When did rural Louisiana get electricity?

Electricity came to rural Louisiana very late in comparison to its introduction in many other states, including some of those in the southern USA. The key cities in Louisiana have been electrified since 1881, when New Orleans first had access to electricity; by the end of 1882, there was a good supply of energy across the city. Inspired by this success, further companies were incorporated until most of Louisiana's major cities had electricity.
By 1920, rural Louisiana, however, was still not supplied with electricity, as no energy company wanted to venture into a region it thought would be unprofitable. The measure implemented by Roosevelt to solve this problem was to create the Rural Electrification Administration, which specifically aimed to encourage companies to electrify rural parts of the United States by providing them with cheap loans. This went into effect in 1935, after which a number of electricity companies were formed to help supply power to rural parts of Louisiana. This process continued throughout the 1940s and 1950s.
http://www.dnr.louisiana.gov/sec/EXECDIV/TECHASMT/electricity/electric_vol1_1994/002.htm

int x / sqrt(9 + 8x^2 - x^4) dx Find or evaluate the integral by completing the square

Recall  that int f(x) dx = F(x) +C where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration..
 For the given problem, the integral: int x/sqrt(9+8x^2-x^4)dx
does not yet resemble any formula from table of integrals.
 
To evaluate this, we are to apply u-substitution by letting:
u = x^2 then u^2 = x^4  and  du = 2x dx  or (du)/2 = x dx .
Then the integral becomes:
int x/sqrt(9+8x^2-x^4)dx =int x dx/sqrt(9+8x^2-x^4)
                                      =int ((du)/2)/sqrt(9+8u-u^4)
Apply the  basic  property of integration: int c f(x) dx = c int f(x) dx to factor out  1/2 .
int ((du)/2)/sqrt(9+8u-u^4) = 1/2int (du)/sqrt(9+8u-u^4)
 The integral does not yet resembles any integration formula.
For further step, we apply  completing the square on the part: 9+8u-u^2 .
Completing the square:
Factoring out -1 from 9+8u-u^2 becomes: (-1)(-9-8u^2 +u^2) or -(u^2 -8u-9) .
u^2 -8u-9 resembles ax^2 +bx+c where:
a=1 , b= -8 and c=9 .
To complete the square we add and subtract (-b/(2a))^2 .
Plug-in the value of a=1 and b=-8 in  (-b/(2a))^2 :
(-b/(2a))^2 =(-(-8)/(2*1))^2
             =(8/2)^2
              =4^2
              =16.
Adding and subtracting -16 inside the ():
-(u^2 -8u-9) =-(u^2 -8u-9+16-16)
 To move out "-9" and "-16" outside the (), we distribute the negative sign or (-1).
-(u^2 -8u-9+16-16) =-(u^2 -8u-9+16) +(-1)(-9)+ (-1)(-16)  
                                         =-(u^2 -8u-9+16) +9+ 16
                                         =-(u^2 -8u-9+16) +25
Factor out the perfect square trinomial: u^2 -8u+16 = (u-4)^2
-(u^2 -8u+16) + 16 = -(u-4)^2+25
Then it shows that 9+8u-u^4 =-(u-4)^2+25
                                               =25-(u-4)^2
                                                 = 5^2 -(u-4)^2
Then,
1/2 int (du)/sqrt(9+8u-u^4)= 1/2int (du)/sqrt(5^2-(u-4)^2)
 The integral part resembles the basic integration formula for inverse sine function:
int (du)/sqrt(a^2-u^2)= arcsin(u/a)+C
Applying the formula, we get:
1/2int (du)/sqrt(5^2-(u-4)^2) =1/2 arcsin ((u-4)/5) +C
Plug-in u =x^2  for the final answer:
int x/sqrt(9+8x^2-x^4)dx =1/2 arcsin ((x^2-4)/5) +C 

How does Hester suffer in The Scarlet Letter?

Hester Prynne suffers from public shame, guilt, and embarrassment after being forced to stand on the scaffold in front of the community of Salem. She is also forced to wear the scarlet letter each day throughout the community as punishment for committing adultery. Hester lives as an outcast in Salem and watches as people gossip about her sins publicly. In addition to Hester's continual public shame, she is also suffering from the stress and burden of keeping Dimmesdale and Chillingworth's secrets. Hester promises both men that she will not reveal their relationships with her, and watches helplessly as Chillingworth gradually harms Reverend Dimmesdale. Hester also suffers from her inability to have an open relationship with Dimmesdale, Pearl's biological father. She wishes to be with Dimmesdale and happily raise Pearl in a healthy home. 
Hester also suffers from her daughter's capricious nature and has a difficult time raising Pearl. Pearl is a constant reminder of her sin, and Hester is forced to raise Pearl as a single mother. Hester lives the majority of her life alone and is continually reminded of her sin each time she wears the scarlet letter. Her inner anguish is a result of keeping Dimmesdale and Chillingworth's secrets, which only exacerbates her negative situation. 

First, Hester suffers because she cannot be with the man she loves, Reverend Dimmesdale.  She will not tell the ministers in town who her fellow sinner was, and Dimmesdale is too cowardly to confess his sin openly until the very end of the novel, right before he dies.  Second, Hester suffers as a result of her guilt.  She feels guilty about committing an act that turns her once peaceful and kindly husband, now called Chillingworth, into a devil hell-bent on revenge.  She also feels guilty about not telling Dimmesdale—at least, for a long time—that Chillingworth is her husband; she watches for years as Dimmesdale gets more and more sickly under Chillingworth's care, but she does not reveal his identity to Dimmesdale until they meet in the forest, some seven years after their initial "sin."  Third, Hester's daughter, Pearl, constantly does things that hurt Hester: she flings flowers at Hester's scarlet "A," and she dances each time she hits it; she also decorates her own breast with grass in the shape of an "A" and so forth.  Hester also knows that her own sin taints her daughter's life, and this causes her to suffer as well.

What are the similarities between the characters of the Invincible Louisa and the characters of Little Women?

There are more than a few similarities between the March girls and the Alcott sisters. Alcott herself admitted that the first part of "Little Women" was based in fact, while the second half was more along the lines of what she wished for her family. 
Abba Alcott is very similar to Marmee—in fact, Louisa and her sisters used this affectionate name for Abba. Like Marmee, Abba was very kind and supportive of both her husband and her daughters. She often filled the role as breadwinner and did her best to protect her daughters from the harsher realities of life. 
Louisa had an older sister named Anna who became a teacher, just as Meg did. Her sister Elizabeth died young, just like Beth March, who succumbs to scarlet fever. While the youngest Alcott sister, May, did not marry a wealthy man like Amy March did, she found her own success as an artist and even partnered with Louisa at times. 
Jo March and Louisa Alcott are undoubtedly the characters that are most closely aligned. Alcott admitted that she was a tomboy and boisterous, at times causing trouble for her mother. She loved to read and write creatively—a talent that was supported by both her parents. Louisa eventually began to support her family through her writing. Unlike Jo, she never married but took care of her parents throughout her life. 
 
http://teachersinstitute.yale.edu/curriculum/units/1999/1/99.01.06.x.html

Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 18

Solve the equation: $\displaystyle \left| \frac{2}{3}x - 1 \right| = 5$

We can solve this compound equation as follows


$
\begin{equation}
\begin{aligned}

\frac{2}{3}x - 1 =& 5 && \qquad \text{or} &&& \frac{2}{3}x - 1 =& -5
&&
\\
\\
\frac{2}{3}x =& 6 && \qquad \text{or} &&& \frac{2}{3}x =& -4
&& \text{Add } 1
\\
\\
x =& \frac{18}{2} && \qquad \text{or} &&& x =& \frac{-12}{2}
&& \text{Multiply } \frac{3}{2}
\\
\\
x =& 9 &&\qquad \text{or} &&& x =& -6
&& \text{Reduce to lowest terms}

\end{aligned}
\end{equation}
$



The solution set is $\{ -6,9 \}$.

Can Big Brother decide what is real and what is not?

The method by which a totalitarian society such as that depicted in 1984 operates is essentially to try to destroy the concept of objective reality. "Truth" is made into not what people's own senses tell them—what they factually observe and remember—but instead what the Party tells them it is. The most obvious case in which this is shown to Winston is when, during his "re-education" process, O'Brien tortures him into "believing" the number of fingers he is holding up is not what Winston sees, but whatever the Party tells him to see. Earlier in the story, the Oceanians are suddenly told that they are at war with Eastasia and in alliance with Eurasia and have always been—the exact opposite of the truth—and yet everyone is expected to believe this as if nothing out of the ordinary has happened. Thus, Big Brother, as the face of the regime, is dictating "reality" to the population. It is absurd, of course, but Orwell's depiction is merely an exaggerated form of what the Communist and Fascist regimes of the twentieth century were doing in manipulating their own people—feeding them "alternative facts" in contradiction to the actual reality observed by people.

Absolutely -- this is George Orwell's scary thesis of 1984. Big Brother warps everyone's sense of reality through indoctrination programs (like the programmed displays of "hate"), historical manipulation (like Winston's responsibility to discard information that portrays the Party unfavorably), over-stimulation, and propaganda. When introduced to this world, the reader might ask themselves: "Can't someone in this world know the truth? Doesn't everyone have the capacity to know it deep inside themselves?"
This is the question that drives Winston Smith through the story. The Party decides that "2 + 2 = 5," where very basic instinctual logic dictates that 2 + 2 =4. You could say that Winston's desire is to bring back a society where 2 + 2 = 4, where the truth can be openly admitted and appreciated. O'Brien, a character supposedly belonging to a revolutionary group called the Brotherhood, inspires Winston to take action. Winston meets with him, hoping they will form a rebellion. When it turns out that O'Brien is actually a member of the Party, Winston Smith is tortured and told to admit that "2 + 2 = 5." Eventually, he does. 
So, back to the original question: can Big Brother control what is real?
The answer is yes and no. If someone lives under Big Brother, they may have intuitions and a sense of the truth, but Big Brother will find out. When he does, they will inevitably submit.
 
  

In 1984, Big Brother can absolutely decide what is real and what is not. In fact, to do this, all Big Brother and the Party need to do is to control the flow of information, and as we see from the story, that is constantly happening in Oceania.
Let's take Winston's job for example. It is his responsibility to rewrite the past according to the Party's instructions. When he is told to write about an upcoming chocolate ration, for example, Winston is rewriting the past and changing what is real. It doesn't matter that the Party said there wouldn't be a chocolate ration; that phrase has been erased from history and is no longer real, because it doesn't exist.
Similarly, when it comes to the war in Oceania, the Party switches from having a war with Eurasia to Eastasia. As Winston says in part 2, chapter 9, the Party does not admit that a change has taken place. It doesn't have to because nobody would dare to argue otherwise. What this shows is that the Party is able to determine what is real and what is not, without explanation, because people are too afraid to disagree. They simply accept what they are told as fact.

Why does Nag keep Rikki engaged in conversation when they first meet?

When Rikki and Nag first meet near the beginning of "Rikki-Tikki Tavi," the tailorbird named Darzee has just told Rikki about how Nag ate one of his babies the day before. Rikki has just recently been rescued and does not know who Nag is, which prompts Nag to appear. Nag, a cobra, fears mongooses like Rikki, as mongooses are capable of killing cobras. As a result, Nag hopes to keep Rikki engaged in conversation while his wife Nagaina approaches in the bushes. Their goal is for Nagaina to attack Rikki when he is not expecting it. Attacking Rikki by surprise is the cobras' best chance of killing him. Darzee notices Nagaina in the grass, though, and is able to warn Rikki in time for him to take action.

He jumped up in the air as high as he could go, and just under him whizzed by the head of Nagaina, Nag's wicked wife. She had crept up behind him as he was talking, to make an end of him. He heard her savage hiss as the stroke missed.

Darzee's warning allows Rikki to get out of the way of Nagaina's strike in time.