Does a person's appearance tell you anything about who they are in the novel? ( Persuasion by Jane Austen )

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Describe Juliet's relationship with the Nurse and explain how it changes and why.

At the beginning of the play up until Romeo is banished, Juliet
and the Nurse have a very close relationship, much like a daughter and a mother. Juliet is more
willing to share her thoughts with the Nurse than her mother. When she meets Romeo, Juliet tells
the Nurse all about it, and the Nurse is involved in their plans for marriage. The Nurse truly
cares about Juliet's happiness. However, she makes a big mistake when Romeo kills Tybalt and is
banished as a result. The Nurse turns against Romeo and suggests that Julieit should go ahead and
marry Paris, even though she's married to Romeo. This is when Juliet stops confiding in the Nurse
and depends solely on Friar Laurence for help. Juliet can no longer trust the Nurse if she does
not support her marriage to Romeo.

How can I prove that " 1 - (sin^2x / 1 + cotx) - (cos^2x / 1 + tanx) = sinxcosx " using trig identities?

We need to prove that:

1- ( sin^2
x/ ( 1+ cotx) - ( cos^2 x/ (1+ tanx) = sinx*cosx

We will start from
the left side and prove that it equals the right side.

Let us
preview some trigonometric properties:

We know that
:

tanx = sinx/cosx

cotx = cosx/
sinx

==> 1- ( sin^2 x/ ( 1+ cosx/sinx) - ( cos^2 x / ( 1+
sinx/ cosx)

==> ( 1- ( sin^2 x/ ( sinx+cosx)/sinx) - ( cos^2
x/ ( cosx+sinx)/cosx

==> ( 1- ( sin^3 x)/ (sinx+ cosx) - (
cos^3 x/ (cosx+ sinx)

==> (sinx+cosx - sin^3 x - cos^3 x) /
(cosx + sinx)

We will combine similar terms
together.

==> (sinx-sinx^3 x + cosx - cos^3 x)/(cosx +
sinx)

Now we will factor sinx from the first 2 terms and cosx from
the last two terms.

==> sinx(1-sin^2 x) + cosx( 1- cos^2 x) /
(cosx+sinx)

Now we know that: sin^2 x + cos^2 x =
1

==> 1-sin^2 x = cos^2
x

==> 1- cos^2 x = sin^2
x

==> (sinx*cos^2x + cosx*sin^2x)/
(cosx+sinx)

We will factor
cosx*sinx

==> cosx*sinx( cosx + sinx)/(cosx +
sinx)

==> cosx*
sinx................q.e.d

State the main idea in "Poetry and Unreality" by Plato.

The main argument in Plato's assertion is that poets
conceal the reality that the philosopher is trying to expose.  In their desire to want
to be appreciated by the masses, the poet essentially that what they are exploring is
truth.  It is within this element that a critical contention of Plato emerges.  Not
everyone is able to appreciate or fully comprehend the nature of truth, the essence of
being.  The poet, for Plato, pretends and does a disservice to the quest in trying to
allow others to see what this truth is and through their work, they actually do more
harm than good because the poet seeks public adulation, which is fickle and can be
contingent on many variables.  This, for Plato, is "unreal" because it does not reveal
the form, the very essence of what truth is.  In Plato's mind, the poet's desire to be
embraced by others for their work and for public acknowledgement creates a realm that is
dependent on popularity and public appreciation, thereby contributing to its "unreal"
nature.

Is it a funny portrayal of religion?

The story is amusing and entertaining, and one does not
need to be especially religious to appreciate the humor. Thus, we may laugh at Jackie’s
embarrassment at his grandmother’s habits, his interest in Mrs. Ryan’s half-crown (the
equivalent of a large amount of money today), the priest’s prediction about how someone
will go after Nora with a knife and not miss, and Nora’s bewilderment after Jackie’s
"first confession." In discussing the causes of laughter, students should note the
relationship of situations such as these to principles of rigidity and incongruity as
described by Henri Bergson in his study of laughter. Thus Jackie in the communion class
should be considering the state of his soul, but instead he demonstrates a little boy’s
concern for Mrs. Ryan’s money (in this way fitting his rigidly childish perspective into
a situation requiring thought and fear). In addition, sober and proper behavior is
expected in a confessional, so that Jackie’s antics, so clearly out of place and
inappropriate, are funny.

if f'(x) = ( x*cosx + 7) /x and f(0) = 5. find f(x).

f'(x) = (x*cosx + 7) /x

Let
us simplify the function.

f'(x) = xcosx/x +
7/x

       = cosx +
7/x

==> f'(x) = cosx +
7/x

Now we know that f(x) = integral
f'(x).

==> f(x) = intg f'(x)
dx

             = intg (cosx + 7/x)
dx

             = intg cosx dx  + intg 7/x
dx

             = sinx + 7*ln x +
C

==>f(x) = sinx  + 7*lnx +
C

f(0) is not a valid point
because lnx is not defined at x= 0.

A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.

There are two independent events:  (i) tossing a coin and
rolling 6 sided die.

When we toss an unbiased  coin we may
get a head or a tail up. So getting head or tail are equally likely . So the probability
getting a head = 1/2.

When an unbiased  6 sided die is
rolled , we may get any one of the number from 1 to 6. So there are 6 equal choices.
Getting 3 is one choice out of 6 choices. So the probability of getting 3 =
1/6.

Since the two events - getting a head in a coin in a
toss and getting  a 3 in a rolling of die - are independent , the happening of  both
events is the product of the probabilities = (1/2) (16) =
1/18.

Therefore , the probability of getting a head in a
toss of the coin and  getting a number 3 in a rolling of a die is
1/18.