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:

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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,

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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.