels is horrified to think the harming of one butterfly has so radically changed the course of human history. 

Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 44

A carpenter is building a wood door frame. The height of the frame is 1 ft less than three times the width. What is the width of the largest door frame that can be constructed from a board 19 ft long?

If we let $h$ and $w$ be the height and width of the door frame respectively, then we get

$h = 3w-1 \qquad$ Equation 1

And

$w+2h = 19 \qquad$ Equation 2

By substituting equation 1 to equation 2, we have


$
\begin{equation}
\begin{aligned}

w+2 (3w-1) =& 19
\\
w+2 (3w) - 2(1) =& 19
\\
w+6w -2 =& 19
\\
7w =& 21
\\
w =& 3

\end{aligned}
\end{equation}
$


Thus, the width of the door's frame is 3 ft.

Briefly discuss the story "Equal Opportunity" by Walter Mosley.

This story focuses on a man called Socrates. He is 58 years old and has spent 27 years of his life in prison as a result of two murder charges. Now a free man, Socrates wants to find a job, but there are none available to him in his deprived neighborhood of Watts. (There isn't even a supermarket.) So Socrates travels 14 miles to apply for a job in a supermarket on Venice Boulevard.
The manager's reaction to Socrates is very negative. She says that Socrates cannot have a job because he does not have a phone (to enable him to find out if his application is successful). Socrates, however, does not give up and returns to the store four days in a row to see if his application has been successful. On the fourth day, Socrates is greeted by some security officers, called in by the manager. Eventually, Socrates is offered a job at another supermarket in Santa Monica, where ex-convicts are given a second chance.
The key to this story is the attitude of the supermarket manager. By portraying the manager in this way, Mosley draws attention to the fact that a convicted felon may have served his time, but society never truly accepts him. He will always be socially tainted by the crimes of his past.

In the short story "Equal Opportunity," Socrates Fortlow goes to a Bounty Supermarket on Venice Boulevard to find a job. He is enthralled by the wealth around him. He thinks, "There was a definite religious feel to being in the great store. The lofty ceilings, the abundance, the wealth." Socrates has served twenty-seven years hard time for killing two of his buddies. There are no supermarkets in Watts, where he lives, so he has to travel 14 miles to Venice Boulevard to ask for a job. The white manager turns him down because Socrates doesn't have a phone, and the manager claims he needs to tell applicants if they've been accepted by phone. Socrates returns for four days asking for a job, and he is told that if he returns again, he will be arrested. Instead, when he comes back, he tells the security guards that he has been treated unfairly for not having gotten a chance to prove himself. Finally, the security officers decide he should get a job at the Santa Monica store, and Socrates celebrates his success. The story is about how hard it is for an African-American ex-con to get a chance to better his life after leaving prison. 

Why did the US Federal Reserve not rescue banks from deflation after the stock market crash in 1929?

The Federal Reserve was unprepared for the depth of the disaster of the stock market crash late in 1929. It was a decentralized institution, split into districts with different governors. Although these governors understood that they should coordinate their efforts and tried to do so, they could not agree about the best solution to the crisis.
Since so much money was wiped out by the stock market crash, the supply of money in the US economy fell by almost 30 percent between 1930 and the winter of 1933. Because people had so much less money to buy goods, the price of goods naturally dropped by an equal amount, a significant deflation. This was destabilizing for the economy. For example, if you figure prices will go down, then you will wait to make purchases. If you have debt, then you are going to run into trouble. For instance, if the value of your house dropped from $10,000 to $7,000 and you owed $8,000, you could not very well sell the house to clear the debt. Also, with less money available (this was before the days of widespread consumer credit) people had less to spend, which contributed to a severe downward spiral: as businesses sold fewer goods, they had less money and so they laid off more people.
The Federal Reserve's biggest failure was its inability to prevent the deflation. It could have, for example, lent banks money so they did not collapse and wipe out people's savings or they could have printed more money. Normally printing money causes inflation, but in this case it would have merely prevented deflation.
As stated in the first paragraph, people with the power to change the course of the economy were surprised by the collapse and were confused about what had gone wrong. Decentralization meant nobody had sufficient authority alone to do what needed to be done in order to prevent deflation. Some thought raising interest rates and reducing the amount of money in the economy, although it was deflationary, was the cure. Now we know that was wrong, but hindsight is 20/20 and the people in charge had to deal with an unprecedented crisis in real time without a reliable road map. 
https://www.federalreservehistory.org/essays/great_depression

What is the allusion to David Belasco in The Great Gatsby?

On his first visit to Gatsby's mansion, having been invited to one of his parties, a slightly tipsy Nick ends up in Gatsby's library, where he meets Owl Eyes, another guest. In the library, Owl Eyes calls Gatsby a

a regular Belasco. It’s a triumph. What thoroughness! What realism!

David Belasco was a famous theater producer known for his lavish sets. Owl Eyes is indicating that he knows Gatsby is simply putting on a show with his mansion and his wild parties. Nevertheless, he is impressed that Gatsby has not simply ordered cardboard book backs to simulate a library: instead, he has purchased genuine books. The only problem is, he has not cut open the pages, which you would have had to do at the time so that you could read the book.
Owl Eyes captures in the uncut books the enigma of Gatsby. Gatsby goes ninety percent of the way to create his illusion—more than most people would— but in the end, can't quite be totally convincing as the wealthy man who comes from old money.
Interestingly, the book Owl Eyes pulls down is of lectures by Stoddard, presumably the racist Lothrop Stoddard Fitzgerald is alluding to when Tom mentions reading "Goddard." According to Tom, Goddard has written The Rise of the Coloured Empires. Stoddard wrote The Rising Tide of Color against White World Supremacy. Presumably, if Gatsby had read the Stoddard book, he might have been better prepared for Tom's racism.

David Belasco was a famous theatrical producer and impresario renowned for the realism of his productions. But though his impressive creations were realistic, they weren't actually real. In fact, they couldn't be; there's always going to be a difference between art and reality.
Gatsby's library is also realistic but not real. It looks just like a regular library, the kind that a wealthy, well-read aristocrat would have in his stately home. But is isn't. Like everything in Gatsby's West Egg mansion, it's all for show. On closer inspection, Owl Eyes can see that the books in Gatsby's library haven't been read, indicating that Gatsby's carefully-constructed persona of an educated Oxford graduate is completely false.
Gatsby has been playing a role all along, acting out a part he's written for himself and performed on a stage where he prefers to remain one of the supporting characters. He's a regular David Belasco alright, but as with the Broadway legend, he can never successfully bridge the gap between fantasy and reality.

The allusion of David Belasco in The Great Gatsby functions to emphasize both the flaws and the success of the disguise Jay Gatsby has designed for himself. David Belasco was a theater legend, making his mark on audiences with his lavish productions and his own attempts at playwriting. Though Belasco was definitely successful at creating fictional worlds (just as Jay Gatsby himself was successful, to a certain degree), he was also criticized for his focus on realism. Belasco employed excessively complex systems on his sets in order to create a realistic situation for his theatergoers; one production even involved a decision to place real sheep on stage. This attention to detail is something Jay Gatsby could likely relate to, as Gatsby also sought to create convincing environments for his guests to enjoy. Like Belasco, Gatsby went to extremes to convince others of his fictional world. These attempts, for both men, were successful in many ways, but ultimately, they collapsed under the weight of reality.

The allusion to David Belasco appears in chapter 3 when Owl Eyes is looking around Gatsby's library. He says:

This fella’s a regular Belasco. It’s a triumph. What thoroughness! What realism!

To understand this allusion, you need to know that David Belasco was a theater producer, well-known in the 1920s for creating sets that were very realistic.
By using this allusion, Owl Eyes is saying that Gatsby's library is just like one of Belasco's sets. Instead of being a real library, Gatsby's library is a fake set, designed to trick people into thinking that he is an educated and well-read man. Owl Eyes has discovered this by carefully looking around the library. He sees that the books are real but that the pages have not been cut. This proves that Gatsby has never read them.
Gatsby, therefore, has faked this library, just like the rest of his persona. It is all part of a well-designed and well-crafted ruse designed to impress Daisy Buchanan so that she will come back to him.

Why does Gulliver cooperate with the Liliputians ?

Gulliver cooperates with the Lilliputians because he is so interested in them. He could, obviously, squash them underfoot, but he seems to be fascinated with and impressed by them, especially their military. Gulliver is interested in learning their language and finding out about their culture, almost from an anthropological perspective, and he therefore needs to win them over. In addition to this, Gulliver finds the Lilliputians to be very beautiful, with very fine skin and dainty features (of course, this has a great deal to do with their very small size relative to Gulliver himself). Gulliver is also, at first, honored by audiences with the emperor as well as several other notable personages. In short, he is treated relatively well (after the Lilliputians get over their fear of him and before he angers the emperor by refusing to enslave the citizens of Blefuscu), and he wants to maintain good relationships in order to continue to learn about this place.

We should remember that Gulliver is a prisoner of the Lilliputians. Under the circumstances, it's in his best interests to cooperate with them. If he does, then he figures that perhaps they'll untie him, and maybe let him go. The Liliputians' arrows are tiny—by Gulliver's standards, of course—but they still hurt like mad when several of them are fired into his hand. It's not surprising, then, that Gulliver should want to cooperate.
Apart from anything else, he's well and truly out of his comfort zone, completely adrift in a strange environment where everyone's six inches tall. Although it must be tempting for him to use his vastly superior size and physical strength to crush the Liliputians, he charitably refrains from doing so. Gulliver really isn't that kind of man. Far better, then, to get this strange race of people on his side and make them accept him.

How far is it true that body and mind are at war in Swift's writings?

In Gulliver's Travels, Jonathan Swift explores a variety of themes in an elaborate and far-reaching satire, and a conflict between the mind and the body is certainly one of these themes. For example, Gulliver's travelogue is presented as a series of rational observations, with Gulliver reporting everything he experiences more or less truthfully and in a tone that suggests careful, reasoned analysis of the customs and traditions he observes. However, Gulliver's physical body also figures in his adventures; in his first journey, he is larger than the Lilliputians, in the second adventure he is much smaller than the Brobdingnagians, and in his final adventure he resembles the barbaric Yahoos. Thus, Gulliver's observations depend in large part upon his physical perspective of events, and this physical/bodily perspective subtly informs his rational reports. This fact is brought home to us at the end of the story especially, at which point Gulliver is so disgusted by humanity's resemblance to the Yahoos that he prefers the company of horses to that of other people. This is a prime example of one way Gulliver's physical perspective gets in the way of his ability to act rationally. By the end of the story the human body, resembling the repulsive Yahoos, has become so detestable that Gulliver chooses to fraternize with the supposedly rational horses, although these horses are not the wise Houyhnhnms but normal horses, which in turn forces us to evaluate the rationality of Gulliver's decision. This interpretation is only one way of looking at the narrative, but it's an intriguing one, nonetheless.

What did the Victorians think about the book Dracula?

The ancient stories of werewolves and vampires already existed in the psyche of Victorian society. Even twenty-six years before Dracula's 1897 publication, Victorians had already met Carmilla in the novel of the same name by Joseph Sheridan Le Fanu. Carmilla, or Mircalla, which was her real name, was a female vampire in pursuit of a young woman named Laura. What Bram Stoker did was take that same idea of a pursuing vampire and add his own social commentary by creating characters and situations that were very representative of his time.
These characters and situations in Dracula drove conversations that connected the novel to the newsworthy events taking place in those days, ranging from the boom of psychology to Darwin to the Industrial Revolution, and even the Jack the Ripper murders of 1888.
Also very prevalent was the topic of the incoming Aliens Act, which was officially approved in 1905. This was an Act that restricted immigration from Eastern Europe. This part of the world was once the land of Vlad the Impaler, who inspired the character of Dracula.
Judging by what critics said of the novel at the time, we can safely argue that people gave less importance to the vampire figure and focused more on the collateral things taking place in the novel. This is the reason why, upon reception, Dracula drew negative and positive opinion just like any other novel.
Remember also that Victorians, unlike us, did not possess the pre-conception that we, as modern readers, have of the iconic "Dracula." Being new to the idea of Count Dracula, Victorians embraced the character as another welcome addition to other newly-created mysterious characters that would become icons throughout the next 120 years in novels like Mary Shelley’s Frankenstein, H.G. Wells’s Invisible Man, and Oscar Wilde’s Picture of Dorian Gray, among others.
The Manchester Guardian published one of the first reviews of Dracula on June 15, 1897. We can argue that the critic represented the mainstream Victorian opinion about the novel:

The plot is too complicated for reproduction . . . In spite of its absurdities, the reader can follow the story with interest until the end.

The reviewer also said that Stoker made a mistake in filling the entire novel with "horrors" from start to finish. The review even suggests that, if Stoker had toned the horror down a bit, the novel would have been believable. This may seem comical to the twenty-first-century modern reader, who has seen Dracula in a variety of settings and automatically recognizes him as a scary fictional character.
The Spectator also published a review in July, 1897. This one also states that the novel was rather lackluster and that Stoker should have considered a more historical and less “modern” setting for his novel, by Victorian standards.

Mr Stoker has shown considerable ability in the use . . . of all the available traditions of vampirology, but we think his story would have been all the more effective if he had chosen an earlier period.
The up-to-dateness of the book—the phonograph diaries, typewriters . . . hardly fits in with the mediaeval methods which ultimately secure the victory for Count Dracula’s foes.

This is an amazing observation, because we draw our modern fascination for Dracula partly from its Victorian setting. What they considered too "up to date," we consider perfectly "antique," so to speak.
Therefore, Victorians did not see Dracula from our perspective, as readers who have gone as far as romanticizing vampire stories. We love the idea of the gothic vampire because it is so distant from our current reality.
To Victorians, however, this may have been yet another story about vampires that touched on social commentary. Interestingly, Dracula has survived the passing of time and seems to be more popular with readers almost 120 years after its publication than it was when it was first published.

How did Renaissance art differ from Medieval art?

A few of the key differences between European art in the medieval period and European art in the Renaissance include the following:
A move toward naturalism in the Renaissance.
The painters of the Renaissance sought to make everything in their paintings look as photorealistic as possible. Artists closely studied human anatomy to make sure their bodies had proper proportions, which were often lacking in medieval art. They also began using natural backgrounds, even in portraiture (think of the Mona Lisa). Flemish artists like Robert Campin (see his Merode Altarpiece) and Jan van Eyck (see the Arnolfini Portrait) were particularly renowned for the realism of their work. Oil-based paints became more popular in the Renaissance. These paints allowed for more subtle coloring, which made paintings look more realistic.
On the other hand, medieval artists, particularly those who were still heavily influenced by Byzantine trends, loved elaborately decorated backgrounds and the use of gold leaf (this tendency can be found even in very late medieval/early Renaissance painters like some of the Sienese masters of the fourteenth century).
The reintroduction of Classical Greek and Roman aesthetics in the Renaissance.
The painters of the Renaissance, unlike the painters of the medieval period, were able to easily study examples of Greek and Roman sculpture. As Dr. Leonard Barkan tells us in his book Unearthing the Past, the discovery of fragments like the Belvedere Torso (on display at the Vatican Museums) helped spur a revolution in European painting and sculpture.
Gothic artists (who worked during the medieval period) had a hard time representing bodies in motion. If you look at the statues on the facade of a Gothic cathedral, for example, you'll note that almost all of them are very static. The figures face straight ahead, and there is little twisting in the torso or legs. You will see the same sort of flatness if you look at how Christ's body is represented on an early medieval crucifix.
The rediscovered classical statuary showed figures in motion, and artists were able to visit Rome to do drawings and copies so they too could learn how to portray bodies that have a sense of motion. To take one extremely famous example, Michelangelo's work in the Sistine Chapel clearly shows that he studied classical examples. An excellent example of a late Gothic style side-by-side with an early Renaissance style can be found in the Brancacci Chapel in the church of Santa Maria del Carmine in Florence. The chapel features some very famous frescoes of Adam and Eve. In one set, done by the artist Masolino, the figures are beautiful but still seem flat and as though they were imposed on the black background. On the other hand, a second set, done by the artist Masaccio, shows Adam and Eve in motion. Eve's body is modeled on a standard classical pose, and Masaccio uses shadows to create a sense of depth.
Renaissance painters showed their interest in Classical Greece and Rome in other ways. Architects like Brunelleschi and Alberti revived the use of classical orders in buildings. The High Gothic style of architecture fell out of favor and buildings with mathematically regular proportions and "clean" Romanesque arches were preferred by patrons. Artists like Botticelli drew inspiration from classical mythology and painted large-scale secular works (consider Botticelli's famous Birth of Venus), which were virtually unheard of in the medieval period. Artists were also comfortable creating nude figures, which had also not been common in the medieval period.
Renaissance artists were able to use perspective to create realism.
Artists like Brunelleschi used mathematics to help develop linear perspective, which was essential to help create a sense of realistic depth in their paintings. Linear perspective allowed artists to arrange the pictoral space effectively. Later Renaissance artists combined a knowledge of perspective and a desire to replicate reality as closely as possibly. They created trompe d'oeil ("trick of the eye") paintings. One excellent example is Mantegna's Camera Picta. The artist painted an oculus (the opening at the top of a dome, like in the Pantheon) in a ceiling to make it look like there was an actual opening. The illusion is very effective.

I am writing a book report on the book Rain Reign. What would be some good words to describe the main character, Rose Howard?

Ann M. Martin's Rain Reign has as its protagonist a young girl named Rose Howard. Rose is quick to point out that her name is a homonym, as is the name of her dog, Rain. One of the first things the reader learns about Rose is that she can be described as a rule follower. Rose shares in chapter 1, "Some of the things I get teased about are following the rules." In her list of things she likes, "Rules" happens to be second on her list. Rose also does her best to follow rules of conversation. She often considers these rules as she is speaking, and has certain "conversation starters" that she refers to when talking with others. Finally, Rose has rules that she follows depending on her father's demeanor when he is home in the evenings. She shares, "If my father comes home and doesn’t say anything, but walks into his own room, then Rain and I should not go near him at all."
Misunderstood is another word to describe Rose. Rose is the only one in her class with a love of homonyms. This sometimes gets her in trouble in class because she blurts out whenever she hears one. Her father once says to her, "Rose, for god’s sake, keep your mouth closed when you think of a homonym." He is often frustrated with her because he doesn't quite understand her, and her teachers question whether their school is appropriate for her. Rose's father shakes her at one point and says that she needs to stop certain behaviors. In response, Rose simply shares with her dad that her name is a homonym.
As she tells her story, the reader discovers that Rose is precise. Since she loves numbers, she remembers factual information that most people would either forget or never notice. She knows her father's age, height, the length of his scar, when he was born, and the phase of the moon on that day. She knows distances to places she is familiar with, and the dates and times of many important and sometimes traumatic events in her life. On the night her father brought her a dog, Rose recalls, "It was 7:49 p.m., which meant that the J & R Garage had been closed for two hours and 49 minutes."
Rose is also brave and determined. Aware of her differences, she continues to move along in a world where her peers often see her as strange. She goes to a school where she has teachers that feel she doesn't belong most of the time. One of her teachers, Miss Croon, asks Rose's father, "Are you sure you don’t want to look into another program for Rose?" Most importantly, the reader sees evidence that Rose is brave and determined when she loses her dog and is forced to put herself into situations that are difficult and uncomfortable for her.

How is family portrayed in A Christmas Carol?

The view of family is dependent upon which character's view is being looked at as well as what point in the story we are discussing.
Bob Cratchit views his family as very important.  His family spends time together dining over a very meager meal, but the important part is that they are together.  They are all so happy when Martha is able to make it home to be with the family for the holiday.

Thank you, dear Lord for your many gifts...our dear children, our wonderful meal: our love for one another....

Fred, Scrooge's nephew, certainly sees the importance of family.  That is why he continues to invite Scrooge to his home even when Scrooge is not at all receptive to the idea.
Scrooge does not see the importance of family at all in the beginning of the story.  He is bothered by the fact that Bob Cratchit wants Christmas Day off from work so he can spend it with his family.  His view is that children are just an expense.  This view is certainly changed by the end of the story when he visits his nephew's home and joins them for a meal.  Scrooge has discovered that there are things in life that are more important than money.

In this novel, family is portrayed as one of the most important elements of one's happiness. Fred, Scrooge's nephew, continues to invite him, year after year, to his Christmas celebration; why do this if not because family makes Fred happy? He certainly doesn't do it because his invitations are well-received!
Further, Scrooge is very upset when he is shown his former fiancee, Belle's, happy family. She is surrounded by children and is the beloved wife of a man who cares deeply for her; Scrooge realizes that he put his love of money ahead of his love for Belle, just as she said. His money has not made him happy, in the end, but Belle obviously looks very happy with her family.
When the Ghost of Christmas Present shows the Cratchit family to Scrooge, Scrooge eventually comes to the realization that Bob may be poor in wealth, but he and his family are rich in other, more important ways. They are happy because they are together, and it is only the prospect of one of them being unable to come to Christmas dinner that can upset Bob. It is no matter that their dinner is scant and their pudding smells like laundry.
Moreover, being at Fred's with the ghost and listening to the games may be the happiest we ever see Scrooge. Even though one game is played at his expense, he doesn't mind, because being with loved ones makes him so happy. Ultimately, he goes to spend his holiday with Fred and Fred's wife because he seems to have recognized how joyful it would be; further, he allows the Cratchits to have their own family holiday together (without interruption by him), and he offers Bob the partnership when he returns to work the next day.

Calculus of a Single Variable, Chapter 2, 2.1, Section 2.1, Problem 19

By limit process, the derivative of a function f(x) is :-
f'(x) = lim h --> 0 [{f(x+h) - f(x)}/h]
Now, the given function is :-
f(x) = (x^3) - 12x
thus, f'(x) = lim h --> 0 [{{(x+h)^3} - 12(x+h)} - ((x^3) - 12x)}/h]
or, f'x) = lim h --> 0 [{{(x+h)^3} - (x^3) - 12h}/h]
or, f'(x) = lim h --> 0 [{(x^3) + (h^3) + 3x(h^2) + 3(x^2)h - 12h - (x^3)}/h]
or, f'(x) = lim h --> 0 [{(h^3) -12h + 3x(h^2) + 3(x^2)h}/h]
= [(h^2) + 3xh + 3(x^2) - 12]
putting the value of h = 0 in the above expression we get
f'(x) = 3(x^2) - 12

Describe the merry war of wits between Beatrice and Benedict in Act 1 of Much Ado about Nothing.

Leonardo describes the relationship between Benedict and Beatrice thusly,

There is a kind of merry war betwixt Signior Benedict and her.  They never meet but there's a skirmish of wit between them.  

In the very next few lines, we see this "merry war" Leonardo is referring to.  It is a war of wits as each insults the other through puns, jokes, sarcasm, and irony.  What is obvious to all but the two young people is that they are in love with each other, and their outward shows of wit cover up their true feelings.  The scenes in which they engage in this competition of insults, of sorts, are some of the most entertaining in the play.  
So let's look at their first dialogue more closely.  Beatrice begins the attack by claiming that Benedick has no need to talk because no one is paying attention to him.  He returns the insult by calling her "Lady Disdain" and feigns surprise that she is still living.  She answers with the claim that Disdain cannot die when it has such meat as Benedick to feed on.  And Benedick vows that all women except Beatrice love him, but he loves no one.  And on it goes until Benedick ends with comparing the speed of his horse to the speed of Beatrice's tongue.  But Beatrice gets the last word by saying that he always ends with a "jade's trick."  This is a horseman's term for an abrupt stop.  
You get the idea.  What is important to note, however, is that intellectually the two are matched very well.  Both are proud, smart, quick-witted, funny, and not unkind.  Unlike in The Taming of the Shrew, Shakespeare does not let Benedick get the upper hand in the relationship (as Petruchio did).  We see this through their dialogue in Act 1 and are anxious to see how this relationship develops.  

x=3t^2 , y=t^3-t Determine the open t-intervals on which the curve is concave downward or concave upward.

Given parametric equations are:
x=3t^2,y=t^3-t
We need to find the second derivative, to determine the concavity of the curve.
dy/dx=(dy/dt)/(dx/dt)
Let's take the derivative of x and y with respect to t,
dx/dt=3*2t=6t
dy/dt=3t^2-1
dy/dx=(3t^2-1)/(6t)
dy/dx=(3t^2)/(6t)-1/(6t)
dy/dx=t/2-1/(6t)
(d^2y)/dx^2=d/dx[dy/dx]
=(d/dt[dy/dx])/(dx/dt)
=(d/dt(t/2-1/(6t)))/(6t)
=(1/2-1/6(-1)t^(-2))/(6t)
=(1/2+1/(6t^2))/(6t)
=((3t^2+1)/(6t^2))/(6t)
=(3t^2+1)/(6t^2(6t))
=(3t^2+1)/(36t^3)
Curve is concave upwards if second derivative is positive and concave downwards if it is negative,
So, the curve is concave upward for t>0
Curve is concave downward for t<0

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 28

Determine $y'$ and $y''$ of $\displaystyle y = \frac{\ln x}{x^2}$
Solving for $y'$

$
\begin{equation}
\begin{aligned}
y' &= \frac{d}{dx} \left( \frac{\ln x}{x^2} \right)\\
\\
y' &= \frac{x^2 \frac{d}{dx} (\ln x) - \ln x \frac{d}{dx} (x^2) }{(x^2)^2}\\
\\
y' &= \frac{x^2 \left( \frac{1}{x} \right) - \ln x \cdot 2x }{x^4}\\
\\
y' &= \frac{x - 2x \ln x}{x^4}\\
\\
y' &= \frac{x(1-2 \ln x )}{x^4}\\
\\
y' &= \frac{1-2 \ln x }{x^3}
\end{aligned}
\end{equation}
$


Solving for $y''$

$
\begin{equation}
\begin{aligned}
y'' &= \frac{d}{dx} \left( \frac{1-2 \ln x}{x^3} \right)\\
\\
y'' &= \frac{x^3 \frac{d}{dx}(1- 2 \ln x) - (1 -2 \ln x) \frac{d}{dx} (x^3)}{(x^3)^2}\\
\\
y'' &= \frac{(x^3)\left( \frac{-2}{x} \right)-(1-2\ln x)(3x^2) }{x^6}\\
\\
y'' &= \frac{-2x^2 - 3x^2 + 6x^2 \ln x}{x^6}\\
\\
y'' &= \frac{-5x^2 + 6x^2 \ln x}{x^6}\\
\\
y'' &= \frac{x^2(6 \ln x - 5)}{x^6}\\
\\
y'' &= \frac{6 \ln - 5}{x^4}
\end{aligned}
\end{equation}
$

What were the cultural changes of the 1960s?

The 1960s saw the birth of a new form of counterculture and witnessed significant changes in the roles of women, African Americans, and others in society. The early 1960s were a time of hope, but after John F. Kennedy's assassination in 1963 and the worsening of the conflict in Vietnam in the mid and late 1960s, people began to question authority and traditional institutions such as schools, churches, and the government. 
Students played prominent roles in new forms of activism through organizations such as Students for a Democratic Society (SDS) and SNCC, or the Student Nonviolent Coordinating Committee, which advocated African American rights and equality. In the late 1960s, youth culture was popularized through rock and roll and in concerts like Woodstock in 1969. College campuses became places of protests and revolt against the war in Vietnam, among other causes.
Women's rights became a focus of popular protests, and the role of women changed as women pushed for equal pay and equal rights. Many formerly all-male colleges and graduate schools began to admit women, and more professions began to open their doors to women. During the 1960s, women also had greater sexual freedom than ever before, in part because of the invention of the birth control pill (which the FDA approved as a contraceptive in 1960). The idea that a woman had to get married began to fade away as more women delayed marriage or did not marry at all. In addition, starting with the Stonewall Riots of 1969 in New York City, people in the LGBTQ community began to advocate for their rights and fight against police harassment of their community.
As a result, many hidebound institutions (for example, marriage and regular church worship) that had defined earlier eras began to crumble. By the end of the 1960s, the expectations of women had changed radically, and women, African Americans, and others began a crusade for equality that continues until today. 
https://learningenglish.voanews.com/a/american-history-the-1960s-10-years-that-changed-a-nation-134041543/114624.html

Can you please explain the canto VII, XX and LXXVIII of the poem In Memoriam?

In Canto VII Tennyson is reminded of his late friend, Hallam, by visiting the place (the "dark house") where Hallam once lived. At night, the memory keeps Tennyson awake, and so he finds himself wandering around the house. In the early hours, he opens the door, half-expecting to find his friend there, but of course he isn't. The day comes to life, the hustle and bustle of the streets heard through the falling drizzle.
This canto poignantly expresses Tennyson's enormous sense of loss over the death of Hallam. Even though his friend is no longer with him, he still feels his presence.
In Canto XX Tennyson uses servants as a metaphor to describe what he calls his "lesser griefs," that is, the ordinary little everyday miseries that affect most of us in life. These "servants" will never have another "master" to serve like Tennyson's dear, departed friend. In his absence they can do no more than acknowledge how good and kind he was.
When we reach Canto LXXVIII Tennyson and his family are once more celebrating Christmas without Hallam. On the surface, everything seems fine, with everyone enjoying the festive season. Appearances are deceptive, however. For the joy of the Christmas holiday merely serves to remind Tennyson of happier times, of past Christmases spent with his special friend. He indulges in festive games with his family and friends, just as he once did with Hallam, but it is not quite the same. And although Tennyson doesn't cry, he still feels so terribly sad inside.

Consider a cylinder of radius R , mass M , length z , and density rho(r)=Ar that rolls without slipping down an inclined plane of height h at an angle theta . What is the velocity of the cylinder at the bottom of the inclined plane?

We will use conservation of energy to solve this problem. We need to consider the rotational energy of the cylinder and the translational energy of the center of mass.
E_i=E_f
U(h)=K_(trans)+K_(rot)
Mgh=1/2 Mv^2+1/2 I omega^2
Mgh=1/2 Mv^2+1/2 I (v/R)^2
We need to find the moment of inertia.
I= int r^2 dm=int r^2 rho(r) dv
I=int_0^R r^2 rho(r) z (2pi r) dr
I=2pi zA int _0^R r^4 dr
I=(2pi zAR^5)/5
Now to get A in terms of M .
M=int dm=int_0^R rho(r) z(2pi r) dr
M=2A z pi int_0^R r^2 dr=2A z pi (1/3)R^3
A=(3M)/(2z pi R^3)
I=(2pi zAR^5)/5=(2pi z)(3M)/(2z pi R^3)*(R^5/5)=3/5MR^2
Now solve the energy equation for v .
Mgh=1/2 Mv^2+1/2 I (v/R)^2
2Mgh=Mv^2+(3/5MR^2)*(v/R)^2
2gh=v^2+(3/5)v^2
2gh=(8/5)v^2
5/4 gh=v^2
sqrt(5gh)/2=v
http://hyperphysics.phy-astr.gsu.edu/hbase/rotwe.html

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 24

y=1/x^2-1/(x-2)^2
To determine the asymptotes, express the function as a single fraction. Since the LCD of the two fractions is x^2(x-2)^2, then, the function becomes:
y = 1/x^2 * (x-2)^2/(x-2)^2 - 1/(x-2)^2*x^2/x^2 = (x-2)^2/(x^2(x-2)^2)-x^2/(x^2(x-2)^2)=(x^2 - 4x+4)/(x^2(x-2)^2) - x^2/(x^2(x-2)^2)
y=(-4x+ 4)/(x^2(x-2)^2)
Then, refer to the degree of the numerator and denominator to get the horizontal asymptotes. The degree of the numerator is 1 and the degree of the denominator is 4. Since the degree of the numerator is less than that of the denominator, thus, the horizontal asymptote is y=0 .
To get the vertical asymptotes, take note that in fraction zero denominator is not allowed. So, solve for the values of x that would result to zero denominator.
x^2(x-2)^2=0
Set each factor equal to zero.

x= 0


x-2=0
x=2
Hence, the vertical asymptotes are x=0 and x=2 .
Next, plot the asymptotes.

Notice that it divides the xy plane into six regions. To determine which region will the curves belong, determine at least two points for the region at the left of x=0, between x=0 and x=2 and at the right of x=2.
For the region at the left of x=0, the points are:
y=1/(-3)^2 - 1/(-3-2)^2=16/225 (-3,16/225)
y=1/(-1)^2 - 1/(-1-2)^2=8/9 (-1,8/9)
So at the left of x=0, the curve is located above the horizontal asymptote.
For the region between x=0 and x=2, the points are:
y=1/(1/2)^2-1/(1/2-2)^2=32/9 (1/2,32/9)
y=1/1^2-1/(1-2)^2=0 (1,0)
At region between the x=0 and x=2, the curve crosses the horizontal asymptote.
And for the region at the right of x=2, the points are:
y=1/3^2-1/(3-2)^2=-8/9 (3,-8/9)
y=1/5^2-1/(5-2)^2=-16/225 (5,-16/225)
So at the right of x=2, the curve is located below the horizontal asymptote.
To determine the maximum and minimum points, take the derivative of the function.
y=1/x^2-1/(x-2)^2 = x^(-2) - (x-2)^(-2)
y'=-2x^(-3)-(-2)(x-2)^(-3)
y'=-2/x^3 + 2/(x-2)^3
Then, solve for the critical numbers. To do so, set the derivative equal to zero.
0=-2/x^3 + 2/(x-2)^3
0= -2/x^3*(x-2)^3/(x-2)^3+2/(x-2)^3*x^3/x^3
0=(-2(x^3-6x^2+12x-8))/(x^3(x-2)^3)+(2x^3)/(x^3(x-2)^3)
0=(-2x^3+12x^2-24x+16)/(x^3(x-2)^3)+(2x^3)/(x^3(x-2)^3)
0=(12x^2-24x+16)/(x^3(x-2)^3)
0=12x^2-24x+16
0=3x^2-6x+4
Apply quadratic formula to solve for x.
x=(-b+-sqrt(b^2-4ac))/(2a)
x=(-(-6)+-sqrt((-6)^2-4(3)(4)))/(2*3)=(6+-sqrt(-12))/6
Since the number inside the square root is negative, the values of x are non-real number. It means that there are no values of x that will result to y'=0.
However, to get the critical numbers, consider also the values of x which make the first derivative undefined. y' is undefined when its denominator is equal to zero.
x^3(x-2)^3=0
Set each factor equal to zero.


x=0

(x-2)^3=0
x-2=0
x=2
So the critical numbers are x=0 and x=2. Notice that these are also the vertical asymptotes. This means that the function has no maximum or minimum points.
Next, determine the intervals in which the function is increasing and decreasing.
Take note that the boundaries of the interval in which the function is increasing or decreasing are the critical numbers x=0 and x=2. So the intervals that should be considered are (-oo, 0) , (0,2) and (2,oo) .
Then, take the a test value for each interval. Plug-in them to the first derivative.

y'=-2/x^3 + 2/(x-2)^3
If the result of y' is negative, the function is decreasing in that interval. If it is positive, the function is increasing in that interval.
For the first interval (-oo, 0) , let the test value be x= -1.
y'=-2/(-1)^3+2/(-1-2)^3=2-2/27=52/27 (increasing)
For the second interval (0,2), let the test value of be x=1.
y'=-2/1^3+2/(1-2)^3=-4 (decreasing)
And for the third interval (2,oo) , let the test value be x=3.
y'=-2/3^3+2/(3-2)^3=52/27 (increasing)
Thus, the function is increasing at intervals (-oo, 0) uu (2,oo) . And it is decreasing at interval (0,2) .
Next, determine the inflection. So take the second derivative of the function.
y'=-2/x^3 + 2/(x-2)^3=-2x^(-3)+2(x-2)^(-3)
y''=6x^(-4)-6(x-2)^(-4)
y''=6/x^4-6/(x-2)^4
Then, set the second derivative equal to zero.
0=6/x^4-6/(x-2)^4
0=6/x^4*(x-2)^4/(x-2)^4 - 6/(x-2)^4*x^4/x^4
0=(6(x-2)^4)/(x^4(x-2)^4)- (6x^4)/(x^4(x-2)^4)
0=(-48x^3+144x^2-192x+96)/(x^4(x-2)^4)
0=-48x^3+144x^2-192x+96
0=-48(x^3-3x^2+4x-2)
0=x^3-3x^2+4x-2
To solve, factor it by grouping.
0=x^3-1 - 3x^2+4x - 1
0=(x^3-1) - (3x^2-4x+1)
0=(x-1)(x^2+x+1) - (x-1)(3x-1)
0=(x-1)[(x^2+x+1)-(3x-1)]
0=(x-1)(x^2-2x+2)
Here, consider only the factor (x - 1). It is because setting the factor (x^2-2x+2) equal to zero would result to a non-real number.
0=x - 1
1=x
Hence, the change of concavity occurs only at x=1.
Next, determine the concavity of the intervals (-oo, 0) , (0,1) , (1,2) and (2,oo) . To do so, assign a test value for each interval and plug-in them to the second derivative.
y''=6/x^4-6/(x-2)^4
Take note that if the resulting value of y" is positive, the function is concave up in that interval. And if the resulting value of y" is negative, the function is concave down.
For the first interval (-oo,0) , let the test be x=-1.
y''=6/(-1)^4-6/(-1-2)^4=160/27 (concave up)
For the second interval (0,1) , let the test value be x=1/2.
y''=6/(1/2)^2-6/(1/2-2)^4=2560/27 (concave up)
For the third interval (1,2), let the test value be x=3/2.
y''=6/(3/2)^4-6/(3/2-2)^4=-2560/27 (concave down)
And for the last interval (2,oo) , let the test value be x=3.
y''=6/3^4-6/(3-2)^2=-160/27 (concave down).
Thus, the function is concave upward in the intervals (-oo,0) uu (0,1) . And it is concave downward in the intervals (1,2) uu (2,oo) .
Therefore, the graph of the function y = 1/x^2-1/(x-2)^2 is: