Three forces acting at a point are F1=2i-j+3k, F2=-i+3j+2k, F3=-i+2j-k.Find the directions and magnitude of F1+F2+F3, F1-F2+F3.

In order to add 3 vectors, F1, F2, F3, we'll add or
subtract algebraically the coefficients of correspondent unit vectors:
i,j,k.

F1+F2+F3 = (2i-j+3k) + (-i+3j+2k) +
(-i+2j-k)

We'll remove the brackets and combine like
terms:

F1+F2+F3 = i(2-1-1) + j(-1+3+2) +
k(3+2-1)

F1+F2+F3 = 0i + 4j +
4k

So, the resultant vector of the sum of 3
vectors F1+F2+F3 has no component in the x direction, but it has a component of 4 units
in y direction and a component of 4 units in z
direction.

The magnitude of
the resultant vector is:

|F1+F2+F3| = sqrt (0^2 + 4^2 +
4^2)

|F1+F2+F3| = sqrt
32

|F1+F2+F3| =
4sqrt2

|F1+F2+F3| = 5.66
units

The resultant vector has
a magnitude of 5.66 units and it is located in y-z plane. The vector makes an angle with
y axis.

What is the length/width/height of a rectangle in metres, that's volume is 8,000 cubic feet?

The volume V of of the rectangular prism  is the product
of length l, width w and height h and  is given by:

l*w*h =
V.

l*w*h = 8000 c ft.

We can
have many solutions. Some are as follows:

20'*20'*20'
=8000c ft, if l=w=h = 20' =  20*0.3048 m =6.096 m, as  1 ft  =
0.3048meter.

For different length, width and heights , here
are some solutions.

40'*20'*10' = 8000 c ft . So  l=  40
ft, w=20 ft, h = 10 ft. Or l,=40*0.3048 m = 1.192, W = 20*0.3048 = 6.096m and h = 3.048
m

50'* 20'*8 ' = 8000 cft. So l=50', w = 20' and h = 8' Orl
= 15.24m wl= 15.24m, h = 2.4384

100 '* 10' * 8' = 8000 c
ft. So, l=100, w = 10' and h= 8'. Or l = 30.48, w = 3.048m , h =
2.4384m.

Explain the vices or problems Tartuffe represents and explain whether or not Tartuffe is the only to blame for the problems in Tartuffe.

Tartuffe is an extremely
entertaining, satirical play, written by Moliere, a famous playwright with a flair for
comedy--with the purpose of pointing out the foibles of society.  In this case,
Moliere's intention is to highlight the hypocrisy of French society regarding its
tendency to preach religious and moral standards to others, while disregarding those
same standards for themselves.

In this play, Tartuffe is a
charming con man.  He makes the acquaintance of a very wealthy man, Orgon.  Without much
thought, Orgon takes Tartuffe into his home as a guest although Tartuffe is a
stranger.

Tartuffe acts like a very holy and religious man.
 Orgon, taken in by this charlatan, asks Tartuffe to reside with the family as a moral
guide, and he offers Tartuffe the best of everything, including his attention and
affection--even better than what Orgon's family receives. Orgon even goes as far as to
plan Tartuffe's marriage to Orgon's daughter.

Although he
is warned by others that Tartuffe is a fraud, Orgon can see no fault in Tartuffe until
Orgon catches the con man making advances toward his own
wife.

However, Tartuffe is not wholly to blame.  Moliere
structures the play around Tartuffe who represents the hypocrisy of French society, as
Moliere sees it.  (The Church banned the play for several years.) However, Tartuffe is
simply the foil used to expose Orgon, who represents that portion of society that is
gullible and foolish.  Had Orgon not been so easily duped, if he had been able to
consider the advice of those around him in seeing Tartuffe more objectively, Tartuffe
would certainly never have been allowed to have his way in Orgon's home.  It is only
when Orgon can see for himself (another character of human nature) that the foolish man
finally believes what others have been trying to tell
him.

In the meantime, as he tries to throw Tartuffe out,
Tartuffe threatens revenge by taking secret documents Orgon had told Tartuffe about, to
the King.  It looks like Orgon is about to lose everything for having foolishly taken
Tartuffe into his confidence, but at the last minute, the King's men arrest Tartuffe for
other crimes he has committed.  The play ends as Orgon tries to put his life back in
order.

Orgon has learned that although Tartuffe is to blame
for specific misdeeds against Orgon and his family, that Orgon himself is guilty of
letting Tartuffe into his home and putting those closest to him in jeopardy by placing
Tartuffe above them in his heart and mind.

Which female character in Chopin's stories possesses true love for her husband? Calixta, Louise or Desiree?

Chopin’s stories often depict women who are trapped by
gender role expectations and pressured to conform to societal norms. In these instances,
all three characters - Calixta (“The Storm”), Louise (“The Story of an Hour”) and
Desiree (“Desiree’s Baby”) – are each married. However, only Desiree truly loves her
husband.

Calixta demonstrates (through her passionate act
with Alcee) that her commitment to her marriage is brittle and weak. Though her remarks
do not betray contempt for her marital union, her spontaneous and lustful reaction to
Alcee’s advances suggests that she feels less than fulfilled within her marriage. When
her husband returns following the storm, she easily falls into what seems to be a
monotonous routine.

The character of Louise Mallard is also
dissatisfied with her marital arrangement. According to the text, she “did not hear the
story as many women have heard the same, with a paralyzed inability to accept its
significance.” Rather, she immediately gave way to tears, crying and sobbing in her
sister’s arms. Her tears flow rapidly and abundantly. Then, they are gone. Louise goes
upstairs to her room and tries to resist feelings that seem to overpower her. She
attempts to halt a feeling of freedom and to suppress her joy at being released from an
unfulfilling marriage. Finally, she acknowledges her joy and her husband returns. She
drops dead from the shock, demonstrating that she was so discontented with her marriage
that the realization that she was still bound to her husband was so disappointing that
it killed her.  

Desiree Valmonde married Armand Aubigny
because she loved him entirely. Her first desire was to please her husband and she was
certain that she succeeded when she gave him a son. She felt that her good marriage was
bettered by the presence of her child. She was content to be loved by a husband whom she
adored.  Unfortunately, when Armand began to change for the worse, neglecting and
avoiding her and her marriage began to fall apart. When he accusingly suggests that she
is not white and openly shows his disgust for her, she still holds out the hope that her
love will soothe and conquer his disquietude. Instead, he rejects her and she lovingly
leaves her home to appease him. Her love for Armand was strong enough to endure
heartbreak, sacrifice and shame.

How would you describe Mayella and her home life?

Living in her rundown house situated between the town dump
and the Negro Quarters, Mayella is cast as a lonely and mistreated older teen who has
reached adulthood but has no one with which to share her life. Her mother has been dead
a "long time," and she seems befuddled when Atticus asks her while on the witness stand
if she has any friends. Her loneliness is so great that she has saved her nickels so she
can send her brothers and sisters out of the house in order to be alone in order to lure
Tom Robinson inside. She has never been kissed, and though Tom is black, he is her best
chance for a quick bit of romance. To Mayella, Tom is like forbidden fruit, but her
choices are limited, and he is one of the only people who ventures onto the property. We
also discover that her father has probably beaten her before, and there is even an
underlying hint that he may have taken advantage of her sexually in the
past.

Two fair dice are thrown.Let ‘A’ denote the event that first die shows an odd number and ‘B’denote the event that the second die shows a...

The dice role is random. So each die consists of a set {1
.. 6}. Knowing what was rolled on one die provides no information on what was rolled on
the second die. Pretend the die A is labeled {1 ..6 } while die B is labeled { A .. B }.
There is no union between these two sets, so the event of rolling the die remains
independent. So the answer to your question is that, yes events A and B
are independent.

You can see this by examining the
conditional probability. Two events are independent
if:

P(A|B) = P(A)

P(A|B) = 1/2
= P(A)

P(B|A) = 1/2 =
P(B)

If A and B were on the same die,
the answer would be different.

The standard definition
of independence is:

Two events A and B are independent if
and only if Pr(A ∩ B) = Pr(A)Pr(B).

A is the set: {1,3,5}
--> P(A) = 1/2

B is the set: {1,2,3,5} -->
P(B) = 2/3

A ∩ B is the set : {1,3,5} --> P(A ∩ B) =
1/2

Pr(A ∩ B)
≠ Pr(A)Pr(B)

Therefore these events are
not independent.

What were Professor Joshua Chamberlain's reasons for joining the military in The Killer Angels?

A professor of rhetoric at Bowdoin College in Maine before
the war, Colonel Joshua Chamberlain had enlisted in the Union army because of a simple
belief: the dignity of man. The Southern cause supported slavery, and this Chamberlain
could not abide.

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This was the land where no man had to bow... The
fact of slavery upon this incredibly beautiful new clean earth was appalling, but more
even than that was the curse of old Europe, the curse of nobility, which the South was
transplanting to new soil... Chamberlain had come to crush
it.

He believed that in his
United States, unlike in other countries, the American fought for mankind and freedom.
He would fight for the people, not the land. Chamberlain also tells his men that joining
the army was " 'the right thing to do.' " They would not be fighting for the land, he
repeats, but instead for each other.