How does Shakespeare capture Juliet's awkwardness and isolation from Paris at Friar Laurence's cell in Romeo and Juliet?

In this scene (Act IV scene 1), Juliet's lack of interest
in Paris--and in fact her frustration with his professions of love--is apparent in her
ambiguous speech.  Juliet's comments upon finding Paris with the Friar may sound
courteous on the surface, but they mostly serve as a screen for her true feelings.  If
you look closely you will find that many of Juliet's lines have a double meaning, often
revealing her true indifference to Paris and her loyalty to
Romeo.

After expressing concern that Juliet's tears have
marred her face, Paris adds, "They face is mine, and thou hast slandered it." Juliet
replies, "It may be so, for it is not mine own" (ln
37).

In the above line Juliet admits she is not being
herself--that she has presented a false face to Paris.  The dashes that follow indicate
that she quickly turns to the Friar as a means to escape further conversation with
Paris.

Is Sydney Carton static or developing in A Tale of Two Cities?

I asked the same questions to my students when studying
this book, and they decided that Sydney Carton was definitely a developing character in
this novel. Of course, in a sense, he is the hero or one of the main protagonists of
this great work of literature. Key to realise and focus on is how he is transformed by
his love for Lucy, even though he knows that his love is
hopeless.

Let us focus on how Sydney Carton is presented at
first. As the "jackal" to Stryver's "lion," he is shown to do all the hard work without
receiving any of the credit. Although he is a man of talent, it is clear he chooses not
to apply himself as he needs to to get on in life. Note how he is described at the end
of Chapter 5:

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Sadly, sadly, the sun rose; it rose upon no
sadder sight than the man of good abilities and good emotions, incapable of their
directed exercise, incapable of his own help and his own happiness, sensible of the
blight on him, and resigning himself to let it eat him
away.

This clearly presents a
very sad picture of Sydney Carton. Likewise at the end of Chapter 4, Sydney Carton
berates himself in the mirror after his talk with Darnay, saying, "A good reason for
taking to a man, that he shows you what you have fallen away from, and what you might
have been!" Therefore Sydney Carton seems to be well aware of the kind of man he could
have been, but for whatever reason, is unable to
be.

However, when Sydney reveals his heart to Lucie, in the
chapter ironically entitled, "The Fellow of No Delicacy," he shows how Lucie's presence
in his life has given him hope, but that he has rejected that hope as a
"dream":

"I
wish you to know that you have been the last dream of my soul. In my degradation I have
not been so degraded but that the sight of you with your father, and of this home made
such a home by you, has stirred old shadows that I thought had died out of me. Since I
knew you, I have been troubled by a remorse that I thought would never reproach me
again, and have heard whispers from old voices impelling me upward, that I thought were
silent for ever. I have had unformed ideas of striving afresh, beginning anew, shaking
off sloth and sensuality, and fighting out the abandoned fight. A dream, all a dream,
that ends in nothing, and leaves the sleeper where he lay down, but I wish you to know
that you inspired
it."

Clearly the role of
Lucie in Sydney's life is incredibly important in provoking that change that he seems to
find so unlikely and impossible. And change he does, for, as we know, this man that
describes himself as being full of "sloth and sensuality" goads himself into action to
bring happiness to Lucie by sacrificing himself. Ironically, in his death, Sydney Carton
finally finds the peace and wholeness that eluded him in life. Note how the bystanders
described him as having the "peacefullest man's face ever beheld there." Others
described him as "sublime" and "prophetic." The unforgettable and moving ending of this
novel shows how one man is able to resurrect himself (a key theme in this novel) through
sacrificing himself to death, showing that Sydney Carton is undoubtedly a dynamic
character that develops as the novel advances.

Determine the complex number z if (z'+7i)/z=6?

Let the complex number z = x + iy. The complement of z ,
z' = x - iy.

As (z' + 7i)/z =
6

=> ( x - iy + 7i)/ ( x + iy) =
6

=> x - iy + 7i = 6*(x +
iy)

=> x - iy + 7i = 6x +
6*i*y

=> x - 6x - iy - 6iy + 7i =
0

=> -5x - 7iy = -7i +
0

Equate the real and complex
parts

=> -5x =
0

=> x = 0

-7iy =
-7i

=> y =
1

Therefore the complex number z is
i.

We can see : (-i + 7i)/i = 6i/i =
6.

How is focusing on industrial agriculture beneficial for a nation?

When a nation starts to grow economically there is usually
a major shift from agriculture to industries. With economic growth there is increased
consumption and it is important to focus towards increasing
efficiency.

As industries take up most of the attention of
governments in framing policies beneficial for them and most of the economic resources
are diverted in that direction, agriculture is not given the importance it should even
though all the food required to feed a growing population originates from
there.

Industrial agriculture is a way of improving
agricultural efficiency. This can be done with the use of research to create seeds that
produce better yielding crops, new fertilizers and pesticides and better planning on the
whole. There is also a requirement to store the agricultural produce and process it to
increase its nutritional value. Processing of food is also a lot more profitable than
the actual production of food.

To ensure that farmers who
have not received the benefits they should have due to the economic growth are benefited
too, there is always a requirement to switch to industrial agriculture. This decreases
the income gap between farmers and those who work in other industries, allow people to
benefit by continuing to remain in the field of agriculture and most importantly ensure
the food safety of the whole nation.

What is the solution of sec x = tan x + cot x in the interval [0, 2pi]?

The question asks for the solution of sec x = tan x + cot
x in the interval [0,2pi].

=> sec x = tan x + cot
x

=> 1/cosx = (sin x/cos x )+ (cos x/ sin
x)

=> (sin x) (cos x) [1/cos x] = (sin x) (cos x) [
(sin x/cos x) +( cos x/sin x)]

=> sinx = sin^2(x) +
cos^2(x)

=> sinx =
1

The sin of 90 degrees is
1.

The solution is 90 degrees or
pi/2.

What do Wolfsheim's cufflinks reveal about him in The Great Gatsby?

This is a very interesting detail that Fitzgerald gives us
about Wolfsheim. Note how the fact that Wolfsheim has human molars, which, in his words,
are the "finest specimens of human molars," add a sinister note to his character that
has already been established by his obvious involvement in the gangster society of
America and the corruption of such institutions such as the World Series. In addition,
the fact that they are human teeth adds overtones of perhaps cannibalism or death to his
character. He is clearly someone that does not mind getting his hands dirty to achieve
his goals, and represents a corrupting force that taints even the supposed purity of
Gatbsy and his ideals and dreams. This of course is one of many hints that are given in
the book about the corruption and illegal activities that lie behind the charismatic and
idealistic face of Gatbsy.

What do Piggy's glasses and the conch have in common in the book, specifically for Chapters 1-2?

Both the glasses and the conch serve as a reminder of the
civilized world that the boys in Lord of the Flies have left
behind. Piggy's glasses serve two purposes: They allow him to see clearly, and they
serve as the all-important fire-starter to keep the signal smoke going. The conch also
symbolizes democracy and civilized behavior, allowing the person who holds it to be
heard and his words recognized by the others. They also become important objects for
whoever possesses them. When the boys take the glasses from Piggy, they leave him weaker
and unable to see clearly; the new owners then possess the power of the
fire.