At the end of the story, when Jane is crawling around the room and she "creeps" right over her husband who fainted, she says "I've got out at last." Does this mean that Jane has prevailed, or would you say that she has not been liberated (and has not prevailed) because now she really is insane? Not sure how to view this ending. She feels she has escaped, but her mental state has declined so greatly that she actually is mad now. Please explain if Jane's ending is a success regarding her inner struggle and independence or not!

We know that the narrator first loathed the wallpaper and then attributed consciousness and intention to it; then, she begins to ponder it; then, she actually comes to think it is helping her to feel better.  Near the end, she begins to feel that there is a woman trapped in the wallpaper, behind the bars that form the outermost layer.  The narrator says, "Through watching so much at night, when [the wallpaper] changes so, I have finally found out.  The front pattern does move—and no wonder!  The woman behind shakes it!" 
Keep in mind that, by the end of the story, the narrator's husband has confined her—essentially imprisoned her—in this house and this room.  She has not been allowed to see friends, to read or write, and so forth. Moreover, it is clear that this is a highly intelligent and creative woman.  There are bars on her windows, a gate at the top of the stairs, "rings and things" in the wall (perhaps to chain her and keep her still?), and the bed is nailed down.  Her husband's intentions may be good, but make no mistake: she is a prisoner.  She knows it.  She trusts him less and less, and by the end, she says, "He asked me all sorts of questions, too, and pretended to be very loving and kind.  As if I couldn't see through him!"
Throughout the story, the narrator is not always able to recognize herself as responsible for the ravages she sees in the room.  She talks about the "even smooch" around the walls, down by the mopboards, but she does not realize that she is the one who made it.  She talks about the bed being "fairly gnawed," blaming it on the children she thinks lived there before, only to tell us later that she "got so angry [she] bit off a little piece at one corner."  
When the narrator makes up her mind to help the woman in the wallpaper, it seems to empower her in a way that she is not able to help herself.  She says,

As soon as it was moonlight and that poor thing began to crawl and shake the pattern, I got up and ran to help her.  I pulled and she shook, I shook and she pulled, and before morning we had peeled off yards of that paper.

The narrator may not be able to free herself from her prison, but—in her mind—she can free this other woman.  Therefore, it is not so surprising when, toward the end of the story, she says, "I don't like to look out of the windows even—there are so many of those creeping women, and they creep so fast.  I wonder if they all come out of that wall-paper as I did?"  Throughout the story, the narrator, Jane, seems to have done things that she does not realize she did, paving the way for this total break in her identity. She begins to identify as the woman she believed she freed from the wallpaper.  This woman, from the wallpaper, is free; she was not.  She becomes the wallpaper woman in order to be free. 
On one hand, she believes herself to be free (which is good), but it is only because her mental health has degenerated to such a significant extent that she does not know who she really is (which is bad).  Jane achieves independence but only through a complete mental break.  Ultimately, I do not think Gilman wants us to be happy for Jane; a bright and vibrant woman has completely lost herself as a result of the backwards thinking and condescending treatment of her husband and doctors.  

A piece of iron at 215 deg C and a 20 kg piece of copper at 140 deg C are placed in 25 kg of water at 10 deg C. At thermal equilibrium, the temperature is 40 deg C. What is the mass of iron?

When the warmer objects (pieces of iron and copper) are placed in contact with the colder object (water), there will be a transfer of heat so that the iron and copper will cool off and the water will heat up. 
According to the law of the conservation of energy,
Q_(hot) + Q_(cold) = 0 .
Here,
Q_(hot) is the heat leaving the warmer objects (it will have a negative value), and
Q_(cold) is the heat acquired by the colder object as the result.
In this case,
Q_(hot) = c_im_i(T_e - T_(ii)) + c_cm_c(T_e-T_(ic))
and Q_(cold) = c_wm_w(T_e-T_(iw))
Here, c's denote the specific heat of iron, copper and water, m's denote the masses and T_i
 - initial temperature of the objects.
 T_e
is the equilibrium temperature.
Plugging in the values for given quantities (masses are in kilograms), and the table values for specific heat (in J/(kg*C)), we get
448*m_i*(40-215) + 387*20*(40-140) + 4186*25*(40-10) = 0
From here,
-78400*m_i - 774000+3139500 = 0
Solving for the mass of iron results in
m_i = 30.17 kg 
The mass of iron is 30.17 kilograms.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/calor.html

https://www.physicsclassroom.com/class/thermalP/Lesson-2/Calorimeters-and-Calorimetry

27^(4x-1)=9^(3x+8) Solve the equation.

27^(4x-1)=9^(3x+8)
To solve, factor the 9 and 27.
(3^3)^(4x-1)=(3^2)^(3x+8)
To simplify each side, apply the exponent rule (a^m)^n=a^(m*n) .
3^(3*(4x-1))=3^(2*(3x+8))
3^(12x-3)=3^(6x+16)
Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right.
12x-3=6x+16
12x-6x=3+16
6x=19
x=19/6
Therefore, the solution is  x = 19/6 .

What were some cultural advantages that allowed Britain to develop industry?

It is still debated among economists and historians why exactly Britain was the first country in the world to industrialize, and if you ask different people you'll get different answers. However, there are certain definite advantages Britain had that may have contributed to their early industrialization:1. Britain was already rich by world standards at the time. While their level of income seems small to us today, it was larger than that of most other countries in the world; people had enough income to be consumers and investors rather than simply working to survive.2. Britain has one of the most stable, long-standing governments in the world. Whereas most countries go through a revolution every few generations, Britain has undergone a process of gradual reform that has preserved the same core---a constitutional monarchy with Parliament as the primary governing body---for some one thousand years. Even by the start of the Industrial Revolution Britain had already been in its current form of government for over 700 years.3. Britain has a very strong and stable currency (the pound), allowing them to purchase imports cheaply from the rest of the world. Their central bank has never defaulted on debt in centuries, and thus has the highest level of credibility for borrowing; so they are essentially unconstrained in how much money they can borrow when they need it.4. Britain has well-established property rights and relatively free markets. While they are certainly not wholly unregulated (and were considerably more tightly regulated in the 18th century than today), markets in Britain generally have been more limited and permissive in their regulations, allowing private innovation to flourish without excessive barriers or heavy-handed government intervention. Their court systems have a reliable record of establishing and enforcing clear property rights.
5. Britain has a very high level of education. The educational system in Britain has been one of the best in the world for centuries, especially at their very top universities such as Oxford and Cambridge (both of which were founded hundreds of years before the industrial revolution!). This high level of education allowed them to produce the large numbers of highly-qualified scientists and engineers necessary to establish an industrial economy.
6. Britain has enormous reserves of coal. Coal was the chief fuel of the industrial revolution, and Britain had at that time one of the largest proven reserves of coal in the world. This made coal cheap and easy to get, and thus made it much more profitable for businesses to industrialize.
Beyond that, it is difficult to say which of these factors was most important, and there are very likely other important factors as well.
https://www.historytoday.com/industrial-revolution-why-britain-got-there-first

What was the outcome of the presidential election of 1800?

The presidential election of 1800 was notable for being the first partisan contest in American political history. The campaign was extremely bitter and rancorous, with insults, smears, and personal abuse very much the order of the day. The two candidates were the sitting president John Adams, representing the Federalists, and his Republican Vice President Thomas Jefferson. Adams and Jefferson heartily detested each other, which accounted for the deeply personal tenor of this hard-fought campaign.
It was generally thought a foregone conclusion that Adams would lose. He was a deeply unpopular president, accused by his Republican opponents of wanting to turn himself into a king. President Adams had signed into law a number of draconian measures such as the Alien and Sedition Acts, which had, among other things, restricted free speech in the name of national security. Republicans were outraged at these measures, seeing them as an attack on the cherished tradition of American liberty. No wonder they thought that Adams wanted to establish himself as another King George III.
As expected, Jefferson and his running-mate Aaron Burr won the election. However, due to the unusual system in force at that time, the House of Representatives had to decide which of the two would become president, as they were tied in the Electoral College. As the outgoing House had a Federalist majority—the party of Adams that had just lost the election—Jefferson and his supporters feared that his opponents would use their majority in the House to deny him the presidency.
After a lengthy process, with involved all kinds of deals being conducted behind closed doors, Jefferson was finally declared the winner. This was due in no small part to the tireless efforts of the arch-Federalist Alexander Hamilton. Hamilton had no time for Jefferson but regarded him as a less dangerous figure than Burr, who would in due course become a danger to Hamilton on a much more personal level.

In “Mrs. Dalloway” by Virginia Woolf, what event preoccupies Mrs. Dalloway in the opening sequence of the novel? What does this reveal about her social class and character?

Virginia Woolf's Mrs Dalloway is a novel which conveys a range of information about its protagonist, Clarissa, while being ostensibly set over the course of only one day. Its famous opening line states that Mrs Dalloway intended "to buy the flowers herself" for a party she will be throwing that evening. This line alone gives us some indication of where in society Clarissa fits, as a woman for whom it might be remarkable for her to buy her own flowers. Clarissa is a member of London's high society—but not confidently so. She is a woman who has lived in Westminster for over twenty years, and yet, knows her neighbors only in the passing sense of Westminster inhabitants; Clarissa is a woman who was once said to eventually marry a Prime Minister and who also yearns for a lost love. As such, because these things have not happened to her, little things such as throwing a party become immensely important. Clarissa does not need to buy her own flowers, but she does need to feel as if she is justifying her own existence as part of a society which, she fears, has forgotten her.

What becomes of Desiree and her baby?

When Desiree's husband discovers that his child is half African American, he tells Desiree to leave.  She walks off the plantation, not using the road but seeming to head in the direction of her parents' place.  However, Chopin writes, "She disappeared among the reeds and willows that grew thick along the banks of the deep, sluggish bayou; and she did not come back again."  This line indicates that Desiree and her baby end up drowning in the bayou, which is a marshy lake common to Louisiana.  
That is not where the story ends.  Chopin takes the reader back to L'Abri, Armand's plantation, where he is burning all of Desiree and the baby's belongings.  In that inferno, Armand has also put a letter from his mother to his father, which indicates that she was of African-American heritage, and his father knew this and married her anyway.  

At what price level must air carriers set their fares to maximize revenues?

The student’s question clearly specifies “revenues” and not “profits.” The distinction is important, as “revenue” refers to the total amount of money generated as income; “profit” is how much “revenue” is left over after expenses are paid, such as labor and material costs.
Large commercial aircraft consume a great deal of fuel, as much as one gallon per second. For transcontinental flights, that is a lot of jet fuel. Even short commercial flights are expensive, as a disproportionate amount of fuel is burned during routine take-offs. Additionally, there are substantial labor costs associated with operating a commercial airline, including salaries for pilots, flight attendants, ground crew, administrative personnel, and so on. Insurance costs alone can represent a major strain on airline companies’ budgets, especially when commercial airliners are intentionally or accidentally shot down by militants or governments. Revenues must cover, at a minimum, these basic expenses. Airline companies, then, maximize profits through careful determinations of how much they can charge passengers relative to their competitors. With air travel increasingly characterized by significant additional charges (beyond the use of a seat), for carry-on as well as checked baggage, and for food (which used to be included as part of the initial charge for a seat), the cost of a flight for a family going on vacation has become more burdensome than in the past.
Operating an airline is like many businesses, with material costs in particular fluctuating due to perturbations in fuel and lubricant costs. Airline executives must routinely sit down and calculate anticipated revenue measured against anticipated expenses. They maximize revenues by performing the best calculations they can of the amount then can charge customers relative to their competitors and relative to the cost of operating the airline.
https://therocketscienceblog.wordpress.com/2016/08/01/how-much-fuel-does-an-airplane-use/

https://www.ft.com/content/d57bc542-0e62-11e4-a1ae-00144feabdc0

Calculus of a Single Variable, Chapter 8, 8.6, Section 8.6, Problem 40

To evaluate the given integral problem: int_0^4 x/sqrt(3+2x)dx , we determine first the indefinite integral function F(x). From the table of indefinite integrals, we may consider the formula for integrals with roots as:
int u/sqrt(u+-a) du = 2/3(u-+2a)sqrt(u+-a)+C
Take note that we have "+ " sign inside the square root on int_0^4 x/sqrt(3+2x)dx then we will follow:
int u/sqrt(u+a) du = 2/3(u-2a)sqrt(u+a) +C.
We may let a = 3 and u = 2x or x= u/2
For the derivative of u, we get du = 2 dx or (du)/2 = dx .
Plug-in the values: u = 2x or x=u/2 ,and (du)/2 = dx , we get:
int_0^4 x/sqrt(3+2x)dx =int_0^4 (u/2)/sqrt(3+u)* (du)/2
=int_0^4 (u du)/(4sqrt(3+u))
Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int_0^4 (u du)/(4sqrt(3+u)) =1/4 int_0^4 (u du)/sqrt(3+u)
Apply the aforementioned integral formula from the table of integrals, we get:
1/4 int_0^4 (u du)/sqrt(3+u) =1/4*[2/3(u-2(3))sqrt(u+3)]|_0^4
=1/4*[2/3(u-6)sqrt(u+3)]|_0^4
=2/12(u-6)sqrt(u+3)|_0^4
=1/6(u-6)sqrt(u+3)] |_0^4or((u-6)sqrt(u+3))/6|_0^4
Plug-in u = 2x on((u-6)sqrt(u+3))/6 +C , we get:
int_0^4 x/sqrt(3+2x)dx =((2x-6)sqrt(2x+3))/6|_0^4
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
((2x-6)sqrt(2x+3))/6|_0^4 =((2(4)-6)sqrt(2(4)+3))/6-((2(0)-6)sqrt(2(0)+3))/6
=((8-6)sqrt(8+3))/6- ((0-6)sqrt(0+3))/6
=(2*sqrt(11))/6- (-6sqrt(3))/6
= sqrt(11)/3-(-sqrt(3))
= sqrt(11)/3+sqrt(3)
= (sqrt(11)+3sqrt(3))/3 or 2.84 (approximated value).

Single Variable Calculus, Chapter 6, 6.5, Section 6.5, Problem 12

Given that $\displaystyle f(x) = \frac{2x}{(1 + x^2)^2}$ with interval $[0,2]$.

a.) Find the average value.


$
\begin{equation}
\begin{aligned}

f_{ave} =& \frac{1}{b - a} \int^b_a f(x) dx
\\
\\
f_{ave} =& \frac{1}{2 - 0} \int^2_0 \frac{2x}{(1 + x^2)^2} dx
\\
\\
\text{Let } u =& 1 + x^2
\\
\\
du =& 2x dx

\end{aligned}
\end{equation}
$


Make sure that your upper and lower limits are also in terms of $u$.


$
\begin{equation}
\begin{aligned}

f_{ave} =& \frac{1}{2} \left( \frac{1}{2} \right) \int^{1 + (2)^2}_{1 + (0)^2} \frac{2}{u^2} du
\\
\\
f_{ave} =& \frac{1}{2} \int^5_1 u^{-2} du
\\
\\
f_{ave} =& \frac{1}{2} \left[ \frac{u^{-1}}{-1} \right]^5_1
\\
\\
f_{ave} =& \frac{1}{2} \left[ - \frac{1}{5} \left( \frac{-1}{1} \right) \right]
\\
\\
f_{ave} =& \frac{2}{5}

\end{aligned}
\end{equation}
$


b.) Find $C$ such that $f_{ave} = f(c)$.


$
\begin{equation}
\begin{aligned}

f_{ave} =& f(c)
\\
\\
\frac{2}{5} =& \frac{2c}{(1 + c^2)^2}
\\
\\
(1 + c^2)^2 =& 5c
\\
\\
1 + 2c^2 + c^4 =& 5c
\\
\\
c^4 + 2c^2 - 5c + 1 =&0

\end{aligned}
\end{equation}
$


We got 4 values of $c$. However, we omit the complex roots. So, we have it supposed to have 4 values of $c$. So that,


$
\begin{equation}
\begin{aligned}

& c \approx 0.21979
\\
& c \approx 1.20684

\end{aligned}
\end{equation}
$



c.) Sketch the graph of $f$ and a rectangle whose area is the same as the area under the graph of $f$.

What are the metaphors in "Sonnet 65"?

Shakespeare uses the military metaphor of a besieged city to emphasize the fragility of all that is worldly. No matter how strong the gates of such a city, even if they are made of steel, they are still subject to the decay of time. Yet Shakespeare knows of something stronger, much stronger than even the most impregnable fortress: the love immortalized in his works.
In using such a striking metaphor Shakespeare emphasizes the powerful nature of his love. This is something that will live on forever in his many poems, always able to withstand the "siege" of time. Shakespeare presents here a picture of his art which displays a considerable degree of confidence and self-assurance. He's absolutely certain that his work will attain immortality, thus achieving a great victory over the unrelenting forces of time.
https://www.poetryfoundation.org/poems/50646/sonnet-65-since-brass-nor-stone-nor-earth-nor-boundless-sea

William Shakespeare's "Sonnet 65," like many of Shakespeare's sonnets, deals with the effects of the passage of time on the person to whom the sonnet is addressed. The speaker laments that their beauty will inevitably fade but takes comfort in the fact that it can be preserved in poetry. To get this message across, Shakespeare employs several metaphors. Beauty is repeatedly compared to fragile, delicate things and contrasted with stronger, more solid objects. The argument being: if even these sturdier things cannot survive, how can beauty?
In the first quatrain:

Since brass, nor stone, nor earth, nor boundless sea,
But sad mortality o'ersways their power,
How with this rage shall beauty hold a plea,
Whose action is no stronger than a flower?

Beauty is compared to a flower—aesthetically pleasing but not strong enough to withstand the test of time when even metals and stones cannot. Mortality and the passage of time are also personified and ascribed the emotion of "rage." Personification is a type of metaphor whereby inhuman objects, concepts, or animals are imbued with human attributes.

In the next quatrain, beauty is compared to summertime, and it is summer that is personified, described as having sweet-smelling, "honey breath." This is a metaphor for summer wind, which, as a transient, insubstantial thing, cannot be expected to withstand the "wrackful siege" of time. In comparing his lover's beauty to wind, the speaker further emphasizes his point that it cannot last.

In the third quatrain, the speaker once again personifies time, here more explicitly than ever.

O fearful meditation! Where, alack,


Shall time’s best jewel from time’s chest lie hid?

Or what strong hand can hold his swift foot back?

Or who his spoil or beauty can forbid?



The speaker compares his lover's beauty to a jewel and bemoans that it is impossible to hide this jewel from time. He wonders who would be strong enough to fight time off, referring to time as a person with the pronoun "he."

The final couplet offers a bit of hope at last.
O none, unless this miracle have might,
That in black ink my love may still shine bright.

Here the speaker describes poetry as a miracle and conjures the image of his words ("black ink") shining bright with his love's beauty. Ultimately, the only things strong enough to fight time and preserve beauty are words which can capture and describe that beauty long after it has left this earth. The poem leaves us with this final metaphor of words and beauty still shining bright—that is, continuing to be visible years into the future.

What was the most important rule at Lark Creek Elementary?

Chapter 7 of Bridge to Terabithia introduces the reader to the most important rule at Lark Creek Elementary—family came first and family did not get discussed at school.

There was a rule at Lark Creek, more important than anything Mr. Turner made up and fussed about. That was the rule that you never mixed up troubles at home with life at school. When parents were poor or ignorant or mean, or even just didn't believe in having a TV set, it was up to their kids to protect them. By tomorrow every kid and teacher in Lark Creek Elementary would be talking in half snickers about Janice Avery's daddy. It didn't matter if their own fathers were in the state hospital or the federal prison, they hadn't betrayed theirs, and Janice had.

Janice Avery's father beat her. The abuse allegations were incredibly upsetting to Leslie and Jess, but Janice's friends Bobby Sue and Wilma had taken advantage of the situation and blabbed to the whole school after Janie confided in them. By the end of the school day, Janice was mortified to think that people would be laughing at her as she passed them in the hall. By sharing her private information with a couple of close friends, she'd opened herself and her entire family up to ridicule.
Leslie suggests that Janice pretend she has no idea what Wilma and Bobby Sue are talking about in hopes that the vague denial will make the story less interesting and quickly forgotten.

The answer to this question can be found in chapter 7. During the second half of the chapter, Jess and Leslie discover that Janice Avery is having a hard time with something. Jess tells Leslie that they need to find out what it is and try to make it better. Leslie discovers that Janice's father beats her badly on a fairly frequent basis. On this particular day, Janice confides in her friends, and her friends blab about it all over school. Jess is horrified about the entire situation because it is a clear violation of the most important rule of Lark Creek School. The rule is that what happens at home, stays at home.

That was the rule that you never mixed up troubles at home with life at school. When parents were poor or ignorant or mean, or even just didn't believe in having a TV set, it was up to their kids to protect them.

Jess explains to readers that no matter what happens, a person should never betray their own family. Janice Avery betrays her family by confiding in her friends.

How many people died as a result of the revolutionary war

I am going to assume that this question is asking about the American Revolutionary War that was fought to establish independence from Britain. The exact number of soldiers that died as a result of the war is difficult to know. The records were not as robust and well documented as compared to what we have today. Therefore, the death numbers are estimates. Additionally, the question is not clear about whether or not to include deaths that occurred outside of actual combat. Civilwar.org lists that an estimated 6,800 Americans were killed in combat. Another 17,000 died from disease, and somewhere between 8,000 to 12,000 died while being held prisoners of war. That's only American deaths. The British death totals are around 24,000, and nearly 8,000 Hessian soldiers died during the war.
http://necrometrics.com/warsusa.htm

https://www.battlefields.org/learn/articles/american-revolution-faqs

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 42

Find the derivative of the function $y = \sqrt{x} e^{x^2} (x^2 + 1)^{10}$, using log differentiation

$
\begin{equation}
\begin{aligned}
\ln y &= \ln \left[ \sqrt{x} e^{x^2} (x^2 + 1)^{10} \right]\\
\\
\ln y &= \ln \sqrt{x} + \ln e^{x^2} + \ln (x^2 + 1)^{10}\\
\\
\ln y &= \ln x^{\frac{1}{2}} + x^2 + \ln (x^2 +1)^{10}\\
\\
\ln y &= \frac{1}{2} \ln x + x^2 + 10 \ln (x^2 +1)\\
\\
\frac{d}{dx} \ln y &= \frac{1}{2} \frac{d}{dx} (\ln x) + \frac{d}{dx}(x^2) + 10 \frac{d}{dx} \ln (x^2 +1)\\
\\
\frac{1}{y}\frac{dy}{dx} &= \frac{1}{2} \cdot \frac{1}{x} + 2x + 10 \cdot \frac{1}{x^2 + 1} \frac{d}{dx} (x^2 +1)\\
\\
\frac{1}{y} y' &= \frac{1}{2x} + 2x + \frac{10}{x^2 +1} \cdot 2x\\
\\
\frac{y'}{y} &= \frac{1}{2x} + 2x + \frac{20x}{x^2 + 1}\\
\\
y' &= y \left( \frac{1}{2x} + 2x + \frac{20x}{x^2+1} \right)\\
\\
y' &= \left( \sqrt{x} e^{x^2} (x^2 + 1)^{10} \right) \left( \frac{1}{2x} + 2x + \frac{20x}{x^2+1} \right)

\end{aligned}
\end{equation}
$

Why should we donate to organizations to help endangered species?

Endangered species are very important to the world we live in . They must be protected against hunters and poachers , or else they won’t survive . Imagine the worled without elephants . Elephants are seeked after for their ivory. Removing the ivory from the elephants tusks is deadly and many elephants have lost their life due to poaching . As humans , we are meant to protect God’s animals and the Earth we have been granted . 

There are reasons why a person should donate to organizations that work to help endangered species. One reason is that this is a cause in which a person believes. People often donate time or money to help organizations that work to advocate for a cause that is of interest to that person.
Another reason is that these organizations need to lobby the elected officials to support their cause. There are people who want to end or weaken regulations to protect endangered species. Thus, organizations that work to protect endangered species need money to advocate for their cause. They need to hire lobbyists or staff to do this work. They may need to develop flyers, posters, or other printed materials to advocate for their cause. They need to develop connections with elected officials. Donating time and money will help accomplish these tasks.
These organizations have expenses that must be paid such as rent for office space, buying office supplies, as well as paying electric and water bills. Oftentimes, donations are a major source of revenue for these groups. People who donate time can also help the paid staff with the work that needs to be done. Without donations of time and money, these groups might not be able to survive.
There are several reasons for donating to groups that work to protect endangered species.
https://www.onegreenplanet.org/animalsandnature/fantastic-organizations-fighting-to-protect-endangered-species/

Can you give me two solid/short examples of transformative personal experiences which lead you to powerful paradigm shifts in your beliefs?

I would be more than happy to provide those two examples. Just remember that my two experiences are specific to my life and journey so you will have to think hard about the two experiences that you would like to use or highlight. 
In the first instance, before I migrated to the U.S, I always thought that there was a culture of 'freeness' - meaning, that there was plenty of things just being given away. The reality is that there are free items, yes but there are also requirements that need to be fulfilled before you get that 'free' item. What I never stopped to consider prior to my migration was the fact that the U.S played host to a variety of cultures that had been amalgamated to form what is thought of as American Culture. That there were different elements that helped to make up what was projected in the advertisements that I viewed on cable prior to my migration. 
In the second instance, I was witness to a situation where someone I knew closely was arrested for alleged child abuse. It turned out that the child was only spanked but decided to get the parent in trouble for the spanking and thus the entire debacle that went down. What caused the paradigm shift in this instance was the way in which the CPS and Police were quick to assume that the parent was abusing the child and did very little investigation. The charges against my friend were all dropped and her children returned to her care. What shocked me the most, and helped me to realize that in these instances these agencies presume guilt and then worry about proving innocence. I was always told and had always heard that you were 'innocent until proven guilty' but in the instance of my friend, she was presumed guilty until she could prove her innocence. 
What you need to keep in mind as a student answering this type of question is that in using these experiences that have shaped your perception of the world around you, it gives you a chance to explore what helps make you the person that you are and that will always translate to in-depth and knowledgeable writing on assignments like these. 

I would be happy to provide a couple of examples. Bear in mind, of course, that these are my examples—you will have to come up with your own to complete the assignment! However, I hope that the stories I share help you answer the question on your own. As you read my examples, keep an eye out for several key features:
A clear comparison of the differences in my beliefs before and after the experience
A succinct description of the event that changed my mind and how it affected me in the moment
The rough time frame over which I held the old and new beliefs and indications of when the change occurred
A respect for others who may hold different paradigms of belief
My first major example is religious. To reiterate, I am sharing my own beliefs, not what I think others should believe. If you decide to share a similar example, I recommend keeping your description matter-of-fact to avoid the appearance of proselytization.
As a young teen, I held a deep belief in the collective unconscious. While I did not believe in any particular deity, I held the firm conviction that supernatural beliefs had to come from somewhere and that superstition and worship were an essential part of being a complete person.
Then, in high school, I took a class on comparative religion. My teacher shared sociological theories that illustrated the practical ends religion could provide for groups, and my teacher demonstrated how evolutionary pressures could create a predisposition toward belief. I also learned about the wide scope of human religions and the many beliefs that I came to view as mutually incompatible.
Ultimately, this knowledge led me to stop identifying as a deist, and I began to call myself an atheist. I chose to focus on science, rather than spiritualism, as my primary means of understanding the world.
My second example is much less contentious but no less important. If you decide to go with something like my next case, make sure to emphasize its widespread impact on your life. Mundane examples do not have the same weight as religion, politics, and morality, so it is up to you to prove that they are substantial.
One night, my wife was worried about a nocturnal animal scurrying about on our street. I told her not to worry because skunks were harmless. She looked at me like I had grown a second head and said that it was an opossum. I lectured her on how it was obviously a skunk because it had black fur and a stripe. She angrily replied that she had lived in a neighborhood with opossums for years, and she knew exactly what they looked like. 
I pointed it out. "You're telling me that that's a opossum?"
She pointed to the other end of the street. "I'm telling you that that is a opossum!" she said.
We were both right: we had a skunk and a opossum on our street, and we were talking about different things entirely.
After that, I looked back at dozens of fights I had been in with dozens of people in the past. How many of them were because we had simply talked past each other? How many occured because we were holding two different conversations without realizing it? Since that day, I have been much slower to assume that my conversational partners are clueless and much more thorough about defining terms and finding common ground before wading headfirst into a debate.

What separates George from the rest of the characters in Of Mice and Men?

This is a great question. George is an unusual character in Steinbeck's novel in that he has a measure of humanity when it comes to Lennie and is the only one truly devoted to him. He has been with Lennie through some pretty rough events (the girl in the red dress being one mentioned in the book, but surely there have been other incidents), and he alone gives Lennie the mercy he deserves at the end. George could have abandoned Lennie at any time. But he didn't. Candy wouldn't have released Lennie (look at his actions with his beloved dog). Slim more than likely wouldn't have been able to protect Lennie, no matter how Jesus-like Steinbeck makes him out to be. Only George possessed the love required to take Lennie out to protect him from the horrors that would have descended upon him if Curly had gotten to him first. George is Lennie's only family and his only true friend.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 43

By using implicit differentiation, show that any tangent line at a point $P$ to a circle with center $O$ is perpendicular to the radius $OP$.

Assuming that the circle is centered at origin, its equation is

$x^ 2 + y^2 = r^2$

Taking the derivative of the curve implicitly we have,


$
\begin{equation}
\begin{aligned}

2x + 2y \frac{dy}{dx} =& 0
\\
\\
\frac{dy}{dx} =& \frac{-x}{y}


\end{aligned}
\end{equation}
$


Thus the slope of the tangent at $P(x_1, y_1)$ is $\displaystyle \frac{-x_1}{y_1}$

Also, the slope of the radius connecting the origin and point $P(x_1, y_1)$ can be completed as $\displaystyle m = \frac{y_1 - 0}{x_1 - 0}$

But, we know that the slope of the normal line is equal to negative reciprocal of the slope of the tangent line so..


$
\begin{equation}
\begin{aligned}

m_T =& \frac{-1}{m_N}
\\
\\
\frac{-x_1}{y_1} =& \frac{-1}{m_N}
\\
\\
m_N =& \frac{y_1}{x_1}
\qquad \qquad \text{which equals the slope of the radius}

\end{aligned}
\end{equation}
$



Therefore, it shows that any tangent line at a point $P$ to a circle with center $O$ is perpendicular to the radius $OP$.

In Pride and Prejudice, what does Elizabeth mean when she says, "Nothing so easy, if you have but the inclination, we can all plague and punish one another. Tease him—laugh at him.—Intimate as you are, you must know how it is to be done"?

Just prior to this statement, Mr. Darcy spoke and fairly explicitly explained why he would not wish to join the women in their stroll around the room. He says they likely know their figures appear to "greatest advantage" while moving in this way, so he can admire the two women best while seated. Miss Bingley, with false alarm and fake offense, asks Elizabeth how they should "punish" Mr. Darcy for such a claim. Although Miss Bingley is not sincere and truly has no wish to punish Mr. Darcy for anything—this is all just a part of her terrible and totally unrequited flirtation with him—Elizabeth answers her sincerely. She claims the best way to punish Mr. Darcy would be to laugh at him, implying that wounding his pride would be the surest way to punish him for anything. Further, because the Bingleys and the Darcys are such good friends (this is the "Intimate as you are" part), she believes Miss Bingley is well-qualified to ascertain on which subjects Mr. Darcy could be teased.

What does the Wife of Bath think of marriage?

The Wife of Bath is one of Chaucer's most enduring characters, especially since she functions as a remarkably early example of a feminist. Indeed, the Wife seems to reject traditional notions of femininity, as she values her independence and has a refreshingly unconventional philosophy when it comes to marriage. Flouting the idea that married women should meekly submit to the authority of men, the Wife suggests that women should have the power in marriage. She cements this idea by telling a tale focused on what women want (this turns out to be sovereignty), and she ends this story with a woman winning authority and power within marriage. As such, while the Wife does not object to marriage (indeed, since she's been married five times, she seems to rather enjoy it), she does want to change traditional notions of matrimony, as is evident from her belief in the need for female sovereignty.  

How did Bartolome de Las Casas characterize the native population? How do you think they would have responded to this description?

In short, Bartolome de Las Casas is an example of an early and very influential reformer, one who viewed Native Americans with empathy and humanity. But in many ways, Las Casas adheres to a "noble savage" trope that was already common in European literary depictions of Native Americans. He describes them as "innocent Sheep," people devoid of "Craft, Subtlety and Malice."
Of course, there is a sense in which Las Casas, in describing them in this way, denies them their humanity, portraying them as passive, weak figures. But it is important to note that he did so in order to juxtapose them with the Spaniards, who he consistently refers to as "Christians" in order to dramatize their brutality and greed. They treated the natives not simply as animals but as the "most abject dung and filth of the Earth," murdering them indiscriminately, stealing their wealth, and—perhaps most abominable to Las Casas—denying them the ability to become Christians.
This is actually another key point that Las Casas makes. The Natives, he argues, are ideal candidates for conversion to Christianity, precisely because he sees them as meek and guileless people. He notes that very few of the native peoples in the areas he visited were actually converted to Christianity, though he claims they were "apt to receive the principles of Catholic Religion." In this way, the Spanish conquerors had not only abused, tortured, and massacred these people, they had failed to live up to their responsibilities to God.
Las Casas, a witness to the horrors he described, sought to idealize Native Americans in order to demonstrate the brutality of the Spanish. He did so in order to advocate a more humane approach to dealing with Native Americans, one which would have the effect of leading more people in the Spanish Empire to Christianity.
https://teachingamericanhistory.org/library/document/a-short-description-of-the-destruction-of-the-indies/

https://www.americanyawp.com/reader/the-new-world/bartolome-de-las-casas-describes-the-exploitation-of-indigenous-peoples-1542/

The Dominican friar Bartolomé de las Casas's view of the native peoples he encountered in the New World is a stark departure from the view of most of his Spanish contemporaries. In his account, Historia de las Indias de las Casas describes the native peoples he encountered and his views on Spanish imperialism. In his work, he repeatedly refers to the natives as "sheep," indicating that they were unable to defend themselves from the Spanish "wolves and tigers." Also, by calling them sheep, he indicates that they were God's innocent creatures who should have been protected, not slaughtered. Bartolomé de las Casas often refers to the yearning the native peoples had to be free from subjugation, but he also refers to their complete helplessness at the hands of the Spanish.
It is hard to say exactly how the native population would have responded to Bartolomé de las Casas's description of them. They likely would have agreed with his statements about their desire to be free from Spanish subjugation and cruelty. Bartolomé de las Casas viewed them as human beings worthy of compassion and respect. They probably would have lauded him for that view. However, they may have taken exception to being described as completely helpless to defend themselves. There were indeed a number of courageous, yet ill-fated, native uprisings against the Spanish. However, it is easy to see why Bartolomé de las Casas thought the native peoples were helpless. Nearly all of them, including mighty nations such as the Inca and Aztec, were completely defeated and enslaved in a short amount of time.

Las Casas characterized indigenous people as human beings in a setting where they were seen as objects of material wealth.
Las Casas was passionately against slavery because he saw its targets as human beings.  Unlike many of his contemporaries, who supported the institution of slavery, he did not see the indigenous population as solely objects of material wealth.  Rather, when he participated in the colonization of Cuba, he saw victims of slavery as human beings: "I saw here cruelty on a scale no living being has ever seen or expects to see."  When Las Casas writes of cruelty, he displays empathy with those who have suffered injustice.  Las Casas saw indigenous people as ends in and of themselves, and not as a means to an end:  “The reason why the Christians have killed and destroyed such an infinite number of souls is that they have been moved by their wish for gold and their desire to enrich themselves in a very short time.”
Las Casas saw the "wish for gold" and the coveting of material profit as driving forces behind slavery. In his writing, Las Casas sought to create a  compassionate portrait of indigenous people.  He characterized them in traditional Christian terms of charity, good will, and obedience:  "And of all the infinite universe of humanity, these people are the most guileless, the most devoid of wickedness and duplicity, the most obedient and faithful to their native masters and to the Spanish Christians whom they serve." Las Casas suggested that those who were targeted as slaves were "most devoid of rancors, hatreds, or desire for vengeance of any people in the world."  In his writing and advocacy, Las Casas saw indigenous people as more than just tools for profit.  His characterizations reflected depth, understanding, and empathy.
Once convinced of slavery's immorality, Las Casas spent the bulk of his time in Spain trying to eradicate the institution.  Indigenous people would have responded favorably to Las Casas and his ideas.  His understanding towards those victimized by slavery was radical, reflective in the resistance that fellow Spaniards displayed towards him.  His actions underscored the courage of his convictions.  Las Casas himself was the owner of slaves and possessed an encomienda in Cuba.  However, when he realized that slavery was antithetical to Christian ideals, Las Casas gave up his holdings and freed his slaves.  It is fair to say that those who were freed would have viewed Las Casas as different than other Spaniards. They would have seen him as honorable and decent, and much different than others who participated in the slave trade.

How does the theme of Emily Dickinson's "Because I could not stop for death" compare to that of John Donne's "Death, be not proud"?

Perhaps the most interesting point of comparison between these two poems is the fact that, in each, Death is portrayed as subservient to humanity and powerless in the face of "Immortality."
In Donne's poem, the speaker has taken exception to the personified Death, and he expresses the command that he "be not proud." He points out that, far from being "mighty and dreadful," "yet thou canst not kill me." Death is not actually in control of who lives or dies but instead is "slave to fate, chance, kings and desperate men." That is: Death does not decide when he should arrive and intervene in the lives of people on earth; on the contrary, he is summoned by the invitation of "fate" or by the decrees of "kings" like a service man to take away the dead. And, in the end, Donne says that after "one short sleep . . . we wake eternally." Thus, only Death shall die, while humans will actually live.
Dickinson's speaker has had no altercation with Death; she does not find him to be "proud." However, she is not subservient to his wishes—she "could not stop for Death," with Death instead stopping for her, suggesting that he actually is tied to her timetable rather than she to his. Nor is he the only person who accompanies her on the final journey. On the contrary, "the carriage held but just ourselves / And Immortality." In traveling with Death, Dickinson does not feel any sense of fear or of being controlled by him. It is almost as if Death is an usher accompanying her "toward Eternity." While the behavior of her personified Death is gentler than that of Donne's, the poem shares the theme of Donne's that Death serves us, rather than we him and that ultimately he is only there to escort us towards immortality.

In their poems, Dickinson and Donne both express the idea that death is not something to fear or dread.  Their methods of expressing this theme, however, vary greatly.  Even though both personify death, they differ in their characterizations of death.  In Dickinson's poem, death is portrayed as a kindly gentleman who thoughtfully stops for the speaker, who was too busy with her daily affairs to stop for him.  He gently and slowly drives her to her final resting place, which is portrayed as a 

little house that seemed
A swelling of the ground;
The roof was scarcely visible.
The cornice, in the ground.  

Her grave is described as a house, certainly nothing to be afraid of.  But she also knows that this is the home where she will be forever.  The carriage holds Immortality, and the horses' heads "were toward eternity."  This poem, though seemingly a strong statement of faith in the afterlife, is somewhat ambiguous.  "Surmised" is an interesting word choice because it means to guess without sufficient evidence.  Perhaps the speaker only thought the horses were heading toward eternity and since she stepped into her carriage centuries ago has has only experienced a vast void. She does not mention heaven or really even the afterlife--only the slow journey to the end.  So, the reader is left to question whether Death is the kindly gentleman the speaker once thought he was and wonder whether what looks like a home is in actuality a cold, dark tomb where she will remain in limbo.  
Donne's sonnet personifies death as a pompous bully who truly has no power over any mortal.  Although many may fear death, death, like a bully, only blusters about with no true ability to harm.  Donne relies on paradox to prove his point: 

Death shall be no more; death, thou shalt die.

This paradox is resolved by Donne equating death to sleep, from which we awaken to eternal life.  When all people have died and reawakened, then death can be no more, and therefore we all can transcend death.  Even though Donne uses paradoxes throughout his poem, his message, unlike Dickinson's, lacks ambiguity.  Eternal life is clearly something to be desired; death is not to be feared.  It is instead something, like sleep, from which we derive much pleasure.

 . . our best men with thee do go,
Rest of their bones and soul's delivery.

In Dickinson's poem the speaker is compliant and perhaps duped.  In Donne's poem, the speaker, in the face of death, is defiant and victorious.  

How is the tension in the relationship between Elizabeth and John Proctor evident in The Crucible?

The tension between John and Elizabeth Proctor becomes evident in Act II.  Early in this act, John tells his wife, "I mean to please you, Elizabeth," and she replies, "I know it, John," but "it is hard [for her] to say," according to the stage direction.  Then, when John moves to kiss her, she merely "receives it" but does not kiss him back.  He is visibly disappointed.  The fact that it is difficult for Elizabeth to acknowledge that her husband is making an effort to make her happy is telling, and her inability (or unwillingness) to return his affectionate touches is also a major clue that all is not well in their relationship. 
A few moments later, John asks her if she is "sad again" and though "she doesn't want friction," according to stage direction, "she must" voice her concerns and suspicions about his whereabouts that evening.  That Elizabeth anticipates "friction" means that there must have been a good deal of it lately, as well.  Further, the narrator tells us that "A sense of their separation rises" up between them.  There seems to be a wide gulf between them as the scene continues: John is caught in a small lie, and Elizabeth grows instantly suspicious of him; he is angered by her suspicion, and the tension grows.   

What are some philosophical interpretations of the poem "Mending Wall"?

That is an interesting question to ask. In this context, I am interpreting "philosophical" to mean some timeless and universal meanings for Frost's "Mending Wall." The two that I take away after reading it are that we should tamper with nature only for some good purpose and that the structures created by humankind may interfere with relationships amongst people more than they aid them.
The first few lines of the poem tell us that nature does not like human-built barriers. The narrator says, "Something there is that doesn't love a wall" (line 1). That something is nature, which does its best to break up the wall with its cycles of freezing and warming. The narrator goes on to point out that, while there could be a purpose to building a wall, he clearly sees no such purpose in this situation.  Therefore, if we are going to build walls, or anything else, interfering with nature's natural course, we should do so only for a very good reason, to the benefit of someone or some ones. 
The narrator also sees that building can create a barrier and harm relationships:

Before I built a wall I'd ask to know
What I was walling in or walling out,
And to whom I was like to give offence (lines 32-35).

He understands that building a wall keeps people out as well as keeping something or someone in, and he sees that not having walls or other barriers might make for better neighbors than having walls. It is not too great a leap to infer from this that the narrator sees building upon the landscape as something potentially harmful to human relationships. If a structure is not enhancing our ability to get along with one another, perhaps it is a structure that should not be.

y'=arctan(x/2) Solve the differential equation.

Given ,
y'= tan^(-1) (x/2)
we have to get the y
so ,
=> y = int (tan^(-1) (x/2)) dx
By Applying the integration by parts we get the solution
so,
let u=tan^(-1) (x/2) => u'= (tan^(-1) (x/2) )'
let t= x/2
=> u' =(du/dt)*(dt/dx) = (d ((tan^(-1)(t))/(dt))(d/dx (x/2))
=(1/(t^2+1))*1/2
=(1/((x/2)^2+1))*1/2
=(4/(x^2+4))*1/2
=2/(x^2+4)
 
and v'=1 =>v =x
now by Integration by parts ,
int uv' dx= uv-int u'v dx
so , now
int (tan^(-1) (x/2))dx
= xtan^(-1) (x/2) - int 2x/(x^2+4)dx
let x^2+4 = q
=> 2x dx= dq
so ,
int (2x)/(x^2+4)dx = int 1/q dq = ln(q)+c =ln(x^2+4)+c
 
= x(tan^(-1) (x/2)) -ln(x^2+4)+C

"Math, statistics & psychology" course essay topic. Please explain the following in simple laymen's terms: How can you assess the amount of variation in one variable that is accounted for by the other? Also, why is this important to know?

In an experimental study (in the field of psychology or indeed any scientific field) variables are broadly split into two types: dependent and independent.
The dependent variable is the outcome variable of interest in the study. Changes in the dependent variable across various scenarios are measured, the scenarios being governed by experimenter-controlled adjustments to the independent variables.
Hence the independent variables are altered and controlled in a measured way in the experiment and the effect on the dependent variable is measured accordingly.
An assumption made when carrying out a scientific study is that there is an underlying relationship or equation relating the dependent and independent variables. There is also an understanding that, when observing real-world values of the variables, random noise will be naturally present. The experimenter hopes to see through the experimental noise to the underlying relationship between the variables. Bias in the measurement process should either be anticipated with accuracy or be kept to a minimum by taking sufficient precautions. Controlled randomized studies are the best way to achieve this, where the independent variables are fully controlled by the experimenter, study subjects are randomized to reduce individual bias and outcomes are measured with accuracy and good forward planning.
The decision as to which variables to choose as independent ones and which as dependent is governed of course by practical constraints, but most importantly the causal direction should make logical sense. It should be that the experimenter is assessing how the independent variables cause associated change in the dependent variable(s) and not the other way round.
The mathematical method to asses the causal relationship between dependent and independent variables is called statistical regression analysis.
In this, the dependent variable (Y) is regressed on the independent variable (X) (X and Y might be unit-valued or could also be vector-valued, that is have more than one component variable). By using the Gaussian method of least squares, the measured variation in Y conditional on the controlled variation in X is quantified so that, in the most basic case we can write the linear relationship
Y ~ a + bX
that is Y is approximately (where approximate means stochastic as opposed to deterministic) related causally to X by a straight line with intercept 'a' and slope 'b'. If X describes/causes Y in a statistically significant way, the slope coefficient 'b' is significantly different from zero. This is found if the F-test for the regression analysis gives a p-value less than or equal to a type I error alpha (alpha is usually set to 5%, p =0.05, or tighter still at 1%, p=0.01).
If X has a significant effect on Y then it accounts for variation observed when measuring Y. In that case 'b' would be statistically significantly different from zero. In cases where there are a few independent variables included in a study (this is of course common), those with numerically larger 'b' coefficients (amongst variables of comparable significance) are of more practical significance in that they result in bigger changes in Y.
If the slope 'b' for any independent variable is not seen to be significantly different from zero in the regression analysis, this suggests that the independent variable in question provides no relevant measurable information about Y.
The aim of scientific studies is to find independent variables that explain away (stochastic) variability in the dependent variable(s). If all independent variables of value are found then simple white noise should be left once the variability due to the independent variables is subtracted out of the total variability of the dependent variable. This is a perfect statistical model, rarely seen in practice. 
Once dependent variables can be stochastically modelled by independent variables they depend causally on, the dependent variables can be used as surrogates for the independent variables. This is particularly useful if, say, the independent variables are expensive or difficult to measure. More generally, causal trees of measurable variables build up a picture of a field of study. If any key variable on the tree is missing in future studies, its value can be imputed using knowledge of the causal tree worked on in earlier studies. Meta analysis where research results from similar competing studies are merged together aim to rework the tree to become more accurate and hence more useful.
I attach a link to a bbc programme website, cats versus dogs, where they worked with teams of scientists to compare differential behaviours between cats and dogs. The key independent variable is type of animal, and the dependent variables in each experiment address various attributes we typically associate with one or other animal. These experiments challenge traditional perceptions about traits the two animals have.
http://people.duke.edu/~rnau/regintro.htm

https://www.bbc.co.uk/programmes/b070ndj2

What are Columbus's thoughts about his journey and mission?

The prevailing theory about Columbus' motivation in journeying west into unknown territory is that he desired to gain wealth and glory for himself and Spain. However, as we know, he reached America, not Asia as he intended. It did not take long before other Europeans realized America and Asia were separate continents. Nevertheless, Columbus remained resolute in his assertion that he had reached India, or at least someplace nearby.
Many people find Columbus' resistance to the "New World" concept puzzling; as an explorer, for instance, he could have received far more glory for finding an entirely new continent than for finding a new route to Asia. 
However, an alternative theory about Columbus' motivations might help explain this. According to some recent historians, Christopher Columbus believed God had called him to lead a religious crusade against the Muslims, who had recently (1453) conquered the previously Christian stronghold of Constantinople. To finance this crusade, he sought a sea-route to India and the gold mines of Asia.
Assuming that Columbus' personal mission was religious in nature--to reclaim Christendom for the Christian Europeans--helps explain why he continued to believe he had reached Asia. Recognizing America as a new continent would have required him to doubt the divine blessing of his crusade (or at least cause him to rethink its specific nature).

What is a good quote about the conch from Golding's Lord of the Flies that shows the kids being civilized?

Two quotes about how the conch demonstrates civilization on the island include the boys coming when the conch is blown or listening to the person who is holding the conch.
The conch is a special shell that makes a loud sound when you blow into it.  Ralph and Piggy find it, and Piggy tells Ralph to blow into it.  When he does, all of the boys come to join him.  The conch is the thing that brings them all together. 

Signs of life were visible now on the beach. The sand, trembling beneath the heat haze, concealed many figures in its miles of length; boys were making their way toward the platform through the hot, dumb sand. (Ch. 1) 

The boys use the conch from then on to run their meetings.  The person who has the conch is the one who talks, and the other boys are supposed to obey the conch and listen.  It works pretty well for a while. 
When the little kids are afraid that there is a Beastie on the island, one of the littlest kids speaks up at the meeting, which is unusual because they are normally dominated by older kids.  This shows that the conch allows the boys to be more democratic, giving everyone a chance to speak. 

“Let him have the conch!” shouted Piggy. “Let him have it!”
At last Ralph induced him to hold the shell but by then the blow of laughter had taken away the child’s voice. Piggy knelt by him, one hand on the great shell, listening and interpreting to the assembly. (Ch. 2) 

The conch allows for civilization because it symbolizes order and power.  It is what brought all of the boys together, so it has great meaning.  The boys come when called.  They raise their hands.  They listen to the person who has the conch, no matter how small.

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 20

Factor the polynomial $P(x) = x^2 - 8x + 17$, and find all its zeros. State the multiplicity of each zero.

To find the zeros of $P$, we set $x^2 - 8x + 17 = 0$, by using quadratic formula


$
\begin{equation}
\begin{aligned}

x =& \frac{-(-8) \pm \sqrt{(-8)^2 -4(1)(17)}}{2(1)}
\\
\\
=& \frac{8 \pm \sqrt{-4}}{2}
\\
\\
=& \frac{8 \pm 2 \sqrt{-1}}{2}
\\
\\
=& 4 \pm \sqrt{-1}
\\
\\
=& 4 \pm i

\end{aligned}
\end{equation}
$


By factorization,


$
\begin{equation}
\begin{aligned}

P(x) =& x^2 - 8x + 17
\\
\\
=& \left[ x - (4 + i) \right] \left[ x - (4 - i) \right]

\end{aligned}
\end{equation}
$


Therefore, the multiplicity of each zero is $1$.

Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 112

Graph $3x+ y = -5$ by using $x$- and $y$-intercepts

$x$-intercept:


$
\begin{equation}
\begin{aligned}

3x+ y =& -5
&& \text{Given equation}
\\
3x+ 0 =& -5
&& \text{To find the $x$-intercept, let } y = 0
\\
3x =& -5
&& \text{Divide by } 3
\\
x =& \frac{-5}{3}
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $\displaystyle \left( \frac{-5}{3}, 0 \right)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

3x+ y =& -5
&& \text{Given equation}
\\
3(0)+ y =& -5
&& \text{To find the $y$-intercept, let } x=0
\\
y =& -5
&&

\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,-5)$

Graph the ordered pairs $\displaystyle \left( \frac{-5}{3}, 0 \right)$ and $(0,-5)$. Draw a straight line through the points.

Calculus of a Single Variable, Chapter 8, 8.4, Section 8.4, Problem 60

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

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

Discuss the known hate groups that have risen up in recent years in America. How do these groups stereotype against minority groups? Do you think white privilege plays a role in the rise of these hate groups?

According to the Southern Poverty Law Center (SPLC) monitoring group, there are 917 hate groups currently operating in the US. The year 2009 had 932 groups, with consecutive years showing a marked increase in numbers. However, figures started decreasing in 2012 (1007 groups) finally reaching a low of 784 groups in 2014. It is important to note that the year 2009 marked President Barrack Obama’s first term in office. After 2014, hate group figures increased, partly due to the difficult presidential campaign of 2016 that fueled extremist ideas. Some categories of hate groups listed by the center are Ku Klux Klan, Neo-Nazi, White Nationalist, Racist Skinhead, Black Separatist, Anti-LGBT, and Anti-Muslim.
The SPLC report also states that the highest increase in hate groups is to be found among the Anti-Muslim groups. Anti-Muslim groups depict Muslims as irrational, violent and intolerant of women and LGBT rights. They portray Islam as an evil religion. These groups increased in numbers after the World Trade Center terrorist attack of September 11th, 2001. Examples of anti-muslim hate groups are the ACT for America, Altra Firearms, Bomb Islam and Center for Security Policy.
White Nationalist hate groups focus on stereotyping non-white communities, which are portrayed as inferior. Groups such as the Ku Klux Klan, Racist Skinhead and Neo-Nazi can also be termed as White Nationalist, as their activities are geared towards demeaning other non-white communities. The largest group in this category of hate groups is the Council of Conservative Citizens. Since March 2016, the SPLC has seen increased fliering activities in college campuses, done by this type of hate group with an aim of attracting and recruiting students.
Black separatist groups are anti-white and generally oppose racial integration. They are interested in having separate institutions for black people. It is thought that theirs is a reaction to years of exposure to white racism. Examples of Black separatist groups are the Black Riders Liberation Party and the Israel United in Christ.
White privilege has to some extent played a role in the rise of these hate groups. The “Black Lives Matter” social media campaign, for example, exposed instances of white privilege and racism within America. Through it, attention was brought to police brutality against black people.
 
https://www.splcenter.org/hate-map

What happens to Julian?

Julian is a leading member of an anarchist rebel group called The Five Fishes. She's at the center of a love triangle between the so-called Warden of England, the dictator Xan, and his cousin, the story's protagonist, Theo Faron. Julian and Theo, along with other members of the rebel group, go on the run from the authorities. Julian is pregnant, and her unborn baby is a symbol of hope and renewal in a society where chronic infertility is the norm.
However, Xan cynically sees Julian's baby as a chance to consolidate his own power as dictator. He will be able to present himself as the man who finally put an end to England's infertility crisis. But he's unable to put his dastardly plan into effect as Theo kills him. Julian gives birth to a healthy baby boy; the hopes and dreams of millions have finally been fulfilled. Yet at the same time, Julian is deeply troubled by Theo's putting on Xan's Coronation Ring, the symbol of dictatorial power. It seems that there hasn't been any real change, after all; one dictator has simply been replaced by another.

What does Anna do when the circus tent pole is struck by lightning?

When the circus tent pole is struck by lightning, Anna does a number of important things. First of all, when Harry does not catch her, she realises that something is wrong and she removes her blindfold. Secondly, she watches as Harry moves past her, on the wrong side, and suddenly realises that she must choose between saving her husband and saving her unborn child. (Remember that Anna is seven months pregnant.)
In that moment, Anna chooses to save her child: she changes the position of her body, twisting forward towards a heavy wire which she grabs hold of. The wire is extremely hot because of the lightning but Anna is able to safely descend to the ground. She does, however, suffer burns to her hands from the wire and a broken arm as a result of an "overeager rescuer" but is otherwise unharmed.

What are the similarities of social classes in Great Gatsby?

One of the most important similarities between the social classes is their firm attachment to the American Dream. Whether it is the old money elite of East Egg, the parvenus of West Egg, or the lower-class denizens of the Valley of Ashes, everyone it seems is committed to the headlong pursuit of riches and the opulent lifestyle that it brings. The consequences for all classes is damaging in some way, but it is notable that the less socially prominent, in the shape of Myrtle Wilson and Gatsby, are the ones who come off the worst. The main reason for this is that both Myrtle and Gatsby are striving for something they do not have; both yearn for acceptance from the established upper class and seek to escape their humble backgrounds. The likes of Tom and Daisy, however, already enjoy what Jay and Myrtle can only dream of. However, the American Dream also has a negative impact upon them, corrupting their souls as they indulge themselves in a shallow, vacuous existence.

What foreshadowing can be seen when Montresor ensures the secrecy of his actions?

Foreshadowing is a warning or hint of an event that is going to occur later on in a story, movie, or novel. In "The Cask of Amontillado," Poe uses foreshadowing by suggesting something very bad is going to befall the clueless Fortunato. We learn in the first paragraph that Fortunato has injured Montresor in unspecified ways and that Montresor has revenge in mind. This warns the reader that revenge will be central to this tale. Other instances of foreshadowing include the fact that Montresor's servants are all away partying during the Mardi Gras, leaving his house empty and leading the reader to wonder why Montresor doesn't want anybody around. Secresy, including taking Fortunato deep into the catacombs, far from any human eyes, makes us nervous about what Montresor has in mind. We don't do evil deeds before witnesses, if we can avoid it. Further, once they are in the catacombs, Montresor, knowing his "friend" will refuse, urges Fortunato to "go back before it is too late." He seems, in the moment, to be responding to Fortunato's cough, but the ominous words "before it is too late" hint that Montresor has a plan in mind. The fact that the two lead characters are surrounded by the bones of dead bodies foreshadows death.
All through the story, Montresor suggests that he is going to do something terrible, and the end of the story does not disappoint. At the end, we might be shocked, but we probably are not surprised: Poe has given us enough indications of Montresor's intentions that the fantastic murder is believable to us. 

What evidence suggests that Eliezer is devoutly religious?

The main character in Elie Wiesel's novel Night is a young boy named Eliezer. This story is about Eliezer's experiences during World War II. Throughout the story, Wiesel presents evidence that support the idea that Eliezer is devoutly religious.
In chapter one, Eliezer states that he studies the Talmud daily and also goes to the Temple every night. The Talmud is the body of Jewish civil and ceremonial law. Despite his father believing that he is too young, Eliezer also wants to study Kabbalah. Kabbalah is a Jewish school of thought. One night when he is at the temple, Eliezer meets Moishe the Beadle who happens to know a lot about Kabbalah and begins to teach him.
As the novel progresses, Eliezer mentions his faith multiple times and continues to pray regularly. Eliezer is forced to see many horrific things while living in a concentration camp called Auschwitz and his faith is challenged. He wonders if his God is a just God, a God who can be indifferent to the suffering he is witnessing, if his God is a good God. Despite having these thoughts and feelings, Eliezer remains devoutly religious and continues to pray for strength.

At the beginning of the novel, Eliezer mentions that he devoted his life to understanding the Talmud and studying Kabbalah while living in Sighet. Eliezer says that by day he would study the Talmud which is the central text of Rabbinic Judaism, and at night he would weep over the destruction of the Temple. Although Eliezer's father discourages him from studying Jewish mysticism known as Kabbalah, he becomes friends with Moishe the Beadle who teaches him the Zohar. Eliezer mentions that Moishe the Beadle would spend hours on end explaining the mysteries of Kabbalah. Even after Moishe the Beadle is deported by the Hungarian police, Eliezer continues to visit and pray in the synagogue. As the novel progresses, Eliezer becomes a prisoner who is forced to work in the inhumane concentration camps. He experiences horrific tragedies but continues to pray to God. Unfortunately, Eliezer loses his faith after witnessing innumerable tragedies such as the death of his father. 

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 10

A quadratic function $f(x) = x^2 + 8x$.

a.) Find the quadratic function in standard form.


$
\begin{equation}
\begin{aligned}

f(x) =& x^2 + 8x
&&
\\
\\
f(x) =& (x^2 + 8x + 16) - (1)(16)
&& \text{Complete the square: add } \left( \frac{8}{2} \right)^2 = 16 \text{ inside parentheses, subtract $(1)(16)$ outside}
\\
\\
f(x) =& (x + 4)^2 - 16
&& \text{Factor and simplify}

\end{aligned}
\end{equation}
$


The standard form is $f(x) = (x + 4)^2 - 16$.

b.) Find its vertex and its $x$ and $y$-intercepts.

Using the formula of standard form of a Quadratic function,

$f(x) = a (x - h)^2 + k$

We know that the vertex is at $(h, k)$, so the vertex of $f(x) = (x + 4)^2 - 16$ is at $(-4, -16)$.


$\begin{array}{llll}
\text{Solving for $x$-intercepts} & & \text{Solving for $y$-intercept} & \\
\text{We set } f(x) = 0, \text{then} & & \text{We set } x = 0, \text{ then} & \\
0 = (x + 4)^2 - 16 & \text{Add } 16 & y = (0 + 4)^2 - 16 & \text{Substitute } x = 0 \\
16 = (x + 4)^2 & \text{Take the square root} & y = 16 - 16 & \text{Simplify} \\
\pm 4 = x + 4 & \text{Subtract } 4 & y = 0 & \\
x = \pm 4 - 4 & \text{Simplify} & & \\
x = 0 \text{ and } x = -8 & & &
\end{array}
$


c.) Draw its graph.

Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 22

We will solve the problem using Wolfram Mathematica (you can also use Wolfram Alpha which is free).
Graph of
Plot[1/(1 + E^Tan[x]), {x, - Pi/2, Pi/2}]
Plot[1/(1 + E^Tan[x]), {x, -6 Pi, 6 Pi}]
First line of code is used to make the first image and second to make the second image. The vertical lines in the second image are actually asymptotes.
Finding
Simplify[D[1/(1 + E^Tan[x]), x]]
In the code line above command Simplify is there to simplify the result obtained by differentiation.
The result is f'(x)=-(e^tan(x) sec^2(x))/(1 + e^tan(x))^2

How was the stable buck injured in Of Mice and Men?

Crooks is the name of the ranch's stable buck. In Chapter 2, Candy tells George that the boss was upset they did not show up to work in the morning. He says the boss gave the stable buck hell. George then asks why the boss would give the stable buck hell, and Candy tells him the stable buck is a Negro. Candy goes on to tell George that the stable buck was injured after a horse kicked him and gave him a crooked back. Candy then tells George that Crooks is a nice man who usually keeps to himself and reads a lot. Later in the novella, Lennie enters Crooks's room, which is segregated from the bunkhouse because he is black. Crooks is a lonely man who attempts to pick on Lennie about George not returning to the ranch. After Lennie physically threatens him, Crooks stop picking on him and listens as Lennie tells him about owning their own home.

How does Odysseus show hospitality in The Odyssey?

According to the Oxford English Dictionary, hospitality is defined as the friendly and generous reception and entertainment of guests, visitors, or strangers. Using this definition, there is only one place Odysseus could show hospitality, and that is when he returns to his home in Ithaca. For the majority of Homer's epic poem, Odysseus is far from home and is himself the guest of others. Odysseus showed passive or unwilling hospitality with the hundreds of suitors who came to his house and feasted on his wine and meat. In the quote below, Athena is asking Telemachus about the suitors:

And Athena said, "There is no fear of your race dying out yet, while Penelope has such a fine son as you are. But tell me, and tell me true, what is the meaning of all this feasting, and who are these people? What is it all about? Have you some banquet, or is there a wedding in the family—for no one seems to be bringing any provisions of his own? And the guests—how atrociously they are behaving; what riot they make over the whole house; it is enough to disgust any respectable person who comes near them."

In the next quote, it is interesting to note that the servants were mixing water with the wine. In ancient Greece, how much water was mixed with the wine was a sign of the status of the guest. This quote shows that these guests were not highly regarded:

Men-servants and pages were bustling about to wait upon them, some mixing wine with water in the mixing-bowls, some cleaning down the tables with wet sponges and laying them out again, and some cutting up great quantities of meat.
https://www.lexico.com/en/definition/hospitality

When Odysseus is disguised as an old beggar, brought to his home in Ithaca by Eumaeus, his loyal swineherd, the suitors force him into a fight with another local beggar, Irus. One way in which Odysseus shows hospitality to Irus, his opponent in the match, is that he doesn't kill him. This might sound like an odd way to define hospitality to a present-day reader; however, Odysseus and Irus have been pitted against each other by the suitors, and the suitors have said that whichever of them wins the fight gets to eat.  Odysseus is still the master of this house, even if no one is aware that he is home, and he shows Irus hospitality by merely knocking him out instead of killing him. Athena has filled out Odysseus's muscles, making him even more powerful, and yet he restrains himself and allows the old man to live.

What role does Ben Du Toit, in A Dry White Season, represent in the South African society under apartheid?

Ben Du Toit represents a minority of white South Africans who took an active role in objecting to the draconian laws of Apartheid that were in place from 1948 to 1994. While some members of this group became conscientious objectors, objecting to doing their compulsory military service, Du Toit took his stand in a different way.
Upon finding out that Jonathan had been a victim of the type of police brutality that was so common during Apartheid, Ben adopts the role of resistor, protector, and activist.
When Jonathan's father, Gordon, disappears while looking for his son in police custody, Ben's role is to take up this search, and for playing the role of investigator, he ends up paying the ultimate price.
While most white South Africans either sat back and enjoyed reaping the benefits of Apartheid or turned a blind eye to it, Ben Du Toit is portrayed as one of the rare characters who could see the regime for the disgrace that it was.

Ben Du Toit is one of a relatively small number of South African whites during the apartheid era to stand up and publicly oppose the regime. He seethes at the racial injustice around him, which is brought home to him by the suspicious disappearance of his black gardener, Gordon. Ben sets out to uncover the truth of what happened to Gordon, but this is a dangerous undertaking. South Africa at that time was a virtual police state, with sudden disappearances and extra-judicial killings of the regime's opponents frighteningly common. Ultimately, and perhaps inevitably, Ben's incredible bravery costs him his life.
Ben's courage stands as a stark contrast to the general apathy of many white South Africans in the 1970s, the time in which the story is set. The title of the book itself is an allusion to this general malaise as it manifests itself in the life of the unnamed narrator. But Ben's selfless sacrifice acts as an inspiration to the narrator, holding out the possibility that other white South Africans may follow his shining example and stand up to challenge a system based on racism, injustice and brutal repression.

How did John Milton impact the Renaissance era?

Milton's impact on English literature overall did not really occur until after his death. By this time the period we label "the Renaissance," even in its broadest sense, was over. When Paradise Lost was published in the late 1660's, the Restoration of the Stuart monarchy had occurred and Milton, because of his unchanged political views and his having served in the Commonwealth under Cromwell, was now persona non grata with the regime. Apart from the personal isolation (and even his brief time in jail) this entailed for Milton, Paradise Lost was stylistically out of touch with current trends. Milton wrote in blank verse when the new trend was to employ rhymed couplets. The severe religious message of his epic was also out of step with the more carefree, anything-goes literary and social atmosphere of the Restoration.
Soon after his death, however, Milton came to be recognized by many as the greatest of all English poets. Despite political, religious and aesthetic differences, John Dryden and Alexander Pope considered Milton an epic poet equalling or even surpassing Homer and Virgil. Decades later, in his Lives of the English Poets (1779), Samuel Johnson expressed similar views. Despite the changed aesthetic of the nineteenth century, the Romantic and Victorian writers extolled and idolized Milton, seeing in him not only a great poet but a courageous individual who remained firm in his beliefs while others conveniently switched their political allegiances in accordance with the regime changes of the time.

Renaissance literature is known for the elevation of the sonnet form and the drama. John Milton, a poet and scholar, influenced the period by ushering in the return to the epic, a longer poetic form. Milton wrote in a variety of poetic forms, including the sonnet, but is best known for the epic Paradise Lost.
As a Puritan and supporter of Cromwell in the English Civil War, Milton approached the story of Lucifer's fall from Heaven and the subsequent temptation he poses to Adam and Eve as an allegory. On one level it retells the story of Genesis with purely religious implications. On another level, he uses that very story to describe the English Civil War, with the omnipotent God representing the king, and the inspirational Lucifer, who demands equality with God, representing Cromwell.
The political and religious implications of the work influenced the culture and society of the time. Additionally, the actual poetic form encouraged a transition to longer works by Alexander Pope and others who transitioned from the Renaissance to the Enlightenment.

Dear Educators, Write a short analysis of the following characters, themes, and symbols from the play (one analysis for each): Dona Ana de Pantoja Brigida Captain Centellas Don Rafael de Avellaneda Pascual Lucía Hate and Love (theme) Betrayal (theme) Faith (theme) Hope and Despair (theme) Cloak (symbol) If you could think of two extra symbols or motifs, that would be great too. Thank you.

Don Juan Tenorio is the story of two men who make a bet to see who can do the most damage in a year. When that bet spawns another, Don Juan has to try to seduce Don Luis's fiancee and kidnap his own bride. These actions lead to many deaths, the prospect of Don Juan facing eternal damnation, and, finally, Don Juan finding forgiveness with God.
Dona Ana de Pantoja is the fiancee of Don Luis. She is loyal and promises him that she will not sleep with Don Juan. Unfortunately, she is tricked into thinking that Don Juan is Don Luis and thus is unable to marry Luis. She is very wealthy. After she is tricked and cannot marry Don Luis, she is left abandoned and bereft.
Brigida is the servant of Dona Ines, Don Juan's promised bride. She is sneaky and motivated by money. When Ciutti approaches her with the plan to turn Ines's mind toward Don Juan, she takes the money and agrees to do it. She manipulates Ines into thinking that Don Juan is wonderful and desirous of her. She says, "I have convinced her in such a clever way she'll follow you, any day, like a little lamb." Brigida seems to pity Ines's isolation somewhat and calls her a "poor little bird in a cage."
Captain Centellas believes that Don Juan is more evil than Don Luis. He says that he is wagering everything he has on Don Luis. He is perceptive enough to recognize Don Juan even when he wears a mask. He is a God-fearing man who warns him to fear those who are of God.
Don Rafael de Avellaneda bets on Don Luis to win the wager. He is an impulsive man who says that even though he does not know anything about Don Juan, he believes he knows enough of Don Luis's deeds to wager blindly.
Pascual is a servant of Don Luis who agrees to help him with the second bet between Don Luis and Don Juan. He says he will serve him until death. He is loyal and also grounded. He tells Don Luis to forget the bet.
Lucía works for Dona Ana and is selfish and driven by money. Even though she knows Dona Ana is engaged, she agrees to let Don Juan in for 200 gold pieces. At first, he offers 100, but he then doubles it when she hesitates.
The theme of hate and love is prevalent in the play. Everyone is doomed by hate, and Don Juan is redeemed by the love of Ines. When Don Luis and Don Gonzalo refuse to stop their persecution of Don Juan, who says that he loves Ines and is a changed man, he chooses to kill them instead. He says Don Gonzalo is taking his salvation. In the end, Ines loves Don Juan enough that she gives her soul to save his own and literally pulls him from the cusp of Hell.
The theme of betrayal is best shown between Don Luis and Don Juan. By the terms of their second bet, Don Juan has to try to sleep with Don Luis's fiancee, Ana. Because he does not yet know how much he loves her, Don Luis agrees to this bet, betraying Ana. Ultimately, Don Juan betrays Don Luis by both sleeping with his fiancee and pretending to be Don Luis to do so.
Faith is an important theme in the play. Don Juan does not have faith in God and tries to find his salvation in worldly pleasures. He is only redeemed at the end when Ines—who is pure and faithful—agrees to bind her soul to his and either be saved or damned with him. At the last moment of his life, he finds faith and calls to God for forgiveness. They both go to Heaven.
Hope and despair also play an important role in the play. When Don Juan is in despair because he cannot find forgiveness with Don Gonzalo or Don Luis, he acts out in rage and kills them. This sends him deeper into despair and forces him to be away from Spain for five years. Only the hope Ines had that Don Juan could find God and ask for forgiveness saved him from Hell at the end of the play.
Cloaks and masks are major symbols in the play. They prevent people from being seen as they are. They allow the characters to hide things and to lie to each other. They show people refusing to be their true, authentic selves. For example, when Don Luis comes to get revenge on Don Juan, he comes wrapped in a cloak. Don Juan's servant is not able to identify him to his master.
Other important symbols in the play are snakes and ashes. They appear instead of food at the ghostly banquet hosted by Don Gonzalo. They represent Don Juan's eternal reward if he does not choose to repent and find forgiveness with God.

do you believe the federal government of the 1920s could have taken a more active role in helping to regulate the economy and would this have prevented the stock market crash of 1929 and the Great Depression? Is it the government’s responsibility to be involved in the economy? Support your answer with specific examples and make sure to cite all of your sources

During the 1920s, the government adopted a laissez-faire attitude towards businesses and the economy. There were few regulations placed on businesses during this time. It can be argued that this contributed to the start of the Great Depression. Because there were few controls on banks and on the stock market, banks invested money that had been deposited in the banks into the stock market. Additionally, people were able to buy stocks by only making a small deposit. This lack of regulation set up the potential for disaster, which occurred when the stock market crashed.
It is because of many situations similar to this that more people began to feel the government should have some role in regulating the economy. These people pointed to abuses in the past in the workplace, such as poor, unsafe working conditions and the use of child labor, as reasons why the government should be involved in the economy. They also pointed to the bad conditions that had existed in the meat industry as another example why the government needs to have some regulation of the economy. Finally, the events leading to the Great Depression described above gave further support to the idea of the government having a role in the economy. These people believe that the government needs to have a role in the economy to prevent abuses from occurring.
https://smallbusiness.chron.com/role-government-business-803.html

https://www.u-s-history.com/pages/h1564.html

Explain how Ichabod Crane is positive and comical on one hand and negative on the other.

In Irving's "The Legend of Sleepy Hollow," Ichabod Crane can be seen as a comical character first because of his appearance: 

He was tall, but exceedingly lank, with narrow shoulders, long arms and legs, hands that dangled a mile out of his sleeves, feet that might have served for shovels, and his whole frame most loosely hung together. His head was small, and flat at top, with huge ears, large green glassy eyes, and a long snipe nose, so that it looked like a weather-cock, perched upon his spindle neck, to tell which way the wind blew.

The narrator goes on to compare Ichabod Crane's appearance to that of a scarecrow, making his pursuit of the beautiful and wealthy Katrina Van Tassel seem ludicrous, especially when contrasted with his rival, Brom Bones, a young man "of Herculean frame" and athleticism.
It is also comical that a man as educated and intellectually gifted as Ichabod is so easily duped by Brom Bones into believing that the ghostly decapitated body of a Hessian soldier from the Revolutionary War stalks about at night and could harm him.  
What is negative about Ichabod Crane is his falseness, greed, and avarice.  He comes to Sleepy Hollow as a teacher, traditionally a "helping" profession. However, once he sees the bounty of Sleepy Hollow and the wealth of Katrina's family, he pursues her not for love, but for what he will gain from marriage into a wealthy family. He greedily helps himself to all the delicious and plentiful food his hosts offer, dreaming of the day he can abandon the schoolroom and be the master of a bountiful farm.

Who was the 42nd President of the United States?

William Jefferson Clinton was the 42nd President of the United States, serving from January 20,1993 through January 20, 2001. Clinton, a Democrat, defeated incumbent Republican George H. W. Bush with 370 electoral votes to Bush’s 168. The weakening economy damaged the incumbents high approval ratings along with his broken promise of no new taxes which Clinton used adroitly to propel himself into the White House at the age of 46, which at that time made him the third youngest president and first Baby Boomer to be elected.
Clinton served two terms as President, winning his second term in 1996, defeating Republican Senator Bob Dole (KS) with 49.2%of the popular vote. Clinton became the first Democrat since Franklin D. Roosevelt to win more than one term.

The 42nd President of the United States was Bill Clinton. Clinton ran as a member of the Democratic Party and was first elected in 1992, beating out the Republican Party incumbent George H. W. Bush convincingly. He was reelected in 1996, receiving about 50% of the popular vote while running against Republican candidate Bob Dole.
Clinton was an effective leader, guiding the United States through most of the 1990s, a period of prosperity and economic growth. He sought to spearhead a major health care reform in the United States during his time in office, but he did not succeed in implementing his program while President.
Clinton was quite bright and talented when young. After earning an undergraduate degree from Georgetown University, he ended up a Rhodes scholar and studied at Oxford. Thereafter, he studied law at Yale University and then went into politics in his home state of Arkansas. He was elected governor there in 1978.

Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 74

Add: $(-6m^3 + 2m^2 + 5m) + (8m^3 + 4m^2 - 6m) + (-3m^3 + 2m^2 - 7m)$

Remove the parentheses that are not needed from the expression.
$-6m^{3}+2m^{2}+5m+8m^{3}+4m^{2}-6m-3m^{3}+2m^{2}-7m$


Since $-6m^3$ and $8m^3$ are like terms, subtract $8m^3$ from $-6m^3$ to get $2m^3$
$2m^{3}+2m^{2}+5m+4m^{2}-6m-3m^{3}+2m^{2}-7m$


Since $2m^3$ and $-3m^3$ are like terms, add $-3m^3$ to $2m^3$ to get $-m^3$
$-m^{3}+2m^{2}+5m+4m^{2}-6m+2m^{2}-7m$


Since $2m^2$ and $4m^2$ are like terms, add $4m^2$ to $2m^2$ to get $6m^2$
$-m^{3}+6m^{2}+5m-6m+2m^{2}-7m$


Since $6m^2$ and $2m^2$ are like terms, add $2m^2$ to $6m^2$ to get $8m^2$
$-m^{3}+8m^{2}+5m-6m-7m$


Since $5m$ and $-6m$ are like terms, add $-6m$ to $5m$ to get $-m$.
$-m^{3}+8m^{2}-m-7m$


Since $-m$ and $-7m$ are like terms, subtract $7m$ from $-m$ to get $-8m$.
$-m^{3}+8m^{2}-8m$

Why do Tom and Daisy stay together?

We're never told exactly why Daisy and Tom stay together. We know from early on in the novel that Tom is having an affair with another woman. We know that Daisy knows about the affair, though not who the woman is, and we learn that it makes Daisy unhappy. Later, we find out that from the earliest days of their marriage, Tom found lower-class women to have affairs with. Nevertheless, he seems to consider Daisy a highly cherished possession.
Beyond that, they seem to have a special bond. We see this on three occasions. The first is when they come together to one of Gatsby's parties for the first time. Neither of them like the party—they seem to think it is beneath them, full of vulgar people. Because Gatsby suddenly sees his parties through Daisy's eyes, he abruptly stops having them.
The second is after Tom has discovered her affair. He knows how to get Daisy back. At the Plaza, he says:

And what's more, I love Daisy too. Once in a while I go off on a spree and make a fool of myself, but I always come back, and in my heart I love her all the time.

When Gatsby presses Daisy to say she never loved Tom, Daisy says:

I did love him once but I loved you too.

She goes on:

"I can't say I never loved Tom," she admitted in a pitiful voice.

Tom then moves in for the kill and verbally attacks Gatsby as a criminal. Gatsby tries to defend himself to no avail. Nick states that,

with every word she [Daisy] was drawing further and further into herself, so he [Gatsby] gave that up, and only the dead dream fought on as the afternoon slipped away, trying to touch what was no longer tangible, struggling unhappily, undespairingly, toward that lost voice across the room.

At this point, Tom knows he has won and feels safe enough to let Daisy and Gatsby drive home alone together.
The third point that shows their bond is when Nick, after the accident, sees them through the pantry window:

Daisy and Tom were sitting opposite each other at the kitchen table, with a plate of cold fried chicken between them, and two bottles of ale. He was talking intently across the table at her, and in his earnestness his hand had fallen upon and covered her own. Once in a while she looked up at him and nodded in agreement.
They weren't happy, and neither of them had touched the chicken or the ale and yet they weren't unhappy either. There was an unmistakable air of natural intimacy about the picture, and anybody would have said that they were conspiring together.

From these episodes, it seems clear that a bond of class, of familiarity, of intimacy, and even of love holds Tom and Daisy together. Daisy is weak and Tom protects her.
 
 

When does Doug's father start acting nicer?

The inciting incident that sparks Doug's father's change of character comes in chapter 8, after Christopher has just been arrested for burglary. Doug finds his father with Ernie Eco, as usual. After receiving the news of his son's arrest, Doug's father doesn't react as expected. He looks straight at Ernie Eco. His reaction implies that for the first time, he is seeing the effects of his dishonorable behavior. Though for most of the book so far, Doug's father has acted selfishly and cruelly, this is the first time that he has really had the chance to see how his actions have affected his sons in particular. His glance at Ernie also implies that he knows what Ernie has done. Doug's father is forced to witness the punishment for someone else's wrongdoing borne out on his own son. Later on in the same chapter, Doug sees Ernie wearing the missing Yankees jacket. His father is there and is again forced to witness the consequences of his own behavior and of Ernie's crime. The transformation that Doug's father has undergone becomes evident in the last chapter. It is clear he is hurting. It is also clear that he is trying his hardest to mend his family's emotional wounds. He is learning to love them again.

What is the connection between the novel and JFK?

In Valerie Sayers's novel Who Do You Love, President John F. Kennedy plays an important, yet indirect role within the plot. Set in the 1960s, Who Do You Love follows the Rooney family. A group of Irish Catholic misfits, the Rooneys are going through hard times that include financial difficulties, intellectual differences, and yet another pregnancy.
Not only was John F. Kennedy the sitting president at the time of the novel, but he was also an Irish Catholic—just like the Rooneys. They respect him immeasurably because of his presidency, and they relate to him mostly due to his religion.
In the novel, President Kennedy isn't just busy uniting the nation—after his brutal assassination, the Rooneys (and everyone else in America) are thrown into terrible grief that ultimately unites them together. While finances and other difficulties were ready to break them all apart, it is the tragic death of JFK that allows them to unite in spectacular grief and stay together as a family.

What images of coldness can you find in "The Cold Equations"?

The story is indeed full of imagery expressing the "coldness" inherent in the decision to jettison Marilyn into space. Here's an example:

“And it won’t come back—but there might be other cruisers, mightn’t there? Isn’t there any hope at all that there might be someone, somewhere, who could do something to help me?” She was leaning forward a little in her eagerness as she waited for his answer. “No.” The word was like the drop of a cold stone and she again leaned back against the wall, the hope and eagerness leaving her face. “You’re sure—you know you’re sure?”

The word "no" is likened to the "drop of a cold stone." The lone word is grim in its finality and does little to comfort Marilyn. The decision to jettison Marilyn is a calculated, uncompromising one. The pilot simply tells Marilyn that "there is nothing and no one to change things." Essentially, the softer impulses (such as mercy or pity) will never be part of any scientific equation.
Another example of "cold" imagery is:

They would hate him with cold and terrible intensity, but it really didn’t matter. He would never see them, never know them. He would have only the memories to remind him; only the nights of fear, when a blue-eyed girl in gypsy sandals would come in his dreams to die again . . .

The pilot knows that his decision is based on cold, hard math. Yet, he also understands that Marilyn's parents would never forgive his detachment; he fears that their hatred would be unrelenting, unswerving, and irrevocable in its intensity. 
The text tells us that the laws of nature are "irrevocable and immutable" and that "Men could learn to use them, but men could not change them." Although the pilot can provide logical reasons for jettisoning Marilyn, he knows that her parents will never view his decision as anything other than a vile, merciless move to preserve the status quo. Their hatred towards him will be as "cold" and deliberate as his decision.
 

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 78

arctan(xy) =arcsin(x + y)
First, take the derivative of both sides of the equation using implicit differentiation.
d/(dx)[arctan(xy)] = d/dx[arcsin(x + y)]
Take note that the derivative formula of arctangent is

d/dx[arctan(u)]=1/(1+u^2)*(du)/dx
And the derivative formula of arcsine is

d/dx[arcsin(u)] = 1/sqrt(1-u^2)*(du)/dx
Applying these two formulas, the equation becomes
1/(1+(xy)^2)*d/dx(xy) = 1/sqrt(1 - (x+y)^2)*d/dx(x+y)
To take the derivative of xy, apply the product rule.

d/dx (u * v) = u *(dv)/dx + v *(du)/dx
Applying this formula, the equation becomes
1/(1+(xy)^2)*(x*d/dx (y) + y*d/dx(x))= 1/sqrt(1 - (x+y)^2)*(d/dx(x)+d/dx(y))
1/(1+(xy)^2)*(x*(dy)/dx + y*1)= 1/sqrt(1 - (x+y)^2)*(1+(dy)/dx)
Then, isolate (dy)/dx .
x/(1+(xy)^2)*(dy)/dx +y/(1+(xy)^2)=1/sqrt(1 - (x+y)^2) +1/sqrt(1 - (x+y)^2)*(dy)/dx
x/(1+(xy)^2) *(dy)/dx - 1/sqrt(1-(x+y)^2)*(dy)/dx = 1/sqrt(1-(x+y)^2) - y/(1+(xy)^2)
(x/(x+(xy)^2)-1/sqrt(1-(x+y)^2))*(dy)/dx= 1/sqrt(1-(x+y)^2) - y/(1+(xy)^2)
(dy)/dx =(1/sqrt(1-(x+y)^2) - y/(1+(xy)^2))/(x/(1+(xy)^2) - 1/sqrt(1-(x+y)^2))
(dy)/dx =(1/sqrt(1-(x+y)^2) - y/(1+(xy)^2))/(x/(1+(xy)^2) - 1/sqrt(1-(x+y)^2)) * (((1+(xy)^2)sqrt(1-(x+y)^2))/1)/(((1+(xy)^2)sqrt(1-(x+y)^2))/1)
(dy)/dx = ((1+(xy)^2)-ysqrt(1-(x+y)^2))/(xsqrt(1-(x+y)^2)-(1+(xy)^2))
(dy)/dx = (1+(xy)^2 - ysqrt(1-(x+y)^2))/(xsqrt(1-(x+y)^2 )-1-(xy)^2)
Then, plug-in the given point to get the slope of the curve at that point. The given point is (0,0).
(dy)/dx= (1+(0*0)^2 -0*sqrt(1 - (x+y)^2))/(0*sqrt(1-(0+0)^2)-1-(0*0)^2)=(1+0+0)/(0-1-0)=1/(-1)=-1
Take note that the slope of a curve at point (x,y) is equal to the slope of the line tangent to that point. So the slope of the tangent line is
m=(dy)/dx = -1
Then, apply the point-slope form to get the equation of the line.
y - y_1 = m(x - x_1)
Plugging in the values, it becomes
y - 0=-1(x - 0)
y = -1(x)
y=-x

Therefore, the equation of the tangent line is y = -x .