Explain the use of irony in this exchange from Romeo and Juliet: - Benvolio and...

The general name given to literary techniques that involve
surprising, intriguing, or amusing contradictions, irony falls into three
categories:

1. verbal irony in which words are used
   to suggest the opposite of their usual
   meaning


2. situational irony in which an event occurs that
   directly contradicts the expectations of the reader or the
   audience


3. dramatic irony in which there is a contrast
   between what a character thinks and what the reader or audience knows to be
   true.

In Act II, Scene 1 of Romeo and
Juliet, Mercutio and Benvolio seek Romeo, whom they believe is hiding, but
because they do not know of Romeo's new love Mercutio calls to him in the name of
Rosaline:

I
conjure thee by Rosaline's bright eyes,

By her high
forehead and her scarlet lip,

That in thy likeness thou
appear to us! (2.1.19-21)

It
is dramatic irony that is exemplified in this scene as
Mercutio teases Romeo about Rosaline, not realizing that Romeo no longer is lovesick and
Rosaline's name now means nothing to him, for he is instead infatuated with Juliet. 
And, when Benvolio says,

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Come, he hath hid himself among these
trees,

To be consorted with the humorous
night.

Blind is his love, and best befits the dark.
(2.1.32-34)

his words, also,
exemplify dramatic irony as Benvolio, also, believes that Romeo is moody and hiding
because he is still upset over his rejection by Rosaline.

In The Great Gatsby, what is a quotation that shows Daisy is misled by appearances or wealth?

This question could be interpreted in two ways, both in
terms of plot and of theme. When Daisy Fay meets Gatsby in Louisville during World War
I, he is a young officer in uniform, one of many dashing young men of rank who vie for
Daisy's attention. His uniform gives him standing and respectability in her eyes. Gatsby
does not overtly lie to Daisy about his personal circumstances, but she is misled by his
appearance. Nick explains:

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. . . he had deliberately given Daisy a sense of
security; he had let her believe that he was a person from much the same strata as
herself--that he was fully able to take care of her. As a matter of fact he had no such
facilities--he had no comfortable family standing behind him . . .
.

Gatsby's uniform creates a
false appearance in that it masks his poverty and lower-class roots in North
Dakota.

Daisy is also misled by appearances when she
chooses to marry Tom Buchanan. His great fortune and membership in the upper class of
American society make Daisy believe that life with Tom will be a good life. It is not.
Although she enjoys the luxuries Tom's money provides, Daisy's life becomes endless days
of superficial activities. Hers is a hollow life without purpose, and Tom's infidelities
cause her pain and anger. In Chapter I she argues with Tom privately when Myrtle Wilson
calls their home; in Chapter VII her resentment boils over when she tells Tom, "You're
revolting." The emptiness of Daisy's life is first suggested in Chapter I when Nick
comes to dinner at the Buchanan estate. When Jordan Baker suggests they should "plan
something," Nick recalls her response:

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"All right," said Daisy. "What'll we plan?" She
turned to me helplessly. "What do people
plan?"

Daisy's life with Tom
Buchanan does not turn out to be what she had expected it to be. Once again, appearances
have been deceiving.

What does the narrator mean by “a moment of temporary mental apparition”?

Sam and Bill are obviously swindlers, confidence men, who
specialize in cheating simple rustic people out of their money with various schemes.
Both men have cultivated big vocabularies in order to impress the yokels. They are
similar in this respect to the two rapscallions in Mark Twain's The Adventures
of Huckleberry Finn who call themselves The King and The Duke but who are
really only ignorant petty crooks. Both Sam and Bill use big words inappropriately.
These are called "malapropisms." What Sam the narrator is trying to say is that Bill
expressed the idea of kidnapping a child "during a moment of temporary
aberration." Part of O. Henry's reason for portraying these two
would-be kidnappers as men who are not as smart as they think they are is to explain how
they could have made so many mistakes and gotten themselves into so much
trouble.

In Hollywood parlance "The Ransom of Red Chief"
would be called "a busted caper story." There have been many films in which crooks plan
a crime (a "caper") carefully but things start going wrong because of unforeseen
circumstances. An excellent example of a "busted caper" film is
Fargo (1996), starring William H. Macy as the man who hires a
couple of incompetents to kidnap his wife so that he can collect a million dollars in
ransom from her wealthy father.

According to
Wikipedia:

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The word malapropism comes
ultimately from the French mal à propos meaning "inappropriate" via
"Mrs. Malaprop", a character in the  href="http://en.wikipedia.org/wiki/Richard_Brinsley_Sheridan">Richard Brinsley
Sheridan comedy  href="http://en.wikipedia.org/wiki/The_Rivals">The Rivals (1775)
who habitually misused her
words.

In addition to
malapropisms, there are other misuses of language in the story. For example, Sam
says:

There
was a sylvan attitude of somnolent sleepiness pervading that section of the external
outward surface of Alabama that lay exposed to my
view.

The words "somnolent"
and "sleepiness" mean the same thing, as do "external" and
"outward."

A large part of the comedy in O. Henry's "The
Ransom of Red Chief" comes from the fact that the kidnap victim's father, whom they take
to be an ignorant country bumpkin, outsmarts the two city slickers. This sort of theme
has been a staple of American humor for many years.

What do you think Aristotle means by "pleasure proper to tragedy?"

The "pleasure" of which Aristotle speaks is more of an
appreciation of the beauty of a work of art that embodies tragedy.  I think that
Aristotle is bringing out the idea that art, while it can depict the worst of
consciousness, can be beautiful in this depiction.  For example, art can display the
most painful of conditions but do so in a manner whereby one can only express
appreciation of it.  When I speak with students about "favorite movies," I always
indicate "Schindler's List" or "Sophie's Choice."  Almost a patterned response that the
kids have upon hearing this is, "That's so depressing!  How could you like that!"  I
think that Aristotle's understanding of "pleasure" might be evident here.  When a work
embodies the principles that Aristotle attributes must be contained in an effective
work, it is in this light that tragedy can contain a level of "pleasure" for the work
has impacted the audience on both an emotional level of fully understanding the tragic
predicament of the protagonist, and has done so in an aesthetic light where its
construction has captured the audience's imagination.

What is the the degree of polynomial P defined by : P(x) = -5(x - 2)(x^3 + 5) + x^5?

To find the degree of the polynomial P(x) = -5(x - 2)(x^3
+ 5) + x^5.

The degree of the polynomial is the degree of
the highest term.

So we expand the right
side:

P(x) = -5(x-2)(x^3+5)
+x^5

P(x) = -5(x^4
+5x-2x^3-10)+x^5.

P(x) = -5(x^4-2x^3+5x-10)
+x^5.

P(x) =
-5x^4+10x^3-25x+50+x^5.

We arrange the terms on the right
side.

P(x) = x^5 -5x^4
+10x^3-25x+50

The highest term is x^5 with degree
5.

So the degree of the polynomial is
5.

How can I restate my thesis? My thesis is below.In the beginning of Arthur Miller's revolutionary play "The Crucible" there are witch trials that...

Abigail Williams and John Proctor had an affair. It seems
like you are saying that Abigail conspired to frame Elizabeth and possibly other women.
This would get Elizabeth out of the way and allow her to pursue her affair with John.
Or, if this backfired, it would at least give her some revenge on John, who has decided
to put an end to their affair. I think your thesis has to support or refute the idea
that Abigail understood the religious fervor of Salem and knew they would react
irrationally to the idea of girls dancing in the woods at night. Abigail conspired to
start hysteria of witches in Salem, hoping to replace Elizabeth as John Proctor’s wife,
or to get revenge on John for ending their relationship.

I
think this is a good thesis, but I think you might have to say that it became much
bigger than Abigail could have imagined. Maybe she did start this hysteria for revenge.
Maybe she started it to get Elizabeth arrested so she could be with John. I doubt she
could foresee how far it would go. That is something you probably should address as you
support your thesis. It doesn’t affect your thesis at all but it would help to clarify
the development throughout the play. Abigail started this thing for the reasons you’ve
mentioned. But then you need to address if she planned the whole thing or if it got out
of control. Abigail started everything but if it did get out of control, then others
also at fault.

Find the equation of the tangent at the point (x1.y1) to the curve x^m/a^m+y^m/b^m=1

The curve we have is :
x^m/a^m+y^m/b^m=1

If we differentiate the two sides we
get:

(1/a^m)(m*x^(m-1)) + (1/b^m)(m*y^(m-1))dy/dx =
0

=> dy/dx =
[-(1/a^m)(m*x^(m-1))]/[(1/b^m)(m*y^(m-1))]

The slope of the
tangent to the the curve at the point (x1, y1) is the value of the first derivative at
(x1 , y1) which
is:

[-(1/a^m)(m*x1^(m-1))]/[(1/b^m)(m*y1^(m-1))]

The
equation of the tangent passing through (x1, y1) is that of a line with a slope we have
derived above passing through the point (x1, y1)

This is (y
- y1)/(x - x1) =
[-(1/a^m)(m*x1^(m-1))]/[(1/b^m)(m*y1^(m-1))]

The
required equation of the tangent is (y - y1)/(x - x1) =
[-(1/a^m)(m*x1^(m-1))]/[(1/b^m)(m*y1^(m-1))]