What are the solutions of the equation x^4+4x^3+2x^2-4x-m=0 and what is the value of m if equation has real solutions?

We'll re-write the equation into an equivalent
form:

x^2(x+2)^2 - 2x(x+2) - m =
0

We'll substitute the product x(x+2) by
t:

t^2 - 2t - m = 0

We'll
apply the quadratic formula:

t1 = [2 + sqrt(4 +
4m)]/2

t1 = [2 +
2sqrt(1+m)]/2

t1 = 1 +
sqrt(1+m)

t2 = 1 -
sqrt(1+m)

But t = x(x+2)

We'll
remove the brackets:

x^2 + 2x - t1 =
0

x^2 + 2x - 1 - sqrt(1+m) =
0

x1 = -1+sqrt[2+sqrt(1+m)]

x2
= -1-sqrt[2+sqrt(1+m)]

x^2 + 2x - t2 =
0

x^2 + 2x - 1 + sqrt(1+m) =
0

x3 = -1+sqrt[2-sqrt(1+m)]

x4
= -1-sqrt[2-sqrt(1+m)]

The roots x1,x2,x3 and x4 are real
if and only if the m satisfies the
constraints:

1+m>=0 =>
m>=-1

2 - sqrt(1+m) >=
0

m belongs to [-1 ; +infinite) and (-infinite ;
3]

For the equation to have all real
solutions, m = [-1 ; 3].

In A Tale of Two Cities, how does Lucie influence the following characters through love: Doctor Manette, Darnay, Mr. Lorry, and Carton?

In A Tale of Two Cities by Charles
Dickens, Lucie Manette somehow inspires love in all the other main characters; however,
the reader must accept this inspiration without understanding how it is effected since
the character of Lucie is not brought to life by Dickens and remains
passive.

DOCTOR MANETTE

In
"Book the First," it is her golden hair that elicits the memory of his wife for Dr.
Manette; and, then, the realization that he has a living daughter brings Manette back to
the real world. As a hero of the Revolution, Manette is inspired to try to aid Darnay as
the Revolutionaries arrest him because the son of his enemy is married to his belove
daughter.

CHARLES DARNAY

As a
character, Darnay is also passive.  With his tendency to get himself in trouble and be
sent to jail, he is perfect for inspiring the compassion of Lucie's
heart.

MR. LORRY

For Mr.
Lorry, Lucie and Dr. Manette represent the family that he has never had.  In his
position with Tellson's Bank, Mr. Lorry assumes a protective role towards Lucie when she
is but a baby.  From France, he takes Lucie as an infant to England; then, he rescues
her father.  Mild-mannered and affectionate, he is moved by these same qualities in
Lucie and feels a fatherly affection for her and grows to like and respect Dr.
Manette.

SYDNEY CARTON

Carton,
as Charles Darnay's double, is equally attracted to the pretty Lucie.  Seeing Darnay's
and Lucie's love for each other makes Carton envious of Charles Darnay as he realizes
that he could also have  a happy relationship if he had not wasted his life in drink. 
Feeling that he cannot complete with Darnay, he remains in the background as Darnay
proposes to Lucie, but he does pledge his platonic love to Lucie, promising her that he
will do anything to protect her when she anxiously talks of the "echoing footsteps."  He
feels that if he can perform worthy deeds for Lucie and his family, he can, at least, be
respected by someone.  Later, of course, he makes the ultimate sacrifice for the
Darnays, inspired by his love for Lucie.

In Mrs. Dalloway, how does Virginia Woolf treat sexual attraction?

Sexuality, particularly the type of sexual attraction that
Clarissa detects in herself, is treated in a very delicate manner and giving specific
consideration to the circumstances of the characters, their roles in life, and pasts,
and the connection of their characters with those of Shakespeare's
Othello, with whom Woolf compares the story lines of each
individual.

Clarissa is in her 50's, and has just realized
that society expects her to be frigid, nun-like, and to go back to a life of
nothingness: No passion is allowed for her for she has already been a wife and a mother.
Hence, alone and with grown children, she has to find her role in society once more on
her own.

This being said, Clarissa is in a journey of
self-contemplation. This contemplation has led her to realize that she is actually
sexually attracted to another woman, Sally. This is where Virginia Woolf uses her most
delicate descriptions and comparisons to Othello, particularly on
the subject of missed opportunities at love, the conventionalism that leads nowhere, and
the expectation that women are supposed to behave, feel, and hope in a specific
way.

When the novel ends, we realize the deep regret that
Clarissa feels at not being able to fulfill her passion, and her realization that she
simply needed a different kind of life altogether to match the different emotions in her
heart.

In "The Scarlet Ibis," what is the narrator's overall attitude toward life?

Above all, the narrator's attitude to life seems to be
shaped by his own health and well-being, which of course, heightens the contrast between
himself and his younger brother, Doodle, who is defined by his inability to do all the
things that his brother can and wants him to do. Perhaps what most clearly reveals the
kind of attitude that the narrator, the elder brother of Doodle, has concerning life is
in his hopes for a younger brother. Note what the narrator reveals to
us:

I thought
myself pretty smart at many things, like holding my breath, running, jumping, or
climbing vines in Old Woman Swamp, and I wanted more than anything else someone to race
to Horsehead Landing, someone to box with, and someone to perch with in the top fork of
the great pine behind the barn, where across the fields and swamps you could see the
sea. I wanted a
brother.

Therefore the
narrator defines himself as a typical young boy who delights in physical activity and
enjoying life outdoors, playing in nature and getting up to the kind of mischief that
boys of his age normally do. Of course, having a younger brother like Doodle, who is
unable to do all the things that the narrator enjoys doing, seriously embarrasses the
narrator, leading him to try to change his younger brother and to teach him how to do
all the things that he wants Doodle to be able to share with
him.

What is t if u(v(t))=1? u(v)=cosv v(t)=t^2

To find t if u(v(t))=1 , u(v)=cosv and
v(t)=t^2.

Given u(v) = cosv and v(t) =
t^2.

Therefore the composite function u(v(t)) = 
cost^2.

Therefore u(v(t)) = 1 implies cost^2 =
1.

cost^2 = 1 => t^2 = 2n*pi, where n =
0,1,2,3,.....

t = +sqrt(2n*pi),
or t = -sqrt(2n*pi), for n =
0,1,2,3...

Discuss Jack's use of Bunburyism in act one, and it's larger implications for Jack's sense of identity and family. Narrow your argument. This is a...

Jack's use of Bunburyism is no different than Algernon's,
although Jack criticizes it.

Jack, in his own words is
"Earnest in the country, and Jack in the city". His situation is that he is a ward to a
young lady, the manager of a huge estate, and in general he is a man with
responsibilities in the country.

He, however, needs to lose
himself and finds freedom in the city. In London, he lives at Albany B4, changes his
name to Earnest, and does all the wicked things that he cannot do in the country: Runs
huge restaurant bills at restaurants, has creditors haunting him, and just enjoys the
pleasures of dandyism.

It is as Earnest that he meets
Algernon- the original bunburyist. In Algernon's case, he invents an invalid friend
called Bunbury, and claims to go to take care of him when, in fact, it is just an excuse
to go party around town. This is what validates the argument that Jack's use of
bunburyism (disguised as an evil twin brother in the city named Earnest) is no different
than that of Algernon's although Earnest thinks that Algernon, by doing this, is
immoral.  

As far as implications of Jack's personal life
and his family, what this might mean is that Jack was simply bored of playing a paternal
role to Cecily and even more overwhelmed to have been left with the many
responsibilities of money, land, and estate. He was not an old man, and yet he had to
find his fun only by escaping his life of seriousness and get in all sorts of scrapes in
the city. This was maybe his only way to keep his youth from fading, and keeping his
inner heat going.

What improvements in the 18th century contributed to the decline of famine?

Since famine is what happens when there is not enough food
for all the people, the best way to stop having famines is to grow more food.  This is
exactly what happened in the 18th century -- the Europeans learned to grow more
food.

There were a couple of major types of improvments. 
First, there was a continuing movement away from the open field system where a whole
village of farmers cultivated small individual strips of common land.  This was a
wasteful system and doing away with it improved
productivity.

In addition, there was a great deal of
technological improvement.  For example, there was the invention in 1701 of the seed
drill.  This made planting much easier and efficient and, thereby, increased
productivity.

Improvements like this meant more food could
be grown and that led to a decrease in famines.