Explain how Robinson Crusoe's father believes his son to be in a "middle state," in Defoe's story, Robinson Crusoe. Explain how Crusoe's father...

In Daniel Defoe's novel, Robinson
Crusoe, Crusoe's father refers to his son as being in a "middle state." This
generally relates to what is common (as his father sees it) among adventurers in
general, based on their financial position in life.

His
father says that it is men of "desperate fortunes" who go on adventures such as Crusoe
plans, or men of "of aspiring superior fortunes," who hoped to improve their lot in
life. Following an uncommon path, these men hope to become famous. Crusoe's father then
tells Crusoe that Crusoe doesn't fit in either of these categories.
They were either "too far above" him, or "too far below." He labels Crusoe's position as
"middle states." Crusoe's father explains that Crusoe's position within society brings
the most happiness and is envied by others: Crusoe need not face "miseries and
hardships" or the hard work most others of the world need to do, and he does not have to
deal with "pride or...envy" from the upper classes. His father notes that "middle
states" is also...

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...what might be called the upper station of low
life, which he had found, by long experience, was the best state in the world, the most
suited to human happiness, not exposed to the miseries and hardships, the labour and
sufferings of the mechanic part of mankind, and not embarrassed with the pride, luxury,
ambition, and envy of the upper part of
mankind.

Crusoe's father goes
on to explain, as an example, that even kings wished to be in such a place, between the
poor ("mean") and great— for an easier life. He continues by saying that a wise man
prays to avoid poverty as well as riches. All in all, his father insists that those in
the "middle state" have the best life of all.

If Crusoe
proceeds with his plans, his father believes he will be miserable. He mentions the death
of his brother, whom his father also tried to dissuade from going to war—who was killed
while fighting, having ignored his father's advice: the same advice he was now giving to
Robinson. He tells his son to be satisfied with what he has in life, for he is extremely
fortunate.

Find x using logharitms. 4^(2x-1)-11=0

The first step is to shift 11 to the right
side.

4^(2x-1) = 11

Now, to
find out x, we'll take log on both sides:

log 4^(2x-1) =
log 11

We'll use the power rule of
logarithms:

(2x - 1)*log 4 = log
11

We'll divide by log 4 both sides of the
equation:

(2x - 1) = log 11 / log
4

We'll add 1  both sides:

2x
= (log 11 / log 4) + 1

We'l divide by
2:

x = [(log 11 / log 4) +
1]/2

The solution of the equation is: x =
[(log 11 / log 4) + 1]/2.

In Shakespeare's Macbeth, how can I explain Macbeth's murder of Banquo ?

In Shakespeare's Macbeth, after
Macbeth kills Duncan and takes the throne, Macbeth is aware that in order to guarantee
his place as King of Scotland, he must kill Banquo. Even though the
two men are close, their moral compasses are nothing alike. Though Lady Macbeth fears
her husband is not brave enough to take the quickest way to become king, practice makes
perfect, and Macbeth now knows that Banquo must die. He is the only person who was
present to hear the witches' first set of predictions. They also gave Banquo
predictions, but Banquo did not act on them—as Banquo suspects
Macbeth has done. Banquo privately considers Macbeth:

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Thou hast it now: King, Cawdor, Glamis,
all,

As the weird women promised, and I
fear

Thou play'dst most foully for't…
 (III.i.1-3)

Macbeth asks
Banquo how far out he will ride, in order to know about what time  he will return, which
he will the murderers he has hired—having convinced them that their misery in life is
Banquo's fault. (Ironically, Macbeth "orders" Banquo not to miss
the feast, even knowing that he will be dead. However, Banquo is true to his word,
showing up as a ghost and reducing Macbeth to a sniveling wretch as opposed to the
powerful man described earlier in the play.)

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MACBETH:

...Is't
far you
ride?

BANQUO:

As
far, my lord, as will fill up the time

’Twixt this and
supper. Go not my horse the better,

I must become a
borrower of the night

For a dark hour or
twain.

MACBETH:

Fail
not our
feast.

BANQUO:

My
lord, I will not.
  (III.i.26-32)

Macbeth
realizes that he has risked all to take the throne. After everything he has done, even
sacrificing his immortal soul (because the Elizabethans believed it
was a mortal sin to kill a king), Macbeth realizes that as long as Banquo knows of the
predictions, he will have second thoughts about his Macbeth. Banquo has already told
Macbeth that he will support him as long as he is not asked to do anything
that would compromise his integrity. Macbeth knows that Banquo cannot be
turned "to the dark side." The only solution is to kill his friend. And because the
witches told Banquo that his "issue" (descendants) would be kings,
Macbeth knows that unless he kills Fleance, too, the throne will move into Banquo's
family, as Macbeth has no children. He says that in this case, he has sold his soul
("mine eternal jewel") for someone other than his own
son.

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MACBETH:

To
be thus is nothing,

But to be safely thus. Our fears in
Banquo

Stick deep, and in his royalty of
nature

Reigns that which would be fear'd...There is none
but he

Whose being I do fear...He chid the sisters
[and]...

They hail'd him father to a line of
kings:

Upon my head they placed a fruitless
crown

...to be wrench'd with an unlineal
hand,

No son of mine succeeding. If't be
so,

For Banquo's issue have I filed my
mind,

For them the gracious Duncan have I
murdered,

...Only for them, and mine eternal
jewel

Given to the common enemy of
man,

To make them kings, the seed of Banquo kings!
(52-74)

This series of events shows us how Macbeth has lost
all touch with the valiant man he was at the play's beginning, compared to Banquo will
not be swayed to follow Macbeth, regardless of the reward—if Macbeth is acting in any
way unsuitable for a king. Macbeth's descent into murder and madness is evident and he
continues to kill in order to maintain his
place.

In To Kill a Mockingbird, what is Atticus really trying to imply when he says that "ALL Negros lie, ALL negros are basically immoral beings"?

These dramatic words are from Atticus Finch's closing
argument in defense of his client, Tom Robinson- a black man falsely accused of raping
and beating a white woman.

Atticus is one of the few people
in Macomb who recognizes no cultural nor racial differences among people. As an educated
man, he knows what weaknesses and strengths every individual possesses. As a learned man
in life, he respects everyone equally.

With these words,
Atticus is merely repeating the common notion of the people of
Macomb:

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"........that you gentlemen would go along with
them on the assumption, the evil assumption, that all Negros lie, all Negros
are basically immoral beings, all Negro men are not to be trusted around our
women. An assumption that one associates with minds of their caliber and
which is itself gentlemen a lie which I do not need to point out to
you.

Therefore, what Atticus
actually does is to reflect the mentality of the Macomb folk and expose it for what it
is: A very ignorant, limited, and reduced view of the world which can only be inherent
to ignorant, limited, and reduced people.

Hence, Atticus
uses the views that Macomb has on black people, and turns those views back onto the
people, themselves. As a result, even though the outcome is not rosy, at least
the citizens of Macomb may have experienced for the first time a closer look on their
ignorant perception of reality.

In Act I, scene 1 of Othello, why does Iago say he hates Othello?

In Act I scene 1, Iago reveals to the discontented
Roderigo that he hates Othello because, although he had three people present his "suit"
to be promoted to become lieutenant, Othello ignored their words, and instead chose
Cassio to be his lieutenant, a man who is younger than Iago and has not seen military
service. Iago thinks that he has much more experience of real battle and therefore
should have received the promotion. The way that Othello has overlooked him in this way
and promoted someone who is "Mere prattle without practice" over him has filled him with
rage and anger. Note what Iago himself says to Roderigo about
Cassio:

A
fellow almost damned in a fair wife

That never set a
squadron in the field

Nor the division of a battle
knows

More than a spinster--unless the bookish
theoric,

Wherein the toged consuls can
propose

As masterly as
he.

Thus, overtly, as we can
see from this scene, Iago hates Othello for the way that he was not selected for
promotion, and instead one who was unworthy was selected. Now, of course, Iago must
serve under Cassio in the chain of command, which would not help his anger and
resentment.

Describe the main compromises that were part of the "Great Compromise."

The Great Compromise is also known as the Connecticut
Compromise.  It was mainly a compromise between the bigger states like Virginia and the
smaller ones like New Jersey.

The two main compromises had
to do with the way that the Congress was to be organized and with how many
representatives each state would have.  First, the compromise created a bicameral
legislature.  This allowed each house of the legislature to be set up in a different
way.

The second compromise had to do with how each house of
Congress was to be set up.  The Senate was set up with each state having the same number
of members, just as the small states had wanted.  The House was set up with each state's
number of representatives determined by the state's population.  This was the way the
big states had wanted things.

In this way, the Great
Compromise allowed both big and small states to be somewhat satisfied with the set up of
the Congress.

Prove: sin A + sin B + sin C >2 if A+B+C=180 A

We'll re-write the
constraint:

A+B = 180-C

We'll
apply sine function both sides:

sin(A+B) = sin(180-C) = sin
C

We'll divide by 2 the
constraint:

(A+B)/2 =
(180-C)/2

We'll apply sine function both
sides:

sin (A+B)/2 = sin (180-C)/2 = sin (90 -C/2) = cos
C/2

Now, we'll manage the left side of the inequality,
replacing sin C by sin(A+B):

sin A + sin B + sin(A+B)
> 2

We'll transform into a product the sum sin A +
sin B:

2 sin [(A+B)/2]* cos [(A-B)/2] + sin(A+B) >
2

We'll use the double angle identity for
sin(A+B):

sin(A+B) = 2 sin [(A+B)/2]* cos
[(A+B)/2]

2 sin [(A+B)/2]* cos [(A-B)/2] + 2 sin [(A+B)/2]*
cos [(A+B)/2]>2

2 sin [(A+B)/2]* {cos [(A-B)/2] +cos
[(A+B)/2]} > 2

sin [(A+B)/2]* {cos [(A-B)/2] +cos
[(A+B)/2]} > 1

We'll transform into a product the
sum cos [(A-B)/2] +cos [(A+B)/2]:

2*sin [(A+B)/2]*cos
[(A-B+A+B)/4]*cos[(A-B-A-B)/4] > 1

2*sin
[(A+B)/2]*cos [(2A)/4]*cos[(-2B)/4] > 1

We'll
replace sin [(A+B)/2] by cos C/2, we'll simplify inside brackets and we'll cancel the
minus sign, since the cosine function is even.

cos (A/2)
*cos (B/2) *cos (C/2)> 1/2

Since the values of the
angles are smaller than 90, then all the angles are located in the 1st quadrant, where
the values of the function cosine are positive.(the direction of the inequality remains
unchanged).

We'll consider the values of the angle A = 60,
B=45 => C = 75, for the sum of the angles to be of 180
degrees.

cos 60/2* cos 45/2* cos 75/2 >
1/2

We'll use the half angle
identity:

cos 45/2 = sqrt [(1+cos
45)/2]

cos75/2 = sqrt [(1+cos
75)/2]

cos 60/2*sqrt [(1+cos 45)/2]*sqrt [(1+cos 75)/2]
> 1/2

We'll raise to square to eliminate the square
root:

3/4*[(1 + sqrt2/2)/2]*{[1+sqrt2/2*(sqrt3/2 - 1/2)]/2}
> 1/4

Computing the left side, we'll
get:

(12 + 3sqrt6 + 6sqrt2 - 3sqrt3 - 3sqrt3 - 3)/4
> 4

25.74/4 >
4

6.435 >
4

Therefore, the identity sin A + sin B + sin
C >2 is verified, under the given
constraints.