Single Variable Calculus, Chapter 2, 2.4, Section 2.4, Problem 12

Suppose that the relationships of the temperature $T$ in degrees celcius and the power input $w$ in watts of a certain device is given by $T(w) = 0.1 w^2 + 2.155w + 20$

(a) How much power is needed to maintain the temperature at $200^0 C$

$200 = 0.1 w^2 + 2.155w + 20$

$0.1w^2 + 2.155w - 180 = 0$

Using quadratic formula

$\displaystyle w = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}$

$\displaystyle w = \frac{-2.155 \pm \sqrt{(2.155)^2 - 4 (0.1)(-180)}}{2(0.1)}$

$w = 33 watts$ and $w = -54.55 \, watts$

We only choose $w = 33 watts$ because there is no such negative power.

(b) If the temperature is allowed to vary from $200^0 C$ by up to $\pm 1^0 C$, what range of wattage is allowed for the input power?

$T(w) = 0.1w^2 + 2.155w + 20$

$0.1w_1^2 + 2.155w_1 + 20 = 200 + 1$

$0.1w_1^2 + 2.155w_1 - 181 = 0$

Using Quadratic Formula

$w_1 = 33.1124 \, watts$

$T(w) = 0.1w^2 + 2.155w + 20$

$0.1w_2^2 + 2.155w_2 + 20 = 200 - 1$

$0.1w_2^2 + 2.155w_2 - 179 = 0$

Using Quadratic Formula

$w_2 = 32.8839$ watts

The allowed wattage should be the closer to the ideal value which is 33.1124 watts and the tolerance can be computed as 33.1124 - 33 = 0.1124 watts.
Therefore, in order to fit in the tolerance of $\pm 1^{\circ} C$ in temperature, the allowed range of input power should be $\pm 0.112$ watts withinn the ideal value 33 watts.
(c) In terms if the $\varepsilon, \delta$ definition of $\lim \limits_{x \to a} f(x) = L$, what is $x$? What is $f(x)$?
What is $a$? What is $L$? What value of $\varepsilon$ is given? What is the corresponding value of $\delta$?


In terms of the definition of the precise limit,


$
\begin{equation}
\begin{aligned}
& x && \text{corresponds to input power in watts}\\
& f(x) && \text{for Temperature}\\
& a && \text{ is the ideal input power of } 33 \, watts\\
& L && \text{ is the target temperature of } 200^0 C\\
& \epsilon && \text{ corresponds to the tolerance } \pm 1^0 C \text{ in temperature}\\
& \delta && \text{ is for the allowed range of input power } \pm 0.112 \, watts


\end{aligned}
\end{equation}
$

What were/are the political goals of the Religious Right?

The Religious Right has played a prominent role in American politics since the late 1970s. In particular, it has developed into a powerful, vocal element within the Republican Party. All of the various political objectives of the Religious Right are in some way related to a specific brand of Christianity, one which embraces the core tenets of both evangelical and fundamentalist Protestantism.
When it first emerged on the political scene in the 1970s, the Religious Right saw the Cold War in terms of an apocalyptic struggle between the forces of good and evil. This Bible-based approach to foreign affairs found expression in a famous speech by President Reagan in which he described the Soviet Union as "the evil empire." Reagan and his supporters of the Religious Right saw the USSR not just as a rival power but as the embodiment of evil, the chief promoter of atheism in the world. Though Reagan later adopted a more pragmatic approach towards dealing with the Soviets, his fundamental worldview remained similar to that of the Religious Right.
The Religious Right has also been at the forefront of attempts to abolish, or at the very least restrict, abortion. The landmark Supreme Court ruling in Roe v. Wade (1973) spurred religious conservatives into action, leading them to become more organized and better funded in their attempts to get the decision reversed. To date, conservative activists have not been successful in their endeavors, but they have made progress at the local level as a number of state legislatures have severely restricted access to abortion as well as contraception in general.
The issue of abortion highlights the fact that the main focus of the Religious Right has always been on social policy. In particular, religious conservatives have been keen to halt what they see as the decline of the traditional family. To that end, they have been very active in opposing the legalization of same-sex marriages and same-sex adoptions. The conception of marriage which they advocate is based upon an understanding of the Bible that sees homosexuality as a sin and marriage as a special gift from God that can only take place between a man and a woman.
https://oxfordre.com/religion/view/10.1093/acrefore/9780199340378.001.0001/acrefore-9780199340378-e-97

What did Steve say he was doing the day of the robbery?

What did I do? I walked into a drugstore to look for some mints, and then I walked out. What was wrong with that? I didn't kill Mr. Nesbitt.

In the young adult novel Monster, the black teenager Steve Harmon is accused of being an accomplice to a robbery in Harlem. Though he isn't one of the men who killed the shop owner, the prosecution claims he was acting as a lookout. According to their version of events, he came out of the store just before the robbery to signal to the two robbers that the store was empty.
Steve claims, however, that he was scouting for film locations for his new film. Unfortunately, his alibi is difficult to prove, as he was by himself. The only thing he can prove is that he is a member of a film club.
In the end, his lawyer gets him acquitted, first by making sure "the law works for you as well as against you, and to make you a human being in the eyes of the jury," and, second, by proving that Steve did not receive a cut of the money and that he hadn't even spoken to the two robbers, Ellis and Richard Evans, for months.

Later on in the novel, Steve Harmon takes the witness stand to testify and the prosecuting attorney, Sandra Petrocelli, asks him several questions regarding his involvement in the robbery and murder of Aguinaldo Nesbitt. When Petrocelli asks if Steve was in the drugstore the day of the robbery, Steve testifies that he was not. Petrocelli then asks Steve where he was at on the day of the robbery if he wasn’t in the store. Steve says that he doesn’t know exactly where he was at while the robbery was happening, but he does remember walking around his neighborhood taking mental notes of places he’d like to film for an upcoming school project. Steve also mentions that he was planning on doing a film about his neighborhood over the holidays. The jury ends up believing Steve’s alibi because he has a reputation as a good student who enjoys making films in his high school.

yy' = -8cospix Find the general solution of the differential equation

The general solution of a differential equation in a form of f(y) y'=f(x) can
 be evaluated using direct integration.
We can denote y' as (dy)/(dx) then, 
f(y) y'=f(x)
f(y) (dy)/(dx)=f(x)
Rearrange into : f(y) (dy)=f(x) dx
To be able to apply direct integration : intf(y) (dy)=int f(x) dx.
 Applying this to the given problem: yy'=-8cos(pix) ,  we get:
y(dy)/(dx)=-8cos(pix)
y(dy)=-8cos(pix)dx
int y(dy)=int-8cos(pix)dx
For the integration on the left side, we apply Power Rule integration: int u^n du= u^(n+1)/(n+1) on int y dy .
int y dy = y^(1+1)/(1+1)
            = y^2/2
For the integration on the right side, we apply the basic integration property: int c*f(x)dx= c int f(x) dx and basic integration formula for cosine function: int cos(u) du = sin(u) +C
int -8 cos(pix) dx= -8 int cos(pix) dx
Let u = pix then du = pi dx or (du)/pi=dx.
Then the integral becomes:
-8 int cos(pix) dx=-8 int cos(u) *(du)/pi
                              =-8/pi int cos(u) du
                             =-8/pi*sin(u) +C
Plug-in u=pix in -8/pi*sin(u) +C , we get:
-8 int cos(pix) dx=-8/pi*sin(pix) +C
 
Combing the results, we get the general solution for differential equation (yy'=-8cos(pix)) as:
y^2/2=-8/pi*sin(pix) +C
2* [y^2/2] = 2*[-8/pi*sin(pix)]+C
y^2 =-16/pi*sin(pix)+C
The general solution: y ^2=-16/pisin(pix)+C can be expressed as:
y = +-sqrt(-16/pisin(pix)+C) .

According to the narrator of "Dusk," who does the dusk hour belong to?

Dusk is defined as the darkest period of twilight. According to the narrator of Saki's story "Dusk," the time was about six-thirty in early March. At that time of day and at that time of the year it would be getting quite dark in a northern place like London. The narrator devotes a whole paragraph to describing the people who haunt the park at that hour, as viewed by Norman Gortsby.

Dusk, to his mind, was the hour of the defeated. Men and women, who had fought and lost, who hid their fallen fortunes and dead hopes as far as possible from the scrutiny of the curious, came forth in this hour of gloaming, when their shabby clothes and bowed shoulders and unhappy eyes might pass unnoticed, or, at any rate, unrecognised.

Gortsby himself identifies with these people.

He was in the mood to count himself among the defeated. Money troubles did not press on him; had he so wished he could have strolled into the thoroughfares of light and noise, and taken his place among the jostling ranks of those who enjoyed prosperity or struggled for it. He had failed in a more subtle ambition, and for the moment he was heartsore and disillusioned, and not disinclined to take a certain cynical pleasure in observing and labelling his fellow wanderers as they went their ways in the dark stretches between the lamp-lights.

The young man who sits on the bench beside Gortsby stands out in contrast to all the others in the park. He presents himself as a country gentleman who has plenty of money but is temporarily financially embarrassed because he left almost all of it in his hotel room and now can't find his hotel. His story is intended to make Gortsby believe that he might be able to make a friend of a man who is of a superior social class, because the young grifter tells him he doesn't know a soul in London. These words from his hard-luck story have been carefully crafted.

"There's a nice predicament for a fellow who hasn't any friends or connections in London!"

Obviously, he would be deeply grateful if Gortsby could lend him a little money. He might show his appreciation by inviting Gortsby to dinner when he found his hotel, and he might even invite him down to his parents' estate for shooting or riding. All of this is implied, not stated.
Gortsby is cynical. But when he finds the cake of soap on the ground near the bench, he goes rushing after the hustler and apologetically offers him the loan of a sovereign to get him through the night at a different hotel.
The point of Saki's story is that many people seem glad to lend a hand to those above them on the social ladder but reluctant to help those who are really in dire need. This truth is illustrated in Mark Twain's story "The Million Pound Bank Note" and in "The Umbrella Man" by Roald Dahl.

What was Elie's main thought as the men and women were being herded from the train?

When Elie and the other prisoners disembark at Birkenau, he fears being separated from his father and of being alone in the camp. Before reaching Birkenau, no one was aware of the full extent of the death camps and the operations that facilitated the Nazi plan known as the Final Solution (1941–1945). In the early years of the war, the Jews were aware of or experienced the atrocious circumstances of the work camps and the ghettos. As the death camp operations multiplied, stories were spread by the few Jews who managed to escape from the killing centers. However, nothing could have prepared them for the true extent of the Auschwitz complex: Auschwitz I, the main camp and administrative headquarters; Auschwitz II–Birkenau, a combined concentration and extermination camp; and Auschwitz III–Monowitz, a labor camp.

The Jews of Sighet do not think a day will come when they will be taken prisoner and subjected to the atrocities they will experience in the camps. They ignore warnings of the impending danger and grow confident in their ability to escape the ordeal based on news that the Red Army is making progress. However, events take a drastic turn after German soldiers arrive in Sighet. The soldiers’ arrival is quickly followed by transportation of the Jews out of Sighet and into the concentration camps.
When Eliezer and the other prisoners reach Birkenau, they are asked to disembark from the cattle cars, and all that occupies Eliezer's mind is the thought of not losing his father and remaining alone. By this time, the men have already been separated from the women. Elie ensures that he is not separated from his father and lives in constant fear of separation until his father dies in the camps.

My hand tightened its grip on my father. All I could think of was not to lose him. Not to remain alone. The SS officers gave the order. "Form ranks of fives!"

What could be a thesis statement for the short story "Good Country People" by Flannery O'Connor?

You will have to decide what position you would like to take in your thesis, but here are a few ideas.
Flannery O'Connor's short story, "Good Country People," focuses on a mother/daughter relationship that is failing. Joy changes her name to Hulga, which irritates her mother in every possible way. Joy/Hulga also goes out of her way to act unpleasantly and says she believes in nothing. On the other hand, Mrs. Hopewell does not accept Joy/Hulga for who she is. She continues to call Joy/Hulga, Joy. As well, she disapproves of her daughter's education and even her daughter's dress.
Through this characterization, you could form a thesis such as:
Through the characterization of Mrs. Hopewell and her daughter, Joy/Hulga, in the short story, "Good Country People," Flannery O'Connor illustrates a failed mother/daughter relationship.
or
Flannery O'Connor weaves the theme of manipulation and its results through her characters' actions in the short story "Good Country People." For this thesis, you could discuss how all the characters (or the characters you would like to discuss) try to manipulate each other and the effects of that manipulation.
Good Luck!

Your thesis statement is your position and lets your readers know what you intend to prove in your essay. The following are some ideas of possible positions you could take on Flannery O'Connor's short story, "Good Country People."
Flannery O'Connor's use of situational irony in this story highlights the motivations of the characters. Joy, who renamed herself Hulga, is Mrs. Hopewell's thirty-two-year-old daughter with a false leg and a Ph.D. She meets a simple young man who is selling Bibles door-to-door, and is described by her mother as "salt of the earth." She believes he is innocent but is fooled when he uses her intellectual vanity to rob her. 
Flannery O' Connor's story "Good Country People" is a study of the ways in which people deceive each other and themselves. Mrs. Hopewell deludes herself into thinking that if she has enough hope, things will turn out well for her daughter. She works at not seeing her daughter for who she is, but who she wants her to be. Joy/ Hulga uses her intellectual pride as a shield to keep others from knowing her in intimate ways. When she does concede to let someone in, Manley Pointer, she finds that he has deceived her completely. Manley Pointer is able to see Joy/ Hulga's weakness and exploit it for his own personal gain. He deceives others as a career and pastime. 
No one is what they appear to be, especially not Good Country People. Mrs. Hopewell had a value of simple, honest, good people. She distinguishes this type of people from "trash." No one she knew, though—including herself—fit her description of Good Country People. Her daughter was sullen, dishonest, and prideful. Her help, Mrs. Freeman, was unable to admit wrongdoing in any way. Manley Pointer presented himself as good country folk, but he was a liar and con man. Mrs. Hopewell herself was self-deluded and shallow. She pretended to be kind and caring, but it was superficial at best.

What is Summer's response when people ask her why she hangs out with the ''freak'' so much?

Summer responds with the simple answer that she hangs out with Auggie because he is nice.
To go deeper, she also confronts them by asking why they call him "the freak" and tells them that they should stop. She explains that just because someone looks different on the outside, does not mean that they should not get to know them on the inside. It is unfair to not give someone a chance by the way they look.

When asked why she hangs out with “the freak,” Summer says that it is because he is a nice kid. She also asks those children who refer to August as “the freak” to stop calling him that. She believes that the other children are unfair to August because they judge him by his external looks, instead of trying to know him and appreciate him for who he really is.
Summer sits with August during his first lunch at Beecher Prep. This is after everybody else avoids his table. She says that she sat next to him that first day because she really felt sorry for him. She did not like how everybody stared at him and talked about him in whispers. Afterwards, she spends time with him because he is fun, and this is in spite of the fact that he is a “messy eater.” In August’s own words, he “eats like a tortoise.” This is because of the many surgeries he has had to undergo to rectify his cleft palate, so that he now chews food from the front of his mouth, resulting sometimes in pieces of food shooting off his mouth. Summer likes August because he does not care much about “hanging out” and “talking” during lunch break, like the other children. Instead, he is willing to play games like “four squares” with Summer.

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 7

Suppose a parking lot charges \$3 for the first hour (or part of an hour) and $\$ 2$ for each succeeding hour
(or part), up to a daily maximum of $\$ 10$.

(a) Illustrate a graph of the cost of parking as a function of time.








(b) Explain the discontinuities of this function and their significance to someone who parks in the lot.

The function is discontinuous at $t = 1, 2, 3, 4$, and it means that the extra cost will be charged only if
someone wanted to extend his/her parking time. Also, the parking fee will be fixed at $\$ 10$ if the parking time of the car
had reached 4 hours and beyond.

Within a technology-enhanced learning environment, what tech devices and their attributes (such as the use of YouTube or other emerging techs) would make for an appropriate selection for sound design in technology-enhanced learning for middle school students?

There are many ways to use technology to enhance middle school learning across the curriculum and to differentiate teaching strategies so that students are given different methods of learning and various ways to show what they know. Differentiated learning is the basis of sound teaching.
For example, the Edutopia article in the link below discusses the use of a tool called Photo Story, which is part of Windows. This tool allows students to create pictures, and they can also add sound effects. The article recommends this tool for the writing of dialogue in stories, and it might also be used to help students hear and comprehend sections of books or plays. By hearing the words, students who learn better by hearing can have a way to access the reading that is tailored to their learning style. Students who learn by seeing will be helped by creating pictures. Students can also use Garage Band to write and record a song that encapsulates part of their reading or that summarizes an episode in history. 
Simple blog posts, which students can do on Word Press, can also help students learn from other students. For example, students can post their answers to questions or can comment on readings in different areas. Then they can read their fellow students' posts. In this way, they can create a dialogue that fosters learning outside the classroom. 

Choosing from the characters from Jewish religion which one would you like to meet and why?

Personally, I would like to meet Abraham.  There are a few reasons why.  Abraham's story is probably one of the most inspirational when it comes to questions of faith.  Abraham and his wife prayed for a child for many years, and when they were in old age, they were finally blessed with their son, Isaac.  They believed that God granted them this child.  So it was heartbreaking when God asked Abraham to sacrifice Isaac to Him.  Abraham, despite having prayed for this child, was so loyal to God that he agreed to kill his own son.  Abraham took Isaac away from home, fully intending to kill him, and God stopped Abraham when He saw how willing Abraham was to give everything he loved to God.  This story is held up as an example of how believers are expected to worship God. 
Another reason I would like to meet Abraham is it is believed that three major religions branched off from Abraham: Christianity, Judaism, and Islam.

ylnx - xy' = 0 Find the general solution of the differential equation

For the given problem: yln(x)-xy'=0 , we can evaluate this by applying variable separable differential equation in which we express it in a form of f(y) dy = f(x)dx .
to able to apply direct integration:  int f(y) dy = int f(x)dx .
Rearranging the problem:
yln(x)-xy'=0
yln(x)=xy'  or xy' = y ln(x)
(xy')/(yx) = (y ln(x))/(yx)
(y') /y = ln(x)/x
Applying direct integration, we denote y' = (dy)/(dx) :
int (y') /y = int ln(x)/x
int 1 /y (dy)/(dx) = int ln(x)/x
int 1 /y (dy)= int ln(x)/x dx
 
For the left side, we apply the basic integration formula for logarithm: int (du)/u = ln|u|+C
int 1 /y (dy) = ln|y|
For the right side, we apply u-substitution by letting u= ln(x) then du = 1/x dx .
int ln(x)/x dx=int udu
 Applying the Power Rule for integration : int x^n= x^(n+1)/(n+1)+C .
int udu=u^(1+1)/(1+1)+C
          =u^2/2+C
Plug-in u = ln(x) in u^2/2+C , we get:
int ln(x)/x dx =(ln(x))^2/2+C
Combining the results, we get the general solution for differential equation (yln(x)-xy'=0)  as:
ln|y|=(ln|x|)^2/2+C
 
The general solution: ln|y|=(ln|x|)^2/2+C can be expressed as:
y = C_1e^((ln|x|)^2/2)+C .

In "Princess September," how has Maugham shown that jealousy can reach extreme heights leading to the suffering of others?

In the story "Princess September," jealousy can be found within the title character's sisters.  Because the princess of Siam, named Princess September, was the last daughter to be born, she was not subject to having her name changed again and again.  First, the king of Siam named the daughters (when he had only two) after day and night.  Next, the king renamed them after the seasons (when he had four).  Third, the king renamed them after the days of the week (when he had seven).  Finally, the king was in the middle of renaming all of them after the months of the year when Princess September was born.  The remaining children were boys; therefore, the king ceased the naming escapade.  All of these name changes caused the older princesses to be jealous of Princess September.  In fact, when Princess September receives a beautiful bird as a gift, the sisters convince her to lock the bird in a cage.  Before being caged, the bird gave Princess September much happiness.  The sisters wanted to take away that happiness due to their jealousy; therefore, they "suggested" caging the bird.  Of course, as soon as the bird was caged, it stopped singing and interacting with Princess September.  Princess September became so distressed that she set the bird free.  Thus, you can see how the sisters' jealousy led directly to Princess September's unhappiness.

Who has the most power in A Raisin in the Sun? What type of power does he or she possess?

One could argue that Lena Younger possesses the most power throughout the play A Raisin in the Sun. Lena Younger not only controls the financial destiny of her family but also emotionally influences Walter Jr. to make the right decision at the end of the play. Lena Younger initially receives the ten thousand dollar insurance check after her husband passes away and it is her decision how to spend the money. Even though Lena does not possess any significant dreams of her own, she wishes to benefit her entire family. Unfortunately, each person in the Younger home has their own idea of how the money should be spent. Beneatha wants to use the money to pay for her college education while Walter dreams of owning a liquor store. After Lena initially rejects Walter's dream, he is driven to despair, which profoundly impacts her decision to lend him the money. Many can argue that Brother's ability to emotionally manipulate his mother gives him power over Lena, but I would argue that Lena's charity and sympathy for her son are the reasons she chooses to lend him the money. Lena also makes the important decision to put a thirty-five hundred dollar down payment on a home in Clybourne Park, which is a significant aspect of the play. After Walter Jr. learns that Willy Harris took the sixty-five hundred dollars Lena had given him, he calls Mr. Linder to discuss selling the house back to the white community. However, it is Lena Younger who influences Walter Jr. not to sell the home. She says the following:

"No. Travis, you stay right here. And you make him understand what you doing, Walter Lee. You teach him good. Like Willy Harris taught you. You show where our five generations done come to. Go ahead, son—Go ahead" (Hansberry, 63).

In the end, Lena Younger's dream of providing a comfortable home for her family comes true. Her ability to control the family's finances and influence Walter Jr. at the end of the play are evidence that she possesses the most power in the household.

What is the direct characterization and indirect characterization of the main characters in the "The Lady or the Tiger"?

An author uses direct characterization to tell his/her readers what a certain character is like. For example, an author can state that the hero in his novel is fearless, stubborn, or even meticulous. In direct characterization, the author directly reveals to us the personality of the character by using adjectives and other descriptive words and phrases.
For example, we are told that the king in the story is "semi-barbaric" or "barbaric" in nature. He is also said to be a man of "exuberant fancy," with "an authority so irresistible that, at his will, he turned his varied fancies into facts." He is introspective, a man "greatly given to self-communing."
Similarly, his daughter is directly characterized as having the same barbaric nature; she is also "intense and fervid" (passionate) in temperament.
In indirect characterization, an author reveals what a character is like through an account of his/her thoughts, actions, speech, facial expressions, and effect on others. In the story, the king commissions a special amphitheater to be built. According to the text, the king's arena is to be "an agent of poetic justice, in which crime was punished, or virtue rewarded, by the decrees of an impartial and incorruptible chance."
On any given day, an accused lawbreaker must choose between two doors to open in the king's arena. A beautiful maiden stands behind one door and a fearsome tiger behind the other. Here, the king's actions show that he is primarily focused on fulfilling the dictates of his "barbaric idealism." Through the king's actions, the author indirectly shows us that the king is iron-willed and imperious in nature.
In indirect characterization, authors may also reveal to us the thoughts of certain characters. In the story, we are told what the princess thinks of the beautiful maiden who stands behind one of the doors and what she thinks about her lover possibly meeting a violent end. Here are some quotes that reveal to us the princess' thoughts. They tell us much about the kind of person she is:

Often had she seen, or imagined that she had seen, this fair creature throwing glances of admiration upon the person of her lover, and sometimes she thought these glances were perceived, and even returned. 
...with all the intensity of the savage blood transmitted to her through long lines of wholly barbaric ancestors, she hated the woman who blushed and trembled behind that silent door.
How in her grievous reveries had she gnashed her teeth, and torn her hair, when she saw his start of rapturous delight as he opened the door of the lady!

Through her thoughts, we can see that the princess has a jealous and possessive nature. The author ends the story ambiguously; we are left to decide for ourselves whether the princess will succumb to the dictates of her possessive nature or whether she will yield to compassion. The beauty of indirect characterization is that it allows the reader to come to his/her own conclusions about a particular character.
http://www.readwritethink.org/files/resources/lesson_images/lesson800/Characterization.pdf

Why does Scout get into trouble with Calpurnia and have to finish her lunch in the kitchen?

In Chapter 3, Scout has to finish her meal in the kitchen because she was being rude to their guest, Walter Cunningham.
That morning in school, Scout had gotten in trouble for trying to defend Walter Cunningham. In her young mind, Scout blames Walter for this. She responds by attacking Walter in the schoolyard. Jem breaks up the scuffle and invites Walter home with them for lunch. Scout, not one to let bygones be bygones, continues to act rudely to their guest. She mocks Walter for pouring molasses all over his vegetables. This makes Walter clearly self-conscious and embarrassed. That is why Calpurnia calls Scout into the kitchen where she gives her a proper scolding. As a guest in their home, Walter is entitled to eat his food however he wants. To mock him for this would be a violation of the tenets of southern hospitality. As a result of her ungracious behavior, she is made to finish her lunch in the kitchen.

In chapter 3, Walter Cunningham Jr. eats dinner with the Finch family and politely asks Atticus to pass him the syrup. After Calpurnia returns from the kitchen with some syrup, Walter Jr. proceeds to pour it all over his vegetables and meat, which disgusts Scout. Scout cannot control herself and rudely asks what the "Sam Hill" Walter is doing. Walter Jr. gets embarrassed, and Scout continues to draw attention to his odd table manners. Calpurnia then takes Scout into the kitchen and chastises Scout for her rude behavior.
Calpurnia tells Scout that she should never contradict anybody on their eating habits and should consider Walter Cunningham Jr. their guest. Calpurnia then chastises Scout for acting so "so high and mighty" and says that it does not matter if Scout's family is considered better than the Cunninghams. Calpurnia demands that Scout show Walter Jr. respect and tells her,

If you can’t act fit to eat at the table you can just set here and eat in the kitchen! (Lee, 25). 

y = 2arcsinx , (1/2, pi/3) Find an equation of the tangent line to the graph of the function at the given point

Equation of a tangent line to the graph of function f   at point (x_0,y_0)  is given by y=y_0+f'(x_0)(x-x_0).
The first step to finding equation of tangent line is to calculate the derivative of the given function.
y'=2cdot1/sqrt(1-x^2)  
Now we calculate the value of the derivative at the given point.
y'(1/2)=2/sqrt(1-(1/2)^2)=2/sqrt(1-1/4)=2/sqrt(3/4)=2/(sqrt3/2)=4/sqrt3=(4sqrt3)/3
We now have everything needed to write the equation of the tangent line.
y=pi/3+(4sqrt3)/3(x-1/2)
y=(4sqrt3)/3x+(pi-2sqrt3)/3  
Graph of the function along with the tangent line can be seen in the image below.                                                                                             
https://en.wikipedia.org/wiki/Tangent

What's a recurring question in Louisa May Alcott's Little Women?

A recurring thematic question in Little Women is the way in which Jo will define herself as an adult woman. While growing up, she wants to be a writer, and she doesn't see that work as compatible with traditional marriage. When Laurie proposes to Jo, she declines because she doesn't think she can be married to him while continuing to write. The marriages of her sisters, Meg and Amy, are more traditional, as it's understood that they will not continue to work once they are married. Amy in particular will have the life of a pampered woman after marrying Laurie, who is quite wealthy. At the end of the book, Jo agrees to marry Professor Bhaer, as she knows that he accepts her need to work and takes her writing seriously. After Aunt March dies, Jo turns her aunt's house, Plumfield, into a school that she runs with her husband. In the end, her marriage is one of equals and co-workers. 

Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 58

How many liters of a $10\%$ alcohol solution must be mixed with $40$ L of a $50\%$ solution to get a $40\%$ solution?

Step 1: Read the problem, we are asked to find the amount of the $10\%$ alcohol solution.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x = $ amount of the $10\%$ alocohol solution.


$
\begin{array}{|c|c|c|c|}
\hline
& \text{Liters of solution} & \text{Percent Concentration} & \text{Liters of Pure Alcohol} \\
\hline
10\% \rm{alcohol} & x & 0.10 & 0.10x \\
\hline
50\% \rm{alcohol} & 40 & 0.50 & 0.50(40) \\
\hline
\text{Resulting mixture ($40\%$ alcohol)} & x + 40 & 0.40 & 0.40(x + 40) \\
\hline
\end{array}
$

The sum of the quantities of each solution is equal to the quantity of the resulting solution

Step 3: Write an equation from the last column of the table
$0.10x + 0.50(40) = 0.40(x + 40)$

Step 4: Solve

$
\begin{equation}
\begin{aligned}
0.10x + 20 &= 0.40x + 16 \\
\\
0.10x - 0.40x &= 16 - 20\\
\\
-0.30x &= -4\\
\\
x &= \frac{40}{3}
\end{aligned}
\end{equation}
$


Step 5: State the answer
In other words, $\displaystyle \frac{40}{3} L$ of $10\%$ alcohol solution.

Marxism Throughout Le Guin’s novel, the tension between capitalism and Marxism is palpable. However, Le Guin’s work is not didactic (it does not wholly champion that Marxism is good and capitalism is evil). Rather, The Dispossessed complicates this binary opposition by examining the advantages and disadvantages of both economic systems. Analyze the advantages and disadvantages of the economic bases of Urras and Anarres and the superstructures they produce. Through this examination, what can we glean about how economic systems influence human relationships? I need a six-sentence outline that answers this question.

Thesis: The contrast between Urras, a planet divided between capitalism and a form of authoritarianism, and its twin planet, Anarres, which is Marxist, show the problems with the class-based systems of capitalism and Soviet-style communism on one hand and with the communitarian system of Marxism on the other hand. The governments on both planets show that economic systems can affect people's ability to form relationships with others and achieve their goals. 
1. Urras:
Urras, while rich in natural resources, has been exploited to the point of depletion, and its governmental systems--whether capitalist, Soviet-style communist, or a kind of developing world system--involve the exploitation of the vast majority of the population. The riches of the planet are available only to the privileged few and humans' relationships with each other are marked by greed and possession; for example, only the wealthy can afford to pay for school, which is for boys.
2. Anarres:
Anarres, on the other hand, is a poor planet, rich only in minerals, which are sent to Urras. While people share what they have, a reality even mirrored in the language people use in which they are not supposed to show personal possession, the society also discourages the type of achievement that Shevek hopes to pursue, and human relationships are so free that they are often marked by a sense of non-commitment. 

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 77

Recall that the Divergence test follows the condition:
If lim_(n-gtoo)a_n!=0 then sum a_n diverges.
For the given series sum_(n=1)^oo n/sqrt(n^2+1) , we have a_n=n/sqrt(n^2+1)
To evaluate the a_n=n/sqrt(n^2+1) , we divide by n with the highest exponent which is n or sqrt(n^2) . Note: n = sqrt(n^2) .
a_n=(n/n)/(sqrt(n^2+1)/sqrt(n^2))
= 1 /sqrt((n^2+1)/n^2)
= 1/sqrt(n^2/n^2+1/n^2)
=1/sqrt(1+1/n^2)
Applying the divergence test, we determine the limit of the series as:
lim_(n-gtoo)a_n =lim_(n-gtoo)n/sqrt(n^2+1)
= lim_(n-gtoo)1/sqrt(1+1/n^2)
=[lim_(n-gtoo)1] /[lim_(n-gtoo)sqrt(1+1/n^2)]
= 1 / sqrt(1+ 1/oo)
=1 / sqrt(1+0)
=1 / sqrt(1)
= 1/1
=1
The lim_(n-gtoo)n/sqrt(n^2+1)=1 satisfy the condition lim_(n-gtoo)a_n!=0.
Therefore, the series sum_(n=1)^oon/sqrt(n^2+1) is a divergent series.
We can also verify with the graph of f(n) =n/sqrt(n^2+1) :

As the "n" value increases, the graph diverges.

What are five adjectives for the girl in the poem "Barbie Doll" by Marge Piercy?

First, let us review what an adjective is. Adjectives are words you use to describe nouns (or pronouns). If I write, "I just finished walking my noisy dog," the word "noisy" is an adjective telling you something about my dog (the noun).
In "Barbie Doll," Piercy uses adjectives to describe the girl she's writing about directly. She also uses adjectives to describe specific parts of the girl. Finally, she uses adjectives to describe objects belonging to the girl, which still end up describing her through implication.
Piercy describes the girl directly in lines like "She was healthy, tested intelligent." In that line, "healthy" and "intelligent" are adjectives describing the girl.
Piercy describes the girl's body parts in lines like "You have a great big nose and fat legs." There, "great" and "fat" are adjectives.
Piercy also describes the girl indirectly when talking about her possessions, with lines like "miniature GE stoves and irons/ and wee lipsticks the color of cherry candy." In that excerpt, "miniature" and "wee" both describe the girl's possessions, thereby describing her as small or diminished.
Now, if you want to come up with your own adjectives about the girl, you would read the poem and synthesize the points Piercy makes. The girl would be, for example, apologetic in the second stanza. 
https://www.dictionary.com/browse/adjective

List a word and three actions to describe Holden's emotional state as he leaves Pencey in chapter 7.

Holden thinks to himself: "I felt so lonesome, all of a sudden." This word, especially, is indicative of the alienation that Holden is feeling as he prepares to leave Pencey Prep.
Holden is seeking the reassurance of a human connection when he goes into Ackley's room and asks if he wants to play Canasta. Holden also asks if he might sleep in Ackley's roommate's bed since it is empty.
Holden returns to his room and packs his belongings. He counts his money and makes a plan to lie low in a New York hotel room before he goes home. He comments that packing the skates his mother had bought him "depressed" him "a little."
Holden, "sort of crying," puts on his red hunting hat and yells "sleep tight, ya morons!" as he leaves Pencey. He could have slipped away silently, but by yelling, it is a form of goodbye for Holden, though no one returns it, underscoring his alienation.

Are there any metaphors in "The Hermit's Story"? What are they?

There aren't many metaphors in this story, though there are some examples of personification. Personification is the literary device with which writers attribute human characteristics to nonhuman things—so in some ways, we might consider it a kind of metaphor. For example, consider this passage:

Blue creeping up fissures and cracks from depths of several hundred feet; blue working its way up through the gleaming ribs of Ann's buried dogs....

In the above quote, "blue" is a reference to the fields of snow that have turned to vast sheets of glazed ice. The ice shimmers blue in the moonlight. Personification gives "blue" the human quality of intention, comparing it in a way to a living thing, one that creeps up fissures in the earth and envelops the dogs in frosty layers of freezing cold.
Another example of a metaphor from the story is the following:

The quail would fly off with great haste, a dark feathered buzz bomb disappearing quickly into the teeth of the cold....

Here, the "cold" is personified, and the extreme weather Ann and Gray Owl encounter on their journey is given "teeth." We also have the strongest example of a true metaphor here as a bird is compared to a "buzz bomb."

Why would the Oracles' words be deceiving?

The oracles of the classical Greek and Roman world were notorious for prophecies that were extremely obscure and often led to destruction when they seemed to point to good fortune.
One famous example of this is in the work of Greek historian Herodotus. In book one of his Histories, Herodotus tells the story of Croesus, a powerful king of Lydia who consulted the oracles of Apollo at Delphi to see if he should attack the rising empire of Persia. The oracles replied that if Croesus attacked Persia, he would destroy a mighty empire—but it turned out to be his own, as he was defeated by Cyrus and the Persians. Herodotus puts the blame for this on Croesus, who misinterpreted the ambiguous prophecy and was thus destroyed for his hubris.
Another example, even closer to real deception, is found in the Latin epic The Aeneid. The hero, Aeneas, journeys to the underworld, where he meets his friend Palinurus, who had been lost overboard during their voyage. Aeneas says,

Speak, hurry! For, not found deceitful to me before,
With this one response Apollo deluded my spirit,
Who prophesied you would be unharmed at sea and come
To Ausonian borders. See, is this his promised faithfulness?
(Book 6, lines 343–346, my translation)

It turns out that Apollo's prophecy was technically true: Palinurus fell into the sea but didn't drown. Instead, he floated for three days before he caught sight of Ausonia, another name for Italy. He was washed to shore, where, just as he grabbed the rocks to climb onto the land, he was attacked and killed by the inhabitants. So, he did arrive at Ausonia unharmed—but for Apollo, the god of prophecy, to be barely correct on a technicality doesn't really seem like "faithfulness."
Part of Milton's point here is that Jehovah, the god of the Old Testament, is faithful: rather than toying with mortal human beings, using double meanings and technicalities, he clearly promised his Messiah, without double meanings, and the promise is truly and completely fulfilled at the Nativity, the birth of Christ.

When John Milton said 'the oracles are dumb' and 'deceiving', he was asserting that his own religion, Christianity, held more truth or legitimate dominance over, for example, Greco-Roman polytheism, or what's often referred to as Hellenistic religion. Milton demonstrates his strong faith in his own Protestant Christianity with his statement about the oracles, which is one based on Plutarch's own words about how the oracles 'fell silent'. Milton was, ultimately, using his familiarity of particular pagan beliefs or rituals to denounce them.
Milton was a Renaissance artist, often described as puritanical, and therefore he regularly applied Christian theology to the classical motifs, and often critically. This is supported by his next line in the poem, which is 'Apollo from his shrine: Can no longer divine', meaning the Greco-Roman god of the Sun could no longer offer salvation through worship in light of Jesus Christ and Christianity being supreme.
He goes on to say: 'With hollow shriek, the steep of Delphos leaving. No nightly trance or breathed spell inspires the pale-eyed priest from the prophetic cell.' Milton is referencing the Delphic Oracle practice and Plutarch's words again here specifically, along with the actual location of Delphi, in order to say that the site and its practices are both physically and spiritually abandoned for being unwholesome or mystical. When Milton writes 'prophetic cell', he means that the practice of seeking an oracle has the trappings of superstitious or delusional thinking, and therefore Milton is expressing the need to reject this form of suffering in favor of a Christian perspective.

RESOURCES:
https://tspace.library.utoronto.ca/html/1807/4350/poem1442.html
https://en.wikipedia.org/wiki/Religious_views_of_John_Milton

As both a devout Christian and a great scholar steeped in classical learning, Milton is well-placed to judge the respective merits of the two traditions. And though much of Milton's work draws extensively upon the intellectual and mythological heritage of the ancients, he nevertheless asserts the superior truth of Christianity.
In this particular stanza of the poem, Milton is insisting that all the ancient oracles of antiquity—such as the Delphic Oracle—have now been rendered silent (or "dumm," to use Milton's word) by the birth of Christ. Pagan oracles and soothsayers were unable to predict the nativity; they simply had no inkling of what it could possibly mean. Now that God's son has been born, the falsity of the pagan gods has been exposed once and for all. The oracles' prophecies were all based on deception, as the ancients had not been exposed to the truth of the Christian message. They could not help but deceive, yet deceive they did, though all were equally deceived in the time before the birth of Jesus Christ.
https://www.dartmouth.edu/~milton/reading_room/nativity/text.shtml

"All the world's a stage," says Jaques famously. What other characters refer to the concept of living life as "acting in a play"? Using specific examples from the text, discuss the extent to which "acting" helps bring about the conclusion of As You Like It.

Acting and artifice are key tenets of As You Like It, a play whose plot is driven by themes of concealment, and whose romances come about as a result of characters adapting, inhabiting, and removing various guises. At the end of the play, we even see a metatextual monologue delivered by the actor playing Rosalind. The character implores the audience to "like as much of this play as it please you," highlighting the fact that the play has been an act. The speaker declares, "If I were a woman, I would kiss as many of you as had beards that pleased me," reminding the audience that only their suspension of disbelief has enabled them to see what would have originally been a boy actor as a woman throughout the play. The gender-switching and confusion is famously threefold in As You Like It, which would have originally featured boys-playing-girls-playing-boys, in the case of Rosalind and Celia. Interestingly, Orlando falls for Rosalind first in the guise of Ganymede, and he is confused until she reveals herself to be a woman. This does beg the question: would Orlando have fallen for her if he had not first seen her acting as a boy?
Scholars have suggested that artifice in As You Like It was so prominently foregrounded by Shakespeare because the plot of the play, adapted from a much longer work, requires the audience to imagine vast landscapes—the forest—which could not really be represented with scenery. When Rosalind asks Orlando to "pretend" that she is "Rosalind," we watch a boy playing a girl, disguised as a boy, asking to be treated as a girl. However, in Rosalind's mind, the love between Phebe and Silvius is equally "a pageant truly play'd / Between the pale complexion of true love / And the red glow of scorn" (act 3, scene 4). According to this statement, love and other human relationships necessarily involve an element of pretense and acting. In Phebe's case, Rosalind feels she has acted her part wrongly, and she tells her so.
Rosalind and Celia don masculine clothing for their own "safety" (act 1, scene 3) to protect themselves from potential sexual assault. As a man, she has a greater element of control over her environment and even over herself, as we see when she takes on the "disguise" of Rosalind for Orlando, stating "She will do as I do." Rosalind's play-acting in both forms is what enables her to progress on her journey through the text.

Discuss the major causes of pulmonary vasoconstriction

If you check the internet for pulmonary vasoconstriction, every hit names the condition as hypoxic pulmonary vasoconstriction. That should clue you in to its major cause: hypoxia, or a lack of oxygen in the body. 
Hypoxic pulmonary vasoconstriction is a body's way of channeling deoxygenated blood to the most effective areas of the lung for oxygenation. When alveoli are blocked, damaged, or diseased, specialized membranes react and trigger a tightening of smooth muscles around small arteries leading to those parts of the lungs. This funnels blood to the working parts of the lung, preventing damaged lobes from being overloaded and returning blood to the body without enough oxygen.
Unfortunately, certain circumstances can trigger pulmonary vasoconstriction across 100% of the lungs' capacity. This reduces the body's ability to process air and increases the load on the heart, sometimes leading to bleeds and clots in the lungs. One of the main causes of this detrimental form of pulmonary vasoconstriction is high altitude, where thinner air and lower oxygen can trick the body into harming itself.

In the Red Kayak, the Corsica River seems to take on a personality. Explain what this means, and cite examples.

In the book, the narrator, Brady Parks, tells us that the Corsica River is a "pretty river" but that it "doesn't have a heart." Brady characterizes the Corsica River as a merciless entity. He believes that it should be held liable for Ben DiAngelo's death. In the story, Ben is only three years old. After Brady's friends drill holes in the DiAngelo's red kayak, it capsizes. Mrs. DiAngelo (who was in the kayak) survives, but Ben later dies.
To Brady, the Corsica River shows no respect for age or innocence. It is a malignant force, endangering anyone who dares to traverse its length. Privately, Brady is filled with guilt for his likely role in Ben's death. When he first receives news about Ben's death, however, Brady blames the Corsica River.

Unfair, I thought. My teeth clenched and a tremendous surge of anger burst out of me. "You didn't have to kill him!" I screamed at the river. . . . "You didn't have to be so cold, " I accused, but the anger was gone, turned into something else already. . . . I cussed out the river. And you know what? Nothing happened. When I finished crying, there wasn't a sound to be heard, except for the gentlest lap of waves on the nearby sandbar. The river didn't care.

In Brady's mind, the river takes on the personality of a silent, callous murderer, one that respects neither age nor innocence. His rage at the river feels cathartic, but his relief is temporary. Brady is soon forced to face his own demons and confess his part in Ben's accidental death. In the end, Brady comes to terms with the river, and it ceases to be a threat to his peace.

Why does the Happy Prince rely on the swallow to know about his city?

The Happy Prince is a statue and so is unable to move. Nonetheless, from his position high up on a pedestal, he's still able to witness scenes of extreme poverty and suffering. When the prince was alive, he never knew about any of this; he lived a happy life of ease and luxury in the royal palace. But now, with his spirit embodied in the statue, he's truly shocked and horrified at what goes on in the city he never really knew when he was alive. The prince wants to make amends; he wants to help alleviate some of the social evils of the world down below.
As a little bird, the swallow is able to fly all over the city. This gives him the opportunity to see more of urban life, giving him a greater knowledge of the city than the prince has ever had or ever will have. He's ideally placed to respond to the prince's request and take valuable objects from his statue and dispense them to the city's poor and needy. The Happy Prince becomes even more reliant on the swallow after the little bird removes the sapphires from his eyes, because then the prince cannot see and so must depend on the bird for knowledge of the city beneath his statue.

Was the British colonization of America a failure?

The British were very successful, on the whole, in colonizing the eastern seaboard of North America. There were, however, several failed colonies, such as Roanoke, an early attempt to create a permanent settlement in the 1580s in what would become North Carolina, and later, the colony of New Albion. Nevertheless, despite early struggles, the English managed to create flourishing and highly profitable permanent settlements in the New World.
Where the British failed was at holding the colonies as a British possession. The seeds of this failure lay in the success of the colonial experiment. The colonies were so successful that their leaders and many other people began to feel that they had very few ties to England. Especially if they were born in the Americas, they tended to feel more American than British.
Also, unlike in, say, India, the settlers did not have a huge, entrenched native population to contend with. The native population was small to begin with it, and using warfare and the spread of diseases such as smallpox, the English settlers soon eradicated much of the native threat, so that over time there were actually more British than Native Americans in the settled country. The British winning of the French and Indian War further confirmed in the English colonists' minds that the new country was "theirs."
After the Native American threat was largely dealt with, the American settlers felt little need of British help. They also resented and rejected the British idea that they should pay for the French and Indian War (which the British felt largely benefitted the Americans) through increased taxation. The British were not able to handle the tensions that built up, and, as we know, the colonists revolted, defeated the British, and established their own nation.

What do you think Wiesel means when he says, "He [God] has been hanged here, on the gallows"?

In Night, Elie Wiesel recounts a nightmare of reality which is not merely his own experience as a Holocaust survivor, but is in some ways symbolic of all human suffering, especially that of other Holocaust victims.
The huge question which confronted the Jews in the Holocaust was: how could God let this happen? There is, of course, no explanation. To say that God is dead—that God is a victim too, executed by the Nazis, as it were—is Wiesel's metaphorical way of expressing the unthinkable. It is as if the scale of murder and brutality is such that religion has been replaced by a new, alternate-universe reality in which the existence of, or belief in, God has been canceled out and destroyed.
When, at the close of Night, Elie and the other survivors have been liberated, he is able to look in a mirror, and he observes that "A corpse stared back at me." Not only does God seem dead to a survivor, but the survivors have become the living dead. The fact that Wiesel and the countless others who had been through this did continue to live—that he became a great writer and was able to tell the truth so eloquently to the world—alludes to the possibility that if man can triumph over this, then perhaps God is still alive.

What events brought Mao to the decision to rely on the PLA to restore social order? What were the conditions in Chinese society like by this point?

Mao's decision to use the People's Liberation Army (PLA) to restore social order emerged in the context of the Cultural Revolution. It involved his inability to control aspects of that social transformation. Particularly problematic were the Red Guards, a kind of paramilitary youth movement that initially had Mao's support. The problem of the Red Guards was somewhat analogous to that of student movements and radicalism in the West, like the Students for a Democratic Society (SDS) in the U.S. It was, however, far more serious and violent.
The Red Guards first served Mao's purposes, helping him destroy the last vestiges of a pre-Communist China. They were involved in significant actions to destroy symbols of an older China. But as the Cultural Revolution progressed (one might say "devolved") the Red Guards became increasingly violent and uncontrollable.
Their mass movement tactics of murder and humiliation (which led to many suicides) eventually became unsustainable, and when Red Guards got out of hand in 1967, students were told to desist and return to "normal" and go back to school. When it proved impossible to control them Mao decided to turn the PLA loose. This resulted in brutal military reprisals and the dissolution of the Red Guards throughout 1968.

How are imperialized people viewed by Rudyard Kipling in The White Man's Burden? Specific examples required.

The overall portrayal of indigenous peoples in "The White Man's Burden" is far from flattering, to put it mildly. In fact, it is condescending and deeply offensive. The very title is problematic, for one thing. The vast colonial empire of the West is a framed as a burden, not to the native people being exploited but to the white colonialists themselves. Right from the first stanza, colonized people are infantilized, not fully regarded as adult human beings with the ability to make decisions of their own. As such they are in need of the benevolent guidance of the White Man, who is burdened with the expectations of his race's divine civilizing mission:

Take up the White Man's burden—Send forth the best ye breed—Go bind your sons to exileTo serve your captives' need;To wait in heavy harness,On fluttered folk and wild—Your new-caught, sullen peoples,Half-devil and half-child.

When people have been effectively dehumanized ("Half devil and half child") it is much easier to justify manipulating and controlling them. The poem says indigenous folk are also highly superstitious and primitive. It asserts that if you are not careful all the hard work the colonial powers have done in building their empires will be undone by the natives' laziness and ignorance:

Fill full the mouth of FamineAnd bid the sickness cease;And when your goal is nearestThe end for others sought,Watch sloth and heathen FollyBring all your hopes to nought.

Kipling believes that white colonizers try their best to prevent famine and stop the spread of sickness and disease, but all their selfless work can still come to nothing because these dreadful savages remain mired in lazy superstition.
Kipling never shied away from the unpleasant consequences of colonial rule, but the implication here is that the natives are largely to blame for their own misfortunes. Kipling invites the White Man to take up his burden but not to take upon himself any ultimate responsibility for the natives' welfare.

Take up the White Man's burden—And reap his old reward:The blame of those ye better,The hate of those ye guard—The cry of hosts ye humour(Ah, slowly!) toward the light:—"Why brought he us from bondage,Our loved Egyptian night?"

As well as being lazy and superstitious, the natives are also portrayed as ungrateful for the benefits of Western civilization. They would much rather remain stuck in their old, exotic ways, blaming all their troubles on their "betters:" their colonial masters who have sacrificed so much to free them from their erstwhile slavery.

Why do you think Melville specifically chose a first-person narrative, rather than, for instance, using a third person omniscient narrator? What impact does this choice have on the content of the story and the development of its themes?

Melville chooses the lawyer who hired Bartleby to narrate Bartleby's story. The lawyer writes in the first person. I believe Melville made this decision because he wanted to convey an outsider's view of Bartleby, in order to highlight the mystery of why Bartleby behaves the way he does.
The lawyer is a seemingly level-headed person who views Bartleby with sympathy and wants to help him. Still, he never truly gets inside of Bartleby's head. At best, he can only guess what caused Bartleby to say, "I prefer not to" in regard to not working.
A third person narration would potentially allow omniscience, which would make it possible to explain why Bartleby did what he did. So would a first-person narration from Bartleby's point of view. But Melville wants to leave us with a sense of mystery that will encourage us to think for ourselves, the lawyer is the perfect vehicle for this. We identify with him as he tries to unravel the "why" behind Bartleby's self-destructive passivity. He comes up with the Dead Letter Office as a possible explanation. But, in the end, the lawyer is simply an ordinary Everyman, leaving us as readers to grapple with Bartleby in our own ways.
One of Melville's themes in the story is the essential mystery of human behavior, and the lawyer's limits in only being able to see Bartleby from the outside help to reinforce this theme.

Is the The World's Wife collection of poetry by Carol Ann Duffy only effective because it's based on actual fairy tales and myths?

Certainly, a strength of Duffy's work is that it uses figures and circumstances represented in well-known fairy tales and myths, but I would not say that it is only effective because it does so. Duffy's The World's Wife is a collection of poems that inverts or re-conceptualizes well-known stories by centering female figures who otherwise appear only on the peripheries of stories, or whose perspectives are neither considered nor taken seriously. For example, "Mrs. Freud" is a poem in which Sigmund Freud's wife, Mrs. Freud, talks about how tired she is of hearing about male genitalia; "Medea" talks about how this mythological figure becomes so enraged and volatile. Her work is effective in part because it forces readers to consider the perspectives of those whose feelings, emotions, thoughts, actions, and behaviors are not unpacked and remain, in many cases, misunderstood or mysterious. She is able to do this by meeting the reader where they are, or, in other words, she plays with people's general understandings and interpretations of these relatively well-known texts by pushing them in unexpected directions. The fact that she is responding to texts that are culturally significant in some way or another is merely a tool she uses to convey her larger views about the pervasiveness of male perspectives and narratives, but I do not think that her poems are only effective because they utilize this particular means of engaging with these themes.
One way to think about the other ways that her poetry is effective is to think about how you might respond to one of her poems, where the backstory (e.g., the myth or fairy tale she uses) is something with which are not familiar. What else do you gain from reading this poem? Minimally, I would say that analyses of her use of first-person narration, the centering of female characters, the perceived audience each of the narrators addresses, and the form of her poems can add to our understandings of how we (can) read poetry, how it resonates with us as individuals, and how poetry can and has helped to shape our world views.

What are some examples of segregation from 1940s - 1960s?

It may be difficult for younger people to imagine this, but there was substantial segregation from the 1940s through the 1960s.  Public water fountains and bathrooms were segregated.  Hotels were, too.  Black people could only sit in the balcony at movie theaters.  Black people could not be served at lunch counters.  They had to sit at the back of a bus.  Hospitals had separate wards for black people, too.  Much of the segregation was in the South, but by no means all of it.  For example, a park in Pittsburgh, PA closed its swimming pool, rather than integrate it. Black entertainers in northern cities could not eat in the restaurants nor stay at the better hotels because they were segregated. A special road guide for black people who wanted to travel listed the places it was safe for them to stay or to eat.  Southern schools were segregated, and it took federal troops to integrate them in Little Rock, Arkansas, the local opposition was so fierce.  Brown v. Board of Education was not decided until 1955, so up to that point, school segregation was perfectly legal.  And in fact, it was not until the Civil Rights Act of 1964 was passed that most segregation became unlawful.  Even after the statute was passed, it took marches and protests and sit-ins to make the point. 
http://www.pbs.org/independentlens/blog/green-book-helped-keep-african-americans-safe-on-the-road/

https://www.loc.gov/exhibits/brown/brown-aftermath.html

Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 66

Solve the equation $\displaystyle x - \frac{2}{5} = \frac{3}{5}$ and check
if your answer is correct.

$
\begin{equation}
\begin{aligned}
x - \frac{2}{5} + \frac{2}{5} &= \frac{3}{5} + \frac{2}{5} && \text{Add $\displaystyle \frac{2}{4}$ from each side} \\
\\
x &= \frac{5}{5}\\
\\
x &= 1
\end{aligned}
\end{equation}
$

By checking,

$
\begin{equation}
\begin{aligned}
1 - \frac{2}{5} &= \frac{3}{5} && \text{Replace the variable by the given number, } 1\\
\\
\frac{5-2}{5} &= \frac{3}{5} && \text{Evaluate the numerical expressions}\\
\\
\frac{3}{5} &= \frac{3}{5} && \text{Compare the results}
\end{aligned}
\end{equation}
$

The results are same; Therefore, $1$ is a solution of the equation $\displaystyle x - \frac{2}{5} = \frac{3}{5}$

Why is intelligence important for the Receiver of Memory to have in The Giver?

We can see why intelligence is an important quality for the Receiver by examining how Jonas uses his intelligence as the Receiver.
One reason why the Receiver might need intelligence is because the Receiver is learning about things that do not currently exist. The concept of color is an example. Jonas notices that there is something different about Fiona's hair, but he has difficulty describing it because he has no concept of color, until the Giver helps him see through transmitting memories. I think that Jonas's intelligence makes him more open to learning about new concepts such as color and feelings.
While the Receiver learns about these new concepts, they are not allowed to discuss them with others. Jonas must communicate with those around him without giving away what he's learned. I think intelligence is a good trait to have so the Receiver knows what language to use when talking to others who do not understand concepts beyond Sameness.

Intelligence is an important skill to possess as the community's Receiver of Memory because the Receiver of Memory must exercise their knowledge when the Committee of Elders consults them regarding a significant decision or change in policy. The Giver explains to Jonas how the Committee of Elders once sought his advice about increasing the rate of births in order to have more Laborers. Fortunately, the Giver was intelligent enough to articulate the dangers regarding overpopulation, which would result in hunger, starvation, and war. Having the intelligence to discern when possible political decisions could be dangerous is an important skill that the Receiver of Memory must possess.
The Receiver of Memory must also have the intelligence to recognize how past events affect the current conditions in the community. Understanding the nuances of each decision made to create a comfortable, structured, safe community requires intelligence.

In Freak the Mighty, what are two differences between the book and the movie in which the director changes something in the movie version? I would like to talk about the following differences: 1 - The quote Loretta said about Freak being a birth defect in the book; Freak says it about himself in the movie. 2 - The movie shows a bigger picture of the negative effect Killer Kane had on his family; I need to explain how.

Since you have already outlined two differences between the book version of Freak the Mighty and the movie adaptation, let's focus on explaining how and/or why those differences manifest. 
First, in Chapter Eleven of the book, Freak and Max go to the house of Loretta Lee in order to return her purse to her (which they had discovered in a storm drain in the previous chapter). Once there, Loretta behaves with extreme nastiness toward the boys, pointing out that Max is the son of Kenny "Killer" Kane and must be "some kind of retard," while Freak is the son of "stuck-up Gwen" and a "dwarf." She points out with great cruelty that Freak's father had abandoned him, stating:

Your old man was a magician.... He must be a magician, because as soon as he hear the magic words "birth defect," he disappeared. 

In the film version, it is not Loretta who makes this statement, but rather Freak himself. After Loretta reminds Max about his father, she insults him, recalling that he was just a "poor little mute boy, all alone up there on the witness stand." Max takes off running and tells Freak to stay away from him, claiming that he's been "nothing but trouble" and that his "life was fine before you and your stupid quests." Freak then tells Max:

My father was a magician. At least that's what my mom says. He heard the words "birth defect" and he disappeared. But I don't really care, you know, 'cause I don't even know who my father is. I just know that's not who I am. And that's not who you are, either. 

The director of the film, Peter Chelsom, and writer, Charles Leavitt, clearly decided to make this change to give Freak more agency. Rather than being hurt by this truth, he is owning it and using it to empower Max to realize that he is not his father; he is not destined to be a killer. It becomes a moment of liberty rather than a moment of injury. 
Second, as you pointed out, the film shows the larger consequences of Killer Kane's actions in that we get a more thorough perspective from Max and his grandparents.
In the film, we clearly see the bullying that Max faces as a result of his father's actions and the negative impact this has on the boy's psyche. He's called at various times "a freak of nature" and a boy with "no friends." He's blamed for creating trouble that he did not create and given detention. He is also subjected to repetition of the terrible song that the other children have made up: "Killer Kane, Killer Kane, had a son who's got no brain!"
This treatment results in Max retreating into his head to the "cool and dim" place where he can "float like a cloud." He is clearly withdrawn and unable to connect with others as a result of his father's behavior. He lives in constant fear that he might turn out to be like his dad, stating, "I look in the mirror and I see him. I hear my voice and I hear his!" This insight is aided by the voiceover narration provided by Max throughout the film.
We also see how this has devastated Gram and Grim, who have to live with the knowledge that their daughter's husband murdered her. Grim keeps a gun in the house in order to shoot Kane if he ever comes back, which Gram detests. She states emotionally:

Our Annie's gone. All we have left of her smile... all we have left of her heart is in that boy down there. I'm not gonna have hatred coming into this house and poisoning him. 

The revelation that Kane will be released shortly on parole creates tension in the family in that they don't know what to believe; lawyers claim that Kane will be put back in prison if he comes within five miles of Max or the house, and yet it is lawyers who have enabled Kane to be released in the first place.
All of this conflict naturally comes to a head when Kane kidnaps Max and takes him to Loretta's house, where he tries to strangle her. Seeing this triggers Max's memory of his mother's murder, and he is finally able to own the situation and free himself of its emotional weight, stating:

I wasn't dreaming. I remember. I saw you! I saw you kill my mom! And you're never gonna stop me from saying it again! 

What are the similarities between Frost's "Stopping by the Woods on a Snowy Evening" and Bronte's "Spellbound"?

Quite a few similarities exist between the Frost poem and the Bronte poem. First of all, the setting is quite similar. In "Stopping by Woods on a Snowy Evening," the speaker finds himself in "the woods" which  "are lovely, dark and deep" on an evening when snow is falling. Likewise, in "Spellbound," the speaker finds herself in a snow storm as "the night is darkening round me" and "a storm is fast descending." As well, darkness is emphasized in both poems. However, in the Frost poem, the speaker does not seem to fear "the darkest evening of the year"; whereas, the speaker in the Bronte poem is spellbound "by a tyrant spell" emphasizing a mood of gloom.
A central motif in both poems is isolation. The speaker in Frost's poem finds himself alone with his horse on the winter's eve stopping "without a farmhouse near between the woods and frozen lake." Likewise, the speaker in "Spellbound," finds herself in the woods with a storm nearing but she "cannot go." The isolation of the woods in both poems allows the speakers to contemplate their situation.
Symbolically, in "Stopping by Woods..." the speaker relates that he has "miles to go before I sleep." If sleep is a metaphor for death then the speaker makes the decision to continue on his life journey and not stop for death. Similarly, in "Spellbound," the speaker asserts at the beginning of the poem that she is under a spell and "cannot go." It is unclear whether she is referring to going to either heaven or hell. Yet, at the end of the poem, she states, "I will not, cannot go." Thus, both narrators have free will to make decisions regarding their differing situations in the snowy woods.
https://poemanalysis.com/spellbound-emily-bronte-poem-analysis/

https://poets.org/poem/spellbound

https://www.poetryfoundation.org/poems/42891/stopping-by-woods-on-a-snowy-evening

Why is it important to have laws that stop discrimination?

If a society or a company didn't have laws/rules against discrimination, that society would probably have more people actively discriminating against people.  Not everybody is going to altruistically avoid discrimination.  Having laws against it shows people that there are rules about certain kinds of behavior, and if those rules are broken, then punishments will be issued.  In general, people want to avoid punishment, so rules against discrimination work to encourage people to not discriminate.  Consequently, they avoid punishment.  Additionally, if a work place is unable to discriminate (for whatever reason),  that work place likely becomes a place with more diversity.  That is generally a good thing, because increased diversity allows for more ideas and a wider range of creative thinking.  It is also likely to breed an environment of tolerance.  As people in one environment learn to tolerate diversity, they are likely to extend those skills into other areas of their lives, too.  Finally, laws that work against discrimination also work to protect the people that may be subject to that discrimination.  The laws help put them on an equal footing with everybody else.  
https://www.referenceforbusiness.com/small/Qu-Sm/Racial-Discrimination.html

Analyze the poem "Worsening Situation" by John Ashbery.

 
“Worsening Situation” was published in John Ashbery’s 1975 poetry collection, Self-Portrait in a Convex Mirror.  As the book title suggests, this free-verse poem is in many ways Ashbery’s convoluted consideration of himself.  Although on the surface it reads like meaningless obscurity, which Ashbery often strove for in his art, a deeper analysis will reveal that it is indeed a self-portrait, which projects a dream-like tone of sadness. He opens with a rainstorm washing colors over him. A washing rain is generally considered cleansing; color is usually cheerful. Yet Ashbery says these things cannot help him, giving the analogy of a person unable to eat at a feast because there are too many dishes to choose from.  The sense is that he is overwhelmed.  But by what?
The synecdoche—a form of figurative speech in which a part stands in for the whole—of the severed hand lends a clue. As a poet, it is his hand, somehow separate from him, that places art on the page.  It produces his living, his fame, his connections in life.  And yet John Ashbery—the man inside—seems to feel disconnected from that hand, that part of his life.  It wanders in many directions, “a stranger who walks beside” him.  Ashbery addresses the charlatans on the outskirts who drop his name as if they know him, but they really don’t.  “Everyone is along for the ride, / it seems.” John just wants his name, his privacy, back. He understands that there will be haughty, formal gatherings required of him, but he reaches for the normal things in life: recreation, reading, romance. He is continually affected by this disconnected and disingenuous situation, perhaps to the point of a mental instability.  His admittance that there are  “occasions / for white uniforms” certainly invokes thoughts of the sterile uniforms in a mental hospital.
This brings us to the increasingly strange ending.  The message left on his machine is threatening, manipulative, yet vague, as if it could have been left for anybody.  These overtones echo those Ashbey has voiced about the charlatans. Even in his own home he cannot escape the control his career has over his life.  The message tells him he’s gotten it all wrong and “must correct the situation” quickly, since “much besides your life depends on it.” What could be more important that one’s life?  But that’s Ashbery’s point.  The public demands results from an artist, and the art obscures the person, supersedes him, even.  
In response, Ashbery is considering a whole new self, symbolized by the “old-fashioned plaids.” Yet upon inspection of the white collared shirts, he wonders if there is truly “a way / to get them really white again.”  There is a sadness that he cannot go back to the John Ashbery that he once was.  He wife, who “thinks I’m in Oslo- Oslo France, that is,” doesn’t even really know him any more.
http://coldbacon6.blogspot.com/2007/09/worsening-situation-john-ashbery.html

http://williamwatkin.blogspot.com/2007/04/john-ashbery-self-portrait-in-convex.html

How does the setting contribute to the story?

In order to understand the contribution of the setting to the story, we should begin by looking at our main character, Wakefield. The narrator of the story asks, "What sort of a man was Wakefield?" He then goes on to describe a rather lackluster and middle-aged man. We then see further evidence of his mediocrity when the narrator states, "Had his acquaintances been asked, who was the man in London the surest to perform nothing today which should be remembered on the morrow, they would have thought of Wakefield." Wakefield puts on his coat and hat, smiles to his wife, and leaves. Having received no information to believe otherwise, his wife believes he'll return soon. His return, however, is twenty years later.
Now that we have some information on our main character, we'll look at the setting. The story takes place in busy London. When Wakefield leaves, the narrator warns the reader that we should follow our character, "ere he lose his individuality, and melt into the great mass of London life." Consider the streets of a bustling city with crowds of people. London is even referred to as being "busy and selfish." It is interesting to note here that our character risks losing what makes him different by blending in to the crowd. That is exactly what happens. Wakefield remains unnoticed for twenty years, living one street away from his wife. At one point in the story, the narrator tells of Wakefield's chance encounter with his wife. The city that allows him to remain hidden in its throngs of people, is the same city that forces them into this chance encounter. In this way, the setting contributes to the story. Our character is able to participate in his journey because the city enables him to do so.

Was the American Revolution the first of its kind? Did other countries engage in similar rebellions before the American colonies did?

The American Revolution was one of the few early successful revolts for independence against a European empire, but it was not the first. In the Philippines, for example, rebellions against Spanish presence began shortly after the establishment of the Spanish colonial government in 1521; the First Carib War, a revolt by the indigenous people of St. Vincent and British colonial agents, occurred in 1769, a decade before the American Revolution began. However, rebellions against European imperialism prior to the American Revolution failed to gain independence for the colonized states, unlike the U.S. Additionally, many of these attempts at revolt were by indigenous people resisting the colonization of their land, while the American revolutionaries were colonists who wanted to form an autonomous independent state from the former colonies. The American revolution was inspired largely by Enlightenment ideologies of liberty and democracy, rather than previous revolutions, and it was the first of the 18th century Atlantic Revolutions along with the French, Haitian, and Batavian Revolutions.

Is it significant that the birthmark is in the shape of a hand?

It is significant that Georgiana's birthmark is in the shape of a hand. In the very first paragraph of the story, the narrator says,

The higher intellect, the imagination, the spirit, and even the heart might all find their congenial aliment in pursuits which, as some of their ardent votaries believed, would ascend from one step of powerful intelligence to another, until the philosopher should lay his hand [my emphasis] the secret of creative force and perhaps make new worlds for himself. We know not whether Aylmer possessed this degree of faith in man's ultimate control over Nature.

In other words, then, the narrator describes some individuals who believe that humankind can aspire to create, just as one might conceive of God or Nature as creating. These people think that, with enough intellect, imagination, and passion, a man can "lay his hand"—claim for his own—the ability to create "new worlds." The narrator says that we do not know if Aylmer feels this way, but the events of the story make it seem as though he does.
Later, Aylmer tells Georgiana that she "came so nearly perfect from the hand of Nature" that her birthmark "shocks [him], as being the visible mark of earthly imperfection." In light of these quotations, then, the shape of Georgiana's birthmark seems to symbolize her "Natural" origins. She was created naturally, and as a result she has an imperfection. In fact, she must have have some imperfection because she is earthly, she is human—she is not divine (and thus, perfect). In attempting to lay his hands on the secrets of Nature, so to speak, Aylmer overreaches: when he renders Georgiana perfect by removing her birthmark, she cannot survive because nothing produced naturally can be perfect.

Who are the "ignorant armies"?

Arnold is probably referring to an ancient battle recounted by the Greek historian Thucydides in which the Athenians fought Syracusans at night. In the context of the poem, however, there is a much deeper meaning involved. In "Dover Beach," Arnold is lamenting the growing retreat of religious faith, especially among the educated classes, in mid-Victorian England. The poem is addressed to the speaker's wife, standing at the window while her husband ruminates on the shingle sands beneath. Their marriage provides a haven of stability amid the swirling turmoil about them. Faith, as it currently exists, can no longer provide any of that much-needed stability, so the speaker and listener must to look to themselves and their marital love to provide truth and beauty in an ever-changing world:

"Ah, love, let us be trueTo one another! for the world, which seemsTo lie before us like a land of dreams,So various, so beautiful, so new,Hath really neither joy, nor love, nor light,Nor certitude, nor peace, nor help for pain;And we are here as on a darkling plainSwept with confused alarms of struggle and flight,Where ignorant armies clash by night."

The world is dark, and the coming clash of cultures and ideas will take place in that dark. Nature can no longer provide any illumination. The lovely sea and moon that opened the poem are now also obscured by night and darkness. In the midst of all this confusion, the speaker and listener still have each other, and that's what really matters.

What is the meaning of "square" in the essay?

The work to which I think you're referring is not an essay, but a short story told from the point of view of a white man watching the lynching and public burning of a black man in a public town square. The title of the short work is "A Party Down at the Square." The "square" is the town square, or gathering area, where lynchings were typically held in the South for public viewing.
What is remarkable about this story, which focuses on an action sequence described from the point of view of a white male spectator, is that nearby, an airplane crashes. Inside of the vessel, the crowd finds the dismembered body of a white woman wearing a white dress. This is important because black men in the South were usually lynched for two things—impudence, which could have been anything, really, from not crossing the street when passing a white person on a sidewalk to daring to have a successful business or something else that a white person wanted; the other reason was being accused of having had sexual relations with a white woman. Ellison contrasts the sight of the dead, dismembered white woman, which arouses the shock, horror, and sympathy of the crowd—one white woman "turned . . . almost as black as the nigger"—while people eagerly await the burning of the black man. At the end of the story, the narrator notes how one white woman scratched his face as she, rather literally, clawed her way through the crowd to get a better look at the burning.

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 52

Find all rational, irrational and complex zeros (and state their multiplicities) of the polynomial function $P(x) = 2x^3 + 5x^2 - 6x - 9$. Use Descartes' Rule of signs, the Upper and Lower Bounds Theorem, the Quadratic Formula or other factoring techniques.

The possible rational zeros of the polynomial $P$ is the factor of $9$ divided by the factor of the leading coefficient $2$ which are $\displaystyle \pm 1, \pm 3, \pm 9, \pm \frac{1}{2}, \pm \frac{3}{2}$ and $\displaystyle \pm \frac{9}{2}$. By using Synthetic Division and trial and error







Again, by applying Synthetic Division







Thus,


$
\begin{equation}
\begin{aligned}

P(x) =& 2x^3 + 5x^2 - 6x - 9
\\
\\
=& (x + 3)(2x^2 - x - 3)
\\
\\
=& (x + 3)(x + 1)(2x - 3)

\end{aligned}
\end{equation}
$


Therefore, the zeros of $P$ are $-3, -1$ and $\displaystyle \frac{3}{2}$. Each zeros have multiplicity of $1$.

When did the Great Depression begin?

More information about the Great Depression is posted below.
https://www.history.com/topics/great-depression

https://www.thoughtco.com/causes-of-the-great-depression-104686

The Great Depression began right after the stock market crash on October 29, 1929. It lasted for about ten years from 1929 to 1939, which takes us to the beginning of World War II. So, why did the Great Depression happen?
Generally, the stock market crash was a big factor, although it wasn't the only one. During the era of the roaring twenties, many people bought stocks in order to make money. Others bought stocks on the margin, meaning that very little was put down (about 10%-20%) for the costs; the remainder (80-90%) was borrowed. Investors gambled on the fact that, once stock prices rose, they could sell the stocks, pay off their debts, and reap a nice profit from the sale. So, many investors borrowed substantial amounts of money in order to reap potential profits.
On the surface, the stock market was performing admirably in the roaring twenties. However, the truth was that the stock market was being fueled by speculation and consumer expectation rather than market fundamentals (meaning that public consumption of products was not keeping up with production). When shares began dropping in value on October 24th (Black Thursday), people began to get worried. They commenced selling their shares, hoping to cash in on any profits they could make. Eventually, others began to sell their shares as well. This began an avalanche of selling that eventually caused the stock market to crash.
So many stocks lost their value that companies were forced to lay off their employees. Almost 15 million people became unemployed during the height of the Great Depression. Many unemployed families also lost their homes, which caused a domino effect: as families defaulted on their mortgages, banks began to fail. Since deposits were uninsured at the time, this means that many people lost the money in their checking accounts. So, the less money people had, the less they could buy. It was a vicious cycle, and the United States didn't see any relief until President Roosevelt instituted some fiscal and social changes in the country and the second of the world wars began.
For more on the Great Depression, please refer to the links below.

From the late 1760s to the mid 1770s, an ideology of revolution began to evolve in the colonies. Discuss the foundations and justifications formulating the colonial "philosophy of revolution."

Ironically (at least from a modern perspective), the "ideology of revolution" was initially based on the traditional rights of Englishmen. The colonists claimed that they enjoyed the same rights and protections as those who lived in England and that many of the actions of first Parliament and then the Crown violated these rights. This is why they were so angered by the Stamp Act, which essentially placed a direct tax on Americans—the Act was passed by Parliament, and, because no American colonies were represented in that body, the English constitutional tradition of taxation by consent was violated. So early on, "revolutionary" ideology centered around the violation of time-honored rights of Englishmen. By the time the Revolutionary War broke out in 1775, and certainly into 1776, a different foundation for revolutionary ideology had emerged. This was the idea that the colonists had rights not just as Englishmen, but as human beings. This was most famously expressed in the Declaration of Independence, but also by Thomas Paine in Common Sense. The argument went that all men were born with certain rights and that, since the English had violated these rights, the colonies were justified in rebelling and declaring their independence from the Crown.
https://www.history.com/topics/american-revolution/stamp-act

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 49

(a) there is no vertical asymptotes, f is defined and differentiable everywhere.
When x->+-oo, -x^2->-oo and f(x)->+0, so there is one horizontal asymptote y=0.

(b) f'(x) = -2x*e^(-x^2). It is >0 for x<0 and <0 for x>0,
so f(x) is increases on (-oo, 0) and decreases on (0, +oo).

(c) therefore there is one local maximum x=0. f(0)=1.

(d) f''(x) = e^(-x^2)*(-2 + 4x^2).
This is <0 for x on (-1/sqrt(2), 1/sqrt(2)) , f is concave downward there. And f''>0 on (-oo, -1/sqrt(2)) and on (1/sqrt(2), +oo), f is concave upward there.

(e)

•Traditional culture—can it be protected and betrayed? How is culture preserved? Does change necessarily exclude cultural preservation? Or, can change, progress, and culture coexist?

In “Everyday Use” by Alice Walker, the central conflict surrounds Mama and her daughter Dee, who is an educated cosmopolitan unlike her mother and her sister, Maggie. Dee, who has changed her name to the Africanized Wangero, thinks she knows best how to “preserve” the cultural artifacts of her family’s history, including the handmade quilts Mama has promised to Maggie.
Mama, in contrast, sees these cultural artifacts as everyday items that were created for practicality’s sake. Mama understands that honoring her family’s traditions means continuing to use these objects in the ways they were intended. Dee disagrees, and when Mama refuses to give her the heirloom quilts, Dee accuses Mama of not understanding her own heritage.
Your first question, of course, is seen in Dee’s perspective. One can preserve cultural artifacts, but it requires transforming its original use from practical object into idle decoration. This could be seen as a betrayal of the traditional culture.
On the other hand, one might see continuing to use these cultural artifacts as a destruction of history. Once these objects are destroyed, their connection to heritage will be also. Yet, if one agrees with Mama’s perspective, this “everyday use” is actually the best way to honor one’s traditional culture because it continues the traditions of the past.
It seems that traditional culture can only be preserved in a way so that something must be lost: its usefulness or its existence.