Find the x and y intercept of the curve y=x/(2x-3)^2.

y= x/(2x-3)^2

We need to find
the intercepts.

First we will find the y-intercept. Then
the value of x is zero.

==> y= 0/(2*0 3)^2 =
0

Then the y-intercept is the point
(0,0).

Now we will find the x-intercept. Then the value of
y is 0.

==> 0 =
x/(2x-3)^2

==> x =
0

Then the x-intercept is also
(0,0)

Then we have one intercept for both
axes which is the origin point: x = (0,0) and y =
(0,0).

What is Black Beauty's message?

In the simplest of terms, I think that Sewell's work tries
to bring forth the point that animals are creatures that feel pain, love, and joy.  They
are not objects who lack the sensibilities of feeling creatures.  The idea that Black
Beauty responds to pain and suffering, affirms care and compassion help to deliver the
book's primary message that animals, in this case, horses need care.  At a point where
utilitarian values emphasized the "greatest good for the greatest number," Sewell's work
is a reminder that it is important to not abuse in this name.  The tendency to overwork
or abuse animals is something that has not gone away from modern society.  The desire to
use an animal as a means to an end and not as the end in its own right is something that
Sewell's work criticizes heavily and is something that is brought out as one of the
primary messages of the book.  Sewell intended her work to be a guide on how to tend to
and take care of horses.  In doing so, she makes the statement that animals need to be
treated with care, and not used and abused for the ends of others.  We have seen this,
whether it is with Michael Vick's treatment of dogs for sport, or for greyhounds raced
and treated in an abhorrent manner, or even horses in horse racing that are given drugs
that are contrary to a healthy life in order to gain more profits, the need to halt the
mistreatment of all animals is one of the primary messages of Sewell's
work.

What is sin x*cos x if sin x/cos x=1/5 and x is in the interval (0,pi)

The interval (0,pi) covers the first and the second
quadrant where the values of the sine function are positive and the values of cosine
function are both positive (1st quadrant) and negative (2nd
quadrant).

We'll start with the Pythagorean
identity:

(sin x)^2 + (cos
x)^2=1

We'll divide the formula by  (cos
x)^2:

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

But the ratio sin x /cos x= tan x =>(sin x)^2/
(cos x)^2 = (tan x)^2 = 1/25

The formula will
become:

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

cos x = +1/sqrt[1+(tan x)^2] or cos x = -1/sqrt[1+(tan
x)^2]

cos x =
1/sqrt[1+(1/5)^2]

cos x=
1/sqrt(1+1/25)

cos x = 5/sqrt26 or cos x =
-5/sqrt26

But sin x/cos x =1/5 => sin x = cos x/5
=> sin x = 1/sqrt26

sin x*cos x = 5/26 or sin x*cos
x = -5/26

The requested values of the product
sin x*cos x, in the interval (0,pi), are : {-5/26 ;
5/26}.

Determine the magnitude and direction of the gravitational force exerted (a) on the moon by earth and (b) on earth by moon.Earth's mass: 5.98 x...

Any two bodies with a mass attract each other due to the
gravitational force. The force exerted by each body on the other is towards its center
of mass. In the case of spherical bodies the center of mass lies at the geometric
center.

The force by which each of them is attracted towards the other
is the same.

It is given by the Newton's law of universal gravitation
as F = G*M1*M2/r^2, where G is a constant equal to 6.674*10^-11 N m^2/kg^2, M1 and M2
are the mass of the two bodies and r is the distance between
them.

Here the mass of the Earth is 5.98*10^24 kg, the mass
of the Moon is 7.35*10^22 kg and the distance between the Earth and the Moon is 384,399
km.

The force of attraction is: 1.985*10^20
N.

The Earth attracts the moon by a force equal to
1.985*10^22 N towards its center and the Moon does the same in the opposite
direction.

Are there any good/important GOTHIC quotations in Frankenstein that you can think of?

There are many ways in which one could find Gothic
examples in the novel Frankenstein. (Some would argue that the
novel is one which best matches the work of a Romantic author and not one of a Gothic
author.)

First, many Gothic texts include an atmosphere
which breeds mystery or suspense. Many times throughout the text Victor becomes
suspenseful. The shutting of himself in his laboratory, the search for the monster on
his own, and waking to find himself in a foreign land accused of
murder.

Second, the Gothic text contains omens or
prophecies. Victor dreams about murders and the deaths of those around him. One could
look at these dreams as clues as to what is to come.

Third,
Gothic texts include (perhaps most famously) aspects of the supernatural. Here, giving
life to a long dead and decomposed pieced together man can be considered a supernatural
element.

Fourth, many characters in Gothic texts experience
heightened emotions- ones that boarder hysteria and terror. Victor experiences both of
these emotions. When he discovers that his monster lives, Victor rushes from his flat
terrified. It seems that every time Victor becomes suddenly emotionally charged, he gets
seriously ill.

Compare the relationship between Oliver and Orlando at the beginning and at the end of As You Like It.

It is clear that there is little love lost between Oliver
and Orlando at the beginning of the play and that they, like Duke Ferdinand and Duke
Senior, could aptly be described as feuding brothers. Orlando definitely feels that
Oliver has not obeyed his father's injunction in terms of bringing up Orlando to be a
nobleman. Note how he accuses his brother in Act I scene
1:

My father
charged you in his will to give me good education. You have trained me like a peasant,
obscuring and hiding from me all gentleman-like
qualities.

However, in spite
of the obvious animosity between them, it is clear that the magic of the Forest of Arden
works a transformation in the character of Oliver, who becomes reconciled with his
brother and what is more falls in love with Celia, pledging to marry her and deciding to
live and die in the Forest of Arden and live as a simple shepherd. Note how the
relations are completely reversed by the end in Act V scene 2 when Oliver asks for
Orlando to consent to his marriage to Celia:

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Consent with both that we may enjoy each other.
It shall be to your good, for my father's house and all the revenue that was old Sir
Rowland's will I estate upon you, and here live and die a
shepherd.

Oliver's change in
his relations with Orlando is symbolised by the willingness with which he relinquishes
his wealth, that he at the beginning of the play was so reluctant to share with his
brother.

Why did Wilson write the play Fences?

As with the construction of many literary works, there are
many reasons that inspire creations.  One reason would be to articulate the condition of
African- Americans in the early stages of integrated society.  It is often depicted that
once Brown v. Board of Education became law in the American landscape, that African-
Americans were able to experience full and total opportunities in American society.  The
fact that there was a difficult and grueling process of people of color, specifically
African- Americans, to experience opportunity and success is something that motivated
Wilson, providing the historical context to the drama.  Another rationale that
underscores much of Wilson's work is the depiction of real life for people of color. 
The reality of the condition that surrounds African- Americans and how to navigate the
social constructs of race, class, age, and gender.  These are some of the reasons why
Wilson decides to write Fences.