In Pride and Prejudice, what is Mr. Wickham's motivation especially toward Lizzy, and how does it change through the story, if at all?

Mr. Wickham's primary motivation in the novel is to marry
for financial security.  He is arguably the most selfish character in the novel.  When
he is first introduced he is presented as a charming man who has definite romantic
interest in Elizabeth, but once it becomes clear that she will not have much of an
inheritance, he quickly shifts his attentions to Miss King who has a comfortable amount
of inheritance in the bank.  Lizzy isn't all that interested in Wickham and actually
defends this action to her aunt when they talk about what Wickham has done.  Lizzy fully
understands the necessity of financial security, even if she isn't willing to marry for
it.  At this point in the novel she still believes Wickham's story that Darcy hasn't
been fair in regards to his inheritance from the Darcy
estate. 

As the novel progresses we learn that the
relationship with Miss King has fallen apart and that Lydia is very interested in
Wickham.  Unfortunately, Lydia is very naive and foolish -- she runs off with Wickham
and creates a complete scandal.  Wickham has no intention of marrying a Bennet daughter
-- they have no money!  Wickham only agrees to marry Lydia when Darcy bribes him with an
incredible amount of cash and a commission in the military (higher rank).  By this time,
Elizabeth knows that whole story of Wickham's lies about Darcy, and she is appalled that
her sister now has to be married to the man, but she is relieved that a family scandal
has been avoided.  When she later learns that the marriage came about because of Darcy,
her feelings for Darcy are cemented.  She ultimately marries him for love and tolerates
Wickham as a brother-in-law.

If x=1 is the root of 5x^3-4x^2+7x-8=0, what are the other roots of equation? (use the remainder theorem)

If x = 1 is the root of polynomial 5x^3-4x^2+7x-8, then
the polynomial is divided by x - 1.

We'll apply reminder
theorem:

5x^3-4x^2+7x-8 = (x-1)(ax^2 + bx +
c)

We'll remove the
brackets:

5x^3-4x^2+7x-8 = ax^3 + bx^2 + xc - ax^2 - bx -
c

We'll combine like terms from the right
side:

5x^3-4x^2+7x-8 = ax^3 + x^2(b - a) + x(c - b) -
c

Comparing, we'll get:

a =
5

b - a = -4

b = a -
4

b = 5 - 4

b =
1

c - b = 7

c = b +
7

c = 1 + 7

c =
8

We'll get the quotient:

5x^2
+ x + 8

We'll put 5x^3-4x^2+7x-8 =
0

5x^3-4x^2+7x-8 = 0 <=> (x-1)(5x^2 + x + 8)
= 0

5x^2 + x + 8 = 0

We'll
apply quadratic formula:

x2 = [-1+sqrt(1 -
160)]/10

x2 = (-1 +
isqrt159)/10

x3 = (-1 -
isqrt159)/10

The other 2 roots of the
polynomial are: { (-1 - isqrt159)/10 ; (-1 +
isqrt159)/10}.

I'm doing a map for The Great Gatsby. I need to know where the following are: Long Island and Tom and Myrtle's Love Nest.any information, would...

Long Island is a long, finger-shaped island right off the
shore of New York City to the southeast. It is east of Manhattan. It is surrounded by
the Atlantic Ocean. If you look on a map, you will see it jutting out to the east. There
are a lot of Indian named towns on Long Island (Patchogue, etc.). There are four
counties on Long Island. It is kind of a bedroom community to New York City. Many people
that live there work in "the city."

Tom and Myrtle's love
nest was in Manhattan, which is one of the five bouroughs of New York City. If you look
on a map of New York state, you will see Manhattan on it. Manhattan is where the Twin
Towers used to be (lower Manhattan). East and West Egg were both located on Long
Island.

What is the climax in The Shakespeare Stealer?

The climax of this book is of course when Mr. Armin and
Widge confront Falconer at the point when he has finally gained the copy of
Hamlet that he has been wanting for so long. The duel that Mr.
Armin and Falconer fight occurs in Chapter 27, and it represents the climax of the plot
because this is the conflict that the entire text has been leading up to as Widge
becomes more and more involved in the players and begins to like acting more and more.
The way in which this duel is the climax is indicated through the following quote where
Widge contrasts the fake weapons they use in theatre with the real weapons that are used
in reality:

But this was a grown man's game, and the winner
would not be the one whose weapon survived but the one who lived. And, I thought,
clutchign the play book to my chest, if that one proved to be Falconer, then what would
become of me?

Of course, this climax also results in the
discovery that Falconer himself does not exist, and that he is just another part played
by Simon Bass.

Why is a monument being erected by the State (the government) to the Unknown Citizen? Who is the speaker of this poem?

The monument being erected for the Unknown Citizen is
probably similar to the Tomb of the Unknown Soldier and other monuments praising those
who have fallen and died in the line of duty.  It should be a tribute to those fallen
who could not be identified by name. 

However the speaker
in this poem is being more sarcastic.  Instead of truly being an unknown soldier because
of a violent death in war, the citizen is unknown because of a lack of indivuality or
importance in modern society.  He is simply referred to as a number which is mentioned
in the first two lines:

readability="5">

To JS/07/M/378/ This Marble Monument
Is
Erected by the State

The
speaker is an unnamed commentator who is trying to use veiled sarcasm to show the idea
that people have lost their individuality and are now being lumped into a pile of
conformity. 

The Unknown Citizen is such a person.  His
monument is being erected to celebrate his life, his service to his community, his
family, his responsible nature, and the like.  His days are filled with the monotony of
filing insurance papers, working and purchasing approptiate middle-class
items.

The last line of the poem, however, suggests, the
narrator's true them. 

readability="7">

Was he free? Was he happy? The question is
absurd:
Had anything been wrong, we should certainly have
heard

Is this living "below
the radar" idea, living as drones, truly what makes a person alive?  Through the
sarcasm, the reader understans the answer - NO.

What does Thoreau say about a man keeping pace with his companions?This is an extremely important question about Thoreau's Walden Please...

Henry David Thoreau was himself a man who "marched to the
beat of a different drummer."  For him, and for the other Transcendentalists,
individualism was of paramount important.  Another Transcendentalist, Ralph Waldo
Emerson reiterates this precept of individualism in his
line,

Do not
go where the path may lead, go instead where there is no path and leave a
trail.

Like Emerson,
Thoreau emphasized the importance of nonconformity if one would be an individualist. 
When he goes into the woods to live, as he describes in Walden,
Thoreau observes that people who have fewer possessions have more freedom because they
are not bound to care for what they own.  Instead, they can travel more easily, and need
not worry about anything.

The individual may more easily
communicate with Nature, as well, intuitively experiencing it at his own pace.  In
Chapter 8, "The Village," Thoreau writes that he enjoyed a small amount of gossip, but
too much "numbed the soul."  On one visit to town, he was incarcerated for refusing to
pay taxes, protesting because of his position on slavery.

How does the Thomas Hardy convey his feeling of loss in "The Voice"?

"The Voice" comes as one of a series of poems which
expresses Hardy's attempt to come to terms with the death of his wife and the sense of
immense grief that he feels at her loss. Interestingly, we can link these poems in with
the tone and style of the rest of Hardy's poetic work, identifying similarities in the
way that his work always seems to oscillate between hope and despair, between joy and
depression. In this poem, Hardy tries to recapture Emma's presence and existence,
imagining that he hears Emma's ghostly voice calling to him and saying that she is once
again the young woman that he courted. However, after this tantalising moment of
rapture, Hardy is plunged back into his despair and grief, thinking that it is just the
breeze taunting him.

On key way that the poem emphasises
the feeling of loss of the speaker is through the presentation of the landscape. Note
how its description enhances Hardy's emotional desolation, especially at the end of the
poem. We have returned from the attractive and inspiring picture of Emma in her
pale-blue dress back to the bleak landscape of death and
winter:

Thus
I; faltering forward,

Leaves around me
falling,

Wind oozing thin through the thorn from
norward,

And the woman
calling.

Having had the
respite that his vision has afforded him, Hardy is now left alone once more. Note how in
this final stanza the metre breaks down completely, with an increased number of
stresses. In effect the rhythm stumbles, enacting the "faltering" steps of the aged
speaker as he is forced to cope with the hopes of reunion with dead wife being
destroyed. Clearly, these lines place stress on the effects of natural change and decay,
mirroring the same processes at work in human experience as Hardy is left still with the
woman "calling" in his own mind and he is left to struggle alone, haunted and desolate,
just as the landscape is around him.

How is chapter one in The Kite Runner effective in leading the story to the major themes?

Many of the themes in Hosseini's work is laid for the
reader in the exposition of the novel.  The idea of "being good" and "atonement" are
both revealed in the opening chapter.  The idea of a world before 9/11 and one after it
is brought out in Amir's own state of being in the world.  While it does not focus on
this, it is present from a personal point of view.  The life Amir once led is suspended,
to a certain extent, and the idea of being able to seize upon a moment, an instant,
where some resolution is present is evident.  At the same time, it seems as if Amir is
controlled by some other force, perhaps subconscious, to have to to return to
Afghanistan.  It is revealed that there is a deep and profound connection between Amir
and Afghanistan, something conveyed in the opening chapter of the
narrative.

How did the author use descriptions of settings, events immediately prior to the trial to build and intensify a mood of suspens?Everything that...

Harper Lee used a variety of scenes and sub-plots to set
up the drama of the Tom Robinson trial in To Kill a Mockingbird. In
Chapter 14, Jem and Scout feel the stares and hear the gossip from the people of Maycomb
concerning Atticus defending a Negro. Lee adds the runaway Dill to the mix, giving
Atticus one more problem to ponder before the trial. In Chapter 15, Atticus meets with a
group of concerned citizens who warn him about something that Jem and Scout don't quite
understand. When Atticus heads to the jail later that night, the children follow,
setting the stage for their dramatic rescue of their father from the prospective lynch
mob.

The day of the trial is narrated in great detail by
Scout. It is obviously not a normal day in Maycomb. Throngs of people arrive for the
trial: Religious zealots, out-of-towners, and Negroes make up just some of the people as
"the county went by." Women argured in the street, and the "courthouse square was
covered with picnickers" before Jem, Scout and Dill decided to make their appearance as
well.

In "Babylon Revisited," in what way could economic and domestic elements be considered the heart of the story?

The heart of a short story lies in its central conflict.
The central conflict in "Babylon Revisited" exists between Charlie Wales, Fitzgerald's
protagonist, and Marion Peters, his former sister-in-law. The nature of their conflict
is both domestic and economic, much of it rooted in the story's antecedent
action.

In previous years, Marion, her husband Lincoln,
Charlie, and his wife Helen [Marion's sister] had all lived in Paris, Americans far from
home. Charlie and Helen had been drawn into the decadence of Parisian life, while Marion
and Lincoln had maintained a conventional lifestyle in keeping with American values and
tradition. Theirs had been a stable marriage, while Charlie and Helen's marriage had
been turbulent, fueled by Charlie's alcoholism and Helen's infidelity. Marion felt great
contempt for Charlie's behavior in Paris during those days and her feelings remain
unchanged throughout the story. Furthermore, she continues to blame Charlie for her
sister's tragic death. The contrast between Charlie's former wild Parisian lifestyle and
the stable serenity of the Peters' home plays an essential role in the story's
developing plot.

When Marion has decided to return custody
of Honoria to her father, two of Charlie's friends from his old days in Paris appear at
the Peters' apartment. Their drunken state reminds Marion of the life Charlie had once
lived, and their physical presence in her peaceful home emphasizes the contrast between
that lifestyle and the Peters' stable, conventional way of life. Convinced that Charlie
has not reformed, she changes her mind; she will keep
Honoria.

The conflict between Charlie and Marion is also
rooted in the economic differences between them. As a wealthy American in Paris, Charlie
had been profligate, reckless and wasteful with money. As he and Helen had enjoyed the
comforts of wealth, Marion and Lincoln had lived within very limited means. Marion's
resentment has remained very much a part of her relationship with
Charlie:

When
you were throwing away money we were living along watching every ten
francs.

To further exacerbate
this conflict, when Charlie returns to Paris to reclaim his daughter, he has regained
his lost wealth. Once again he is a rich man, and Marion's continuing bitterness is
evident:

I
suppose you can give [Honoria] more luxuries than we can . . . I suppose you'll start
[throwing away money]
again.

Charlie's response is
significant as he makes an attempt to defend himself:

readability="9">

Oh, no . . . I've learned. I worked hard for ten
years, you know--until I got lucky in the market, like so many people. Terribly
lucky.

Charlie reminds Marion
that at one time he had worked hard, thus aligning himself with the American values she
and Lincoln have lived by; there is some decency in his character, Charlie suggests. His
great wealth, he reminds her, came from simply being lucky. The unspoken message is that
Charlie did not become wealthy because he is superior to Marion and Lincoln. In effect,
Charlie is asking Marion not to blame him because he had money and she did
not.

The sharp contrast between Charlie and Marion in terms
of domestic and economic elements lies at the heart of the conflict between them and
leads to the story's resolution. Charlie will leave Paris, once again, without his
daughter.

How does deception lead to misery, while enlightenment relieves suffering in Twelfth Night?

Since Twelfth
Night is a comedy, there is only one instance of true misery
and that is the wicked joke played upon Malvolio. This much debated joke or prank ties
into one of the thematic concerns of the play: vanity that may inspire
malevolence.

Olivia is consumed by vanity that leads her to
mourn endlessly for her deceased brother and scorn Orsino. Orsino is consumed with
vanity that leads him to endlessly opportune Olivia to be his wife and disregard her
wishes. Both are "sick of self-love," to borrow Olivia's words describing Malvolio.
Malvolio suffers from his own outrageous vanity that makes him "sick of self-love" and
truly inspires malevolence in others.

It is this sickness
of vanity in Malvolio that leads Sir Andrew, Fabian, Maria, and Sir Toby to "gull"
him--or fool him--in Act IV, scene ii. Malvolio knows real misery, which is inflicted
through animosity from Sir Toby and Sir Andrew and as revenge from Fabian, who resents
Malvolio because he caused Fabian to fall out of favor in Olivia's
estimation:

I
would exult, man: you know, he brought me out o'
favour with my lady about a
bear-baiting here.

The
deception these perpetrate against Malvolio leads to the misery of his humiliation and
his imprisonment, for which Olivia promises punishment will be delivered: "Thou
[Malvolio] shalt be both the plaintiff and the judge / Of thine own
cause."

Conversely, enlightenment relieves suffering once
Sebastian's survival is revealed and Viola's disguised identity is revealed. Prior to
this enlightenment, Antonio believes Sebastian has betrayed him: "That most ingrateful
boy there by your side." Olivia believes Cesario has forsaken her: "Ay me, detested! how
am I beguiled!" Yet suffering is relieved when all are enlightened. Not only that, but
the principal players have cause for rejoicing after
enlightenment.

1. What does Jeanne imagine hatred looks like? A. Heavy Stone B. A dark cloud C. A puff of smoke D. A dense fog

You can find the answer to this question in Chapter 19 --
the one entitled "Reentry."  This chapter describes what happens as the Wakatsuki family
is allowed to leave the camp at Manzanar.

Papa buys a car
and the family heads back to Los Angeles.  As they do that, they start to worry about
what kind of a reception they will get from all the white people.  They worry that they
will be hated.  Jeanne imagines that the hate would look like a "dark, amorphous cloud"
that would come down on them.

So the best answer of these
would be B -- a dark cloud.

What is the response elicited in the reader in "Through the Tunnel" by Doris Lessing?

I think it is clear that Lessing wants us to feel that
Jerry has been very brave and strong in terms of going through his own coming-of-age
initiation. He has proved to himself that he is no longer a child, dependent on his
mother, and has grown up. This response is of course linked to the central theme of the
story, which is the way that we all need some kind of coming-of-age initiation which
shows both ourselves and others that we are no longer children. At the end of the story,
we see the mother surprised at an easy victory as she expected a "battle of wills" with
her son. However, for Jerry, now that he has completed his own self-imposed task, we are
told that "it was no longer of the least importance to go down to the bay." We as
readers are left with the impression that now Jerry has done what he set himself to
complete, he does not need to exert his independence in the same way as he did, going by
himself to the "wild bay." We are left with an impression of a boy who has grown
up.

In " Sweat" By Zora Hurston, is Delia right to let Sykes die at the end of the story ?

Delia Jones has been married to Sykes for fifteen years.
After two months of marriage, he gave her the first brutal beating. She works hard and
he spends her money.  He demeans her, harasses her, and now he flaunts his mistress
around town. 

This is the life of the protagonist in the
Zora Neale Hurston story "Sweat." Delia's habitual shyness and sensitivity have allowed
Sykes to dominate her for too long.  She has just about reached her limit. Her tears,
her sweat, her blood--these were what she had given to her
marriage.

Delia worked as a wash woman for the white folks
in a town nearby. Her routine began on Sunday evening after church.  Sykes would always
come in and mess up her piles of clothes or make light of her job working for the white
people.

Ah
don't keer if you neer git through. Ahyhow, Ah done promised Gawd and a couple of other
men. Ah ain't gointer have it in mah house.  Don't gimme no lipneither, else Ah'll throw
em' [the white people's clothes] out and put mah fist up side yo' head to
boot.

Delia was afraid of
snakes.  Sykes knew this, and he began his ploy to get Delia out of the house or to have
her dead.  He really did not care as long as he could move his mistress into the house.
 

• First, Sykes uses a bull whip which looks and
  feels like a snake around Delia's neck. 


• He brings a box
  in saying it is a present. Delia opens it and finds a huge
  rattlesnake. 


• Sykes leaves the snake in a box and tells
  her that it is a pet.


• The rattlesnake begins to move
  around and make noises. 

Delia tells Sykes to
get it out of the house before she gets back from church.  When she comes back, the
snake is gone from the cage.  Delia thinks he has taken the snake with him. She begins
her washing. She opens the wash basket, and there she finds the snake placed there by
Sykes to bite Delia.

Delia runs from the house and hides in
the garden.  Later, Delia sees Sykes tearing up the wire cage to get rid of the
evidence.  He peeks in the window to see if he can see or hear anything.  Slowly, he
opens the door and goes in hoping to find Delia's body; but instead, he finds an angry
rattlesnake. Delia hears some animal screams and knows that Sykes has been
bitten. 

In answer to the question, why does Delia not save
Sykes? He has treated her like a slave and worse for fifteen years.  He placed a snake
in her wash basket to bite her.  If she goes in there, Delia may be bitten herself.  It
is too late to save Sykes from the snake now. 

The reader
understands that Delia will probably not have a regret in her body when she attends
Sykes' funeral.  He went too far!

1. What is the difference between ethnic and social diversity? 2. And why does diversity matter? Help-Questions for question 2 : What is the...

In response to the second question: with more diversity
often comes more discrimination.  Discrimination is treating different things (or
people) differently.  It often takes the form of dislike/hatred and
superiority.  Diversity is difference.

An example of this
prevalent right now in North Carolina (and other states I'm sure) is the discussion in a
few school districts of re-drawing the lines for which neighborhoods feed into which
schools.  What is being said is that they are trying to increase diversity by drawing
from a variety of different socio-economic neighborhoods.  One of the reasons given is
to raise the average test scores of each school (as low socio-economics is statistically
linked to lower test scores).  What is not being directly said, but certainly implied,
is that the "rich white" schools don't want the integration.  It is the mostly white
parents of the upper class neighborhoods who are most opposed to
redistricting.

It is a wonderful thing when increased
diversity is met by open-mindedness and tolerance.  Too often however, increased
diversity only brings out the worst in homogenous cultures.

What news does Scout overhear about Atticus' defending Tom Robinson? Does it give her any comfort?In Chapter 16.

Having spent a tense night before the trial by standing up
to the angry mob, Atticus makes his way to the courthouse.  Outside this courthouse,
Scout overhears the old men in khaki pants and white shirts with suspenders
talking,"resentful of the interruption of their comfortable
routine."

Scout overhears one say that the court appointed
Atticus Finch to defend Tom Robinson.

readability="6">

'Yeah, but Atticus aims to defend him.  That's
what I don't like about
it.'

Scout reacts  to this
news by saying that it puts a different light on things.  Atticus could have used this
as an excuse. But, she is baffleded by the town's being upset with him and having come
as a mob last evening:

readability="9">

He had to, that's why he was doing it, equaled
fewer fights and less fussing.  But did that explain the town's attitude?  The court
appointed Atticus to defend him.  Atticus aimed to defend him.  That's what they didn't
like about it.  It was
confusing.

While this news is
confusing to Scout, it is not to the reader.  For the conventional wisdom is that Tom
Robinson should be convicted because he is a black man who interfered in the lives of
white people.  He simply had no business on the Ewell property.
Period.

According to Hindu beliefs, what river brings life to its people?

The holy river Ganges, originating from the Gangotri
glacier in the Himalayas, is believed to be a source of life to the Hindus in India. The
river is popularly called Ganga which is the name of a goddesss appearing in the epic
Mahabharata.

In popular belief, bathing in the river leads
to remission of sins and attainment of salvation. The Gangetic basin has been extremely
fertile, and thus the river is associated with agricultural prosperity. So many Hindu
pilgrimages such as Rishikesh, Hardwar, Varanasi & Allahabad are located in the
shore of the river.

It is said that the river used to flow
in the heavens, and was ordered to go down to earth. Forceful descent of the river might
have washed the earth away. Lord Shiva broke the fall of Ganga by capturing her in his
mighty locks.

Shakespeare explores the complex nature of revenge in the tragedy, Hamlet.Discuss with reference to the differences between the three sons whose...

This is a very complex task that you have been given.  In
order to organize your thoughts you need to do some brainstorming about each of the
three men and think about how each of them behaves in regards to his desire for
revenge.  The three men are all foils of each other, and the theme of revenge is what
ties them all together.

Ask yourself the following
questions for each of the men:

1.  How did his father
die?

2.  What actions is he taking to exact
vengeance?

3.  What does he say that reveals his attitude
about the need for revenge?

4.  What is the final result
for each of the men?

Here are a few things to consider for
each of the characters.

Laertes:  His father has been
murdered by Hamlet and he storms back from France ready to kill those responsible.  He
has a reckless attitude about the vengeance, claiming "grace and conscience to the
profoundest pit."  He has no thought of loyalty to the throne or to Heaven.  He is
willing to damn his soul in the process of
revenge. 

Fortinbras:  His father was killed several years
earlier in a battle against King Hamlet.  Fortinbras has waited until an opportune time
to seek his vengeance.  Now that King Hamlet is dead, he sees that Denmark may be weak,
so he gathers up a list of mercenaries (not the lawful army of Norway) to strike out. 
He is dissuaded from attacking Denmark by his Uncle/King, but he is still on the hunt
for restoring honor as evidenced by his battle with
Poland.

Hamlet:  His father was killed by his uncle, and he
is informed of this by the ghost of his father.  He swears to get revenge, but wants to
assure himself of Claudius's guilt before he does anything.  He is concerned for his own
soul.  With all of this he is slower and more thoughtful to act.  He recognizes even in
himself that he might be overthinking and losing the name of action, but he can't help
his nature. 

In the end, Laertes is dead because he let
himself be drawn into a dangerous plot with Claudius and the whole plan backfires. 
Hamlet is dead because he didn't kill Claudius when he had the chance, and that allowed
him to live on and plot Hamlet's death with
Laertes.

Fortinbras is the only one to survive and with
"defeated joy" he claims the throne of Denmark.  In the play, Hamlet tells Horatio that
he admires the man who is the best mix of "blood and judgement."  He is speaking of
Horatio in the speech, but perhaps the line foreshadows the ending of the play.  Laertes
has too much blood (passion, energy); Hamlet has too much judgement (thinking,
philosophy).  Does Fortinbras then, in some way, have the best balance of the two in
order to accomplish his goals?

I can't figure out if Nick has real feelings for Jordan or if he just wants to date a girl whom he admires in The Great Gatsby; which is it?

Jordan Baker certainly
intrigues Nick Carraway. As an "innocent" from the Midwest,
Nick is unused to meeting worldy-wise females such as Jordan. When he first sees her at
Daisy's house, he becomes fascinated with her voice and her cool manner (the
stereotypical "hard-to-get" appeal). Later, though, as Nick learns more about New York's
Old and New Money society, he realizes how "incurably dishonest" Jordan is. He notes
that she lies on several occasions, cheats at golf, and drives
recklessly.

At the novel's end, Nick seems to possess
sympathy for Jordan and guilt regarding his distancing himself from her after Gatsby's
death. My take has always been that Nick did not intentionally use Jordan and then
"drop" her as she claims. Rather, I think he was caught up in the idea of her and then
found her and her crowd repulsive when he realized that she was not much different from
Tom and Daisy who smash up people's lives and then retreat into their "cocoon of
wealth."

Do the values of polynomials go on infinity or stop at a certain value?

A polynomial is an expression of finite length formed of
variables and constants  using only operations of addition, subtraction, multiplication
and non-negative whole number exponents. Some examples are
:

p(x) = a0+a1x+a2x^2+a^3+.....an*x^n, is a polynomial is a
sigle vwriable with n terms.

p(x) = x.  A polynomial with a
single term . (Alsocalled monomial).

p(x) = a+bx.  Also
called binomial.

The following are not
examples:

p(x) = 5/x. Reason 1/x or x^(-1) has no
non-negative whole number exponent.

p(x) =  x^2+ x^3/2. The
second term has an exponent which is not a whole
number.

Question:

"Do the
value of a polynomial go on infinity ?..." Hope  you mean whether the polynomial goes on
increasing and approaches infinity as x tends to
infinity.

To decide whether a polynomial increases or
decreases depends on the leading term (or the term with highest exponent) and its
coefficient. If the coefficient of the leading term is positve, the polynomial increses
otherwise it decreases along with x.

The polynomial 
aproaches infinity as x --> infinity if the leading term has a positive
coeffcient. It aproaches minus infinity as x-->infinity ,if the leading term has
a negative coefficient. A plynomial p(x) cannot go for a definite limit when the x (or
the variable) approaches plus or minus infinity.(Please do not get confused with
convergence of a series for |x| <1 and  limit of the nth term a, x^n for large
n). P(x) does not take a finite limit as x--> infinity (or minus infinity).
unless it is polynomial with only a constant
term.

Example : p(x) = x approaches infinity
as x-->inf.

p(x) = x^2  - x approaches ifinity as
x-->plus ifinity or x --> minus infinty, as the  term is x^2 has a
positive coefficient and x ^2

Solve for x: 16^2 + (7 - x)^2 = 22- (2x/5)^2

The equation you gave is : 16^2 + (7=x)^2 = (22-
(2x/5)^2

I think it should be 16^2 + (7 - x)^2 = 22 -
(2x/5)^2, the appropriate changes have been made.

16^2 + (7
- x)^2 = 22 - (2x/5)^2

=> 16^2 + 49 + x^2 - 14x = 22
- 4x^2 / 25

=> (305 + x^2 - 14x)* 25 = 22*25 -
4x^2

=> 305*25 + 25x^2 - 350x = 550 -
4x^2

=> 7625 + 25x^2 - 350x = 550 -
4x^2

=> 29x^2 - 350x + 7075 =
0

x1 = [-b + sqrt (b^2 - 4ac)] /
2a

=> x1 = [ 350 + sqrt ( 350^2 -
820700)]/58

=> x1 = [ 350 + sqrt (
-698200)]/58

=> x1 = 350 / 58 + i* (10/58)*sqrt
6982

x2 = 350 / 58 - i* (10/58)*sqrt
6982

The required solution of x is 350 / 58 +
i* (10/58)*sqrt 6982 and 350 / 58 - i* (10/58)*sqrt
6982

What depresses Holden?He is always depressed about things, but what is the truth behind all of these little things that depresses him?

A. "Now he's out in Hollywood, D.B., being a prostitute.
If there's one thing I hate, it's the movies. Don't even mention them to me"
(2).

1.   So begins Holden Caulfield’s caustic assault on
the Hollywood studio, a symbol of burgeoning 1950s
materialism and artistic
hypocrisy and, closer to home, the corruptor of his brother's
fiction.

2. Since Catcher in the Rye
was published in 1951, Salinger has always refused film rights to his work, especially
his highly demanded novel, saying in short that Holden Caulfield wouldn't like
it

3. Paradoxical love/hate relationship: Holden rarely
misses a chance to see a movie

4. After Maurice punches
him, Holden role-plays a movie gangster pretending to be shot in the gut, a masochistic
homage to Film Noir

5. But what caused Salinger to turn his
back on film was the 1950 Samuel Goldwyn Studio release of My Foolish
Heart, based on his New Yorker story, "Uncle Wiggily in
Connecticut"

6. Salinger’s agent received bid from Steven
Speilberg

B. Holden hates autobiographical details about
his childhood and psychoanalysis.  He therefore, hates the adult world
intruding on childhood.

readability="10">

“If you really want to hear about it, the first
thing you’ll probably want to know is where I was born, and what my lousy childhood was
like, and how my parents were occupied and all before they had me”

C.
Holden is also depressed by the old World: he's Anti-European: “…and all that David
Copperfield kind of crap” (Dickens)

1.     most European
characters define themselves in context of family

2.    
Holden is saying that he doesn’t define himself with others or the past (birth of the
American rebel)

a.     Not defined by
family

b.     Not defined by
society

c.     Not defined by old world
values

d.     Not defined by old
literature

e.     Not defined by old
movies

D. Holden is depressed
by “Phonies”

1.     Glad-handing adults
(headmaster)

2.     Over-sexed teens
(Stradlater)

3.     Pretentious snobs
(Luce)

4.     Celebrity-obsessed girls (in Lavender
room)

5.     Materialistic artists
(D.B.)

What is an example of parallelism in Brutus' speech?

In Act III, scene ii of Julius
Caesar, Brutus uses much parallelism (parallel construction: using the same
pattern of words to show that two or more ideas have the same level of
importance.)

He begins his speech
thusly:

Then
follow me, and give me
audience, friends.

Notice the
repetition of "me" in the object placement in both
clauses.

Later, he says:

readability="7">

Those that will hear
me speak, let 'em stay here;
Those that will
follow Cassius, go with
him;

Notice the repetition of
the "those that will" at the beginning of each
clause.

Still later, he returns to the "me" as object
coupled with the "that you may":

readability="13">

hear me for
my
cause, and be silent, that you may hear:
believeme
for mine honour, and have respect to
mine honour, that
you may believe:
censure me in your wisdom, and
awake your
senses, that you may the better
judge.

The speech builds as
the level of parallelism increases.

Find solution to exercise:What is integral of (cos x)*(e^2x)?

let f(x) = cosx*e^2x

We need
to find the integral of f(x).

==> intg f(x) = intg
cosx * e^2x dx

We will use partial integration to
solve.

Let us assume that:

u=
e^2x   ==>    du = 2e^2x dx

dv = cosx dx 
==>    v = sinx

==> intg udv = u*v - intg
vdu

                     = sinx*e^2x + 2 intg sinx*e^2x
dx.............(1)

Now we will apply the rule
again.

Let u = e^2x  ==>   du
2e^2x

      dv = sinx dx  ==>    v =
-cosx

==> intg sinx*e^2x dx = -cosx*e^2x +2 intg
cosx*e^2x dx

==> But we know that intg cosx*e^2x dx
= intg udv

==> intg udv = sinx*e^2x + 2[
cosx*e^2x -2intg udv]

==> intg udv = sinx*e^2x +
2cosx*e^2x -4intg udv.

==> 5intg udv =
sinx*e^2x +2cosx*e^2x

==> intg udv =
e^2x ( sinx+2cosx) / 5

What is a character analysis of Bob, Don, and Teach in the story American Buffalo by David Mamet?

David Mamet's play American Buffalo
can be said to be a character study of three different types of men. The personalities
of Teach, Don and Bobby are revealed under the pressure of Don's confined and cluttered
junk store.

Teach appears to be the dominant figure of the
trio, vivid, volatile and eventually violent.  He wants to be the leader of the pack but
is always in competition with Don for the position. Teach respects Don more than he
likes him; (there is also a sense that he physically fears the store owner).  He
despises Bobby, and he resents -- and is, possibly, jealous of -- Don's strong emotional
tie to the troubled young man.  The chip on Teach's shoulder is considerable; he is
definitely, in his own estimation, "a man more sinned against than sinning" (cf.
Shakespeare's King Lear).  He is a bundle of nerves and
insecurities.  His entrance into the play, an explosive tirade against a woman named
"Ruthie," reveals far more about himself than it does about his female
nemesis.

Don is seemingly mellow, but he is the true
backbone of the group.  The reader senses that he, not Teach, is the one who would not
crumble in the crucible, not faint under fire.  He likes his buddy Teach but doesn't
respect him beyond someone who can help him better his own position financially.  Don
seems to tolerate him - wary of, but also amused by, his antics.  Don's obvious love and
concern for Bobby is honorable, at times even moving.  He is aware of the young man's
problem with drugs but refuses to focus on it and doesn't allow Teach to.  Don is "a
stand-up guy." (Perhaps if there were ever honor among thieves, he would be its
poster-child.)

Bobby is clearly the youngest and least
stable of the three.  There is little explicit reference to his drug addiction, but
Teach maliciously touches on it now and then, (despite Don's protests).  He loves and
respects Don and wants badly to please his mentor.  (There is the slightest hint of a
homo-erotic involvement between the two, but Mamet never underscores it.)  Bobby is, in
a way, the catalyst to the action; his instability and failings push the threesome to
its crisis.  He always means well, but his circumstances (particularly, perhaps, his
substance abuse) do not allow him actually to do
well.

Teach, Don and Bobby are a combustible combination. 
Their diverse personalities, crystallized under pressure in the claustrophobic setting
of the crowded basement junk store, clearly clash.  Teach's bravado, Don's paternalism
and Bobby's instability lead the three men to what feels like an inevitably violent
conclusion.

Comparisons between The Tempest and Twelfth Night?Would be very grateful if I could have some specific scene comparisons?

Well, the most obvious comparison is that both are
"shipwreck" plays.  Both plays begin with a shipwreck, though The Tempest
actually depicts the shipwreck (Act I, Scene i) and Twelfth Night
simply shows the results of the shipwreck, with Viola and the Captain on
shore (Act I, Scene ii).

Both plays involve shipwrecked
family members who go through the whole of the play imagining that their loved ones are
dead (Alsono and Ferdinand assume this about each other in Tempest,
Viola and Sebastian in Twelfth
Night).

Both plays also derive a great deal of
their comic relief from characters who spend a great portion of the play drunk --
Stephano and Trinculo in Tempest (Act II, Scene ii),  Sir Andrew
and  Sir Toby Belch (Act II, Scene iii) in Twelfth Night.  In
contrast, however, these drunk characters are servants (low born) in
Tempest, but high born (Sir Andrew,
Sir Toby) in Twelfth Night.  However, the
relationships between these comic characters are similar.  Both Stephano and Toby are
leaders, know-it-alls.  Both Trinculo and Andrew are followers -- silly and not very
intelligent.

An interesting case for comparison could be
made between Caliban in Tempest and Malvolio in Twelfth
Night.  Both are in service to their lady love, and both are thwarted in that
love.  Both plays end with the fate of each of these comic villains unresolved.  It is
worth noting that, generally, the audience feels a certain sympathy for both characters
which is almost uniformly NOT felt towards them by the other characters on
stage.

Both plays also end with reconciliation in Act
Five.  Those separated by shipwreck are reunited, and marriage is anticipated for the
lovers in each play.

How does Meursault's decisions throughout the book, The Stranger, by Camus, affect his life at the end?

Meursault, in Camus' short novel, The
Stranger, is a very unusual man.  His life reflects a inordinate lack of
concern, to the positive or negative, about almost anything. He enjoys the repetitive
nature of his existence, sees no need to change anything, will go along with what others
want in order to avoid any crisis or discomfort, and passes from one day to the next
without truly becoming passionate or caring about anything or anyone in his
life.

When his mother dies and he goes to her funeral,
Meursault shows no grief whatsoever.

When his boss offers
him a chance to open a new office in Paris, he really doesn't care that this would be a
fine opportunity for him.

readability="14">

...he wanted to know if I’d like a post
there.

“You’re a young man,” he said, “and I’m pretty sure
you’d enjoy living in Paris. And, of course, you could travel about France for some
months in the year.”

I told him I was quite prepared to go;
but really I didn’t care much one way or the
other.

Regarding
Marie:

Marie
came that evening and asked me if I’d marry her. I said I didn’t mind; if she was keen
on it, we’d get married.

Then she asked me again if I loved
her. I replied, much as before, that her question meant nothing or next to nothing—but I
supposed I
didn’t.

And...

readability="12">

Then she remarked that marriage was a serious
matter. To which I answered: “No.”

She kept silent after
that, staring at me in a curious way. Then she asked: “Suppose another girl had asked
you to marry her—I mean, a girl you liked in the same way as you like me—would you have
said ‘Yes’ to her,
too?”

“Naturally.”

It
is easy to see that Meursault will go along with whatever Marie suggests, but he does
not take marriage seriously, and would have said yes to anyone girl who had asked if he
liked her as much as he liked her. And he cannot tell her he loves her because he does
not. That would be a passionate response, and he seems to have no
emotional responses other than to get annoyed
occasionally.

When Raymond gets into trouble with the
police for beating his girlfriend, he asks Meursault to be his witness about her
infidelity, and Meursault readily agrees, though he has no idea if she was unfaithful or
not. He simply agrees to do so, and when he goes to the police station to give a
statement, no one checks it out.

When Meursault, through a
combination of illness and seeming confusion, kills the Arab, he admits that he is sad
that the man is dead, but shows no remorse for his part in
it.

He feels equally disinterested in whether there is a
God, even though the magistrate, and later the chaplain speak to him about it with great
passion. He doesn't see the need to believe in God. It makes no difference to
him.

This lack of passion, of caring, of being involved in
the world around him and paying more attention is what gets him into trouble. By the
time the court case comes around, there are very few who can stand up for him to attest
to his sincere concern for others, his willingness to be a dedicated friend, to be a
devoted and caring son, or a man of God. His routine of repeating each day without
dedication to anything but maintaining the status quo paints him as a self-centered,
uncaring, Godless man with criminal tendencies, and he is sentenced to
death.

Calculate the value of the sum 1+3+5+....+2n+1. Use the mathematical induction to verify the result of the sum.

We observe that the terms of the sum are the terms of an
arithmetical progression. The ratio of the progression is r=2 and it's calculated using
the first and the second
term.

3-1=2

The number of
terms is n+1.

The sum of n+1 terms of an arithmetical
progression could be written:

Sn = (a1+a(n+1))*n/2, where
a1 is the first term of the progression and an is the last
term.

In our case, a1=1 and a(n+1)=(2n+1). By substituting
them into the formula of the sum, we'll obtain:

Sn =
(1+2n+1)*(n+1)/2

Sn =
(2n+2)(n+1)/2

After factorizing, we'll
get:

Sn = 2(n+1)(n+1)/2

Sn =
(n+1)^2

To demonstrate that the value of the sum is
(n+1)^2, we'll  use the method of mathematical induction, which consists in 3
steps:

1) verify that the method works for the number
1;

2) assume that the method works for an arbitrary number,
k;

3) prove that if the method works for an arbitrary
number k, then it work for the number k+1, too.

After the 3
steps were completed, then the formula works for any
number.

We'll start the first
step:

1) 1=1^2 => 1=1
true.

2) 1+3+5+...+(2k+1)=(k+1)^2 ,
true.

3) If 1+3+5+...+(2k+1)=(k+1)^2,
then

1+3+5+...+(2k+1)+(2k+2+1)=(k+2)^2

Let's
see if it is true.

We notice that the sum from the left
contains the assumed true sum, 1+3+5+...+(2k+1)=(k+1)^2. So, we'll re-write the sum by
substituting 1+3+5+...+(2k+1) with (k+1)^2.

(k+1)^2 +
(2k+3) = (k+2)^2

We'll open the
brackets:

k^2 + 2k + 1 + 2k + 3 = k^2 + 4k + 4
true.

4) The 3 steps were completed, so the identity is
true for any value of n.

1+3+5+...+(2n+1) =
(n+1)^2

What happens between Curley and Lennie in Of Mice and Men?

Curley takes an instant dislike to Lennie, or at least
sees him as a perfect victim for his pugilistic mentality. Lennie is a big man who is
unaware of his strength and is childlike in his speech and mannerisms. Curley is small
and mean. As Candy says-

readability="6">

Curley’s like a lot of little guys. He hates big
guys. He’s alla time picking scraps with big guys. Kind of like he’s mad at ‘em because
he ain’t a big guy. (pg
28)

George warns Lennie to
stay away from Curley but it is inevitable that their paths will cross. George, Lennie
and Candy have been discussing their dream of their own place when Curley bursts in
looking for his wife. Lennie is smiling to himself with the prospect of tending the
rabbits when Curley directs his rage to him-

readability="5">

No big son-of-a-bitch is gonna laugh at me. (pg
62)

 Lennie puts out his hand
to defend himself from Curley’s blows. At George’s command, ‘Get him, Lennie.’
–

 ‘Curley’s
fist was swinging when Lennie reached for it. The next minute Curley was flopping like a
fish on a line, and his closed fist was lost in lennie’s big
hand.(p63)

Curley agrees to
cover up the incident as a machine accident, but his desire for revenge is enough to
make him lead the posse after the death of his wife, intent to make Lennie
suffer-

 I’ll
shoot him in the guts. (p95)

In The House on Mango Street, why are groups that help in such situations absent from the novel?

It is interesting that the very absence of such groups as
social services that should be helping the residents of Mango Street in their various
and manifold problems highlight the way that barrios like the one Esperanza grew up in
did not have the same resources and support available to them. The general picture that
is presented to us is one of crime, robbery, abuse and violence with neglectful parents.
No mention at all is made of any organisation that could help with such issues. Thus
Cisneros makes clear the profound isolation of life for immigrants in the States and the
grim realities that many of them have to face. You could pick any number of female
characters who marry and have children early and suffer such issues as abuse. Consider
"Minerva Writes Poems" and the narrator's assessment of Minerva's
position:

Next
week she comes over black and blue and asks what can she do? Minerva. I don't know which
way she'll go. There is nothing I can
do.

These situations are
presented as being hopeless and without answers. The absence of any form of social
services or other organisations is used to underline the harshness of life of Latino
immigrants who are not able or entitled to access the same support as American
citizens.

When does Victor sail his boat in Frankenstein?

Although Victor sailed on more than one occasion, I will
focus on the specific time in which he sailed after the creation of the second monster,
because it is a more consequential moment in the novel.

On
chapter 3, volume III of the novel Frankenstein Victor is
terrified by the thought of the creature reproducing. The creature had asked Victor to
create another being like himself, because he wanted to have a companion. At that time
in the story, the monster had suffered a number of situations that had left it feeling
more sad and isolated than ever. However, although Victor agreed to create the
second being, he was struck with panic by the thought of a colony of
monsters.

Therefore, after Victor almost finished creating
the second monster, he changed his mind, mounted the boat, and sank what he had made of
the second creature in the middle of the sea.

However, the
experience left him so exhausted that he fell asleep on his boat and drifted, landing in
Ireland. The problems followed him there when he was captured by the police as a suspect
in the nearby death of a local man.

What kind of decision would be made at the different stages of Kolbergs theory regarding whether or not to return money given to you by mistake?

Stage 1 -- all they think about is whether they'll get
punished.  So your return only if you'll get in trouble for keeping
it.

Stage 2 -- is governed by the Golden Rule.  A kid at
this stage might give the money back because that is what is fair and what they would
want someone else to do to them.

Stage 3 -- they are most
concerned with what their in group thinks.  So they'll give it back if their in group
would want them to.

Stage 4 -- you'd give it back because
that's what the rules say to do.

Stage 5 -- you'd give it
back because that's what society would want you to
do.

Stage 6 -- you'd have to decide what's just in the
given case -- what would be most likely to conform to some universal truth.  So you'd
probably give it back unless there were some reason that keeping it was more in line
with universal truths.

How does The Lovely Bones connect to the world in regards to social issues, historical issues, and values/ethics?

There are of course obvious connections (as it is modern
fiction and could have very well taken place in real life, even yesterday): unsolved
crimes, the secrecy of psychopathic rapist killers, feelings of anger/loss/helplessness
from the victim's family and close friends, etc.

I also
think it poses some other big questions: Is there life after death?  Is communication
with Earth possible from the afterlife?  Is that communication
directly affected by injustice?

What do understand by formal and informal groups in a firm?

The more common terms used are formal and informal
"organizations" rather than groups. Formal organization refers to the groupings of all
he persons working for a firm in different divisions, department, sections, etc., that
is formally defined and specified. The formal organization also defines haw the total
work of the firm is divided among such different organizational units or groups and
among persons within each group. The formal organization also determines the
relationship between people within a group and across the group. These relationships are
primarily in terms of boss-subordinate reporting relationships. Work within the
enterprise is carried within the framework of formal organisation
structure.

However the effectiveness of work within any
firm is influenced significantly by informal organization that exists side by side with
the formal one. The informal organization is not designed or implemented by any one
purposely. It develops spontaneously because of interaction between people working
together. The informal organizations is based on personal relationships that exists
between people, rather than on work requirement. The primary purpose of informal
organization is to serve the personal need of the people. However, it invariable impacts
the basic work of the enterprise, and consequently its performance. For example,
friendship between a sales person and someone working in production planning, may enable
the sales person to get information on delivery commitments faster. This will help the
sales effort of the company. However, this may also result the production planning
person playing favourites in delivery of selected orders based on considerations of
friendship. This may hurt the interest of the firm.

In view
of statement made in the post above, it is desirable to clarify that neither the formal
or informal groups need to be ad hoc. Also the informal relationships in firms tend to
be longer lasting than the formal organization structures. Thus, though in some other
settings ad hoc informal groups may form, in firms the informal organizational groups
are not ad hoc.

Does Gertrude think Hamlet is mad in Act III, scene 4 of Hamlet?This is the scene where Hamlet abuses his mother because he is certain that...

After Hamlet mistakenly kills Polonius, he continues his
rant against Gertrude. She keeps asking him to stop. Hamlet’s father, the Ghost, enters
and speaks to Hamlet. Hamlet replies and Gertrude
asks:

Alas,
how is’t with you,

That you do bend your eye on
vacancy

And with the incorporal air do hold
discourse?

Again, Hamlet asks
if she can see the Ghost. She cannot and the Ghost exits. At this point, she must think
Hamlet is mad. But then Hamlet tells Gertrude that he is not mad (crazy). He is
distraught by her and Claudius’ crime and this is why he speaks to the air (Ghost). He
asks here to confess her sins and avoid getting into bed with Claudius. Hamlet then asks
Gertrude to convince the king that he is mad. This is to prevent Claudius from supposing
any plot of revenge.

I don’t think we can be sure about
whether Gertrude thinks Hamlet is mad or not at this point. She saw him speak to the
“incorporal air,” but he told her he was not mad. Later, Gertrude does what Hamlet asks
and tells Claudius that Hamlet is mad. Since she goes along with this, we can assume
that it is more likely that, by the end of this scene, Gertrude does not think Hamlet is
mad.

Gertrude is a difficult character. It is never clear
how much, if at all, she was involved with Claudius' plot in killing the
king.

In The Giver, what happens to the community after Rosemary's release?

When Rosemary was released, the memories that she had
received were returned to the community.  Chaos resulted.  The Giver was distraught and
in morning, so he was not able to guide and comfort the community members.  Although her
memories were mostly positive, the community was not used to having memories.  Those few
memories of pain had terrible consequences for the community members.  Although it is
not described in detail, remember that the community’s main purpose is to avoid any kind
of discomfort.

After Rosemary’s release, the community
waited a long time before choosing another Receiver.  They had to be careful to choose
someone who would be more reliable, and they had to wait for the community to recover. 
Jonas was watched very carefully for any signs of
faltering.

Another result of Rosemary’s release is a change
in the rules for the Receiver of Memory in training.  When Jonas receives his rules, one
of them says he cannot be released.  The Giver notes that this is a new rule.  The rule
is designed to prevent memories from being returned to the community
again.

Prove Sin A + Sin B + Sin C - Sin(A+B+C) = 4 Sin ((A+B)/2) Sin ((B+C)/2) Sin ((C+A)/2)The actual question does not specify the traditional...

Prove Sin A + Sin B + Sin C - Sin(A+B+C) = 4 Sin ((A+B)/2)
Sin ((B+C)/2) Sin ((C+A)/2).

Given  A+B+C = 180
degree.

We use sin x+sin y = 2sin(x+y)/2
*cos(x-y)/2.

So  Sin A+sin B =  2 sin (A+B)/2 *
sin(A-B)/2.

Therefore Sin A+Sin B+ sin C = 2sin (A+B)/2*co
sA-B)/2+ sin (180 -(A+B)),as A+B+C = 180 degrees by data.

=
2sin (A+B)/2* cos (A-B)/2 + sin (A+B) , as sin (180-x) = sin
x.

= 2sin (A+B)/2cos (A-B)/2 + 2sin (A+B)/2*cos A+B)/2, as
sin 2x = 2sin x*cos x.

= 2sin (A+B)/2 {cos (A-B)/2 +cos
(A+B)/2}

= 2sin (A+B)/2 {2 cos A/2*cos
B/2}.

= 4( cos C/2 )(cos A/2)(cos B/2), as sin (A+B)/2 =
sin (90-C/2) =  cos C/2.

Therefore sin A+sin B+ sin C = 
sin A+sin B+ sin C - sin (A+B+C) = 4cos A/2*cos B/2*cos C/2 = 4sin (A+B)/2*sin (B+C)/2*
sin(C+A)/2.

as sin (A+B+C) = sin 180 deg = 0. And sin
(A+B)/2 = cos C/2, sin(B+C)/2 = cos A/2 and sin (C+A)/2 = cos
B/2.

In Twelfth Night, who declares revenge on everyone?I really can't decide. My choices are Feste, Malvolio, Antonio, or Sebastian.

Well, I have good news for you! You don't actually need to
"decide" at all, as if you read the text, you will find the answer clearly in Act V
scene i. This of course, is the final scene of the play and the denouement where all of
the conflict and the problems that have heightened up until this point are straightened
out, happiness is restored and confusion is dispersed. However, to analyse this play
effectively you need to ask yourself which characters are excluded from this circle of
happiness at the end. One of the characters who is definitely left out in the cold as it
were is Malvolio. He, out of all the characters in the play has been "most notoriously
abused" in the words of Olivia by the excesses of Sir Toby Blech's revenge, and as he is
brought into the hall before everyone out of his prison, he declares his intent to gain
vengeance:

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I'll be revenged on the whole pack of
you!

This presents a jarring
note that does not fit well with the otherwise happy ending that the play presents us
with. Thus the answer to your question is Malvolio.

Where is shakespeare's hometown?

William Shakespeare (also known as the "Bard of Avon") was
an English poet and playwright. He was born in 1564 although the exact date is not known
for sure. It is known that he was baptized on April 26th. He lived in
Stratford-upon-Avon and it is believed that he grew up on Henley Street where his
father, John Shakespeare, lived. His father was believed to be a town official and a
businessman. Most scholars agree that Shakespeare was educated at Kings New School that
was in Stratford. Here he would have had an intensive education that included Latin
grammar and classics.

A highly developed civilization that developed in what's now Pakistan is referred to as the what?

I believe you are referring to the Indus Valley
Civilization, also known as Moha-jo-Daro and Harappa civilization, so named after the
first two sites at which remains of these civilization were excavated. The exact history
of origin and development, and decline of these civilization is not very clear. Earlier
these civilizations were supposed be the part of Aryan civilization who were supposed to
have migrated to India displacing the supremacy of the Dravidian people who were
supposed to have been original resident of India, and who were forced to migrate to
south India because of Aryan invasion. However now other alternate theories have also
been developed.

Most probably the Indus valley civilization
is a part of a phase of civilization that might have originated about fifteen thousand
years back in eastern Afghanistan at Mundigak and western Pakistan at Mehrgarh, Starting
from there a string of civilization sites have been found to indicate that people from
this civilization successively abandoned their older locations and moved toward east and
south over a period extending more than ten thousand years. In this way they reached
many places in in central India beyond Delhi (Alamgirpur)  and North Maharashtra India
upto Daimabad. With passage of time and place changes took pace in their ways, but the
signs that these represent gradual evolution of the same original civilization are very
clear.

A good comprehensive description of this
civilization is given at the web site referred below.

What is f(x) if f'(x)=25x^4+2e^2x ?

To calculate a function, when knowing it's derivative,
we'll have to integrate the expression of derivative.

We'll
determine the indefinite integral of f'(x)=
25x^4+2e^2x.

Int f'(x)dx = f(x) +
C

Int (25x^4+2e^2x)dx

We'll
use the property of the indefinite integral, to be
additive:

Int (25x^4+2e^2x)dx  =Int (25x^4)dx + Int
(2e^2x)dx 

Int (25x^4)dx = 25*x^(4+1)/(4+1) +
C

Int (25x^4)dx = 25x^5/5 +
C

Int (25x^4)dx = 5x^5 + C
(1)

Int 2e^2xdx = 2*e^2x/2 +
C

Int 2e^2xdx = e^2x + C
(2)

We'll add: (1)+(2)

Int
(25x^4+2e^2x)dx = 5x^5 + e^2x  + C

So, the function
is:

f(x) = 5x^5 + e^2x +
C

What motivated the two towns to engage in the wall competition in "The Golden Kite, the Silver Wind"? What are the negative effects of the...

We're not really told why Kwan-Si first changes their
walls into the shape of a pig, but the messenger bringing the news seems to think that
by doing so, they have made themselves the more powerful town. A pig will eat an orange,
and so it looks like they are the town of strength. So, the Mandarin immediately orders
the shape of the walls changed to look like a club, to beat the pig away.
The towns prolong this competition because the town with the "strongest"
wall shape would be the winner, and therefore the more prosperous and successful
town. Think of it as a giant game of "Rock, Paper,
Scissors".

Because of this competition, the
townspeople have no time to tend crops or run businesses; instead they are constantly
building and rebuilding the walls. So, they fall ill, lose
money, and begin dying. Even the Mandarins are sick and weak at the end
of the battle. Because of their greed, and refusal to work in cooperation rather than
competition, their towns have suffered greatly.

In The Chrysalids by John Wyndham, how are moral values instilled in Waknuk's citizens?

There are three most prominent modes through which moral
values are instilled in the citizens of Waknuk. One starts earliest with the youngest
children. They learn to be terrified of the Blasphemies as threats of the Blasphemies
are used to punish and control the smallest children. The Blasphemies are mutants who
have been exiled to the Fringes, a desolate land beyond the Wild Country. In the
Fringes, mutations occur with alarming proliferation because it received greater nuclear
contamination during the Tribulation. The youngest children are taught that if they are
not good and obedient to the values of Waknuk, they will have to fear the coming of the
Blasphemies who sometimes invade to raid crops and
livestock.

Another mode begins with older children. They
are taught to memorize and recite the "Definition of Man" and portions from the
Repentances and the Bible. These concur with the slogans and mottoes that are hung on
walls as decorations or burned into the wood of houses as reminders of what Waknukians
believe is the right moral and religious path. As David says:

Frequent
references to these texts had made me familiar with the words long before I was able to
read, ... I knew them by heart, ... and a number of others about Offences and
Blasphemies.

The "Definition
of Man," which David recites to help him understand the gravity and import of Sophie's
six toes, reads:

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And each leg shall be jointed twice and shall
have one foot and each foot 5 toes. And any creature that shall seem to be human, but is
not formed thus, is not human. It is a blasphemy against the true image of God, and
hateful in the sight of
God.

The final most prominent
mode used to instill the values of Waknuk in its citizens is the purges of deviations.
When an animal, crop, or human appears in the Waknuk community with a deviation from the
definitions of sacred life forms, like the "Definition of Man," there is a purge. Whole
fields will be burned if there is any sign of deviation in the crop. Animals will be
slaughtered if there is any sign of mutation causing deviation. People are rejected as
nonhuman and exiled, with babies taken away by the time they are one month old. On the
night that David is severely punished for aimlessly suggesting it would be nice to have
a third arm while trying to remove a splinter form his finger, he dreams of his father
burning crops to purge deviations as he often had done with mutated crops--only this
time his father was purging Sophie.

Show the differences between the two sisters which compares both to the author herself? Give examples from the text. What is your opinion of the...

The two sisters in "Everyday Use" are vastly different.
Dee "Wangero" is a modern girl who has gotten an education, left home, explored her
African roots, and come back home after the death of her grandmother. Maggie, on the
other hand, is a simple girl who has lived at home with her mother happily, not really
yearning for more outside of her life of small-town simplicity. Rather than exploring
her African heritage, Maggie sees the importance of her own African American
Southern heritage. Maggie is an unattractive girl, much like Alice Walker, the author,
was disfigured in an accident as a child. She was quiet and shy, and focused on her
writing. Walked is also similar to the character Dee, though, in that she went to
college on scholarship and left her town. It is arguable which character draws more
parallels to the author's life, but I personally believe that due to the message of the
story, that family loyalty and value of one's personal heritage can be valued over
academia in some cases, Walker must relate more to Maggie.

I need 4 possible reasons for the trend toward a "snacking lifestyle."

Snacks were traditionally designed to assuage hunger in
between meals. However, a snacking lifestyle makes own think that the meal itself is
consumed quickly and not necessarily on nutritious foods. Perhaps one reason is because
it is available easily and needs little preparation.
Another reason is because of the taste;snack foods are
generally sweet, salty, rich in fats and therefore taste good to most
people. Busy lifestyles may be another reason for a
snacking lifestyle as people may not all be present in the household to sit down to a
traditional meal. It may also be less cost prohibitive to
eat meals that are snacks than a large, home-cooked traditional
meal.

How can one change the base of logarithms?

We know that if  a^x = y, then log (a) y =
x.

Or if log (a) y = x, then a^x =
y.

Now how to change the base log (a) y = x to the base
b:

a^x = y.

Let b^c =  a which
implies log(b) a = c.

Then  a^x = y implies ( b^c)^x =
y.

b^cx = y implies log (b) y =
xc.

=>lg(b) y = xlog
(b)a.

=> log(b) y / log (b) a =
x.

Therefore if log(a) y = x, then  log(b) y / log (b) a =
x.

Example and
verification:

We know log (100) 100 00 00 = log(100) 100^3
= 3.

log (100) 1000000 = {log (10) 1000000}/log(10) 100 =
{log(10) 10^6}/ log (10) 10^2 = 6/2 = 3.

Is William Blake a symbolist and a realist?

William Blake was definitely a symoblist and a realist.
One of his themes is the energy developed from contraries, so it is in keeping with his
poetry that he could philosophically be a realist and a symbolist. I'd say Blake was an
indirect Realist. He preferred a more clearly defined visual art, which is certainly a
more empirical view of art than, say, an impressionistic one. At the same time, Blake
believed in the primacy of the inner life of the individual over the socially
constructed (and thereby, oppressed) view of the empirical world. I call Blake an
indirect Realist because he believed so powerfully in contraries and in the individual
perception that he thought the individual's perception itself imagined reality. This is
a more metaphysical (while still being physical – contraries) take on ‘the world is what
we make it.’ Like symbolist thought, Blake was interested in spiritualism and the
perception itself, so Blake has no problem being labeled a Realist as long you label him
a Symbolist in that imagination (inner) plays a role in the perception of the world
(outer).

In his poem “London,” Blake empirically describes
a gloomy scene in London (Realism), but the implication is that this reality is the
result of a socially oppressed reality. Therefore, overcoming that oppression requires a
vision outside that society to overcome that oppression. Outside that society would be
Inner (mental) vision of an individual(s); Symbolism. Blake wanted to symbolically
imagine a better outer Reality. Blake frequently used symbolic icons such as angels and
devils to foster a more energetic vision and wider perception of
reality.

Discuss the role of northern capital in the development of the New South.

Without northern capital, there likely would not have been
a "new South."  It was money from the North that drove the industrialization of the
South after Reconstruction.

The movement of manufacturing
(especially textiles) to the South was similar to the "offshoring" that we see today. 
Northern industrialists moved textile mills out of New England and into the South
because they knew they could get lower costs in the South.  They knew that workers in
the South would work for lower wages.  Because of this, Northerners invested heavily in
Southern industry.  Their capital helped create the "new South."

Please provide an analysis of The Castle of Otranto, by Horace Walpole, as a gothic novel.

With regard to The Castle of Ortranto: A Gothic
Story, and the Gothic horror genre:

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Gothic fiction (sometimes referred to as Gothic
horror) is a genre of literature that combines elements of both horror and romance. As a
genre, it is generally believed to have been invented by the English author Horace
Walpole, with his 1764 novel The Castle of
Otranto...

It is generally regarded as the
first gothic novel, initiating a literary genre which would become extremely popular in
the later 18th century and early 19th
century.

It
was presented as a translation from
the Italian, believed to be based on an earlier version from the 1500s, which was said
to have been based on an even earlier story dating to the Crusades
(details which were all created by Walpole).

The novel
predates other Gothic horror writers that would follow, such as Bram Stoker
(Dracula) and Mary Shelley (Frankenstein).
Romantic writers also contributed to this genre with works such as Coleridge's
The Rime of an Ancient Mariner.

There
are many characteristics of Gothic horror (or fiction). Generally speaking (among
others), look for:

• a remote, foreign or
  mysterious location (often in a castle)


• elements of the
  supernatural (ghosts, hauntings, etc.)


• a tormented
  protagonist and/or a damsel in distress (i.e., Jane
  Eyre)

Based on a summary of the plot, the
elements that support the story as a Gothic piece of literature include a possible
hereditary curse against the Otranto family (the supernatural), the setting in a remote
location (castle), as well as a tormented antagonist (Manfred) and a damsel in distress
(Isabella). As with other stories of this kind, there was also death (when Manfred loses
his son at the beginning, and later when he kills Matilda by
accident).

Based upon the plot developments of the story
and the elements of the Gothic horror genre, The Castle of Otranto
is an example of Gothic fiction.

What is x if (1+cos2x)/2=sin(-2x)?

We'll recognize in the first term the formula of the half
angle.

(1+cos2x)/2 = (cos
x)^2

We also know that the sine function is odd, so
sin(-2x) = - sin 2x.

We'll re-write the equation,
substituting sin 2x by 2sinx*cosx.

We'll re-write now the
entire expression.

(cos x)^2 = - 2sin x * cos
x

We'll add 2sin x * cos x both
sides:

(cos x)^2 + 2sin x * cos x =
0

We'll factorize by cos x and we'll
get:

cos x * (cos x + 2sin x) =
0

We'll put each factor from the product as
0.

cos x = 0

This is an
elementary equation.

x = arccos 0 +
2k*pi

x = pi/2 +
2k*pi

or

x = 3pi/2 +
2k*pi

cos x + 2sin x = 0

This
is a homogeneous equation, in sin x and cos x.

We'll divide
the entire equation, by cos x.

1 + 2 sinx/cos x =
0

But the ratio sin x / cos x = tg x. We'll substitute the
ratiosin x / cos x by tg x.

1 + 2tan x=
0

We'll subtract 1 both
sides:

2tan x = -1

We'll
divide by 2:

tan x = -1/2

x =
arctg(-1/2 ) +k*pi

x = - arctg(1/2) +
k*pi

The solutions of the equation
are:

{pi/2 + 2k*pi}U{3pi/2 + 2k*pi}U{-
arctg(1/2) + k*pi}

In The Mayor of Casterbridge, what is Michael Henchard's tragic flaw, and how can I describe it in a thesis statement?

Michael Henchard's heroic tragic flaw is related to
Hardy's theme of how a person's inner character traits interact with blind Fate. Hardy's
point is that for every choice a person makes, future choices are either broadened or
narrowed and Fate is either advanced or forestalled. An example of this is that early
on, Henchard resisted disencumbering himself of Susan and the baby, even though he
believed they were holding him back. With these moral choices, Fate was forestalled. Had
Henchard continued in this path of moral choice, Hardy suggests, his end in life would
have been a different one. Conversely, at the drunken moment that he agrees to a drunken
opportunity to sell Susan and their baby, Henchard makes a decision that so curses and
narrows his future choices that a blind destructive Fate is aided and hastened. It takes
some mental effort to keep the threads of Fate and Choice separate, especially when
Hardy is showing their interaction, but the message is that had Henchard displayed
different character traits, Fate would have brought forth different opportunities, or
the opportunities Fate did bring forth would have been rendered
powerless.

That being said, Henchard's tragic character
flaw is the dichotomy within his nature. He is honest to a fault as seen when he doesn't
deny the furmity woman's accusations. Yet he is also self-protective to a fault as seen
when he disencumbers himself of his family because they are holding him back and when he
lies to Newson by saying Elizabeth-Jane is dead.  He is faithful to his word and always
conducts his business on the highest standards. Yet he can explosively declare rash and
cruel things the pursue them as though they were reasonable and right things, again as
in the sale of Susan and the baby. He has determination and will power and can keep a
promise for years and decades. Yet he can't think with foresight and foresee disastrous
ramifications of impulsive thoughtless acts. He has a deep sense of justice, as in his
attitude toward himself when his is alone and forsaken at the end of his life. Yet he is
petty and mean spirited as was the case in his feelings toward the loving and accepting
Elizabeth-Jane the morning after the two paternity revelations. It is this unintegrated
duality, this combination of light and dark, that constitutes Henchard's tragic flaw:
though he has high values, he lacks the ability to think through and foresee future
affects of present choices and acts.

A good thesis
statement might incorporate this dichotomy and duality, this combination of light and
dark impulses, and relate it to Hardy's theme of interaction between personal choice and
Fate. Possibly something like this might work: Henchard's tragic flaw is the dark versus
light dichotomy of his nature that proves character-determined personal choice spurs on
or forstalls the realization of Fate.

Solve the system of equations algebraically x^2+2y^2=10 3x^2-y^2=9

We'll multiply the second equation by
2:

6x^2 - 2y^2 = 18 (3)

We'll
add the 3rd equation to the first one:

x^2 + 2y^2 + 6x^2 -
2y^2 = 10 + 18

We'll combine like
terms:

7x^2 = 28

x^2 =
4

x1 = 2 and x2 = -2

Now,
we'll substitute x = 2 in the 1st equation:

2^2 + 2y^2 =
10

4 + 2y^2 = 10

2y^2 =
6

y^2 = 3

y1 = sqrt3 and y2 =
-sqrt3

We'll substitute x = -2 in the 1st
equation:

4 + 2y^2 = 10

2y^2 =
6

y^2 = 3

y3 = sqrt3 and y4 =
-sqrt3

The solutions of the equation are the
ordered pairs: (2 ; sqrt3) ; (2 ; -sqrt3) ; (-2 ; sqrt3) ; (-2 ;
-sqrt3).

In A Raisin in the Sun, what does the setting add to the story?

The play is set in the mid-1900s in a small apartment in a
Chicago tenement. In her author's notes at the beginning of the script, Lorraine
Hansberry describes the Youngers' home in detail. A home to Mama, Beneatha, Walter,
Ruth, and their son Travis, the living quarters are cramped. Mama and Beneatha share the
only bedroom, Walter and Ruth's "bedroom" is a converted breakfast room, and Travis
sleeps in the living room. There is no separate kitchen, only a kitchen area ; meals are
eaten in the living room. Also, the family shares a bathroom in the hall with other
residents in the building. The only light in the apartment comes through one small
window in the kitchen area.

Hansberry also describes the
apartment's furnishings in detail. The couch is worn, covered with doilies and covers
that are also worn. The carpet is worn, too; various pieces of furniture have been
placed to cover up the worn spots. She sums up the furnishings of the Youngers'
home:

[They]
have clearly had to accommodate the living of too many people for too many years--and
they are tired.

Hansberry
also establishes the feel of the apartment:

readability="9">

Everything has been polished, washed, sat on,
used, scrubbed too often.

The
setting adds important elements to the story. It establishes that the Younger family
lives together out of necessity; they are poor. However, there is pride here, also. The
worn furniture had once been new, carefully selected by Mama Younger and her husband,
now deceased, and it has been cared for even as it has worn out. The apartment is clean,
"polished" and "scrubbed." The Youngers are poor people, but their strength of character
and the nature of their family is reflected in the setting of the
play.

In Romeo and Juliet, what does the Nurse think about love and marriage in Act I?

It is Act I scene 3 that you need to examine carefully to
find the answer to this question. You might want to think how this scene would be
staged. It appears that the Nurse has a comic function as she constantly gives her
commentary on what Lady Capulet is trying to say when she has a serious talk with Juliet
about the husband her parents have selected for her. Though well-intentioned, it is
clear that her interruptions could be viewed as annoying or humorous. Many productions
have Lady Capulet either ignoring the Nurse or getting increasingly annoyed with her
comments, and some have Juliet moving to protect
her.

However, it is clear that the Nurse believes that
marriage is a good thing and should be aspired to. No mention of course is made of love.
Marriage for the Nurse is obviously about marrying for advancement. Note how the Nurse
says that her one wish is to see Juliet married. When Juliet says marriage is "an honour
that I dream not of," the Nurse agrees with her, saying she has obviously "sucked wisdom
from thy teat." When Lady Capulet announces who the man is, the Nurse's agreement only
focuses on the physical appearance of Paris:

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A man, young lady! Such a
man

As all the world.--Why, he's a man of
wax.

The Nurse clearly
focuses on the outward appearance. To her, Paris is wealthy, of good social standing and
handsome. What more could her Juliet want? Note her comment to Lady Capulet's words that
Juliet would make herself "no less" by marrying
Paris:

No
less? Nay, bigger! Women grow by
men.

This is a very revealing
remark. From the Nurse's point of view, marriage was the only way for a woman to "grow"
and to become more important. Love does not enter into the equation. This is why we can
see later on in the play that the Nurse urges Juliet to forget about Romeo and marry
Paris. Marriage is an alliance designed to improve your position and nothing
more.

What does this saying by Shakespeare mean? When daffodils begin to peer... Why, then comes in the sweet o' the year... Good morrowHe used Old...

This is from the song that opens Act 4, scene 3 of
The Winter's Tale.  The rogue Autolycus is singing about how, as
the first response noted, it is springtime, the sweetest time of the year, during
which he can chase after women, engage in thievery, and drink
ale. 

Also, Shakespeare did not write in Old English.  If
you take a look at the poem Beowulf in the original, that is Old
English.  Grab a copy of Chaucer's Canterbury Tales in the original
to see what Middle English looks like.  Shakespeare is actually modern English, although
the spelling of various words has changed over time.  What you see when you grab a
modern edition at the library or bookstore is something that has been edited: the
spelling cleaned up, the punctuation regularized, etc.  But it is still modern English. 
With practice and some good footnotes to help with the obscure words, Shakespeare needs
to no translation (at least not like Beowulf
does).