How do I make the best introduction for a scholarship essay?

Scholarship essays are a great challenge to write. Because you may be competing with hundreds or even thousands of other applicants, the first sentence and first paragraph of your essay are extremely important.
Of course, this is not to limit the significance of the rest of your essay; however, the first sentence and first paragraph are the initial part of your essay the reviewer or admissions officer will read. One of the best ways to distinguish yourself from other people is to tell a story (in the first paragraph) or use an anecdote that leads in to the rest of your essay. If you can make it unusual and relevant at the same time, you will likely catch the attention of the reviewer.
Consider this: when you open the pages of a thriller or murder mystery, what will you likely read in the first sentence? It's usually something attention-grabbing, isn't it? Let's take a look at the first sentence of Catherine Coulter's FBI thriller, Whiplash:

Erin used her third-generation lock picks. She knew each one intimately, having successfully, and in excellent time, learned to unlock by the age of six and a half whatever her father hid under her pillow.

Okay, that's two sentences, but I bet you read the second one, too, didn't you? The first sentence is attention-grabbing. Erin is using her third-generation lock pick, but why? Is she from a family of professional thieves? The first sentence or two makes us want to read a little more. Erin knows her lock pick "intimately." That's a very descriptive word, conjuring up any number of fascinating images in our mind about Erin, and this is just the first paragraph. Remember reviewers have to read through stacks of essays. It is a tedious task, at best, so you will want to make their job as enjoyable as possible when it comes to reading yours.
Since scholarship essays and essays to Ivy League colleges are challenging ones to write, I would like to share two links with you. In the first link, you can read the essay of a high-school senior who was accepted to Stanford and five Ivy League colleges. The second link allows you to read admission officers' comments on her essay. It's quite illuminating!
https://www.businessinsider.com/5-former-ivy-league-admissions-officers-talk-about-college-admissions-essays-2016-4

https://www.businessinsider.com/high-school-senior-who-got-into-5-ivy-league-schools-shares-her-admissions-essay-2016-4

How did eliezer lose his gold tooth

In a concentration camp, just about anything can become a highly-prized item. The only law is the law of the jungle. Everyone has to do whatever they can to survive, and if someone has anything of value, then they must be prepared to protect it at all costs. In such an unmitigated hellhole, where human life is cheap, a gold tooth such as Eliezer's is almost priceless. Indeed, a dentist at the camp ends up being hanged for dealing in gold teeth, so it's just a matter of time before Eliezer's tooth attracts attention.
And so it does. Franek, the brutal prison foreman, notices Eliezer's gold tooth and immediately demands it. Eliezer refuses, so Franek beats up Eliezer's father until he finally relents. Franek then gets a dentist to pry it out with a rusty spoon. A gold tooth may be priceless in a concentration camp, but Eliezer knows that the life of his father is so much more valuable.

y = log_3(x) , (27,3) Find an equation of the tangent line to the graph of the function at the given point

y=log_3(x)
The line is tangent to the graph of the function at (27,3). The equation of the tangent line is _____.
To solve, the slope of the tangent line should be determined. Take note that the slope of a tangent line is equal to the value of the derivative at the point of tangency.
To determine the derivative of the function, apply the formula d/dx[log_a(u)]=1/(ln(a)*u)*(du)/dx.
(dy)/dx = d/dx[log_3 (x)]
(dy)/dx =1/(ln(3)*x) * d/(dx)(x)
(dy)/dx =1/(ln(3)*x)*1
(dy)/dx = 1/(xln(3))
The point of tangency is (27,3). So plug-in x = 27 to the derivative to get the slope of the tangent.
m=(dy)/dx = 1/(27ln(3))
Hence, the line that is tangent to the graph of the function at point (27,3) has a slope of m = 1/(27ln(3)) .
To get the equation of the line, apply the point-slope form.
y-y_1=m(x - x_1)
Plugging in the values of m, x1 and y1, it becomes:
y - 3= 1/(27ln(3))(x - 27)
y-3=1/(27ln(3))*x - 27 * 1/(27ln(3))
y - 3 =x/(27ln(3)) - 1/ln(3)
y =x/(27ln(3)) - 1/ln(3)+3
 
Therefore, the equation of the tangent line is y =x/(27ln(3)) - 1/ln(3)+3 .

In Of Mice and Men what was bunkhouse culture like in regards to women?

The bunkhouse is a dusty, rectangular building without amenities, where the workers sleep and spend the majority of their downtime on the ranch. The bunkhouse is described as having plain whitewashed walls and an unpainted floor with eight bunks inside. Above each bunk is an open apple box, where the men keep their small personal belongings. There is also a square table in the middle of the bunkhouse, where the men play cards. The bunkhouse is strictly designed to accommodate hardworking men, who do not mind living in a rough environment. There are no decorations or amenities which could be described as being convenient or pleasant to women, and the culture inside the bunkhouse is void of a woman's touch. Only men reside in the bunkhouse, and Curley's wife occasionally peeks her head inside to look for her husband. There is a general absence of female culture on the ranch, which further emphasizes Curley's wife's loneliness. There is essentially no place on the ranch where she is welcome, and Curley would lose his temper if she were to spend time with the male workers in the bunkhouse. Overall, the bunkhouse is void of any trace of female culture and is strictly a place where men reside.

What are the positive effects of FDR's New Deal?

The New Deal was a series of legislation passed beginning at the height of the Great Depression, in order to provide relief for the poor and stimulate the economy. The Great Depression began in 1929, largely as a result of the stock market crash, and by 1932, approximately one-quarter of the workforce was unemployed. During that year, President Hoover preached patience to the citizens. In stark contrast, when Americans were demoralized and devastated, a new president offered hope to the country. President Roosevelt took office in 1933. On March 4, 1933, he delivered his inaugural speech in which he stated, "the only thing we have to fear is fear itself."
Most of the legislation that came to be included as part of the New Deal was passed under President Roosevelt. One of his first plans was to stabilize banks. The American people lost faith in banks and were withdrawing their money. Roosevelt's Emergency Banking Act was passed, and, as a result, people began putting their money back into banks. The passage of the Tennessee Valley Authority Act was another step taken by Roosevelt that reaped positive benefits. Results were the creation of jobs for the building of dams and more widespread availability of electricity.
President Roosevelt's first 100 days in office saw the passage of other acts aimed at offering relief and assistance. However, more was needed. In 1935, he responded with what was called the Second New Deal. The Works Progress Administration and the Social Security Act are two examples of additional steps taken.
President Roosevelt's numerous plans provided positive benefits to the American people. Unemployment rates dropped, jobs were created to build roads, hospitals, and dams, and Americans experienced a restored confidence in the economy. Roosevelt's "fireside chats" provided people with a piece of mind. The Democratic party also received long-lasting popularity because of his actions. While his legislation had critics who complained of too much government or that not enough action was taken to help minorities, Roosevelt's New Deal assisted in helping America get back on its feet.
http://www.loc.gov/teachers/classroommaterials/presentationsandactivities/presentations/timeline/depwwii/newdeal/

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 26

Determine all rational zeros of the polynomial $P(x) = x^4 - 2x^3 - 3x^2 + 8x - 4$, and write the polynomial in factored form.

The leading coefficient of $P$ is $1$, so all the rational zeros are integers:

They are divisors of the constant term $-4$. Thus, the possible candidates are

$\pm 1, \pm 2, \pm 4$

Using Synthetic Division







We find that $1$ is a zero and that $P$ factors as

$x^4 - 2x^3 - 3x^2 + 8x - 4 = (x - 1)(x^3 - x^2 - 4x + 4)$

We now factor the quotient $x^3 - x^2 - 4x + 4$. Its possible zeros are the divisors of $4$, namely

$\pm 1, \pm 2, \pm 4$

Using Synthetic Division







We find that $1, 2$ and $-2$ are zeros and that $P$ factors as

$x^4 - 2x^3 - 3x^2 + 8x - 4 = (x - 1)(x - 1)(x - 2)(x + 2)$

The zeros of $P$ are $1, 2$ and $-2$.

Based on “Rogue Agencies Gut State Banking Laws” and the decision in Bank of America v. City and County of San Francisco, et al., please discuss the tension between state and federal laws. How has the concept of "preemption" affected banking laws since the 1990s? http://www.ilsr.org/rogue-agencies-gut-state-banking-laws/ http://caselaw.findlaw.com/us-9th-circuit/1343285.html

The article "Rogue Agencies Gut State Banking Laws" discusses how federal agencies, such as the Comptroller of Currency and the Office of Thrift Supervision, undermine state laws designed to protect consumers in the banking industry. Both of these agencies are staffed through presidential appointments rather than elections. As a result, the voting public has no say in who is chosen to head these agencies, despite the fact that they have a significant impact on consumer rights. The author of the article places this issue in the context of the tension between state and federal laws through the concept of preemption. State laws designed to prevent banks from reducing market competition have been preempted by these federal agencies, exercising national authority that conflicts with state-level policies.
In the Bank of America v. City and County of San Francisco, et al. case, the issue of state and federal laws is addressed practically. The counties of Santa Monica and San Francisco prohibited financial institutions from charging fees to non-depositors to use their ATMs. These ordinances allowed consumers to sue for actual damages if they were charged a fee for using an ATM anyway. The cities also claimed that such fees reduce competition among local banks. In turn, the banks argued that the fees allowed them to maintain ATMS without suffering a net loss. Without ATM fees for non-depositors, the banks claimed they would lose up to $11,000 annually on each ATM they maintained. As a direct result of the ordinances, local banks stopped offering ATM services to consumers who did not bank with them and filed a complaint against the ordinances. This case demonstrates the ongoing struggle between federal and state laws. State laws are often designed to prevent consumers from being taken advantage of in local markets, while financial institutions and other organizations that operate across state lines typically argue that they are federally protected in certain business practices that allow them to compete in the national market. When discussing this issue, it is important to remember that the tension between state and federal laws often goes unresolved and must be determined on a case-by-case basis. 
https://ilsr.org/rogue-agencies-gut-state-banking-laws/