Calculate tan(x-y), if sin x=1/2 and sin y=1/3. 0

We'll write the formula of the tangent of difference of 2
angles.

tan (x-y) = (tan x - tan y)/(1 + tan x*tan
y)

Now, we'll have to establish the signature of tan x a
and tan y. We know from enunciation that, tan x belongs to the first quadrant and it is
has positive and tan y belongs to the second quadrant and it is
negative.

tan x=sin x/cos
x

cos x = sqrt[1 - (sin
x)^2]

cos x = sqrt[1 -
(1/2)^2]

cos x = sqrt(1 -
1/4)

cos x = sqrt3/2

tan x =
(1/2)/(sqrt3/2)

tan x = sqrt
3/3

tan y = -(1/3)/sqrt[1 -
(1/3)^2]

tan y =
-(1/3)/sqrt(8/9)

tan y =
-1/2sqrt2

tan y =
-(sqrt2)/4

tan (x-y) = [(sqrt 3)/3 +
(sqrt2)/4]/[1 - (sqrt6)/12]

Analyse how Dickens uses parallelism to state themes that might be developed in A Tale of Two Cities.The opening paragraph of A Tale of Two Cities...

You are right in identifying parallelism as a major
stylistic tool that is employed in this incredible novel. The main conflicts of the
novel are referred to in the famous opening chapter, that draws our attentions to the
strange dichotomy of the times:

readability="16">

It was the best of times, it was the worst of
times, it was the age of wisdom, it was the age of foolishness, it was the epoch of
belief, it was the epoch of incredulity, it was the season of Light, it was the season
of Darkness, it was the spring of hope, it was the winter of
despair...

You might want to
think how such opposition is created by the way that characters are matched against each
other and also events repeat themselves. For example, Charles Darnay and Syndey Carter
are doubles of each other, with Charles Darnay representing the goodness that Syndey
Carter seems unable to find within himself until the final pages of the novel. Equally,
both Dr. Manette and Madame Defarge are victims of the French aristocracy. Charles
Darnay suffers two trials in the pages of the novel, one where he is charged as a
traitor of Britain, the other when he is charged as a traitor of France. Lucie is
opposed to Madame Defarge, who, towards the end of the novel, increasingly
psychologically dominates her. And lastly, of course, lest we forget the title, this is
a tale of two cities and how both effect each other. Doubles or matches abound in the
novel, and parallelism is established as a manner of introducing conflict and
highlighting themes.

If we accept Romeo's love for Juliet as immature, how does it affect our predisposition that this play is an archetypal love story?This question...

In studying Shakespeare's Romeo and
Juliet, I do not believe that it serves as an archetypal love story. I
believe it is archetypical of the "star-crossed lovers" love
story.

In terms of Shakespeare and prevalent themes in his
plays, change plays an enormous role in providing his plays with in-depth and believable
characters, and these changes drive the plot. The protagonists, for example, in
Macbeth and Hamlet, go through extensive
changes based upon who they are, their journeys of self-discovery, and their interaction
with the other characters.

Romeo is a young man, and his
experience of life is limited. It would appear that he has never truly been in love, but
has been infatuated with Rosaline, another member of the Capulet household. We never
meet the object of his affection, but certainly see enough of his
immaturity—perhaps a "puppy love"—that has no real substance; but we see a great deal of
"suffering" on the part of Romeo. The fact that he transfers his affections so quickly
to Juliet may be the clearest, and perhaps the last, indicator of his immature outlook
on love, and life.

Once Romeo commits himself to Juliet,
every step seems sincere, and the very adult world around him brings clarity where there
has been none before. Mercutio, Romeo's close friend, is killed by Tybalt; Romeo kills
Tybalt, Juliet's cousin. The casual nature of Romeo's existence, once spent mooning over
Rosaline, has altered forever. It could be argued that these things, as well as Juliet's
total acceptance of him regardless of his family's name, force him to turn a distinct
corner in "growing up." The fact that he takes his own life when he believes Juliet is
dead could be an indication of the depth of his dedication, but
this is debatable: is it mature to commit suicide in the face of
loss?

I personally see no difficulty in perceiving Romeo as
an immature young man at the start of the play. However, I do not believe an audience is
predisposed to see this as an archetypal love story—there are many doomed romances in
Shakespeare's tragedies. Romeo and Juliet are seen as archetypical sweethearts whose
fate is predestined—they are doomed before they meet, their ending "written in the
stars." (See the Prologue.) There is much discussion, in fact, as to whether the lovers
could have done anything to change the outcome of the
play.

The archetypical love story, in general, does not, I
believe, require death and/or unrequited love. If we look at this love story as
archetypical of Shakespearean love in his tragedies, where there
are no happy endings, perhaps there is validity to the concept. The Bard's happy endings
seem reserved (obviously) for his comedies. However, in general
terms, I don't see Romeo and Juliet's tragic relationship as the model for an
archetypical love story.

What does accommodation mean to Booker T. Washington? How does W.E.B. DuBois respond? I know that DuBois felt that Washington was compromising...

Booker T. Washington and W.E.B. Du Bois had different
views of how African-American should try to get their rights. Booker T. Washington
believed African-Americans should get their economic rights settled before pursuing
their political rights. He believed that African-Americans should get vocational
training so they would be able to get jobs and become more secure financially. This
position, known as the Atlanta Compromise, suggested economic rights should be pursued
before going after political rights.

W.E.B. Du Bois
believed African-Americans should get all of their rights at the same time. He believed
it was wrong to pursue only economic rights and not pursue political rights. W. E. B. Du
Bois believed African-Americans deserved all their rights at the same time and should
work to achieve gaining both economic rights and political rights. He and Booker T.
Washington had differing views on how African-Americans should pursue their
rights.

In Act III, scene 2, why may the establishment of Claudius's guilt be considered the crisis of the revenge plot?

The crisis of a drama usually proceeds and leads to the
climax.  In Shakespeare's Hamlet, the proof that Claudius is guilty
leads to Hamlet's decision to not kill Claudius while he's at prayer--and that is the
climax of the play.

Hamlet, until he sees Claudius's
reaction to the "play within the play," isn't entirely sure Claudius is guilty.  He has
no real proof--only the word of a ghost, who, he says in Act 2.2.565-572, could be a
devil trying to deceive him (as, by the way, the witches do to Macbeth in his play of
the same name).  Hamlet needs proof.  He is too reasonable to act like Fortinbras or
Laertes and just jump into revenge without thinking it
through.

The king's reaction to the murder scene in the
play gives Hamlet the proof he needs, though, and he sets off to kill the king.  He gets
an opportunity but decides not to take it.  Why?  Because he thinks Claudius is
confessing (he isn't, but Hamlet doesn't know that), and killing him immediately after
he confesses his sins would send Claudius straight to heaven.  And Hamlet doesn't want
to send Claudius to heaven, not when his father is suffering in a purgatory-like state,
and when Hamlet might be sent to hell because he kills
Claudius. 

The problem is, though, that when Hamlet decides
not to kill Claudius because he doesn't want to contribute to his salvation, he is
playing God.  Salvation is God's business, not Hamlet's.  Hamlet is messing where he
shouldn't be messing.

The result--you see it in Act 5:  the
sight Fortinbras says doesn't belong in a castle, only on a battlefield.  Death
everywhere. 

When Hamlet walks away from his rightful
revenge, by playing God, he dooms himself and so many others.  This is the climax. 
His receiving proof of Claudius's death could be considered the crisis, and Hamlet's
refusal to kill Claudius while the king's at prayer is the climax.  One leads to the
other.  

In Lois Lowry's The Giver, how does the writer use character to express conflict?

You might want to examine this question by looking at the
way in which Jonas's job as Assistant Memory Keeper produces conflict between him and
his former friends. A key moment that demonstrates this is in Chapter Seventeen, when
the children enjoy an unscheduled holiday. Jonas is looking forward to playing with his
friends, but as they play a game whose meaning has been lost, Jonas recognises it for
what it is: a child's version of a war. Jonas is overwhelmed by memories that have been
"shared" with him of pain and conflict, and the game halts awkwardly. Asher and Fiona
are unable to comprehend or understand the viewpoint of Jonas, and we are left with an
image of Jonas by himself, overwhelmed by loneliness and
loss:

Jonas
trudged to the bench beside the Storehouse and sat down, overwhelmed with feelings of
loss. His childhood, his friendships, his carefree sense of security--all of these
things seemed to be slipping away. With his new, heightened feelings, he was overwhelmed
by sadness at the way the others had laughed and shouted, playing at war. But he knew
that they could not understand why, without the memories. He felt such love for Asher
and for Fiona. But they could not feel it back, without the memories. And he
could not give them
those.

Note here how Jonas,
in a sudden moment of realisation, realises how conflict has been produced from his
assignment. His knowledge of the past and the memories that have been shared with him
has produced conflict and division between him and his former friends, such as Asher and
Fiona. With sadness, Jonas realises that now his relationships have been irrevocably
affected for the worse.

Describe the mystique that surrounds Gatsby The Great Gatsby by F. Scott Fitzgerald..

Nick Carraway first encounters Jay Gatsby at the end of
Chapter One of Fitzgerald's The Great Gatsby, but only for an
illusionary moment.  Gatsby stands with his arms outstretched, trembling and gazing at
the green light at the end of Daisy's pier, and then he is gone.  Gatsby is an
enigmatic man who longs to recreate his romanticized past because he has no future, only
the present.

Gatsby has a mystique about him because very
little is known of  him; only distant impressions are suggested.  Just as he suddenly
appears on a lawn in West Egg, Jay Gatsby spontaneously has parties with strangers who
know nothing of each other as well as nothing of Gatsby.  In Chapter Four, he asks Nick,
"What is your opinion of me?" and states that he is going to tell Nick about himself so
that there is no "wrong opinion" of him.  But, it is not until Chapter Six and Seven,
the reader does not learn of Gatsby's background or of his criminal activity.  Until
this point, Nick and the reader only are told that Gatsby had parents from the Midwest,
but when Nick asks specifically, Gatsby says, "San Francisco."  He claims to have gone
to Oxford, but only produces a photograph that was supposedly taken while he was in
college, and chokes on the words.  Nick narrates,

readability="14">

He hurried the phrase" educated at Oxford," or
swallowed it, or choked on it as though it had bothered him before.  And with this
doubt, his whole statement felll to pieces, and I wondered if there weren't something a
little sinister abou him, after all....For a moment I suspected that he was pulling my
leg, but a glance at him convinced me
otherwise.

Something in
Gatsby--"the great Gatsby"--hints at magic and illusion as in "the Great Blackstone" and
other vaudeville personages.  He has beautiful, but unknown guests at his opulent
parties, his library has real leatherbound books, his car possesses mythological
characteristics with its "fenders like wings," and its fenders that reflect the light. 
Gatsby, too, creates an aura of luxury and charm that has no history behind it.  He is
seen with unsavory characters such as Meyer Wolfscheim, but appears at a party in white
flannels with a golden tie.  He claims to have visited the capitals of Europe--Paris,
Venice, Rome--yet he possesses an absolutely loyal heart. Jay Gatsby is an enigmatic
character who bases his sense of worth upon the approval and love of Daisy Buchanan, and
who 

believed
in the green light, the orgastic future that year by year receded before
us.

Find the polynomial having roots at 0, 2i and 3 - i, and passing through (1, –5).

A polynomial  which has the complex roots 2i and 3-i, must
have also the roots which are the conjugates of 2i and
3-i.

Therefore the give polynomial has the a ral root 0,
and complex roots 2i and -2i, 3-i and 3+i.

If a, b, c, are
the roots of a polynomial y(x), then y(x) =
k(x-a)(x-b)(x-c).

Therefore y(x) =
k(x-0)(x-2i)(9x-2i){x+3-i)(x-(3+i)) is the polynomial with roots 0, 2i, -2i, 3-i and
3+i.

y(x) =
kx(x^2+4)((x-3)^2+1).

y(x) = kx(x^2+4)(x^2-6x+10). This
polynomial should pass through (1-5).

Therefore
substituting (x ,y) = (1, -5) in y(x) = kx(x^2+2)(x^2-6x+10), we
get:

-5 =
k(1)(1+4)((1-6+10).

-5 =
k*25.

Therefore k = -5/25=
-1/5.

Therefore the required polynomial which has roots, 0,
2i, and 3-i and passes through the point (1,-5) is given
by:

 y(x) =
(-1/5)x{x^2+4)(x^2-6x+10).

Why do Jem and Scout feel guilty when Mr. Avery tells them that children who disobey, smoke, and make war on each other can cause the seasons change?

They felt guilty because since 1885 Maycomb had not
reported any snow during Winter. Yet, during the specific winter when the action of the
story takes place there was a bit of snow mounted in the yards that was identified as
"flurry". It was very minimal, but it was big enough for Mr. Avery to find in it a
consistent proof of what he had been proposing: That bad behavior in children is what
makes the weather change.

Therefore, to see this sudden
change in Maycomb(although small) was a big deal for the children whose behaviors were
no different than any other child, but were chastised probably much harshly than
children are chastised in modern times. For this reason, the kids felt that their "bad
behavior" was the causative factor for this onset of snow after so many
years.

I need to write a persuasive essay about Global Warming. Can someone help me please.

This should be a direct topic, as there is much
information on the topic.  As with all essays, I think that the first step is to check
with your task description and instructor to make sure that you have included all the
necessary parts of the paper.  The next step would be to take a position on the topic in
terms of what you believe and what you think the evidence indicates about global
warming.  Establishing this will be important.  For example, are you going to argue that
global warming is a concern or something that has been manipulated to be seen as one? 
Are you going to argue that it is caused by human made factors or that it is a natural
climate process?  I think that these positions are, infact, positions on the topic and
can be defended with evidence.  Arranging and understanding the evidence out there and
what you are going to say about it will be of vital importance in the
paper.

Please answer these questions about Lennie and the deaths he causes in Chapter 5 of Of Mice and MenONLYCHAPTER 5,How does Lennie react to...

In Steinbeck's Of Mice and Men,
Lennie also tries to cover the puppy up and hide it.  If he can keep George from finding
out that he has killed the puppy, he won't get into trouble.  He is also somewhat
comforted by Curley's wife, who tells him the pup is nothing and can easily be
replaced.

In contrast, Lennie, after killing Curley's
wife, very quickly sneaks out of the barn and, the reader learns later, goes to the spot
George told him to go to if he gets in trouble. 

This does
demonstrate that Lennie understands the difference between killing a puppy and killing a
human being.

What is the angle x if tan 3x -tan^3 x=0?

To find the angle x if tan 3x -2tan^3
x=0.

tan3x = (3tanx-tan^3x) / (1-3tan^2x) is an
identity.

So we use this in the given
equation:

(3tanx-tan^3x) / (1-3tan^2x) - 2tan^3x =
0.

(3tanx-tan^3x) -  (1-3tan^2x)*2tan^3x =
0.

tanx {3 -tan^2x - 2tan^2 + 6tan^4x} =
0

tanx (3-3tan^2+6tan^4x) = 0. We divide by
3.

tanx (tan^4x-3tan^2x +1) =
0.

tanx(tan^2x-1)(1+2tan^2) =
0.

tanx = 0, tan^2-1 = 0, or 1+2tan^2x =
0.

tanx = 0, ortan^2 =1, or tan^2 = 1. So tanx = +or-
1.

So x = npi, or x= npi+pi/4, or npi - pi/4, for n =
0,1,2,..

How is Anne's goal of wanting "to go on living even after my death" fulfilled in Anne Frank: The Diary of a Young Girl?I didn't get how it was...

I think you are right! I don't believe that many of the
Jews who were herded into the concentration camps actually understood the enormity of
the horrible situation in which they were being placed. Most of them probably could not
visualize their own mass extinction at the hands of their own fellow Germans. Anne
probably did not foresee this either, but she decided to keep a diary to document her
daily thoughts and activities. Whether she ever believed that it would be read at all is
uncertain, but she could never have recognized the power that it would eventually have
over the millions that have read it. Her diary has been translated into dozens of
languages, and it's still a relevant documentation of one of humanity's worst episodes.
The fact that it is still being taught regularly in schools throughout the world has
made it a certainty that Anne Frank will never be forgotten.

If f(x) = 2x -5 and g(x) = lnx + 8x find fog(1)

Given the functions:

f(x) =
2x-5

g(x) = lnx + 8x

We need
to find fog(1)

First we will determine the function
fog(x)

==> fog(x) =
f(g(x))

                 = f( lnx +
8x)

                  = 2(lnx + 8x)
-5

                    = 2lnx + 16x -
5

==> fog(x) = 2lnx + 16x 
-5

Now we will substitute with x =
1

==> fog(1) = 2ln1 + 16*1
-5

                 = 2*0 + 16 -5 =
11

==> fog(1) =
11

Discuss the role of the U.S. in political affairs of other countries and the U.S. and Soviet responses to each other during the Cold War.i need...

The topics that are the focus of your paper seem to take
US history from the time of early imperialism under Teddy Roosevelt in the first decade
of the 1900s to the time when the Cold War was beginning to heat up in the late 1940s
and early 1950s.

So with those two larger topics in mind -
imperialism and the Cold War, you may want to talk about the development of the
first:

* how the United States became an empire and
expanded its territories to include the Panama Canal, control over the Caribbean, with
heavy influence over Latin America and the Philippines.  Include why the US would do
this - for world power in competition with other empires, and for control of resources
which would aid our economy

And the beginning of the Cold
War second:

*how our goal of expanding our control as an
empire changed into a foreign policy of containing the Soviet empire's expansion, and
controlling more resources and influencing other countries with economic and military
aid so they wouldn't be communist, or so the Soviet Union would not gain access to their
resources.

Please explain the bolded words below from this passage in "Compliments of the Season."i want to know the meaning of :- His hand was itching to...

In the part of the story that you quote for us, Fuzzy has
found the doll but does not know of its significance.  Black Riley does know that he
could get money for the doll.  This is the background to the passage that you have
given.

There are two parts of the passage that must be
explained.  First, the part about the Romans and the Sabine.  In Roman legends, there is
an episode in which Roman men supposedly went and took wives from a neighboring
community.  You can find more about this episode in the link below (the Rape of the
Sabine Women).  So what O. Henry is saying here is that Black Riley wants to take the
doll away by force.

Second, there is the phrase
"merry-andrew."  This is a phrase that is used to refer to a clown or a buffoon of some
sort.  So, by including this phrase, O. Henry is is showing that Black Riley looks down
on Fuzzy and thinks that he is some sort of an idiot.

Were all the townspeople devil worshippers as Young Goodman Brown thought?

This is not clear. We never know if Young Goodman Brown
actually experienced all of this or if it was a dream. Hawthorne did this deliberately.
The story is about the duality of humanity. We all, or all the townspeople, are capable
of good and evil. This is not to point out that we all are hypocrites. The point is that
good people are capable of bad deeds and vice versa.

The
other point of the story is that a failure to accept this is a denial of the reality of
the world. Goodman Brown believes he has lost his religious faith and his faith in
humanity at the very thought that a seemingly pious person, like Goody Cloyse, could
speak, let alone worship the devil. Brown thinks that if evil exists to that extent,
then there is no goodness in the world powerful enough to combat
it.

To rephrase your question in a metaphorical sense, I’d
ask if all the townspeople had evil thoughts, were tempted by evil deeds or actually
committed evil things. The answer is yes, but everyone to greater or lesser degrees.
Every human faces this duality. Everyone in the town has “walked with the devil at
night,” which is to say that even if someone chooses the righteous path, he/she must
have also contemplated the evil path. This is just the logic of choice. You can’t make a
choice unless you are presented with two or more options. This is the good/bad duality
characteristic of human nature.

Even Goodman Brown was left
wondering if it was a dream or not. In the end, it doesn't matter. Whether it was a
dream or a real experience, Brown could not accept the thought of such
evil.

In Lord of the Flies, how is the brutality within each individual often more dangerous than evil from an outside source?I really need help with...

In the final chapter, Ralph "argue[s] unconvincingly" with
himself that the hunters will leave him alone or,
perhaps,

make
an outlaw of him.  But, then the fatal unreasoning knowledge came to him
again. 

Too late, Ralph
recognizes the evil that men do is innate, and is quite dangerous because it is so often
not recognized.  For, if Ralph and Piggy were to recognize the innate sadism in Roger
when he picks up the stone--"that token of preposterous time," as Golding writes--and
throws it and others all around little Henry at the water's edge in Chapter Four, they
may have prevented Roger's sadistically gleeful hurling of the pink granite boulder that
takes Piggy's life.  

Similarly, were Ralph capable of
recognizing in Chapter One the threat that Jack's statement "of simple arrogance"--"I
ought to be chief"--suggests, he may have been able to avert the regression of the boys
to even and all the conflicts involving the hunters and his followers, the groups that
formed after this confrontation.  Certainly, Ralph and Piggy would have been more
attentive to the message that Simon attempted to communicate that the Lord of the
Flies provides him in Chapter Eight:  "I'm part of you....I'm the reason why it's no
go?  Why things are what they are?"  Then, perhaps, Simon would not have been bludgeoned
to death, or SamnEric terrorized and Ralph hunted.

Give some examples of the use of simile and metaphor from chapters 4 to 9 of Night by Elie Wiesel?

Night, by Elie Wiesel, traces Elie's
own experiences of life as a young Jew during the Second World War (WWII), sent with his
father to the concentration camps. He would never see his mother and siblings
again.

In describing Wiesel's experiences, it would be
difficult to describe the fear, the uncertainty, the hate and the disbelief through the
use of factual language as mere words could never describe the suffering. Images need to
be created in the mind's eye so that the reader can become engrossed in the reality and
can believe what actually happened. Without using metaphors, simile, personification,
rhetorical questions and irony, the story would be one of graphic abuse and torture;
something that would possibly preclude some people and dissuade others from reading it.
here are just a few examples.

Towards the end of
Night, the images that are created are stark reminders of how even
simple things can have enormous significance and the reader is aware that nothing should
ever be taken for granted. For Elie and his weakening father, they have been reduced to
something almost, "like a wild beast" and Elie's father is
recognizable more as "a wounded animal," than his own dear
father as he gracefully accepts Elie's offer of a sip of coffee.
 

Even in the midst of terror, Elie feels guilty
for his own desire to survive. He tells the reader that, "My heart was
heavy," because, although he is sharing his soup with his sick father, he
is doing so "grudgingly." His father has been denied food because, as a person close to
death, it would apparently be nothing more than "a waste of food" to give him his own
ration. The irony of Elie's own statement, of his own sense of guilt which he feels on
various occasions, sometimes wishing to be free of his responsibilities, is intensified
by the cruelty by which he is surrounded but he is the one feeling ashamed and his
captors feel nothing.

Elie describes his father as he
continues to get weaker with his, "Face the color of dead
leaves," and being so ill that, "He went by me like a
shadow."  The reader has no doubt that his father is fading away, this
metaphor and simile confirming how Elie's father barely exists. It is ironic as he is
treated as if he has already died by not receiving food rations.
  

As the war comes to an end, "The wheel of
history turned." It is possible that Wiesel is comparing this "wheel" to
the wheel of fortune. Just as the wheel of fortune is a game of chance so too, when the
war ends, the fate of the Jews is still uncertain. "Fortune" can also mean "fate" and so
Wiesel's suggestion that things are about to change - history- is a good thing but the
scars run so deep that, for some there will be no respite and, of course, for others, it
is too late anyway. 

Beside the work on the windmill, what other hardships do the animals have to face in Chapter VII in Animal Farm?

Chapter 7 is really one of the low points for the animals
of Animal Farm.  As you mentioned, they have to work really hard trying to build the
windmill.  But there are other things going on as
well.

• The winter is a really hard one --
  terrible weather.


• They did not have enough food.  Their
  corn ration was cut back and the potatoes that were supposed to make up for that
  spoiled.


• The other thing that I see as a hardship is all
  the executions and the fact that Napoleon is forcing the hens to allow their eggs to be
  sold.