Comment on the setting and character of "The Fall of the House of Usher."How does setting act as a character?

Excellent observation, as it identifies how the settings
of Poe's stories reflect the characters of their protagonists. Whether it is the
catacombs in "The Cask of Amontillado" that reflect Montresor's disturbed and twisted
character of the House of Usher, whose dilapidation reflects the own mental instability
of its owner, Roderick Usher, Poe always uses setting to great effect in his gothic,
spine-chilling tales of horror. Consider what we are told about the House of
Usher:

Its
principal feature seemed to be that of an excessive antiquity. the discoloration of ages
had been great. Minute fungi overspread the whole exterior, hanging in a fine tangled
web-work from the eaves. Yet all this was apart from any extraordinary dilapidation. No
portion of the masonry had fallen; and there appeared to be a wild inconsistency between
its still perfect adaptation of parts, and the crumbling condition of the individual
stones. In this there was much that reminded me of the specious totality of old woodwork
which has rotted for long years in some neglected vault, with no disturbance from the
breath of the external
air.

Note the overall
emphasis on rottenness and decay. The setting of course is a symbol that could be said
to represent the madness and mental disturbance at the heart of the owner of the house.
At first glance it appears to be of sound quality, but closer examination reveals issues
that could indicate serious structural problems. Remember, the narrator has journeyed
here, not out of choice, but because Roderick Usher, his childhood friend, has written
to him to come and be with him as he is suffering from a "nervous agitation" and a
"mental disorder". How mentally disturbed he is will only be revealed at the end of the
story... Your question correctly identifies that in a sense the house is a symbol of the
diseased and rotting character who owns it.

In "The Sniper", how would you format the summary below into a topic sentence?I need help on how to put this bit of the plot into this format topic...

I would have to say that the answer to this question
depends a lot on what you are actually trying to say. What is the point that you are
trying to argue? It seems you have started off the wrong way round - you appear to be
taking a summary of the story and then looking at how to include it in your essay. This
is a great way to ensure that you get low marks. What you need to do is work out your
thesis statement on this piece and then your points that go towards proving it. Then,
when you have done this, you can back up your thesis statements and your points by
referring to specific quotes that support your points. Then, lastly, you can comment on
those quotes, making it absolutely crystal clear how they support your
points.

For example:

In "The
Sniper", the author uses suspense as a key tool to maintain reader interest and convey
the life-and-death struggle of the rooftop battle that is progressing. For example, note
how the sudden shot from the opposing sniper is used to heighten the tension and
suspense as we wait desperately to find out what will happen to the
sniper:

readability="6">

Suddenly from the opposite roof a shot rang out
and the sniper dropped his rifle with the curse... He stopped to pick the rifle up. He
couldn't lift it. His forearm was
dead.

Note how the word
"Suddenly" quickens the pace as the author describes the shot, and also note the detail
given about the wound the sniper has received and the fact he is unable to use his
rifle. We are left wondering, just like the sniper, how on earth he is going to escape
this new threat alive.

Hopefully you can identify a
structure above - I call it point, proof and deduction, but you can use your topic
paragraph structure too. Good luck!

In Act IV of The Crucible, what is Hale's mission?

Hale's mission in Act IV is to ensure that innocent people
aren't put to death. By this point, he has seen enough spectral evidence to know that
the girls are faking it, and he has heard enough testimony in and out of the courtroom
to know that the people who are on trial are not deserving of the punishment they are
about to receive for the crime they did not commit.

This is
different because prior to his opportunity to get to know these people after their
duration in jail, he was just like everyone else, ready to see these people hung and
believe that they were witches just because someone else said so. Hale came to the town
as an expert in the field, and here he has had no success, and it changed
him.

Describe Burris Ewell in To Kill a Mockingbird by Harper Lee.

Poor Burris Ewell.  He is definitely a product of his
environment.  He lives next door to the dump, has an abusive father, and there is very
little hope for a bright future.  He has taken on the qualities of his father; he is
mean, abusive, and ignorant.  Like his father, he has a nasty reputation with his peers
and intentionally makes Miss Caroline cry on the first day of school.  He comes to
school on the first day only because the law requires it. He is dirty and has a head
full of lice.  He has probably been abused like his other seven brothers and sisters,
and Burris must scavenge for basic necessities in the town dump.  Burris’ mother’s
whereabouts is unknown; she is either dead or has run off from her abusive situation. 
He has been raised by his sister, Mayella, and has probably not experienced much love or
affection.

In the novel, Burris Ewell and his family are
symbols of southern white poverty where the need to survive causes them to do desperate
things for respect and power. This is also shown through Bob Ewell's attack on Scout and
Jem, through his beating of Mayella, and through accusing Tom Robinson of rape.  Burris
is just following in his father's footsteps.

I need a quote on the scar in Lord of the Flies and its symbolism.Anything that has to do with the boys destroying the island is good but...

You are probably having a difficult time finding a quote
because the scar is not related to the boys destroying the island.  The scar is the path
of burned island made by the plane as it went down and the storm dragged it into the
ocean.  The boys destroy the island by fire.  The two ideas are somewhat related because
the destruction on the island is caused by humans--both human error and
malice. 

The scar made by the plane is a constant reminder
of why the boys are on the island.  They were being moved to safety, away from the world
war that made where they lived unsafe--most likely the German bombing of London during
World War 2.  The scar ties the violence that occurs on the island to that of the world
as a whole.  The boys' inability to get along on the island reflects the adults'
inability to get along as well. 

The first reference to the
scar is as follows:

readability="10">

"When we was coming down I looked through one of
them windows.  I saw the other part of the plane.  There were flames coming out of
it.""

He looked up and down the
scar.

"And this is what the cabin
done." 

How was popular sovereignty supposed to work?

In addition to the good information in the above post,
"popular sovereignty" was part of the compromise hammered out in 1850, largely by
Senator Henry Clay, which allowed Texas in as a slave state, and Maine as a free state. 
This maintained the balance in Congress between free and slave
states.

The westward movement and Manifest Destiny had
thrown a monkey wrench in the balance, and the old Mason-Dixon dividing line between new
free and slave states wouldn't work anymore after the Mexican-American War.  Almost all
of the new states from the Mexican Cession would end up being slave states that
way.

So popular sovereignty imagined that once a territory
reached 50,000 residents and qualified for statehood, an election could be held where
the majority rule of the new state could decide its slavery status.  This seems
democratic, and respectful of the culture and opinions of the territories that were to
enter.

Its authors did not foresee the large influx of
radicals from both pro and anti-slave forces that would bring so much violence to
Kansas.

What is the author's tone in Kaffir Boy, and how does he use language to achieve a specific tone? I need two examples.

In Kaffir Boy, the author Mark
Mathabane describes his experiences coming of age in apartheid South Africa. The tone of
the book ranges from fearful and angry to hopeful and
determined.

Through much of the story, Mathabane merely
describes the events from his perspective. In these sections, the tone is often fearful
or confused. In one section when Mathabane is a young child, his father is arrested for
failing to carry a proper pass, a kind of ID book that white South Africans used to use
to keep track of the whereabouts of black South Africans. Mathabane asks his
mother:

"How
come we won't be celebrating Christmas this year,
Mama?"

"Your father isn't here," my mother
said.

"But Christmas is here," I
said.

"Yes, I know," my mother said sadly. "But we don't
have the money to celebrate it
with."

In this segment,
Mathabane matter-of-factly portrays a scene of sadness and confusion, using details
important to a child to show how the absence of his father affected his
family.

In other sections, Mathabane is much more didactic.
Instead of merely relating the events of his life, he comments on them, making direct
points about his beliefs. For instance, he describes how he stood apart and refused to
debase himself as others sometimes did, even if it meant missing the opportunity to earn
money for food:

readability="11">

Throughout all the years that I lived in South
Africa, people were to call me a fool for refusing to live life the way they did and by
doing the things they did. Little did they realize that in our world, the black world,
one could only survive if one played the fool, and bided his
time.

Such passages help to
reinforce Mathabane's themes of the importance of trusting and respecting
oneself.

What are the mood and tone of The Scarlet Pimpernel?

The mood--what the author
makes you as the reader feel--is primarily one of suspense.
Orczy superbly creates an entangled plot which causes her readers to wonder if
Marguerite will ever know her husband's true identity as The Scarlet Pimpernel, or more
importantly, if she will ever see his truly brave character. Similarly, readers are
intrigued by Sir Percy's rather elaborate plots and disguises and question whether he
will be able to escape the snare set for him by
Chauvelin.

The tone--the
author's attitude toward his or her subject--of the novel is a little more complex.  The
Baroness Orczy was certainly judgmental of the treatment of
aristocrats during the French Revolution.  Her portrayal of most of the aristocrats as
innocent, sympathetic characters demonstrates this attitude. Orczy also presents a
tone of admiration toward those who defied the new French
regime and risked their lives to try to save the royalty and aristocracy. Sir Percy has
few negative qualities, and his heroic acts further Orczy's doting attitude toward a
British aristocrat who seeks to save others.  This is perhaps because she and her
husband were part of the British aristocracy, and she perhaps felt somewhat
defensive of her position in society after the French
Revolution's illumination of the aristocracy's many flaws.

What does the narrator think of the char women who ride the bus with him in To Sir, with Love?

The narrator is amused by the char women who ride the bus
with him, and looks upon them with respect, seeing in them "their own kind of dignity."
He describes them as

readability="16">

"thick-armed, bovine women, huge-breasted, with
heavy bodies irrevocably distorted by frequent childbearing, faces pink and slightly
damp from their early labors, the warm May morning and their own energy. There (is) a
look of indestructibility about them, from the tip of each tinted head in its gaudy
headscarf, tightly tied to expose one or two firmly fastened curls, to the solid legs
and large feet which (seem) rooted in the
earth."

The women remind the
narrator of peasants, even though they obviously live in the city. Their coarse and
earthy jokes are told without guile, and, as they "(josh) and (chivvy) each other and
the conductor in an endless stream of lewdly suggestive remarks and retorts," the
narrator is impressed with their openness and uncomplicated approach towards the world.
The narrator is charmed by "the essential naturalness of these folk whe (are) an
integral part of one of the world's greatest cities and at the same time as common as
hayseeds." In their lack of sophistication, the narrator senses a refreshing
genuineness; having lived "too intimately with poverty and danger and death," the char
women understand the things that are important and are not spoiled by the petty
prejudices of those who feel they must make an impression (Chapter
1).

solve x : x^4 -4x^2 -32 = 0

x^4-4x^2-32 = 0 To solve for
x.

Solution:

This is a
quadratic equation in x^2. So we solve it  by factoring as a
quadratic.

t^2-4t-32 = 0, where t=
x^2

t^2-8t+4t-32 =
0

t(t-8)+4(t-8) = 0

(t-8)(t+4)
= 0

t-8 = 0 or t+4 = 0

t-8= 0
gives x^2 = 8 , x = +or- sqrt8 = 2sqrt2 or -2sqrt2

t+4 = 0
gives x = sqrt(-4) = +or-2i

So the solution set is {
-2i,2i, -2srt2, 2srt2}

In A Raisin in the Sun, why does Beneatha attack Assagai's dream about Africa?

I believe that Beneatha does so for a couple of reasons. 
First Asagai makes Beneatha realize that she is self-centered.  While Asagai dreams of
returning to his homeland and making it a better place, Beneatha flits from one hobby
and college major to another, trying to find something that pleases her and disregarding
how she could use her intelligence and education for the benefit of
others.

Secondly, Beneatha's life experience had caused her
to be cynical.  She has watched her brother Walter struggle with his own dream.  She has
no respect for him and think that his goals are worthless and unattainable.  When
another male--Asagai--discusses his dream with Beneatha, it is natural for her to doubt
that he will accomplish his goals because she has not observed anyone else doing
so.

Does the ability to speak or reason lead to any of the vices that Old Major attributes to humans in Animal Farm?

Old Major's stirring speech in Ch. I reveals the vices of
human beings. They are:

1. Man is the only
creature that consumes without producing: Man according to Old Major is
lazy and exploitative and lives off
others.

2. The tyranny of human beings:
Man is cruel and heartless. After exploiting to the maximum the animals
he gets rid of them once they have  become
useless.

3. Man serves the interests of
no creature except himself: Man is selfish and he is not concerned about
the well being of the animals whom he exploits.

Nowhere
does Major say that these vices are a result of man's ability to speak or reason. But he
certainly implies that man has the ability to reason and argue to safeguard his own
selfish interests when he remarks,

readability="7">

No argument must
lead you astray. Never listen when they tell you that Man
and the animals have a common interest, that the prosperity of the one is the prosperity
of the others. It is all
lies.

So,
although Old Major does not state explicitly that man's ability to speak and reason is
the reason why man is selfish, exploitative, greedy and tyrannical he certainly hints at
and warns his comrades  against man's ability to smooth talk the animals into believing
and accepting as truth whatever man  says.

Demonstrate that: 3^sqrt 5

We'll apply the 4th consequence of the Lagrange's
theorem.

In fact, we'll have to prove
that:

n^sqrt(n+2) < (n+2)^sqrt
n

We'll take natural logarithms both
sides:

ln n^sqrt(n+2) < ln (n+2)^sqrt
n

We've taken natural logarithms both sides, to have a base
of logarithms (the base is e = 2.7...) that is > 1 and the direction of the
inequality to hold.

We'll use the power property of
logarithms:

sqrt(n+2)*ln n < sqrt n*ln
(n+2)

We'll divide both sides by sqrt
n:

sqrt(n+2)*ln n/sqrt n < ln
(n+2)

We'll divide both sides by sqrt
(n+2):

ln n/sqrt n < ln (n+2)/sqrt
(n+2)

We'll take the function f(x) = ln x/sqrt x, where x
is in the interval [3 ; 5].

If we demonstrate that the
function is increasing over the interval [3 ; 5], the inequality is
true.

A function is increasing if and only if, for x =
3<x = 5, we'll get:

f(3) <
f(5)

Let's prove that the function is increasing. For this
to hapen, the derivative of the function has to be positive. We'll do the derivative
test:

f'(x) = (ln x/sqrt
x)'

We'll apply the quotient
rule:

(u/v)' =
(u'*v-u*v')/v^2

u = ln x, u' =
1/x

v = sqrt x , v' = 1/2sqrt
x

(ln x/sqrt x)' = (sqrtx/x - ln
x/2sqrtx)/x

(ln x/sqrt x)' = (2sqrtx -
sqrtx*lnx)/2x^2

It is obvious that (ln x/sqrt x)' >
0 over the interval [3 ; 5], so f(x) is increasing.

ln
3/sqrt 3 < ln 5/sqrt 5

Describe Macbeth's state of mind in scene 3 in Macbeth.

Concerning Shakespeare's Macbeth, you
don't identify which act you're asking about.  I have a hunch you mean Act 1.3, so I'll
answer accordingly.

First, whatever state of mind Macbeth
is in, it echoes the witches' state of mind, since he echoes their sentiment that foul
is fair and vice-versa.  This is a bad thing. 

Then he
starts, or flinches, when the witches hail him as Thane of Cawdor and king.  Banquo
laughs off the witches, but Macbeth takes them very seriously and is anxious to hear
more.  He appears to be motivated by ambition and to have becoming king on his
mind. 

His flinch at such welcome news might also indicate
that he is already aware of what becoming king means--he would have to kill Duncan to
get the crown.  Why else would he flinch?  The flinch is surprising to Banquo, which
suggests it is motivated by something Banquo is not aware of and does not comprehend. 
Macbeth may already be haunted by the thoughts that moments later horrify him--thoughts
of killing Duncan (see his aside starting at line 130).  Macbeth is already a mixture of
fair and foul.

Macbeth is already torn, then, in Act 1.3,
between what he wants and what he has to do to get it.  He's obviously excited about the
possibility of becoming king, but torn about what it will take to achieve the throne. 
He is not prepared to blindly go after what he wants, though.  He is aware how horrible
what he's thinking about is.

What roles were women expected to fill during the Gilded Age? Did this in anyway affect their choices?

The Gilded Age, historically speaking, is made up of a
social group that is  no different than the Georgian, Victorian, nor Edwardian England
in terms of the expectations of women's roles.

During this
time, as it is evidenced in Edith Wharton's The House of Mirth
women obtain their benefits through marriage, and are expected to fulfill the
roles of doting wives. This, however, differs from the previous eras in that the Glided
Age does not have to deal with the financial inadequacies of the British rule. Instead,
the Gilded Age is the poster child of capitalism: Those who have,
are.

Hence, women in good marriages during the Gilded Age
are your typical socialites who enjoy their own or their husband's riches, enjoy
themselves in exquisitely sumptuous extravagances, and have no shame of enjoying their
sex lives outside of the marriage. In an age of excess anything is permitted as long as
it is kept secret. Therefore, the gilded age will expect women to fulfill the
traditional roles in the outside, yet it allows women to carefully exploit their goods
in the inside with the utmost delicacy.

Contrast and compare "The Story of an Hour" by Kate Chopin to Trifles by Susan Glaspell.

In addition to the points above, it is important to note
that both stories discuss specifically what it feels like for a woman to be trapped in a
marriage. While Minnie Wright from Trifles is much more proactive
in escaping her "trap," Chopin makes it quite clear in "Story" that Louise Mallard has
felt trapped for many years in her marriage but was either unwilling or unable to take
action to escape.

Similarly, both works portray a natural
tension between the sexes. In Trifles, the men trivialize Mrs.
Hale's and Mrs. Peters' comments and abilities which causes them to completely
underestimate them. John Wright minimized his wife's needs and desires and probably
never suspected that she would be strong enough to present any danger to him. In "The
Story of an Hour," everyone pities and caters to Louise Mallard after her husband's
death, assuming that she is devastated by the loss of her provider and protector when in
reality she is overcome with joy at the thought.

What is the difference between using 'a' or 'an'?

The indefinite articles [a type of
adjective] a and
an indicate a noun that is one of
many. Some grammar books refer to them as "noun markers." That is, a common noun that is
not specified as a certain one is preceded by
a or
an. When, for example, a person asks
for "a pencil," it does not matter which pencil the person has, just as long as it is a
pencil that works, probably (one of many).  However, if a person asks for "the pencil,"
he or she refers to a specific pencil, not just any one.  The article
the, therefore, is termed a definite
article.

In determining the use of
an as opposed to
a, whenever the noun that the article
modifies begins with a vowel, or a vowel sound--e.g. an original idea, an
hourly rate--Standard American English calls for the use of
an. While there are some exceptions
such as in the phrase, a unique experience, the noun that the
indefinite article modifies begins with a cosonant or a cosonant sound, Standard
American English calls for the use of a--e.g. a
glorious sunset.

Analyze the conversation between Cassius and Brutus in Act I. sc. Indicate what it reveals about their characters and about the characters of...

We learn a great deal about the major players in
Julius Caesar in Act I, scene 2.

It is
clear that both Brutus and Cassius are concerned over Caesar's growing power.   Cassius
is sounding Brutus out as to his feelings and he questions how Caesar has gown so strong
when he himself has observed his weaknesses.  Cassius then compares Brutus to Caesar and
shows him that Caesar is no greater.  Brutus comes from an old and well respected
Patrician family.  The Republic is important.  Cassius needs Brutus for his plan to
work.

Brutus listens but does not commit himself to
Cassius.  He is cautious and has strong feelings for Caesar as a
friend.

Of the two, Cassius is the more ruthless.  He has
decided that the only solution to Caesar's growing popularity and power is to
assassinate him.

For his part, Caesar seems to enjoy the
adulation of the mob and Mark Antony seems like a young man who has curried favor with
Caesar.

Any ideas for a paragraph on "Where is the best place to relocate?"

A paragraph is short, of course, so you aren't going to
get to say very much.  That doesn't mean you should not have an organizational plan and
some interesting ideas.  You'll first have to choose where you think a good place to
relocate might be.  You should probably pick someplace you know well or at least have
been to so you can write with some firsthand knowledge and authority on the matter.  It
can be a big-picture choice, like a country, a region of the country or a state, or it
can be something quite specific, like a city or even a
neighborhood. 

Once you've chosen your dream destination,
decide on two or three reasons which make this place so appealing that one would want to
pack up everything to move there.  Perhaps the weather, the people, the sights, or the
geography would be attractive reasons to move.  Choose two or three of your strongest
reasons and be prepared to expand on them for at least a sentence or two.  This should
be fun once you decide on that perfect relocation destination!

What kind of economic system does the United States have?

There are a number of different types of economies
throughout the world.  Economic systems determine how the people of a country buy and
sell goods and how production processes are controlled.  The United States has a mixed
economy based primarily on principles of private ownership.  Individuals own the goods
and services that they make or provide.  Furthermore, private businesses control factors
of production.  This is known as a free enterprise system.
 

In addition, the United States' economic system is often
characterized as a 'market system' because it is controlled by the market.  The market
is where producers and consumers come together in the exchange of goods and services.
 This interaction drives prices in the United States, unlike in many other countries
where prices for certain goods are set by the government.
 

The reason that the United States' economic system is
considered to be a mixed system is because the government is involved in the regulation
and guidance of the United States' economy.  Although it is more 'hands-off' than in
some countries, the U.S. government still plays a significant role in the country's
economy.  There are a number of services which are provided by the government in the
United States in lieu of private business.  These services include:  education, roads,
postal systems, policing, the court system, and more.

I wanna know the examples epic simile in Beowulf!

An epic simile is an extended simile that compares one
composite action with another.  The device was originally used in the poetry of Homer
and has since been utilized in other epic works.  This passage from the beginning of
Beowulf is an epic simile because it relates the story of Beowulf’s past.  Readers see
the simile introduced with the traditional “like” keyword at the beginning and Beowulf
tell his story comparing it to the pain and struggle an old may have had to endure when
watching his son executed.

It was
like the misery felt by an old man
who has lived to see his son's
body
swing on the gallows. He begins to keen
and weep for his boy,
watching the raven
gloat where he hangs; he can be of no help.
The
wisdom of age is worthless to him.
Morning after morning, he wakes to
remember
that his child is gone; he has no interest
in living on
until another heir
is born in the hall, now that his first-born
has
entered death's dominion forever.
He gazes sorrowfully at his son's
dwelling,
the banquet hall bereft of all delight,
the windswept
hearthstone; the horsemen are sleeping,
the warriors under ground; what was is
no more.
No tunes from the harp, no cheer raised in the yard.
Alone
with his longing, he lies down on his bed
and sings a lament; everything seems
too large,
the steadings and the fields.

I have to compare and contrast Beowulf's style of speech with Sir Gawain's style of speech.I have a few points brought out about the way they talk...

For one thing, Beowulf is more verbose than Gawain; Gawain
says far less at any one time. For instance, in an early speech Beowulf goes on for 46
poetic lines )"Hygelac's, we, / fellows at board; I am Beowulf named") whereas Gawain
talks in prose for the equivalent of 33 poetic lines ("I beseech ye, my lord, let this
venture be mine"). Beowulf is self-vaunting, bragging ("Truth I claim it, / that I had
more of might in the sea / than any man else"), whereas Gawain is modest and humble (" I
am the weakest, I wot, and the feeblest of wit"). When Beowulf speaks to the woman
Wealhtheow, he speaks of two things: (1) he would fight till victory or death were won
("or fighting fall in death,") and (2) he would do the will of Wealhtheow's people ("I
would work the will of your people / fully"). When Gawain speaks to Lady Bertilak, he
reiterates that he is unworthy of his task ("unworthy am I")--which is decidedly unlike
Beowulf--and tells her that he will do her will ("I wot I will do even as it may please
ye").

In this brief overview, it is clear that Beowulf and
Gawain differ in their styles of speech in point of personal assessment and
self-description. While Beowulf speaks in glowing terms of his prowess and his
accomplishments and his expectations of accomplishment, Gawain speaks in humble phrases
about his prowess and abilities and discounts the value of his service to his king and
his host. It is also clear that both Beowulf and Gawain have a code of doing the will of
the person they deem to be in a higher position than themselves, kings and women both.
This presupposes that they have no suspicion or fear that such a person will attempt to
use them for dishonorable ends or will seek in any way to mistreat them: It presupposes
a mutually understood and acted upon code of honor and
trustworthiness.

Verify the identity sin^2b+sin(a+b)*sin(a-b)=sin^2a.

We'll re-write the product sin(a+b)*sin(a-b), using the
formulas for the sum and difference of the angles a and
b.

sin(a+b) = sina*cosb +
sinb*cosa

sin(a-b) = sina*cosb -
sinb*cosa

sin(a+b)*sin(a-b)=(sina*cosb +
sinb*cosa)(sina*cosb - sinb*cosa)

We notice that the
product is the difference of squares:

(sina*cosb +
sinb*cosa)(sina*cosb - sinb*cosa) = (sina*cosb)^2 -
(sinb*cosa)^2

We'll re-write the identity, substituting the
product:

(sinb)^2 + (sina*cosb)^2 - (sinb*cosa)^2 =
(sina)^2

We'll subtract (sina*cosb)^2 both
sides:

(sinb)^2- (sinb*cosa)^2 = (sina)^2 -
(sina*cosb)^2

We'll factorize by sin b to the left side and
we'll factorize by sin a, to the right side:

sin b(1 -
(cosa)^2) = sin a(1 - (cosb)^2)

sin b(sin a)^2 = sin a(sin
b)^2

We'll divide by sin b and sin a both
sides:

sina=sinb

What are the relative abundances of Sb isotopes?

The stable isotopes of antimony (Sb) are 121 Sb and 123
Sb

We'll suppose that the  lighter isotope is 121 Sb.
Therefore it must be more abundant.

The atomic mass of
antimony is 121.760

121.760 = 120.904x + 122.904y
(1)

x is fractional abundance of 123
Sb

y is fractional abundance of 121
Sb

y = 1-x

We'll substitute y
= 1-x in (1):

121.760 = 120.904x +
122.904(1-x)

We'll remove the
brackets:

121.760 = 120.904x + 122.904 -
122.904x

We'll combine like terms and we'll solve for
x:

-2x = -1.144

x =
0.5720

The fractional abundance of 121 Sb is
0.5720. That means that the fractional abundance of 121 Sb is
0.4280.

In The Death of a Salesman, how does Biff as a football hero embody his father’s dreams?

Willy , in the play "Death of a Salesman," is the
representation of a man in search of the American Dream.  One aspect of the American
Dream is to have a son who is smart and athletic.  Willy did not have the advantage to
become a football player, but in his son's athletic abilities he sees a chance to be a
part of that piece of the dream.  He is unable to see the reality of his son's lack of
effort in school and issues.

Willy follows the son's
actions and muddles over them making his son the super star he himself never was. 
However, Willy is so wrapped up in the dream of what he wants his son to be that he can
not see who his son really is.  Because Willy can not come to terms with his own role in
life he lives through his son's actions.

What type of brother does O'Flaherty mean in "The Sniper" in the last line when he writes, "and looked into his brother's face"?

I think that you can say that they are brothers in a
couple of different ways.  I do not think that there is any evidence in the text to say
that one or the other of these is wrong or right, though.

I
have always taken this literally.  I believe that the enemy sniper was the actual
brother of the sniper from whose point of view this story is told.  I am just taking
this from the literal words of the last line.

However, you
can also argue that the word brother is metaphorical.  After all, these two guys are
doing the exact same job, just on different sides of the conflict.  It is said that
soldiers on opposite sides of wars have more in common with each other than with their
own people who have not been in combat.  You can say that this is what is going on with
these two snipers -- they are brothers because they are both in the same
role.

I tend to believe that they really are brothers.  I
say this because I think a major point of this story is that these conflicts are
needlessly turning people against each other when they really are similar people. 
Having the two be brothers is a way of dramatizing this dynamic.

How does Minerva in In the Time of the Butterflies portray courage throughout the story?

Minerva is arguably the lead protagonist of the novel and
shows many acts of bravery and courage throughout the novel.  As a young woman she
defiantly slaps Trujillo for what she considers inappropriate behavior and defends
herself and her friends from his attitudes.  As you grows into full adulthood she joins
and becomes a leader of the resistance group who are determined to overthrow the same
dictator, Trujillo.  She transports weapons and actively recruits others to join the
resistance.  Her actions are clearly viewed as dangerous by the regime, so much so, that
she and her sisters are imprisoned for no legitimate reason.  She bravely faces the
situation and uses it as a means to furth promote the cause.  She also bravely befriends
the more criminal women in prison and uses the time to teach them to live better lives
and in the cause of the resistance.  She faces extreme interrogations and physical
torture, but she can't be broken.  She makes jokes and taunts Trujillo's men who spy
around her home.

Another side of her courage is her
determination to do the right thing, even when those things are hard.  She treats her
father's illegitimate daughters with respect and ensures that they all receive an
education and support.  She perservers after the time in prison, even though she reveals
that she is tired and wants to quit it all. 

It can be
safely stated that most all of Minerva's actions in the novel can be viewed as examples
of some kind of courage.

Analyze the relationship between Emily and Toby?What is your opinion of Emily's servant?

Toby is an interesting character and we can't help but
wonder what he knew and why he stayed until the day of Miss Emily's death.  I think it
is completely reasonable to assume that Toby knew that Homer was dead in the bed
upstairs and perhaps even knew that Miss Emily went up there to be with the dead body. 
How could he not know that the horrid smell that had nieghbors calling for action was
actually coming from the upper floors of the house he was responsible for?  Then you ask
yourself why didn't he say something, do something, or just leave?  It must have been so
awful!  But alas, what would a black man in the deep South at the turn of the 19th
century truly have been able to do?  Report the death to the authorities?  He probably
would have been lynched by the end of the day either accused of actually committing the
crime himself or with having the audicity to accuse Miss Emily of such a horrific
crime.  If he ran they might have assumed foul play.  Toby doesn't have many options. 
On a more sympathic end, perhaps he felt sorry for Miss Emily in much the same way the
townspeople did, and couldn't just leave her to her own means.  He stayed out a sense of
duty and loyalty, much like the town does.  Either way, Toby is no fool.  He walks out
that door at the first chance he has because he does NOT want to be there when the
townspeople discover the remains of Homer in the attic.  Toby would have no answers that
would satisfy them and he would be in as much danger then as he would have been the in
the days it all happened.

"Proctor is a decents man, but he brought his diaster upon himself." Do you agree? Throughly justify your opinion.

I think that the statement has some validity, but it fails
to take into account the fluid nature that Proctor represents throughout the play.
 Certainly, Proctor would be the first to admit that his affair with Abigail was a
mistake.  He seems genuinely remorseful about it and seeks to make right by it.  The
construction of the house of lies that enveloped Salem, though, is not his doing.  He
has little to do with that, and Proctor is genuinely horrified by how it has taken over
the town. Over the course of the drama, his fluid nature is shown to be an individual
that struggles to do the right thing to one that is galvanized by his resolve to stand
up for what is right, something that he did not do at the start of the play.  In the
end, this is what defines him and, in my mind, what shows me that he did not bring
disaster upon himself.   His downfall is caused by his refusal to acquiesce to what so
many others are doing.  His refusal to validate the current state of affairs that
rewards deception and treachery and punishes righteousness and independence is what ends
up causing his downfall.  I cannot blame him for this.  I think that a case could be
made that he should have "just gone along" with what is going on, but in response to it,
Proctor says:

readability="8">

Because it is my name! Because I cannot
have another in my life! Because I lie and sign myself to lies! Because I am not worth
the dust on the feet of them that hang! How may I live without my name? I have given you
my soul, leave me my
name!

These are
fairly quoted lines, but I think that that they show that he is committed to what is
right and what he believes to be true.  This cannot be something to be sacrificed and
when we ask if he brought disaster upon himself versus abdicating what he knows to be
right, then I think that the former is what overrides all else.

From Beowulf I. Grendel, give two examples of kennings and two examples of alliteration . Provide the line numbers.

A kenning is generally a two-word, figurative substitution
used in place of a noun. Kennings are interesting because they are an example of the
ancient author and story-teller using figurative language before they realized exactly
what figurative language was. I tell my students that they are especially effective
because they encouraged the listener to figure out something on his own - kind of like
an easy riddle within the text that kept them interested and active in the story-telling
process. Some examples in the text are whale-road (line 10 - ocean), word-hoard (line
258 - vocabulary) war-board (line 438 - shield). As you can see, these require the
listener or reader to sort of figure out exactly what the compound word
references. 

Alliteration is repetition of similar
consonant sounds. Again, similar to kennings, alliteration was used in this ancient text
before the author or listeners knew exactly what it was. They did, realize, however,
that it is pleasing to the ear to hear alliteration, which is important because Beowulf
was originally told aloud. Some examples are: "Whichever one death fells must deem it a
just judgment by God" (lines 440-441) and "He will carry me away as he goes to ground,
gorged and bloodied" (lines 446-447). Once these are identified, it's easy to see that
they create a more pleasing effect on the listener. 

What satisfaction can be derived from a nonfiction book like The Devil in the White City that cannot be found in novels?Please help me!!!!!I will...

Excellent question!  I'm a literature teacher, so I love
the genre of fiction.  I read The Devil in the White City last
summer and really enjoyed it, as well.  Reading most non-fiction  is a little different
than reading most fiction., and so are the results. 

First,
you discover for characters who are real, not aggrandized or romanticized.  That doesn't
mean they're boring or lackluster, but the realities of life are generally less
"glittery" than fictionalized characters.  When they are, though, it's quite impactful
to remind yourself they're real--and they could figuratively have been living down the
street from you.

Second, you learn something you presumably
didn't know before. That may or may not happen in works of fiction.  This novel, in
particular, is interesting because so much of the setting and plot --a world's fair--is
unfamiliar to modern readers.   

Third, there is something
quite satisfying, to use your word, about making connections between real thngs you
know and the new real things you discover
through reading.  In this book, for example, we learn how a very commonplace object--a
ferris wheel--was created and perceived by the original riders.  Making those
connections is what makes history interesting, as well; and it's not something every
novel can do.

The genre of historical fiction does manage
to do both--put fictional characters in a more realistic historical setting.  The
problem with this is that sometimes it's hard to discern between fact and fiction.  With
non-fiction work, the lines are clearly drawn--it's all true and you know what you're
getting.  When I want to know about the Great Depression, I want my
reading to be non-fiction.  If I want to feel what it must have
been like to live during that time, I prefer to read The Grapes of
Wrath.

One other comment.  We're living in a
world where people are writing such hybrids as "fictionalized autobiography."  Movies
have done this for years--taken a true story and embellished and changed it until the
lines of reality are blurred.  These texts are satisfying only if you know that's what
you're getting.

Hope that helps!

Ronald Reagan, "Speech on the Challenger Disaster" (Jan 28, 1986)How did the Challenger tragedy affect the United States' space program?

Some context is needed here in order to fully grasp the
impact of the Challenger disaster.  The growth of the NASA space exploration program was
something that grew leaps and bound in the 1980s.  In the most symbolic of ways, it was
seen that NASA's growth and prosperity mirrored America's growth and prosperity in the
1980s.  There was an unbridled sense of enthusiasm and zeal in NASA and its symbolic
implications for America.  This was a time when kids actually grew up to say, "I want to
become an astronaut," demonstrating that the space program was actually becoming a part
of the American cultural experience.  The 1986 Challenger disaster brought all of that
to a screeching halt.  There were a couple of unique elements behind this launch.  The
most obvious of them was the presence of schoolteacher, Christa McAuliffe, striving to
become the first teacher launched in space.  The other development which proved to be
prophetic were the frigid temperatures in Florida that put back the launch a couple of
days.  The disaster itself was one of those moments that made Americans stop and catch
their breath.  Of particular mention would be the number of children who either watched
the event live on CNN or Nasa TV due to McAuliffe's ascent into space, or caught it on
replay within the first two hours that followed it.  Kids went home for lunch and came
back to school telling their friends of the horror they saw on television.  It happened
so quickly, and with so much force that Americans could not reconcile the image they
were seeing on screen with the smiling faces of the astronauts who boarded the vessel,
armed with the passion and enthusiasm that so many Americans had come to associate with
the space program.  Reagan captured this moment in his eulogy to the fallen
astronauts:

readability="27">

On the day of the disaster, our nation
held a vigil by our television sets. In one cruel moment, our exhilaration turned to
horror; we waited and watched and tried to make sense of what we had seen. That night, I
listened to a call-in program on the radio: people of every age spoke of their sadness
and the pride they felt in `our astronauts.' Across America, we are reaching out,
holding hands, finding comfort in one
another.

The sacrifice of your loved
ones has stirred the soul of our nation and, through the pain, our hearts have been
opened to a profound truth - the future is not free, the story of all human progress is
one of a struggle against all odds. We learned again that this America, which Abraham
Lincoln called the last best hope of man on Earth, was built on heroism and noble
sacrifice. It was built by men and women like our seven star voyagers, who answered a
call beyond duty, who gave more than was expected or required, and who gave it with
little thought to worldly
reward.

Interestingly
enough, Reagan also pointed to Astronaut Dick Scobee's words that in the event of a
disaster, he hoped that the NASA program would not be cut short.  In the end, the
Challenger disaster resulted in an three year stoppage of all missions, as NASA took
heavy hits in the realm of public relations and scientific inquiry, as it admitted a
lapse in judgment on several design issues and rushing the launch over the voices of
dissenting scientists, demonstrating a capacity to embrace the ends of scientific
progress rather than placing primacy on the process, itself.  The end result was that
Americans saw fallibility in NASA, a bond that was never fully
repaired.

Can a contraction of the muscle ever be reversed with physical therapy before the muscle gets too contracted?

Yes, absolutely. Contractures of the muscles are due to
inactivity and disuse. Even if the person has suffered an illness like a CVA and the
extremity is paralyzed, contractures of the muscles can be prevented with regular range
of motion (ROM) exercises performed by a physical therapist. This is especially relevant
for nurses and assistants who work in long term care facilities. Passive ROM exercises
can be performed while giving a bed bath.

Bed-bound
patients are susceptible to all sorts of contractures of the limbs, even if the patient
suffers from some debilitating neuromuscular disease, contractures should never occur.
This is an illness of neglect and can be readily prevented.

List 15 important points in chapter 1 of John Steinbeck's Of Mice and Men.

In chapter 1 of Of Mice and Men,
Steinbeck introduces the major characters and themes of the
novel:

1. Chapter 1 begins with a painstaking
   description of California's Salinas
   River Valley. 


2. Steinbeck lingers over the details of the
   river valley for one critical reason. He wants to be sure that when his migrant ranch
   labourers George and Lennie appear, they are authentic constituents of this
   setting.


3. Into this tranquil setting step the principal
   characters of the novel: George, "small and quick," and Lennie, "a huge man," as rabbits
   scurry into the brush and a heron lifts off over the river.
   


4. As Lennie laps up the water thirstily, George orders him
   not to drink so much. In this scene we become aware of George's authority over the
   larger man as Lennie carefully mimics his guardian's manner of
   drinking.


5. In George's irritation with Lennie's
   forgetfulness - he can't remember that they're heading to a ranch in Soledad - we learn
   that the latter is slow-witted.


6. As George primes
   Lennie's memory, he learns that the big man has picked up and hidden a dead mouse in his
   pocket.


7. Angrily, George throws it into the brush to
   Lennie's consternation who only wanted something soft to pet while he walked along. His
   obsession with 'soft things' is a critical motif in the remainder of the
   novel.


8. While pretending to gather firewood, Lennie
   retrieves the dead mouse which George promptly confiscates again. Lennie protests and
   recalls a lady who used to give him mice to pet. She was Lennie's Aunt Clara, George
   explains, and we learn that there is a familial connection between the two
   men.


9. When Lennie expresses a desire for ketchup with his
   dinner of beans, George, angry again, ruminates on the kind of life he could have had
   without Lennie: "...you lose me ever' job I get....You do bad things and I got to get
   you out."


10. In his angry tirade, George reveals the latest
    'bad thing' Lennie did. The two had to run away from their last workplace, in Weed, when
    a girl whose dress Lennie touched because it was pretty, brought a charge of assault
    against him.


11. Faced with Lennie's threat to go off into
    the hills to live by himself, George softens, promises to keep watch over Lennie, and
    tells the dream "about the rabbits." Thus, in this first chapter we are introduced to
    the incantatory story of every ranch hand in America - to own a piece of property, and
    earn a living by it.


12. To Lennie's delight and
    word-for-word recollection of the dream, George describes how he and his companion are
    not like other ranch hands, who drift from place to place. No, they have a future and
    each other. One day, with enough money saved, they will buy a farm, settle down, "an'
    live off the fatta the lan'."


13. Lennie's role in the
    dream is to tend the rabbits. Thus, the essential tragedy of the novel is set from the
    beginning: George cannot fulfill his dream with Lennie at his
    side.


14. Lost in a reverie, George impatiently interrupts
    himself to return to more practical matters: Finishing dinner, getting some sleep, and
    reminding Lennie to let him talk to the boss on the
    morrow.


15. The first chapter ends with the novel's most
    significant foreshadowing: George instructs Lennie to return to the quiet spot on the
    river in the event he encounters trouble at the
    ranch.   

What were the highs and lows in Rhode Island in the 1600's

The New England Puritan communities were intolerant of
those who refused to conform to the rigid ideology of those in power. Over time there
were Puritans that were expelled from the Massachusetts colony. These expulsions led to
the founding of other colonies, in this case the colony of Rhode Island founded by Roger
Williams. One of the benefits of this colony was that the colony was founded upon more
tolerant principles among which welcomed the Jewish and Quakers. However, when
Massachusetts exile Anne Hutchinson was given refuge by the tolerant Roger Williams in
Rhode Island her beliefs proved intolerant even to the tolerant. The 'lows' you ask
about are definitely grounded in the limits of even the colonies that were founded upon
tolerance.

What issues were at stake for the United States in El Salvador and Nicaragua?History 2

Time frame is important with this question, as we have
been involved in those countries for quite some time.  I am assuming, since you chose
those two in particular, that you mean our involvement with them in the 1970s and 80s
when there were revolutions/rebellions in both.

At that
time, the Cold War was still going strong, and as many times before, we had allied
ourselves with sometimes brutal dictatorships in order to protect US business interests
there and to keep those countries non-communist.  To be clear, there was little threat
to actual US national security if either of these countries actually had gone
communist.  They have little in the way of resources or exports that we need or needed. 
Companies like United Fruit and others, however, had large tracts of land ownership, and
had for decades put pressure on the US government to protect their interests
there.

In a larger social and political sense, Presidents
Jimmy Carter and Ronald Reagan did not want to seem soft on communism and have the red
shade of the globe expanded on their watch, so we gave large amounts of military aid to
both countries - in El Salvador to fight the FMLN communist rebels, and in Nicaragua to
try and save the Somoza regime, and when that failed, to fund a rebellion known as the
Contras.

In summary, business interests mostly, but also
larger Cold War containment and political image issues at home.

What type of people do you think should read this book(2-3 reasons) a paragraph of why.Alexandre Dumas's The Count of Monte Cristo

Like all classics, Alexandre Dumas's novel The
Count of Monte Cristo has the great appeal of an intriguing plot, as well as
what defines every classic: memorable characters.  Extremely popular as a writer in his
time, Dumas's appeal is to all ages and genders.

The
historical context of the play provides much intrigue. That the Abbe Faria is imprisoned
for the opposite reason that Edmund Dantes stimulates interest in the history of France
as well as the mystery of the Abbe's acquiring of the treasure of Monte Cristo and the
mystery of Gerard de Villefort's father, Monsieur de Noitier. Of course, the cleverness
of Dantes as Monte Cristo with all his disguises as he accomplishes his goals as the
paraclete of Providence who avenges injustice is among the creme de la
creme.

Finally, while Edmund Dantes does avenge
himself, he is no Madame DeFarge, a flat character of one demanding idea.  Instead, his
vengeance is that of the type in Old Testament-style and is tempered by his loyalty and
generosity to the Morrel family.  The once young sailor has never forgotten the love and
kindness that M. Morrel showed to Edmund's father while he was in prison; so, he pays
the debts of the shipowner and saves him from bankruptcy and disgrace.  Likewise, he
rescues Morrel's son Maxillian from despair, teaching him to "Wait and
Hope."

Having worthwhile themes, an intriguing plot, and
memorable characters, The Count of Monte Cristo is a classic that
yet delights young and old, male and female.  It is a novel that has been read by the
twelve-year-olds who happily map their way through the heavy two volumes, and then by 
young adults and again by older adults, who all find meanings of their own.  Indeed, it
is a wonderful novel, a delight for all who enjoy adventure and love--but, most of all,
excellent tales.  Even some reluctant readers have been converted and have enjoyed this
novel.

What is the difference in the energy consumed by three resistors of 10 ohm, 25 ohm, 20 ohm if they are attached in series and in...

We know that when two resistors a and b are connected in
series the equivalent resistance of the system is a + b. Now we are given the three
resistors as 10 ohm, 25 ohm and 20 ohm. When they are connected in series the equivalent
resistance is 10 + 20 + 25 = 55 ohm. When the combination is connected across a voltage
V the energy consumed is V^2/ R = V^2/ 55.

Now, when two
resistors a and b are connected in parallel the equivalent resistance is given as (1/a +
1/b) ^ (-1). So for the three resistors connected in parallel the equivalent resistance
is (1/10 + 1/20 + 1/25) ^-1 = (0.1 + 0.05 + 0.04) ^-1 = 1/ 0.19 = 5.26 ohm. Now the
energy consumed is V^2 / 5.26

So we can see
that the resistors in parallel consume more energy than they do when they are connected
in series.

Compare and contrast Elizabeth's response to the marriage proposals of Mr. Collins and Mr. Darcy. What effects have these proposals created?in...

It's always been ironic to me that Elizabeth, the
brightest and most savvy of the Bennet girls, so clearly sees Mr. Collins's proposal as
loveless and merely expedient--yet she fails to recognize that Mr. Darcy's offer of
marriage is genuine and based on love.

Both proposals are
rather abrupt and even business-like; both offers are rebuffed by Elizabeth,  though she
is perfectly content with that answer only in the case of Mr. Collins.  After her
ranting and raving (and Darcy's thunderous leave-taking), Elizabeth is forced to
reconsider her position and face her own emotions when she receives a letter from her
future husband.  She has no such second thoughts and undergoes no emotional examination
after the first proposal--because, of course, there were no emotions
involved. 

Both offers are unexpected, in part for the same
reason--before their proposals, Elizabeth had no indication that either man feels any
kind of love for her.  Her exchanges with Mr. Collins were insipid compared to the
fireworks which inevitably resulted from time spent with Mr. Darcy, but neither kind of
encounter reflected love.  At some point, of course, Darcy has realized this is the kind
of relationship he wants for the rest of his life--money and position or not.  It takes
Elizabeth longer to get there, probably because the figurative "step up" for her is more
difficult to contemplate than the figurative "step down" is for
Darcy.

Elizabeth, who has thought of herself as being
relatively open-minded and not as particularly class-conscious, is offered two potential
lives.  With Mr. Collins, aside from the lack of love, she knows she would always
be made to feel as if she should be grateful for the gift of his name.  She knew that
was not the life for her--and sees it first-hand later in the
novel.

With Mr. Darcy, despite his wealth and position in
society, Elizabeth eventually realizes she will be his equal in all the ways that
matter.  It takes them both a while to get there; however, once they overcome their
pride and prjudice, theirs will be a match of love.

How does Beowulf preparation for battle differ from when he fought the dragon and Grendel?v

Beowulf battles three major foes throughout the course of
the epic poem of the same name: Grendel, Grendel’s Mother, and the dragon. When Beowulf
fights his first battle against Grendel, he is a young, haughty warrior who boasts of
his prowess and former daredevil deeds. Not only does he promise to slay Grendel, but he
also boasts that he will do so alone, and in hand-to-hand combat—without any weapons!
Later, Beowulf sleeps in Hrothgar’s mead hall, awaiting the monster. Traditionally,
Anglo-Saxon warriors slept in their armor, but Beowulf divests himself before going to
bed, once again boasting his abilities in a manner that is both admirable and
daring.

Fifty years later, a slumbering dragon
awakes to find his treasure is missing. The dragon soars over Geatland, unleashing his
fiery fury. The older, wiser Beowulf is now king, and takes his best men to accompany
him to the dragon’s lair, insisting they wait outside as he goes in to battle the beast
alone. Unlike his first battle, Beowulf is more cautious; he wears his armor and helmet
and takes his sword with him. Beowulf receives a mortal wound while attacking the
dragon, and one of the warriors, Wiglaf, comes to his aid. It is only with Wiglaf’s help
that Beowulf is able to defeat the dragon.

How does the title "The Jungle" relate to the themes of the novel? Give specific examples.

The novel’s title symbolizes the competitive nature of
capitalism; the world of Packingtown is like a Darwinian jungle, in which the strong
prey on the weak and all living things are engaged in a brutal, amoral fight for
survival. The title of the novel draws attention specifically to the doctrine of Social
Darwinism, an idea used by some nineteenth-century thinkers to justify the abuses of
wealthy capitalists. This idea essentially held that society was designed to reward the
strongest, best people, while inferior people were kept down at a suitable level. By
relating the story of a group of honest, hardworking immigrants who are destroyed by
corruption and evil, Sinclair tries to rebut the idea of Social Darwinism, implying that
those who succeed in the capitalist system are not the best of humankind but rather the
worst and most corrupt of all.

Calculate the expressions E(x)= 1+ sinx + cosx E(x)= sinx - cosx E(x)= 1 - cosx

For the third expression, we'll transform the
difference of 2 trigonometric function, with the same name, into a
product.

We'll write the expression E(x)= 1 - cosx as
a difference of 2 function with the same name, in this case,
"cosine".

We'll substitute the value 1 = cos 0, so
the 

E(x)=1-cos x <=> E(x)=cos 0-cos
x.

We'll transform, the difference into a
product:

E(x)=2sin[(0+x)/2]*sin[(0-x)/2]=2sin(x/2)*sin(-x/2),

But
sin(-a)= -sin a, so E(x)=
-2sin(x/2)*sin(x/2),

E(x) =
-2sin(x/2)]^2

 

In
order to solve the expression E(x)=sin x-cos x, we'll try to  write the value cos x=sin
[(pi/2)-x]. So,

E(x)=sin x-cos
x

E(x)=sin x-sin
[(pi/2)-x]

E(x)=2cos{[x+(pi/2)-x]/2}sin{[x-(pi/2)+x]/2},

We'll
eliminate like
terms

E(x)=2cos(pi/4)sin{[(2x/2)-(pi/4)]}

E(x)=2*(sqrt2)/2*sin{[(2x/2)-(pi/4)]}

E(x)=(sqrt2)*sin{[(2x/2)-(pi/4)]}

 

Now,
we'll solve the first expression:

E(x)= 1+
sinx + cosx

We'll write the expression  1 +
cosx as a sum of 2 function with the same name, in this case,
"cosine".

We'll substitute the value 1 = cos 0, so
the 

1+cos x <=> cos 0+cos
x.

We'll transform, the difference into a
product:

2cos[(0+x)/2]*cos[(0-x)/2]=2cos(x/2)*cos(-x/2),

But
cos(-a)= cos a, so 
2cos(x/2)*cos(-x/2)=2cos(x/2)*cos(x/2),

2cos(x/2)*cos(-x/2)=2cos(x/2)]^2

So,
the expression will become:

E(x)= 2cos(x/2)]^2+
sinx

We'll write sin x = sin 2(x/2) =
2sin(x/2)*cos(x/2)

E(x)= 2[cos(x/2)]^2+
2sin(x/2)*cos(x/2)

We'll factorize by
2cos(x/2):

E(x)= 2[cos(x/2)]*[cos(x/2) + sin
(x/2)]

We'll write cos (x/2) = sin
[(pi/2)-(x/2)]

E(x)= 2[cos(x/2)]*{sin [(pi/2)-(x/2)] + sin
(x/2)}

E(x)= 2[cos(x/2)]*{2sin [(pi/2 - x/2 +
x/2)/2]*cos[(pi/2 - x/2 - x/2)/2]

E(x)=
4[cos(x/2)]*[sin(pi/4)]*[cos(pi/4 -
x/2)]

E(x)=2sqrt2*cos(x/2)*cos(pi/4 -
x/2)

Explain some similarities in imagery and poetic devices in Thomas Hardy's "The Voice" and Ted Hughes' "Full Moon and Little Frieda."

This is a tall order because Hughes' poem and Hardy's poem
are nothing alike in mood, tone, theme, metaphor, emotional impact or imagery. However,
let's give it a go. One similarity is that in both poems, there is listening. In Hughes'
"Full Moon and Little Freida," the narrator says Little Frieda is listening ("And you
listening") after having listed the sounds she hears, sounds that define the night
because the perfect darkness veils all sight ("a dog bark and the clank of a bucket").
In Hardy's "The Voice" the poetic speaker (in this case, Hardy himself) says that he
hears the woman he has lost to death calling to him ("how you call to me, call to me, /
... / Can it be you that I hear?"). A common poetic device they both use is the poetic
technique of metaphor. Hughes uses a metaphor to compare the walking cows to a "dark
river" and "boulders," and Hardy uses a metaphor to compare the north wind to ooze, a
liquid that moves slowly through small narrow places, like barren "thorn"
branches.

Hughes employs nature imagery related to a farm
on a pleasant though dark evening, mentioning "spider's web," "dew," stars, "Cows," a
lane, "hedges," "wreaths of breath." Finally the "Moon! Moon!" appears to light the
night and give Little Frieda a happy thrill before bedtime. Hardy employs nature imagery
related to a desolate barren meadow swept by a cold northern wind, implying spring time
("when our day was fair"), a road leading to a town ("I drew near the town"), mist ("wan
wistlessness") and mentioning "breeze," "wet mead" [meadow]), leaves of late autumn or
early winter ("leaves around me falling"), north wind and barren thorn bushes ("Wind
oozing thin through the thorn from norward").

Calculate f(-7) if f(7)=7 f(x)= ax^7 + bx^3 + cx - 7

If f(x)=a*x^7 + b*x^3 + c*x – 7,
then

f(-x)= a*(-x)^7 + b*(-x)^3 + c*(-x)
–7

f(-x)=-a*x^7 - b*x^3 - c*x
–7

If we calculate the
sum

f(x)+ f(-x)= a*x^7 + b*x^3 + c*x – 7-a*x^7 - b*x^3 -
c*x –7

f(x)+ f(-x)=-14

From
the sum above, we’ve noticed that regardless the value of x, the sum will have always
the same value “-14”.

So the sum is not depending on x. The
conclusion would b that:

f(7)+
f(-7)=-14

But f(7)=7, the value being given in  the
enunciation. So we’ll substitute it in the sum:

7+
f(-7)=-14

f(-7)=-14-7

f(-7)=-21

What change do the choir boys undergo on the island?

The choir boys make two transitions in their character
under the leadership of Jack Merridew. At first, the choir boys enter the scene as an
older group, and they appeared still in their
uniforms.

After time to establish roles and leadership
personnel, we find the choir boys take on two responsibilities: tending the fire, and
hunting for food. These are rather adult-like roles and they demonstrate the ability to
tackle the bigger tasks.

However, after the fire goes out
in chapter 4, we begin to see these boys undergo a great change. They rebel against the
idea of hunting for the sake of responsibility. Their new purpose in the later chapters
is to become savage and violent. It may be that this has occured and was not something
they could control. But given the circumstances of having no one who could make them
maintain order they turn primitive and even take life from another
human.

What is tragic comedy?

You will see the term tragic comedy, often shortened to
tragicomedy, in theatrical works quite often. While the overall play is a tragedy, the
playwright uses humor, sometimes satirical, to advance the storyline or to deliver a
message.

Verna Foster notes in the literary encyclopedia
that the definition of this term is often "slippery" in that is hasn't been truly
solidified, tey tragicomedy appears in even our earliest dramatic works. She
writes:

readability="17">

Tragicomedy is a slippery genre. As well as
incorporating elements from tragedy and comedy, tragicomedy has often been crossed (and
sometimes confused) with pastoral, romance, satire, serious drama, black comedy, and
other genres. Not surprisingly, the term “tragicomedy” has been used vaguely and
loosely, especially as the genre seems to reinvent itself every time it appears in the
history of drama and theatre. In one sense, tragicomedy is coterminous with literature
and life itself. But in dramatic practice tragicomedy comes into being or at least can
be recognized only after tragedy and comedy have first established themselves. While
plays that combine tragic and comic effects in various ways may be identified in all
periods of
drama.

Additionally, the
encyclopedia Britannica provides a fine analysis of the history of the genre and
includes examples of plays which have been considered
tragicomedies:

readability="16">

Despite its affront to the strict Neoclassicism
of the day, which forbade the mixing of genres, tragicomedy flourished, especially in
England, whose writers largely ignored the edicts of Neoclassicism. John Fletcher
provides a good example of the genre in The Faithful Shepherdess
(c. 1608), itself a reworking of Guarini's Il pastor
fido, first published in 1590. Notable examples of tragicomedy by William
Shakespeare are The Merchant of Venice (1596-97), The
Winter's Tale (1610-11), and The Tempest
(1611-12).

Do you think Angel is worthy of Tess's love and sacrifice? Give reasons.Thomas Hardy's Tess of the D'Uberville

This is kind of an opinion question that can be argued
either way. So, I will give you my opinion. When I was a young person and read this
novel, I disliked Angel intensely, believing him to be very unworthy of Tess' love and
sacrifice. I found him to be an immature idealist that did not appreciate how much Tess
loved him. When he refused to forgive her relationship with Alec after she forgave him
for his "affair", I found that to be selfish and cruel. When he abandoned her, that was
the ultimate betrayal.

After I lived for awhile, though, I
have come to view Angel in a different light. He was young, confused, trying to find
himself and make a place for himself apart from his family. He loved Tess, but he was
too immature to appreciate her unconditional love because his love had conditions.
However, he grows in the novel and at the end, he redeems himself, even honoring Tess
after her death by marrying her sister. So, ultimately, is he not another imperfect
human in need of a bit of grace and forgiveness? From this viewpoint, perhaps none of us
is worthy of the love we receive from our relationships, but isn't that what love is
supposed to be? It is not based on the worth of the other individual and often is not
based on how much the other individual returns that love. This view is perhaps a
bit unorthodox, but Hardy's novels contain very complex characters and Angel is one of
them.

What do you think?

Where are the places that a Christian worships?

A Christian can worship anywhere in the sense that prayer
is worship and prayer can be done literally anywhere and at any
time.

As far as more formal worship goes, Christian worship
is generally done at church services.  This can be done in actual church buildings, but
it can also be done in other places where a church group is allowed to meet (here in my
town, church groups even meet at a local movie theater).  Christ is quoted as saying
that a church is wherever "two or three are gathered in my
name."

Most Christian sects worship on
Sunday.

How do you prove that the null set is a subset of all sets?No.

The null set is an empty set, and includes nothing within
the brackets.  Every set that has at least one element, has a subset that is lacking any
elements, also known as the null set. 

Let's look at the
set of numbers that includes 1, 2, & 3.

It would be
written {1,2,3}

subsets would be {1,2}, {1,3}, {2,3}, {1},
{2}, {3}, and {}. 

Let's look at this from a completely
different perspective.  You have a fresh baked apple pie.  The pie (set) is divided up
(subsets) and eaten.  You are left with an empty pie plate.  The pie plate represent the
brackets and the emptiness is your nul set. 

I hope this
helps explain. 

In The Crucible, what is the deal with John Proctor and Abigail in Act One?

An important 'deal' between the two of them is John's wife
Elizabeth. They even refer to her in this scene. Abigail sees John as a stud. She thinks
he is going to waste because his wife is not that hot. Abigail describes her as "sickly"
whether that means in looks, attitude, or actually her health, we don't
know.

As John defends Elizabeth, Abigail defends herself by
noting that Elizabeth is talking trash about Abigail in the
town.

John seems to want to be a man that does the right
thing which includes being loyal to his wife now even though he made a mistake in the
past. Abigail thinks his marriage is a lost cause anyway, so why not have fun? This
incident between the two of them triggers much of what happens the rest of the play.
Enjoy the drama.

If the first stanza of the woman's song has a significance, what is the significance of the second stanza?

Here's the second stanza of the woman's
song:

They
sye that time 'eals all things, 

They sye you can always
forget; 

But the smiles an' the tears across the
years 

They twist my 'eart-strings
yet!

Orwell gives us the
analysis himself in his narration:

readability="16">

She knew the whole drivelling song by heart, it
seemed. Her voice floated upward with the sweet summer air, very tuneful, charged with a
sort of happy melancholy. One had the feeling that she would have been perfectly
content, if the June evening had been endless and the supply of clothes inexhaustible,
to remain there for a thousand years, pegging out diapers and singing rubbish. It struck
him as a curious fact that he had never heard a member of the Party singing alone and
spontaneously. It would even have seemed slightly unorthodox, a dangerous eccentricity,
like talking to oneself. Perhaps it was only when people were somewhere near the
starvation level that they had anything to sing
about.

The significance of
the song is not the lyrics; it's the fact that she sang "alone and spontaneously."
 Whereas the Party members recite nationalistic verses in unison and without feeling,
the woman sings a folk song, a kind of blues that aches with comic and tragic
feeling.

Psychoanalytically, a woman hanging diapers must
remind Winston of his mother, whom he lost.  Her lyrics about "time heals" and "never
forget" and "smiles and tears across the years" reveal his desire to be nurtured and
loved.  There, with Julia, must be the first time in years that's he's felt that safe
and vulnerable, so her song triggers his memory of childhood.

Find the range of the 3 domains given d: {0,1,2}Are teacher gave us a review and told us to do it for are test tomorrow but the funny thing is she...

In mathematics ,  a relation is  over a set of elements A
is identified with  elements in another set B.

Let R be a
relation from set A to B. Then, R is a subset of A X B . Then the set of all first
elements is called the domain of the relation  R and the secod set od elements in this
relation in B is called range or image.

Your teacher has
give you only the domain d : { 0, 1,2 } and has not given you any
range.

You should find three realtion and find 3 ranges 
over the domain d: {0 , 1 , 2}

So let  A = { d:  0 ,1
,2}

Let  the relation R = f(3d). Then B = { 3*0 ,  3*1 ,
3*2} = {0 , 3, 6 } is the range.

Now let us find the range
if the relation R = d^3. Then B = (0^3 , 1 ^3 , 2^3} =  {0 , 1 ,8} is the
range.

We shall have one more range: Let the relation be, R
= (d+5)^2.

Then for each of the element in the domain A =
{d: 0 ,1, 2 }, the range set is B = { (0+5)^2 , (1+5)^2 , (2+5)^2 } = {25 , 36 ,
49}

Finally the term 'range' is also there in  Statistics
where the variable characteristics may be hieght of students  or marks obtained by
students etc. Here the range is defined as the difference between the highest and the
lowest values of the variable. But  term range of Statistics and the term in
mathematics  are different in meaning and the concepts are also
different.

How are joints classified ?

Joints are classified in two ways: structure (how the
bones are connected) and function (how many degrees of freedom the joint
has).

There is a third category of joints called
biomechnical joints that include all surgical implants that replace damaged organic
tissue (surgical knee, shoulder, and hip joints for
instance).

Within the structure classification you have
fibrous joints (like skull sutures), which are connected by fibrous connected tissue,
cartilaginous joins (like vertebrae), which are connected by cartilage, and synovial
joins (like the shoulder, hip, elbow, knee, etc.), which are not directly connected at
all.

Within the functional classification you have
synarthrosis (little or no mobility, usually fibrous joints), amphiarthrosis (slight
mobility, usually cartilaginous joints), and diarthrosis (lots of movement, usually
synovial joints).

What lesson we can learn from the story of "Desiree's Baby"?

I think this short story teaches how destructive prejudice
can be. Armand was deeply in love with Desiree, telling her that her uncertain ethinic
roots did not make any difference to him. Ah, but he did not consider that she might
have some Black blood in her. When their baby is born and the child is obviously of
mixed race, he automatically assumes that it is from HER side, not his. After all, he is
a blueblood, an aristocrat. His racial prejudices are so strong and his pridefulness in
his own bloodlines so deep, that he lets the child, the symbol of race, destroy what is
beautiful, his love for Desiree.

The great irony of the
story is that the mixed race comes from HIS family, not hers. So in the end, he loses
everything; his wife, his baby and his cultural pride.

What are some promising developments in criminal investigation technology that have emerged in recent years?

I would have to highlight the recent advances in DNA
technology as one of the more important crime fighting advances in the last 20 years. 
It has gotten so much more reliable that dozens of people who were wrongly convicted
have been released from prison with compensation, while the maintenance of a prisoner
DNA database has helped to capture many criminals who had otherwise gotten away clean. 
Rapes and murders long since considered cold cases have been solved even decades
afterwards.  This is better for society and the institution of law as a whole.  It gives
us more confidence in our verdicts and our courts, and offers better protection from
crime.  Add to that the knowledge that DNA is so much more accurate probably serves as a
deterrent to some criminals, and reduces crime in that way as
well.

Combine DNA technology with computerized record
keeping and the way in which the states share information and combine their law
enforcement efforts, and we have a more effective system for stopping
crime.

What does Miss Pross do to protect Lucie and her child?What sacrifice must she make to defend them?

In A Tale of Two Cities, Miss Pross
is the staunch defender of Lucie Manette (later Lucie Darnay), her "ladybird," from the
first time we meet her to the last chapter of the novel.  In the beginning, Miss Pross
feels the need to defend her young charge from the "businessman" Jarvis Lorry.  Later,
once the family makes its way to Paris, Miss Pross has more serious threats with which
to contend. 

Once Lucie and Jarvis are on the road (with
Charles and young Lucie) heading out of Paris (and ultimately back to England), Madame
Defarge showed up at the apartment  ready to take Lucie into custody for an eventual
trial and beheading.  Jerry Cruncher has gone to get their hired carriage (for the two
of them, plus all the luggage), leaving Miss Pross alone with the angry Frenchwoman. 
She understands, despite the language barrier, that Madame Defarge is willing to kill
her to get to her ladybird.  The two women have a literal hand-to-hand fight, and the
gun which Madame Defarge produced goes off between them.  The result is a dead
Frenchwoman and a deaf Miss Pross.  She never regained her hearing from that
altercation, but she was glad to sacrifice for the family she
loved. 

What causes cysts on your ovaries?

Ovarian cysts form for numerous reasons. The most common
type is called a follicular cyst. A follicle is the fluid-filled sac that contains the
egg. Follicular cysts form when the follicle grows larger than normal during the
menstrual cycle and does not open to release the egg. Normally, follicular cysts resolve
themselves over time.

Another menstrual cycle-related
ovarian cyst is a corpus luteum cyst. The corpus luteum is an area of tissue within the
ovary that appears after an egg has been released from a follicle. If a pregnancy
doesn't occur, the corpus luteum usually breaks down and disappears. It may, however,
fill with fluid or blood and develop as a cyst on the ovary. This cyst is typically
found on only one side and has no symptoms.

Some other less
common types of cysts that develop in the ovaries include cystic teratomas, dermoid
cysts, and endometrioma.

What are the essentials of the Vampire story? Please apply this to a literary work you have read or viewed.This is a question regarding chapter 3...

The most elemental example that I can come up in
fulfilling the standard of an older man who "preys" on younger women would be Nabokov's
work, "Lolita."  I think that the vampire idea might very well apply to Humbert Humbert.
 Both he and Qwilty are older men who have this rather "dark" quality to them, despite
the public accolades and credible perception they both project.  Especially valid with
Humbert, his coveting of the concept of the young girl is something that might fulfill a
characteristic of being a "vampire."  Humbert is attractive and charming, but is fairly
self centered in the way he covets Lolita and seeks to make her his own.  At the same
time, the "mark" of taking her sexuality is something that he pursues when her mother is
dead.  This would be another example of his selfishness.  He might also fulfill another
element of the vampire narrative in that he presents himself as tormented and
experiencing a level of pain at his condition.  He argues that his love of young girls
is akin to a "poet," yet he is also aware that he bears full responsibility for Lolita's
condition, to the point where he recognizes his "obsession" with her "broke" her life.
 This might be another example of the vampire theme in Nabokov's
work.

In what year did America drop the atomic bombs on Japan?

There have been only two instances of atomic bombs being
dropped in a war. Both these bombs were dropped by the US over Japan during the close of
World War II in August 1945.

The first bomb was dropped on
on Hiroshima on August 6, 1945, This bomb was dropped by a B-29 bomber named
Enola Gay. The second bomb was dropped on Nagasaki on August 9,
1945. The bombs killed an estimated 110,000 people immediately. Many others died later,
and suffered severe medical complications. In response to dropping of these bombs, Japan
agreed to end the war on August 14, 1945, and formally surrendered on September 2,
1945.

What does the blue light represent?"The Gilting of Granny Weatherall"

Traditionally, blue is the color of stability, calm, and
order; however, it also respresents other feelings such as depression.  As the color of
the sky, blue has an expansiveness to it, too.  In Katerine Anne Porter's short story,
"The Jilting of Granny Weatherall, blue is prevalent througout the narrative,
representing the various stages of Granny's life.  In the beginning of the story, Granny
reflects that it is good to have everything in order, "clean and folded away."  The
white linen is folded the shite stone-china jaras with "blue whirligigs" are laid out in
rows.  She also recalls having lighted the lamps when young and her children came into
the house, providing them security in the evening, 

readability="7">

Their eyes followed the match and watched the
flame rise and settle in a blue curve, then they moved away from it....they didn't have
to be scared and hang on to mother any
more.

Then as Granny reflects
upon her jilting by John,

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streamers of blue-gray light like tissue paper
[move] over her eyes.

These
streamers of light make Granny worry that she will have nightmares, remembering times
that have troubled her. This faded blue represents Granny's troubles, her "blues." 
Later after the priest visits to admnister the Last Rites, Granny eyes begin to fade. 
She opens them widely and sees a picture of John on a black dresser.  Enlarged from a
small picture, John 's eyes appear to be very black, but Granny knows they should have
been blue.  The "light was blue" from Corneli'a silk
lampshades:

No
sort of light at all, just flippery.  You had to live forty years with kerosene lamps to
appreciate honest
electricity.

Here blue
represents the new world that has left Granny behind.  Finally, this blue light
draws"into a tiny point in the center of her brain, symbolizing the life of Granny that
also has dwindled and become worthless.

readability="8">

The blue light from Cornelia's lampshade drew
into a tiny point in the center of her brain, it flickered and winked like an eye,
quietly it flutterd and
died.

Granny
pictures herself blowing out the candles and the light in her mind faded
out.

How is Christ depicted as a hero in "The Dream of the Rood?"

In The Dream of the Rood, Christ is
not only depicted, but also proclaimed a hero. The best answer to your question is to be
found in the explanation of lines thirty-nine through forty-two which (in the
mondern-language translation) read:

The young
hero stripped himself--he, God Almighty--

strong and stout-minded. He mounted
high gallows, 40

bold before many, when he would loose
mankind.

I shook when that Man
clasped me. I dared, still, not bow to
earth,

Line 39 says that the 'young
hero' stripped himself. In other words, He was not stripped, but of his own
volition went unclothed so that we would not have to stand naked before the throne of
God. It also refers to the great emptying spoken of in Philipians 2:5 -
8:

5  Let this mind be in you, which was also in
Christ Jesus:
6  Who, being in the form of God, thought
it not robbery to be equal with God:
7  But made himself
of no reputation, and took upon him the form of a servant, and was made in the likeness
of men:
8  And being found in fashion as a man, he
humbled himself, and became obedient unto death, even the death of the
cross.

This great emptying, where Christ--God
Almighty--empties Himself of his supremacy, His holiness, His very divinity, and takes
upon Himself the likeness, humility, sinfulness, and humanity of mankind. He does this
voluntarily. Theologians do not make light of Christ's physical sufferings, His beating,
the way the onlookers plucked out His beard by the roots as He passed, the nails which
pierced His hands or the spear His side, but many often assert that His first and
greatest sacrifice of suffering was when He did empty Himself and voluntarily place
Himself under obedience--even obedience to the cross.

In
Line 40 the passage continues: Strong and stout-minded He mounted high
gallows...What a marvelous image of confidence and control, Christ mounts the
cross as a warrior mounts his steed; He is not coerced, or forced, but He goes
willingly, even eagerly.

Line 41: bold before many, when He
would loose mankind. He knew the result of His sacrifice, just as He knew the
requirement for the sin-debt of mankind. He knew the price of freedom and had come to
pay the cost of it.

In line 42, speaking as the
cross he says: I shook when that man clasped me... Again, Christ takes hold
of the cross, He was not bound to it, but bound the cross to
Himself.

In all of these lines, the poem depicts a person
who is in the process of deciding His own fate; fate is not decided for or pressed upon
Him. Additionally, the language depicts His choices as confident and masterful, He
'mounts' the gallows, he 'clasped' the cross.

In one of the
Wheel of Time books, one heroic character says, "When you go to the gallows, go with a
coin for the hangman, a joke for the crowd and a smile on your face." I think this
realistic depiction of Christ more than exemplifies this heroic
mien.

The Dream of the Rood is one of
the greatest Christian poems and the first to truly depict Christ as a conquering king
outside of the scriptures themselves.

Modern-language
translation of The Dream of
the Rood