Discuss Shakespeare's deviation from the conventions of the Petrarchan sonnet.

I believe that this question is asking about the structural deviations that Shakespeare's sonnets demonstrate vs. the Petrarchan sonnet format.
Let's start with a similarity and go from there. Both the Shakespearean sonnet and the Petrarchan sonnet are sonnets, which means they are both 14 lines long and written in iambic pentameter. That means each line has 10 syllables in an alternating unstressed/stressed rhythm.
In order to best show how Shakespeare changed the sonnet form, let's look at the traditional Petrarchan sonnet format. This sonnet type divides the poem into two stanzas. The first stanza is eight lines (an octave), and the second stanza is six lines (a sestet). The rhyme scheme of the Petrarchan sonnet is abbaabba, cdecde or cdcdcd. In general, the octave sets up some kind of argument, and the sestet contains the counter argument.
In contrast, the Shakespearean sonnet is made of three quatrains followed by a couplet, and the rhyme scheme is abab cdcd efef gg. In this format, the final couplet is often one of the most important pieces of the entire poem. It usually drives home some kind of conclusion about the previous stanzas. The final couplet is also well known for refuting the previous information of the preceding stanzas, depending on the sonnet in question.

int_0^3 sqrt(x^2+16) dx Use integration tables to evaluate the definite integral.

Recall indefinite integral follows int f(x) dx = F(x)+C
 where:
f(x) as the integrand
F(x) as the antiderivative of f(x)
C as the constant of integration.
From the table of integrals, we follow the formula:
sqrt(x^2+-a^2) dx = 1/2xsqrt(x^2+-a^2)+-1/2a^2ln|x+sqrt(x^2+-a^2)|
 From the given problem int_0^3 sqrt(x^2+16) dx , we have a  addition sign (+) in between terms inside the square root sign. Then, we follow the formula:
int sqrt(x^2+a^2) dx = 1/2xsqrt(x^2+a^2)+1/2a^2ln|x+sqrt(x^2+a^2)|
 Take note that we can express  16 = 4^2 then the given problem becomes:int_0^3 sqrt(x^2+4^2) dx .
 The x^2 +4^2 resembles the x^2 +a^2 in the formula. Then by comparison, the corresponding values are:  x=x  and a=4.
Plug-in x=x and a=4 on the formula, we get:
int_0^3 sqrt(x^2+16) dx =[1/2xsqrt(x^2+4^2)+1/2*4^2ln|x+sqrt(x^2+4^2)| ]|_0^3
=[1/2xsqrt(x^2+16)+1/2*16ln|x+sqrt(x^2+16)|]|_0^3
=[1/2xsqrt(x^2+16)+8ln|x+sqrt(x^2+16)|]|_0^3
Apply definite integral formula:  F(x)|_a^b = F(b) - F(a) .
[1/2xsqrt(x^2+16)+8ln|x+sqrt(x^2+16)|]|_0^3
=[1/2*3sqrt(3^2+16)+8ln|3+sqrt(3^2+16)|]-[1/2*0sqrt(0^2+16)+8ln|0+sqrt(0^2+16)|]
=[3/2sqrt(9+16)+8ln|3+sqrt(9+16)|]-[0*sqrt(0+16)+8ln|0+sqrt(0+16)|]
=[3/2*5+8ln|3+5|]-[0*4+8ln|0+4|]
=[15/2+8ln|8|]-[0+8ln|4|]
=15/2+8ln|8| -0-8ln|4|
=15/2+8ln|8| - 8ln|4|
=15/2+8(ln|8| - ln|4|)
Apply natural logarithm property: ln(x)- ln(y) = ln(x/y) .
=15/2+8ln|8/4|
=15/2+8ln|2|
Apply natural logarithm property:  n*ln(x) = ln(x^n) .
=15/2+ln|2^8|
=15/2+ln|256|  or 13.05 ( approximated value)
 

In Haywood's Fantomina, Beauplaisir is equally as important as Fantomina is. Would you say he is more or less the victim in the story? Give both sides of the argument, using specific examples to support each claim.

While it is clear that there are arguments that both Beauplasir and Fantomina can be considered victims in this story, Beauplasir's victimization seems insignificant compared to Fantomina's.
The notion of victimization requires implicitly that the victim be a victim of someone or something. Fantomina and Beauplasir are both victims of one another; Fantomina lies and deceives at the same time as Beauplasir is inconsistent with his affections and continues to leave women behind (not knowing, of course, that they are all the same woman). But far worse than the victimization Fantomina and Beauplasir suffer at the hands of one another is the victimization Fantomina suffers because of the oppressive and restrictive nature of the society that she lives in.
First, the sexual and social repression causes Fantomina to pretend to be a prostitute in the first place. She is curious about all the things she has been restricted from doing. Additionally, it is written into the norms of the society that an upper-class gentleman will have affairs with and then leave women who are situated lower down in society than they are (prostitutes, maids, etc.), regardless of the consequences to these women. In a time and place where virtue (virginity) is so important to women, it is expected that as soon as Fantomina loses her virtue, her fate will inevitably be something like what happens to her at the end of the story: pregnancy and a future in a convent.
The middle section of the story is almost liberating for Fantomina. She gains power and confidence with each iteration of her disguise. But still, while these suggestions are pushing the boundary of acceptability in prose for the time, Haywood must reign in Fantomina's liberation with a restrictive conclusion that shows she receives the consequences for breaking many of society's female social norms. By contrast, Beauplasir suffers none of these things. There are no consequences for his actions, and he is not tied to Fantomina's decisions. He is not a victim of society, making the victimization that he suffers much less significant compared to Fantomina.

I think the interesting thing about Fantomina's story is the role reversal aspect. That is, whereas in other eighteenth-century fictions (Richardson's Pamela, for instance) the story is about a male seducer seeking to corrupt an innocent woman, here the woman plots to present herself in different guises to her lover, at once gratifying her sexual desires and exposing his inconstancy. In this sense Beauplaisir can be thought of as a victim—he is misled—but it is hard to have much sympathy for him. It is also true that in the end, Fantomina pays the price for her subterfuge: when she is found to be pregnant, Beauplasir is named the father, but it is the girl who is punished, by being banished to a convent. So, in that sense, it is the girl who is the victim, in that she is punished for indulging in the same sexual gratification as Beauplaisir.

The character of Beauplaisir in Eliza Haywood's Fantomina can be seen as both a victim and a villain. Fantomina herself victimizes him: she is in disguise when she meets him and sleeps with him and never chooses to be honest about her true self. Instead, she continues to be his lover while playing the character of a prostitute. When he seems to be moving on, she creates a succession of new disguises, including a widow, a maid, and a mysterious masked woman, each of which lures him again into bed. When she eventually becomes pregnant, he is summoned to her hospital bed, but he does not recognize her as her true self, and so it seems to be a ploy to force him to support a strange woman financially.
However, Beauplaisir does have many villainous character traits. He attempts to discard a series of lovers when he grows tired of them, unaware that they are all the same woman.
Beauplaisir's ignorance is not evil but shows a lack of attention and intelligence that makes him simultaneously a villain and a victim.

In the movie called The Crucible the church and court both state all liars will be damned, but only God can tell who the real sinners are. What does this mean? What are they trying to say ?

The movie of The Crucible is a film version of a play by Arthur Miller. I should note that close analysis is much easier if you read the text of the play.
Miller wrote the play as a critique of the ideologically grounded persecutions of people suspected of being communists or sympathizing with them in the United States in the 1950s. He equates religion with other forms of persecution grounded in narrow-minded ideological certainties. 
Miller's argument here is that human beings should not attempt to enforce divine justice because they lack divine omniscience. In other words, within Christian theology, it is believed that God knows people's innermost hearts and thus can judge them on the basis of their ideas and feelings as well as actions. Human beings on the other hand, whether affiliated with state or church, lack such knowledge and thus cannot and should not condemn people on ideological grounds.
For Miller, both church and state could condemn someone for specific acts such as murder or assault, but not for heresy or other beliefs as questions of belief involve understanding people's souls, something that God may be able to do but humans can't manage. 

Who was the first Secretary-General?

The first Secretary-General of the United Nations was the former Norwegian foreign minister Trygve Lie. He served in this capacity in London, as this was where the Norwegian government-in-exile was based after the German invasion and occupation of Norway. After the war, Lie became a leading figure in the establishment of the United Nations, of which he was elected the first Secretary-General in 1946. Lie's term of office was marked by numerous diplomatic crises such as the Berlin blockade and the Korean War. Lie was criticized for his handling of these and numerous other challenges he had to face. Under attack from both the Soviet Union and from hard-line anti-Communists alike, Lie's position as Secretary-General became untenable, and under mounting pressure he resigned his post in 1952.

Why did Sal's father start chipping away at the plaster wall in their house in Bybanks, Kentucky?

Sal tells us this story at the end of the first chapter, called “A Face at the Window.” She says that when they lived in the old farmhouse, her parents were taking the time to restore it. This explains why her father was “chipping away” at the plaster wall in the living room, at first. When he got the news that his wife (Sal’s mother) was not coming back to Kentucky, “he pounded and pounded on that wall with a chisel and a hammer,” Sal says. This time, he was probably taking out his anger, frustration, and grief on the wall. He uncovered a brick fireplace hiding behind it, too. This quick vignette foreshadows the truth unspoken throughout most of the book—the mystery of what happened to Sal’s mother. Here, Sal also uses it as a metaphor in the telling of her own story:

The reason that Phoebe’s story reminds me of that plaster wall and the hidden fireplace is that beneath Phoebe’s story was another one. Mine.

Is Miss Brill a believable character?

I would suggest that she is. But it's important to see Miss Brill as she sees herself: as a character in a play. Miss Brill is enjoying a Sunday afternoon in the park. Everything seems perfect; the band is playing beautifully and everyone seems to be in their rightful place, acting out their roles as if part of a gigantic stage production. Miss Brill, too, is playing her part in the enveloping human drama, expressing her eccentric individuality through the unseasonal wearing of fur.
Sadly for Miss Brill, her perfect day at the park, her own private performance, is ruined when the two lead "actors" unexpectedly break character. Miss Brill's subsequent retreat to a grim life of loneliness and isolation is sadly all-too-common, especially among people of a certain age. This is what makes Miss Brill such a believable character. Most people will doubtless know someone just like her.
Miss Brill's eccentricities help to make sense of an often senseless world. This world can be a harsh place sometimes, and so it's often necessary for people to indulge in little fantasies to enable them to cope with life's slings and arrows. Some people may find Miss Brill a somewhat absurd, pathetic character. But she, like her fantasies, is completely harmless and unthreatening. And before we judge her too harshly, we should stop to think of how often we ourselves engage in role play, such as when we go online, for example.