College Algebra, Chapter 4, 4.4, Section 4.4, Problem 66

Determine how many positive and how many negative real zeros the polynomial $P(x) = x^4 + x^3 + x^2 + x + 12$ can have, using the Descartes' Rule of signs. Then determine the possible total number of real zeros.

$P(x)$ has no variation in sign, so there are no positive roots.

Now,


$
\begin{equation}
\begin{aligned}

P(-x) =& (-x)^4 + (-x)^3 + (-x)^2 + (-x) + 12
\\
\\
P(-x) =& + x^4 - x^3 + x^2 - x + 2

\end{aligned}
\end{equation}
$


So $P(-x)$ has four variations in sign. Thus, $P(x)$ has either $4, 2$ or negative roots, making a total of either $5, 3$ or $1$ real zeros. Since is a zero but is neither positive nor negative.

The Articles of Confederation created what type of system of government?

The Articles of Confederation set up a system of governance in which the federal government was much less centralized than in our current system. Within this system, states and local governments were given much more power. Through this, those in favor of the Articles of Confederation believed common folks would be able to have more control over their lives and the political process. The decentralization also allowed less room for enacting large-scale laws that weren't relevant for large portions of the population. Under the Articles of Confederation, the federal government was unable to draft people into a national military or interfere in many state decisions. The decentralization of the federal government, however, did make the continuation of slavery in southern states more cemented because there was no strong government entity that could stop its continuation or expansion.

The Articles of Confederation created a confederation type of government. In a confederation form of government the states retain most of the power. When the Articles of Confederation were written, the federal government had significant limits put on what it could do. For example, the federal government couldn’t levy taxes. The federal government couldn’t make people join the military. The federal government also couldn’t resolve disputes between the states.
Because of these limits, the federal government created under the Articles of Confederation had many issues. There were financial issues. It was difficult for the government to pay its debts. It had trouble dealing with countries like Great Britain and Spain that were pushing us around and interfering with our trade. The federal government also had trouble keeping order. This was very clear when Shays’ Rebellion occurred.
Thus, the Article of Confederation created a system of government in which the federal government had limited powers while the state governments had many powers.
https://www.history.com/topics/early-us/articles-of-confederation

In Neil Gaiman's "How to Talk to Girls at Parties," what do you think Vic sees at the end of the story that upsets him so much?

At the end of the story, Vic hurries Enn home. Vic is visibly nervous and agitated about what he's just seen.
Although the author is ambiguous about the reason for Vic's angst, the text provides some hints:

We ran then, me and Vic, away from the party and the tourists and the twilight, ran as if a lightning storm was on our heels. . . I held on to a wall, and Vic threw up, hard and long, into the gutter. (Because of what he's seen, Vic is upset enough to throw up). He wiped his mouth. "She wasn't a--" He stopped. (The girl Vic was with, Stella, wasn't human). He shook his head. Then he said, "You know. . . I think there's a thing. When you've gone as far as you dare. And if you go any further, you wouldn't be you anymore? You'd be the person who'd done that? The places you just can't go. . . I think that happened to me tonight." (Does Vic metaphorically or literally mean that he's gone as far as he dares?)

Although this portion of the text is frustrating (perhaps because it's so ambiguous), it's also humorous. On one level, human girls can be so alien in temperament and emotional make-up to boys that they invite curiosity and amusement from their male counterparts. On another level, Gaiman explores how an interplanetary being could actually be so unusual to a human boy that, upon disrobing, she would devastate him. From the text, we can extrapolate that the experience of trying to bed an alien girl was extremely traumatizing for Vic. He was so traumatized by what he saw that he wasn't prepared to go any further. In fact, Stella's emphatic "I am not finished. There is yet more of me" further repels Vic.
So, it appears from the story that Neil Gaiman is posing a distinctly amusing question: if a male teenager thinks that girls are strange, what will he do when he meets a real, interplanetary female alien?

What are some ideas for a thesis statement about choosing to die?

A thesis statement should offer your reader a concise summary of the argument you are going to try to persuade them of in your essay. It indicates your position on the subject; therefore, before you begin writing your thesis statement, you need to decide how you feel about the subject at hand.
You don't say how you feel about the idea of choosing to die. There are two key positions on this controversial topic, which oppose each other. Either you believe that it is the right of an individual to choose euthanasia for themselves, or you believe that it isn't. There is greater nuance to this, of course--you may feel, morally, that people in pain should be able to choose to die, but that the system is too open to abuse for it to be legally advisable. Or you may feel that it should be for God to decide when individuals die, and that allowing euthanasia is morally wrong. On the other hand, you could argue that the right to choose death is a fundamental human right for those who are suffering and in pain, and that it is an indignity to force humans to live on in states we would not tolerate in an animal.
Whatever your opinion on the subject, your thesis statement should establish whether you support the right to die or not, and give some indication as to why. You should also, however, acknowledge that there are multiple positions on the issue, as you will need to explore these in your essay. For example:
While it can seem difficult to justify prolonging the suffering of humans in pain, the concept of the "right to die" can open the door to many conflicting moral issues and could introduce a system that would be open to abuse, having ramifications far beyond the individual.
OR
While many oppose the idea of euthanasia on moral or religious grounds and it could be difficult to implement a system of euthanasia legally, the right to die should be in enshrined in law as a means of offering dignity and control to those who choose to escape their physical suffering.

How to write an essay on moral theology?

Moral theology, a Catholic teaching, is:

A branch of theology, the science of God and Divine things . . . [which] is limited to those doctrines which discuss the relations of man and his free actions to God, and his supernatural end, and propose the means instituted by God for the attainment of that end.

In other words, moral theology is interested in how a person's actions line up with divine intent. It assumes that God has created humans with the free will to make their own choices and that he has provided us with methods and instructions to act in accordance with his will. If morality is a discussion of how actions are determined to be right or wrong and theology is the study of God and his nature, then moral theology is the intersection between divine will and human action. Moral actions would be those that line up with divine will, while immoral actions would be those that deviate from it. 
There are a few approaches you could when writing an essay on moral theology. First, you could summarize and examine what moral theology is and what it teaches (as done above). Second, you could explore figures and teachings in Catholic history that are relevant to the development of moral theology. St. Thomas Aquinas, John Finnis, and the various papal encyclicals that deal with human action would be good sources to investigate. Third, you could look at how Catholic moral theology compares and contrasts to other sets of ethics. Within Christianity, you could compare Catholic morality to Protestant morality, or you could compare it to Buddhist or Islamic ways of thinking. 
The links below can provide further information to help you. Good luck!
http://www.newadvent.org/cathen/14601a.htm

http://www.pathsoflove.com/blog/2010/02/aquinas-moral-theology/

https://www.ethicssage.com/2012/09/the-role-of-ethics-in-religion.html

Did barbarian invasions worsen or improve the condition of women in western Europe? What were gender roles in the Roman empire and early Germanic society?

The late Roman Empire was defined by a strict adherence to Christianity. In fact, the Olympic Games were briefly cancelled due to their connection with and ostensible worship of the pagan god Zeus.
Christianity without a doubt promoted the idea of specific and unequal gender roles in society. Since the disciples of Jesus were all male, only men were allowed to become priests. This idea reinforced separate gender roles, and men were granted more rights in the Roman Empire than women. Women were expected to handle the domestic tasks in the household. As the Roman Empire become older, the citizens became lazier and began outsourcing defense by hiring barbarian mercenaries to defend their border.
On the other hand, the barbarians and early Germanics did not embody these same gender roles. Women took leadership roles within barbarian society. So, in the short term, the barbarian invasions helped improve the condition of women in western Europe.
However, in the long run, the influence of Christianity prevailed, and there is evidence that the Dark Ages, which followed the fall of the Roman Empire, reinforced the Christian gender roles. So, the condition of women did not significantly improve following the barbarian invasions, primarily due to the mass adoption of Christianity.

An interesting question. The barbarian invasions of Rome represented a dramatic shift in European power dynamics. The Fall of Rome, marked by most as occurring in 476 CE when the last Roman Emperor was eclipsed by a German barbarian leader, led to important changes. Some of these changes involved gender roles.
Roman society was highly gendered. It was a true patriarchy, and the role of women was to be entirely subservient to men. Many are the Roman funerary monuments attest to the value of a woman's role being thoroughly domestic. Women were definitely second-class citizens, not even allowed to watch the gladiatorial combats close up, unless they were Vestal Virgins.
Barbarian societies and early Germanic society, in contrast, tended to be more egalitarian. Or at least, that's was how it was portrayed. There were cases of famous women leaders, such as Boudica, who led the Welsh in their resistance against the Romans in the 1st c. CE. But much of this may be exaggeration and mythology.
What is clear is Christianity had a major impact on the post-Roman Empire barbarian cultures, which only reinforced more traditional gender roles and the power of patriarchy. Still, one suspects there was more equality in these Dark Ages barbarian societies than in the Roman Empire.

How is Our Town a modern American play?

Thornton Wilder's Our Town is not only a masterpiece of American drama but one of the earliest and finest works of modernism in theatrical plays. The play, which is set entirely in Grover's Corners, New Hampshire, focuses heavily on the passage of time and the infinite transience of life.
Our Town finds its roots in modernism through many characteristics of the play itself, most predominately its minimalist stage settings and theatrical style, its focus on the universality of ordinary American life, and the narrator's frequent engagement with the audience.
At the beginning of the play, the narrator—also known as the Stage Manager—speaks directly to the audience. While a technique similar to this had been used for centuries before (particularly in Richard III and several other Shakespeare works, in which a character shares motivations, thoughts, or sly comments with the audience) it is used here in a unique way. The Stage Manager describes the world of Grover's Corners, sets the particular date, introduces several characters, and sets any necessary backstory through exposition. This is a modernist technique that strays from the traditional narrative forms of theater, drawing instead on traditions found in written novels with omniscient narrators.
The bare and minimalist stage settings require active participation from the audience in the form of imagination. Where other plays may utilize extravagant costumes and lush theatrical sets, Our Town transcends the particularity that a crafted set might offer.
Through its many inventive and bold approaches to theater, Our Town was an early example of the countless opportunities that creative freedom would offer in American theater. From the grounds laid down by Thornton Wilder and Our Town, many other modernist American plays, such as Death of a Salesman and The Glass Menagerie were able to sprout.

What is the name of Harpo's new club?

Celia refers to the jukejoint in her letters as Harpo's. At one point she states that Harpo would cross out the names of jukejoints from old jukejoint signs he was given and replace them with his name and location so "The Lucky Star of Coalman Road" would become "Harpo's of ___ Plantation (the blanks also appear in Celia's letters)
Harpo starts building the jukejoint after Sofia leaves him. Since she had left he says he had found a knack for making money. Celia questions why he would build a bar back in the woods, but he tells her "Jukejoint 'sposed to be back in woods... the polices don't know where to look." He puts his signs up on the trees by the roadside and waits for people to come.
Business finally perks up when Shrug begins performing there every weekend "First night or two her songs come out good but a little weak, now she belt them out"
Celia describes Harpo's as

It's nice at Harpo's. Little tables all round the room with candles on them that I made, lot of little tables outside too, by the creek. Sometime I look down the path from our house and it look like a swarm of lightening bugs all in and through Sofia house.

Harpo's new club is called Harpo's jukejoint, and he builds it, getting it up and running after Sofia leaves him. This is where Shug Avery resumes her singing career, after her prolonged illness and during her initial stay at Celie and Albert's house. It is where Shug first performs "Celie's Song," the one she says that Celie scratched out of Shug's head when Shug was sick. This is also where Squeak, later called Mary Agnes, gets her start as a singer—that is, of course, after her initial fight with Sofia (when she slaps Sofia in the head for dancing with Harpo, and then Sofia punches Squeak in the mouth, knocking out two of her teeth). Harpo's Jukejoint becomes a kind of family business.

In "The Most Dangerous Game," what happens to the men if they choose not to be hunted?

In the short story “The Most Dangerous Game” by Richard Connell, people who refuse to be hunted are beaten to death by Ivan, a giant of a man who used to whip people to death for the Czar of Russia.
In this story, the villain is a man named General Zaroff.  Zaroff lives on “Ship Trap Island,” which is somewhere in the Caribbean Sea. Zaroff’s life passion is hunting. During his career as a hunter, he eventually became bored because hunting wild animals is too easy. He decided he wanted to hunt human beings since they are intelligent and would be more challenging to hunt. Humans are “the most dangerous game” to which the story’s title refers. Zaroff obtained Ship Trap Island and uses shipwrecked sailors (including some whose ships were wrecked thanks to false navigational lights that Zaroff rigged up at sea) as his prey.
When Zaroff tells Rainsford this, Rainsford wonders how he gets the men to agree to be hunted. Zaroff tells Rainsford that the men have the choice of possible death in the hunt or certain death at the hands of Ivan. When Rainsford asks, “Suppose he refuses to be hunted,” Zaroff replies,

"I give him his option, of course. He need not play that game if he doesn't wish to. If he does not wish to hunt, I turn him over to Ivan. Ivan once had the honor of serving as official knouter to the Great White Czar, and he has his own ideas of sport. Invariably, Mr. Rainsford, invariably they choose the hunt."

As you can see in this link, the knout was a brutal whip used in Russia to flog criminals. Very often, the criminal was beaten to death. Ivan performed this duty for the Czar and, Zaroff implies, enjoys inflicting pain on people.
The answer to your question, then, is that people who refuse to be hunted are handed over to Ivan to be beaten to death.

How is the election of Abraham Lincoln as U.S. president in 1860 connected to the Confederate attack on Fort Sumter on April 12-13, 1861?

Abraham Lincoln was elected in November 1860; by December, South Carolina would host a secession convention, thus becoming the first state in what would become the Confederate States of America. South Carolina slave owners and many others in the Deep South feared that Lincoln's election meant the end of slavery, even though Lincoln's political platform only mentioned stopping slavery where it had already existed. Before April 1861, the Lower South had already seceded. South Carolina seized Fort Moultrie as it was on what they regarded as their property, even though it was a federal military installation. In the waning days of the Buchanan presidency, he sent a ship to resupply another beleaguered garrison at Fort Sumter--the ship was fired upon by Confederate shore batteries. Lincoln therefore did nothing to relieve the fort but did not give the commander there, Major Robert Anderson, permission to surrender. Lincoln did not send ammunition to the fort but rather waited for the Confederacy to fire the first shots of the war, which it did on April 12, 1861.

After Abraham Lincoln was elected in early November of 1860, the Confederate states began to secede from the country. South Carolina was the first Confederate state to secede, in December of 1860. When this occurred, the federal troops that had been stationed in Charleston, South Carolina, evacuated from the city and relocated to Fort Sumter in Charleston Harbor. The federal troops regarded the fort as located on federal ground, but the Confederates claimed the fort as their own. After Lincoln assumed office in March of 1861, he was pressured to take some action about Fort Sumter, as the troops in the fort (who had been sent supplies by the previous President, Buchanan, in January of 1861), were running out of supplies. In early April, Lincoln decided to send supplies to the fort but said he would not send ammunition if the Confederacy did not attack. However, on April 12, 1861, the Confederacy fired on the fort, and the Civil War began. 

What impression of the main character and his situation is created by the opening dialogue, in which he begs his son to medicate?

In the opening section of Juan Rulfo’s “Tell Them Not to Kill Me!”, the impression of Juvencio Nava, the main character, is that of a desperate, selfish, and terrified individual who will do anything to stay alive. Rulfo paints the situation as incredibly dire—Juvencio’s life is in jeopardy. However, there is a role reversal here as well. Typically, we are all trained to believe that parents will do anything to protect their offspring. However, in the story’s opening dialogue, we see Juvencio willingly and passionately put his own life before his son’s. After Juvencio asks Justino to intervene on his behalf, Justino protests and says, “If I keep bothering them they’ll end up knowing who I am and will decide to shoot me too.” This statement does nothing to stop Juvencio from continuing to beg his son for help. When Justino expresses concern over who will care for his own children if he is killed trying to help his father, Juvencio’s only answer is that God will care for them. So here we have a man so desperately selfish and afraid that he is willing to put his own life before the welfare of his son and his (eight) grandchildren. Although Juvencio’s survival instincts are relatable, his willingness to risk his own family’s welfare just so he can save himself is despicable.

In the short story "Tell Them Not to Kill Me!", by Juan Rulfo, Juvencio, now an old man, is pleading with his son, Justino, to speak to the colonel and beg for his father's life.
The reader gets the impression that Juvenico is in a dire situation. He is tied to a post begging his son to attempt to save his life, "For God's sake! Tell them [not to kill me]" (para 1). Juvenico brutally killed a man thirty-five years earlier and has been hiding from the law ever since. Now that he is an old man, he feels that he is close to death anyway and shouldn't be executed for the crime that took place so long ago. It is clear he will do anything to save his life, including endangering his son.
Justino does not want to speak to the sergeant or the colonel because he fears for his own life if they discover he is Juvencio's son. As well, the son has a wife and children and asks his father what will happen to them if they shoot him.
The reader gets the impression that Juvencio will do anything to save his own life. By the end of the story, this is reinforced as we discover that he has spent his entire life simply trying to stay alive no matter what the cost.

When Juvencio is exhorting his son to try to intervene (mediate) on his behalf, the reader's impression of him is that he is desperate to remain alive; so much so, in fact, that he ignores the fact that he might endanger his son. His behavior arouses the sympathy of the reader; what person wouldn't want to avoid execution? At the same time, his lack of concern for the perilous position he would be putting his son in seems morally repugnant. The situation is definitely one of life and death, and, at the beginning of the story, it is not yet clear which man will lose his life, or if perhaps they both will. Justino, Juvencio's son, agrees to try to intervene, though it is clear that he is conflicted and worried about what would happen to his family if he were to be killed as a result of getting involved in his father's problem. Juvencio's assurance that God would look after Justino's family is shocking, because of Juvencio's selfishness in expecting his son to gamble with his life on his behalf.

A particle has the wavefunction Psi(x)=A(1-x^2) for |x|

The probability that a particle with the wavefunction Psi(x) will be found in some region R is  int_R |Psi(x)|^2 dx. In our problem it is
int_(-oo)^0 |Psi(x)|^2 dx =int_(-1)^0 |Psi(x)|^2 dx =int_(-1)^0 (A(1-x^2))^2 dx.
We can compute this integral in terms of A and can even find A from the normalization condition  int_(-oo)^oo |Psi(x)|^2 dx = 1, but it is not necessary for this particular problem.
Because this wavefunction is even, its square is also even and the integral over the left semiaxis is the same as over the right semiaxis. Together these equal integrals give 1, thus each of them is equal to 1/2. This is the answer: the probability the particle will be found in the region xlt0  is 1/2.
 
http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_6/node1.html

Finite Mathematics, Chapter 1, Review Exercises, Section Review Exercises, Problem 16

Determine an equation in the form $y = mx + b$ (where possible) for the line
that goes through $(2,-3)$ and $(-3,4)$
Let $(x_1 , y_1) = (2, -3)$ and $(x_2 , y_2) = (-3, 4)$.

$
\begin{equation}
\begin{aligned}
y - ( - 3) &= \frac{4 - (-3)}{-3 - 2} (x - 2)\\
\\
y + 3 &= \frac{4 + 3}{- 3 - 2} ( x- 2 )\\
\\
y + 3 &= \frac{-7}{5} (x - 2)\\
\\
y + 3 &= \frac{-7}{5}x + \frac{14}{5}\\
\\
y &= \frac{-7}{5}x - \frac{1}{5}
\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 8, 8.3, Section 8.3, Problem 10

Indefinite integrals are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
To evaluate the given problem int sin^4(6theta) d theta , we may apply u-substitution by letting: u = 6theta then du = 6 d theta or (du)/6 = d theta .
The integral becomes:
int sin^4(6theta) d theta=int sin^4(u) * (du)/6
Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int sin^4(u) * (du)/6=1/6int sin^4(u)du .
Apply the integration formula for sine function: int sin^n(x) dx = -(cos(x)sin^(n-1)(x))/n+(n-1)/n int sin^(n-2)(x)dx .
1/6int sin^4(u)du=1/6[-(cos(u)sin^(4-1)(u))/4+(4-1)/4 int sin^(4-2)(u)du] .
=1/6[-(cos(u)sin^(3)(u))/4+3/4 int sin^(2)(u)du]
For the integral int sin^(2)(u)du , we may apply trigonometric identity: sin^2(x)= 1-cos(2x)/2 or 1/2 - cos(2x)/2.
We get:
int sin^(2)(u)du = int ( 1/2 - cos(2u)/2) du .
Apply the basic integration property:int (u-v) dx = int (u) dx - int (v) dx .
int ( 1/2 - cos(2u)/2) du=int ( 1/2) du - int cos(2u)/2 du
= 1/2u - 1/4sin(2u)+C
or u/2 - sin(2u)/4+C
Note: From the table of integrals, we have int cos(theta) d theta = sin(theta)+C.
Let: v = 2u then dv = 2du or (dv)/2= du
thenint cos(2x)/2 du =int cos(v)/2 * (dv)/2
= 1/4 sin(v)
= 1/4 sin(2u)
Applying int sin^(2)(u)du=u/2 - sin(2u)/4+C , we get:
1/6int sin^4(u)du=1/6[-(cos(u)sin^(3)(u))/4+3/4 int sin^(2)(u)du]
=1/6[-(cos(u)sin^(3)(u))/4+3/4 [u/2 - sin(2u)/4]]+C
=1/6[-(cos(u)sin^(3)(u))/4+(3u)/8 - (3sin(2u))/16]+C
=(-cos(u)sin^(3)(u))/24+(3u)/48 - (3sin(2u))/96+C
Plug-in u =6theta on (-cos(u)sin^(3)(u))/24+(3u)/48 - (3sin(2u))/96+C to find the indefinite integral as:
int sin^4(6theta) d theta =(cos(6theta)sin^(3)(6theta))/24+(3*6theta)/48 - (3sin(2*6theta))/96+C
=(cos(6theta)sin^(3)(6theta))/24+(18theta)/48 - (3sin(12theta))/96+C
=(cos(6theta)sin^(3)(6theta))/24+(3theta)/8 - (sin(12theta))/32+C

What were the results of bombing Nagasaki and Hiroshima during World War II?

Long-term, the bombings of Nagasaki and Hiroshima showed the world the power of an atomic weapon.  The Soviet Union distrusted America for using the weapon to end the war and the Russians started to capture nuclear scientists all over their sector of Germany in order to work on their own version of "the bomb."  After the Soviets developed nuclear weapons, both sides sought to increase their nuclear capacity, because in a nuclear war, it was understood that whoever fired first would win, and that nuclear warfare would most likely cause destruction all over the world.  The Soviets and Americans soon developed bomber fleets, intercontinental ballistic missiles, and nuclear submarines in order to bomb cities.  Politicians in both countries used nuclear preparedness as a rallying cry, and John F. Kennedy was elected in 1960 because the previous administration created an alleged "missile gap" which did not exist.  The Cuban Missile Crisis was sparked by the threat of a nuclear war, and it opened up negotiations between the White House and Kremlin.  The United Nations took an active role in deciding which nations could have nuclear weapons after the fall of the Soviet Union, and this fear of nuclear proliferation has meant economic sanctions for North Korea and regime change in Iraq.  
There were some peaceful things to come out of the nuclear arms race, however.  Scientists developed nuclear power, and "nuclear" became a positive buzzword of the 1950s.  The ideal family was said to be "nuclear" if it had a mom, dad, and children.  Through developing intercontinental ballistic missiles, scientists also developed the rockets needed to go into space.  America poured more money into teaching children math and science in order to create a new generation of scientists.  
Short-term results of the bombing are that Nagasaki and Hiroshima were wiped off the face of the Earth, thousands died due to radiation poisoning and the blast itself, and imperial Japan surrendered, thus making unnecessary the invasion of Japan slated for November 1945.  America became the sole occupier of Japan, tried its war criminals, and assisted with the creation of the new Japanese constitution that was more liberal than America's at the time.  

Based on The Scarlet Letter, do we assume that we should be without flaw or sin? Should we never show that we have made a mistake?

In the final chapter of the novel, "Conclusion," the narrator says that "in the view of Infinite Purity, we are sinners all alike."  Therefore, despite the fact that some people try to live without sin—and some others pretend to do so—as human beings, we are fundamentally flawed and incapable of perfection.  If we were perfect, we would be gods.  The narrator claims that we are all sinners, every one of us, and so we cannot ever be totally without sin or flaw in the eyes of God.
Further, the narrator says,

Among the many morals which press upon us from the poor minister's miserable experience, we put only this into a sentence: "Be true!  Be true!  Be true!  Show freely to the world, if not your worst, yet some trait whereby the worst may be inferred!"

In other words, more important than being sinless—which the narrator has already identified as an impossibility—the narrator claims that we should be honest about our sinfulness.  If we are all, at least, honest about our sinful natures (if not our specific sins), then perhaps we will be less likely to judge one another (as the Puritans in the story do) and the guilt we feel for our sins will not be allowed to eat away at us (as Dimmesdale's guilt done to him). 

How is Stargirl different from other girls?

With a character named Stargirl, a reader could only hope for someone fabulously captivating—and that is exactly what Jerry Spinelli delivers in this novel. But to contrast Stargirl with "other girls" would require putting all "other girls" in a box together, and that isn't really possible. Stargirl would probably not even be cool with that herself. So let's instead look at how Stargirl is one of the most individualistic characters of all time, regardless of gender.
Stargirl is compassionate beyond measure. The girl sends thoughtful gifts anonymously to unsuspecting people just to be kind. She cheers when a kid on the other team makes a basket. She attends the funeral of a stranger. Stargirl doesn't just make a halfhearted effort to spread love to the world; she really engages with people on a deep level. She seems to feel both the world's collective pain and its joy and takes active measures to connect with people in both situations. Sadly, many of her efforts only create anger and resentment at her school, isolating her from the very people she cheers on. Which brings us to another unique personality characteristic of Stargirl:
She really and truly doesn't seem to care what people (collectively) think about her quirkiness. Lots of people lay claim to this feeling, but as a whole, people dress and act a certain way because society and/or the group they long to be a part of have particular expectations for these behaviors. Stargirl dresses as she wants. She befriends whom she wants. She doesn't seem to care about the expected social norms at her high school (even cheering for people who stop to pick up litter) and when people get mad at Stargirl for acting very much like Stargirl, Leo notes that "she did not seem to notice" (chapter 11).
One more characteristic distinguishing Stargirl from the masses is that she seems to view the world in endless beauty and full of fascinating possibilities. She takes time to note the struggle of ants. She watches a lone man sitting on a park bench and dances in the rain. Stargirl is a true free spirit who cannot be easily classified.
Stargirl represents one of those characters everyone longs to meet in real life—someone who is passionate, loyal, and forever concerned with the welfare of the universe. Her unique personality makes her one of literature's most unforgettable characters.

Stargirl isn't only different from other girls. Stargirl is different from everybody. I would say the main character trait that makes her stand out from everybody else is her self-confidence. She simply does not care what other people think. That is how she is most definitely different from other high school girls her age. Stargirl does not care about fashion trends. She wears what she wants to wear regardless of what is in fashion. She does not play favorites, as illustrated by her cheering for both sports teams and singing Happy Birthday to strangers. Additionally, Stargirl most definitely does not spread catty rumors about people the way Hillari Kimble does. Stargirl embodies love. She loves everybody equally, and she loves them even when they don't love her in return. That's how she is different.  

Calculus of a Single Variable, Chapter 2, 2.1, Section 2.1, Problem 37

The given line is :-
x + 2y - 6 = 0
or, y = -(1/2)x + 3 (the line is represented in slope intercept form)
Thus, the slope of the line = -(1/2)
Now, the tangent to the curve f(x) = 1/(x^(1/2)) is parallel to the above line
Thus, the slope of the tangent = slope of the line = -(1/2).......(1)
The given function is:-
f(x) = 1/(x^(1/2))
differentiating both sides w.r.t 'x' we get
f'(x) = -(1/2)*[1/{x^(3/2)}]
Now, slope of the tangent = -(1/2)
Thus, -(1/2)*[1/{x^(3/2)}] = -(1/2)
or, x = 1
Putting the value of x =1 in the given equation of curve, we get
f(1) = y = 1
Hence the tangent passes through the point (1,1)
Thus, equation of the tangent at the point (1,1) and having slope = -(1/2) is :-
y - 1 = (-1/2)*(x - 1)
or, 2y - 2 = -x + 1
or, 2y + x - 3 = 0 is the equation of the tangent to the given curve at (1,1)

What is the conflict in the book Many Waters?

The major conflict in Many Waters is the fact that Sandy and Dennys Murry have been transported back to Biblical times (before the great flood) after interfering with their father's computer. Mr. Murry is an astrophysicist who studies space and time, so when Dennys types "take me someplace warm" into the computer, it transports them through time, and the twins find themselves in an unknown desert. The boys are burned badly by the sun and do not know where they have been transported. Throughout the book, the fact that the twins are in another time, away from their family, and unsure of how to go back is a major conflict, as they desire to return home even after adapting to the location and developing relationships with other characters.

College Algebra, Chapter 1, 1.4, Section 1.4, Problem 34

Evaluate the expression $i^{1002}$ in the form of $a + bi$.


$
\begin{equation}
\begin{aligned}
&= i^{1002}\\
\\
&= i^{1000+2}\\
\\
&= i^{1000} \cdot i^2\\
\\
&= (i^2)^{500} \cdot i^2\\
\\
&= (-1)^{500} \cdot i^2\\
\\
&= i^2\\
\\
&= -1
\end{aligned}
\end{equation}
$

In the novel Of Mice and Men how is George as a friend?Explain in one paragraph.

George is a relatively compassionate, understanding friend who protects and guides Lennie as they travel throughout the country looking for work. Even though George comes across as insensitive and short-tempered at times, he is always quick to apologize for his behavior and console his mentally handicapped friend. George is also aware of what motivates Lennie and leverages Lennie's affinity for rabbits to reinforce his positive behavior. Despite Lennie's lack of intelligence and propensity to cause trouble, George is a faithful friend who never leaves him behind. George is more than Lennie's companion; he is also Lennie's caretaker. George gives Lennie valuable advice throughout the novella, warning him to keep his mouth shut, stay away from Curley and his wife, and meet him by the river if anything goes wrong. George's decision to take Lennie's life before the lynch mob catches him also demonstrates George's love and devotion to Lennie. George calmly reiterates their dream to Lennie before pulling the trigger, which allows Lennie to die a peaceful death. Overall, George is a faithful, compassionate friend who protects and sticks beside Lennie through difficult times.

Does a bee have a penis?

Male bees do have a penis. When a male bee or drone mates with the female queen bee, its penis which is located internally is everted which means is turned inside-out during the process of mating and the sperm is deposited inside the female's vagina. Bees mate during flight. The sperm is ejected forcefully into the queen's genital tract. Queens can store sperm for a long period of time until their eggs are fertilized. 
When mating has concluded, the partners separate however, the bulb of the penis remains inside the queen's genital tract. This causes the male to die off soon after mating. It also insures a great deal of semen remains inside the queen's genital tract. Queens can mate with several different partners. 
I have included a link which has diagrams of the reproductive tracts of immature and mature drones and another describing honey bee mating.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1847503/

https://www.orkin.com/stinging-pests/bees/mechanics-of-honey-bee-mating

Why is Roger afraid in "Thank You, M'am"?

When Roger attempts to steal Mrs. Luella Bates Washington Jones's pocketbook, he trips, and Mrs. Jones quickly grabs him by the collar. As soon as Mrs. Jones grabs him by the collar and refuses to let go, Roger attempts to escape and becomes frightened that she will punish him for his attempted robbery. Roger believes that Mrs. Jones will either physically punish him or report him to the authorities. Mrs. Jones proceeds to drag Roger back to her home before she lets go of him and asks him several questions about his background and motivation to steal her pocketbook.
Immediately after Mrs. Jones lets go of Roger, he asks her if she is going to turn him into the police. As a young black male, Roger understands that the law is not on his side and fears being arrested. Ironically, Mrs. Jones does not punish or lecture Roger about his behavior and proceeds to make him a hot meal before giving him ten dollars to buy blue suede shoes. Mrs. Jones's benevolence and hospitality have a significant impact on Roger, who is astonished and appreciative of her generosity and forgiveness.

When Mrs. Jones takes hold of Roger and refuses to let him go, Roger is described as being "frightened." It is easy to see why Roger is afraid of Mrs. Jones. After all, he has just tried to steal her pocketbook and her reaction is one of anger. She tells Roger that she will wash his dirty face for him and teach him right from wrong. Moreover, Roger is afraid because she will not let him go, no matter how much he protests.
Like Roger, the reader might expect that Mrs. Jones will contact the police or, perhaps, take Roger back to her home and punish him. But the events which follow this scene could not be further from our expectations, thereby providing an example of situational irony. Mrs. Jones does take Roger home, but she washes and feeds him. She behaves kindly towards him and even gives him the money to buy a pair of suede shoes.

y=(x+4)/(x-3) Graph the function. State the domain and range.

To be able to graph the rational function y =(x+4)/(x-3) , we solve for possible asymptotes.
Vertical asymptote exists at x=a that will satisfy D(x)=0 on a rational function f(x)= (N(x))/(D(x)) . To solve for the vertical asymptote, we equate the expression at denominator side to 0 and solve for x.
In y =(x+4)/(x-3) , the D(x) =x-3.
Then, D(x) =0  will be:
x-3=0
x-3+3=0+3
x=3
The vertical asymptote exists at x=3 .
To determine the horizontal asymptote for a given function: f(x) = (ax^n+...)/(bx^m+...), we follow the conditions:
when n lt m     horizontal asymptote: y=0
        n=m     horizontal asymptote:  y =a/b
        ngtm       horizontal asymptote: NONE
In y =(x+4)/(x-3) , the leading terms are ax^n=x or 1x^1 and bx^m=x or 1x^1 . The values n =1 and m=1 satisfy the condition: n=m. Then, horizontal asymptote  exists at y=1/1 or y =1 .
To solve for possible y-intercept, we plug-in x=0 and solve for y .
y =(0+4)/(0-3)
y =4/(-3)
y = -4/3 or -1.333  (approximated value)
Then, y-intercept is located at a point (0, -1.333) .
To solve for possible x-intercept, we plug-in y=0 and solve for x .
0 =(x+4)/(x-3)
0*(x-3) =(x+4)/(x-3)*(x-3)
0 =x+4
0-4=x+4-4
-4=x or x=-4
Then, x-intercept is located at a point (-4,0) .
Solve for additional points as needed to sketch the graph.
When x=2 , the y = (2+4)/(2-3)=6/(-1)=-6 . point: (2,-6)
When x=4 , the y =(4+4)/(4-3) =8/1=8 . point: (4,8)
When x=10 , the y =(10+4)/(10-3)=14/7=2 . point: (10,2)
When x=-16 , the y =(-16+4)/(-16-3)=-12/(-19)~~0.632 . point: (-16,0.632)
Applying the listed properties of the function, we plot the graph as:

You may check the attached file to verify the plot of asymptotes and points.
As shown on the graph, the domain: (-oo, 3)uu(3,oo)
and range: (-oo,1)uu(1,oo).  
The domain of the function is based on the possible values of x. The x=3 excluded due to the vertical asymptote.
The range of the function is based on the possible values of y . The y=1 is excluded due to the horizontal asymptote. 

What is the relevance of the myths used in Hamlet?

There are a couple of key myths referenced in Hamlet. The most notable are the figures of Hyperion, Pyrrhus, and Hecuba.
In act 1, scene 2, Hamlet references the sun god Hyperion and compares him to his father. He says "so excellent a king, that was to this Hyperion to a satyr" (1.2.143-144). This is a short reference to a myth, but the comparison is used to express how perfect Hamlet believes his father was. He compares him to a sun god, but compares Claudius to the mischievous satyr, which is a creature that is half man and half goat.
In act 2, scene 2, when Hamlet encounters the players, he asks them to re-enact the story of Pyrrhus. This is significant, because in Virgil's Aeneid, Pyrrhus is a vengeful son of the warrior Achilles. Pyrrhus takes revenge on Priam and hacks him to death as revenge for the death of his father. This is significant in Hamlet because Hamlet is also seeking revenge for the death of his father.
After the players deliver the speech about Pyrrhus, they also describe the grief of Hecuba. This is significant for two reasons. Hecuba was Priam's wife, and she grieved wildly for him after his death. This is noticeably different from how Gertrude is behaving. Secondly, the actor playing Hecuba appears to genuinely be moved by extreme grief, and Hamlet is once again amazed at how an actor can feign such passion and grief, but he himself cannot bring himself to avenge a real situation.
https://iiste.org/Journals/index.php/JLLL/article/viewFile/29638/30431

https://www.folgerdigitaltexts.org/html/Ham.html

Determine the area "S" which the triangle "R" Project vertically upon the hemisphere. Check the attachment

Hello!
If a surface is given as an image of a scalar function y=f(x,z), defined on some region D on (x,z) plane, then the corresponding surface area is
int int_D sqrt(1+((del f)/(del x))^2+((del f)/(del z))^2) dx dz.
We have f(x,z) = sqrt(4-x^2-z^2), so (del f)/(del x) = -x/(sqrt(4-x^2-z^2)) and (del f)/(del z) = -z/(sqrt(4-x^2-z^2)). The expression under integral therefore is
sqrt(1+x^2/(4-x^2-z^2)+z^2/(4-x^2-z^2)) = 2/sqrt(4-x^2-z^2).
The problem is to express the double integral int int_D (2 dx dz)/sqrt(4-x^2-z^2) as a sequential one-dimensional integral. Because of the symmetry we can integrate only by a half of the triangle and then multiply by 2. The integration region is from -1/2 to 1 by z and from 0 to (1-z)/sqrt(3) by x.
A = 2 int_(-1/2)^1 (int_0^((1-z)/sqrt(3)) 2/sqrt(4-x^2-z^2)dx) dz.
This integral isn't so simple (inner integral is relatively simple), but at least we can compute it approximately. The answer is about 1.343.

Who is the main character, Sonny or the narrator? How would this story be different if it were told by Sonny?

The main character of "Sonny's Blues" is the narrator, who tries to come to terms with what has happened to his brother. At the outset of the story, after he hears that his brother has been arrested for selling heroin, the narrator says, "I couldn't believe it: but what I mean by that is that I couldn't find any room for it anywhere inside me." The story revolves around the narrator's attempt to make sense of what has happened to his brother by going back into their past and then watching his brother play music, an experience that helps the narrator understand who his brother is and what he values.
If Sonny had told the story, it would have been very different. Instead of Sonny's brother trying to figure out Sonny, Sonny could have told his own tale of what happened. Sonny would've explained what drove him to do drugs and how the narrator, his brother, and his family had not understood him. He would have perhaps included other reasons why he turned to drugs. "Sonny's Blues" involves one character trying to unravel the psychological mysteries of another character; if Sonny had told the story, it would have involved less psychological mystery and would have been a more straightforward narrative. 

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 6

Determine the equation of the tangent line to the curve $y = 2x^3 - 5x$ at the point ( -1, 3)

Using the definition (Slope of tangent line)


$
\begin{equation}
\begin{aligned}


\displaystyle m =& \lim \limits_{x \to a} \frac{f(x) - f(a)}{x - a}\\
\\
\text{We have } a =& -1 \text{ and } f(x) = 2x^3 - 5x, \text{ So the slope is }\\
\\
\displaystyle m =& \lim \limits_{x \to -1} \frac{f(x) - f(-1)}{x + 1}\\
\\
\displaystyle m =& \lim \limits_{x \to -1} \frac{2x^3 - 5x - [2 (-1)^3 - 5(-1)]}{x + 1}
&& \text{ Substitute value of $a$ and $x$}\\
\\
\displaystyle m =& \lim \limits_{x \to -1} \frac{(2x^3 - 5x - 3)}{x + 1}

\end{aligned}
\end{equation}
$



Using Synthetic Division to obtain the factor of the numerator










$
\begin{equation}
\begin{aligned}

\displaystyle m =& \lim\limits_{x \to -1} \frac{ (2x^2 - 2x - 3)\cancel{( x + 1)}}{\cancel{x + 1}}
&& \text{ Cancel out like terms}\\
\\
\displaystyle m =& \lim \limits_{x \to -1} (2x^2 - 2x - 3) = 2(-1)^2 - 2(-1)-3
&& \text{ Evaluate the limit }\\
\\
m =& 1

\end{aligned}
\end{equation}
$


Using point slope form


$
\begin{equation}
\begin{aligned}

y - y_1 =& m ( x - x_1)\\
\\
y - 3 =& 1 ( x + 1 )
&& \text{ Substitute value of $x, y$ and $m$}\\
\\
y - 3 =& x + 1
&& \text{ Combine like terms}\\
\\
y =& x +4
\end{aligned}
\end{equation}
$



Therefore,
The equation of the tangent line at (-1,3) is $y = x + 4$

Who was Martha Washington? How was she Helen's good companion?

Martha Washington was the daughter of Helen Keller’s family cook and was her friend and playmate when she was younger.
When Helen was little, Martha Washington was her playmate but hardly her equal. 

In those days a little coloured girl, Martha Washington, the child of our cook, and Belle, an old setter, and a great hunter in her day, were my constant companions. Martha Washington understood my signs, and I seldom had any difficulty in making her do just as I wished. (Ch. 2)

Because Helen was blind and deaf, she liked the fact that Martha Washington could understand her signs.  Young Helen found it very hard to communicate with anyone, so this was a big benefit.  The other advantage was that Martha let her push her around.  Young Helen was a bit bossy.  The fact that Helen mentions her at the same time as the dog shows that she considered her more of a companion than an equal.
In addition to the race difference, Helen Keller notes there was also an age difference between the two girls.

Martha Washington had as great a love of mischief as I. Two little children were seated on the veranda steps one hot July afternoon. ... One child was six years old, the other two or three years older. The younger child was blind–that was I–and the other was Martha Washington. (Ch. 2)

It seems like Martha Washington enjoyed getting into trouble with Helen Keller though.  Little Helen was very intelligent, and even though she could not speak like a normal person or hear what Martha was saying, they could still play together and be very creative in getting into trouble.
Once Helen started working with Anne Sullivan, she learned sign language and was able to communicate more fully with more people.  She was able to learn a more standard language.  Her early childhood was pretty lonely though.

In poem "Snaps," how does Espaillat transform silence into observation of the gendered universe her poetry examines and explores?

The title of the poem, "Snaps," refers to two snapshots of a female: one when she is a little girl and one taken when she is 17. Photos are silent: they cannot speak in literal words. The figure in both poems is rendered even more silent by being a carefully posed object in a photograph. In both photos, she looks the way other people want her to look, and in both her personality is flattened. Both photos, thus, become a metaphor for the way a woman in patriarchal society is not allowed a voice and is forced to conform to the image others want her to convey.
We see in stanza one an image of a girl who is "neatly dressed" in "white," a color typically associated with purity, and posed in "old light" that falls "flat" on a "featureless expanse of chest." Words like "old light," "flat" and "featureless" emphasize how the girl has been flattened out and made generic. She is depicted as the stereotype of any good little girl.
In the second stanza, her 17-year-old self is also forced to conform to "good girl" gender norms. "Ankles crossed," hands in lap, and "clean sweater" show without any words how she is pressed into what stanza three calls her "obedient pose." She also wears a "gold cross," showing she conforms to her family's religious faith. In stanza four, we learn "mama's touch" "bent" her "to the law," and "to sanctities of custom." In other words, the second photo also is supposed to convey that she is her mother's idea of a good girl: docile, constrained, religious, and clean.
But the silence of these "snaps" also communicates another side to this girl that is different from the perfect obedience, cleanliness and docility that gender traditionally assigns to a female. Behind her silence and outward conformity, the girl speaks another language to the narrator. In stanza five's "sharp tilt of the the jaw" and "small thrust of hip," the girl asserts her individualism and independence. The narrator ends by stating, in the final stanza, that although the silent snaps are supposed to convey that the girl will fulfill her gender role ("not cross this line," "[not] talk back," not take any risks, never deviate from being "good"), underneath the  surface they communicate that she will rebel: "flashing me a sign...yes, we would." 

Who does Don Quixote think he is?

In Miguel de Cervantes's Don Quixote, first published in the early 17th century, we follow the story of a man named Alonso Quixano (the narrator does not actually know the correct spelling of this man's last name), who has essentially "lost his wits," specifically meaning he no longer has the ability to determine fantasy from reality.
Heavily influenced by the enormous number of chivalric romances he's been reading, Quixano takes on the name Don Quixote and believes himself to be a knight-errant. Specifically, a knight-errant is a fictional type of knight found in literature that travels about the land, searching for chivalrous deeds to do, people to save, and battles to fight. The following quote, from the first chapter, shows us Quixote's exact goals in being a knight-errant:

In short, his wits being quite gone, he hit upon the strangest notion that ever madman in this world hit upon, and that was that he fancied it was right and requisite, as well for the support of his own honour as for the service of his country, that he should make a knight-errant of himself, roaming the world over in full armour and on horseback in quest of adventures, and putting in practice himself all that he had read of as being the usual practices of knights-errant; righting every kind of wrong, and exposing himself to peril and danger from which, in the issue, he was to reap eternal renown and fame.

Don Quixote builds up an entire world of romantic fantasy in his mind, and his idealistic delusions of being a knight on a grand adventure lead him to nothing but trouble.

How does Appia die?

Prince Appia is killed by the scheming Ababio. Ababio is power hungry and realizes that he won't be able to control the new Prince who is following the ways of the Healers. As such, Ababio has the Prince Appia brutally tortured and murdered. Appia has his limbs severed and is hung from a tree. Appia dies from this hanging. His death being so brutal is representative of the power Ababio has and his vindictiveness. Ababio is not accustomed to being thwarted and makes sure that Appia and his mother pay dearly for not coming under his control. Appia's brutal death also serves as a warning to the next in line for the throne on the consequences of not following Ababio.

In the story, the prince Appia was murdered in a most brutal manner. In chapter 5, we are told that his corpse is discovered hanging from the largest bough of a guava tree. 
From the text, we can conclude that Appia died from his neck wounds. His eyes had also been gouged out, and his arms and legs had been mutilated. The only part of the prince's body that was left untouched was the trunk. So, although Appia suffered extreme torture before his death (his eyes were torn from their sockets with an extremely sharp instrument), he likely died from blood loss through his terrible neck wounds.
The text also tells us that Appia's arms and legs were likely mutilated after his death. Two slivers of flesh had been removed from each upper arm. Similarly, two pieces of flesh had also been cut out from the calf muscle behind each leg. 

Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 70

Find the integral $\displaystyle \int^2_1 \frac{(x - 1)^3}{x^2} dx$


$
\begin{equation}
\begin{aligned}

& \int^2_1 \frac{(x - 1)^3}{x^2} dx = \int^2_1 \frac{x^3 - 3x^2 + 3x - 1}{x^2} dx
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = \int^2_1 \left( \frac{x^3}{x^2} - \frac{3x^2}{x^2} + \frac{3x}{x^2} - \frac{1}{x^2} \right) dx
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = \int^2_1 \left( x - 3 + \frac{3}{x} - \frac{1}{x^2} \right) dx
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = \int^2_1 \left( x - 3 - \frac{3}{x} - x^{-2} \right) dx
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = \left[ \frac{x^2}{2} - 3x + 3|n|x| + x^{-1} \right]^2_1
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = \frac{(2)^2}{2} - 3(2) + 3 ln 2 + \frac{1}{2} - \left[ \frac{(1)^2}{2} - 3 (1) + 3 ln 1 + \frac{1}{1} \right]
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = 2 - 6 + 3ln 2 + \frac{1}{2} - \frac{1}{2} + 3 - 3(0) -1
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = 3ln 2 - 2
\\
\\
& \int^2_1 \frac{(x - 1)^3}{x^2} dx = \int^2_1


\end{aligned}
\end{equation}
$

What physical destruction resulted from the Civil War?

The physical damage of the Civil War is estimated to total over $1.4 billion. That estimate is based on the value of money in 1865. The destruction caused by the conflict between the states is hard to fathom. Cities that were bombarded with artillery fire during siege campaigns were reduced to rubble. These cities were primarily in the south with Charleston, Atlanta, Richmond, and Columbia being prime examples.
The war also had a dramatic environmental impact that would take decades to heal. Farmlands were converted to battlefields and were physically damaged by the onslaught. Some of the farmlands were deemed important as memorials or cemeteries and were never again used for agriculture. Antietam, Gettysburg, and Arlington are great cases for this point. Deforestation was another environmental concern as artillery fire would commonly destroy forested areas. Forest fires were common during the Civil War as cannon fire would inadvertently set the woods ablaze.
The Civil War also destroyed much of the infrastructure of the South. Railroad lines, water systems, and roads were often deliberate targets for destruction. The demolition of infrastructure added to the costs of rebuilding the South.
 
http://nationalhumanitiescenter.org/tserve/nattrans/ntuseland/essays/amcwarb.htm

https://eh.net/encyclopedia/the-economics-of-the-civil-war/

https://www.pecva.org/madison-and-the-civil-war/after-the-civil-war

The Civil War was very destructive. Since most of the fighting occurred in the Confederacy, the South was hit very hard. While there was some destruction in the North, it was far greater in the South. Toward the end of the Civil War, the Union used a method called total war. With this technique, the Union soldiers destroyed everything in their path as they marched throughout the South, moving from Atlanta to Savannah, and then heading northeast through South Carolina and North Carolina.
As a result of the fighting, much land was destroyed. The South experienced food shortages because so much farmland was destroyed. Livestock was destroyed, as were homes and other buildings. Even fences were ripped out of the ground. The Union soldiers also destroyed miles and miles of train track, impacting local transportation. The physical destruction of the South would lead to the rebuilding of the South, which was known as Reconstruction.
https://www.pecva.org/madison-and-the-civil-war/after-the-civil-war

What is the difference between Mrs. Maloney and the Landlady?

The main difference between the two ladies lies in the nature of their respective acts of murder. Mrs. Maloney kills her husband in a sudden, unprecedented fit of rage after he tells her he's leaving. There's nothing premeditated about Mary's fatal assault upon her husband. The landlady, on the other hand, commits several acts of premeditated murder upon various young men who come to stay at her bed and breakfast. We're never sure exactly why she does this; her lack of obvious motive makes her crimes all the more chilling and disturbing. Perhaps she's gaining revenge for something bad that happened to her many years ago, perhaps she has mental health issues, or perhaps her unhealthy obsession with taxidermy has just got a little out of hand. We will never know.
But in any case, the landlady's murders are her way of imposing herself upon the world, a highly unconventional means of expressing her eccentric personality. Mary, on the other hand—a meek, unassertive woman—is reacting to the sudden intrusion into her life of a brutal, unforgiving world, one where people such as herself are often hurt and destroyed. Yet by cleverly covering up her murderous act, Mary quickly learns to assert herself, albeit in a way that's much more conventional than that of the landlady.

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 88

Find the diameters of the cylindrical can if it has a volume of $40 \pi cm^3$ and height of $10 cm$.

Recall that the volume of the cylinder is..


$
\begin{equation}
\begin{aligned}

V =& \pi r^2 h
&& \text{Model}
\\
\\
40 \pi =& \pi r^2 (10)
&& \text{Substitute the given}
\\
\\
\frac{40 \pi}{10 \pi} =& r^2
&& \text{Simplify}
\\
\\
r^2 =& 4
&& \text{Solve for } r
\\
\\
r =& \pm 2
&& \text{Take the square root}
\\
\\
r =& 2 cm
&& \text{Choose } r > 0
\\
\\
d =& \frac{r}{2}
&& \text{Formula for diameter with respect to radius}
\\
\\
d =& \frac{2}{2}
&& \text{Substitute } r
\\
\\
d =& 1 cm
&& \text{Solve for } d

\end{aligned}
\end{equation}
$

Assess the role played by the Marshall Plan in United States' economic imperialism in Europe.

The Marshall Plan, commonly called the European Recovery Program, was a plan developed by the United States after World War II ended to keep communism from spreading in Europe. The Soviet Union was trying to spread communism while we were trying to prevent it from spreading. We gave economic aid to European countries that were fighting the spread of communism. For example, we gave aid to both Greece and Turkey. Neither of these countries became communist. We believed that if a country's economy was strong, they would be less likely to turn to communism. Since Secretary of State Marshall announced this plan, it is also called the Marshall Plan. 
By providing economic aid to some of the European countries, the United States was able to spread its economic influence in Europe. When the European countries received the aid from the United States, they often spent the money on products made in the United States. This helped keep people in the United States employed, which was good for our economy. The development of this program was part of the reason why we were prosperous after World War II ended. 
The United States not only spread its economic influence in Europe with this plan, it also helped our economy at home.
https://www.history.com/topics/world-war-ii/marshall-plan-1

Explain why the philosophes criticized the Rococo art.

Rococo was an ornate style of painting, sculpture, and furniture that was in vogue in the early 18th century in France (and that later spread to the rest of Europe). The style is characterized by lightness, curving lines, and ornamentation. The word "Rococo" is from the word "rocaille," a technique in which pebbles, seashells, and other items were placed on objects, and the motif of these objects was used in the style of art. Diderot and other philosophes criticized the Rococo style as too superficial to really constitute the beauty that was the essence of art. Diderot saw the Rococo style as pleasing, but not constituting true art or beauty. Other philosophes saw Rococo artwork as too superficial and limited to be of true value or worth, and the style became out of vogue.

The term "rococo" is a playful variation on the French word rocaille, meaning "rock garden."
Rococo art, which originated in France but also became popular in Austria and Russia, is known for its highly ornate style, an even more stylized version of Baroque art. Rococo influenced painting but particularly influenced architecture and decor given its flagrant promotion of wealth.
Rococo painters, particularly Antoine Watteau and Jean-Honore Fragonard, depicted fetes galantes—that is, scenes in which members of the aristocracy were shown enjoying leisurely moments in natural settings. Several philosophes including Denis Diderot and Voltaire found the paintings trivial and disliked their "elegant eroticism." Diderot wanted a "nobler art" that would more directly address the human condition. Neoclassism and Romanticism, genres of art which depicted political figures (such as Napoleon), historical scenes, and political issues (such as the slave trade), emerged after the decline of rococo, which coincided with the French Revolution.

At the conclusion of the French and Indian War (Seven Years' War), few within the British Empire or the American colonies could have imagined that fifteen years later the American colonies would be fighting England for independence. Discuss reasons for the American colonies' desire for independence.

There were several reasons for the American colonists to seek independence following the French and Indian War (Seven Years War). The reason that is most often cited by scholars is the taxes that the British Empire began levying on colonists to pay England's debts from the Seven Years War. Prior to this, the colonists had local assemblies who chose what would be taxed, but desperate for funds, the British government implemented laws like the Stamp Act which impacted the colonists. There is also evidence of an ideological gap developing between the colonists and Britain at this time. Men like Sam Adams and the Sons of Liberty did not like that the colonies were being governed by a Parliament that was thousands of miles away. This handful of radical thinkers used a fairly new invention, the printing press, to widely publish their views and win other colonists over to their side.

The American colonies had many reasons to seek their independence after the French and Indian War. The first reason was a general distrust between Britain and the colonies. The colonies tried to unite under the Albany Plan in order to better help the British war effort in America, but Parliament quickly refused this idea. Some in the colonies started to suspect that Parliament did not want to deal with a united front in America. Also, British officials learned firsthand that the Americans were quite adept at smuggling and flouting navigation acts levied by Parliament. American merchants thought nothing of trading with the French or Spanish if it meant getting a better deal—even though these countries were Britain's chief enemies. Britain saw that Americans were good at bribing tax collectors, many of whom did not want to be in the colonies anyway and were more than happy to take a bribe as a perk of the job.
After the war, Parliament realized that it needed to reform its tax plan if it wished to maintain a solvent treasury. Parliament appointed more stringent tax collectors. It also created the Proclamation Line of 1763, which many colonists hated because it promised land west of the Appalachian Mountains to the Indians—Indians who had long threatened American settlement. Parliament claimed that it was doing this to protect Americans from Indians by creating a barrier, but even in 1763, some colonists were claiming that this was an attempt to keep the colonists on the coast in order to make them easier to tax. Britain soon passed the Stamp Act and the Sugar Act, which levied taxes on official documents and sugar. Most colonists grumbled but still paid the tax, but a small group of colonial leaders started to agitate that they were being taxed unfairly and without representation. This practice went against the salutary neglect that the colonists had enjoyed for generations. Parliament claimed that they were not a legislative body. In order to placate colonists, Parliament repealed the Stamp Act and issued the Declaratory Act, which gave Parliament the right to govern as they saw fit. Most colonists saw the repeal as a victory and did not care about the Declaratory Act. Britain then taxed tea—not its consumption but its import into the country. Many in America saw this as corrupt, as it gave the East India Tea Company a monopoly on tea, and many individuals in Parliament had money tied in to the business. When citizens of Boston attacked the shipment, Parliament passed the Intolerable Acts, which quartered troops in Boston and closed the port. Instead of isolating the colony, the colonists rushed to Boston's aid by sending supplies. Soon groups of militia started to drill, which led to more British troops being sent to America in order to keep the peace. This escalation would finally end with the Battles of Lexington and Concord, launching the American Revolutionary War.

Find the wavelength of the photon emitted during the transition from the second excited state to the ground state in a harmonic oscillator with a classical frequency of 3.72 x 10^13 Hz. My buddy says it equals 4.03mum m but I keep getting 8.06mum can I really just be forgetting to divide by two somewhere?

First, compute the energy level for each state. The formula of energy level of a harmonic oscillator is:
E_n=(n+1/2)hf
where
n is the quantum number
h is the Planck's constant (6.625 x 10^(-34)Js) and
f is the frequency of the oscillator
At second excited state, the quantum number of harmonic oscillator is n=2. So its energy level at this state is:
E_2= (2+1/2)(6.625 xx 10^(-34)Js)(3.72xx10^13 Hz)
E_2=6.126125 xx 10^(-20) J
At ground state, the quantum number of harmonic oscillator is n=0. So its energy level at this state is:
E_0= (0+1/2)(6.625xx10^(-34)Js)(3.72xx10^13 Hz)
E_0=1.23225 xx 10^(-20) J
Then, determine transition energy from n=2 to n=0.
\Delta E = E_2 - E_0
\Delta E = 6.126125 xx 10^(-20)J - 1.23225 xx 10^(-20)J
\Delta E = 4.929 xx 10^(-20) J
So during the transition from n=2 to n=0, 4.929 x 10^(-20) J of energy is emitted.  This is the energy of the photon emitted during the transition.
Energy of photon, E = 4.929 xx 10^(-20) J
To determine the wavelength of the photon, apply the formula of energy of photon.
E=hf
where f is the frequency of light.
Since the frequency of light is  f = c/ lambda , the formula can be re-written as:
E = h * c/ lambda
where 
c is the speed of light  (3 xx10^8 m/s) and
lambda is the wavelength of photon
Isolating the wavelength, the formula becomes:
lambda = (h*c)/E
Plugging in the values, the wavelength will be:
lambda = ((6.625xx10^(-34)Js)*(3xx10^8 m/s))/(4.929xx10^(-20)J)
lambda= 4.03 xx 10^(-6) m
lambda =4.03 mum
 
Therefore, the wavelength of the photon emitted is 4.03 mum .

Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 73

Add: $(12z^2 - 11z + 8) + (5z^2 + 16z - 2) + (-4z^2 + 5z - 9)$

Remove the parentheses that are not needed from the expression.
$12z^{2}-11z+8+5z^{2}+16z-2-4z^{2}+5z-9$

Since $12z^2$ and $5z^2$ are like terms, add $5z^2$ to $12z^2$ to get $17z^2$
$17z^{2}-11z+8+16z-2-4z^{2}+5z-9$

Since $17z^2$ and $-4z^2$ are like terms, add $-4z^2$ to $17z^2$ to get $13z^2$
$13z^{2}-11z+8+16z-2+5z-9$

Since $-11z$ and $16z$ are like terms, subtract $16z$ from $-11z$ to get $5z$.
$13z^{2}+5z+8-2+5z-9$

Since $5z$ and $5z$ are like terms, add $5z$ to $5z$ to get $10z$.
$13z^{2}+10z+8-2-9$

Subtract 2 from 8 to get 6.
$13z^{2}+10z+6-9$


Subtract 9 from 6 to get $-3$.
$13z^{2}+10z-3$

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 16

The Rolle's theorem is applicable to the given function, only if the function is continuous and differentiable over the interval, and f(a) = f(b). Since all polynomial functions are continuous and differentiable on R, hence, the given function is continuous and differentiable on interval. Now, you need to check if f(-1) = f(1).
f(-1) = ((-1)^2-1)/(-1)= 0
f(1) = (1^2-1)/(1)= = 0
Since all the three conditions are valid, you may apply Rolle's theorem:
f'(c)(b-a) = 0
Replacing 1 for b and -1 for a, yields:
f'(c)(1+1) = 0
You need to evaluate f'(c), using quotient rule:
f'(c) = ((c^2-1)/c)' => f'(c) =((c^2-1)'*c - (c^2-1)*c')/(c^2)
f'(c) = (2c^2 - c^2 + 1)/(c^2)
f'(c) = (c^2+1)/(c^2)
Replacing the found values in equation f'(c)(1+1) = 0
2(c^2+1)/(c^2)= 0 =>c^2 + 1 = 0 => c^2 = -1!in R
Hence, in this case, there is no valid value of c in(-1,1) , for the Rolle's theorem to be applied.

What part does Zeus play in the odyssey

In The Odyssey, Zeus does not frequently appear; yet, when he does, he certainly utilizes his significant influence. In a sense, Zeus even sets forth the entire plot of The Odyssey, for, after being begged by Athena to assist Odysseus, Zeus offers his permission to intervene in Odysseus's journey. Furthermore, Zeus even makes the promise to help Odysseus return safely.
Zeus also sends a message in the form of an omen to Penelope's suitors. Telemachus pleads with these inconsiderate suitors to leave his home in the name of Zeus; of course, when they refuse, Zeus sends forth a pair of eagles that fight and tear at each other violently. The suitors struggle to understand what this vague message means, while the prophet Halitherses properly interprets the omen as a sign of Odysseus's inevitable return.

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 12

int_0^1 (x-4)/(x^2 - 5x + 6) dx
sol:
int_0^1 (x-4)/(x^2 - 5x + 6) dx
First let us solve the integral and then apply the limits later
so,
int (x-4)/(x^2 - 5x + 6) dx
=int (x-4)/(x^2 - 3x -2x + 6) dx
=int (x-4)/(x(x - 3) -2(x -3)) dx
=int (x-4)/((x -2)(x -3)) dx
Now by taking he partial fractions of (x-4)/((x -2)(x -3)) we get
(x-4)/((x -2)(x -3)) = A/(x-2) +B/(x-3)
= (A(x-3)+B(x-2))/((x -2)(x -3))
so equating the numerators we get
x-4 = A(x-3)+B(x-2)
= x(A+B)+(-3A-2B)
Now equating the co efficients of x and the constants we get
A+B =1
=> A=1-B
-3A-2B =-4
=>3A+2B=4
=> 3(1-B)+2B=4
=> 3-3B+2B=4
=>3-B=4
=> B= -1 so A = 1-B = 2
Then
(x-4)/((x -2)(x -3)) = A/(x-2) +B/(x-3)
= (2/(x-2)) - (1/(x-3))
Now,
int (x-4)/(x^2 - 5x + 6) dx = int(x-4)/((x -2)(x -3)) dx
= int ((2/(x-2)) - (1/(x-3))) dx
=>int (2/(x-2)) dx - int (1/(x-3)) dx
=> 2ln(x-2) - ln(x-3) + c
Now applying the limits 0 to 1 we get
int_0^1 (x-4)/(x^2 - 5x + 6) dx = [2ln(x-2) - ln(x-3) ]_0^1
= [2ln(1-2) - ln(1-3) ]-[2ln(0-2) - ln(0-3) ]
= [2ln(-1) - ln(-2) ]-[2ln(-2) - ln(-3) ]
=[ln(1^2) - ln(-2) ]-[ln((-2)^2) - ln(-3) ]
=[ln(1) - ln(-2) ]-[ln(4) - ln(-3) ]
= ln((-1)/2)) - ln((-4)/3))
=ln(((-1)/2)/((-4)/3))
= ln(3/4*2)
= ln(3/8)
is the solution
:)

What does the open door represent?

In Langston Hughes's "Thank You, M'am," Roger gets more than he bargains for when he attempts to steal the purse of Mrs. Luella Bates Washington Jones. He finds himself being lectured, reprimanded, and dragged to her home. Once there, Mrs. Jones instructs him to wash his face. The reader learns that Roger "looked at the door—looked at the woman—looked at the door—and went to the sink."
The open door represents a choice for Roger. He has an opportunity to escape, or he can choose to remain and accept whatever comes next from Mrs. Jones. It is interesting to note that although she holds him in a "half-nelson about his neck" to get Roger inside, she leaves the door open. Perhaps she is intentionally providing him with this choice in an effort to show that when good behavior and positive choices are the expectation, he will live up to that expectation.

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 34

Expand the expression $\displaystyle \log \left( \frac{a^2}{b^4 \sqrt{c}} \right)$, using Laws of Logarithm


$
\begin{equation}
\begin{aligned}

\log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& \log a^2 - \log (b^4 \sqrt{c})
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
\log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& \log a^2 - (\log b^4 + \log \sqrt{c})
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
\\
\\
\log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& 2 \log a - \left( 4 \log b + \frac{1}{2} \log C \right)
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
\\
\\
\log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& 2 \log a - 4 \log b - \frac{1}{2} \log c
&& \text{Distributive Property}


\end{aligned}
\end{equation}
$

What moral is Gary Schmidt trying to teach with the cream puff in The Wednesday Wars?

Mrs. Baker gives Holling the job of transporting cream puffs up to the classroom from the cafeteria. The cream puffs are supposed to be for a gathering of the Wives of Vietnam Soldiers. He brings 12 trays, one at a time, upstairs to Mrs. Baker's room.
Mrs. Baker then assigns Holling the task of pounding out erasers that are dirty with chalk. She promises to give him a cream puff if he does a good job; however, he pounds them out by the windows, causing the dust to float over the cream puffs. Holling sees the cream puffs are ruined, but he doesn't do anything about it. Instead, he is "hoping that the Wives of Vietnam Soldiers would not notice the chalk dust all that much." They do, of course, and they blame the woman who made them in the cafeteria, who eats a cream puff to prove they are safe and has to go to the hospital. Meanwhile, the other students in Holling's class beg him for cream puffs, which he can't deliver. The lesson or moral the author is trying to impart is that being dishonest makes a situation worse. By not telling the truth about what happened to the cream puffs, Holling allows several people to become sick or disgusted from eating them.

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 94

Two ships $A$ and $B$ depart a harbor at the same time, $A$ is traveling east, the other south. $A$ travels $3 mi/hr$ faster than $B$. After two hours, the ships are $30 mi$ apart. Find the speed of $B$.

Let $x$ be the speed of $B$, so $x + 3$ will be the speed of $A$.

So the distance of $B$ after 2 hours is $2x$, while $A$ is $2(x + 3)$.







By using Pythagorean Theorem,


$
\begin{equation}
\begin{aligned}

(2x)^2 + (2(x + 3))^2 =& (30)^2
&& \text{Model}
\\
\\
4x^2 + (2x + 6)^2 =& 900
&& \text{Distribute 2}
\\
\\
4x^2 + 4x^2 + 24x + 36 =& 900
&& \text{Expand}
\\
\\
8x^2 + 24x + 36 =& 900
&& \text{Combine like terms}
\\
\\
8x^2 + 24x - 864 =& 0
&& \text{Subtract 900}
\\
\\
x^2 + 3x - 108 =& 0
&& \text{Divide both sides by 8}
\\
\\
(x + 12)(x - 9) =& 0
&& \text{Factor}
\\
\\
x + 12 =& 0 \text{ and } x - 9 = 0
&& \text{ZPP}
\\
\\
x =& -12 \text{ and } x = 9
&& \text{Solve for } x
\\
\\
x =& 9 mi/hr
&& \text{Choose } x > 0

\end{aligned}
\end{equation}
$


The speed of $B$ is $9 mi/hr$.

Calculus of a Single Variable, Chapter 7, 7.1, Section 7.1, Problem 72

Given ,
y^2=4-x , x = 0
=>x=4-y^2 , x=0
first let us find the total area of the bounded by the curves.
so we shall proceed as follows
x=4-y^2 ,x=0
=> 4-y^2=0
=> y^2 -4 =0
=> (y-2)(y+2)=0
so y=+-2

the the area of the region is = int _-2 ^2 ((4-y^2)-0 ) dy
=>int _-2 ^2 (4-y^2) dy
=[4y-y^3/3] _-2 ^2
=[ [8-8/3]-[-8 -(-8)/3]]
=[[8-8/3]+[8 +(-8)/3]] = (16-16/3)=(2*16)/3=32/3
So now we have to find the vertical line that splits the region into two regions with area 16/3 as it is half of area of region covered by two curves y^2=4-x and x=0.
as when the line x=a intersects the curve x=4-y^2 then the area bounded is 16/3 ,so
let us solve this as follows
first we shall find the intersecting points
as ,
4-y^2=a
4-a=y^2
y=+-sqrt(4-a)
so the area bound by these curves x=a and x=4-y^2 is as follows
A= int _-sqrt(4-a) ^sqrt(4-a) (4-y^2-a)dy = 16/3
=> int _-sqrt(4-a) ^sqrt(4-a)(4-y^2-a)dy=16/3
=> [(4-a)(y)-y^3/3]_-sqrt(4-a) ^sqrt(4-a)
=>[(4-a)(sqrt(4-a))-(sqrt(4-a))^3/3]-[(4-a)(-sqrt(4-a))-(-sqrt(4-a))^3/3]
let t= sqrt(4-a)
so,
=>[t^2*(t)-(t)^3/3]-[t^2*(-t)-(-t)^3/3]
=>[t^3-t^3/3 +t^3-t^3/3]
=>2(t^3-t^3/3]
=>4/3t^3

but we know half the area of the region between x=4-y^2, x=0 curves =16/3
so now ,
4/3 t^3=16/3
=>4t^3 = 16
=>t^3=4
Substituting t = sqrt(4-a) ,
(4-a)^(3/2)= 4
4-a=4^(2/3)
a=4-4^(2/3)
=1.4801

so a= 1.4801