Why does Beatty believe that sports are good for society?

Captain Beatty supports government censorship and is vehemently opposed to literature, preserving knowledge, and engaging in intellectual pursuits. Beatty is in favor of any type of entertainment that distracts the citizens and prevents them from exercising their minds or analyzing their superficial society. Therefore, Captain Beatty is a proponent of sports because they are a form of mindless entertainment that amuses the vast majority of the population. In Bradbury's dystopian society, sports have become an outlet for citizens to exert their pent-up energy in a harmless way that poses no threat to the government or upsets the majority of the population. The citizens are particularly attracted to violent sports, which is something Beatty also supports. Overall, Beatty is a proponent of virtually any form of mindless entertainment that allows the population to remain passive and ignorant. Similar to interactive televisions and psychological medications, sports distract the population from recognizing and analyzing society's ills.

Beatty believes that sports are good for society because sports, like cartoons and pictures, reduce the need for the mind to work and to learn. Books are dangerous because they encourage thinking, and if the people in society are thinking, they may realize they are unhappy and want to do something about it.
Sports are straightforward and simple to understand. The point of sports is to give the participants and audience members an opportunity to be distracted; everyone can enjoy mindless entertainment and forget about their questions and problems. Also, it is the nature of sports to enjoy them in groups. As a result, the spirit of fun is contagious amongst a group of people, and this group experience minimizes opportunities for society members to be individuals and think independently for themselves.

Can you help me scan "The West Wind" by John Masefield?

Although the poem does seem to have an inconsistent number of syllables in each line, the scansion of its rhythms and meter are actually fairly consistent if you emphasize the appropriate words. Sometimes with a poem like this, you have to read it aloud to find the appropriate emphasis, as it does not just fall in line with the number of syllables. The emphasis in terms of scansion is on the words that create the image or meaning in each line. Modern poetry often does not conform precisely to these meters in the same way poetry from earlier centuries does.
If one considers Masefield may be paying homage to Percy Bysshe Shelley's poem "Ode to the West Wind," which is written in iambic pentameter, then we can see Masefield's poem may be scanned as if it is also in iambic pentameter.
In this way, we san see a reading of the first line of Masefield's poem should emphasize the words "warm," "west," "full," and "cries." This gives the poem an iambic meter and feeling and is appropriate to its structure.
https://poets.org/poem/ode-west-wind

How does Hamlet work to examine human behavior and psyche, and what role does Act V play in establishing this depth/connection? Why is Hamlet so often referred to as Shakespeare's (and literature's) greatest achievement and how is Act V the crowning moment?

Hamlet examines human behavior and the psyche in several different ways. One is by its portrayal of madness. Hamlet announces that he will feign madness, but his behavior, as well as several of his soliloquies, suggest that his madness may be authentic. He experiences bouts of melancholy, expresses uncontrollable rage, and generally behaves erratically throughout the play. The characters in the play are generally convinced that he is insane, and the audience is forced to contemplate the fine line between madness and sanity as part of the human condition as well as in the title character. Beyond this, we encounter in Hamlet a character wracked by self-doubt, a trait most people can identify with. At times he doubts himself capable of avenging his father's death and continues to stall throughout much of the play. He declines, for example, to kill Claudius when it would have been very easy to do so, citing the fact that his uncle is praying. His tortured relationship with his mother and with Ophelia (whose own decline into madness also suggests the frailty of the human psyche) show him to be a intensely conflicted character. Act V is in many ways the crowning achievement of the play, as the audience witnesses a resolution to the conflicts between Hamlet and Claudius, Hamlet and his father's ghost, and Hamlet and himself. The first scene of the act witnesses Ophelia's tragic death and Hamlet's extended and melancholy speech on mortality (occasioned by his discovery of Yorick's skull). The second scene closes the play with the death of Claudius and Hamlet, whose vacillations in seeking revenge give way to focus as he kills his uncle.

Why were freedmen not able to enjoy the freedom that they received as a result of the 13 amendment

 
The 13th Amendment to the United States Constitution states as follows:

Section 1. Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction.
Section 2. Congress shall have power to enforce this article by appropriate legislation.

By "freedmen," the generally understood meaning is former slaves who were under involuntary servitude (slavery) to slave masters in southern states where slavery was legal prior to the ratification of the 13th Amendment. Perhaps the most significant reason why many freedmen were unable to enjoy fully the freedoms provided under the 13th Amendment was the substantial efforts many (if not all) Democrat-controlled states in the South (the Confederate States) immediately undertook in a deep-seated effort to preserve a culture of racism.
As a direct response to the passage and ratification of the 13th Amendment across southern states, state and local jurisdictions in southern states enacted a series of racially-restrictive statutes, ordinances, and rulings (commonly referred to as "Black Codes"). For example, without the ability for now-former slave masters to lawfully secure labor at low or no cost through the mechanism of slavery, the assumption was that Black Codes permitted a way around the intent of the 13th Amendment while in principle not directly violating the 13th Amendment. Black Codes went far beyond merely creating barriers to reasonable wages and fair labor laws but also affected the ability of blacks to obtain and enjoy such rights as equal access to housing, a fair and speedy trial, the right to bear arms, the ability to attend public schools, and a host of other rights provided to non-black citizens of the United States.
State and local laws viewed as Black Codes, in many cases, were painstakingly-crafted not to be outright racist against blacks on their face. However, the application of such laws created a net effect that such laws were in fact racist in a way that unfairly, unjustly, and unconstitutionally violated the rights of blacks to access and benefit from equal rights and liberties as enumerated under the United States Constitution.
That said, many of the state and local laws passed following the ratification of the 13th Amendment outright prohibited blacks from enjoying equal rights. Many of these Black Codes were quickly challenged at the state and federal level as unconstitutional and subsequently repealed. However, many of these laws remained in full force and effect for a number of years to follow. Southern states also worked around the invalidation of Black Codes by coming up with a more insidious plan to preserve de jure segregation in most sectors of society. State and local laws (commonly referred to as "Jim Crow laws") enforcing racial segregation for the remainder of the 19th century until 1965 continued to restrict the civil rights and civil liberties of blacks, particularly in southern states where the bulk of Jim Crow laws existed.

Why was Putnam brought into the court?

Giles Corey storms into the courtroom at the beginning of act 3, insisting that "Thomas Putnam is reaching out for land!" Deputy Governor Danforth has Giles removed from court and questions him outside. When Danforth glances over Giles's deposition, he asks that Mr. Putnam—who is already in the courtroom—be brought in to this other room by Reverend Parris. When Putnam enters, Danforth says,

"Mr. Putnam, I have here an accusation by Mr. Corey against you. He states that you coldly prompted your daughter to cry witchery upon George Jacobs that is now in jail."

Putnam, of course, denies this charge. As Giles points out, if Jacobs is convicted of witchcraft, then his land goes up for public auction, and, he says, "there is none but Putnam with the coin to buy so great a piece." Giles believes that Putnam prompted his daughter, Ruth, to accuse George Jacobs so that his land would become available and Putnam would then be able to purchase it legally. Putnam is essentially asked to address this charge, and all he has to say is that it is untrue. At this point, the magistrates begin to question Giles as to the identity of his supposed informant. However, because Giles knows that this man will be arrested and likely found guilty of wrongdoing himself, he will not give the name. Eventually, Danforth holds him in contempt of court for his refusal to do so.

Mr. and Mrs. Putnam are two of the main characters perpetuating witchcraft hysteria throughout the community. They are both deeply involved in the witch trials, and Giles Corey mentions that Thomas Putnam is reaching out for land at the beginning of act 3. Deputy Governor Danforth calls into the court to speak with Thomas Putnam, who is more than likely watching the witch trials with the rest of the community. Deputy Governor Danforth then tells Thomas Putnam that Giles Corey has a deposition from a respected community member who claims to have heard Putnam telling his daughter to accuse George Jacobs of witchcraft. According to Salem's laws, if any citizen admits to being involved in witchcraft, their land automatically goes up for sale. Because Thomas Putnam is the only citizen with enough money to purchase extensive plots of land, he uses his daughter to accuse innocent citizens of witchcraft so that he can acquire more land. However, Thomas Putnam denies Giles Corey's claim, and Giles is arrested after refusing to name the citizen who said he overheard Thomas Putnam speaking to his daughter. 

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 42

Determine the $\displaystyle \lim_{x \to 0^+} \sin x \ln x$. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.
$\displaystyle \lim_{x \to 0^+} \sin x \ln x = \lim_{x \to 0^+} \frac{\ln x}{\csc x} $


By applying L'Hospital's Rule...

$
\begin{equation}
\begin{aligned}
\lim_{x \to 0^+} \frac{\ln x}{\csc x} &= \lim_{x \to 0^+} \frac{\frac{1}{x}}{-\csc x \cot x} \\
\\
&= \lim_{x \to 0^+} \frac{\left( \frac{1}{x} \right)}{-\frac{1}{\sin x} \left( \frac{\cos x}{\sin x} \right)}\\
\\
&= \lim_{x \to 0^+} \frac{- \sin^2 x}{x \cos x}
\end{aligned}
\end{equation}
$


We can rewrite the limit as...

$
\begin{equation}
\begin{aligned}
\lim_{x \to 0^+} \frac{-\sin^2x}{x \cos x} &= - \lim_{x \to 0^+} \left( \frac{\sin x}{x} \cdot \frac{\sin x}{\cos x} \right)\\
\\
&= - \left[ \lim_{x \to 0^+} \frac{\sin x}{x} \cdot \lim_{x \to 0^+} \tan x \right]\\
\\
\text{Recall that } \lim_{x \to 0^+} \frac{\sin x}{x} &= 1 \text{ ,so...}\\
\\
&= - \left[1 \cdot \lim_{x \to 0^+} \tan x \right]\\
\\
&= -[1 \cdot 0]\\
\\
&= 0
\end{aligned}
\end{equation}
$

Describe the first plan that Faber and Montag come up with.

When Montag initially visits Faber's home, he suggests that they get a printing press and begin making copies of illegal books to distribute throughout society. Faber immediately tells Montag that he would not be interested in the plan and suggests that he might participate in a plan that would destroy the fireman structure from the inside. Faber then suggests that they could possibly make copies of books and plant the illegal novels inside firemen's homes, which would sow seeds of suspicion throughout the organization. After describing his plan, Faber immediately retracts his statement and mentions that his plan would be far from a guarantee. Before Faber can dismiss Montag, Montag grabs his attention by ripping pages out of the Bible. Faber then agrees to help Montag and gives him a two-way communication device known as the green bullet.