What are the solutions of the equation 4*2^(x^2)/2^(3x)=64?

We'll divide both sides by
4:

2^(x^2)/2^(3x) = 16

We'll
re-write the equation, using quotient property of exponentials, in this
way:

2^(x^2-3x)= 2^4

Since the
bases are matching now, we'll apply one to one rule and we'll
get:

(x^2-3x) = 4

We'll
subtract 4 both sides:

x^2 - 3x - 4 =
0

We'll apply quadratic
formula:

x1=[(-3)+sqrt(9+16)]/2

x1=(3+5)/2

x1=4

x2=[(-3)-sqrt(9+16)]/2

x2=(3-5)/2

x2=-1

The
real solutions of the given exponential equation are: {-1 ;
4}.

'Mary hath chosen the best part, which shall not be taken away from her' - Explain what this means.

This remark was made by Jesus when he visited the home of
Mary and Martha. Martha was distracted with preparing the meal and other household
necessities; while Mary seemed intent on listening to Jesus' words. Martha complained
that Mary was neglecting her household responsibilities; but Jesus emphasized to her the
importance of listening to his words. The meaning is, of course, that daily household
preparations are temporary and have no lasting significance, but the words of Jesus
would have a far more lasting and meaningful effect than day to day chores. Jesus seemed
to emphasize the importance of his teachings at another point when he
said:

Heaven
and earth shall pass away; but my words shall not pass
away.

The Prophet Isaiah
said,

The
grass withers, the flower fades, but the word of our God stands
forever.

So, by saying that
Mary had chosen the best part; Jesus meant that she had made the wiser choice. One might
even say that she had exercised the better part of discretion.

Solve the equation: 6a^-2 + a^-1 = 2

The value of a has to be determined given that 6a^-2 +
a^-1 = 2

Note that the exponent of a^-2 is twice that of
a^-1. It is possible to convert 6a^-2 + a^-1 = 2 into a quadratic
equation.

6a^-2 + a^-1 = 2

Let
x = a^-1.

6x^2 + x = 2

6x^2 +
x - 2 = 0

6x^2 + 4x - 3x - 2 =
0

2x(3x + 2) - 1(3x + 2)
=0

(2x - 1)(3x +2) = 0

x = 1/2
and x = -2/3

Now x = a^-1

a =
2 and a = -1.5

The equation 6a^-2 + a^-1 = 2 has solution a
= 2 and a = -1.5

Analyze the quote below from Twelfth Night:My master loves her dearly; And I, poor monster, fond as much on him; And she, mistaken, seems to dote...

In this play of "erotic lunacy," as Harold Bloom dubs
Twefth Nigh/What You Will, the passage, from Act II, Scene 2, is a
soliloquy by Viola/Cesario.  As the central character who is the only one aware of the
charades of herself and motives of others, Viola is able to more objectively assess what
occurs in the play.

In this soliloquy--a literary device
designed to provide the audience with insights into the character as well as the play
itself--Viola reflects upon the theme of Appearances vs. Reality. Comments are made upon
the weakness of women who fall in love with "a dream," as Olivia does with Cesario. 
Viola also realizes the "tangled web" that has been woven with her deception of
disguising herself as a man.  Orsino loves Olivia, but Olivia in an act of "what you
will" chooses to love the deception, Cesario.  Viola herself is in love with Orsino, but
because he believes her to be a man, Viola has no recourse to love and her "state is
desperate."  At the end of her soliloquy, Viola realizes that the situation is too
complicated for her to "untangle" or resolve.

What would be some examples of what Huckleberry has learned through the course of The Adventures of Huckleberry Finn that would help him gain...

Huck has many experiences that should and do help him
grown and attain insights. He does not, however, always retain these lessons and these
insights as he moves forward. 

Early in the book, Huck
pretends to be a girl so that he can find out what the town is saying about Jim and what
they are saying about Huck's "death". In this episode, Huck is found out right away. The
woman he speaks to helps him anyway. This moment offers Huck the opportunity to see that
some people can be trusted and that lying is not always a necessary defense. Honesty can
serve just as well. 

Huck, nonetheless, continues to lie
throughout the novel. He does, at one point, repent for his deception. When he hurts
Jim's feelings and Jim articulates a disapproval of this behavior, Huck humbles himself
and vows not to fool Jim again. He realizes that his actions have an effect on
others. 

This lesson is put to the test when Huck finds
himself in the mess of the Wilks funeral with the King and the Duke. There, he decides
to be honest rather than to continue to hurt innocent
people. 

However, in the final, extended episode of the
novel, Huck once again chooses to lie and deceive. He plays a part in torturing both Jim
and Mrs. Phelps in order to carry out Tom's elaborate plan to free Jim. The lesson of
the benefits of honesty and the insight that his actions could bring emotional harm to
others seems to have faded quickly from Huck's mind. 

How does Heart of Darkness by Joseph Conrad parallel Chinua Achebe's Things Fall Apart?

I think the obvious point of comparison between these two
great texts is the way in which both present Africa as being profoundly impacted in a
negative form by colonialism. In Heart of Darkness, it is clear
that again and again the only legacy that the white's colonialism of Africa has brought
is death, decay and exploitation. Perhaps one of the most chilling examples of this is
seen in the "grove of death," where the blacks who are presented to us are clearly
dehumanised and have become nothing more than
objects:

readability="13">

"Near the same tree two more bundles of acute
angles sat with their legs drawn up. One, with his chin propped on his knees, stared at
nothing, in an intolerable and appalling manner: his brother phantom rested its
forehead, as if overcome with a great wearines; and all about others were scattered in
every pose of contorted collapse, as in some picture of a massacre or a
pestilence."

Clearly the
tragedy that Marlow sees in this grove of death is a comment on imperialism and
colonialism which has only brought difficulties to
Africa.

Likewise, in the same way, Things Fall
Apart spends many chapters introducing us to an African culture that is shown
to exist perfectly well by itself. However, it is the arrival of the white missionaries
which herald problems for this culture, and divide it and begin to destroy it. Africa
yet again is presented as only being impacted negatively through Western involvement in
its affairs and business.

This I think is the most obvious
parallel. You might like to think as well about the specific way in which Africans are
presented in both novels after the impact of the whites, and how, even with laudable
intentions, the overall impact of colonialism is shown to be profoundly
negative.

What aspects of the human condition can we find in Shirley Jackson's "The Lottery" as they relate to the main themes of the story?

There are several themes identified in Shirley Jackson's
"The Lottery." Those that resonate with me are violence and
cruelty, and custom and
tradition.

In reading the story the first time,
we are probably struck by the sense of the "everyday" in terms of the characters and
plot. This sense of the ordinary is what creates an environment of surprise and horror
when the plot becomes apparent to the reader. It rattles the reader with
Jackson...

readability="6">

...suddenly interjecting into a seemingly
ordinary environment the horrifying reality of the
lottery.

First and foremost
is the theme of custom and tradition. This particular activity has been going on for
years. There is vague discussion that other towns nearby are doing away with it, though
we don't know what "it" is when this statement is made. The fact that everyone is so
accustomed to doing the same thing each year and that no one questions it is a part of
the human condition. How long did slavery continue in this country until it was finally
challenged? How long did it take for women to earn the right to vote in the United
States? The status quo is part of the comfort of the human condition: doing it because
it has always be done "this way."

Another element of the
human condition is the lack of concern as long as one is in no danger. Conversation when
everyone arrives is mundane: with small talk and kidding. Even Tessie is involved. Her
attitude changes dramatically when her family is targeted by the lottery. She speaks out
in fear to complain, and her husband tells her to shut-up. The other families are "off
the hook," so they can have no sympathy for Tessie and her family: "Better-you-than-me"
is the prevalent attitude. No one has any patience with Tessie's resistance because it
cannot touch them, another aspect of the human
condition.

The last element I notice is Tessie's complaint
that her daughter and her husband are not included with the family. A mother would
generally do anything to protect her children, but Tessie's desire to survive is a basic
instinct. When reason disappears in the face of disaster, a survival instinct comes into
play. We see this with the rush of adrenaline one feels during a time of emergency when
someone is excessively strong or fast in the face of danger: it is an animal
instinct.

The aspect of violence and cruelty is also a part
of the human condition. It has been a part of mankind's behavior since the beginning of
time, with the murder of Abel by his brother Cain. People throughout history have found
the most horrific ways to punish the human body, though it may be disguised as an
honorable task, as with the Spanish Inquisition. In this community, the violence and
cruelty of the lottery is as much a part of the community's standard behavior as a
community picnic or a funeral. It is accepted by the community in general, no one
questions it, and in light of this, no one is guiltless in the act as it is carried out
year after year.

The human condition is evident throughout
"The Lottery." Custom and tradition allow for this violent and cruel practice to
continue year after year. Those who are not personally affected have no sympathy for
those who are. People are satisfied as long as it does not harm them. No one takes a
stand against this brutal custom because it's always been done this way. The victim does
all she can to avoid her death—a survival instinct attempting to avoid a sentence of
death. These are all aspects of the human condition.

At what points is the curve y=x/(2x-3)^2 concave up and concave down.? Thank you very much!

To verify if a function is concave up or concave down,
we'll have to do the 2nd derivative test. It means that we have to differentiate the
given function twice.

We'll diiferentiate the
function:

f'(x) ={(x)'*(2x-3)^2 -
(x)*[(2x-3)^2]'}/(2x-3)^4

f'(x) = [(2x-3)^2 -
4x(2x-3)]/(2x-3)^4

f'(x) = (2x-3)(2x - 3 -
4x)/(2x-3)^4

f'(x) =
-(2x+3)/(2x-3)^3

Now, we'll differentiate twice, with
respect to x:

f''(x) = {[-(2x+3)]'*(2x-3)^3 +
-(2x+3)*[(2x-3)^3]'}/(2x-3)^6

f''(x) = {-2*(2x-3)^3 +
6*(2x+3)*[(2x-3)^2]}/(2x-3)^6

f''(x) = (2x-3)^2*[-2*(2x-3)
+ 6*(2x+3)]/(2x-3)^6

f''(x) = (-4x + 6 + 12x +
18)/(2x-3)^4

f"(x) = (8x +
24)/(2x-3)^4

f"(x) =
8(x+3)/(2x-3)^4

Now, we'll determine the intervals of x
values where the function is concave up or concave
down.

8(x+3) = 0

x + 3 =
0

x = -3

Since the denominator
is always positive, except the value x = 3/2 that cancels it, we'll discuss if f"(x) is
positive or negative, considering the x values of
numerator.

The 2nd derivative f"(x) <
0, if x is in the range (-infinite,-3) and the function is concave down over the range
(-infinite,-3). The 2nd derivative f"(x) > 0, if x is in the range (-3,infinite)
and the function is concave up over the range (-3,infinite).

Choose a poem from Walt Whitman and explain how it reveals Romantic thinking. Support with specific examples from the poem.

In Walt Whitman's "A Noiseless, Patient Spider," there are
a number of characteristics of American
Romanticism.

Characteristics, in general, include: the
emotional, individualism, a love of separateness or nature, creative vitality...,
and...introspection, among several others.

I chose this
poem because it provided an easy identification of these characteristics. In the poem,
the speaker watches a spider as it patiently builds its web, repeating its movements
over and over and over again. The spider is on an isolated "promontory" from which it
throws out "filament, filament, filament" giving one the sense of quiet concentration
and continuous endeavor, in order to explore the "vacant, vast surrounding" as it
continues to work tirelessly.

readability="25">

A noiseless, patient
spider,

I mark'd, where, on a little promontory, it stood,
isolated;

Mark'd how, to explore the vacant, vast
surrounding,

It launch'd forth filament, filament,
filament, out of itself;

Ever unreeling them--ever
tirelessly speeding them.

In
the second stanza, Whitman makes a connection between the life of a spider and a human
being. The speaker notes that he, too, is surrounded by enormous, immeasurable space:
"ceaselessly musing, venturing, throwing" to learn of his environment, much like the
spider. This continues until man can build an anchored bridge to connect the spheres of
life with a "thread" that will somehow connect him to the world—connect his soul to the
world.

And
you, O my Soul, where you stand,

Surrounded, surrounded, in
measureless oceans of space,

Ceaselessly musing, venturing,
throwing,--seeking the spheres, to connect them;

Till the
bridge you will need, be form'd--till the ductile anchor
hold;

Till the gossamer thread you fling, catch somewhere,
O my Soul.

The
emotional essence is most evident in the poem's last line, where
the speaker hopes that the "thread" flung will find a connection for his soul. A sense
of the individualism is found in the second stanza, where a man
addresses his own soul, on its personal journey through the universe, trying to find a
"joining" of some kind. Nature is evident with the metaphor the
speaker uses when comparing the work of the patient spider to the work of a man, even to
referring to the "filament" of the spider, and the "gossamer thread" of the
man.

The aspect of creative energy is
also present in comparing the microcosm of the spider's world to the microcosm of the
speaker— as isolated as the spider, but looking for a link between a world of solitude
and one of community with someone or something greater than himself. Lastly, there is
the use of introspection present as the speaker looks at the
example of the spider and finds a parallel with his own life, to find some meaning in
his life experience; the work of the spider and the man are metaphorically similar, but
the speaker's ability to find meaning in his existence alludes to a higher plane of
existence.

What does the word 'comfortable' have to do with using a printing company?

If a printing company describes themselves as being
'comfortable', it just means that they go to extremes to make the printing process
painless for you.  They take extra care to meet your needs and explain things in a way
you can understand, even if you are not experienced at dealing with professional
printing companies.

There is a collection of very
particular vocabulary and jargon when it comes to printing processes. There are
different paper types, and paper weights, and varnishes, and processes that you can
choose to create different effects on your prints.  Printing companies that describe
themselves as being comfortable have representatives or possibly very user-friendly
online software that will walk you through the process of ordering the kind of prints
you want without assuming that you already know the print shop
jargon.

What is a thesis statement I can use to compare and contrast "The Nymph's Reply to the Shepherd" and "The Passionate Shepherd to his Love"?

Both of these excellent poems deal with pastoral imagery,
or the simple delights of the countryside and the closeness to nature that is promised
in one of these poems and questioned in the other. The speaker in "The Passionate
Shepherd to His Love" is eager in painting a highly idyllic picture of the various
pleasures that the countryside can offer his love, such as "beds of roses" and "A gown
made of the finest wool." However, the nymph in "The Nymph's Reply to the Shepherd" is
not so easily seduced by such attractive images, pointing out that "flowers do fade" and
all of the things the shepherd promises "Soon break, soon wither, soon forgotten." A
good way to focus on how you can compare these two poems would therefore be to explore
"the romantic getaway" and the different attitudes of the two poems towards this. You
might like to think about the following statement:

Comment
on the romantic getaway through comparing and contrasting "The Passionate Shepherd to
His Love" and "The Nymph's Reply to the Shepherd."

This
would allow you to explore the difference in views between the two poems. Good
luck!

Why did Black Americans fail to receive full freedom after the end of the Civil War in 1865?

I would argue that this failed to happen because there
were not enough whites (in the North or the South) who were actually dedicated to the
idea of "full" freedom for blacks or for the idea (which may be the same as "full
freedom") that blacks deserve to be equal to whites in the eyes of the
law.

Not surprisingly, much of the South wanted to retain
white supremacy.  This had been a cornerstone of their whole social and economic system
and the loss of the war could not easily change it.  Blacks' only hope, then, was that
the North would force the South to accept full freedom for African Americans.  But this
did not happen because whites in the North were not sufficiently wedded to the idea of
black equality.  They were not willing to maintain the anti-democratic aspects of
Reconstruction simply in order to bring about racial
equality.

Thus, overt racism in the South and a lack of
strong sentiment for equality in the North made it impossible for blacks to receive full
freedom in 1865 or for decades after that.

Verify if the fraction (x-1)(x^3+1)x/(x^3-x) >0, if x is a real number?

First, we'll factorize the denominator by
x:

(x-1)(x^3+1)x/x(x^2-1)

We'll
reduce by
x:

(x-1)(x^3+1)/(x^2-1)

Since
x^3 + 1 is a sum of cubes, then it could be written as it
follows:

x^3 + 1 = (x+1)(x^2 - x +
1)

Since x^2 - 1 is a difference of squares, then it could
be written as it follows:

x^2 - 1 =
(x-1)(x+1)

We'll re-write the
fraction:

(x-1)(x^3+1)/(x^2-1) = (x-1)(x+1)(x^2 - x +
1)/(x-1)(x+1)

We'll simplify by
(x-1)(x+1):

(x-1)(x^3+1)/(x^2-1) = x^2 - x +
1

We'll verify if the quadratic has any
zeroes:

x^2 - x + 1 = 0

delta
= (-1)^2 - 4 = 1 - 4 = -3 < 0

Since the discriminant
is negative, then the quadratic is not intercepting x axis and it is located above or
below x axis. Since the coefficients of x^2 is positive, then the quadratic x^2 - x + 1
is positive for any value of x.

Therefore,
the statement that the fraction (x-1)(x^3+1)x/x(x^2-1) is positive for any value of x is
true.

I need to analyze and show key image, symbol or theme in Quote#171 "Flamesin the forehead of the morning sky:"

This is an excellent question, focusing in real detail on
the actual phrasing of the poem.

1. The image
   implied by the verb “Flames” is appropriate to the poem in various ways. For instance,
   the poem is very much concerned with literal and emotional darkness. Lycidas has died
   and his body has sunk beneath the waves into what seems a kind of permanent darkness. 
   The flames can therefore be seen as implying the light associated with his
   resurrection.  Just as flames are usually considered the opposite of water, so the fact
   that Lycidas “Flames” like the sun is appropriate to poem emphasizing watery
   death.


2. The fact that Lycidas “Flames” like the sun also
   associates the risen Lycidas with God, the source (for Milton and his contemporaries) of
   all light and life and power.


3. The idea that Lycidas now
   “Flames” like the rising sun is a potent symbol of renewed life. Even the sky is treated
   here as if it were a living being (since it is said to have a “forehead”). The entire
   final section of the poem brims with symbols of renewed vitality, and the flaming sun is
   one of them.

How would you describe Shukhov's personality in the begining of the novel, and is there any thing heroic about him?

In the begininning of the novel, Shukhov is a resourceful,
hard-working, and intelligent person with a sense of self-worth and integrity. The
opening pages show how he always gets up early so that he can earn a little extra before
the day begin, but is not so desperate as to demean himself (by licking empty bowls, for
example). He is sick but gets up anyway, showing his
determination.

However, Shukhov is not heroic. It is the
point that he be an everyman figure, and has little to separate him from any other man
in the camp. He has personality and good traits, but he is not heroic because that would
mark him as special, when the purpose of the novel is to reveal the everyday horrors
that any camp worker experiences.

Describe American neutrality in light of Roosevelt's foreign policy.

Given the policies of Pres. Roosevelt in the time between
the start of WWII in Europe and the Pearl Harbor attack in December of 1941, the best
way to describe American neutrality is to say that it was only skin deep.  In other
words, America was neutral in name only.

In truth, the US
was taking the Allies' side.  The US took many steps to aid the Allies.  The most
blatantly non-neutral of these was the US policy (started in the spring of 1941) of
escorting convoys across the Atlantic.  The US Navy did this to allow merchant ships to
have a better chance of getting to England carrying supplies from the US.  The US Navy
would alert the British navy to any German ships they saw.  By doing these sorts of
things, the US was clearly taking the Allies' side.

Because
FDR took this and other actions (such as Lend-Lease) it is clear that American
neutrality was not sincere.  In truth, the US was doing all it could to help the Allies
short of actually joining the war.

How did changes in voting procedures enable government leaders to be elected more democratically?

I assume that you are talking about the changes in voting
procedures that happened during the Progressive Era.  During this time, there were a few
changes, mainly at the state and local level, that allowed more democratic
elections.

The most important of these was the secret
ballot.  In many cities before the Progressive Era, secret ballots were not used.  The
use of secret ballots was meant to help break the power of urban political machines and
allow more democratic elections of city officials.  This was also the reason for the
institution of non-partisan and at-large city elections.

On
the state level, many states started using primary elections during this time.  This
allowed people to actually vote to decide who the candidates for each party would be
instead of having party bosses make the choices.  This was an important step towards
democracy.  Finally, the 17th Amendment required US Senators to be directly elected by
the people instead of being selected by state
legislatures.

All of these changes in voting procedures
increased the amount of democracy in the US.

Vo for photo electrons emitted from a surface by light of wavelength 4910 A is 0.71 V. When the incident wavelength is changed the Vo is 1.43...

The external photoelectric effect happens when an incoming
photon strike an electron into an atom on the surface of a metal. If the energy of the
photon is greater than the work function of the metal (energy necessary to move the
electron from its energy level into the atom to infinite distance) than the electron
will be released from the atom having a certain kinetic energy. The kinetic energy of
the electron emitted is usually measured by stopping it into a reverse electric
potential. Hence the law of the photoelectric effect
is:

+(m*v^2)/2

For initial photon from text we have and
. The work function of the metal is

(h*c)/lambda-e*U_1 =(6.626*10^-34*3*10^8)/(4910*10^-10) -1.6*10^-19*0.71 = 2.91*10^-19 J
=1.82 eV

For the second photon the stopping potential is

=(6.626*10^-34*3*10^8)/((1.82+1.43)*1.6*10^-19)=3822.7 A

The new photon wavelength is 3822.7
Angstrom.

What is the Ernest Hemingway story that tells about the "running of bulls" in Spain?

One of the greatest of all American novels is Ernest
Hemingway's The Sun Also Rises. It tells the story of a group of
American ex-patriots living in Paris during the decade following World War I. The story
is set in several locales, particularly Paris, and Hemingway's description of the
nightlife and debauchery of the French capital in the 1920s is probably the most
memorable ever set to print. The latter section of the novel is dedicated to the
Festival of San Fermin, in Pamploma, Spain--another example of wild drinking and sexual
tension run amok--and highlighted by the famous "running of the bulls." Although the
event had been staged for many years, Hemingway's novel put this festival on the map,
transforming it into an international destination for many tourists seeking a dangerous
twist to their travels.

What was the conclusion of the Spanish American War?

The Spanish-American War concluded with the United States
winning the war very easily.  At the conclusion of the war, many of Spain's remaining
overseas possessions were taken from Spain and either given their independence or put
into the possession of other countries.

The United States
took a few of Spain's possessions for itself.  For example, it took Puerto Rico, the
Philippines, and the island of Guam in the Northern Mariana Islands (in the western
Pacific).  Cuba, which was one of the major reasons for the war, was given at least
nominal independence.

With its military decisively defeated
and its territories taken away, Spain came out very badly at the conclusion of this
war.

Calculate sin^2 1+sin^2 2 +...+ sin^2 90.

Let

(1) S = sin^2(1) +
sin^2(2)+ ...+sin^2(88) + sin^2(89)

we know sin(k) =
cos(90-k) for k = 1, 2, ..., 89, so we have

S = cos^2(89) +
cos^2(88) + ... + cos^2(2) + cos^1(1).

reverse the order of
summation, we have

(2) S = cos^1(1) + cos^2(2) + ... +
cos^2(88) + cos^2(89)

Add (1) and (2)
together;

2S = (sin^2(1) +
cos^2(1)) + (sin^2(2) + cos^2(2)) + ...+ (sin^2(89) +
cos^2(89))

= 1 + 1+ ... + 1    (the total is
89)

=
89

so devide both sides by 2,
S = 89/2 = 45.5.

"Leaders are born and not made." Explain this.

Many psychological, neurological, and
sociological tests have been conducted by scientists to discover if
leadership truly can be a learned trait, and studies generally indicate that
leaders truly are born with different personality traits
and different thinking skills that make them leaders rather than
followers.

Geneticists at
the University College London experimented on 4,000
individuals to find that those who are supervisors all have the rs4950 gene. Also,
psychologists and neuroscientists at the Wake Forest
University, North Carolina, discovered that those in leadership positions
have more brain activity in their frontal and
prefrontal lobes. The frontal lobe is responsible for cognitive skills,
such as expressing emotions, solving problems, the ability to judge, and the ability to
retain memory and use language skills. The prefrontal lobe is involved in even more
complex cognitive skills, such as making decisions, regulating social behavior, and
expressing personality. All of the above skills are critical for leadership
roles.

In addition, a joint sociology and animal
behavior study on stickleback fish at the University of
Cambridge showed that the leadership role cannot be
learned. Stickleback fish are group animals, and within the group,
different fish show different levels of boldness; the bolder fish initiate an activity,
such as coming out of hiding to forage, while the shyer fish follow. The scientists took
pairs of shy and bold fish and used food rewards to try and change the behavior of both
the leader and the follower. What they found is that, while the leader
could be trained to learn to follow, the follower could
never be trained to be bold enough to
lead.

Hence, though some scientists still question if
leadership skills can truly be learned, other scientists
conclude that while some leadership skills can be learned, there will
always be certain people for whom those skills come more easily, just like math skills
come easily to certain individuals while language skills come more easily to others. All
people, within limits, can be taught to learn more math and language skills, but those
who are weak in math or language will always struggle more with the subject. The same
holds true for leaders. We can learn leadership skills, but
it's not the skills alone that make us actual
leaders.

Calculate the difference cos75-cos15.

Since the functions are matching, we'll use the
identity:

cos a - cos b = 2 sin [(a+b)/2]*sin
[(b-a)/2]

a = 75 and b =
15

cos 75 - cos 15 = 2 sin
[(75+15)/2]*sin[(15-75)/2]

cos 75 - cos 15 = 2 sin
45*sin(-30)

Since the sine function is odd, then sin(-30) =
-sin 30

cos 75 - cos 15 = -2
(sqrt2/2)*(1/2)

cos 75 - cos 15 = -
(sqrt2/2)

The requested difference is: cos 75
- cos 15 = - (sqrt2/2).

If cosec θ – sin θ = b, sec θ – cos θ = a sinθcos θ = ???

I'm going to use x instead of
theta.

It is given that cosec x - sin x = b and sec x - cos
x = a.

We need to find sin x *
cos

sec x = 1/cos x and cosec x  = 1/ sin
x

cosec x - sin x = b and sec x - cos x =
a

=> 1/ sin x - sin x = b and 1/cos x - cos x =
a

b = [1 - (sin x)^2]/sin x and a = [1 - (cos x)^2]/cos
x

=> b = (cos x)^2 / sin x and a = (sin x)^2/ cos
x

b *a = [(cos x)^2 / sin x]*[(sin x)^2/ cos
x]

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

=> sin x * cos
x

This gives us (sin x)*(cos x) =
a*b

Discuss the myths you can identify in the play The Laramie Project. How are they relevant to the play as a whole?

I think that the use of myths is extremely important to
Kaufman’s work.  It is mythology that makes Matt Shepard’s murder and the denial
surrounding it a reality.  It is mythology that confounds the people of Laramie, the
outsiders who come in to visit it, as well as the Tectonic Actors, who must make sense
of why these myths exist and their significance to what happened to Matt Shepard.  One
such myth is about the issue of being gay.  There are many myths that are associated
with homosexuality that are explored in the play.  From the religious condemnation, to
the townspeople who do not openly say anything against it, but are not supportive, to
those who cleave to Laramie’s supposed goodness in the attempt to not have to face the
awful truth about what happened to Matt Shepard, all of these myths play a significant
role in the play.  I would say that another myth that is present is one responsibility. 
This myth says that Shepard’s murder and gruesome death were isolated incidents and do
not signify a larger pattern. This is a myth that is exposed for what it is in the
drama, also.

Julius Caesar Conflicting Perspective Essay; How would I conflict the following?I want to do one paragraph on Mark Antony's Funeral Oration and one...

William Shakespeare's play Julius
Caesar is replete with conflicting perspectives.  While this motif does not
always include the plebians, one salient example of this duality and contradiction
occurs in Act V, Scene 1 as Cassius goes against his words to Brutus in Act I, Scene 2
when he solicits him as a conspirator in the assassination of Caesar. For, when Brutus
seems reluctant to join in the conspiracy because the "eye sees not itself," Cassius
urges him to create his own destiny,

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Men at some time are masters of their fates:

The fault, dear Brutus, is not in our stars,
But in ourselves,
that we are underlings.
(2.1.145-146)

Yet, later in
the play, it is Cassius who becomes superstitious, finding omens in certain occurrences
in Act V. Anxious about the forthcoming battle with the Philippi, Cassius tells Messala
that he has seen omens:

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Two mighty eagles fell, and there they perch'd,

Gorging and feeding from our soldiers' hands,
Who to Philippi here
consorted us.
This morning are they fled away and
gone,

And in their steads do ravens, crows, and kites

Fly o'er our heads and downward look on us,
As we were sickly
prey. Their shadows seem
A canopy most fatal, under which
Our army
lies, ready to give up the
ghost.(5.1.87-95)

Another
example of duality of perspective occurs with Marc Antony, who is Act III portrays the
loving Roman who is loyal to the Caesars and mocks Brutus for his dishonor. Yet, after
he has been in the triumvirate with Octavius Caesar and M. Aemilius Lepidus after the
death of Caesar, Antony displays shamelessly a disloyalty to the Roman people and to
Lepidus in Act IV when he sends Lepidus on an errand to fetch the will of Caesar so that
Antony can lessen some of the legacies promised to the plebians.  After Lepidus departs,
Antony feels no guilt about his treacher as he tells
Octavius,

This
is a slight unmeritable man,
Meet to be sent on errands. Is it fit,

The three-fold world divided, he should stand
One of the three to
share it  (4.1.13-16)

Later,
then, Antony contradicts himself as he accuses Brutus and Cassius of the same expediency
of which he himself is guilty in ridding himself of
Lepidus:

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Villains! You did not so when your vile daggers

Hack'd one another in the sides of Caesar.
You show'd your teeth
like apes, and fawn'd like hounds,
And bow'd like bondmen, kissing Caesar's
feet;
Whilst damned Casca, like a cur, behind
Struck Caesar on the
neck. O you flatterers!
(5.1.42-47)

In "In Praise of the F Word," why does Mary Sherry consider many diplomas that will be handed out to be meaningless?"tens of thousands of...

Mary Sherry considers these diplomas (or at least those
handed out 20 years ago when she was writing) to be worthless because too many of the
people who receive the diplomas have not actually learned the skills that they ought to
have learned by the time they finish high school.  She says that many of the graduates
are "semiliterate."

The "F Word" that Sherry is praising
here is "flunk."  She thinks that the school systems in the United States are too
unwilling to let students fail.  She says that they simply pass the students so as not
to embarass them or because we feel sorry for them since they come from poor
backgrounds.  Sherry argues that this kind of softheartedness simply cheats the
students, robbing them of their chance to get the sorts of skills they need to actually
succeed in life.

In "The Metamorphosis," what happens to Gregor when he leaves the room to meet the office manager?

Remember that this is the first time that his family have
actually seen Gregor in his new, transformed state, so when he rushes out of the room to
try and speak to his office manager and somehow manage to keep his job, they are
obviously incredibly shocked and surprised at his appearance. His mother in particular
is incredibly shocked, then terrified as she knocks over a pot of coffee and Gregor
snaps his jaws at it. The office manager runs away down the stairs, but Gregor is able
to distinctly hear him say "Ugh!" It is his father, however, who responds in the most
violent way:

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...the father, with his right hand, grabbed the
cane that the office manager, together with a hat and overcoat, had forgotten on a chair
and, with his left hand, took a large newspaper from the table. Stamping his feet, he
brandished the cane and the newspaper at Gregor in order to drive him back into his
room.

Notice how this shows a
certain presence of mind. Gregor's father is the one character who is able to cope with
his shock and channel it to do something that helps the situation, although this of
course shows significant cruelty to Gregor.

In Bless Me, Ultima, what page is the quote "The people need good leaders, and the greatest leader is a priest" on?

Of course, my edition of this book might be slightly
different from yours, but this quote comes on page 179 in Chapter Fifteen, as part of
the conversation that Antonio's mother had with Antonio after he recovers from the fever
he contracted after healing Andrew with Ultima. The conversation again conveys the
pressure that Antonio is under from his mother to become a Luna and lead his people as a
priest. Antonio, throughout the novel, is trying to search for knowledge, for answers to
questions that he has such as the reason for the existence of evil. He asks his mother
whether at First Communion he will be given "the knowledge of God," and his mother
replies in the affirmative:

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I hope you will use your knowledge to carry out
God's will. You are a very bright boy, you understand so much, you can be a great
leader, a priest--I do not want you to waste your life in dreams, like your father. You
must make something of yourself, you must serve the people. The people need good
leaders, and the greatest leader is a
priest--

Note the way that
this introduces one side of the conflict that Antonio endures as he has to face the
wishes of his mother that he would become a priest on the one hand, and then the wishes
of his father that he follows his family and becomes a restless wanderer on the
plains.

Can you please help me identify this movie:I saw this movie few years ago. It was about a girl that had hands for feet, and it was an action movie....

The movie you are thinking of is called Aeon Flux and was
brought out in 2005. It stars Charlize Theron as a member of "The Mohicans," a rebel
group who are working against the government of the post-apocalyptic remnant of
humanity. The vast majority of humanity has been eradicated by a killer disease, and now
the remnant find themselves in a protected city called Bregna. All "Mohicans" are given
orders telepathically and led by a rebel figure called "The Handler." Aeon is struck by
tragedy when her beloved sister is thought to be a "Mohican" and killed as a result. She
is given a mission to kill the leader of the government, Trevor Goodchild, but makes a
series of discoveries about humanity, the government and the Mohicans as she tries to
complete her mission, resulting in some major twists and turns in the
plot.

What is your evaluation of the ending of Poe's story "The Cask of Amontillado"?

At the end of the story The Cask of
Amontillado, by Edgar Allan Poe, we find Montressor and Fortunato inside the
former's (Montressor's) catacombs in a quest for a cask of Amontillado wine, which is
quite precious and is one of the very rich possessions of Montressor. This wine is meant
as bait for Fortunato--a man who enjoys his drink--since Montressor is planning his
horrid murder. Therefore, Montressor wants Fortunato to be drunk with wine so that he
can bury Fortunato alive within the catacombs.

What strikes
the reader the most is that Montressor, as he narrates his actions, still has the gall
to call Fortunato his "friend," even as he builds the walls within which he is to trap
Fortunato alive. The last time Montressor calls Fortunato his "friend" is the moment
when he leads Fortunato straight to the "bait," which was the
wine.

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[MONTRESSOR]: The Amontillado!” ejaculated my
friend [Fortunato], not yet recovered from his
astonishment.

Soon after this
incident, the deed begins to take place, and we see the coldness with which Montressor
continues to narrate his actions. This is the part that is shocking and morbid, even
sadistic, to the average person.

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[MONTRESSOR]: My heart grew sick; it was the
dampness of the catacombs that made it so. I hastened to make an end of my labour. I
forced the last stone into its position; I plastered it up. Against the new masonry I
re-erected the old rampart of bones. For the half of a century no mortal has disturbed
them. In pace
requiescat!

Here
we see more sadistic behavior. He is unmoved by his crime. He blames the dampness of the
catacomb for the "sickness" of his heart. He hurries up to finish his work and ensures
that it is done correctly. In a more sociopathic twist, he even offers his respects to
what will be Fortumato's remains and wishes that the man may rest in peace. What this
shows is a disturbed, confused, and sick mind that finds pleasure in his task. Nothing
more than the behavior of a sociopath and psychologically deranged
man.

In Johnny Tremain, what is the significance of Pumpkin

Johnny Tremain is set during the time
of the Revolutionary War, in which America battles England for its independence. Pumpkin
(his nickname based on his bright red hair) is a horse-boy for the British soldiers, and
he comes to love the openness of America and wants to quit the British
Army.

When Johnny is riding through the British camp and
finds himself in some trouble, Pumpkin helps him break free. In exchange, Johnny
arranges for Pumpkin to fulfill his dream. This young British citizen no longer wants to
be part of the fighting; instead, he is entranced by the open space and farmland,
something he did not experience back in England. Pumpkin's simple dream is to leave the
army and go work on a farm, and Johnny arranges for him to do that--provided he let
Johnny have his uniform.

The exchange is made, and Johnny
gives the British uniform and musket to Rab. Shortly after, Johnny finds himself an
unwilling witness to a hanging for treason. Pumpkin is hanged as an example to others
who are contemplating desertion.

When the War has begun and
Johnny must find a way to get to the battlefront to check on Rab, he remembers the
uniform and wears it to get himself where he wants to be. The significance of Pumpkin's
British uniform, then, is that it is instrumental in getting Johnny safely to the battle
to be with his friend who eventually dies. What is hateful and unwanted to Pumpkin is
that which saves Johnny's life.

Prove that sinx+sin3x+sin5x=(1+2cos2x)*sin3x .

Since the added trigonometric functions are matching,
we'll apply the identity:

sin a + sin b = 2 sin
[(a+b)/2]*cos[(a-b)/2]

We'll add the first and the 3rd term
from the left side:

sin x + sin 5x = 2 sin
[(x+5x)/2]*cos[(x-5x)/2]

sin x + sin 5x = 2 sin
3x*cos(-2x)

Since the cosine function is even,we'll
get:

sin x + sin 5x = 2 sin 3x*cos
2x

We'll re-write the
expression:

sin 3x + 2 sin 3x*cos 2x =
(1+2cos2x)*sin3x

We'll factorize by sin 3x to the left
side:

sin 3x*(1 + 2cos 2x) =
(1+2cos2x)*sin3x

We notice that managing the
left side, we'll get LHS = RHS , therefore the given identity sin x + sin 3x + sin 5x =
(1+2cos2x)*sin3x is verified.

What does the speaker have in common with the lamb and the lamb's creator?

Little Lamb, I'll tell thee, 
Little Lamb, I'll
tell thee. 
He is called by thy name, 
For He calls Himself a
Lamb. 
He is meek, and He is mild; 
He became a little
child. 
I a child, and thou a lamb, 
We are called by His
name.

These lines from
William Blake's poem, The Lamb contain the answer to your question.
The speaker who addresses the lamb in the poem is a child, a human child, endowed with
the gift of language, whereas the addresse, a lamb, is a non-human child, a dumb child.
In these lines the speaker explores in his simple language of childhood innocence how
the creator of the lamb who is also the creator of the child is both a child and a lamb.
Christ Himself was referred to as "the Lamb of God", and the creator was born in the
form of a human child: the babe in the manger. The creator is
"meek" and "mild", and the speaker does have these features of "meekness" and 'mildness"
in common with the lamb and its creator.

Which character change/progresses the most in Death of a Salesman? What types of changes occur to this character? What is some evidence to prove...

I would say that Biff changes the most in the play as he
realises that he has control over not only his own success and failure, but his
father's.

Biff was seen as the hero, with prospects,
sporting prowess and good looks. He also possessed some of his father's rose-tinted
optimism in teh early days. Biff however clearly gave up on striving for success and
recognition after he saw his father with the other woman. From that point he sees his
father as a 'fake' and has avoided dealing with the crushing disappointment of his
father's fallibility. Once he is made aware of the seriousness of Willy's mental state,
he steps up to support his parents-

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BIFF: ...I've been remiss. I know that, Mom. But
now I'll stay, and I swear to you, I'll apply
myself.

Unfortunately Biff is
unable to get the truth about both of their failures through to his father, and though
he tries to comfort his mother, Willy is beyond help in terms of seeing
reality-

BIFF:
I am not a leader of men, Willy, and neither are
you.

Willy's last thoughts
are of Biff scoring a touch down for him as he promised. Willy's suicide can be seen as
prompted by him finally accepting what Biff tried to tell him all
along.

How to rationalize the denominator of the fraction (3*sqrt 2 - sqrt 6)/(4*sqrt 2 + sqrt 6)

To rationalize the denominator, we'll have to multiply
both the numerator and denominator by the conjugate of the
denominator:

(3sqrt2 - sqrt6)(4sqrt2 - sqrt6)/(4sqrt2 +
sqrt6)(4sqrt2 - sqrt6)

The product of denominator returns a
difference of two squares:

(3sqrt2 - sqrt6)(4sqrt2 -
sqrt6)/(4^2*2 - 6)

We'll remove the brackets from the
numerator:

(12*2 - 3sqrt12 - 4sqrt12 +
6)/(32-6)

We'll combine like terms inside
brackets:

(30 -
7*2sqrt3)/26

(30-14sqrt3)/26 = 2(15 -
7sqrt3)/26

2(15 - 7sqrt3)/26 = (15 -
7sqrt3)/13

The rationalized fraction is (15 -
7sqrt3)/13.

Is the narrator content after killing Fortunato? "The Cask of Amontillado" by Edgar Allan Poe

After Montesor, who is the narrator of "Cask of
Amontillado" walls his his foresworn enemy, he repeats the words of Fortunato with an
emphasis toward his justification of his revenge:  "Yes,...for the love of God." 
However, when Fortunato does not reply, Montesor grows impatient and shouts his victim's
name.  Still, Fortunato does not reply, and Montesor cannot delight in his cruel revenge
as he wants:

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There came forth in return only a jingling of the
bells.  My heart grew sick--on account of the dampness of the catacombs.  I hastened to
make an end of my labor.  I forced the last stone into its position; I plastered it
up.

Montesor as narrator then
remarks that for fifty years no one has disturbed this grave of Fortunato. 
"In pace requiescat!" he states ironically.  However, the irony
seems to be spent upon Montesor himself as it is he who is disturbed by the horror of
his act.  For, the perpetrator of the horrible deeds in this gothic tale is no
supernatural power, but the terrible act of one human being against another.  It is this
realization of the real horror lying within himself that disturbs Montesor, that makes
him call out to Fortunato, and that keeps him for resting in peace over the murder he
has committed. 

How is the plot of John Steinbeck's "The Chrysanthemums" embellished?

Usually "embellish" is what someone does who adds to a
story they have heard, adds more to an experience than what really happened, or outright
makes up lies about someone or something. It can also refer to
"ornamentation."

Dictionary.com defines "embellish"
as:

to enhance
(a statement or narrative) with fictitious
additions.

In embellishment
with literature, I expect this means that more information is provided than might
otherwise be necessary in the telling of the tale. Of course, when
the author does this, he adds details that provide a clearer image of a character and/or
a better understanding of the plot.

In John Steinbeck's
short story "The Chrysanthemums," the part that impresses me the most comes in the
character of the tinker or peddler. The "meeting" of the dogs leads to the casual dialog
that connects Elisa and her visitor.

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The rangy dog darted from between the wheels and
ran ahead. Instantly the two ranch shepherds flew out at him. Then all three stopped,
and with stiff and quivering tails, with taut straight legs, with ambassadorial dignity,
they slowly circled, sniffing daintily...Now the newcomer dog, feeling outnumbered,
lowered his tail and retired under the wagon with raised hackles and bared
teeth.

The man on the wagon seat called out, "That's a bad
dog in a fight when he gets started."

Elisa laughed. "I see
he is. How soon does he generally get started?"

The man
caught up her laughter and echoed it heartily. "Sometimes not for weeks and weeks," he
said.

The other embellishment
that adds to the significance of the tinker's visit is found in all the details of their
"small talk" before the man gets down to the business of asking for work. During this
discussion, the reader notes that this is a traveling man who
easily makes conversation with complete strangers. However, he
seems genuine and easy to relate to. His arrival in the story also allows the author to
present the idea that Elisa envies his way of life—important to understanding that she
is not totally satisfied with her own circumstances.

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He drew a big finger down the chicken wire and
made it sing. "I ain't in any hurry, ma am. I go from Seattle to San Diego and back
every year. Takes all my time. About six months each way. I aim to follow nice
weather."

Elisa took off her gloves and stuffed them in the
apron pocket with the scissors..."That sounds like a nice kind of a way to live," she
said.

The tinker is able to
wheedle some work out of Elisa with his charm and humor—and an expression of interest in
her flowers.

readability="9">

The irritation and resistance melted from Elisa's
face. "Oh, those are chrysanthemums, giant whites and yellows. I raise them every year,
bigger than anybody around
here."

He says he knows a
woman who would love them, and Elisa generously offers some. These plants are like her
children—they are very dear to her.

When the man leaves, we
don't realize how much we have learned about Elisa. He could simply have stopped to ask
for work and Elisa could have given it to him, but instead we learn of her wish to
travel without being tied down—not appropriate for a woman of her era. We see her
loneliness as he expresses interest in her flowers—her resistance "melts." There is
generosity when she shares her flowers. And we learn how fragile she is when she and her
husband drive to town for dinner: there on the side of the road are the discarded
plants, where the charming and (we now know) manipulative tinker dumped them once he
left Elisa.

What characters can be identified as being "wanton" in David Copperfield?

The answer to this question depends on what you mean by
wanton. A dictionary will give you something like the following definition: a wanton
character is one who is merciless, lewd, malicious, undisciplined and spoiled. Given
these adjectives, and thinking about this excellent bildungsroman from Dickens, the
major character that could be described as wanton would be James Steerforth. In the
novel, he is an attractive, charming individual who nevertheless shows himself to be
completely unprincipled and incredibly selfish in the way that he uses others,
especially David Copperfield in his innocence and naivety. Throughout the novel,
Steerforth only uses David for his own ends: to gain prestige and status through the
connections that David has and then to cruelly betray him. The way that he preys on the
innocence of the title character is obvious to us as onlookers, but is used to emphasise
the innocence of the narrator.

What are three examples of each of the four freedoms being either expressed or denied in To Kill a MockingBird?The four freedoms are freedom of...

FREEDOM OF SPEECH.  I'm not
sure there are many examples in the novel of a person's freedom of speech being denied.
Certainly, Jem and Scout knew to hold their tongues in some instances, such as when they
were being scolded by Atticus, Calpurnia or their Aunt Alexandra. Examples of speech
being freely expressed are frequent.

• B. B.
  Underwood's editorial in the local paper compared Tom's death with the "senseless
  slaughter of songbirds."


• Atticus begs the jury to
  overlook their racial prejudice and judge Tom fairly.


• Bob
  Ewell is allowed to tell his side of the story in the courtroom, even though it is
  inflammatory and it is apparent that he is
  lying.

FREEDOM OF
WORSHIP.  Likewise, I don't recall any examples of the denial of free
worship. Although it is almost certain that Maycomb's Negroes would not have been
welcome in the town's all-white churches, the narrator never mentions this in the
novel.

• When Jem and Scout joined Cal at the
  First Purchase Church, they were confronted by Lula, who objected to the white children
  attending their church.


• Boo's parents were known to be
  highly religious, but they chose to worship within the walls of their own
  house.


• Miss Gates points out the injustices that
  Germany's Jewish population felt under Adolf
  Hitler.

FREEDOM FROM
WANT.  Several examples arise during Scout's first day at
school.

• Walter Cunningham Jr. has no lunch or
  lunch money, nor can he pay back the money offered by Miss Caroline. Feeling sorry for
  him, Jem invites Walter to eat lunch at the Finch
  house.


• Burris Ewell comes to school filthy and
  lice-ridden. He announces that he won't be back, signifying his father's total disregard
  for his children's welfare and education.


• It can be
  argued that Boo Radley is forced by his family to remain inside their home, where he has
  no friends or other human contact. Even when Boo attempts to make friends with Jem and
  Scout via the secret knothole, Boo's brother cements the tree, effectively ending their
  relationship.

FREEDOM FROM
FEAR.

• Bob Ewell's ability to roam
  the town at will obviously worried Aunt Alexandra, though Atticus tried to downplay the
  depths of Bob's revenge.


• School children feared Boo
  Radley, but Boo may have also feared others who misunderstood
  him.


• Atticus feared that there would be an attempt to
  take Tom from the jail, and both he and Tom were lucky that the lynch mob left
  empty-handed.

Discuss how Bigger approaches both murders he commits in Native Son.

I think that both murders represent a great deal of
similarity and simultaneous difference. Analyzing what brought both murders to fruition
requires an analysis of why Bigger did what he did, or his motive, and then examining
the exact nature of each murder.  I think that the motive of each is equally similar,
yet different.  Bigger wanted to silence both women’s voices. His attempts to do so
result in violent means of accomplishing that goal.  Mary’s murder was accidental
suffocation, in that he wanted to keep her quiet so he would not be discovered as being
with her.  Certainly, he did not mean to kill her, but his use of violence or physical
means to ensure her silence resulted in her death.  Desiring to keep Bessie silent is
what motivates Bigger to silence Bessie, yet this murder featured a motive of self
preservation.  Bigger recognizes that Bessie is going to divulge his and her involvement
in criminal activity.  In the attempt to ensure her silence, he kills her.  This intent
is a bit different than what was involved in Mary’s murder.   On one hand, both are
fairly brutal.  Bigger did not need much in way of weapons in order to kill both women. 
At the same time, the fact that both murders are deliberate crimes against women is
another factor that helps to add to the brutality of each. The sexual violation of
Bessie prior to her death and then throwing her down a staircase is another version of
the post- mortem gruesome brutality of Mary in stuffing her remains in the furnace.  In
the end, Bigger shows that he lacks the vocabulary and the means to effectively
articulate his helplessness that he feels in American society.  Murder, sex, and
violence are the only means he is able to control, and while this does not excuse his
actions, it widens the understanding around them.

there is a theme of betrayall in othello,in your own words describe how shakespeare potrayed this theme and give examples from the text?

In 'Othello' the central theme is jealousy and betrayal.
Iago inspires jealousy in several of the central characters, most notably, Roderigo and
Othello.

Iago sets in place malice in Roderigo towards
Othello for marrying Desdemona but what Roderigo does not realise is that he is being
duped by Iago who not only has no intention to promote Roderigo to Desdemona but is also
milking Roderigo for every penny that he is
worth.

Iago plants seeds of doubt about
Desdemona's faithfulness to Othello informing him that she has been unfaithful to him
with Cassio and as a result he murders her and asks Iago to kill Cassio on his
behalf.

Eventually, all parties come to realise
that Iago has betrayed them all.

He betrays Othello by
lying about Cassio and Desdemona

He betrays Roderigo by
lying about Cassio and Desdemona and subsequently killing
him.

He betrays his wife by killing her when she exposes
him.

He betrayed Desdemona by lying about her
virtue.

He betrays Cassio by engineering his
demotion.

Othello is not
innocent:

He also betrays
Desdemona

He betrays
Cassio

and to a certain extent he betrays himself by
succumbing to jealousy and fulfilling the expectations that Venetian society had of him
based on race.

He also betrays the audeince because in the
final Act when we think he is going to come clean and explain his actions he does the
opposite and decides to remain silent.

If you are looking
for key quotations, Act 3 Scene 3 is the central scene and marks the turning point of
the play. In this scene, there are several quotations that relate to jealousy and
describe it as being a poison or disease. In terms of betrayal the final Act provides
several good examples of how Othello copes with the realisation of his betrayal of
Desdemona.

How can the US improve exports?

The only thing that any country can really do to improve
its ability to export is to increase its comparative advantage in some way.  A country
has to identify what advantages it has over other countries and maximize those as much
as possible.

In the case of the United States, the most
likely comparative advantage is in technology and education.  Americans as a group are
well-educated and should therefore be able to compete well with other countries in areas
needing a great deal of "brain work."  In order to maximize this comparative advantage,
the best thing for the US would be to improve support for education and for research and
development.  American firms need to work on producing higher technology using greater
brainpower than other countries.  The government needs to spend its money promoting
education and technological development.  This is how the US could increase its ability
to export.

What is the equation of the line that passes through (-3,7) and parallel to the line 2y-4x +2 = 0

Given the point (-3,7) passes through the
line.

Then we know that:

y-y1
= m(x-x1)

==> y-7 =
m(x+3)

Now we will determine the
slope.

Since the line is parallel to the line 2y-4x +2 = 0,
then the slopes are equal.

==> We will rewrite into
the slope form.

==> y= 2x
-1

==> Then the slope is m=
2

==> y-7=
2(x+3)

==> y-7 = 2x +
6

==> y= 2x +
13

Then the equation of the line is y=
2x+13.

Prove Pascal's rule(n,k)+(n,k+1)=(n+1,k+1)

We'll use combinatorial way to prove this
identity.

We'll recall the factorial formula of
combinations of n elements taken k at a time:

C(n,k) =
n!/k!*(n-k)!

Now, we'll write the factorial formula of
combinations of n elements taken k+1 at a time:

C(n,k+1) =
n!/(k+1)!*(n-k-1)!

Now, we'll write the factorial formula
of combinations of n+1 elements taken k+1 at a
time:

C(n+1,k+1) =
(n+1)!/(k+1)!*(n+1-k-1)!

We'll reduce like terms within
brackets form denominator:

C(n+1,k+1) =
(n+1)!/(k+1)!*(n-k)!

Now, we'll re-write the identity that
has to be demonstrated:

n!/k!*(n-k)! + n!/(k+1)!*(n-k-1)! =
(n+1)!/(k+1)!*(n-k)!

We'll create the same denominator at
the fractions from the left side:

[n!*(k+1) +
n!*(n-k)]//(k+1)!*(n-k)!

We'll remove the brackets from
numerator:

(n!*k + n! + n!*n -
n!*k)/(k+1)!*(n-k)!

We'll eliminate like terms within the
brackets:

(n! +
n!*n)/(k+1)!*(n-k)!

We'll factorize by
n!:

n!*(n +
1)/(k+1)!*(n-k)!

But n!*(n + 1) =
(n+1)!

The left side will
become:

n!*(n + 1)/(k+1)!*(n-k)! =
(n+1)!/(k+1)!*(n-k)!

We notice that the LHS =
RHS, therefore the Pascal's rule is verified, so that n!/k!*(n-k)! + n!/(k+1)!*(n-k-1)!
= (n+1)!/(k+1)!*(n-k)!.

How do we write and solve the statement " the difference between a number and 3 is less than 15" What are possible values of the number?

Let us assume that the number required is
x.

Then we need to find the
difference.

==> l x - 3l <
15

Now we will solve the inequality with the absolute
value.

We will
rewrite:

==> -15 < x-3 <
15

Now we will add 3 to both
sides.

==> -12 < x <
18

Then the values of the number are the
interval (-12, 18).

The function f is defined as f(x)=(2x+1)/(x-3). Find the value of k so that the inverse of f is f^-1(x)=(3x+1)/(x-k).

We'll determine the inverse function
f^-1(x).

Let f(x)=y, such
as:

y = (2x+1)/(x-3)

We'll
multiply both sides by (x-3):

xy - 3y =
2x+1

We'll move 3y to the
right:

xy = 2x + 3y +1

We'll
subtract 2x both sides:

xy - 2x = 3y +
1

We'll factorize by x to the
left:

x(y - 2) = 3y + 1

We'll
divide by (y-2):

x =
(3y+1)/(y-2)

The inverse function is: f^-1(x) =
(3x+1)/(x-2)

Comparing with the given
expression of f^-1(x) = (3x+1)/(x-k), we'll identify k =
2.

reflect on what pip's reaction reveals about his character when he meets the true benafactor magwitch

Pip is horrified (to put it mildly) and devestating when
he learns Magvitch is his benefactor. He is devestated because he truly believed Miss
Havisham was his benefactor, and that she was arranging it so Pip could marry Estella.
As for being horrified, Pip's true character is revealed at this point: he has become a
snob. He has allowed his new position in life (gentleman) to ruin his true person. Pip
was once a boy/teenager who knew what it meant to have to work for something, but
because of his benefactor, he has grown lazy and greedy. He feels he deserves the money
he received; he feels it is his destiny to be a gentleman and to be with Estella. By
revealing the truth to him, Magvitch has crushed all of Pip's expectations. Pip feels
that Magvitch's money and intent are below him. He despises the criminal in spite of all
the criminal has done for him. At the start of the book, the crinimal appears hard and
cruel; now it is Pip who is the cruel one.

In Othello, who is responsible for Desdemona's death?

Desdemona is killed by her husband, Othello. He smothers
her in the belief that she has been unfaithful to him with a Cassio, a member of
Othello's staff. Desdemona tells us of her innocence in Act V Scene
ii- 

O,
falsely, falsely
murdered!

And indeed Othello
confesses to his crime-

readability="5">

She's like a liar gone to burning hell;

'Twas I that kill'd
her.

However, it is through
the cruel machinatios of Othello's ensign, Iago, that Othello has believed the tale that
Desdemona was unfaithful. Once Emilia is able to piece together Iago's wicked plot, she
directs the guilt squarely at her husband -

And
your reports have set the murder on.

In
the final lines of the play it is clear whom Lodovico, as representative of the Venetian
government, believes is responsible for the tragedy which has befallen as he addresses
Iago-

O Spartan dog;
More fell than anguish,
hunger, or the sea!
Look on the tragic loading of this bed;
This
is thy work.

Is there a commutative property of addition, subtraction, multiplication, or division and does order matter when doing any of them, why or why not?

Addition and Multiplication ARE commutative, while
Subtraction and Division are NOT commutative.

e.g, in
simple addition and multiplication, no matter what the order, the result is still the
same. Whereas, subraction and division need to have a particular order or the result
will change.

When doing more complex expressions and
equations, order IS important or the answer will change
completely.

An easy way to remember order is
BIMDAS

B -
Brackets
I -
Indices
M - Multiplication (from
left of expression to right)
D - Division (from
left of expression to right)
A - Addition(Left of
expression to right)
S- Subtraction (Left of
expression to right)

Hope that
helped.