(m+n) + (5m-2)

Since it is not specified what is the request of the
problem, we'll simplify the given expression and we'll
get:

We'll remove the
brackets:

m+ n + 5m - 2

We'll
re-arrange the terms and we'll combine like terms:

(m+5m) +
(n-2)

The simplified expression
is:

(m+n) + (5m-2) = 6m + n -
2

If the request of the problem was to
determine m and n, we'll solve the problem:

(m+n) + (5m-2)
=  0+0

We'll put the first bracket as
0:

m + n = 0 (1)

We'll put the
second bracket as zero:

5m - 2 =
0

We'll add 2 both sides:

5m =
2

We'll divide by
5:

m = 5/2
(2)

We'll substitute m in
(1):

5/2 + n = 0

We'll
subtract 5/2 both sides:

n =
-5/2

Find the polar form of the complex number 7 – 5i.

The polar form of x+yi =  r(cost+isint), where r =
sqrt(x^2+y^2).

cost = x/sqrt(x^2+y^2) , sint = 
y/(x^2+y^2).

r is called the modulus of x+yi and t is called the
aruement or ampitude of x+yi.

Therefore the given complex number,
x+yi = 7 - 5i

r = sqrt {(7^2+(-5)^2} = sqrt(25+49) =
sqrt74.

Therefore  cos t = 7/sqrt74 and sin t
=-5/sqrt74.

Therefore  t =  arc tan (-5/7) = -0.6204 rad
appr.

Therefore  7-5i = sqrt74{ cost+isint) , where t = -0.6204
rad.

7-5i = sqrt74({cos (arc tan (-5/7) +i sin arctan(-5/7)} in
polar form.

Evaluate lim [sin(pi/3+ h) - sin(pi/3)] / h as h---> 0

lim [sin(pi/3 + h) - sin(i/3) / h  as h-->
0

It is obvious frm the definition of the derivtive. we
know that:

f'(x)= lim (f(x+h) - f(x)]/h   as h -->
0

Thenwe will assume
that:

f(x) =
sinx   

==> f'(pi/3) = lim [sin(pi/3 + h) - sinpi/3]
/h  as h-->0

Now we will differetiate
f(x)

f'(x) = cosx

==>
f'(pi/3)= cos(pi/3)

                   
=cos60

                     =
1/2

==>lim [sin(pi/3 + h) -
sin(pi/3)]/ h   as -->  is 1/2

In The Adventures of Huckleberry Finn, how long did it take Huck to apologise to Jim?

The answer to your question can be found in Chapter Fifteen of
this great story. Remember that key to understanding this tale is that we witness the gradual
coming of age and moral maturity of Huck, the central protagonist. The event you allude to marks
a key moment in his moral growth, as he defies social conventions and customs and apologises to a
runaway slave, admitting he was wrong and understanding how he hurt Jim in the process. For a
white boy to do this to a runaway slave shows incredible force of character, as Huck was going
against everything he had learnt and been taught in his upbringing. Note what Huck tells us about
his apology:

It was
fifteen minutes before I could work myself up to go and humble myself to a nigger; but I done it,
and I warn't ever sorry for it afterwards,
neither.

So, we can see that it took
Huck fifteen minutes to resolve his inner conflict and follow his heart rather than his
head.

Beginning with the serving of coffee Bronte shifts her narrative into the present tense. Why does she do this, and what is the effect on the...

Bronte switches to the present tense to communicate Jane's
heightened state of awareness and sensation around Mr. Rochester, after she tried to convince
herself of the fact that they'll never be together. Prior to this moment, we've read about how
attracted Jane is to Rochester, how strong a connection she feels to him, how much she treasures
and values his differences. Yet Bronte ends this moment with Jane concluding that she must
abandon the hope of them ever being together.

The present tense in
this passage gives the reader a sense of almost being in the room, enriching the words with a
vividness and energy, that it's as if we're in the drawing room as well, looking around at all
the characters.

What is value of the derivative of x^3 + y^3 = 14xy at (7,7)?

Given the equation:

x^3 + y^3 =
14xy

We need to find the value of the first derivative at the point
(7,7).

First we will use implicit
differentiation.

==> (x^3)' + (y^3)' =
14(xy)'

==> 3x^2 + 3y^2 *y' = 14[
(x'y+xy')]

==> 3x^2 + 3y^2 y' = 14(y +
xy')

==> 3x^2 + 3y^2 y' = 14y +
14xy'

Now we will combine terms with
y'.

==> 3y^2 y' - 14xy' = 14y -
3x^2

==> y' ( 3y^2-14x) = 14y -
3x^2

==> y' = (14y-3x^2)/
(3y^2-14x)

Now we will substitute with
(7,7)

==> y'(7,7) = (14*7 - 3*7^2) / (3*7^2 -
14*7)

= 98-147 / 147-98

= -49/49 =
-1

Then the value of the derivative is
(-1).

What is the point of view in "The Masque of the Red Death"?

While Poe's story is apparently told from third-person objective
point of view with a narrator recounting an allegorical story, there are other interpretations of
Poe's narrator in "The Masque of the Red Death."

One interpretation
of Poe's narrator is that of Leonard Cassuto who contends the narration is that of the Red Death
himself.  Since Prince Prospero dies about a paragraph and a half before the end of the story,
this interpretation certainly seems plausible.  Added to this, the last line appears to express a
rather victorious view:

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And the flames of the tripods expired.  And Darkness and
Decay and the Red Death held illimitable dominion over
all.

Another interpretation--somewhat
Freudian, it seems--holds that the narrator is the subconscious of Prince Prospero himself. 
Thus, the narrative is the workings of his mind as he wrestles with his own mortality and his
death is not literal, but psychological.  Still, yet another interpretation holds that "The
Masque of the Red Death" is a Biblical morality tale in which God sends a pestilence to punish
the people for their evil and debauchery.  As such, the narrator, then, is a divine
being.

Perhaps, the ambiguity of who is the narrator of his macabre
story make exist because Poe wishes to express what Ugo Betti has
written:

Every tiny
part of us cries out against the idea of dying, and hopes to
live forever.