In Silas Marner, what action does hope lead Silas to take?

I’m not sure to which hope you are referring, but I think
the one of the most significant (and subtle) moments of hope is just after Dunstan has
stolen Silas’ money. He is grief-stricken, but it is the beginning of his detachment
from that money; a detachment from inanimate things. Over the course of the holidays,
although he is still despondent, he begins to show glimmers of hope and the villagers
have also begun to show him more sympathy and Dolly begins to visit him occasionally.
Because Silas is freed of his attachment to the money and because he receives attention,
actual human interaction from the community, he begins to open up – even in small ways
like leaving his door and shutters open. He does this mostly in the hopes that his money
will return. But it is hope nonetheless and in general and literally, he begins to ‘open
up’ to the outside world. It is because of this general hope that he leaves his door
open which allows Eppie into his life. His hope leads him to open up to the outside
world and to literally open his door.

The angle of elevation of the sun is decreasing at a rate of .25 rad/h.How fast is the shadow cast by a 400-ft-tall building increasing when the...

Let x be the angle of
elevation.

Let the house be  represented by BC the vertical
line , and the shadow be represented by BA, the horizontal
line.

Now consider the the triangle ABC in the vertical
plane. x = angle BAC is the angle of elevation.

Therefore
tanx = BC/AC.

Therefore AC = BC/
tanx.

Let AC = f(h) = BC/tanx =
400/tanx.

Differentiating with respect h, we
get:

 f'(h) =  d/dh {400/tanx} = d/dx {400/tanx}
*dx/dh

f'(h) =  [(-1)400/(tanx)^2] (secx)^2 *
dx/dh

f'(x) = -400[1+(tanx)^2]/(tanx)^2}{
dx/dh}

Given  x= pi/6, then (tanx)^2 = 1/3. Also given 
dx/dh = -0.25.

Therefore f'(pi/6)) = -400{1+1/3}/(1/3)
}(-0.25).

f'(pi/6) = -400
+(4*)(-0.25)

f'(pi/6) =
400.

Therefore , when the angle of elevation is x= pi/6
radians, the shadow is increasing at the rate of 400 times with respect to the time in
hour.

In "The Friends," how do Phyllisia and Edith contrast?Please list how they both act. For ex.: Phyllisia

Although Phyllisia Cathy values her friendship with Edith, she
finds herself embarrassed by Edith's appearance, and this attitude is what most differentiates
the two. Phyllisia is intelligent (like her mother) and strong-willed and opinionated (like her
father). She thinks a little too highly of herself, and she is bothered by the taunts she
receives from schoolmates because of her West Indian accent and her brains. Edith, on the other
hand, is a cheerful, happy-go-lucky type, despite her poor family life; Edith basically takes
care of the family's younger children. Edith is also thoughtful (as displayed by the flowers she
takes to Phyllisia's sick mother) and loyal, valuing their friendship far more than Phyllisia.
Both have a rough family life, but in the end, Phyllisia appears to make up with her father,
while Edith's life spirals downward.

Analyze Ivanich's argument against happiness in "Gooseberries." Why does he claim that there is nothing sadder than the sight of a happy person?

In Anton Chekov's "Gooseberries," Ivanich claims there is
nothing sadder than the sight of a happy person.

Thinking upon this,
after reviewing the story, I believe there are two reasons he might say this. Ivanich tells the
story of his brother, a man who wanted nothing more than to have a home in the country and grow
gooseberries. His dream becomes his obsession: he believes that if he can reach these goals, he
will be truly happy. He works hard, marries for money, scrimps and saves, and finally gets his
house with gooseberries growing outside.

When Ivanich goes to visit
him, he sees what a toll life has taken on his sibling as he has scratched through his days to
achieve the things he thinks will bring him satisfaction at last. The sight of his brother
saddens Ivanich. Even the gooseberries his brother so adores are in reality sour and hard, but in
this brother's mind, because they were his dream, they are wonderful and he cannot resist them.
Ivanich thinks his brother is deluded. However, regardless of the manner in
which his brother finds joy in his life, he still feels wonderful for what he has...and Ivanich
does not.

When he becomes more philosophical,
Ivanich seems to believe that happiness is only possible when one is unaware of the unhappiness
of others. (And since there will always be the unhappy, it should be impossible for anyone to be
happy.) Only by putting their heads in the sand, hiding from the sad realities of others, will
people be able to maintain their joy with their
circumstances.

Ivanich, now that he has taken this idea to heart,
appears to believe that he is too old to find happiness and mourns the loss of his youth. He
admits that once he was happy, but finds himself now discontented. It seems that he believes it
is because he is aware of the sadness of others, but I don't think this is an accurate perception
on his part.

Perhaps Ivanich's sense of sadness simply comes down to
his own personal lack of success in finding something that he can celebrate. He says he is too
old himself to struggle to become happy, and now must mourn the lost days of his youth, and look
bleakly into his future with the knowledge that life for him will never be good. However, the
sadness he experiences in seeing a happy person is of his own making. I
doubt Ivanich can see this.

Ivanich feels that those who are happy
are that way because they do not see the reality of others' lives—therefore he thinks they are
delusional. The truth is probably that Ivanich is the deluded one. Despite
the "blindness" others experience, life still brings them joy. Ivanich thinks he has figured out
that happiness comes at the expense of others, but this is not necessarily so. However, because
he believes these things, he sees only gloom for himself, and it is doubtful
that he will ever know another happy day in his life. His outlook on life, and nothing more,
makes it so.

What does atticus mean when he says you never really understand a person......

The quote in full
says 

The
message is quite simple: You have to be in someone's shoes in order to clearly appreciate what
they are going through. One cannot assume that people are supposed to act in one way or another,
or make this or that decision only because it is what we would have
done.

Atticus is trying to explain to Scout that life is not about
expectations but about understandings. People can change in front of our very eyes, or end up
being someone we never saw coming. Yet, it is a fact of life, and it is what it is. Therefore, it
is better to just try and consider the circumstances surrounding a person to clearly judge the
character of the individual and, more than anything, accept the
differences.

l x-3 l = l 2x+5 l find x values

We are given l x-3 l = l 2x+5
l.

Now l x-3 l is equal to (x-3) if (x-3) is greater than
or equal to 0 and is equal to -(x-3) if (x-3) is less than
0.

Similarly l 2x+5 l is equal to (2x+5) if (2x+5) is
positive or is equal to -(2x+5) if (2x+5) is negative.

Now
if x-3 < 0

=> x <
3

=> 2x + 5 can be positive or
negative.

Therefore -( x-3 ) = 2x +
5

=> 3 - x = 2x +
5

=> 3x = -2

=>
x = -2/3

or -(x - 3) = -2x -
5

=> 3-x = -2x -
5

=> x = -8

Now if x -3
> 0

=> x >
3

=> 2x +5 >
0

Therefore (x-3) =
(2x+5)

=> x =
-8

Therefore the possible values of x are
-2/3 and -8

Solve the following equations using Cramer's Rule: 5x-4y+6z=58 -4x+6y+3z=-13 6x+3y+7z=53

We can apply Cramer's rule if and only if the determiant
of the system is different from zero.

We'll calculate the
determinant:

det A = 5*6*7 + (-4)*3*6 + 3*6*(-4) - 6*6*6 -
3*3*5 - 7*16

det A = 210 - 2*4*18 - 216 - 45 -
112

det A = 210 - 517

det A =
-307

Since det A is different from zero, we'll apply
Cramer's rule:

x = det X/detA, y = detY/detA, z =
detZ/detA

5x-4y+6z=58

-4x+6y+3z=-13

6x+3y+7z=53

detX
= 58*6*7 - 13*18 - 12*53 - 53*36 - 9*58 + 13*28

detX = 2436
- 234 - 636 - 1908 - 522 + 364

det x =
-1228

x =
-1228/-307

x =
4

y =
614/-307

y =
-2

In the same way, we'll determine det y
and det z, substituting the column of the coefficients of the variable taht has to be
determined, by the column of the coefficients of the right
side.

Now, we'll substitute x and y in the first
equation:

20 + 8 + 6z = 58

6z
= 58 - 28

6z =
30

z =
5

The solution of the system
is {4 ; -2 ; 5}.