Who was John Locke?

John Locke was a major political philosopher of the Age of
Enlightmentment.  He is best known today (at least in the United States) because his
thoughts and writings were major influences on the founders of the United States.  For
example, his ideas are pretty much repeated word for word in the Declaration of
Independence -- the part where Jefferson talks about the self-evident truths about
government and what it is created for.

Locke was an
Englishman who was born in 1632, long before the Revolution that his ideas helped to
start.  His best known works are probably his Two Treatises on
Government.  He is one of the major thinkers associated with the idea of
government that is based on a social compact.

Describe Macbeth's vision at the end of Act II, Scene 1 in Macbeth.

After Banquo, Fleance and the servants have exited the scene,
Macbeth is left alone onstage to converse with the audience.  He asks, "Is this a dagger I see
before me/The handle toward my hand?"  His vision is of a dagger, which seems to be offering
itself to him rather than threatening him, since "the handle" is pointed "towards" his
hand.

Macbeth goes on in this soliloquy to describe how he clutches
for it, but cannot grasp it.  However, there is question about whether an actual image of a
dagger appears during this soliloquy.  Macbeth asks:

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. . .art thou but

A dagger of
the mind, a false creation,

Proceeding from the heat-oppressed
brain?

So, Macbeth is acknowledging
that he might, in fact, be tormented by an image from his own mind -- his conscience? -- rather
than observing an actual dagger floating in the air before
him.

Either way, he definitely makes the image of a dagger real in
his next line.

I see
thee yet, in form as palpable

As this which now I
draw.

And with the drawing of his own
actual weapon, Macbeth seals his decision to go through with the murder, invoking the dark
spirits of night to aid him in his treason.

For more on this scene,
please follow the links below.

In "The Tell-Tale Heart," how does the tension increase and decrease throughout the story, and why?

To be honest I don't think there is much decreasing in
tension in this short story - it gradually raises the tension until it reaches fever
pitch at the very end as the narrator declares himself for who he really is and the
terrible crime he has committed.

From the very first
paragraph, that makes it clear we are presented with an unreliable narrator, we are
plunged into a scary world of imminent violence and madness. Every paragraph raises the
tension another notch as we wonder what the narrator will do and then think about what
will happen in consequence of his actions. Consider the second
paragraph:

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Passion was there none. I loved the old man. He
had never wronged me. He had never given me insult. For his gold I had no desire. It was
his eye! yes, it was this! He had the eye of a vulture - a pale blue eye, with a film
over it. Whenever it fell upon me, my blood ran col; and so by degrees - very gradually
- I made up my mind to take the life of the old man, and thus rid myself of the eye
forever.

We are presented
almost at the beginning of the story with the plan of a narrator who we suspect of being
mad to cold-bloodedly kill an acquaintance for what seems to be the most ludicrous of
reasons. How he does it, the reaction of the old man and what happens afterwards only
serves to keep the tension rising in this rapid and terrifying
tale.

√(x - 3) ≥ 1/(x - 3) help on how to solve please!!!

Before solving the inequality, we'll impose constraints of
existence of square root.

x - 3
>=0

We'll add 3 both sides:

x
>= 3

The interval of admissible values of x is [3 ,
+infinite)

We'll raise to square both sides, to get rid of the
square root:

(x - 3) ≥ 1/(x -
3)^2

We'll subtract 1/(x - 3)^2 both
sides:

(x - 3) - 1/(x - 3)^2 ≥  0

We'll
multiply by (x - 3)^2 both sides:

(x-3)^3 - 1 >=
0

We'll apply the formula of difference of
cubes:

a^3 - b^3 = (a - b)(a^2 + ab +
b^2)

(x-3)^3 - 1 = (x-4)[(x-3)^2 + x - 3 +
1]

We'll square raise and we'll combine like
terms:

(x-3)^3 - 1 = (x-4)(x^2 - 5x +
7)

(x-4)(x^2 - 5x + 7) >=0

A
product is positive if and only if the 2 factors are both negative or both
positive.

Case
1)

x-4>0

x>4

x^2
- 5x + 7 > 0

x1 = [5+sqrt(25 -
28)]/2

Since delta = 25 - 28 = -3 < 0, the expression x^2 -
5x + 7 > 0 for any value of x.

From both
inequalities, the interval for admissible values for x is (4; +
infinite).

Case
2)

x-4<0

x<4

x^2
- 5x + 7 < 0

But the expression is always
positive, for any value of x, so x belongs to empty set.

Prove that 1/a(a+1) = 1/a - 1/(a+1)

We notice that the denominator of the left side ratio is
the least common denominator of 2 irreducible ratios.

We'll
suppose that the ratio 1/a(a+1) is the result of addition or subtraction of 2 elementary
fractions:

1/a(a+1) = A/a + B/(a+1)
(1)

We'll multiply the ratio A/a by (a+1) and we'll
multiply the ratio B/(a+1) by a.

1/a(a+1) = [A(a+1) +
Ba]/a(a+1)

Since the denominators of both sides are
matching, we'll write the numerators, only.

1 = A(a+1) +
Ba

We'll remove the
brackets:

1 = Aa + A +
Ba

We'll factorize by a to the right
side:

1 = a(A+B) + A

If the
expressions from both sides are equivalent, the correspondent coefficients are
equal.

A+B = 0

A =
1

1 + B = 0

B =
-1

We'll substitute A and B into the expression
(1):

1/a(a+1) = 1/a -
1/(a+1)

We remark that we've obtained the
request from enunciation.

The identity has
been proved.

What's the plot of "The Rocking-Horse Winner"?

Young Paul is concerned about his family's lack of money, and he
even hears the voice of the house whispering to him--"There must be more money!" His mother tells
him that they have no money because Paul's father is unlucky. Paul, however, has been told by God
that he IS lucky. He determines to change the family's financial misfortunes by picking winners
of horse races. How does he do it? He simulates each race by mounting and riding his childhood
wooden rocking horse, on which he envisions the eventual
winners.

Paul's accuracy is amazing, and he soon presents a gift of
a thousand pounds to his mother. Instead of being happy, however, she is "cold and indifferent."
Paul eventually gives her his entire winnings--five thousand pounds--but this only upsets the
voices of the house, which Paul now hears as a "mad" roar of screams. Hearing voices and obsessed
with picking the winner of the upcoming Derby, Paul's anxiety becomes overwhelming. When his
parents attend a party but leave him at home, they return to find Paul maniacally riding his
rocking horse, urging it on to the imaginary finish line. Before falling to the floor
unconscious, Paul cries out, "It's Malabar!" The parents fail to recognize the name, but Paul's
Uncle Oscar does: It is a horse running in the upcoming derby. Uncle Oscar places the bets,
Malabar wins, and just before his death, Paul is told that the horse has won the family a
fortune--80,000 pounds.

What are two possible themes for the play Othello?Where can I find the details that support these themes?

Two of the most common themes associated with
Othello are jealousy/revenge and appearance versus reality (or
"seeming").  Both of these are common themes in Shakespeare's plays, ones that you will
see re-investigated over and over.

Jealousy appears in Act
I, scene i when Iago is talking about being passed over for promotion.  Othello has
promoted Cassio instead of Iago.  Iago says:

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I know my price, I am worth no worse a
place.

But he, as loving his own pride and
purposes,

Evades them. . .for "Certes," says
he,

"I have already chosen my
officer,"

And what was he?. .
.

One Michael Cassio. . .mere prattle without
practice

Is all his
soldiership.

So, Iago shows
his reason for jealousy towards Cassio, and goes on to explain his revenge against
Othello.

Othello also displays his jealousy and thirst for
revenge.  Iago has led him into believing that Cassio is having an affair with his wife,
Desdemona.  In Act IV, scene i, once Othello thinks he has the proof, his thoughts turn
to murder as his revenge:

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I will chop her into messes. . .Cuckold
me!

Iago

O,
tis foul in
her.

Othello

With
mine
officer!

Iago

That's
fouler.

And so, Othello's
jealousy overtakes everything else and leads him to kill the thing he loves
best.

The theme of appearance versus reality is actually
shown in both of these same characters.  Iago decides to hide how he really feels about
being passed over, appearing to loyally follow the man (Othello) that he hates.  Back
again in Act I, scene i, he says:

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In following him, I follow but
myself.

Heaven is my judge, not I for love and
duty,

But seeming so, for my particular end. . .
.

But I will wear my heart upon my
sleeve,

For doves to peck at:  I am not what I
am.

And so he continues
throughout the play, sharing his inward thoughts and schemes with the audience, while
playing the dutiful ancient with Othello.

Othello is caught
up in the dilemma of appearance versus reality as well.  He swallows, hook, line and
sinker, all of the suggestions and false "evidence" that Iago presents him that
Desdemona is unfaithful.  The events of Acts III and IV surrounding the handkerchief are
the ones that, in reality, are the most false, but appear to be the most
damning.

These are merely a few of the examples of the
themes of jealousy/revenge and appearance versus reality in the play
Othello.  For more on these and other themes, please follow the
links below.