Why does the community get mad when Junior makes the decision to change schools?

When Junior decides to attend the affluent white school in Reardan (twenty-two miles away from his reservation), his parents are happy for him but also anxious about his future. First, they are concerned that no one on the reservation will understand their son's decision. Second, they are worried that Junior will be stigmatized by his determination to go against the prevailing public opinion on their reservation. Third, Junior will be the first person to leave the reservation for anything.
For an indication of why the community reacts negatively to Junior's decision, let's take a look at Rowdy's reaction when Junior talks to his best friend about attending Reardan together. Remember that Rowdy and Junior have been best friends for fourteen years; they are almost like brothers and have been involved in the football, baseball, and basketball teams at Wellpinit for many of their years in school together. When Junior breaks the news to Rowdy, Rowdy is initially incredulous. However, when he realizes that Junior is serious, he becomes violently angry. His anguish is expressed in a terrible and prolonged scream. Junior states that his best friend's scream is the worst thing he's ever heard.
To make matters worse, Rowdy accuses Junior of thinking that he's better than everybody else on the reservation. Junior denies this, but Rowdy refuses to be placated by his friend's assurances. Grieved beyond measure at what he thinks is Junior's betrayal, Rowdy punches Junior in the face before walking off. Rowdy's reaction highlights his fear of the unknown and his anguish at losing his best friend. Perhaps there is the fear too that Junior will forget his Indian roots and the great relationship the two friends have shared for many years. More than anything, Rowdy's reaction highlights the prevailing Indian belief that only white people are destined for success in life.
So, any Indian who tries to change his destiny is immediately perceived to be arrogant and presumptuous. Perhaps, on a deeper level, Junior's community is merely afraid that there isn't any real possibility for someone from their reservation to be successful in life.
Because of their fears, they feel threatened by Junior's determination. Additionally, Junior's community may also feel betrayed by the fact that he has chosen to attend a white school in lieu of a reservation school. For his part, Junior knows that he must overcome his community's disapproval in order to be successful; because of his goals, he's willing to travel to where the opportunities are, even if this means attending a white school and upsetting his community.
 
 

In the Seamus Heaney poem "Digging," how does the poet feel about his father's work?

I think the speaker has significant respect for his father's work. The speaker expresses astonishment and admiration—"by God"—for the skill with which his father, just like his grandfather, managed a spade and enacted his role as a digger of potatoes. The speaker, himself not a digger of potatoes, evidently thinks of men like his father and grandfather as admirable men of a particular group—"men like them"—and wishes that he had sufficient skill and capacity to follow them. However, the speaker recognizes that people contribute different things to the world. While his father and grandfather were able to contribute work to the world via their digging of potatoes, he himself is not able to work in such a physical way. Instead—while he feels that it is a valuable occupation to contribute to the world as a digger of potatoes—the speaker contributes instead through his own preoccupation, that of writing poetry.

First of all, you should develop the habit of referring to the voice in the poem as the speaker, not the poet himself (or herself). Poems are often autobiographical or semi-autobiographical, but not always.
The speaker in this poem has great admiration and pride for the physical labor his father does. The poem's diction and imagery emphasize the efficiency and prowess the father demonstrates when he is planting potatoes.
The speaker also has great admiration for the work his grandfather, his father's father, did in cutting turf. In Ireland and elsewhere, peat turf was cut to burn as fuel to warm homes. He boasts that his grandfather cut more turf than any other man digging in a particular peat bog. He recalls a specific memory of his grandfather barely taking a break when the speaker brought him a bottle of milk.
Both the speaker's father and grandfather are favroably described as machines—efficient and tireless.
The speaker is careful to characterize his decision to be a writer instead of a laborer as a different, not better, choice.

5. You throw a golf ball straight up at 10 meters per second. a. What is the velocity when you catch the golf ball after its return trip? b. How long did the golf ball’s total trip take (in seconds)? c. What is the total distance the golf ball traveled (up and down)?

When you throw a golf ball straight up, assuming that wind and air resistance are irrelevant, it is pulled back down by gravity, which decelerates it by 9.8 meters/second every second. That deceleration is constant through its rise and fall, creating a parabolic arc when considering its speed graphically.
The answer to part a) is 10 m/s. No calculation is necessary. Acceleration curves are symmetrical; in the absence of air resistance, a rising and falling object will always land at the same speed at which it was launched.
To answer part b), we can do a simple calculation involving the gravitational constant. Gravity robs the golf ball of speed at its constant rate, so it will take 10 / 9.8 = ~1.02 seconds for the golf ball's velocity to reach zero at the apex of its flight. Because rise and fall are symmetrical, we do not need calculations to know that it will take another 1.02 seconds for the upward motion to reverse, reaching your hand once again. The total time the golf ball travels is 2 * ~1.02 = ~2.04 seconds
Finally, part c) is once again fairly simple. Because acceleration is constant, the average velocity of a fall is always equal to exactly half the final velocity. Because of the symmetry of physics, the acceleration upwards perfectly mirrors the fall back down. Since the golf ball started and ended its flight at 10 m/s, its average speed is 5 m/s, meaning it traveled a total distance of 5 * 2.04 = 10.08 meters. 

I've been assigned an essay on "The Overcoat" which asks the following question:Explain how the metaphor of copying successfully advances Nikolai Gogol's purpose in "The Overcoat." I do not understand where the metaphor of copying lies in the story beyond his job involving copying.

A central theme or purpose of Gogol's short story is to expose people's lack of compassion. He also shows that acts of inhumanity are copied by others.
People do not "see" Akaky beyond his outward appearance as a lowly copying clerk who wears an old coat. He is treated rudely by his superiors and his coworkers because of how he appears on the outside: low status and poorly dressed with imperfect social skills. Nobody truly understands him in his inner humanity.
Akaky is a copy clerk, and he loves his job. He loves copying and derives satisfaction from doing his job well. You can find a number of quotes in the story referring to how much Akaky likes his job; Gogol emphasizes this because it is important.
Getting the new overcoat made, however, comes to rival copying in capturing Akaky's interest and attention. When he gets the new overcoat, he feels his self-esteem rise. If copying made Akaky feel good internally, the coat makes him feel like a new person on the outside. It also excites other people's interest and leads to the party being thrown for him.
When robbers steal Akaky's coat, two inhumanities occur: the first is the inhumanity of stealing a coat from someone in the middle of a Russian winter. The next is the way people go back to treating Akaky as lowly when he shows up in his old, tattered coat. If success (the "success" of gaining a new overcoat) breeds success, so does inhumanity breed inhumanity.
At the end of the story, after Akaky dies, people believe the ghost of this copy clerk is engaging in copycat crimes, namely, ripping overcoats off the shoulders of living people. Akaky's role as a copy clerk ultimately entails his role as a ghost copying misdeeds done to him. This seems to reflect people's haunting anxiety that those who have been treated with little compassion will come back to "copy" inhumane treatment. 

sum_(n=1)^oo ((3n+2)/(n+3))^n Use the Root Test to determine the convergence or divergence of the series.

To apply Root test on a series sum a_n , we determine the limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
In order to apply Root Test in determining the convergence or divergence of the series sum_(n=1)^oo ((3n+2)/(n+3))^n , we let:  a_n =((3n+2)/(n+3))^n.
We set-up the limit as: 
lim_(n-gtoo) |((3n+2)/(n+3))^n|^(1/n) =lim_(n-gtoo) (((3n+2)/(n+3))^n)^(1/n)
Apply the Law of Exponents: (x^n)^m= x^(n*m) .
lim_(n-gtoo) (((3n+2)/(n+3))^n)^(1/n) =lim_(n-gtoo) ((3n+2)/(n+3))^(n*1/n)
                                   =lim_(n-gtoo) ((3n+2)/(n+3))^(n/n)
                                  =lim_(n-gtoo) ((3n+2)/(n+3))^1
                                   =lim_(n-gtoo) (3n+2)/(n+3)
To evaluate the limit lim_(n-gtoo) (3n+2)/(n+3) , we divide each term by the highest denominator  power: n .
lim_(n-gtoo) (3n+2)/(n+3)=lim_(n-gtoo)((3n)/n+2/n)/(n/n+3/n)
                      =lim_(n-gtoo) (3+2/n)/(1+3/n)
Apply the limit property: lim_(x-gta)[(f(x))/(g(x))] =(lim_(x-gta) f(x))/(lim_(x-gta) g(x)).
 
lim_(n-gtoo) (3+2/n)/(1+3/n) =(lim_(n-gtoo) (3+2/n))/(lim_(n-gtoo)(1+3/n))
                    = (3+2/oo)/(1+3/oo)
                    = (3+0)/(1+0)
                    =3/1
                    =3
The limit value L = 3 satisfies the condition: Lgt1 since 3gt1 .
Conclusion: The series sum_(n=1)^oo ((3n+2)/(n+3))^n is divergent.    

Why does Montag get sick and need to take time off work?

The story would eventually reveal that Montag himself is in possession of books. This makes him equally guilty with the woman whom they just burned for the same crime. On top of that, Clarisse, the girl who helps him find all the questions he needs to see the truth right in front of him, suddenly disappears.
The guilt, the longing and the bothering image of a burning woman, would knock any normal person out of his senses. Thus, a time off from work would be the next logical step. In this case, the time off signals the turning point, not only in the events that would follow but also in the character development of Montag. This is also the part of the story which shows the effects of society, reality and Clarisse to the decisions that he will make afterwards.

There are a couple of reasons why Montag gets sick and needs to take some time off work. First of all, during the previous night, Montag and the other firemen set fire to a woman who refused to hand over to her books. This incident has a profound effect on Montag because he starts to think that there must be something powerful contained inside books. Otherwise, why would a woman choose to sacrifice her own life?
In addition, the disappearance of Clarisse contributes to Montag's sickness. Just as Montag is going to bed, Mildred tells him that Clarisse was hit by a car four days earlier. The next morning, Montag wakes up feeling unwell. As we have seen in the story, Clarisse exerts a powerful influence over Montag because she shows him a different way of living. She makes Montag question his sense of happiness and how he feels about being a fireman.
Montag's sickness, therefore, comes about as a result of these two events and demonstrates to the reader that Montag is undergoing a considerable change in his character and values.

How did American foreign policy change as a result of involvement in Vietnam?

One of the most significant political effects of the Vietnam War was the change in American Foreign Policy. America entered the Vietnam War as the world's leading superpower but left Vietnam defeated after the longest and most debilitating war both nations had ever seen.  The war left America with a crippled economy and unfair balance of trade.  The loss of American lives was significant at 58,000 soldiers and the harrowing loss left Americans back at home divided and mistrustful of the government.  The war also damaged America's long-standing reputation as a swift, competent and powerful leader. As a result, American leaders in the 70s, 80s, and 90s were reluctant to send troops overseas unless absolutely necessary.  This reluctance, known as the United States' "non-intervention policy", still impacts Foreign Policy today as the American government continues to proceed into other countries with caution, making sure they have "sold" the American public on the need to intervene and when they believe there is a high probability of a quick, inexpensive win.

Part of America's change in foreign policy was a willingness to use special operations soldiers in advancing American interests. In an attempt to drive out the Viet Cong from the Ho Chi Minh Trail, the United States invaded Laos and Cambodia. The Viet Cong were still able to use the trail, and the American invasion destabilized these two countries, thus making the postwar refugee situation worse.
As a result of Vietnam, the American people did not wish to send troops into protracted wars. Policy makers declared that they wanted "No more Vietnams!" The military had very short, successful missions in Grenada and Panama, and the CIA provided assistance to Afghan fighters during the Soviet-Afghan War, but the American people did not want any major wars. The first major war that took place after Vietnam was the first Gulf War in which the United States used its technology and military might to overpower the Iraqi Army. This war was over in a matter of hours and was quite popular in that it had a clear objective: remove Iraq from Kuwait. The United States is still seeking out answers to fighting guerrilla soldiers (as evidenced by its actions in Afghanistan and Iraq), but since the Vietnam War, there has been more of an attempt to have a clear enemy and a clear objective to sell to the American people when it comes to foreign policy, especially in armed conflict.