How did the twins play tricks on the ghost?

Unlike the English, the American Otises have no fear of the Canterville ghost, and the Otis twins go as far as turning the tables on him. Sir Simon, the ghost, tries to theatrically scare them with terrifying costumes and sudden, dramatic, nighttime appearances, but, instead, they frighten him with all-American practical jokes.
Practical jokes are physical and concrete: the humor comes not from wordplay or sophisticated understanding but from someone falling or some other kind of crude, slapstick humor. In this story, the twins pull out such classics as creating a butter slide, shooting at the ghost with a pea shooter, and propping a bucket of water at the top of the door of their room. Luckily for the ghost, he has dressed up in a headless guise the night the bucket of water falls on him.
Although a ghost traditionally terrifies humans, in this case, the twins terrify the ghost with their tricks.

In The Canterville Ghost, the twins play lots of tricks on the ghost. These tricks begin in chapter 3 when the twins attack the ghost with their pea shooters during his second appearance. Later, when the ghost tries to take revenge for this attack, the twins terrify him by creating the Ye Otis Ghoste, a mock ghost with "hollow eyes." Terrified, the Canterville ghost retreats.
The twins' tricks continue in chapter 4 with their creation of a butter slide which causes the Canterville ghost to fall and hurt himself. Shortly after, the twins drench the ghost by pouring a jug of water over him, which is hanging above a doorway.
Instead of being afraid of the ghost, the twins delight in playing tricks on the ghost. This adds an element of humor to the story while also creating sympathy for the plight of the Canterville ghost.

int (x^2+5) / (x^3-x^2+x+3) dx Use partial fractions to find the indefinite integral

Indefinite integral are written in the form of int f(x) dx = F(x) +C
 where: f(x) as the integrand
           F(x) as the anti-derivative function 
           C  as the arbitrary constant known as constant of integration
To determine the indefinite integral of int (x^2+5)/(x^3-x^2+x+3) dx , we apply partial fraction decomposition to expand the integrand: f(x)=(x^2+5)/(x^3-x^2+x+3)
The pattern on setting up partial fractions will depend on the factors  of the  denominator. The factored form of x^3-x^2+x+3 =(x+1)(x^2-2x+3) .
For the linear factor (x+1) , we will have partial fraction: A/(x+1) .
For the quadratic factor (x^2-2x+3) , we will have partial fraction: (Bx+C)/(x^2-2x+3) .
The integrand becomes:
(x^2+5)/(x^3-x^2+x+3) =A/(x+1)+(Bx+C)/(x^2-2x+3)
Multiply both side by the LCD =(x+1)(x^2-2x+3) .
((x^2+5)/(x^3-x^2+x+3) )*(x+1)(x^2-2x+3)=(A/(x+1)+(Bx+C)/(x^2-2x+3))*(x+1)(x^2-2x+3)
x^2+5=A(x^2-2x+3)+(Bx+C)(x+1)
We apply zero-factor property on (x+1)(x^2-2x+3) to solve for values we can assign on x.
x+1 =0 then x=-1
x^2-2x+3=0 then x=1+-sqrt(2)i
To solve for A , we plug-in x=-1 :
(-1)^2+5=A((-1)^2-2*(-1)+3)+(B*(-1)+C)(-1+1)
1+5=A(1+2+3)+(-B+C)*0
6 = 6A
6/6= (6A)/6
A=1
To solve for C , plug-in A=1  and x=0 so that B*x becomes 0 :
0^2+5=1(0^2-2*0+3)+(B*0+C)(0+1)
0+5=1(0-0+3)+ (0+C)(1)
5 = 3 +C
C= 5-3
C =2 .
To solve for B , plug-in A=1 , C=2 , and x=1 :
1^2+5=1(1^2-2*1+3)+(B*1+2)(1+1)
1+5 = 1 (1-2+3)+(B+2)(2)
6 = 2 +2B+4
2B = 6-2-4
2B=0
(2B)/2 = 0/2
B =0
Plug-in A = 1 , B =0 , and C=2 , we get the partial fraction decomposition:
(x^2+5)/(x^3-x^2+x+3) =1/(x+1)+(0x+2)/(x^2-2x+3)
                      =1/(x+1)+2/(x^2-2x+3)
The integral becomes:
int(x^2+5)/(x^3-x^2+x+3) dx = int [1/(x+1)+2/(x^2-2x+3)] dx
Apply the basic integration property: int (u+v) dx = int (u) dx + int (v) dx
int [1/(x+1)+2/(x^2-2x+3)] dx =int 1/(x+1)dx +int 2/(x^2-2x+3)dx
For the first integral, we apply integration formula for logarithm: int 1/u du = ln|u|+C .
Let u =x+1 then du = dx
int 1/(x+1) dx =int 1/u du
                 = ln|u|
                 = ln|x+1|
Apply indefinite integration formula for rational function:
int 1/(ax^2+bx+c) dx = 2/sqrt(4ac-b^2)arctan((2ax+b)/sqrt(4ac-b^2)) +C
By comparing "ax^2 +bx +c " with "x^2-2x+3 ", we determine the corresponding values: a=1 , b=-2 , and c=3 .
The second integral becomes:
int 2/(x^2-2x+3)dx= 2int 1/(x^2-2x+3)dx
=2*[2/sqrt(4*1*3-(-2)^2)arctan((2*1x+(-2))/sqrt(4*1*3-(-2)^2))]
=2*[2/sqrt(12-4)arctan((2x-2)/sqrt(12-4))]
=2*[2/sqrt(8)arctan((2x-2)/sqrt(8))]
=2*[2/(2sqrt(2))arctan((2(x-1))/(2sqrt(2)))]
=2/sqrt(2)arctan((x-1)/sqrt(2))
=(2arctan((x-1)/sqrt(2))) /sqrt(2)
Combining the results, we get the indefinite integral as: 
int (x^2+5)/(x^3-x^2+x+3) dx =ln|x+1|+(2arctan((x-1)/sqrt(2))) /sqrt(2)+C
                                =ln|x+1|+ sqrt(2)arctan((sqrt(2)(x-1))/2) +C
                                =ln|x+1|+ sqrt(2)arctan((xsqrt(2)-sqrt(2))/2) +C

What is strong evidence that proves it was the vulture eye that caused the narrator to kill the elderly man?

One of the most significant pieces of evidence that it is the old man's vulture eye that seems to compel the narrator to kill him is that the narrator admits to having no other motive for murder.  He says,

Object there was none. Passion there was none.  I loved the old man.  He had never wronged me.  He had never given me insult.  For his gold I had no desire.  I think it was his eye! yes, it was this!

In other words, he does not look to gain anything by committing the murder: he is not planning to rob the old man of his fortune or to inherit it upon the old man's death.  Likewise, the narrator does not feel any hatred or ill-will toward the old man; in fact, he says that the narrator has never done anything wrong to him or injured him in any way. There is simply no other reason to kill him.
Once he lands on the idea that it is the old man's eye that spurs him to murder, he describes it in great detail, saying, in part, "Whenever it fell upon me, my blood ran cold; and so by degrees -- very gradually -- I made up my mind to take the life of the old man, and thus rid myself of the eye forever."  He believes that it is the old man's "vulture eye," cloudy, likely, as a result of cataracts (a common optical ailment among the elderly) that prompts him to murder.

How does social media impact communication?

In order to address the question of social media and its impacts on communication, it is important to first present a formal definition of “social media.” Investopedia defines it as “computer-based technology that facilitates the sharing of ideas and information, and the building of virtual networks.” “Virtual networks” are actually social networks created and facilitated online instead of through face-to-face meetings. As such, social media includes all those applications or websites which allow individuals to meet, socialize, and share information with minimal restrictions. From this point of view, one can then easily identify social media sites such as Facebook, Twitter, Instagram, and LinkedIn.
Clearly, social media has helped to improve interaction and communication on a global scale. Today, people from different corners of the globe are able to share information with each other easily and at minimum costs. Unlike the olden days, when one had to, say, send a telegram to pass urgent information, applications such as Skype or Facebook Video Chat can easily be used to convey the same information, almost immediately as the need arises. Important meetings or conferences no longer have to be done face to face, as there exist applications within social media sites that can be used to do this and thus save on time and travel costs, for instance, live video conferencing or webinars. Social media has also impacted communication within the education sector. Students can make use of social media facilities to form group discussions on challenging class concepts. Groups can also be formed for socialization purposes so that students can get to know each other and their course instructors better. This brings a human face to classroom activities. Also, social media is increasingly being used as an instructional tool; for instance, various opportunities currently exist for teaching non-English speakers conversational English via Skype.
On the other hand, social media has negatively impacted written communication by watering down the vocabulary and syntax of written text. In trying to summarize information, users resort to either “broken language” or the more recent “emoji language,” both of which do little to improve the linguistic skills of the users.
https://www.investopedia.com/terms/s/social-media.asp

Two weeks after Sal’s mother left, Sal has a major revelation—what was it?

Two weeks after Sal's mother leaves, Sal has a major revelation. She begins to understand that, even though it will be difficult, she can survive without her mother by her side.
The text tells us that Sal was so emotionally attuned to her mother that she would mirror her mother's emotions. If her mother was sad, Sal would be sad. If her mother was happy, Sal would also be happy. After her mother left, Sal felt a numbing of her emotions. She did not know how to feel anything on her own. Essentially, when her mother left, Sal was left without an emotional compass.
Two weeks after the disappearance of Sal's mother, Sal has an epiphany. While watching a newborn calf find its footing, Sal experiences great joy. The rush of emotions is exhilarating, and this leads Sal to conclude that she can be happy without her mother. To Sal, the revelation is a major one, and although it makes her sad, she understands that the truth is also important.

College Algebra, Chapter 1, 1.7, Section 1.7, Problem 20

Solve the equation $\displaystyle \left| \frac{3}{5}x + 2 \right| - \frac{1}{2} = 4$


$
\begin{equation}
\begin{aligned}
\left| \frac{3}{5}x + 2 \right| - \frac{1}{2} &= 4\\
\\
\left| \frac{3}{5}x + 2 \right| &= \frac{9}{2} && \text{Subtract 20}
\end{aligned}
\end{equation}
$


We have,

$
\begin{equation}
\begin{aligned}
\frac{3}{5} x + 2 &= \frac{9}{2} && \text{and}& \frac{3}{5}x + 2 &= -\frac{9}{2} && \text{Subtract 2}\\
\\
\frac{3}{5} x &= \frac{5}{2} && \text{and}& \frac{3}{5}x &= - \frac{13}{2} && \text{Multiply each side by 10}\\
\\
6x &= 25 && \text{and}& 6x &= -65 && \text{Divide by 6}\\
\\
x &= \frac{25}{6} && \text{and}& x &= -\frac{65}{6}
\end{aligned}
\end{equation}
$

Why does Mary force the police officers to eat the lamb?

Dahl's "Lamb to the Slaughter" is one of the best examples of dramatic irony. At the very end of the story, after Mary has killed her husband with a frozen leg of lamb and the police have come to investigate, Mary ends up feeding the cooked lamb to the policemen, thereby disposing of the murder weapon. While the reader is fully aware of the this, the police continue to enjoy the feast that Mary has provided them.
This act is done to complete the "perfect murder" scenario that Mary has upheld throughout the story. She is the only one who knows that she has a motive to kill her husband; she goes to the grocery store with calm ease; she speaks to the police in a way that communicates both shock and kindness. By ridding herself of the only thing that could point back to her being the murderer, Mary feels relief and almost a giddiness—she has gotten away with murdering her husband. In fact, as the police finish off the leg of lamb, the very last sentence of the short story is, "And in the other room, Mary Maloney began to laugh."

In "Lamb to the Slaughter," Mary forces the police officers to eat the leg of lamb because she does not want her guilt to be revealed to them.
Remember that Mary used the frozen leg of lamb to kill her husband. She hit him over the head with it after he said that he was leaving her. Although her crime was not premeditated, Mary still committed murder, meaning that she would go to prison for a long time if the officers find out what she did.
Instead of facing up to what she has done, Mary concocts a cunning plan. She proceeds to cook the leg of lamb and then offers it to the investigating officers who have stayed late at her house. By doing this, Mary portrays herself as being kind and caring, not a cold-hearted murderess.
This scene, therefore, acts as an example of dramatic irony since we, the reader, know that she is disposing of the murder weapon. The officers, however, think that the meal is just a token of her kindness.