How does Zaroff justify hunting humans in "The Most Dangerous Game" by Richard Connell?

Zaroff tells Rainsford he is bored and the humans he is hunting are inferior, which is how they end up killed. 

Zaroff is an expert hunter. He explains to Rainsford that he became so good at hunting that he could hunt any animal of any size and it was no longer a challenge. Perfection was a bore.

No animal had a chance with me any more. That is no boast; it is a mathematical certainty. The animal had nothing but his legs and his instinct. Instinct is no match for reason. When I thought of this it was a tragic moment for me, I can tell you.

This is the reason, he told Rainsford, that he developed a new type of game. Rainsford was confused by this. He was an avid hunter, too. He wrote books on the subject. He knew Zaroff could not just create a new animal.  

Zaroff explains he bought the island because it was perfect for this new type of game hunting due to its “jungles with a maze of traits in them, hills, swamps.” Zaroff says his new animal can match wits with him, and he is never bored. In Zaroff’s mind, that is also a justification because he is extremely egotistical and it is all about him.

Zaroff justifies hunting people because he is trapping ships and taking sailors. If he kills them, he believes that means they are weak and deserve to die. He uses the survival of the fittest argument, saying,

Life is for the strong, to be lived by the strong, and, if needs be, taken by the strong. The weak of the world were put here to give the strong pleasure. I am strong. Why should I not use my gift? If I wish to hunt, why should I not? I hunt the scum of the earth.

There is a certain amount of racism here, too, since Zaroff claims that the "lassars, blacks, Chinese, whites, mongrels" are worthless human beings. Because of their profession, class, and/ or race, they are thought by Zaroff to be inferior to him, meaning he can do what he wants with them. He is an aristocrat. He has money and power. They do not. 

What Zaroff fails to note in his argument is that he has all the advantages in the hunt. He knows the island. He also has a gun, and all he gives the person he is hunting is "a supply of food and an excellent hunting knife" and three hours' head start. It doesn't negate his advantage.

`dy/dx = (6-x^2)/ (2y^3)` Find the general solution of the differential equation

`(dy)/dx = (6-x^2)/(2y^3)`

This differential equation is separable since it can be rewritten in the form

`N(y) dy=M(x) dx`

So separating the variables, the equation becomes

`2y^3dy = (6-x^2)dx`

Integrating both sides, it result to

`int 2y^3dy = int (6-x^2)dx`

`2*y^4/4 + C_1 = 6x-x^3/3 + C_2`

`y^4/2 + C_1 = -x^3/3 + 6x + C_2`

Since C1 and C2 represent any number, it can be expressed as a single constant C.

`y^4/2 = -x^3/3 + 6x + C`

Therefore, the general solution of the given differential equation is `y^4/2 = -x^3/3 + 6x+ C` .

What different choice could Victor Frankenstein have made after the monster's request for a companion?

When the monster initially requests a companion, Victor agrees, feeling that he has some obligation to make this creature happy.  However, after Victor has some time to consider all the terrible damage this monstrous couple could do if they decided to be evil, he destroys the mate.  This compels the monster to vow that he will exact revenge on Victor by killing everyone he loves and rendering Victor as miserable as he feels himself to be.  Instead of resolving, in the end, not to give his creature a companion, Victor could have decided to do so.  His creature swears that he and his mate would leave the company of humankind forever and never injure anyone else, and it is possible that this is exactly what would have happened.  If Victor has created the female for him, it is possible, then, that Victor's best friend, wife, and father, at least, would have survived, and Victor's life would not have ended so early and tragically.

`(1+0.10/365)^(365t) = 2` Solve the equation accurate to three decimal places

`(1+0.1/365)^(365t) = 2`

In solving these kind of problems we need to use the logarithm.

Take the logarithm on both sides of the equation.

`log_(10)((1+0.1/365)^(365t)) = log_10(2)`

With logarithms we know that,

`log(a^b) = bloga`

using that rule;

`log_(10)((1+0.1/365)^(365t)) = 365tlog_10(1+0.1/365)`

`365tlog_10(1+0.1/365) = log_10(2)`

`log_10(1+0.1/365) = log_10(1.000274) = 0.000119`

`log_10 (2) = 0.3010`

`365txx0.000119 =0.3010`

`t = 0.3010/(365xx0.000119) = 6.931`

So the answer is t = 6.931

In the first five chapters of Bud, Not Buddy, where is Bud's mother mentioned?

Chapter five is your best bet for sentences that are about Bud's mom.  It is also the best chapter to find quotes that are spoken by Bud's mom.  Bud's mom is dead, so chapter five is mainly a flashback.  

One of my favorite lines from Bud's mother is the following:

She'd tell me, "Especially don't you ever let anyone call you Buddy. I may have some problems, but being stupid isn't one of them.  I would've added that dy onto the end of your name if I intended for it to be there. I knew what I was doing. Buddy is a dog's name, or a name that someone's going to use on you if they're being false-friendly. Your name is Bud, period."

I like the quote a lot because people are always shortening my name, which really bothers me.  My own mother actually uses the same argument that Bud's mom uses.  The line shows that Bud's mother was very intentional about her actions and choices.  She further explains why she chose "Bud" and not "Buddy."  

"A bud is a flower-to-be. A flower-in-waiting. Waiting for just the right warmth and care to open up. It's a little fist of love waiting to unfold and be seen by the world. And that's you."

Chapter five also contains a line from Bud's mother that is symbolic throughout the entire book. 

"And Bud, I want you always to remember, no matter how bad things look to you, no matter how dark the night, when one door closes, don't worry, because another door opens."

At that point in Bud's life, he thought that she was talking about an actual door.  But during the rest of the story, Bud realizes that his mother was talking about metaphorical doors.  The doors that she was talking about were opportunity doors.  For example, when the Amos family was going to send Bud back to the orphanage, it gave him the opportunity to begin searching for his father. 

`int 3/(2sqrt(x)(1+x)) dx` Find the indefinite integral

For the given integral: `int 3/(2sqrt(x)(1+x)) dx` , we may apply the basic integration property: `int c*f(x) dx = c int f(x) dx` .

`int 3/(2sqrt(x)(1+x)) dx = 3/2int 1/(sqrt(x)(1+x)) dx` .

For the integral part, we apply u-substitution by letting:

`u = sqrt(x) `

We square both sides to get: `u^2 = x` .

Then apply implicit differentiation, we take the derivative on both sides with respect to x as:

`2u du =dx` .

Plug-in `dx= 2u du` , `u =sqrt(x) ` and` x= u^2` in the integral:

`3/2int 1/(sqrt(x)(1+x)) dx =3/2int 1/(u(1+u^2)) (2u du)`

Simplify by cancelling out u and 2 from top and bottom:

`3/2int 1/(u(1+u^2)) (2u du) =3 int 1/(1+u^2) du`

The integral part resembles the basic integration formula  for inverse tangent:

`int 1/(1+u^2) du = arctan (u) +C`

 then, 

`3 int 1/(1+u^2)  du = 3 * arctan(u) +C`

Express in terms x by plug-in  `u =sqrt(x)` :

`3 arctan(u) +C =3 arctan(sqrt(x)) +C`

Final answer:

`int 3/(2sqrt(x)(1+x)) dx = 3arctan(sqrt(x))+C`

How does Juliet respond to two obstacles she faced in Romeo and Juliet?

Juliet does not really take no for an answer. The first obstacle she faces is that she falls in love with a man who is forbidden to her. Romeo is a Montague, which means he is the sworn enemy of the Capulets. Juliet responds by deciding that his name is not that important:

What's in a name? that which we call a rose
By any other name would smell as sweet;
So Romeo would, were he not Romeo call'd,
Retain that dear perfection which he owes
Without that title. Romeo, doff thy name,
And for that name which is no part of thee
Take all myself (Act II, Scene 2).

Romeo is in love with her, too, and does not care what her name is or if her family will hate him. They decide to marry in secret. Juliet loves Romeo, and she thinks that is all that matters.

Juliet’s second big challenge is when Romeo kills Tybalt and is banished. 

That villain cousin would have kill'd my husband:
Back, foolish tears, back to your native spring;
Your tributary drops belong to woe,
Which you, mistaking, offer up to joy.
My husband lives, that Tybalt would have slain;
And Tybalt's dead, that would have slain my husband (Act III, Scene 2).

Romeo is exiled, and the situation is even worse because her father decides to marry her off to Paris. Juliet is already married, her husband is banished, and she is supposed to marry someone else.

Again, Juliet does not just accept her situation. She goes to Friar Laurence and asks for help. He agrees to give her a potion to fake her death. Although she is nervous about being alive in a tomb, she agrees.

Things do not end well for Juliet. She wakes to find her husband dead. Romeo did not get the letter telling him what was going on. He found Juliet in her tomb, thought she was dead, and drank poison. Juliet is so devastated to find him deceased that she takes his dagger and kills herself. This again solves her problem, though tragically.