Single Variable Calculus, Chapter 4, 4.7, Section 4.7, Problem 56

Suppose that a man sells a necklace for \$10 each and his sales averaged $\displaystyle 20 \frac{\text{per}}{\text{day}}$. When he increased the price by \$1, he found that the average decreased by two sales per day.
a.) Find the demand function, assuming that it is linear.
b.) If the material for each necklace costs \$6. What should the selling price be to maximize the profit of the man?


a.) Let $P(x)$ be the demand function. If $P(x)$ is linear, it means that the line $y = P(x)$ passes through the point $(20,10)$ and $(18,11)$.
By using Point Slope Form,

$
\begin{equation}
\begin{aligned}
y - 10 &= \frac{11-10}{18-20} (x - 20)\\
\\
y &= - \frac{1}{2}x + 20
\end{aligned}
\end{equation}
$


Therefore, the deman function $\displaystyle P(x) = - \frac{1}{2}x + 20$.


B.) If the demand is $P(x)$, then the revenue $R(x) = x P(x)$
$\displaystyle R(x) = x\left( -\frac{1}{2}x + 20 \right) = -\frac{1}{2}x^2 + 20x$
Thus, we have...

$
\begin{equation}
\begin{aligned}
\text{Profit } &= \text{Revenue } - \text{ cost}\\
\\
P(x) &= R(x) - C(x)\\
\\
P(x) &= -\frac{1}{2}x^2 + 10x - 6x\\
\\
P(x) &= -\frac{1}{2} x^2 + 14x
\end{aligned}
\end{equation}
$


If we take the derivative of $P'(x)$, then...
$P'(x) = -x +14$

when $P'(x) = 0$,
$ x = 14$

Therefore, the selling price for maximum profit is

$
\begin{equation}
\begin{aligned}
P(x) &= - \frac{1}{2} x + 120\\
\\
P(14) &= -\frac{1}{2} (14) + 20\\
\\
P(14) &= \$13
\end{aligned}
\end{equation}
$

How does Clarke bring out the significance of renewing the bond of friendship in "Still Life"? Support your answer with various poetic devices.

In this poem, Clarke uses the extended metaphor of polishing brass to depict the renewal of friendship. Literally, the two friends "polish brass" together, but the act is symbolically representative of far more than that. In performing this act, the friends' hands become "slightly gritty . . . as they would feel / If we'd been in the sea, salty." This simile suggests an allusion to other things the friends might once have done together; the act of polishing the brass not only recalls other good memories but leaves a literal residue on the skin. In performing this act together, a physical reminder is enacted on the body.
The extended metaphor of the brass polishing is used to convey how spending time together in pursuit of an active goal seems to have a similar effect on the friendship itself. In polishing, it is "as if we burnished our friendship . . . until all the light-drowning tarnish of deceit were stroked away." Language like "burnished" and "tarnish" draws the reader's attention because of the assonance in the words but also because of the semantic field they create of light and the absence of light, along with "light-drowning." Deceit has "tarnished" their friendship just as tarnish has darkened the glow of brass, but in the act of rubbing, that tarnish can be rubbed away—it is not permanent.
Even as the tarnish disappears, "patterns of incredible honesty delicately grew." With the removal of the layers of deceit, then, the friends are able to uncover what lies beneath, and this is not difficult—the patterns are revealed "quite openly" under the right attention. The yellow, glowing motif continues to represent the truth of friendship, as the friends create "a yellow-gold still life" out of the pieces they polish, a bright image of their friendship forged by their actions. The heat of each object, Clarke says, is "illusory"—"essentially each object remains cold, separate, only reflecting the other's warmth." Heat and warmth is imparted into a friendship, then, only because the friends reflect each other's warmth and attention. If attention is paid to a friendship, it can easily be rejuvenated, its "tarnish" buffed away, but if it is not cared for, friendship does not have the warmth to sustain itself.

How does Iago's envy contribute to the downfall of Othello?

It is Iago's envy that causes him to hatch his scheme to destroy Othello. This scheme forms the basis for the entire plot. The audience discovers in the first scene of the play that Othello has passed over Iago for a promotion, choosing instead to promote Michael Cassio. Iago and Rodrigo go to Brabantio's house (Brabantio is Desdemona's father) to tell him that Othello and his daughter are sleeping together. This, it turns out, is just the beginning of Iago's scheming. In a soliloquy to end the scene, he resolves to "show out a flag and sign of love" to the Moor, though he says he hates him as he does "hell-pains." Iago's jealousy and scheming sets in motion a series of tragic events that consume Othello, his innocent wife Desdemona, Iago's wife Emilia, and others. Iago's scheme is so vicious and cunning that it seems entirely out of proportion to the grievance that he airs at the beginning of the play. 

According to the narrator’s mother in "Two Kinds" by Amy Tan, what are the “two kinds”?

The "two kinds" that Suyuan is talking about are the two different kinds of daughters that exist.  
The line comes fairly late in the story.  Suyuan has been pushing Jing-mei for months and months to be some kind of child prodigy.  The most recent attempt was to turn Jing-mei into an amazing pianist.  It failed miserably because Jing-mei gave it zero effort.  In fact, Jing-mei intentionally tried to sabotage the entire endeavor.  

So maybe I never really gave myself a fair chance. I did pick up the basics pretty quickly, and I might have become a good pianist at the young age. But I was so determined not to try, not to be anybody different, and I learned to play only the most ear-splitting preludes, the most discordant hymns.

Eventually Jing-mei had to perform in front of a large audience, and it went terribly; however, Jing-mei believed that she had performed poorly enough to cause her mom to stop pushing the piano prodigy dream.  It wasn't to be.  Two days after the piano recital, Suyuan told Jing-mei to begin practicing.  A huge yelling match between mother and daughter ensued.  Jing-mei explicitly told her mother that she would not be pushed into becoming something that she wasn't.  

"You want me to be something that I'm not!" I sobbed. "I'll never be the kind of daughter you want me to be!"

Suyuan immediately responded with the "two kinds" line.  

"Only two kinds of daughters," she shouted in Chinese. "Those who are obedient and those who follow their own mind! Only one kind of daughter can live in this house. Obedient daughter!"

In Suyuan's mind, daughters are either obedient or rebellious.  There is no middle ground.  The result of the comment is that Jing-mei shouts out that she doesn't want to be Suyuan's daughter anymore.  Jing-mei wishes that she were dead like all of her mother's other children.  With those things said, the already strained relationship is broken for years to come.  

What do the frame narratives accomplish in de Navarre’s The Heptameron?

Basically, a frame narrative or story is defined as a story within a story. In Margaret de Navarre's The Heptameron, frame narratives highlight God's providence and man's reliance on divine care. They also highlight the complexities within relationships and the therapeutic effect of stories during times of trial.
There are 72 short stories in The Heptameron; the narrators of the stories are five male and five female aristocrats who have been stranded at the Notre Dame de Serrance monastery after a flash flood. They must wait for a bridge to be rebuilt before they can continue on their journey. In the meantime, the lively group tells stories to amuse themselves. Navarre's narrators use diegesis (both homodiegesis and heterodiegesis, where all speech is filtered through the voice of the narrator) to tell their stories. In homodiegesis, the narrator is a character in his/her story, while in heterodiegesis, the narrator is outside the story. Navarre also allows her narrators to utilize independent dialogue to highlight the voices of characters in the story.
Let's take the first story on the first day. This story is told by Simontault, and it highlights the treacherous nature of immoral women. Simontault himself is not a character in the story; he allows his characters to speak for themselves. The use of heterodiegesis and dialogue in Simontault's frame narrative is followed by Oisille's frame narrative about women's virtue. Both frame narratives allow Navarre to draw attention to dual 16th century narratives regarding female morality.
While Simontault argues that "all women have set themselves to bring about the torment, slaughter and damnation of men" ever since the days of Adam and Eve, Oisille prefers to draw attention to female virtue. She tells the story of a virtuous wife who refuses to sully her chastity when she is propositioned by a licentious servant. Oisille's heterodiegesis at the end of the story highlights woman's pious nature, but it is also Navarre's means of drawing attention to her personal brand of theology. Navarre championed a stronger version of Calvin's "Singular Providence," where worshipers who submitted themselves to God were inspired to live singularly moral lives. In Oisille's story, the wife of the muleteer submits to twenty-five "mortal wounds" from her servant's sword rather than acquiesce to his base intentions. She remains faithful to her moral dictates.
In the end, the muleteer's wife is so weakened from loss of blood that she becomes helpless when the servant ravishes her. Oisille proclaims that the pious woman dies placing "her hope of salvation in Jesus Christ alone" and that she dies with "glad countenance and eyes upraised to heaven." Besides highlighting the widely divergent views regarding feminine piety, Navarre also uses The Heptameron's frame narratives to epitomize the highly complex nature of male/female relationships. For example, the stories on Day Six draw attention to how women and men often deceive and entrap each other through acts of vengeance and moral turpitude.
Last but not least, Navarre's frame narratives highlight God's sovereignty in all matters pertaining to the human world. In this vein, even treacherous weather must be attributed to God's will; it highlights his position as the only one who can bridle the natural world's active chaos. In Navarre's The Heptameron, the narrators are sheltered in a monastery, symbolic of God's protection against the elements. The aristocratic group wait out the storm and amuse themselves by telling stories. Navarre shows that floods and catastrophes are cause for thanksgiving because they bring to light God's continuing mercy upon humankind. It is God who preserves humanity and delivers them from sundry natural disasters.
To recap, Navarre's frame narratives highlight God's providential care for humanity, the complexities inherent in male/female relationships, and the therapeutic effect of stories during times of trial.
Sources:
1) Authorial and Narrative Voice in The Heptaméron by DEBORAH N. LOSSE Renaissance and Reformation / Renaissance et Réforme New Series / Nouvelle Série, Vol. 11, No. 3 (Summer / Été 1987), pp. 223-242.
2) The Pleasure of Discernment: Margaret de Navarre as Theologian by Carol Thysell.

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 40

a) To find the intervals of increasing or decreasing f(x), recall:

--> f'(x) = positive value implies increasing f(x) of an interval I.

--> f'(x) = negative value implies decreasing f(x) of an interval I.

Applying power rule derivative on f(x) = 5x^(2/3)-2x^(5/3) :
f'(x)= (2/3)*(5x^(2/3-1))-(5/3)*(2x^(5/3-1))
f'(x)= (10)/3x^(-1/3) -(5/3)*2x^(2/3)
f'(x)=(10)/(3x^(1/3))- (10x^(2/3))/3
f'(x)= (10)/(3x^(1/3)) -(10x^(2/3)*x^(1/3))/(3*x^(1/3))
f'(x)= (10 -10x)/(3x^(1/3)) Note: x^(2/3)*x^(1/3) = x^(2/3+1/3) or x^1

Solve for critical value x=c by letting f'(x)=0 and D(x)=0.
Let D(x)=0:
3x^(1/3)=0

3x^(1/3)*(1/3)=0*(1/3)
x^(1/3)=0
(x^(1/3))^3=0^3
x=0


Let f'(x)=0:
(10 -10x)/(3x^(1/3)) =0
(10 -10x)= 0*(3x^(1/3))
10-10x=0
10x=10
x=1
Table:
x -1 0 0.5 1 2
f'(x) -6.7 undefined 2.1 0 -2.6
intervals of decreasing f(x): (-oo ,0) and (1,+ oo )
interval of increasing f(x): (0,1)
b) Local extrema occurs at x=c when f'(c)=0.
f'(1)=0 then local extrema occurs at x=1.
Conditions:
f'(a) gt0 and f'(b) lt0 in the interval af'(a) lt0 and f'(b) gt0 in the interval aFrom the table, f'(0.5) gt0 and f'(2)lt0 then local maximum point occurs x=1.
Plug-in x=1 in f(x)=5x^(2/3)-2x^(5/3).
f(1)= 5(1)^(2/3)-2(1)^(5/3)
f(1)= 5-2
local maximum value: f(1)=3
c) According to second derivative test, we follow:
concave up when f"(c) >0 and concave down f"(c) >0 .
Inflection point occurs x=c when before and after x=c.
Applying power rule derivative on f'(x)= (10 -10x)/(3x^(1/3)) or f'(x)= (10x^(-1/3))/3 -(10x^(2/3))/3
f"(x)=(-1/3)*(10)/3x^(-1/3-1) -(2/3)*(10)/3x^(2/3-1)

f"(x)=(-10)/9x^(-4/3) -(20)/9x^(-1/3)
f"(x)=-(10)/(9x^(4/3)) -(20)/(9x^(1/3))
or f"(x)=(-10-20x)/(9x^(4/3))
Solve for inflection point:
(-10-20x)/(9x^(4/3))=0
(-10-20x)=0* (9x^(4/3))
-10-20x=0
20x=-10
x= -1/2 or 0.5

Test of concavity:
x -1 -1/2 -1/3 1
f"(x) (10)/9 0 -1.6

Intervals of concavity:
Concave up: (-oo , -1/2)
Concave down: (-1/2, 0) and (0, +oo )
Inflection point occurs at x=-1/2
Plug-in x=-1/2 in f(x) =5x^(2/3)-2x^(5/3):
f(-1/2)=3.8
Inflection point (c, f(c)): (-0.5,3.8)
d) Graph:

What kind of people are there on planet Venus?

Bradbury does not go into great detail about the people who chose to travel to the rainy planet Venus, where they remain secluded in elaborate underground tunnels and cities. The reader knows that the rocket men and women are American, because Margot was born in Ohio. It is also implied that each family is relatively affluent, assuming that space travel is rather expensive. While Bradbury does not give a specific reason as to why the men and women chose to colonize the rainy planet, he provides some insight into their motivation by writing,

And this was the way life was forever on the planet Venus, and this was the schoolroom of the children of the rocket men and women who had come to a raining world to set up civilization and live out their lives (1).

This quote reveals that the American men and women are interested in building a civilization on the planet, which implies that they are adventurous, determined individuals. They are interested in conquest and exploration, which is why they decide to move their families to Venus. The children on the planet are depicted as cruel individuals, who bully Margot because she is different. Their aggressive demeanor and callous nature may reflect their family's strong, tough personalities, which allow them to inhabit such a treacherous planet.

Venus in this story is devoid of life, except for the humans who have come. From what we see in the story, the people coming to the planet are white, middle-class Americans from the United States. We know that Margot's family came to Venus from Ohio.
Presumably, the families are willing to put up with the endless rain and being so far away from earth in order to earn more money than they could in the US. We know that Margot's parents will make a financial sacrifice if they return to earth next year, losing "thousands of dollars."
The children appear to be a in a typical American-style classroom, where they sing songs and learn about the sun to prepare for its rare appearance. They seem to be ordinary children. They bully Margot for being different, and they enjoy playing in the sun when it comes out.

What techniques does Desai use to develop Ravi in "Games at Twilight"?

Anita Desai uses a combination of direct and indirect characterization to develop Ravi.  
There is quite a bit of direct characterization happening with Ravi in this story. Readers are told many specifics about his build and his thoughts. For example, we are told that Ravi is short when Desai talks about his short legs being the cause of his slow running ability.  
Desai uses indirect characterization early on for Ravi as well. Probably my favorite line about him is the following line.  

Ravi heard the whistling and picked his nose in a panic, trying to find comfort by burrowing the finger deep—deep into that soft tunnel.

Readers are specifically told that Ravi is in a panic and picking his nose to find comfort, but within that sentence is a lot of other information about Ravi. He's not a very confident kid. The kids are playing hide-and-seek, yet Ravi is terrified. He also finds comfort in picking his nose. This tells readers that Ravi is likely that "weird" kid who still picks his nose at an entirely too-old age. He's probably not well-liked, and he doesn't have a lot of friends. Those suspicions are confirmed by the end of the story when readers see that nobody is willing to admit that Ravi won the game. In fact, nobody even remembers that Ravi was playing at all.

What does "light spent" mean?

"On His Blindness" is a sonnet written by Milton as a lament of sorts for his lost vision. Milton is contemplating the fact that he has been stricken with blindness, as the title implies, in a way that makes his "one Talent" very difficult to use. Effectively, Milton is saying that because he is now blind, it is more difficult for him to write in praise of God; but he comes to the conclusion that God does not require man to continually serve him through deeds for the entirety of their lives—on the contrary, "they also serve who only stand and waite."
The first line of the poem, then, reflects Milton's concern about the fact that his "light is spent"—his vision has been lost—"e'ere half my days" (before I have lived half of my allotted lifetime). His "light" here generally seems to be a metaphor for his vision: he is saying that his capacity to see the world has been exhausted too soon. "Light" could also have other connotations: Milton connects his vision to his talent, so there is an implication that, in losing his vision, he also loses his enlightenment, his sense of understanding, and his fresh outlook on the world. Without his "light," he is concerned that he can no longer contribute or make use of his "talent." The word "spent," also, gives the suggestion that there was only ever a finite amount of "light" to be used up, and the poet is concerned that he has exhausted all of it in an unbalanced way—as if his "light" should really have lasted him for the whole of his life, rather than only half of it.

What are great books for a 10th grader to read?

It depends to a large extent on the student. Students have a wide range of interests and of reading skills. Students often enjoy stories featuring people of their own age, and thus Lord of the Flies, To Kill a Mockingbird, or The Catcher in the Rye are often included on reading lists.
Students interested in science can enjoy H. G. Wells, Jules Verne, and works such as 1984 or Brave New World. For students in the United States, reading works set in other cultures such as the Arabian Nights, Things Fall Apart, or even the travel and animal-collecting stories of Gerald Durrell can open up new worlds. Traditional epics, such as the Homeric poems and Beowulf, seem also to be popular, though they work best for the more advanced readers in this age group. Many collections of myth, legends, and fairy tales can also be of interest; the Norse sagas will appeal to those students who have enjoyed recent movies and comics based on them. Shorter fables and fairy tales might work well for less advanced students.
History books, especially local histories or stories of Native American culture, can also spark interesting discussions.

Why did Phyllisia wait so long before answering the teacher's question?

Phyllisia's very much an outsider. As the daughter of West Indian immigrants, she feels somewhat alienated from the rest of society. And her outsider status follows her to school, where, like a lot of children who stand out from the crowd, she becomes a prime target for bullying. As well as her unusual background and exotic accent, Phyllisia stands out for being quite ugly, and that's always a handicap at any school. Furthermore, she's also very intelligent and knows all the answers to the teacher's questions. This makes her even more hated by the other girls in class, who resent her for being "teacher's pet."
But Phyllisia doesn't want to stand out any more than she already does. She doesn't want to make life any harder for herself. That's why she doesn't raise her hand in the air and volunteer to answer the teacher's questions; she only answers if she's specifically asked. So when Miss Lass asks the class which continent Egypt is located in, Phyllisia doesn't say a word until the teacher calls her by name, even though she knows the answer.

Is this story successful in living up to Hemingway's assertion that the "dignity of movement of an ice-berg" has to do with what is submerged?

Hemingway believed that the omission of certain facts about characters or plot helped strengthen his stories. He hoped that readers would bring their own interpretations and abilities to infer important details. For example, in the novel The Sun Also Rises, Hemingway never overtly tells his reader that Jake Barnes is impotent because of a wound suffered during World War I, yet the fact is implied and acts as a metaphor for the impotence of his generation.
On the surface, the short story "Hills Like White Elephants" appears to be about a casual conversation between two lovers as they travel through Spain. Hemingway, however, immediately signals that there is a problem in the first paragraph with his description of the setting. He writes that the train station was "between two lines of rails in the sun," suggesting that this couple may be on the verge of going their separate ways. There is a curtain over the door to the bar, and the couple sits in the shade, implying they may have something to hide.
Eventually the woman observes that the hills in the distance look like white elephants. In many societies, a white elephant is a gift that may prove to be burdensome. Legend has it that the King of Siam would give away albino elephants to his enemies in the hope that the upkeep of the animal would destroy the recipient. In Hemingway's story, the white elephant in question is the unborn baby which the woman carries.
The conversation leads to a rejection of the baby by the man who suggests the woman should have an abortion. He describes the process by saying, "I know you wouldn't mind it, Jig. It's really not anything. It's just to let the air in." The woman seems to repel from the man's advice. When he contends things will be fine between them afterward, she says, "No, it isn't. And once they take it away, you never get it back." Finally, Hemingway hints that this is the end for the couple's relationship by showing them drinking in separate places in the bar:

He drank an anis at the bar and looked at the people. They were all waiting reasonably for the train. He went out through the bead curtain. She was sitting at the table and smiled at him.

In Night by Elie Wiesel, what is a quote that describes the Jews' blindness to how the Nazis were going to treat them?

One quote that describes the ways in which the Jews in Sighet were blind to the atrocities that the Nazis had in store for them was their response to what Moishe the Beadle tells them. When he is expelled from the town as a foreigner, he is sent on a train to Poland. There, he witnesses how the Gestapo kill Jews, including infants, though he is able to escape. When he returns to Sighet, the Jews in the town refuse to believe him. Wiesel writes:

"But people not only refused to believe his tales, they refused to listen. Some even insinuated that he wanted their pity, that he was imagining things. Others flatly said that he had gone mad" (page 7).

The Jews of Sighet refuse to believe Moishe's tales of horror. Instead, they cling to the idea that better days are right around the corner. After they are placed in a ghetto, they believe that they will stay in the ghetto and then be rescued by the Soviet army. As Wiesel writes, "The ghetto was by neither German nor Jew; it was ruled by delusion" (page 12). The Jews exist by deluding themselves into thinking that the Nazis will never choose to harm them, but the Nazis soon decide to liquidate the ghetto and send the residents to concentration camps. 

Think specifically about the setting of the "Greasy lake" at night and then the setting of the lake in the morning as the boys come out of hiding. There is a very distinct contrast in these two descriptions. Explain why this is.

Greasy Lake is a story about what happens when one's fantasies are put to the test of reality. In the beginning of the story, the narrator and his friends are shown to think of themselves as “tough characters,” but in fact they are just teens trying out different identities that they don't truly understand. The setting reenforces this—the lake at night is a place of mystery and uncertainty. The fight that is the central action of the story is a product of this mystery: first, because they mistake one car for another; second, the identity of the man they fight is never clear. The whole sequence, from arriving to the lake, to possibly killing the man with a blow to the head with the tire iron, to the aborted rape of his girlfriend, all takes place in a kind of fog, as if the events were somehow disconnected from reality. When another car comes and the narrator tries to “swim for it” across the lake and finds the corpse and watches as his mother’s car is vandalized, it is as if the reality of his situation finally hits him.
In the daylight, things become clearer. The narrator and his friends emerge from their hiding places; the car, though damaged, is still drivable. There is a sense that they’ve come to realize that being “tough characters” is not what they had thought it would be. It is as if the light of day has chastened them. When the girls show up and start asking about “Al,” the owner of a motorcycle parked at the lake, the narrator says he hasn’t seen him, although the implication is that the body in the lake must have been Al’s. The three friends drive away in their broken car, and the reader is left with the sense that their days of being “tough characters” are over.

What does Zora Neale Hurston mean when she states, “I remember the very day that I became colored” (357)? How did she grow up, and how did that shelter her from racism? How did her experience change when she was thirteen? What does this autobiographical essay suggest about racism in the U.S. in the early decades of the twentieth century?

In her essay, "How It Feels to Be Colored Me," Zora Neale Hurston begins by describing her childhood in Eatonville, Florida—an all-black community. She recalls seeing passing white visitors, usually from the North, and using their presence as an opportunity to turn herself into an informal welcoming committee, despite the nervousness that the foreign white faces inspired in some of the adults:

They were peered at cautiously from behind curtains by the timid. The more venturesome would come out on the porch to watch them go past and got just as much pleasure out of the tourists as the tourists got out of the village. The front porch might seem a daring place for the rest of the town, but it was a gallery seat for me. My favorite place was atop the gatepost. Proscenium box for a born first-nighter. Not only did I enjoy the show, but I didn't mind the actors knowing that I liked it. I usually spoke to them in passing. I'd wave at them and when they returned my salute, I would say something like this: "Howdy-do-well-I-thank-you-where-you-goin'?"

Being in an all-black space, and a thriving black community, contributed to Hurston's experience of not feeling inferior. Unlike her contemporaries who, in her view, belonged to "the sobbing school of Negrohood," she never measured her blackness against whiteness and never envied what white people had.
Her circumstances changed when she went away to Jacksonville to attend school. There, she was "not Zora of Orange County any more," but just another "little colored girl." With this simple and subtle phrase, Hurston reveals how racism reduces a person's identity. She thought of herself as someone with a name and a place of origin, but in Jacksonville, she was defined by her color—an aspect of her being which placed her in the strange space of being both unwanted in public spaces but essential to the maintenance of Jim Crow: "warranted not to rub nor run."
https://www.casa-arts.org/cms/lib/PA01925203/Centricity/Domain/50/Hurston%20How%20it%20Feels%20to%20Be%20Colored%20Me.pdf

what can be a thesis on Magical realism?

Magical Realism in literature originated in Latin America. It owes some debt to extreme realism (in the arts) which was an intense focus on the "real." But Magical Realism in literature owes more to the development of Surrealism in the early 20th century. Simply put, Magical Realism is the fusion of realistic elements with elements of fantasy, the supernatural, or any others that are not realistic. A famous example of this style is Gabriel Garcia Marquez's short story "A Very Old Man with Enormous Wings." Everything about the story is realistic except for the man with wings. It is a mix of realism and fantasy.
In Dreaming in Cuban, a complicated story about family, politics, and identity, there are realistic and fantastic elements. Celia and Felicia have recurring visions of the deceased Jorge (Celia's husband). Pilar, daughter of Lourdes and granddaughter of Celia, becomes increasingly aware of an inner voice, something that is both a realistic urge to connect with her Cuban ancestry and also something that is magical or perhaps even a telepathic connection between her and Celia, her grandmother.
These magical elements link certain characters together—characters who are separated in time or in space (geographically). And in this novel, the real/magical dynamic is an effective parallel between other dichotomies: Cuba/USA, past/present, as well as conflicts between mothers and daughters. So, while magical elements can be used in Magical Realism simply for the sake of more fantasy, they can also illustrate cultural aspects and how mythic connections arise out of strict realism.

Precalculus, Chapter 1, 1.4, Section 1.4, Problem 10

Determine the center and radius of the given circle. Write the standard form of the equation.







Using the distance formula, to solve for the diameter, but $\displaystyle r = \frac{d}{2}$. So we have


$
\begin{equation}
\begin{aligned}

r =& \frac{\sqrt{(1-3)^2 + (0-2)^2}}{2}
\\
\\
r =& \frac{\sqrt{4+4}}{2}
\\
\\
r =& \frac{\sqrt{8}}{2}
\\
\\
r =& \frac{2 \sqrt{2}}{2}
\\
\\
r =& \sqrt{2}

\end{aligned}
\end{equation}
$


To find the center of the circle, we use the Midpoint Formula,


$
\begin{equation}
\begin{aligned}

M =& \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\\
\\
=& \left( \frac{0+2}{2}, \frac{1+3}{2} \right)
\\
\\
=& \left( \frac{2}{2} , \frac{4}{2} \right)
\\
\\
=& (1,2)

\end{aligned}
\end{equation}
$


So the center of the circl is $(1,2)$.

The equation of the circle in standard form is



$
\begin{equation}
\begin{aligned}

(x-1)^2 + (y-2)^2 =& (\sqrt{2})^2
\\
(x-1)^2 + (y-2)^2 =& 2

\end{aligned}
\end{equation}
$

What quotes in A Christmas Carol shows that Scrooge has changed?

At the end of the book, after his encounters with the three Christmas ghosts, Scrooge wakes up in his own bedroom on Christmas morning a very different man from the greedy miser who, the evening before, hated the world, begrudged his clerk Christmas Day off, and wished the poor would die and rid the world of their excess population. Instead, he is overjoyed to be alive. He is in love with the world. One quote that expresses this is the following:

I am as light as a feather, I am as happy as an angel, I am as merry as a schoolboy. I am as giddy as a drunken man. A merry Christmas to everybody! A happy New Year to all the world. Hallo here! Whoop! Hallo!

Further, when he looks out the window, everything he sees seems bright and wonderful to him, showing he has gone from miserable to joyous:

Golden sunlight; Heavenly sky; sweet fresh air; merry bells. Oh, glorious! Glorious!

He also laughs, "Ha ha ha!” We are told he hasn't laughed in a long time and is out of practice but nevertheless offers a "brilliant" laugh.
Showing that he has changed completely from a humorless man who begrudged Bob Cratchit a day off, he now decides to surprise Cratchit with a giant turkey as a surprise, anonymous gift and feels it will be a great joke:

“I’ll send it to Bob Cratchit’s!” whispered Scrooge, rubbing his hands, and splitting with a laugh. “He sha’n’t know who sends it. It’s twice the size of Tiny Tim. Joe Miller never made such a joke as sending it to Bob’s will be!”

Finally, we learn that his changed personality lasts the rest of his life:

He became as good a friend, as good a master, and as good a man, as the good old city knew, or any other good old city, town, or borough, in the good old world.

In "The Chrysanthemums," how are Elisa and the chrysanthemums similar?

The connection between Elisa and her treasured chrysanthemums is illustrated in John Steinbeck's short story "The Chrysanthemums." The opening of the story shows the relationship Elisa has with her flowers; they are almost like her children. She is cutting down the prior year's flowers to make room for the newly budding flowers. The way that she does this is nurturing and loving. She wants to make sure that nothing, no weeds, bugs, or old stalks, will stunt the growth of the new flowers.
Later, when she is conversing with a man from a caravan, she tells the man about the size of her flowers—they have grown "ten inches across." She tills the earth to take care of the flowers, and the flowers, in return, bring her pride and happiness. Elisa and the flowers are intertwined. She needs them, and they need her.
As the story unfolds, readers become aware that the flowers symbolize Elisa's feminity. During her conversation with the man from the caravan, he openly states his appreciation for her gardening. She sees this as a compliment to her as a gardener and a woman. Later, after her conversation with the man, her husband returns home and compliments her on her looks, something she took great care with after the compliment from the man in the caravan.
Most obviously, the connection between Elisa and her flowers is illustrated through the sexuality they both possess. Women and flowers both "bloom." Her flowers bloom literally, growing from seeds and changing into flowers. Elisa, like the flowers, blooms as well. Although readers do not see her sexual "blooming," they can see where her pride as a woman comes from. The compliments she gets from the man in the caravan illustrates a direct reference to her sexuality. As she is gathering and planting flowers for the man to take with him, the text states the following:

She was kneeling on the ground looking up at him. Her breast swelled passionately.

In the end, Elisa and her flowers are directly linked. They both need love, compassion, and someone to care about them in order for them to bloom.

In the story "Hearts and Hands" why does Mr. Easton seem embarrassed when he encounters Miss Fairchild?

Mr. Easton is embarrassed because he doesn't want Miss Fairchild to see how far down in the world he's fallen. When she previously knew him back East, Mr. Easton was a member of the social elite. But now, he's nothing more than a common criminal on his way to the penitentiary. Being incarcerated is not something that usually happens to people of Mr. Easton's social class. But then it's not really the done thing to be a humble sheriff either, which is an additional source of embarrassment. In fact, it's a toss-up as to which is the more embarrassing for Easton: to be thought by Miss Fairchild to be a crook or a law enforcement official.
Although Mr. Easton may be on his way to prison, it's telling that he still appears more concerned by appearances than anything else. He may be a crook, but he still retains his sense of due propriety. It's not so much the going to prison that's a problem for Easton, it's the social disgrace that his crimes will bring. Thankfully for him, Miss Fairchild is so blinded by her own sense of social propriety that she's unable to recognize that it is Easton, and not the man handcuffed to him, who's on his way to prison.

There are two likely reasons that Mr. Easton may be embarrassed to encounter Miss Fairchild on the train.
First, Mr. Easton used to be one of Miss Fairchild's suitors. The text tells us that he once vied with an ambassador for the young lady's hand. So, meeting her on the train with his wrist handcuffed to an imposing man is rather embarrassing. Mr. Easton feels self-conscious because he knows that he is a criminal who is about to spend seven years at Leavenworth prison.
Seeing his discomfort, Mr. Easton's glum-looking partner takes pity on him and pretends to be the criminal instead.
There may also be another reason Mr. Easton is embarrassed to encounter Miss Fairchild on the train: he doesn't wish Miss Fairchild to alert common acquaintances in Washington about his criminal background. From Miss Fairchild's words about the "Washington crowd," it is likely that Mr. Easton was once a well-known figure there. So, he may not be too pleased about exposing his counterfeiting past to such a fashionable crowd.

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 54

(3x+1)/(2x^3+3x^2)
To decompose this to partial fractions, factor the denominator.
2x^3 + 3x^2 = x^2(2x + 3)
Then, write a fraction for each factor. For the repeated factor x, form a partial fraction for each exponent x from 1 to 2. And assign a variable for each numerators.
A/x , B/x^2 and C/(2x + 3)
Add these three fractions and set it equal to the given fraction.
(3x+1)/(x^2(2x+3)) = A/x + B/x^2+C/(2x+3)
To solve for the values of A, B and C, eliminate the fractions in the equation. So multiply both sides by the LCD.
x^2(2x+3) * (3x+1)/(x^2(2x+3)) = (A/x+B/x^2+C/(2x+3)) *x^2(2x+3)
3x+1=Ax(2x+3) + B(2x +3) + Cx^2
Then, plug-in the roots of the factors.
For the factor x^2, its root is x=0
3*0+1=A*0(2*0+3) + B(2*0+3)+C*0^2
1=3B
1/3=B
For the factor (2x + 3), its root is x=-3/2.
3(-3/2)+1=A(-3/2)(2(-3/2)+3)+B(2(-3/2)+3)+C(-3/2)^2
-7/2=A(-3/2)(0)+ B(0)+9/4C
-7/2=9/4C
-14/9=C
To get the value of A, assign any value to x, and plug-in the values of B and C to:
3x+1=Ax(2x+3) + B(2x +3) + Cx^2
Let x = 1.
3*1+1=A*1(2*1+3) + 1/3(2*1+3)+(-14/9)*1^2
4=5A + 5/3-14/9
4=5A+1/9
4-1/9=5A
35/9=5A
7/9=A
So the partial fraction decomposition of the given rational expression is:
(7/9)/x + (1/3)/x^2 + (-14/9)/(2x+3)
This simplifies to:
7/(9x) + 1/(3x^2)-14/(9(2x+3))

To check, express them with same denominators.
7/(9x) + 1/(3x^2)-14/(9(2x+3))=7/(9x) * (x(2x+3))/(x(2x+3)) + 1/(3x^2)*(3(2x+3))/(3(2x+3)) -14/(9(2x+3))*x^2/x^2
= (14x^2+21x)/(9x^2(2x+3)) + (6x+9)/(9x^2(2x+3)) - (14x^2)/(9x^2(2x+3))
Now that they have same denominators, let's proceed to add/subtract them.
= (14x^2+21x+6x+9-14x^2)/(9x^2(2x+3)) = (27x+9)/(9x^2(2x+3)) = (9(3x+1))/(9x^2(2x+3))= (3x+1)/(x^2(2x+3))
= (3x+1)/(2x^3+3x^2)

Therefore, (3x+1)/(2x^3+3x^2)=7/(9x) + 1/(3x^2)-14/(9(2x+3)) .

What are three examples of characters not being what they seem in act one of Hamlet?

Characters who are not what they seem:
1. Claudius Act 1, Scene 2: Claudius is asking Hamlet to stay at home for a time and to not go back to school in Wittenberg. In lines 110–117, Claudius says to Hamlet,

And with no less nobility of love
Than that which dearest father bears his son
Do I impart toward you. For your intent
In going back to school in Wittenberg,
It is most retrograde to our desire.
And we beseech you, bend you to remain
Here in the cheer and comfort of our eye,
Our chiefest courtier, cousin, and our son.

He claims that he wants Hamlet to be home because he loves him and wants him to be the first member of his court. Remember that Hamlet's biological father is dead. Claudius (his uncle) married Hamlet's mom about a month after Hamlet's father's death, so Claudius is now technically Hamlet's step-father. Claudius is only pretending to truly care for Hamlet and only pretending to want to work closely with him. In actuality, he is nervous about Hamlet's connection to the throne and wants to keep him close so that he can control him, preventing any conflict over who truly deserves the throne. So he is not as he seems; his true motivations are hidden.
2. Hamlet Act 1, scene 2: Hamlet obeys his mother and Claudius by agreeing to stay home instead of going back to school. In front of them, he appears agreeable and sincere about this decision. Even though he has been open about his deep sadness over his father's death and his disapproval of his mother's remarriage, Hamlet has not been completely honest about his feelings. He expresses his frustrations and true feelings in a soliloquy when he says,

Oh, that this too, too sullied flesh would melt,
Thaw, and resolve itself into a dew,
Or that the Everlasting had not fixed
His canon 'gainst self-slaughter! O God, God!
How weary, stale, flat, and unprofitable
Seem to me all the uses of this world!
Fie on ’t, ah fie! 'Tis an unweeded garden
That grows to seed. Things rank and gross in nature
Possess it merely. That it should come to this.

Here he even goes as far as to wish that suicide was not a sin; he is deeply depressed. In other words, Hamlet is not as he seems because he is hiding the extent of his true emotions from his mother and from Claudius.
3. Ophelia, Act 1, Scene 3: In this scene, Laertes, Ophelia's brother, and Polonius, her father, both warn Ophelia about Hamlet. They claim that he is not truly interested in her and is only using her. They urge her not to see him again and not to think about him. Ophelia answers her father's requests with "I shall obey, my Lord."
She agrees to follow her father's dictates, coming across as mild and malleable. Later in the play, she goes along with her father and Claudius's plot to trick Hamlet, again allowing her father to make decisions for her. However, after Ophelia's madness and then suicide, the audience realizes that Ophelia may have suffered as a result of the controlling men in her life. In Act 4, she sings,

By Gis and by Saint Charity, Alack and fie for shame,Young men will do 't, if they come to 't; By Cock, they are to blame. Quoth she, 'Before you tumbled me, You promised me to wed.'So would I 'a done, by yonder sun, An thou hadst not come to my bed.

In this part of the play, Ophelia has gone mad. Here she is singing about the hypocrisy of men. So while in Act 1 she may seem to be content to submit to the wishes of the men in her life, by the play's conclusion, we realize that the men around her have caused her irreparable harm. Her relationships, too, have not been all they seemed.

According to Utnapishtim, why did the gods decide to destroy humanity?

The answer to this question partially depends on what translation a student is reading.  One of the problems with understanding Gilgamesh is that the tablets on which it was originally inscribed were already damaged and very hard to decipher when that modern translation process began.  Thus, various translators have drawn from other flood narratives to elaborate on the story.  What has been translated, though, leads to the understanding that the gods were dissatisfied by and angry with the humans--much like in other flood narratives.   In various translations, the god that is portrayed as most angry and the leader in this plan of destruction is Enlil.
In addition to the gods' motivation of anger and dissatisfaction, Utnapishtim lets Gilgamesh know that there is not supposed to be permanence in the mortal world; thus, destroying mankind is actually part of the greater plan.  He also suggests that the gods are capricious and do not always act in ways that mortals can understand. 
The civilization represented in the story is polytheistic, and several of the gods are sworn to secrecy about their plan to destroy mankind.  For whatever reason, though, the god Ea relents slightly and communicates to Utnapishtim that he needs to build a boat so that he can save his family.  After the flood waters recede, Enlil is angry that Utnapishtim and his family have survived, but after being chastised for not seeking the help and counsel of the god Ea (the god of earth and water), Enlil eventually sees the error of his earlier thinking.
Overall, Utnapishtim communicates to Gilgamesh that the gods do what the gods want to do.  Whether it is anger or capriciousness that is the primary motivation depends more on the translation being used.
http://www.fsmitha.com/h1/religion-flood.htm

In Freak the Mighty by Rodman Philbrick, why does Max get bothered by the way Freak speaks?

In Rodman Philbrick's novel Freak the Mighty, Max is not so much bothered by Freak's speaking as he is amazed by it. Max has never encountered anyone who speaks like Freak, whose real name is Kevin. There is no textual evidence to support that Max is bothered by his speech. Consider the following quotes: 

"That's how he talked, like right out of a dictionary. So smart you can hardly believe it. While he's talking he's winding up the bird-thing. There's this elastic band inside, and he goes, 'Observe and be amazed, earthling.' And then he lets go. And you know what? I am amazed, because it does fly just like a little bird, flitting up and down and around, higher than I can reach." 
"This is the first time for me, hearing Freak really talk, and right away I know one thing: when he's talking, you can't take your eyes off of him. His hands are moving, and it's like he's really seeing it, this story about an old king." 
"I think so, but I like hearing Freak talk, so I go, 'better tell me,' and that's when I find out why he's so interested in some clanky old knights." 

These quotes show Max's awe of Freak's vocabulary and speech, but don't support any irritation he feels with Freak's speech. 
Freak's vocabulary is incredibly advanced, and certainly beyond Max's experience. Freak does a good job explaining the words to him, and Max is able to pick up others through the context of Freak's speeches. Here's an example: 

"Pardon my vocabulary. Sobriquet means 'nickname,' and demeanor means 'expression.' I merely postulated that you call your grandfather 'Grim' because he's grim. Postulate means—'
'I know.' I say. Which is a lie, except I can guess what he means, figure it out that way.

Considering Max's learning disability, and subsequent dislike for books, it would be reasonable to infer that Max is bothered by Freak's speech; however, an inference must use the textual evidence plus the reader's background knowledge to form an educated guess. The textual evidence doesn't support Max being bothered by Freak's speech.

Who is speaking? To whom are they speaking?

The speaker in this poem gives away very little about themselves—we do not know whether the speaker is a man or a woman, how old they were, or where they were from. However, we do learn one very important thing from the first line, "I heard a fly buzz—when I died—"
The speaker, then, is a dead person or a ghost; the poem is being relayed to us from beyond the grave.
We do not know from the poem who the intended audience might be. However, we do know that the speaker is somebody who was much beloved in life; "The Eyes around—had wrung them dry—" suggests that the speaker's deathbed was surrounded by mourners, all crying over the loss of this person. We also know that these people were the recipients of "Keepsakes—Signed away," so the speaker was presumably not somebody too impoverished to have had possessions enough to leave to the mourners in their will.
Apart from this, the speaker may be any dead person, and the poem is addressed directly to whoever is reading it. Dickinson's conversational style always lends a sense of immediacy to her work, and for this reason it is possible for us as readers to imagine that the dead speaker is relating this story of their deathbed for our own benefit.

What impact does the development of science and technology have in society

Science and technology impact society in many ways, good and bad. Take for instance technological advancements in the communication industry. Today, our ability to communicate is enhanced by the availability of facilities such as the Internet, wireless communication, electronic mail, cell phones, social media sites, and applications such as Twitter, Facebook, Whatsapp, LinkedIn, Google Hangouts, and Skype. With enhanced communication, information is passed on from one point to the next quickly. People can hold virtual meetings that allow them to communicate without being at the same venue, job applicants can attend virtual interviews that eliminate the need to travel long distances to physical venues, and so on. One by-product of enhanced communication is the increase in telecommuting or remote workers. This is a group of workers who work away from their offices and are dependent on technology for efficient completion of projects—for instance, software engineers who can work from home while using the wide array of project management and communication tools available to connect with team members in other locations.
On the other hand, technological advancements within the communication sector have come with problems such as fake news, cyberbullying, and cyber insecurity. Some countries—such as the United States, Canada, the Philippines, and Australia, just to mention a few—have developed laws that protect citizens against cyber-bullying. Also, many companies have developed strategies aimed at protecting themselves against hackers interested in illegally obtaining private information from companies. Fake news circulating on social media sites can cause alarm and anxiety among people—this can even lead to health problems.
Technology impacts the human life on many levels. I have only looked at communication, and how it affects lives both positively and negatively.

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 48

Determine the $\displaystyle \lim_{x \to 0} (\csc x - \cot x)$. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.

$\displaystyle \lim_{x \to 0} (\csc x - \cot x) = \lim_{x \to 0} \left( \frac{1}{\sin x} - \frac{\cos x}{\sin x} \right) = \lim_{x \to 0} \left( \frac{1 - \cos x}{\sin x} \right) = \frac{1- \cos 0}{\sin 0} = \frac{1-1}{0} = \frac{0}{0}$ Indeterminate.

Thus by applying L'Hospital's Rule...

$
\begin{equation}
\begin{aligned}
\lim_{x \to 0} \left( \frac{1- \cos x}{\sin x} \right) &= \lim_{x \to 0} \left( \frac{0-(-\sin x)}{\cos x} \right)\\
\\
&= \lim_{x \to 0} \left( \frac{\sin x}{\cos x} \right)\\
\\
&= \lim_{x \to 0} \tan x\\
\\
&= \tan 0\\
\\
&= 0
\end{aligned}
\end{equation}
$

sum_(n=1)^oo 1/sqrt(n+2) Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.

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

How does voter turnout in the US compare to the voter turnout in other countries? How do you explain the differences? What were the effects of the two largest reforms in voter registration—the introduction of the Australian ballot and Motor-Voter registration—on the voter turnout rates?

Voter turnout in the United States is significantly lower than in most other developed countries. In 2016, about 55 percent of the voting-age population voted for president. It was more than in 2012, but less than in 2008.
In comparison:
73 percent of the voting-age population of Finland voted in 2015.
87 percent of the voting-age population of Belgium voted in 2014.
78 percent of the voting-age population of South Korea voted in 2017.
73 percent of the voting-age population of New Zealand voted in 2014.
65 percent of the voting-age population of the U.K. voted in 2016.
The United States was number 28 on the list of voter turnout for the most recent national election out of 35 members of the Organization for Economic Cooperation and Development.
The adoption of the Australian ballot and the Motor-Voter Act of 1993 were at least partially intended to increase voter turnout but were not significantly effective. 
The Motor-Voter Act was created to make registering to vote easier. However, it did not significantly increase the number of people who voted—and turnout was actually down a bit from 1993–1995.
The Australian ballot is a secret ballot, where voters cast their vote without anyone knowing who made it. It was adopted in 1890. It did not have a significant effect on voter turnout, though it was implemented at a time when many other voting adjustments—including literacy tests and poll taxes—lowered overall voter turnout in the U.S.
https://prospect.org/power/motor-voter-motivated-voter/

https://www.pewresearch.org/fact-tank/2018/05/21/u-s-voter-turnout-trails-most-developed-countries/

The United States voter turnout is a topic of interest because despite the nation being a strong democracy, it ranks lower in voter turnout compared to other developed countries. The voter turnout was slightly higher in 2016 when compared to 2012, but it remained lower than the record turnout in 2008. In 2016, the voter turnout was estimated to have reached 55.7%, which was lower compared to countries in the Organization for Economic Cooperation and Development (OECD). The highest was Belgium at 87.2%.
In the United States, voter registration by those eligible is voluntary. Thus, the number of registered voters is much lower compared to the number of potential voters. In states where competition is low between the parties, low voter turnouts have been recorded due to minimal interest. Restrictive voting laws such as photo ID mandates have also impacted negatively on turnout.
The Motor Voter law was introduced to improve participation of marginalized groups in polls. However, the law has not yielded the expected results because its main focus is on registration. Marginalized groups have yet to be convinced of the need to turn out and vote. The Australian ballot system serves the purpose of reducing fraud and expanding voter freedom during the actual voting, but it cannot motivate voters to turn out at the ballot. Thus, more needs to be done to motivate and convince the eligible voters to register and participate in electing their representatives.
https://www.pbs.org/newshour/politics/voter-turnout-united-states

https://www.pewresearch.org/fact-tank/2018/05/21/u-s-voter-turnout-trails-most-developed-countries/

In the US, voter turnout averages 60 percent in national elections. In other words, only 60 percent of those who are eligible to vote actually cast their ballot. But this figure varies from state to state, as shown by the 2012 national elections. In Oregon, for instance, 64.2 percent of voters turned out compared with only 49.6 percent in Texas.
Compared with Australia, voter turnout in the US is relatively low. In the 2014 Australian elections, for example, voter turnout was much higher than in the US: it reached 88.5 percent. It is perhaps worth noting that Australia operates a policy of compulsory voting, which likely accounts for such high levels of voter turnout.
In the US, the introduction of the Australian ballot system (in which votes are cast secretly) and the passing of the Motor Voter Act of 1993 (in which people can register to vote at certain state motor vehicle agencies) has not had a significant effect on voter turnout. While the Motor Voter Act did cause an increase in the number of people who registered to vote, voter turnout actually decreased by five percent between the 1992 and 1996 elections.
Because these voting reforms have not increased voter turnout, it might be suggested that voter apathy and a general dissatisfaction with politics are the real culprits. Only by addressing these issues with the voting population can voter turnout be expected to increase.

How does Henry describe his months in the camp in The Red Badge of Courage by Stephen Crane?

Henry Fleming, a young soldier in the Union army during the Civil War, describes his first months in the army as a "monotonous life in camp."
During these months waiting for an assignment, Henry has begun to perceive himself as merely a part of "a vast blue demonstration." Each day the soldiers are drilled and drilled and reviewed; then, they are again drilled, drilled, and reviewed in what becomes tedious repetition. Added to this, random soldiers return to camp, shouting some news that they have supposedly learned. One day, a tall soldier comes running into camp, waving his shirt as though it were a banner. He shouts,

"We're goin' t'move t'morrah--sure....We're goin' 'way up river, cut across, an' come around in behint 'em."

One of the soldiers claims, "It's a lie! that's all it is--a thunderin' lie!" He adds that he does not believe that the troop will ever move. Later on in the day, this information does prove to be false, and the troop remains in the same location. 
While the men wait for orders, Henry tries to measure himself against the others, wondering if they also have doubts about their own courage. Then, one day Henry surprisingly finds himself moving along with the troops. While the other soldiers seem relieved and happy, he is still despondent. A soldier named Wilson exclaims about the upcoming fight, "We'll lick 'em good!"
That evening, as the soldiers bed down, Henry nostalgically thinks of home and the farm; he misses the brindle cow and her mates that he had to milk, even though he sometimes kicked the milking stools in exasperation with the uncooperative bovines. Lying in a strange place, he now feels that he is not meant to be a soldier. As Henry muses, Wilson approaches, sits, and lights his pipe.

"You're getting blue, my boy. You're looking thundering peek-ed. What the dickens is wrong with you?"
"Oh, nothing!"
"We've got 'em now. At last, by the eternal thunders, we'll lick 'em good!" Wilson reiterates, but he admits that the rebels have been winning against them.

The regiment continues to march for another three days, but more hurriedly. Henry returns wearily to his theory of a "blue demonstration." One morning he is awakened by a kick in the leg. "He was about to be measured."

Is it important that Missie May and Joe are a working-class couple? Why or why not?

In Hurston's short story "The Gilded Six-Bits," it is exceedingly important that Joe and Missy Mae are a working-class couple, as it is their position that prompts Missy Mae's choice.
If either Missy May or Joe were wealthy, Missy would not face the temptation of choosing between faithfulness to her husband and the lure of the gilded six-bits. Indeed, even when Missy May does sleep with Mr. Slemmons, she does so, arguably, for her husband's sake. She knows that the two of them need the money, and she sleeps with Slemmons when he offers gold. This occurs after her conversation with Joe about gold. Missy May tells him that he would wear gold more fittingly than Slemmons would and then suggests that they may happen across the gold on the ground.
While it is possible that Missy May truly hopes for such a coincidence to occur, it is equally likely that Slemmons has already propositioned her and that she is preparing a story for when she presents the gold to her husband. If the couple was not a working-class couple, Missy May would not need to sleep with Slemmons to acquire gold for Joe. Joe, like Slemmons, would already be decorated.

In the book Woodsong, how do the dogs react when Paulsen gets injured?

In the book, Paulsen tears his kneecap before his sled shoots off the edge of a frozen waterfall. To make matters worse, Paulsen then drops twenty feet and lands on his injured knee on a frozen pond, just beneath the waterfall.
After a brief loss of consciousness, Paulsen begins to realize his grave danger. He is bleeding profusely and is unable to get to his feet. By his calculations, he is at least twenty miles from home and about eight or nine miles from the closest human dwelling. Paulsen is frightened and worries that he will die out in the cold. As he contemplates his fate, he notices Obeah, one of his dogs, looking down at him from the top of the waterfall.
Usually, sled dogs do not go back for their masters or mushers, but Obeah drags the other dogs down an embankment until they reach Paulsen. The dogs bring Paulsen's sled to him, while another dog, Duberry, begins to lick and clean the wounds on Paulsen's leg. Because of his dogs, our protagonist is able to muster up the last of his energy to get himself onto the sled. Once on the sled, he ties his leg down, and the dogs proceed to pull him home.
When Paulsen gets injured, the dogs do not abandon him; instead, they come to his rescue, offer him comfort, and patiently lead him to safety.

How can you compare Hammurabi’s time period to todays?

There are a number of ways in which Hammurabi's Babylon can be compared to today's society. Hammurabi created one of the earliest known systems of laws. While the laws themselves are very different than what we have in today's legal system, his preoccupation with a codified system of laws was not. Like today's laws, Hammurabi's Code set punishments for certain crimes. A significant difference between our legal system and Hammurabi's is that Babylon was a much smaller and less complicated society. Therefore, its system was much more straightforward than ours and far less nuanced. While payments of indemnity and restitution are common in both Hamurrabi's time and ours, we use incarceration as our most common punishment for crimes. The Babylonians rarely sent convicts to jail.
Many scientific advances were made by the Babylonians. Education was highly valued in Hammurabi's time. He had many schools built, as he saw a connection between learning and the betterment of his kingdom. Educated Babylonians pioneered many astronomic, scientific, and mathematical discoveries. They were marked by having a curiosity about the nature of the universe and how it functioned. Today's scientists and mathematicians continue this work in many ways. Like the Babylonians, our universities and trade schools have specialized programs of study for students preparing for a particular profession.
A major difference between the Babylonians and today's society exists in its overall organization. Hammurabi's world was highly stratified. Nobles, free citizens, and slaves held different roles within the civilization. There was little possibility of movement between these different stratta. Conversely, today's society is premised on the notion that personal achievement can improve one's station.
As two societies separated by nearly 4,000 years, it is difficult to make very many direct connections between the Babylonians and us. Our economies, social structures, and daily lives are vastly different. However, direct comparisons can be made when considering the importance that education, a system of codified laws, and the pursuit of scientific discovery had within both societies.
http://www.historydiscussion.net/essay/contributions-of-the-babylonian-civilization/1897

https://www.ancient.eu/babylon/

What is Nora's attitude toward the porter and what does it show about her character in act 1 of A Doll's House?

As the play opens, Nora is bringing home the Christmas shopping. She carries several packages. Right behind her is a porter, carrying the Christmas tree and a basket. He hands the basket to Ellen, the family’s maid.
Nora inquires how much the porter’s charge is for carrying these things. When he tells her sixpence, she gives him a shilling—twice the amount he stated—and tells him to keep the change. This generosity at holiday time shows that she understands the value of workers’s time and that she is in the holiday spirit.
By establishing the idea that Nora is generous, Henrik Ibsen sets the stage for the subsequent conversation between Nora and her husband, Torvald, who then enters. Torvald teases her excessively about being a spendthrift, as she justifies spending a bit more this year because he is getting a promotion.
It soon turns out, however, that Torvald is completely clueless. Nora is far from frivolous; she has created this false impression in her husband’s mind to disguise the fact that she has been working herself, and scrimping and saving from the household money as well, so that she can repay a loan she obtained under false pretenses.
https://www.gutenberg.org/files/2542/2542-h/2542-h.htm

In act 1, Nora leads the way into her home, followed by a porter, who carries the family Christmas tree and a basket of parcels for her. When he gives everything to Ellen, the family's maid, Nora asks him how much she owes him. He tells her "Fifty ore," and she hands him a crown, telling him to "keep the change." A note in the text tells us that there are one hundred ore in a crown, and so Nora has essentially given him as a tip just as much as she paid for her items. This would be like going out to a $20 dinner and then tipping the server $20: pretty unusual. This helps us to understand that Nora is generous, perhaps to a fault, and also that she spends money quite readily. She is not thrifty, to say the least, much to her husband's, Torvald's, chagrin. Nora's attitude toward the porter is as a person who has a great deal of money—which does not, not yet, at least—to a person performing a service. She is not haughty or snobbish; rather, she is pleasant and generous.

What is the difference between geocentric and heliocentric model of the universe?

The two more commonly believed historical models of the universe include the geocentric model and the heliocentric model. The main difference between these two models is which heavenly body lies at the center of the universe. According to the geocentric model of the universe, the Earth was believed to be the center of the known universe and all the other heavenly bodies were assumed to orbit around our Earth. The heliocentric model, on the other hand, stated that the Sun is at the center of the known universe, with the heavenly bodies orbiting around it.
The geocentric model, also known as the Ptolemaic model, was the commonly believed model of the universe by the Greeks, and this model lasted for a really long time in human history. Nicolaus Copernicus came up with an alternative to the geocentric model, the heliocentric model, in the year 1543.
Hope this helps.

What quotes suggest Cleopatra's madness?

It's act 1, scene 3 and Antony and Cleopatra are having another of their legendary blazing rows. Antony is about to depart for Rome and his Egyptian queen's not too happy about it. She starts getting melodramatic, loudly lamenting to anyone who'll listen how she's always being betrayed. Cleopatra then launches into a passive-aggressive rant, blaming herself for Antony's departure. After all, if Antony could cheat on Fulvia with Cleopatra, why couldn't he also cheat on Cleopatra herself?:

Why should I think you can be mine, and true— Though you in swearing shake the thronèd gods— Who have been false to Fulvia? Riotous madness, To be entangled with those mouth-made vows Which break themselves in swearing!

How could Cleopatra have been such a fool to believe that Antony would stay true to her? Actually, it wasn't just foolishness; it was madness; the kind of madness that clouds the judgment of those in the grip of a passionate, all-consuming love, or amour fou—crazy love—as the French call it.

Please give me a summary of the story "The Stolen Bacillus" by H.G. Wells.

"The Stolen Bacillus" is a short satire that focuses on the role of science in human society, making it thematically similar to many of Wells' other works. The story begins with a bacteriologist and his anxious yet intellectually curious houseguest. Upon request, the scientist shows his guest a vial of living cholera bacteria, and the vial is stolen shortly after the man's departure. The bacteriologist goes on a panicked search when he realizes his houseguest is actually an anarchist who plans to infect London's water supply with cholera.
As the bacteriologist pursues his target, he is in turn pursued by his wife, who thinks he has lost his mind since he ran out of the house without being properly dressed. The bacteriologist finally catches up with the anarchist, who breaks the vial in an attempt to escape. In a desperate effort to bring his menacing plan to fruition, the man drinks the remains of the vial's contents and begins his effort to infect the city with cholera on his own.
As the story comes to a close, the bacteriologist informs his perplexed wife that what was in the vial was not actually cholera. Suspicious of the guest's intentions, the scientist showed him a vial that contained a new microbe that would turn an animal's skin blue. After revealing this twist, he grudgingly returns home with his wife to begin working on a new culture of the strange microbe.
In summary, this story uses irony to tell the tale of a clever scientist and an impulsive anarchist who become involved in a horse-drawn cab chase over a substance that is not at all what it seems. Wells uses this work to discuss the potential role science plays in the facilitation of bioterrorism.
http://medhum.med.nyu.edu/view/12427

College Algebra, Chapter 8, 8.3, Section 8.3, Problem 26

Find the equation for the hyperbola whose graph is shown below.







The hyperbola $\displaystyle \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$ has a vertical transverse axis, its vertices $(0, \pm a)$ and foci $(0, \pm c)$ are located on the $y$-axis. Notice from the graph that the hyperbola have vertices on $(0, \pm 3)$ which gives $a = 3$. Also, if the asymptotes are $y = \pm 3x$, then $\displaystyle \frac{a}{b} = 3$


$
\begin{equation}
\begin{aligned}

\frac{3}{b} =& 3
\\
\\
b =& 1

\end{aligned}
\end{equation}
$


Therefore, the equation is


$
\begin{equation}
\begin{aligned}

& \frac{y^2}{3^2} - \frac{x^2}{1^2} = 1
&&
\\
\\
& \text{or}
\\
\\
& \frac{y^2}{9 } - x^2 = 1

\end{aligned}
\end{equation}
$

Name one specific example of an impact that the Cold War had on the world?

While the Cold War impacted the world in numerous ways, possibly the most visibly jarring result of the conflict was the Berlin Wall. From 1961 to 1989, this concrete and barbed-wire barrier visibly divided Western Europe and the Eastern Bloc, primarily preventing emigration from East Berlin to West Berlin, despite its official purpose of keeping Western fascism out of East Germany. Prior to the wall's construction, residents of East and West Berlin were able to freely cross the border from one side to the other; the creation of the wall restricted access to only three checkpoints, and local travelers were rarely permitted to cross at all. Soldiers patrolled the East German side of the wall with orders to immediately shoot fugitives, and numerous other preventative measures were in place. The head of the East German Communist Party announced on November 9, 1989, that the borders would be opened, and East and West Germany were reunited on October 3 of the following year. Images of German people hacking at and smashing down the wall were widely distributed in news media at the time; this was a physical and symbolic symbol of the breaking down of barriers and of the Cold War's drawing to a close.
https://www.history.com/topics/cold-war/berlin-wall

How does the American Dream give characters in Of Mice And Men hope?

Most of the characters in Of Mice and Men are migrant workers. This means they travel, wandering from job to job on different farms or ranches. Their pay is low, they have no job security, and they can't put down roots in any one community. As we see on the ranch, the men share a bunkhouse, so they have no privacy and are forced to put up with people they may not like. Further, they have no paid holidays or vacations, so they can't take a day off. The work is not very satisfying, and they can never get ahead, so most of the men blow their money on prostitutes and drinking.
The American Dream for George and Lennie is the dream of saving and pooling their money to buy a small farm and living on the "fat of the land." It is appealing and offers hope to the ranch hands because it represents putting down roots, being your own boss, having a private space where you can keep out people you don't like, and being able to take a day off if you wish. It is a dream of freedom, autonomy, and dignity.

Throughout the novella, several characters have dreams that occupy their minds away from the harsh realities of life. George and Lennie are migrant workers who travel throughout America in search of jobs to survive the economic crash. Their transient lifestyle and arduous work make their lives difficult. They lack financial stability, control over their own destiny, and a structured, comfortable environment. Their dream of one day owning their own self-sufficient homestead allows them an opportunity to relax and ease their minds. It gives the two men hope for the future and motivates them to save their money. Candy and Crooks also fantasize about joining George and Lennie on their homestead one day. Candy offers a substantial amount of money to live with the two men and instantly experiences a feeling of relief knowing that his dream is a possibility. Overall, the dream of owning property, being financially stable, and controlling one's destiny offers the workers a mental escape and brief respite from their difficult lives.

In Adam of the Road, what old saying gave Adam encouragement?

There are a few proverbs quoted in the novel but only one that lends encouragement to Adam. 
This proverb is "Whom God will help, no man can harm." The wise saying is located in the chapter called "News of Roger." In this chapter, Adam is looking for his father, Roger. Cold and hungry, he is discouraged that he has yet to find Roger and Nick, his dog.
To buoy his spirits, Adam begins relating to himself the story of Havelok, the prince of Denmark. In the story, Havelok and his sisters have been imprisoned in a tower by Earl Godard. The evil earl plans to appropriate the children's lands for his own. Bereft of their father, the king of Denmark, the children are powerless to protect themselves. Meanwhile, Godard hires Grim, a fisherman, to drown Havelok. However, Grim gets a surprise when he attempts to do so. The sack that encases Havelok's body begins to glow prior to Grim finishing up his terrible task.
The eerie light convinces Grim that Havelok is the true lord of Denmark. The poor fisherman vows that he will care for Havelok until he is old enough to ride a horse. He also promises to feed Havelok with "milk and bread and cheese and custard pastries." Grim ends his monologue with the saying "Whom God will help, no man can harm." This saying so encourages Adam that he is inspired to continue his search for Roger and Nick.
 

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 11

intarctan(4t)dt
If f(x) and g(x) are differentiable functions, then
intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx
If we write f(x)=u and g'(x)=v, then
intuvdx=uintvdx-int(u'intvdx)dx
Using the above integration by parts method,
intarctan(4t)dt=arctan(4t)*int1dt-int(d/dt(arctan(4t)int1dt)dt
=arctan(4t)*t-int(4/((4t)^2+1)*t)dt
=tarctan(4t)-4intt/(16t^2+1)dt
Now let's evaluate intt/(16t^2+1)dt by using the method of substitution,
Substitute x=16t^2+1,=>dx=32tdt
intt/(16t^2+1)dt=intdx/(32x)
=1/32ln|x|
substitute back x=16t^2+1
=1/32ln|16t^2+1|
intarctan(4t)=t*arctan(4t)-4/32ln|16t^2+1|+C
intarctan(4t)=t*arctan(4t)-1/8ln|16t^2+1|+C
C is a constant.

what are some key ways to stop and/or minimize terrorism?

There are several types of terrorism and each need to be addressed separately.
One major type of terrorism in the twentieth and twenty-first centuries is that committed by oppressed minority groups who feel that their languages, religions, ethnic traditions, and cultures are marginalized and who suffer from poverty and lack of economic opportunity. Groups such as the IRA in Ireland, some of the Kurds in Turkey, some Palestinians, Basque and Catalonian separatists, Quebec separatists, the Uighurs in China, and the Chechen in Russia have committed terrorist acts in response to a belief that they were victims of repression and could not get justice any other way. In those cases where there has been successful resolution, such as Northern Ireland and Canada, the solution was political: namely, addressing the grievances to which the terrorist groups were responding.
In the case of Islamic terrorism in the twenty-first century, one of the major causes is a sense of isolation, alienation, disaffection, and resentment among young men who see Islamic jihad as a way to express their sense of rebellion and give meaning to their lives. Interestingly, these are usually not people who were particularly devout before joining jihadist movements, because the more deeply religious members of Muslim communities have more meaningful lives, grounded in faith and close social bonds. This is very similar to the psychology behind many of the mass shooting by domestic terrorists in North America, including both white nationalists and those affiliated with the "incel" movement. The young men involved in such shootings are typically fueled by some sort of rage and resentment, blaming society for their own personal sense of alienation.
Although better and more widely available mental health services and programs that build community and offer social and economic opportunities for more young people would not be a complete solution, they would help. In the United States in particular, stricter gun control measures would reduce the number of deaths from mass shootings.

int xe^(2x)/(2x+1)^2 dx Find the indefinite integral

Given to solve,
int xe^(2x)/(2x+1)^2 dx
let u= xe^(2x) so , u' = e^(2x) +2xe^(2x)
and
v'= (1/((2x+1)^2)) = (2x+1)^(-2)
v= int (2x+1)^(-2) dx
let t= 2x+1 => dt = 2dx
so v' =t^(-2)
=>  v= int t^(-2) dt /2
        = t^(-2+1) /(-2+1) *(1/2)
so v = (2x+1)^(-2+1) /(-2+1) * (1/2)
 = -1/(2(2x+1))
by applying the integration by parts we get ,
int uv' = uv - int u'v
so,
int xe^(2x)/(2x+1)^2 dx
= (xe^(2x))(-1/(2(2x+1))) - int (e^(2x) +2xe^(2x))(-1/(2(2x+1))) dx
= (xe^(2x))(-1/(2(2x+1))) + int ((e^(2x) +2xe^(2x))/(2(2x+1))) dx
=(xe^(2x))(-1/(2(2x+1))) +(1/2) int (e^(2x) (1+2x)/((2x+1))) dx
=(xe^(2x))(-1/(2(2x+1))) +(1/2) int (e^(2x)) dx
as we know int e^(ax) dx = e^(ax) /a
so,
=-(xe^(2x))(1/(2(2x+1))) +(1/2) (e^(2x))/2
= (-xe^(2x))/(2(2x+1)) +e^(2x)/4 +c

How might the history of the South and of the entire United States have been transformed had the filibustering efforts of men like William Walker been more successful?

First, if William Walker and other filibusterers had been successful, it is very likely they would have received the support of the federal government (indeed, Franklin Pierce recognized his conquest of Nicaragua as legitimate). Because Walker intended his conquests to be slave societies, this would have occasioned even more debate about the spread of slavery than was already taking place. Some people at the time believed that people in the Upper and Middle South would sell their slaves into the region, thus "draining" the upper regions of the South of slaves.
It could also be claimed that having territories in Central America might have dampened Southern commitment to securing protection for the institution in the North American West. It is difficult to know if this would have happened. What we can say for certain is that the support of many Democrats for these operations demonstrates the commitment to many in the South to expanding (not just preserving) slavery. So I would argue that Walker's success would have just contributed even more to sectional tensions between the slave South and the free North, tensions which ultimately resulted in secession and civil war.
https://www.historynet.com/william-walker-king-of-the-19th-century-filibusters.htm

College Algebra, Chapter 7, 7.2, Section 7.2, Problem 12

Evaluate $ \left[ \begin{array}{ccc}
2 & 1 & 2 \\
6 & 3 & 4
\end{array} \right]
\left[\begin{array}{cc}
1 & -2 \\
3 & 6 \\
-2 & 0
\end{array} \right]$ or explain why it can not be performed.



$
\begin{equation}
\begin{aligned}

& \text{Entry} && \text{Inner Product of} &&& \text{Value} &&&& \text{Matrix}
\\
\\
& C_{11} && \left[ \begin{array}{ccc}
2 & 1 & 2 \\
6 & 3 & 4
\end{array} \right]

\left[ \begin{array}{cc}
1 & -2 \\
3 & 6 \\
-2 & 0
\end{array} \right]

&&& 2 \cdot 1 + 1 \cdot 3 + 2 \cdot (-2) = 1
&&&& \left[ \begin{array}{cc}
1 & \\
&
\end{array}
\right]

\\
\\
\\
\\

& C_{12} && \left[ \begin{array}{ccc}
2 & 1 & 2 \\
6 & 3 & 4
\end{array} \right]

\left[ \begin{array}{cc}
1 & -2 \\
3 & 6 \\
-2 & 0
\end{array} \right]

&&& 2 \cdot (-2) + 1 \cdot 6 + 2 \cdot 0 = 2
&&&& \left[ \begin{array}{cc}
1 & 2 \\
&
\end{array}
\right]

\\
\\
\\
\\

& C_{21}
&& \left[ \begin{array}{ccc}
2 & 1 & 2 \\
6 & 3 & 4
\end{array} \right]

\left[ \begin{array}{cc}
1 & -2 \\
3 & 6 \\
-2 & 0
\end{array} \right]

&&& 6 \cdot 1 + 0 \cdot 3 + 4 \cdot (-2) = -2
&&&& \left[ \begin{array}{cc}
1 & 2 \\
-2 &
\end{array}
\right]

\\
\\
\\
\\

& C_{22}
&& \left[ \begin{array}{ccc}
2 & 1 & 2 \\
6 & 3 & 4
\end{array} \right]

\left[ \begin{array}{cc}
1 & -2 \\
3 & 6 \\
-2 & 0
\end{array} \right]
&&& 6 \cdot (-2) + 0 \cdot 6 + 4 \cdot 0 = -12
&&&& \left[ \begin{array}{cc}
1 & 2 \\
-2 & -12
\end{array}
\right]


\end{aligned}
\end{equation}
$


Thus, we have

$\displaystyle \left[ \begin{array}{ccc}
2 & 1 & 2 \\
6 & 3 & 4
\end{array} \right]

\left[
\begin{array}{cc}
1 & -2 \\
3 & 6 \\
-2 & 0
\end{array}
\right]

=

\left[
\begin{array}{cc}
1 & 2 \\
-2 & -12
\end{array}
\right]

$

Intermediate Algebra, Chapter 3, Summary Exercises, Section Summary Exercises, Problem 16

Write an equation of the line "through $(-3,6)$ with slope $\displaystyle \frac{2}{3}$".

(a) In slope-intercept form

Using Point Slope Form


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
\\
y - 6 =& \frac{2}{3} [x - (-3)]
&& \text{Substitute } x = -3, y = 6 \text{ and } m = \frac{2}{3}
\\
\\
y - 6 =& \frac{2}{3}x + 2
&& \text{Distributive Property}
\\
\\
y =& \frac{2}{3}x + 2 + 6
&& \text{Add each side by $6$}
\\
\\
y =& \frac{2}{3}x + 8
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$



(b) In standard form


$
\begin{equation}
\begin{aligned}

y =& \frac{2}{3}x + 8
&& \text{Slope Intercept Form}
\\
\\
- \frac{2}{3}x + y =& 8
&& \text{Standard Form}
\\
\\
\text{or} &
&&
\\
\\
-2x+ 3y =& 24
&&

\end{aligned}
\end{equation}
$

College Algebra, Chapter 7, 7.4, Section 7.4, Problem 58

Use a determinant to find the area of the triangle with vertices $(-2,5), (7,2), (3, -4)$ and sketch the triangle.








$
\begin{equation}
\begin{aligned}

\text{area } = \pm \frac{1}{2} \left| \begin{array}{ccc}
-2 & 5 & 1 \\
7 & 2 & 1 \\
3 & -4 & 1
\end{array} \right| =& \pm \frac{1}{2} \left[ -2 \left| \begin{array}{cc}
2 & 1 \\
-4 & 1
\end{array} \right| - 5 \left| \begin{array}{cc}
7 & 1 \\
3 & 1
\end{array} \right| + 1 \left| \begin{array}{cc}
7 & 2 \\
3 & -4
\end{array} \right| \right]
\\
\\
=& \pm \frac{1}{2} \left[ -2 (2 \cdot 1 - 1 \cdot (-4)) - 5 (7 \cdot 3 - 1 \cdot 3) + (7 \cdot (-4) - 2 \cdot 3) \right]
\\
\\
=& \frac{-1}{2} (-66) \quad \text{to make the area positive, we use negative sign in the formula}
\\
\\
=& 33 \text{ square units}

\end{aligned}
\end{equation}
$

What are the pros and cons of mass-marketing?

The pros of mass marketing, especially for companies which are franchises or sell non-speciality types of products, are as follows: there is more room to reach a wide variety of customers and build different customer bases that can be depended on for sales; brand recognition and chance of widespread brand loyalty are more possible; and there is less room for specific variables, such as age range or season, to affect sales in the same way that these variables might affect the sales of companies that use targeted marketing.
The cons of mass marketing are rooted in being less able to pinpoint issues with marketing strategies, as mass marketing is so broad that diagnosing marketing strategy failures can be difficult. Customers are also much less likely to feel specially catered to, which can lead to less brand loyalty.

Mass-marketing is when a firm randomly advertises its products to a large market. The firm uses tv, internet, billboards, and any other form of public media to spread their message to make their brand known.
Some advantages include increasing brand recognition, increasing sales, and having a wider reach. Mass-marketing is a good brand recognition tool. The more people see your advertisements, the more likely they are to know that your business exists. Mass-marketing also has the potential to increase sales volumes. Goods advertised using this method are usually affordable; this means that most people can buy the goods. Additionally, mass-marketing has a wider reach than most marketing campaigns. This is because the advertiser wants to reach as many people as possible with their advertisements.
Some disadvantages of mass-marketing include the expense, the uncertainty, and the effect of social change. Mass-marketing is expensive since the firm has to set aside money for advertisements on various mass media platforms. Furthermore, mass-marketing is not guaranteed to work in the current era. Nowadays, consumers want goods that are catered to their needs. They don't like the idea of a one-size-fits-all approach. What's more, the culture of a society can affect the effectiveness of a mass-marketing campaign. This means that if a mass-marketing campaign worked in one area, it is not guaranteed to work in another because of cultural differences. Some people may view the message as being offensive.

Mass marketing is the practice of a type of marketing strategy in which a company sells the same product or service to everybody in the market at the same price. The purpose of this is to reach as many consumers as possible. This strategy is sometimes called unsegmented or undifferentiated marketing.
One benefit of this approach is that it is cheaper to manufacture goods, as shown by Henry Ford in the early twentieth century. His Model T Ford automobiles only came in one color, black, which kept production costs low. This enabled him to keep the price lower, therefore attracting huge numbers of customers. (See the reference link provided for more information about Ford's approach).
The problem with mass marketing, however, is that it ignores the various differences which exist between the customers in a particular market. It ignores, for example, differences in class, gender, age, psychology, and consumer behavior. Ignoring these various segments in the market can have an impact on sales because the product or service may not be suitable for every single person in the market.
So while sending out a single product can have pros for the manufacturer, failing to acknowledge that different consumers have different needs can have an impact on sales and, therefore, the success of a business.
https://open.lib.umn.edu/principlesmarketing/chapter/5-1-targeted-marketing-versus-mass-marketing/

What is the initiating event in "The Open Window"?

The initiating event in "The Open Window" is the arrival of Framton Nuttel at the home of the Sappletons. He is a complete stranger who comes with a letter of introduction from his sister, a woman whom Mrs. Sappleton may not even remember. Obviously, Mrs. Sappleton is caught off guard. She has to enlist her niece Vera to stand in for her while she gets ready to receive their visitor. The entire story is told through Framton's point of view. He is not a very attractive guest because he is so wrapped up in his nervous disorder. Vera probably doesn't like being dragooned into serving as a substitute hostess at a moment's notice. She may have been interrupted in her reading. The mischievous fifteen-year-old girl decides to play a practical joke on the visitor, and in doing so Vera reveals a lot about the dreary routine of the Sappleton household. The men never think about or talk about anything but shooting birds. Her aunt seems housebound and has probably rarely heard much talk about anything but birds; consequently that seems all she ever talks about herself.
Mrs. Sappleton is devoted to her husband and her two young brothers. Vera knows her aunt will sit there staring at the open window while she talks about birds to poor, ill-at-ease Framton. Her aunt will be looking forward to the arrival of the three hunters for tea. But Vera has spun a story about how the three hunters died three years ago when they were sucked into a bog. Everything her aunt and the three hunters say and do ties in nicely with the girl's ghost story. Framton must believe that Mrs. Sappleton is mentally deranged, as Vera has told him. 

"Poor aunt always thinks that they will come back someday, they and the little brown spaniel that was lost with them, and walk in at that window just as they used to do. That is why the window is kept open every evening till it is quite dusk. Poor dear aunt, she has often told me how they went out, her husband with his white waterproof coat over his arm, and Ronnie, her youngest brother, singing 'Bertie, why do you bound?' as he always did to tease her, because she said it got on her nerves. Do you know, sometimes on still, quiet evenings like this, I almost get a creepy feeling that they will all walk in through that window - "

When Mrs. Sappleton suddenly cries, "Here they are at last!" and Vera is looking at the open window with a faked expression of "dazed horror" on her hitherto "sell-possessed" young face, Framton reacts with terror. The three returning hunters, who have only been gone for the day, look as if they must be Mr. Sappleton and his wife's young brothers returning from the dead.

In the deepening twilight three figures were walking across the lawn towards the window, they all carried guns under their arms...

And Bertie makes their identities certain when he breaks into a song that only he could know.

Noiselessly they neared the house, and then a hoarse young voice chanted out of the dusk: "I said, Bertie, why do you bound?"
Framton grabbed wildly at his stick and hat; the hall door, the gravel drive, and the front gate were dimly noted stages in his headlong retreat. A cyclist coming along the road had to run into the hedge to avoid imminent collision.

In “Goodbye to All That,” Joan Didion writes that the “lesson” of her story is that “it is distinctly possible to remain too long at the fair.” What does she mean? How does the final section of the essay portray how she came to this understanding, her feelings about it, and the consequences of it?

In this classic essay, Didion describes moving to New York City from her native Sacramento at the age of twenty-one, and, as she freely admits, a somewhat naive twenty-one, her mind, "programmed by all the movies I had ever seen and all the songs I had ever heard about New York," with the typical feeling, at that age, that, "nothing like this...has ever happened to anyone before." Intending to stay for only six months, she falls in love with the city. As she says, "I do not mean 'love' in any colloquial way, I mean that I was in love with the city the way you love the first person who ever touches you and never love anyone quite that way again."
This initial love led her to prolong her residency, since, "I still believed in possibilities then, still had the sense, so peculiar to New York, that something extraordinary would happen any minute, any day, any month." But as the next years roll past, and the "new faces" she encounters soon become familiar and that "extraordinary" event eludes her, the city eventually loses its charm. Thus, at the age of twenty-eight, she begins to understand that it is "distinctly possible to stay too long at the Fair."
During this last period of her stay, she loses her ability to relate to other people, often tuning out of conversations. She starts to become annoyed by the signs of wealth and consciously avoids certain areas of the city, among them the most symbolic, such as Time Square and the New York Public Library. Eventually she begins to cry spontaneously, for no reason, and finds herself unable to leave her apartment, classic symptoms of the depression against which she would wage a lifelong battle. Yet, during this dark period, Didion obliquely mentions that she had also gotten married. Possibly thinking a change might help, her husband, John Gregory Dunne, decides to take a six-month leave of absence from his job, and the couple move to Los Angeles.
As Didion summarizes her decision to move, "I was very young in New York, and...at some point the golden rhythm was broken, and I am not that young anymore."

After moving from California to New York City, Joan Didion is captivated by the energy, fast pace, and excitement of her life in the city that never sleeps. She comes to embrace its loneliness and anonymity, and she relishes her newfound independence.
However, she writes that she "was not one to profit by the experiences of others" and goes on to say "that it was a very long time indeed before I stopped believing in new faces."
In making these remarks, Didion is acknowledging that she did not learn from other people's mistakes and that for many years she naively accepted what people told her at face value.
Eventually, she becomes more jaded and cynical. She grows weary of having the same conversations over and over again. She insults and hurts other people and becomes depressed.
After leaving New York City to move to Los Angeles, Didion realizes that she cannot return to New York. It has become too expensive, especially considering how much space her family would now require. She attributes her love affair with the city to her youth and states that the "golden rhythm" has been broken now that she has gotten older.

In "Goodbye to All That," Joan Didion describes moving to New York City from California—ostensibly for a few months—and how she stayed for years. As time went by, the city became less exciting and felt like more of a repetitive trap; this was reflected in her mental state and feelings of depression and anxiety.
When Didion says that "it's entirely possible to stay too long at the fair," she means that if you stay somewhere long enough—even somewhere entertaining and wonderful—it loses its sense of wonderment and becomes somewhere you don't want to be. Even if the place hasn't changed and still offers a sense of magic and wonder to newcomers, you don't feel happy there. For Didion, New York City was the fair and the only way to break the loop of disenchantment was to move back to California with her husband.
The longer Didion lived in New York City, the less capable she was of handling daily tasks. She became incapable of going to certain places. She stopped enjoying parties, because, according to her, everyone was someone she'd seen somewhere else. There were no more new faces, even when she was promised that there would be.
She says that she got married, which was a good choice but poorly timed because it didn't fix problems for her. She would cry in public places and become unable to walk down certain streets. She says she "hurt the people [she] cared about, and insulted those [she] did not." Her husband was the one who decided to take a leave of absence so that they could go live somewhere else together. By the time she wrote the essay, they'd been living in Los Angeles for three years.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 60

Determine the $x$-coordinates of all points on the curve $y = \sin 2 x - 2 \sin x$ at which the tangent line is horizontal.


$
\begin{equation}
\begin{aligned}

y' = m =& \frac{d}{dx} (\sin 2 x - 2 \sin)
&& \text{Where $m = 0$ because tangent line is horizontal}
\\
\\
m =& \frac{d}{dx} (\sin 2 x) - 2 \frac{d}{dx} \sin
&&
\\
\\
m =& \cos 2 x \cdot \frac{d}{dx} (2x) - 2 \cos x
&&
\\
\\
m =& (\cos 2x) (2) - 2 \cos x
&&
\\
\\
0 =& 2 \cos 2x - 2 \cos x
&&
\\
\\
2 \cos 2x =& 2 \cos x
&&
\\
\\
\frac{\cancel{2} \cos 2x}{\cancel{2}} =& \frac{\cancel{2} \cos x}{\cancel{2}}
&&

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

& \cos 2 x = \cos x
&& \text{Using Double Angle Formula $(\cos 2x = 2 \cos^2 x - 1)$}
\\
\\
& 2 \cos^2 x - 1 = \cos x
&&
\\
\\
& 2 \cos ^2 x - \cos x - 1 = 0
&&
\\
\\
& 2 \cos ^2 x - 2 \cos x + \cos x - 1 = 0
&& \text{We let $- \cos x = -2 \cos x + \cos x$ to have a complete factor}
\\
\\
& 2 \cos x (\cos x - 1) + 1 (\cos x - 1) = 0
&&
\\
\\
& (2 \cos x + 1) (\cos x - 1) = 0
&&

\end{aligned}
\end{equation}
$


$\displaystyle \cos x = \frac{-1}{2} || \cos x = 1$







Based from the graph and unit circle diagram

$\displaystyle x = 2 \pi n, \frac{\pi n}{2} \pm \frac{\pi}{3} \qquad $ (where $n$ is any integer)

During the course of the play Macbeth, the roles of Macbeth and Lady Macbeth are reversed. Do you agree?

This question references one of the most powerful aspects of the story arc of Macbeth. In the first act, Lady Macbeth is ruthless, strong, and cunning. Indeed, she resolves to "unsex" herself in order to push her husband, who is "too full of the milk of human kindness" to murder Duncan. Macbeth, on the other hand, is ambitious, to be sure, but has serious reservations about killing the King. He has resolved not to do it, in fact, when Lady Macbeth goads him into the murder by questioning his honor and his masculinity.
After the murder of Duncan, Lady Macbeth is still a strong and ruthless character, but it turns out that her husband no longer needs her influence to persuade him to carry out murders. He has Banquo, his close friend, killed: the last act for which he shows any guilt at all. After this point, Lady Macbeth fades from the play until we encounter her again in the first scene in act 5. She is sleepwalking, frantically trying to scrub imaginary blood from her hands. It is clear that she is emotionally shattered from the guilt of the murders. Macbeth, on the other hand, has become a cruel tyrant. By the time Lady Macbeth kills herself in act 5, scene 5, the tragic transformation is complete. They have, in many ways, swapped roles, a process that eventually consumes them both.