Many literary critics believe that Tom Bombadil is a symbolic character; what do you think Tom Bombadil is a symbol of?

According to Tolkien himself, Bombadil was a representation of the landscapes of his native Oxfordshire, a sort of country spirit who represented the very idyllic existence which Sauron threatened. More broadly, Bombadil could be equated with the woodland spirits of English legend, such as Jack in the Green or the Green Man. Green Man figures typically symbolize the cycle of life and, particularly, pastoral or rural life. If we understand the Shire to be a partial representation of England before the First World War, Tom Bombadil is an archetype who is part of this way of life which, if the dark forces are allowed to enter the Shire, will no longer be free to exist. Bombadil is part of the "good," one of the spirits which, although not a significant part of people's daily existence, sustains the world as it should be and has long been. He opposes the darkness. He is equated with forests and trees: symbolically, when the hobbits return to the Shire, they find that the Party Tree has been cut down. Evil in these stories involves attacks on the landscape because that landscape forms a key, symbolic part of the fabric of the world before the war.

Why did S.E. Hinton create Johnny as a character in The Outsiders?

Johnny Cade plays a significant role in the novel The Outsiders. S.E. Hinton created the character of Johnny to drive the plot of the story and develop other characters in the novel. When Johnny stabs and kills Bob Sheldon, the plot advances, as he and Ponyboy are forced to hide out on Jay Mountain. During their time spent hiding out in the abandoned church, Ponyboy and Johnny become close friends. Through their conversations and experiences, Ponyboy gains perspective on life and becomes a more empathetic character. After Johnny is seriously injured in the church fire, Ponyboy visits him in the hospital. Hinton invokes emotion by depicting Johnny's tragic condition, and Dally is negatively affected by the death of his close friend. Dally ends up losing his mind and is killed by the police after he robs a store. Following Johnny and Dally's deaths, Ponyboy becomes extremely depressed until he reads a note Johnny wrote to him in the hospital. Johnny's note significantly influences Ponyboy and motivates him to tell the story of the Greasers. Hinton created the character of Johnny Cade in order to develop Ponyboy's character, evoke emotion from the reader, and drive the plot of the novel.

What are essential elements of nuisance?

In legal terms, a “nuisance” does not necessarily have to cause harm or damage (though such results can fall under that heading)—it can also be an action that simply creates an annoyance or an inconvenience. When someone’s actions prevent others from using property (public or private) in a way that they could reasonably expect, they can file a nuisance report and possibly seek damages.
A nuisance is not the same thing as trespassing. Someone can create a nuisance for others without ever touching someone else’s property.
A public nuisance is one which affects many people in the area. For example, loud noises or unpleasant odors coming from one house in a neighborhood is a nuisance for everyone else who lives around it.
A private nuisance is one which affects another person’s enjoyment of his or her own private property. Planting a tree in one yard that blocks the light in an adjacent yard would be considered a private nuisance.
The concept of nuisance can sometimes be a gray area. Not everything that is annoying should be considered a legal nuisance—Abhinava Krishna tells us that it has to be “substantial and material in the eyes of the law" (link below). In other words, you cannot file a nuisance report just because your neighbor’s dog barks once in a while, but if the dog barks constantly, you probably have a case. 

Penny purchases 100 tickets for her youth services group to attend a waterpark. Child admissions are $14.00 each while adult admissions are $19.00 each. If the total cost for the tickets was $1470, how many of each type of ticket did she buy?

 
This question requires you to set up a system of equations.  First, you must identify your variables.  Since we want to know how many adult tickets and how many child tickets were bought, those will be our variables.  So let:
a = # of adult tickets sold and c = # of child tickets sold
The first sentence says, "Penny purchased 100 tickets..."  This will be used to make our first equation.  The total number of both adult and child tickets should be 100, so our first equation is 
a + c = 100
Then it says, "Child admissions are $14 each while adult admissions are $19 each."  And it states that the total cost of the tickets is $1470.  This will be used to make our second equation, which is
19a + 14c = 1470
There are a few ways to solve this system of equations.  We'll go through two of them below.
1) One method to solve a system is by substitution.  You must solve one equation for one of the variables, then substitute that into the second equation.  For this problem, the first equation is very easy to use to solve for a variable since the variables do not have coefficients.  So
a + c = 100  becomes  c = 100 - a
This will be substituted into our second equation like so:
19a + 14(100 - a) = 1470
From here you can solve the equation for a using algebra:
19a + 1400 - 14a = 1470
5a + 1400 = 1470
5a = 70
a = 14
Now this value for a can be substituted into either original equation to find the value of c.  The first equation is, again, a very easy one to use:
(14) + c = 100
c = 86
So, Penny bought 14 adult tickets and 86 child tickets.
 
2) This can also be solved using the elimination method.  In the elimination method, you are adding the two equations together in an effort to make one of the variables cancel out (eliminate) so that you have just one varible to solve at a time.  To make this happen, you must often multiply one (or both) of the equations by a coefficient so that a variable will eliminate.  Once again, the first equation is very useful for this.  We can choose a variable to eliminate, let's say c.  In the second equation, the coefficient of the variable c is 14.  So we will multiply the first equation by -14 in order to make those two cancel.  The second equation will look like this:
-14(a+c=100)
-14a-14c=-1400
Now we will add the two equations together to get a new single equation with just one variable.
(-14a-14c=-1400)
+(19a+14c=1470)
5a = 70
a = 14
Once again, we can take this value of a and substitute it into one of the original equations to find c.  And we will again get the value 86.
3) This system of equations can also be solved graphically. If the variables are changed to x and y, they can be graphed as lines.  The point of intersection between the two lines is the solution.
 
Again, the final answer is that Penny bought 14 adult tickets and 86 child tickets.
 
 

How do the hunters damage the wall in "Mending Wall"?

According to the poet, it seems that hunters come by the wall during the winter and remove stones in order to flush rabbits out of their hiding places within the wall. By tearing down sections of the wall, the hunters destroy the rabbits' hiding places, thus allowing their dogs to chase them more easily.
The subtle use of language in "I have come after them and made repair" (line 6) indicates that this is a regular occurrence. The hunters have destroyed sections of the stone wall in the selfish pursuit of their prey and apparently without concern for the landowners, who must work to repair the wall each spring.
It is clear that the narrator does not think highly of the hunters who deliberately destroy the wall. These hunters are unlike the natural forces of destruction, the freezing and thawing of the ground, which destroys parts of the wall as well. The hunters, though, work in concert with these natural forces of destruction. Like the mysterious "something" in the poem's first line, the hunters also don't "love a wall."

In Robert Frost's poem "Mending Wall," the narrator is inspecting the stone wall on his property for damage. He writes that the hunters "have left not one stone on a stone," meaning that they have not simply piled one stone on top of another. Instead, to flush the rabbits out of their hiding places and "please the yelping dogs," the hunters have created gaps between places in the wall. No one hears the hunters making these types of gaps, but the narrator and his neighbor find them in the wall when they go to inspect it in the spring. The types of gaps the hunters make are very different than the effects of the natural swelling of the frozen ground, which makes boulders spill out of the top of the wall and makes very large gaps. 

What are some quotes that illustrate Jack Ryan's proactiveness?

Ryan sat on the corner of the desk and opened his briefcase. He handed Tyler a folder. "Got some pictures I want you to look at." "Okay." Tyler flipped it open. "Whose—a Russian! Big bastard. That's the basic Typhoon configuration. Lots of modifications, though. Twenty-six missiles instead of twenty. Looks longer. Hull's flattened out some, too. More beam?" "Two or three meters' worth." "I heard you were working with the CIA. Can't talk about that, right?" "Something like that. And you never saw these pictures, Skip. Understood?" "Right." Tyler's eyes twinkled. "What do you want me not to look at them for?" Ryan pulled the blowups from the back of the folder. "These doors, bow and stern."

Here we see that Ryan’s proactiveness involved contacting a colleague for assistance. He uses the best resources available to achieve a goal before it is too late to avoid potential consequences.

Ryan knew how to answer this. "Sir, if we followed normal procedure on this, we'd contract one of the Beltway Bandits—," Ryan referred to the consulting firms that dotted the beltway around Washington, D.C., "—they'd charge us five or ten times as much, and we'd be lucky to have the data by Easter. This way we might just have it while the boat's still at sea. If worse comes to worst, sir, I'll foot the bill. I figured you'd want this data fast, and it's right up his alley."

Ryan takes charge again, this time by urging his superiors to consider a different method to handling information-gathering outside the scope of normal procedure. He is familiar with both the limited expectations of his superiors as well as the limited abilities of the firms they usually contract with, so he compels them to consider an alternative source, someone who expects a high price but will deliver vital data in the nick of time. His proactiveness in this instance is unique insomuch that he employs a special kind of diplomacy rather than military heroism or bravado.

To what extent did both rock and roll fans and the Beats offer a serious challenge to American society in the years 1955-63?

The rock-and-roll fans who gravitated toward Elvis Presley were white. So were most of the Beats. However, the teenagers who consumed rock were otherwise mainstream. They were "bobbysoxers"—the supposedly clean and wholesome products of upstanding, middle-class white families. Their interest in rock, a sexually provocative music associated with the black people who had invented it, presented a challenge to notions of propriety among white youth. There were fears that rock-and-roll (named after the movements of love-making) would encourage sexual activity among young people. There were also concerns that an affinity for this music would encourage integration. It is true that the rise of rock-and-roll coincided with the Civil Rights Movement. The Beatles, for example, publicly refused to play before segregated audiences.
The Beats were pejoratively referred to as "beatniks." Beat culture arose in North Beach near San Francisco in the postwar period. "Beatniks" were young men and women who wore all black. They wore berets, too, to signal their alignment with French existentialism. They wore sunglasses at night, spoke in the rhythm of the jazz they loved, they associated with black people, and—most shockingly—they smoked marijuana. The image of the beatnik was the antithesis of the well-scrubbed bobbysoxer. However, the bobbysoxer's love of rock-and-roll created the fear that those wholesome teenagers would veer more closely to the counterculture embraced by the beatniks.
The image of the beatnik was designed to make the Beats look foolish, thereby diminishing their ideas. The actual Beats, represented by the triumvirate of Jack Kerouac, Allen Ginsburg, and William Burroughs, were white men who had eschewed the values that most white men had embraced. They did not desire careers or wives (Ginsburg and Burroughs were gay, and Kerouac was probably bisexual) or houses in the suburbs. They traveled frequently and lived where they wanted. They did drugs. They disliked the ways in which white society limited sexuality and hindered their interactions with people who were not white.
Both rock-and-roll fans and the Beats wanted something new—a new sound or a new mode of living, alternatives to what mainstream society valued as normal and good. The "serious challenge" was simply their courage to be different in an era of extreme conformity.

How did Helen acquire her name? What was the interesting experience related to it?

Being the first child in her family, Helen's naming was significant, and she mentions that everyone was "emphatic" about it. Her father initially wanted to name her Mildred Campbell, who was a highly esteemed ancestor in their family, and stopped discussing the matter shortly after giving his suggestion. However, Helen's mother believed that she should be named after her mother, whose maiden name was Helen Everett. Despite Helen's parents' disagreement on the name of their first child, Helen's father forgot what he wanted to name their child on the way to her christening. This was only natural given the fact that he stopped taking part in discussions shortly after suggesting that his daughter should be named after Mildred Campbell. When the minister asked the name of the child, Helen's father could only remember that it was decided she would be named after her grandmother and gave his daughter the name Helen Adams. Helen's full name is Helen Adams Keller.

As Helen was the first child in the family, her naming was considered very important. Her father wanted to name her after an illustrious ancestor by the name of Mildred Campbell. Helen's mother, however, disagreed, and wanted to name her new daughter after grandmother Helen Everett. On the day of Helen's christening, her father forgot what she was supposed to be called. This isn't too surprising, as he wasn't involved in the naming of Helen after his original suggestion was rejected by his wife. All he could remember was that she was supposed to be named after grandmother. So when it came to the christening, he simply gave the name Helen Keller. That's the name by which she was known for the rest of her life, and as she's still known today.

In the novel, Wade describes his positive experience with virtual school. Why does Wade think that virtual learning is effective, and do any virtual classrooms exist in our present world?

One of the main reasons Wade enjoys learning is because the virtual school environment neutralizes peer bullying, a substantial challenge in the traditional school environment. As Ludus is a no-PvP zone (the simulation disallows combat activity), students cannot indulge in any form of physical violence. Additionally, all students have the ability to mute harassing comments from other students. As a result, teachers can concentrate on what they do best: educating.
In a virtual school environment, students attend field trips as avatars. They are immersed in a 3D learning environment that effectively makes difficult concepts accessible to them. During a world history class, Wade and his peers are given an expansive survey of Tutankhamun's glorious reign in 1334 BC. They also witness the discovery of his tomb by archaeologists in AD 1922. The virtual field trips reinforce the prestige that surrounded Tutankhamun in life and death.
Meanwhile, in biology class, Wade and his peers enjoy an immersive tour of the inside of a human heart. For art class, students visit the elegant Louvre while ensconced on earth in their haptic chairs. There are indeed virtual classrooms today, the most prominent of which is Meisei Cyber Gakushukoku in Japan, where students attend school as uniquely-designed avatars. To date, teachers have incorporated virtual environments such as OpenSim, Second Life, and even World of Warcraft into their classroom experience.

Why was the wife looking at herself in the mirror?

In “Cat in the Rain,” George’s wife studies her features, and especially her face, in a mirror. Afterwards, she concludes that she needs a new hairstyle. Presently, she has her hair cut close, like a boy’s. She wants to grow her hair long so that she can tie it up in a big knot at the back of her head. She says that she is tired of “looking like a boy." However, George thinks that she looks great as she is.
It seems that she has suddenly become aware of the various things that need changing in her life. That, or she is in a complaining mood. She says that she wants a kitty and a set of new clothes, as well as "to eat at a table with her own silver and candles," and “to brush her hair out in a mirror." She also talks about wanting a kitty and a set of new clothes. This change in mood and concern over her looks happens after she went out in the rain to rescue a cat that was sheltering under a table outside of their hotel window. However, by the time she reached the table, the cat had left. She came back to her room disappointed and began to rant about her various desires. Ironically, it is the hotel owner, rather than her husband, George, who discerns her desires and works to satisfy them as best as he can. On this occasion, the hotel owner sends over a maid with a tortoiseshell cat for George’s wife, just as she is ranting about wanting a cat.

What is a neutron's charge?

The charge of the neutron is equal to zero (0), which means that they have no charge. Neutrons are neither positive nor negative. Neutrons are neutral, and that's also the basis for their name.
As neutral particles, neutrons do not contribute any charge to the atom. Neutrons are, however, quite massive. The mass of a neutron is about the same as the mass of a proton. So atoms with many neutrons are heavier. However, no matter how many neutrons you add or take away from an atom, the atom's charge is not affected.
Atoms have other charged particles, namely electrons and protons. Electrons carry negative charge and protons carry positive charge. 
Neutrons help scientists identify between different isotopes of elements. For example, usually the Hydrogen atom has one electron and one proton. However, some hydrogen atoms also have one or more neutrons and are thus heavier. If a hydrogen atom has one neutron, it is called a deuterium, which is a very interesting as it can be used in the design of the powerful hydrogen bombs.
Finally, while neutrons do not attract or repel other particles through electric charge, they can exhibit other strong attraction forces at very close distances, called nuclear forces. These are the forces that keep the protons and neutrons bound tightly in the nucleus of the atom.

Neutrons do not have any charge on them and hence are neutrally charged. In comparison, protons are positively charged and electrons are negatively charged. 
Neutrons are present in the nucleus of an atom along with the protons. For this very reason, protons and neutrons are known as nucleons. The mass number of an atom is defined as the total number of protons and neutrons that it has. For example, sodium has a mass number of 23 and an atomic number (= number of protons) of 11. In other words, it contains 11 protons and 23 nucleons (protons and neutrons). Thus, we can say that a sodium atom has 23-11 = 12 neutrons. 
All the known elements have neutrons, except for a normal hydrogen atom, which only contains a proton in its nucleus, but no neutrons. 
Note that while neutrons do not have a charge, they have mass and, thus, affect the total mass of an atom.

Calculus: Early Transcendentals, Chapter 5, 5.4, Section 5.4, Problem 26

You need to use the following substitution to evaluate the definite integral, such that:
1 - t = u => -dt = du
int_(-1)^1 t*(1-t)^2dt = int_(u_1)^(u_2) (1 - u)*u^2 (-du)
int_(u_1)^(u_2) (u - 1)*u^2 (du) = int_(u_1)^(u_2)u^3 (du) - int_(u_1)^(u_2)u^2 (du)
int_(u_1)^(u_2) (u - 1)*u^2 (du) = (u^4/4 - u^3/3)|_(u_1)^(u_2)
int_(-1)^1 t*(1-t)^2dt = (((1-t)^4)/4 - ((1-t)^3)/3)|_(-1)^1
int_(-1)^1 t*(1-t)^2dt = (((1-1)^4)/4 - ((1-1)^3)/3) - (((1+ 1)^4)/4 - ((1+1)^3)/3)
int_(-1)^1 t*(1-t)^2dt = 8/3 - 16/4 = 8/3 - 4 = -4/3
Hence, evaluating the definite integral yields int_(-1)^1 t*(1-t)^2dt = -4/3.

Compare and contrast Yeats's "Leda and the Swan" and "The Wild Swans at Coole."

Apart from their both dealing with swans, in my view these two poems on first reading have little in common. "Leda and the Swan" is a sonnet based on the incident in Greek mythology in which Zeus takes the form of a swan and seduces (as some accounts put it) or rapes a woman, Leda, who is the wife of Tyndareus, the king of Sparta. "The Wild Swans at Coole" is the reflection of a young person about his own life and his process of maturing, of essentially losing his innocence, while the "nine and fifty" swans he observes at Coole are a constant, unchanging element of nature, never aging. The speaker then speculates that some day, the swans may in fact leave the lake and go elsewhere "to delight men's eyes."
If there is connection of thought or theme between the two poems, apart from the presence of that particular bird in each, I would suggest that it lies in the preternatural quality Yeats attributes to the swan in both. In "Leda and the Swan," the bird is a god in disguise and therefore immortal, mysterious, and all-powerful. It almost carelessly forces itself upon the hapless mortal Leda, and at the end its "indifferent beak" lets her "drop." Yeats alludes to the Trojan War and its aftermath, given that Leda is to become the mother of both Helen of Troy and Clytemnestra (wife of Agamemnon). Thus the rape of Leda is viewed in the context of a collective human tragedy that will result at least in part from this initial act of violent cruelty.
In the other poem, the unchanging and seemingly omnipotent swans are similarly contrasted with the speaker and his own sadness: his "heart is now sore" as he thinks of these brilliant creatures, indifferent to him and the comfort he used to gain from them (which is gone now that he's older). He asks "among what rushes" they will "delight [other] men's eyes" when they have abandoned him, having flown away to give the comfort he has enjoyed to others.
"The Wild Swans at Coole" is the more "conventional" of these two poems, with its oft-repeated trope of a poet addressing and bonding, in some way, with a bird figure that represents or reflects elements of the speaker's mind, his joy and suffering. In "Leda," the swan is a remote figure attacking a human being and a seeming cause of generalized suffering as well. But in both cases, the bird is intimately connected with human experience, for good or ill, mystical and somehow delineating the ups and downs of men and women in its mutely disinterested way.

According to Hegel, true tragedy presents a conflict between differing and opposed aims, which are based on equally valid moral powers. One-sidedness and specific aims lead to dramatic conflict and the subsequent loss of wholeness or universality. For this reason, the tragic reconciliation which comes in the end should be the working of the Divine, which strips away from the conflicting individuals their false one-sidedness to achieve an affirmative harmonization and reveal the eternal substance of things. Please interpret Dryden’s "All for Love" in accordance with Hegel’s theory on tragedy explained above.

It has been argued that Hegel's theory of tragedy encompasses a dialectical model: a proposition (thesis) opposed by another proposition (antithesis) and eventually reconciled by some combination of the two dueling propositions (synthesis). 
Hegel's theory of tragedy follows this model in the sense that the hero or tragic character is a divided self, in conflict against the universal. Thus, reconciliation can only occur when Providence strips the individual of his one-sidedness and reconciles within him the earthly and the divine. In Hegel's theory of tragedy, however, reconciliation doesn't always result in a positive denouement. Sometimes, as in All For Love, reconciliation is negative. What Hegel did propose was that tragedy involved a conflict between differing and equally valid aims, aims that would not be contradictory if circumstances were different. Hegel's concept of tragedy involved the idea that capitulation to one aim often infringed upon the claims of the other. 
This is exactly what happens in All For Love. Antony is torn between his domestic bond (to his wife, Octavia, and his two daughters) and his sensual bond to Cleopatra. Yielding to the demands of one bond would constitute a violation of the other. This tragic conflict ends in Antony's suicidal death. The reconciliation is negative in nature. Torn between the two bonds, Antony chooses death or self-annihilation. Providence does strip Antony of his one-sidedness (his predilection for Cleopatra over Octavia), but it also exposes Antony's failure to reconcile the opposing claims in his life.
In Act One, Ventidius offers Antony help in his war against Caesar. He tells Antony that "twelve legions" await his orders as "chief." However, there is one stipulation: these battle-hardened warriors won't fight for Cleopatra. Antony balks at the idea of relinquishing his sensual bond to Cleopatra in order to achieve military victory. In the end, however, he relents and agrees to leave Cleopatra, even though he loves her "Beyond life, conquest, empire, all, but honour." Of course, Antony's rejection of Cleopatra is temporary. He's too smitten with her to renounce his erotic bond permanently.
In Act Two, Antony wavers, and Ventidius begs him for "manhood's sake" to reject Cleopatra's gifts. However, Antony answers that Ventidius grows "too cynical" and that "A lady's favours may be worn with honour." In Act Three, Octavia and Antony's two daughters make their appearance. Octavia is Caesar's sister, and we are told that Antony wed her in "her pride of youth,/ And flower of beauty." Ventidius argues that Antony's bond with Octavia must take precedence over his bond with Cleopatra. Through Ventidius, we see Antony's practical side struggling for dominance.
However, through Cleopatra, we see Antony's sensual nature wrestling for preeminence. In the play, Cleopatra asserts that she doesn't want Antony's "respect" as "respect is for a wife," for someone like "cold Octavia." What Cleopatra wants is Antony's adoration. The implication here is that Antony's life with Octavia is devoid of the sensual passion he shares with Cleopatra. In Act Three, the argument between Octavia and Cleopatra further reinforces Antony's irreconcilable desires.
Octavia is the "injured wife," banished from Antony's bed and driven from his home. Yet, she will not beg for Antony's love. So, even though her brother, Caesar, makes Octavia's happiness the price of peace, Octavia is unwilling to force Antony's hand. Essentially, she refuses to beg for Antony's love even though her claim as a wife is more valid than a lover's (Cleopatra). Antony's words characterize his private anguish, but Ventidius' answer is noteworthy:

ANTONY. I find a secret yielding in my soul;/ But Cleopatra, who would die with me,/ Must she be left? Pity pleads for Octavia;/ But does it not plead more for Cleopatra?
VENTIDIUS. Justice and pity both plead for Octavia;/ For Cleopatra, neither./ One would be ruined with you; but she first/ Had ruined you: The other, you have ruined,/ And yet she would preserve you./ In everything their merits are unequal.

So it is that, by the time Antony kills himself, we understand why our hero chooses this course of action. Capitulation to the claims of the marital bond would violate the claims of the sensual bond. The two are antithetical in nature. Antony's death is a negative reconciliation of the two opposing claims, reinforcing Hegel's theory of tragedy. However, it can also be said that Antony's final choice reveals the "eternal substance of things," in that there can be no harmony between disloyalty and loyalty. 
https://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=4598&context=ocj

Calculus and Its Applications, Chapter 1, 1.7, Section 1.7, Problem 96

Determine the derivative of the function $f(x) = x\sqrt{4 - x^2}$ analytically. Then use a calculator to check your results.

By using Product Rule and Chain Rule, we get


$
\begin{equation}
\begin{aligned}
f'(x) &= x \cdot \frac{d}{dx} (4 - x^2)^{\frac{1}{2}} + (4 - x^2)^{\frac{1}{2}} \cdot \frac{d}{dx} (x)\\
\\
&= x \cdot \frac{1}{2} (4 - x^2)^{\frac{1}{2} - 1} \cdot \frac{d}{dx} (4 - x^2) + (4 - x^2)^{\frac{1}{2}} (1)\\
\\
&= x \cdot \frac{1}{2} (4 - x^2)^{\frac{1}{2} - 1} (-2x) + (4 - x^2)^{\frac{1}{2}}\\
\\
&= -x^2( 4- x^2)^{-\frac{1}{2}} + (4 -x ^2)^{\frac{1}{2}}\\
\\
&= \frac{-x^2}{(4 - x^2)^{\frac{1}{2}}} + (4 - x^2)^{\frac{1}{2}}\\
\\
&= \frac{-x^2 + 4 - x^2}{(4 - x^2)^{\frac{1}{2}}}\\
\\
&= \frac{-2x^2 + 4}{(4 - x^2)^{\frac{1}{2}}}
\end{aligned}
\end{equation}
$


Thus, the graph of the function and its derivative is



Based from the graph, we can see that the function has a positive slope or positive derivative when it is increasing.
On the other hand, the function has a negative slope or negative derivative when the function is decreasing.
Also, the function has a zero slope at the minimum and maximum point of the graph.

So we can say that both functions agree.

In what ways is Theseus controling?

How is Theseus controlling? To begin with, he kidnaps Hippolyta, his bride-to-be, after defeating her people, the Amazons, and uses force to get her to agree to marry him. As he puts it in act 1, scene 1,

Hippolyta, I wooed thee with my sword
And won thy love doing thee injuries.

Theseus also upholds the patriarchy in this scene, backing Egeus, Hermia's father, in his assertion of his right to decide who Hermia will marry. Theseus tells Hermia he should think of her father as a god. If Egeus thinks Demetrius is a better husband for Hermia than Lysander, Hermia should arrange her mind to think so too, Theseus says. Theseus enforces this sense of male control by telling Hermia she will either marry Demetrius or go to the nunnery for the rest of her life. 
 
Theseus, however, will later prove himself to be a just and even-handed ruler, and in the end, true love will prevail for Hermia and the other young people.

Where does Lyddie go after being dismissed in chapter 22?

Lyddie's main destination after being fired is Boston, as that's where Diana's been living. As Lyddie has no place else to go, she hopes to be able to stay with Diana; that way, the two young ladies can help each other out as they did when they worked together in the factory. When Lyddie shows up on Diana's doorstep, Diana's very pleased to see her old pal. Lyddie tells her all about the circumstances concerning her firing, and Diana agrees that she did the right thing in standing up to the sleazebag that is Mr. Marsden.
Unfortunately, Diana can't let Lyddie stay with her. Diana's already living with a woman who's helping her take care of her baby, and so there's simply not enough room in the house for Lyddie. Lyddie's incredibly sad to hear this, but understands. Desperate for a place to stay, she heads back to Cutler's Tavern, that terrible place where she'd worked herself to exhaustion before moving on to the factory.

It is unclear if this question is asking about a single location or if is asking to list out a few of the places that Lyddie goes to after being dismissed. I would also like to clarify the question a bit. Lyddie is dismissed in Chapter 21. I'll try to list out the many places that Lyddie goes to after being dismissed.
Lyddie goes to the bank to withdraw all of her money.
Lyddie goes to a bookstore and buys another copy of Oliver Twist. She also buys a dictionary.
Lyddie visits Brigid.
Lyddie visits Diana.
Lyddie goes and confronts Mr. Marsden.
Lyddie returns to Vermont and returns to Cutler's Tavern.
Lyddie goes to visit the Phinneys in order to see her brother and sister.
Lyddie returns to her old farm house. Luke Stevens arrives and proposes that they get married. Lyddie asks him to wait for her. She wants to become educated at college first.

Are the characters in "Hunters in The Snow" flat or round?

Most of the characters in "Hunters in the Snow" are flat characters because they do not change or grow during the story. If they were round characters, they would undergo character development and conclude the story changed in some way. Tub, in contrast to Kenny and Frank, is a bit of a round character because he does change after he shoots Kenny.
Frank is selfish from the beginning of the story until the end. He is planning to leave his wife and children to be with a teenage babysitter; he thinks it is true love. He is still intending to leave her at the end. He does not act differently or grow in any way. When Tub confesses that he does not have a gland issue and just likes to eat in secret, Frank orders him pancakes and lets him gorge in front of him—but it is not a change in his character. He does it because Tub has accepted his infidelity and intention to leave his wife. It is still selfishness.
Kenny is cruel at the beginning of the story and does not change before the end. He shoots a post and a dog for no reason and then turns to Tub and seems like he is going to shoot his friend. Once he has been shot, he does not change or regret the joke that led to his friend believing Kenny would shoot him. While he is incoherent in the back of the truck on the way to the hospital, he does not change. He is affected by the injury and unable to even get out of the truck.
Tub begins the story as a person who is unable to stand up for himself and ends it as someone who is more assertive. At the beginning, his friends mock his weight, and he does not really stand up for himself beyond saying that he has been on a diet. After he shoots Kenny, Frank calls him a fat moron, and Tub grabs him and holds him against a fence, shaking him. He tells him, "No more talking to me like that. No more watching. No more laughing." Frank agrees.
In contrast to the other characters, Tub experiences a change in his character. He is able to stand up for himself and is honest with Frank about his lack of a gland issue by the end of the story. For these reasons, he is a round character. The events of the story have changed him.
Two of the main characters begin and end the story as the same people without any character development. If Frank had realized the selfishness of his decision to leave his family or if Kenny had stopped being cruel in the wake of the shooting, they would be round characters. Since they do not change, they are flat characters. Tub, on the other hand, does become more assertive and becomes willing to stand up for himself after he shoots Kenny. Because he experiences change and grows as a character, he is a round character, while Kenny and Frank remain flat.

Why did the grandmother dislike music in "The Portrait of a Lady"?

In the story by Khuswant Singh, the grandmother dislikes music because it has vulgar connotations for her. To the narrator's grandmother, music is for beggars and harlots: those she considers less cultured and sophisticated in nature.
According to the text, the narrator's grandmother holds very conservative views about education. She is also deeply religious. During the narrator's early school days, she accompanied him to school. This was partly because the school was attached to a temple. While the narrator learned the alphabet and the morning prayers, his grandmother read the scriptures in the temple.
At the end of the school day, the narrator and his grandmother walked home together. The two were good friends at the time because the narrator had yet to progress beyond the grandmother's comfort zone. Once the narrator began learning English and subjects outside his grandmother's expertise, he found her less receptive to his efforts to engage her in conversation.
For her part, the narrator's grandmother felt unneeded because she couldn't relate to her grandson's new spheres of interest. In due time, even the music he was learning in school disturbed her. Neither understood the other's inclinations, and because of this, an emotional chasm soon developed in their relationship.

The narrator has developed a close friendship with his grandmother, but he becomes increasingly distant from her after he starts school. There's a clear cultural gulf between the boy and his grandmother, which his education only exacerbates. The boy's learning English, which his grandmother doesn't understand, so he teaches her some words. He also tries to impart little nuggets of Western learning and science, such as the law of gravity and Archimedes's Principle.
But this is a completely alien world for the grandmother. She's unhappy at what her grandson's being taught at the school, not least because there appears to be no room on the curriculum for God and the holy scriptures. She's also none too pleased about her grandson being given music lessons. The grandmother doesn't like music; to her, it has lewd associations. It may be appropriate for prostitutes and beggars, but not for respectable gentlefolk like themselves.

According to The New Jim Crow, what happened after the Civil War?

In The New Jim Crow, Michelle Alexander points out that the freed slaves were not able to automatically exercise their new legal rights. Former slave owners and prejudiced politicians were absolutely opposed the idea of former slaves having equal rights. In order to preserve the status quo, they used both the law and outright violence to prevent former slaves from participating fully in society. In a cruel twist, the very constitutional amendment that outlawed slavery also became the means by which a new and legal slavery-like system was created. The Thirteenth Amendment outlaws slavery “except as a punishment for crime whereof the party shall have been duly convicted.” Perhaps unsurprisingly, many African Americans were unjustly arrested and forced into the penal system in the aftermath of the Civil War. Once they were labelled “convicts” and imprisoned, it became legal to send these individuals out to work on the same plantations that had once used slave labor. Even worse, now that they were no longer the legal “property” of the plantation owners, the plantation owners had no financial incentive to keep the prison workers healthy. As a result, many African Americans were worked to death on the very plantations they had supposedly been freed from. Michelle Alexander argues that, to this day, mass incarceration is the primary means by which the United States unjustly oppresses and controls African Americans.

As an expert on terrorism for the United Nations, what advice would you give to world leaders to help end terrorism?

First, the goal of ending terrorism is very unlikely to be achievable. Since a key feature of good goal setting is to think realistically, it might be best to aim to reduce deaths from terrorism, something that is a more realistic aim.
Next, it would be important to emphasize the need for ongoing study of different terrorist groups and what motivates them and the efficacy of different types of anti-terrorist interventions. This should be done by international panels of social scientists rather than politicians who use fear of terrorism as a way to suppress civil liberties and secure votes. It is important to remember that in an average year many more people die from everyday threats like car accidents than from terrorism and to avoid creating the sort of media hype which only encourages people to engage in terrorist attacks for attention.
In terms of demographics, terrorism seems to appeal primarily to young men who are fueled by feelings of isolation, resentment, and lack of purpose. To reduce the likelihood of their actually committing terrorist acts, community programs are needed to give them other options in their lives.
Another major motivation for terrorism is a feeling of helplessness in the face of injustice. Oppression of minority groups, especially in areas with strong tribal or ethnic loyalties, can lead to outbreaks of violence. Addressing poverty and injustice will also minimize the number of people who resort to terrorism.
Obviously, international cooperation on security is also important, but in the long run, just as preventing diseases is better than curing them after the fact, so too is eliminating the root causes of terrorism more effective in the long run than investing exclusively in trying to catch would-be terrorists.

Explain briefly the functions of the bile duct and the pancreatic juice.

The bile duct is a tube-like structure which carries a digestive juice called bile from the liver and then joins another duct, called the pancreatic duct, that carries pancreatic juice and forms the ampulla of Vater. The contents of both ducts (bile and pancreatic juice) are now discharged into the first part of the intestine called the duodenum through the ampulla of vater.
The pancreatic juice contains enzymes which play a significant role in the digestion of food. The enzymes in the pancreatic juice are responsible for the partial or complete breakdown of carbohydrates, proteins and fat.
One of such enzymes called the pancreatic amylase completes the digestion of carbohydrates. Another enzyme contained in pancreatic juice called lipase is responsible for the breakdown of fat. Two other enzymes contained in pancreatic juice are referred to as trypsin and chymotrypsin. They complete the digestion of proteins.
http://ddc.musc.edu/public/organs/pancreas.html

https://www.reference.com/science/function-bile-digestive-process-8894ab8a7e01c08b

What use of diction is made, and how does it affect the rest of Sonnet CXXX?

Shakespeare uses imagery to convey his impressions of his mistress. For example, he says that her eyes do not resemble the sun and that the color of her breasts is "dun." He writes that "black wires grow on her head." Rather than using lofty images, he uses imagery that conveys that his mistress is far from ideal. He also uses a number of inverted sentences, which refers to sentences in which the predicate comes before the subject (as opposed to the usual order in which the subject comes before the predicate). An example is "And in some perfumes is there more delight." The inverted nature of his diction has the effect of making the entire poem a kind of satire. Rather than stating what his mistress is, he states what she is not. By using this type of diction, Shakespeare is satirizing traditional sonnet writers such as Petrarch, who write about ideal love. In the end, Shakespeare's sonnet is perhaps a more powerful testament to his love. Though he uses down-to-earth imagery and inverted lines, he states at the end that his love is rarer than the ideal women to whom she does not measure up. In other words, he loves her even though she's real and not ideal. 

Shakespeare's diction in Sonnet CXXX mocks the language of the Petrarchan sonnet that employs elegant comparisons. In contrast, with this sonnet the poet describes what his love is not, thus providing a parody of the sonnet model.
The speaker of Sonnet CXXX describes his love in the most unflattering language: Her eyes are not stunning, her lips are not red, and her breasts are not white, but are, instead, dun-colored. The speaker further flaunts the conventions of the sonnet sequence with such lines as these:

If hairs be wires, black wires grow on her head. . . And in some perfumes is there more delightThan in the breath that from my mistress reeks.

Rather than writing about his love as an ideal as in the traditional sonnet, Shakespeare uses diction that indicates his use of parody. This diction also serves another purpose as it lends verity to his ideas. For, when he declares his love for his "mistress," his words ring much truer than if he were to use the flowery language of a traditional Petrarchan sonnet:

And yet, by heaven, I think my love as rareAs any she belied with false compare.

Indeed, the use of unflattering diction indicates the reality of the speaker's love when he declares the rarity and genuineness of his feelings for his "mistress," who lacks many of the stellar qualities of the Petrarchan mistress.

College Algebra, Chapter 4, 4.3, Section 4.3, Problem 58

Prove that $\displaystyle c = \frac{1}{3}$ and $c = -2$ are zeros of $P(x) = 3x^4 - x^3 - 21x^2 - 11x + 6$ and find all other zeros of $P(x)$.

If $\displaystyle P \left( \frac{1}{3} \right) = 0$, then $\displaystyle x - \frac{1}{3} = 0$, so $x - 3$ is a factor. Similarly, if $P(-2) = 0$ then $x + 2 = 0$, so $x + 2$ is a factor. Using synthetic division twice







We see that


$
\begin{equation}
\begin{aligned}

P(x) =& 3x^4 - x^3 - 21x^2 - 11x + 6
\\
\\
P(x) =& \left( x - \frac{1}{3} \right) (x - 3) (3x^2 - 6x - 9)
\\
\\
P(x) =& 3 \left( x - \frac{1}{3} \right) (x - 3) (x + 3)(x - 1)

\end{aligned}
\end{equation}
$

Calculus: Early Transcendentals, Chapter 4, 4.9, Section 4.9, Problem 8

The most general antiderivative F(x) of the function f(x) can be found using the following relation:
int f(x)dx = F(x) + c
int (x^(3.4) - 2x^(sqrt2 - 1))dx = int (x^(3.4))dx - int (2x^(sqrt2 - 1))dx
You need to use the following formula:
int x^n dx = (x^(n+1))/(n+1)
int (x^(3.4))dx = (x^(3.4+1))/(3.4+1) + c = (x^(4.4))/(4.4) + c
int (2x^(sqrt2 - 1))dx = 2*(x^(sqrt2 - 1+1))/(sqrt2 - 1+1) + c
int (2x^(sqrt2 - 1))dx = sqrt2*(x^(sqrt2)) + c
Gathering all the results yields:
int (x^(3.4) - 2x^(sqrt2 - 1))dx =(x^(4.4))/(4.4) + sqrt2*(x^(sqrt2)) + c
Hence, evaluating the most general antiderivative of the function yields F(x) = (x^(4.4))/(4.4) + sqrt2*(x^(sqrt2)) + c.

What do the sandcastles represent in chapter 4 of Lord of the Flies?

One of the most important themes in Lord of the Flies is that man will inevitably descend into savagery in the absence of a structured civilization. In Chapter 4, "Painted Faces and Long Hair," Roger and Maurice are walking along the beach when they find littluns Johnny, Henry, and Percival making sandcastles. Through their play, the littluns are re-constructing something they saw back in civilization; as such, the sandcastles symbolize the civilization from which all the boys have come. The littluns cry as Roger walks through their sandcastles, "kicking them over, burying the flowers, scattering the chosen stones." As Maurice follows, he is "laughing" and Golding says he "added to the destruction." Golding's diction here, with use of the word "destruction," is a clear foreshadowing of the boys' ultimate descent into savagery—the ultimate destruction of the fledgling society they attempt to create while on the island. The chapter title also indicates that things are beginning to shift on the island. The boys' hair is growing, suggesting that as time has passed, the boys look less and less like they would have back in society; this change is something out of their control. However, they are also changing in ways that are within their control. Jack, the most vocal proponent of savagery, paints his face for the first time in this chapter, donning a "mask" that "compelled" the other boys to follow him in the hunt as he makes his first successful kill.

What is the meaning of the poem "String Quartet" by Carl Dennis?

The poem discusses the poet's desire for fulfilling conversation. To him, good conversation is like a finely tuned quartet or orchestra. No one tries to talk over anybody else, and everyone is allowed to add to the conversation. There is no disharmony and no conflict when friends converse respectfully with each other.
In fact, the poet contends that a conversation isn't likely to flourish "When sales technicians come trolling for customers,/ Office-holders for votes, preachers for converts." Here, the poet suggests that religion, politics, and the competitive marketplace are often areas fraught with conflict and strife. He says that, even though there are likely "good people among such talkers," their conversation can never match the well-tuned and disciplined musical discourse of a harmonious quartet. In a good quartet, voices/musical instruments are never at odds; they are never pulled away from their true purpose of giving pleasure to listeners.
The poet talks about his admiration for the quartet in the third stanza. He cites how the cello is often "occupied/ With repeating a single phrase while the others/ Strike out on their own." Yet, invariably, all the four instruments eventually come together again at a later juncture. The reintegration is seamless, and this is what the poet admires about a musical "conversation."

Each near the end swerves back to the path Their friend has been plodding, and he receives them As if he never once suspected their loyalty.

In the fourth stanza, the poet wonders how he will react if he discovers that harmonious conversation can be had in both the musical world as well as the world of human discourse. He says that the quartet may be telling him something: that "conversation like this is available/ At moments sufficiently free and self-forgetful." Basically, people can have the same harmonious and satisfying conversation in both worlds. Also, we are more likely to have fulfilling conversation when we concentrate less on what we want to say ("free and self-forgetful") and more on how we can add to the experience.
In the last stanza, the poet comforts himself that, no matter what happens, he can at least revel in the role of the listener. Listeners are "glad for what they manage to bring to the music/ And for what they manage to take away." Basically, we can learn much from just listening while others talk. Additionally, we add to a conversation when we are good listeners.

Who was Neville?

George Neville is Sir Henry Curtis's long-lost brother. He was lost on an expedition to find King Solomon's Mines. Sir Henry has decided to embark upon an expedition of his own to find him, and asks Allan Quatermain to accompany him and Captain John Good on the journey, which he readily agrees to do.
Neville had quarreled with his family years before. After leaving them, he took off to Africa, where he changed his name. Once there, he set about looking for the fabled King Solomon's Mines, rumored to be the source of fantastic mineral wealth. No one knows for sure if the mines even exist; even a hardened old explorer like Quatermain doesn't know for certain. But whether real or not, King Solomon's Mines exert a strange fascination over men looking to prove themselves in the world and make their fortune. George Neville is one such man.
Unfortunately for him, however, he got lost on his expedition. Yet George need not have fear, for the intrepid trio of Sir Henry, Captain Good, and Quatermain finally manage to track him down after a long, arduous, but highly eventful journey. George is in a bit of a jam when they catch up with him, stranded in an oasis with a broken leg, but he's not too bad otherwise, considering all he's been through.

What figurative language is used in act 2, scene 7 of the Merchant of Venice?

Engraved on all three of the caskets are the riddles or conundrums Portia's suitors have to solve in order to win her hand in marriage. Because they are riddles, their language is figurative, not literal: the suitors have to figure out the underlying meaning of the words.
When the Prince of Morocco asks to see again "this saying graved in gold" (meaning the engraving on the gold chest, which reads "Who chooseth me shall gain what many men desire"), Shakespeare uses both imagery and alliteration. We can visualize the saying engraved in gold on the casket, which is imagery. The repetition of the "g" at the beginning of "graved" and "gold" is alliterative, as is the repetition of the same "g" sound when the prince reads the words "all that glitters is not gold."
The prince uses hyperbole, or exaggeration, when he declares that all the world desires Portia and when he refers to her as a "saint." This shows that he is not the right match for her, as he idealizes her and puts her on a pedestal.

This scene is relatively short, featuring only Portia, the Prince of Morocco, and their trains, with the majority of the dialogue afforded to the Prince. However, there is significant use of figurative language, revolving around the literal symbols of the caskets the Prince must choose between for Portia's love. The caskets themselves are engraved with statements which personify them, such as "Who chooseth me."
"A golden mind stoops not to shows of dross," the Prince says; he is not speaking of a literally golden mind but of one figuratively pure enough to be above "dross." Later, he says, "never so rich a gem was set in worse than gold," referring to Portia as a gem too beautiful to have been set in silver or lead.
Portia, however, questions the Prince's judgment: "All that glitters is not gold." She is saying both that beautiful things are not always pure, as gold is, and that pure things do not always appear as gold.

"Power corrupts and absolute power absolutely." To what extent is this true in Animal Farm?

This is a very accurate phrase to describe the situation which emerges in Animal Farm. Specifically, we can relate this phrase to the pigs and their behavior after the humans are overthrown in chapter 2.
The corrupting influence of power is a major theme in the novel which first emerges when the milk disappears at the end of this chapter. The pigs, who have become the leaders of the rebellion, choose not to share the milk with the other animals. Instead, they take full advantage of their leadership status and keep it for themselves. They then justify it to the other animals by claiming that it has been scientifically proven that pigs are "brainworkers" and need to consume milk for this reason. Power has, therefore, corrupted their sense of equality and fairness.
On the issue of how absolute power corrupts absolutely, take a look at the final chapter of the novel in which the pigs can be seen wearing human clothes, drinking whiskey, and playing cards. In other words, they have been corrupted so absolutely that they have become the very people they once hated.
Moreover, by this point in the novel, they have changed the Seven Commandments into one:

All animals are equal, but some are more equal than others.

This Commandment justifies their every abuse of power and is used by the pigs to solidify their exalted position on the farm. Through a combination of fear and propaganda, the pigs ensure that the other animals are powerless to ever change the situation.

What is chapter 7 of Lyddie about?

In a few of the chapters preceding chapter 7, Lyddie has been hard at work at Cutler's tavern.  She is worked hard there, but she did have a small interaction with a woman that works in the factories and makes a good wage.  At the end of chapter 6, Lyddie is fired from Cutler's tavern, so she decides that she will head to Lowell, Massachusetts in order to find work in the factories there.  Chapter 7 is about her journey there on the carriage.  Lyddie is the only hardworking, streetwise person on the entire carriage.  This becomes evident when the carriage gets stuck.  The men that are riding on the carriage are completely useless and have no idea how to go about getting the carriage unstuck.  Lyddie eventually gets frustrated with their ineffectual efforts, and she steps in to do the job herself.  She successfully gets the carriage unstuck.  The driver is quite impressed with Lyddie's strength, knowledge, and tenacity, and he tells Lyddie where to find lodging with his sister, Mrs. Bedlow. Mrs. Bedlow turns out to be a wonderful resource and helps Lyddie obtain clothing and a place to stay.  Mrs. Bedlow turns out to be a good friend for Lyddie as well. 

Name another living organism,other than plants,that can use light to perform photosynthesis

Photosynthesis is most commonly associated with plants. In this process, plants consume carbon dioxide and water in the presence of sunlight. The resulting products of this process are glucose and oxygen (and energy, in the form of ATP molecules).
However, plants are not the only ones who can carry out this process. Cyanobacteria are also capable of carrying out the process of photosynthesis. These are prokaryotic organisms and have a size ranging from about 1 micron to 100 microns. These are also known as blue-green algae (although technically cyanobacteria are prokaryotes, while algae are eukaryotes). Cyanobacteria have much less complexity as compared to plants and algae.
Cyanobacteria have been present on Earth for a really really long time. They are also thought to be responsible for increasing, through photosynthesis, the oxygen level in our atmosphere in the early age of our planet.
Hope this helps.

College Algebra, Chapter 3, 3.2, Section 3.2, Problem 42

Sketch the graph of the piece wise defined function: $f(x) = \left\{ \begin{array}{cc}
1 - x^2 & \text{if } x \leq 2 \\
x & \text{if } x > 2 \\
\end{array} \right.$

In Freakonomics, though Levitt and Dubner write about some highly charged topics, they write in a manner that does not offend most readers. How do they use language and style to achieve this balance?

The authors of Freakonomics make some bold claims. For example, they claim the legalization of abortion contributes to a decrease in crime in the United States. 
Such challenges and assertions are primed to make people angry. The authors manage not to offend most readers by refraining from using emotional language and by tying these social concepts to economic principles. For example, when dispelling myths of conventional wisdom, they refrain from incendiary language implicating that those who buy into conventional wisdom are foolish or believe in conventional wisdom for stupid reasons. Rather, they lay out straightforward, uncomplicated explanations explaining why these wisdoms are false and then similarly present their alternative hypotheses. 
By avoiding the use of emotional language or insinuations about the reader, Levitt and Dubner manage to avoid the type of prose that could provoke a strong, offended reaction. 

Why did Jimmy make sure to finish his ice cream?

Jimmy's been playing with fire—literally. The devil makes mischief for idle hands, as they say, and one day Jimmy, in what's presumably an effort to cure boredom, starts cutting off bits of his hair and burning them with his mother's lighter. It's a fascinating experience for Jimmy to watch his hair go all frizzly and squiggly. But when his mom finds out, she's not amused. Jimmy's dad gets involved and soon he and his wife are having a blazing row. No pun intended.
In a way, Jimmy feels kind of glad that his parents are arguing with each other; it means he won't get punished. At the same time, he also feels a little guilty for being the cause of their row. Anyway, after his parents are finished arguing, Jimmy's treated to a bowl of raspberry ripple ice-cream by his father. Jimmy makes sure to eat all of his up, as he wants to show his father that everything's ok. At this moment, the last thing that Jimmy wants to do is to make his father think he was feeling bad over having provoked the row. This is an opportunity for cheery father and son bonding, not for upset and recrimination.

Which day does the lottery fall on in Shirley Jackson's "The Lottery"?

The lottery took place on June 27th in the village square. In more populous villages, the lottery took longer to conduct and started two days before the official date. The village in the center of the story only had a population of 300 people, and the lottery took less than two hours to conduct. The people gathered in the square from 10 o’clock in the morning. The children, who were on school break, assembled first. They played around the square, talked about their teachers and books, and made a pile of stones in one corner of the square. Men gathered next, and they talked about farming and taxes. The women were last to assemble. They briefly talked to each other and proceeded to join their husbands in the square.

Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 28

Suppose that a cup of low fat milk has 100 calories. The number of calories in a cup of low fat milk is two-thirds the number of calories in a cup of whole milk.

Use this information to write an equation that can be used to find the number of calories in a cup of whole milk: $\underline{n}$ = $\underline{150}$.

If we let $n$ be the number of calories in a cup of whole milk, then $\displaystyle \frac{2}{3} n$ represents the number of calories in a cup of low fat milk, so



$
\begin{equation}
\begin{aligned}

\frac{2}{3} n =& 100
\\
\\
\left( \frac{2}{3} n \right) \left( \frac{3}{2} \right) =& 100 \left( \frac{3}{2} \right)
\\
\\
n =& \frac{300}{2}
\\
\\
n =& 150

\end{aligned}
\end{equation}
$

In the story "Ramond's Run," who challenges Squeaky?

In "Raymond's Run," a girl named Gretchen P. Lewis challenges Squeaky in the May Day races. At first, Squeaky feels competitive towards Gretchen, as Gretchen is going around telling everyone she is going to win the race. In turn, Squeaky makes fun of Gretchen's freckles. Before the race, the girls don't even smile at each other in a real way because, as Squeaky says, "girls never really smile at each other." She says there is no one to teach girls to smile at each other because grown-up women don't know how to smile at each other, either. Gretchen runs very close to Squeaky during the race, and they both overshoot the finish line. Both girls wonder who actually won the race. It turns out Squeaky wins, meaning Gretchen comes in second. In the end, they smile real smiles at each other out of mutual respect and admiration, and Squeaky thinks Gretchen might help her coach her brother, Raymond, in running.

Intermediate Algebra, Chapter 2, Test, Section Test, Problem 16

Evaluate the inequality $\displaystyle -6 \leq \frac{4}{3}x - 2 \leq 2$. Give the solution set in both interval and graph forms



$
\begin{equation}
\begin{aligned}
-6 + 2 &\leq \frac{4}{3} x - 2 + 2 \leq 2 + 2
&& \text{Add 2 on each side}\\
\\
-4 &\leq \frac{4}{3} x \leq 4
&& \text{Evaluate}\\
\\
-4 \left( \frac{3}{4} \right) &\leq x \leq 4 \left( \frac{3}{4} \right)
&& \text{Multiply each side by the reciprocal $\displaystyle \frac{4}{3}$ to solve for } x\\
\\
-3 &\leq x \leq 3
\end{aligned}
\end{equation}
$

This shows that the solution is the set of all real numbers in between and including $-3$ to $3$. Thus, the solution set in
interval form is $[-3, 3]$

Why do the conspirators want to involve Cicero in the plan? What does Brutus say?

This question refers to act 2, scene 1 of Julius Caesar, in which the conspirators have gathered to discuss their situation. Cassius ventures the idea of involving Cicero in the plan, stating that he thinks he "will stand very strong with us" and that they should "sound" him (see how he seems to feel about the plot).
Cassius and Casca agree, and Metellus Cimber expounds on this, saying that Cicero's "silver hairs will purchase us a good opinion." That is, he feels that because Cicero has a high standing in the city, and because he is an old man, others will believe that the plot has been Cicero's idea all along, and that the young men involved are simply responding to Cicero's leadership. As such, having Cicero seemingly in charge will lend the plot legitimacy, rather than it simply seeming like an uprising of young men who do not know what they are doing.
Brutus rejects this idea, however. He says, "name him not . . . for he will never follow any thing that other men begin." Brutus feels there would be no point in approaching Cicero because he only wants to be involved in things he has thought of himself; he will not want to be the figurehead of an existing movement.

Describe the death of the convict.

Dr. Watson and Sir Henry Baskerville are out on the moors looking for the dangerous escaped convict Selden. But after several hours of searching, they are still unable to find him. The next morning they go to see Barrymore, who, along with his wife, has been protecting his brother-in-law. Barrymore promises to prevent Selden from hurting anyone else until he can make good his escape to South America. In return, Sir Henry will call off the search; he'll even give Barrymore some of his clothing to pass on to Selden. From Barrymore, the two men discover that Selden told him about a strange man living among the stone huts on the moor.
When Watson goes to investigate, he finds none other than Sherlock Holmes. Holmes reveals that the dangerous killer in this case is not Selden, but a man by the name of Stapleton. What's more, this man is a danger to Sir Henry Baskerville and must be apprehended at once. Suddenly, the air is filled with a blood-curdling scream. A man has fallen to his death from a cliff. It later transpires that that man is Selden. He has been chased to his death by a hound belonging to Stapleton, whose real name is Rodger Baskerville. The killer wanted to get his hands on the Baskerville inheritance. He set his hound upon Selden, thinking that he was Sir Henry Baskerville as he was wearing his clothes. Sir Henry's clothes carried his scent and so the dog naturally chased Selden.

What are the chief elder's inner desires?

The text of the book does not give readers specific, textual evidence to answer this question with. We don't get an inside look into the thoughts of any of the elders because the narrative point of view is focused on Jonas. The point of view is third person, but it is very limited; therefore, we know what Jonas thinks about and feels, but we do not know about other characters. We have to make an educated guess as to what the motivations and inner desires are of other characters. I do not believe that the chief elder's main motivation is to stay in a position of power. To me, that feels too selfish, and Jonas's society is built on the concept of having negative emotions removed and encouraging altruism. This is why the kids have to wear the jackets with the buttons in the back. I truly believe that the main concern of the chief elder is to maintain a peaceful society in which each person does the job that they are supposed to do as well as they can. I think the chief concern is the clinical execution of the plan and maintenance of the parts that work the plan. That's a cold and emotionless way of running a society, but that fits the Sameness. If hate, anger, and sadness are totally gone, a person can't actually know what love and happiness feels like. They have nothing to compare it to, so the chief elder is essentially concerned with the efficiency of the society.

The Chief Elder is an enigmatic authority figure throughout the novel, who serves as the spokesperson for the Committee of Elders. She is first mentioned in Chapter 7, where she addresses the community during the Ceremony of Twelve. Given the fact that Jonas lives in an authoritarian society with strict rules, which is controlled by the Committee of Elders, one can assume that the Chief Elder's main concern is maintaining her position of authority while preserving a safe, comfortable, structured society. In Jonas's society, the Committee of Elders is responsible for making all of the community's important decisions. They decide which citizens will get married, how many children are born each year, what the children will be named, what couple raises the children, and also what specific occupations each citizen will be assigned. Given the fact that the Chief Elder has such a tremendous influence on the community, one could infer that her primary inherent desire is to maintain her authoritative role in society. While this suggestion is simply speculation, one can argue that humans inherently enjoy authority and many authoritarian politicians' primary concern is staying in power.

Compare Mr. White's feelings about the monkey's paw when he makes his first, second and third wishes. How does his attitude change?

When Mr. White makes his first wish for two hundred pounds to pay off his mortgage, he does not believe that the monkey's paw will actually work. He casually makes his wish in a light-hearted manner because he is unaware of the paw's malevolent magical powers. After his son dies and they receive two hundred pounds as compensation, Mrs. White remembers her husband's first wish and urges him to use the paw again to wish for Herbert to come back to life. Mr. White is hesitant to make a second wish because of the disastrous outcome of his first wish. However, Mr. White reluctantly makes the second wish and is suspicious that it will come true. When he hears a knocking at their front door later that night, Mr. White realizes that the second wish has also come true and hurries to make a third wish. By his third wish, Mr. White truly believes in the monkey paw's malevolent magical powers and frantically wishes for Herbert's corpse to return to its grave before his wife can open the door. Overall, Mr. White goes from casually making his first wish to desperately making his third wish to prevent his wife from seeing their son's decaying body. His attitude regarding the monkey's paw dramatically changes when he realizes that it does indeed have magical powers. By the end of the story, he fears the monkey's paw and regrets making his first and second wishes.

When Mr. White makes his first wish he does not have much faith in the power of the monkey's paw. He did, however, pay Sergeant-Major Morris a small sum of money for it, so he must have some small credence. He makes a wish for two hundred pounds at the suggestion of his son Herbert. His first wish is modest because he wants to test the paw. The fact that he makes such a modest wish shows that he does not have much faith in the thing. He is aghast at the outcome. His modest wish for two hundred pounds is apparently granted, but at the cost of his son's horrible death at the textile mill.
Mr. White has no desire to make another wish. He is afraid of the monkey's paw because of the consequences of his first wish. But at his wife's insistence he wishes for his son to return to them. Now he is hoping against hope that the paw has no real power and that his wish will not come true. After all, the idea of a shriveled paw possessing any power to grant any kind of wish is fantastic. He tries to make himself believe it must have been a pure coincidence that he received two hundred pounds as compensation for his son's fatal accident.
When Mr. and Mrs. White hear the knocking at their door, both of them feel sure that it is Herbert who has returned to them from the dead. But only Herbert's mother wants to let him in. Herbert's father doesn't want to have to look at his son, who must be a monster. Mr. White had previously told his wife, when she forced him to make his second wish:

"He has been dead ten days, and besides he--I would not tell you else, but--I could only recognize him by his clothing. If he was too terrible for you to see then, how now?"

By the time he makes his third wish, Mr. White loathes the monkey's paw but believes completely in its supernatural power. He uses it to cancel out his second wish, so to speak, and seems to succeed in causing the person outside to stop knocking and go away. The paw has now lost its power, if it ever had any, because the Indian fakir had only specified three wishes for three owners, and Mr. White was the last owner. So there would be no way of testing the paw further.
The reader is left to wonder whether that was really Herbert knocking at the door or some stranger who finally gave up and went away just as Mr. White was making his final wish.
 

Why do you think it helps the neighborhood and the painter to see Jimmy Lyons represented on the wall?

In "The War of the Wall," by Toni Cade Bambara, the narrator and her cousin, Lou, notice that there's a stranger from out of town attempting to paint a wall in the neighborhood. The narrator feels that the wall belonged to the people in their community and that the painter "had no right" to paint it. Most importantly, chiseled into the wall is the name of Jimmy Lyons. He was a member of the community that went to Vietnam and never returned.
Once the project is completed, the people of the neighborhood have something of which they can be proud. The painter has created a colorful mural to pay tribute to Civil Rights activists and to members of the community. Through her art, the painter is offering the people a sense of pride in their heritage and community. This "Wall of Respect" also contains an inscription in which the painter dedicates her work to her cousin, Jimmy Lyons. Her tribute to her cousin may also serve as an act of healing for the loss she has suffered when he did not return from Vietnam. For these reasons, both the neighborhood and the painter receive benefit from the mural.

Please explain how these four primary sources are related to decolonization and anti-imperialism. Provide quotes from each to support your answer. Vietnamese Declaration of Independence https://www.marxists.org/reference/archive/ho-chi-minh/works/1945/declaration-independence.htm The Imperialist Aggressors Can Never Enslave The Heroic Vietnamese People https://www.marxists.org/reference/archive/ho-chi-minh/works/1952/01/x01.htm Cuba: Historical Exception or Vanguard in the Anticolonial Struggle https://www.marxists.org/archive/guevara/1961/04/09.htm Establishing Revolutionary Vigilance in Cuba https://www.marxists.org/history/cuba/archive/castro/1960/09/29.htm

This response will deal with each of these documents in turn. The first, the Vietnamese Declaration of Independence, was delivered as a speech by Ho Chi Minh in 1945. Ho was a Vietnamese resistance leader during the Japanese occupation of his homeland during World War II. He hoped, as did many of his countrymen, that the end of the war would mean an end to French rule (the region, known as French Indochina, was part of the French Empire before the war). When France made it clear that they had no interest in granting independence, Ho Chi Minh declared it in 1945. In many ways, this speech marks an early example of decolonization, though decades of war remained before Vietnam became unified under a socialist government. A remarkable quote from this document is as follows:

For more than eighty years, the French imperialists, abusing the standard of Liberty, Equality, and Fraternity, have violated our Fatherland and oppressed our fellow-citizens. They have acted contrary to the ideals of humanity and justice. In the field of politics, they have deprived our people of every democratic liberty. They have enforced inhuman laws . . .

The Declaration paraphrases both the American Declaration of Independence and the French Declaration of the Rights of Man, turning the egalitarian rhetoric of these documents against the French imperialists.
The second document was a report on the Vietnamese war for independence from France. Issued in 1952, it highlighted the victories of the fighters led by Ho. But most importantly, Ho emphasized the support that the United States gave to France, characterizing them both as "imperialist aggressors." In one passage, Ho describes the economic exploitation of Vietnam that he saw as inseparable from imperialism:

U.S. aid [to France] is paid for at a very high price. In the enemy held areas, French capitalism is swept aside by American capitalism. American concerns like the Petroleum Oil Corporation, the Caltex Oil Corporation, the Bethlem Steel Corporation, the Florid Phosphate Corporation and others, monopolise rubber, ores, and other natural resources of our country. U.S. goods swamp the market.

This document paints the decolonization and anti-imperialist struggle in Marxian terms, arguing that the American presence in the region would be as exploitative as the French presence. As the title suggests, Ho claims in the speech that neither the French nor their American backers will ever achieve victory over the Vietnamese people.
The next document, "Cuba: Historical Exception or vanguard in the anticolonial struggle," was written by revolutionary leader Ernesto "Che" Guevara in 1961. Guevara, having participated in the Cuban Revolution that overthrew the US-backed dictator Fulgencio Batista, is arguing that other states in Latin America should mount a socialist revolution as well. He claims that they face the same circumstances that Cuba did before the revolution, many of which stem from American domination. He warns that although revolutionary struggle will be difficult, because the United States will act to thwart leftist movements in Latin America, the conditions are still right for revolution:

New conditions will make the flow of these revolutionary movements easier as they give the masses consciousness of their destiny and the certainty that it is possible.

Finally, "Establishing Revolutionary Vigilance in Cuba" demonstrates the lengths that Fidel Castro, leader of the Cuban Revolution, was willing to go to in order to maintain and protect the revolution. It also highlights the constant threat that the United States posed to leftist regimes during the Cold War in Latin America. Castro emphasized the urgency of the revolutionary struggle, claiming that the Cubans were "on the frontline, a small country with few economic resources giving battle on the frontline for our sovereignty, destiny, and right." Unlike Ho Chi Minh, who lived in a French colony, Castro and Guevara argue that American influence is more insidious, as they propped up corrupt and exploitative regimes. This was the form of imperialism they sought to overthrow as they attempted to establish socialist revolutions in Cuba and Latin America.
http://historymatters.gmu.edu/d/5139/

What’s the tone?

This short story by Toshio Mori was written in 1939, but it was not published until 1946. It concerns a young Japanese American man, still a "schoolboy" at the age of 31, who is passionately devoted to his dream of becoming a great Shakespearean actor.
The tone of the story is quietly melancholy, echoing the narrator's fear "that Tom's energy and time were wasted" and that he himself is contributing to the problem by encouraging his friend. Tom's hopes—"this was his special role, the role that would establish him in Shakespearean history"—are recorded with gentle irony, as the narrator implies that the hopes can never be realized.
The tone of increasing hopelessness and frustration escalates throughout the story until the narrator begins to "dread [Tom's] presence"; his concern for Tom is palpable. Eventually, Tom stops asking the narrator to listen to him recite. We are told almost in passing that the narrator encounters him later on a subway. The narrator knows he has not made a success of himself, but he is still reading Shakespeare. The narrator "could not forget his simple persistence."
Although the fact that Tom is Japanese is not mentioned outright in the story, the combination of his Japanese surname and the title give some indication that the story is concerned with the disjointedness between Tom's two identities: being Hamlet and being Japanese. He yearns to be a Shakespearean actor, but he feels—or, perhaps, the narrator feels—that the fact that he is Japanese holds him back. The story leaves the reader feeling unsettled. Tom is unable to properly settle into real life because he is so preoccupied with his unreachable dream.

How do civil rights contribute to pluralistic democracy?

Civil rights are defined as the rights of citizens to equal social and political participation in a society. This normally includes a right to vote, freedom of speech and the press, the right to a free public education, protection from arbitrary arrest and imprisonment, and the right to a fair trial.
A pluralistic society is defined as one where people of different backgrounds and with different belief systems are allowed to have a voice in determining social and political policy.
As these definitions show, civil rights are a necessary precondition to the development of a healthy pluralistic society. As many people as possible ought to have as many avenues as possible to express their views without fear if a pluralist society is to develop and flourish. There needs to be, as it is often put, a marketplace of ideas, rather than lockstep thinking.
The opposite of a pluralistic society is a totalitarian or dictatorial regime, in one person (or a small cartel of people with very similar beliefs) makes all the decisions. A pluralistic society is seen as stronger than a totalitarian state because it allows multiple views to be aired and allows as many people as possible to participate in the running of the state.
However, when civil rights are suppressed through polices such as the voting laws that discriminated against black folks in the South in the 1950s or the loss of a free press through mergers and monopolies, fewer people have a voice in setting the goals and agenda of a society. It is very easy in such a situation for many needs to go unheard, leaving problems unaddressed until they fester into social unrest, riots, and revolutions.

A pluralistic society is one where diverse groups thrive together by building a common society that is supportive and understanding of individual differences. Within this society, part of the goal of interactions between groups is to build understanding, even in areas where there are major disagreements between groups. With a pluralistic democracy, the individuals within society also elect their leaders or directly vote on issues. A pluralistic society is the ideal, but creating a society using these principles based solely on the good will of individuals is difficult—a major conflict or difficulty can occur when two groups both have deeply held beliefs that conflict with each other.
Civil rights are the principles used to adjudicate these disputes. They typically are the most highly valued rights of a society. For example, in the United States, the most highly valued civil rights are the rights to life, liberty, and the pursuit of happiness. The United States Constitution, including the Bill of Rights, outlines the rest of the civil rights of the United States. The rights contained within this document are used to decide disputes between groups, in an attempt to use higher principles to decide the issues of the day. The hope is that by using these higher principles, contentious issues of liberty and equality can be decided in a just manner. However, this adjudication must be done by individuals, such as the Supreme Court Justices, and therefore can be skewed by the views of the individuals making the adjudication. Regardless, without civil rights, pluralism on a societal scale becomes very difficult because the views of different groups eventually come into conflict. Thus, civil rights are required for a pluralistic democracy.
http://constitutionus.com/

http://pluralism.org/what-is-pluralism/

https://www.ushistory.org/declaration/document/

Pluralism and civil rights tend to go hand in hand. A democratic society that protects the civil rights of its people will include the voices of every group within it. With greater access to political involvement and with a more equitable distribution of political resources, every group can have a say in democracy. There are many historical and contemporary examples in which a group has been denied their civil rights. This has nearly always led to a lack of representation in government and unequal access to employment and education. However, when the civil rights of all groups are protected, the situation changes into a more pluralistic one.
In the 1960s, political scientist Robert Dahl published an interesting study in which he looked at political power and representation in New Haven, Connecticut. He determined that, as this was a city that did a relatively good job of protecting its citizens' civil rights, New Haven had a truly pluralistic democratic community.
https://books.google.com.co/books/about/Who_Governs.html?id=-L99RHLc3WoC&redir_esc=y

What was the monarchy and government like in 19th century London?

The nineteenth century was a period of dramatic change in England. Legally, England is described as a constitutional monarchy, with the monarch having powers limited by Parliament. The nineteenth century was a period of great change though in how Parliament was elected, the relative powers of the two houses of Parliament, and the relationship of the monarchy to Parliament. 
There were four monarchs during this period: 

GEORGE III 1760 - 1820: Due to his increasingly erratic behavior due to mental illness, his son ruled as Prince Regent from 1811-1820. 
GEORGE IV 1820 - 1830: Note that he had been Prince Regent from 1811-1820 and was a quite colorful character.
WILLIAM IV 1830 - 1837: Brother to George IV.  
VICTORIA 1837 - 1901: Giving her name to the "Victorian" period, Queen Victoria was one of the longest reigning monarchs in English history and presided over a period of great prosperity.

The three Reform Bills of 1832, 1867, and 1884 gradually expanded voting rights from the wealthy to most adult males. The House of Commons became increasingly powerful compared to the upper house. The civil service expanded, with the government beginning to fund and manage such things as public schools, poor relief, marriages, census taking, and citizenship records that had earlier been the responsibility of the church. 
London itself had no municipal government, but rather a miscellaneous collection of parishes and vestries and special-purpose organizations such as the Metropolitan Police (established by Prime Minister Robert Peel, and thus called "bobbies" or "peelers").

How is Pearl Avenue symbolic of Flick Webb's road in life?

In John Updike's "Ex-Basketball Player," Pearl Avenue is described as a very short street that is cut off prematurely before reaching the garage. The speaker writes,

Pearl Avenue runs past the high-school lot,
Bends with the trolley tracks, and stops, cut off
Before it has a chance to go two blocks,
At Colonel McComsky Plaza. (lines 1-4)

This opening description of the street foreshadows the fate of the titular athlete, Flick Webb. He was apparently a phenomenal basketball player when he was young. The speaker even describes him as "the best" and as a county record holder in scoring points in a season. However, Flick now "just sells gas, / Checks oil, and changes flats" (19-20). The word "just" conveys the disappointment both Flick and the county likely feel about his brief basketball career. He was so gifted at the sport, but he does not play any more and "never learned a trade." His potential, like Pearl Avenue, was cut short. The speaker says that many in the town remember Flick's prowess, but ultimately, it no longer matters, as "It makes no difference to the lug wrench" (25). The street described at the start of the poem parallels and foreshadows Flick's brief basketball career, as the poem reflects on wasted potential and the disappearing dreams of youth.

Pearl Avenue is brought up by the poem's narrator in the opening stanza of the poem. We are told that the most noteworthy aspect of Pearl Avenue is its length. It is exceptionally short. It does not even go two full blocks. It has been cut off. The road is symbolic of Flick Webb's life because his fast track to great success has been cut off. In high school, Flick Webb was a basketball phenom. He loved the game, and he had amazing control over the ball. We are told that it looked as if the ball loved Flick Webb back. He even holds a county record for most points scored in a season. Unfortunately, all Flick Webb knows is basketball. He never learned a trade, and he was not quite good enough to take his game to the next level. As a result, he works at a dead-end gas station with essentially no hope of doing anything special with his life. The road has also been cut short and leads to nowhere in particular.

Finite Mathematics, Chapter 1, 1.1, Section 1.1, Problem 32

Determine a equation in slope intercept form (where possible) for the line that goes through $(-2,6)$ and perpendicular to $2x - 3y = 5$

If we transform the given line into point slope form, we have

$
\begin{equation}
\begin{aligned}
2x - 3y &= 5 \\
\\
-3y &= -2x + 5 \\
\\
y &= \frac{-2}{-3} x + \frac{5}{-3}\\
\\
y &= \frac{2}{3} x - \frac{5}{3}
\end{aligned}
\end{equation}
$

Now that the line is in the slope intercept form $y = mx + b$. By observation, $\displaystyle m = \frac{2}{3}$
Thus, the slope of the perpendicular line is
$\displaystyle m_{\perp} = -\frac{3}{2}$. Thus,
By using the point slope form,the equation of the line will be $y - y_1 = m(x - x_1)$

$
\begin{equation}
\begin{aligned}
y - 6 &= -\frac{3}{2} (x - (-2))\\
\\
y - 6 &= -\frac{3}{2} (x + 2)\\
\\
y - 6 &= -\frac{3}{2}x - 3\\
\\
y &= -\frac{3}{2} x + 3
\end{aligned}
\end{equation}
$

Why was the police response to the Columbine shooting criticized? Was the IMS used? If so, what amount of success did it have? If not, why not? What things do you think the police did wrong or handled incorrectly? What should be done in situations like Columbine in the future?

In 1999, when Columbine occurred, school shootings were relatively rare. According to Slate magazine (Cullen 2009), there were 37 school shootings in America between 1974 and 2000. While this may seem like a lot (over one per year), it is a very small number compared to the number of shootings since Columbine. As a result, law enforcement agencies were not well-prepared for such an incident. The law enforcement agencies in Littleton were ultimately criticized for being too slow to respond to Columbine, causing unnecessary loss of life.
There were two major failures in the response to Columbine. The first was that response teams were more trained to handle hostage crises than active shooters. As a result, their standard operating procedure was to surround the building, create perimeters, and then take steps to free the hostages inside. Less-trained forces, such as city police, were also typically instructed to wait for better-equipped, more highly-resourced, and highly-trained agencies to come on the scene rather than acting independently. Eric Harris and Dylan Klebold did not hold hostages; rather, they gunned down people inside the building. As a result, typical hostage-management techniques failed, and far too much time was taken up by using these traditional methods. 
The second major failure at Columbine was the lack of a systematic, well-run incident management system (IMS). While Mell and Sztajnkrycer (2004) noted there was an Incident Command System (ICS) in place and praised the successes of said system, they also noted several flaws. First, there had been few interagency training opportunities, which meant most of the individual responders had not been trained to work with other agencies. This led to issues; for example, one team not understanding another team's language, or confusion as to who had higher authority. Technology also became a problem, as the different agencies had different methods of communicating and used different radio frequencies. Finally, the lack of smooth interagency communication led to many mistakes, including an overrun of surplus volunteers that created many logistical and media challenges.
Unfortunately, there have been many school shootings since Columbine, and law enforcement has much more training now. If a shooting were to happen today, two important steps would be
1) Whoever is first on the scene takes control of the situation, including assessing if there is an active shooter.
2) If there is an active shooter, officers now follow the "active shooter protocol," in which teams of four officers enter the building as soon as possible in a wedge formation. The primary goal of these officers is to take down the shooter as quickly as possible. 
Additional improvements in technology and joint/ interagency training have also allowed law enforcement and emergency response to make great gains in containing shooting situations. A well-run, well-trained Incident Command System/ Incident Management System, with a clear chain of command, is critical in these situations.
http://ispub.com/IJRDM/5/1/12573

https://slate.com/news-and-politics/2009/04/the-four-most-useful-lessons-of-columbine.html

https://www.nytimes.com/1999/04/28/us/terror-littleton-police-response-school-attack-may-bring-changes-police-tactics.html

What does Mae Tuck mean when she says, "Well, boys, here it is. The worst is happening at last"?

The quote in question appears at the very end of chapter five. A lot happens during this chapter. It starts with Winnie Foster testing out her idea of running away. She goes off to explore the woods near her house, and she is startled to see a boy drinking from a small spring. The boy is Jesse Tuck. Jesse and Winnie engage in some small talk, and Winnie eventually asks Jesse if the spring water is good to drink. Jesse is immediately on guard and tries to explain that Winnie should not drink from the spring. 

"Believe me, Winnie Foster," said Jesse, "it would be terrible for you if you drank any of this water. Just terrible. I can't let you."

Winnie is persistent, though, and she keeps trying to take a drink. Jesse knows he's in real trouble in the current situation. He simply doesn't know what else to do.
It's at this moment that Mae and Miles Tuck show up at the spring. Jesse is relieved they are there because they can help deter Winnie. Mae quickly takes in the situation and realizes what has happened.

And at once, when she saw the two of them, Jesse with his foot on the pile of pebbles and Winnie on her knees beside him, she seemed to understand. Her hand flew to her bosom, grasping at the old brooch that fastened her shawl, and her face went bleak. "Well, boys," she said, "here it is. The worst is happening at last."

What Mae Tuck means is that her family's worst fear has just happened. Somebody else has discovered the spring. If it were a normal spring, that wouldn't be a big deal, but the spring grants the person who drinks from it immortality. The Tucks know the spring is both a blessing and a curse, and they do not want knowledge of it spreading around.

Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 184

A person's accurate typing speed can be approximated by the equation $\displaystyle S = \frac{W - 5e}{10}$, where $S$ is the accurate typing speed in words per minute, $W$ is the number of words typed in ten minutes, and $e$ is the number of errors made.

A job applicant took a 10-minute typing test and was told that she had an accurate speed of 37 words per minute. If she had typed a total of 400 words, how many error did she make?

Solving for the number of errors $e$,


$
\begin{equation}
\begin{aligned}

S =& \frac{W - 5e}{10}
&& \text{Given equation}
\\
\\
10S =& W - 5e
&& \text{Multiply both sides by } 10
\\
\\
5e =& W - 10S
&& \text{Add $5e$ and subtract } 10S
\\
\\
e =& \frac{W - 10S}{5}
&& \text{Divide by } 5
\\
\\
e =& \frac{400 - 10(35)}{5}
&& \text{Substitute } W = 400 \text{ and } S = 35
\\
\\
e =& \frac{400-350}{5}
&& \text{Simplify}
\\
\\
e =& 10
&&

\end{aligned}
\end{equation}
$


She make 10 errors.

In what ways is this story about communication and connectedness?

The theme of communication is rather sophisticated in "Cathedral." On the most basic level, Robert is able to communicate with others in a very meaningful way despite being cut off from the sense of sight, while the narrator, despite being able-bodied, cannot really "see" or touch other people on a deeper level.
Robert is blind, so he mainly communicates with the world through touch. When he touches the narrator's wife's face, she feels a great connection with him. This gesture is a little shocking because touch is so intimate and on a narrative level it is a little shocking because the narrator's wife does not seem to feel that same intimacy in a marriage with a closed off man.
When Robert asks the narrator to describe a cathedral to him and he cannot, the narrator is admitting that he values nothing outside his own petty ego. When Robert puts his hand on the narrator's as the narrator draws a cathedral for him, this is the narrator's most intimate moment of communication. He gets to show Robert some of his own world in a small way—and yet this small gesture is the most profound moment of the entire story, opening up the narrator's heart and letting him communicate with someone outside his own little world.

The themes of communication and connectedness are observable throughout Carver's short story "Cathedral." First of all, the narrator's wife communicates with her friend Robert through a variety of modes, and through all of her efforts at communication, she and Robert are able to stay connected to each other. Their communication when they are together involves touch, as she allows Robert, who is blind, to touch her face as a way of communicating with her and understanding her better. She also writes letters to Robert by recording tapes which he can listen to, as he is unable to read letters written conventionally.
Robert's connection to the narrator's wife is at first somewhat threatening to the narrator, until he himself communicates with Robert and develops his own connection with him. They communicate under the influence of marijuana, which seems to minimize the narrator's inhibitions and allows him to feel an openness toward Robert; without this openness, the connection between them could not have developed. They also communicate through touch, as the narrator allows Robert to hold his hand as he draws an image of a cathedral; through this moment of connection to Robert, the narrator learns about his own potential to change by allowing himself to communicate in different and unexpected ways.

The themes of communication and connection are prominent throughout Carver's, "Cathedral." Initially, Robert, the blind man, is presented as a dear companion/friend of the narrator's wife. The narrator's wife connected with Robert while working for him and they kept in touch by communicating through tape recordings. At one point while working for Robert, the narrator's wife experienced a deep connection with him after sharing an intimate moment of Robert touching her face as a way of "seeing" her. This moment was so significant for the narrator's wife that she had attempted to write a poem about the interaction. 
The narrator, on the other hand, is less interested in meeting the blind man that his wife admires and is rather skeptical of his visiting their home. The narrator seems to be uncomfortable with Robert's blindness and his inability to relate to him. Furthermore, he does not understand his wife's near obsession with him. After Robert's arrival, the narrator remains skeptical of the blind man and Carver illustrates their interactions as quite awkward. 
Towards the end of the story, the narrator and Robert are forced to interact exclusively as the narrator's wife has fallen asleep on the couch. It is at this point when these two characters connect. The narrator feels inclined to describe what is being shown on the television screen, a cathedral, to the blind man. The blind man requests that they draw the cathedral together. While drawing, Robert then asks the narrator to close his eyes. It is at this point that the narrator experiences the drawing in the same way that the blind man does. This is the point of deepest connection and communication between the narrator and the blind man. Furthermore, Carver seems to present a certain level of comfort for the narrator at this point in the narrative, connecting the narrator's interaction with the blind man with his wife's intimate interaction with him at the beginning of the story. 

For most of the story the narrator is unable either to connect or communicate with Robert in any meaningful sense. Robert is blind, and this creates what seems to be an insuperable barrier between him and the narrator. Yet the possibility of breaking down this barrier is nonetheless there from the outset.
The narrator's wife shows the way. Years ago, she worked for Robert, reading to him one summer. In subsequent years she'd kept in touch by sending him tapes. And at their last parting, Robert had touched her face, communicating something of the connection he'd developed to her over the course of that unforgettable summer.
The narrator's world is somewhat narrow and insular. He doesn't understand Robert's blindness and, frankly, doesn't want to. In a sense he is more blind than Robert because, unlike Robert, he lacks the ability to communicate and connect with the wider world around him. Ironically, it is only when he closes his eyes and allows his hand to be guided by Robert that he truly feels a part of the world he has so often scorned.
This life-changing epiphany allows the narrator not just to connect to Robert, but also to his wife. Now, for the first time, he understands just how she must have felt when Robert touched her face; a very special connection with the mind's eye of another human being.

Why do the evacuating prisoners clean the barracks?

At the end of chapter 5, Elie recalls that the head of his block ordered that the barracks be cleaned before they leave to go on their Death March to Buchenwald by way of Gleiwitz. Although Elie himself does not give clear explanation as to why this order was given, thinking through the stages of genocide can be helpful when considering this question.
According to the stages of genocide, the last stage is unfailingly denial by the oppressors of the atrocities that took place during the previous stage: extermination. Although this stage manifested in several ways throughout the Holocaust and its aftermath, including the destruction of gas chambers and crematories at many concentration camps, the order to clean the barracks is a small-scale example of the same phase. With the barracks clean, the Russians would not be able to see clear evidence of the level of mistreatment that the prisoners endured at Auschwitz.

The head of Elie's block insists that the barracks must be cleaned in anticipation of the Russians' imminent arrival. His order doesn't seem to make much sense; why on earth should the barracks be cleaned one hour before leaving the camp? What's the point? The block leader says that it's to make a good impression for the Russians when they arrive. He wants the barracks cleaned to show the Russians that men lived there and not pigs. The inmates of the camp have been systematically stripped of their dignity as human beings by the Nazis. By cleaning the barracks from top to bottom they are reasserting their humanity, reminding themselves and the approaching Russians that after all their horrific experiences, they are still men.