Why did people eat crushed emeralds during the plague?

Crushed emeralds was one of many remedies used to treat the bubonic plague.  For those who could afford this expensive remedy, emerald gemstones were ground up into a very fine powder using a mortar and pestle.  The powder would then be ingested by the ill patient.  Sometimes it was mixed with a liquid, and other times it was placed on the tongue and swallowed.  It could also be mixed with food.  Even though the powder was finely ground, it still had the texture of crushed glass.  This emerald powder, like most remedies, did nothing to cure the plague.

Those who became ill with the bubonic plague had few effective treatment options.  Little was known about medicine during the Black Death.  In desperation, many turned to remedies.  Remedies ranged from leeches to draining the buboes to drinking mercury.  Most of these remedies caused more harm to the patient's already weakened body.

How is the term "capital" defined?

Capital can sometimes be a difficult word to understand in the business world thanks to the fact that it is used in a couple of similar—but different—ways. 

Perhaps the most common definition of capital refers to the total number of assets that a business has at its disposal that will be able to help generate income for the organization. When referring to capital, a person may be mentioning physical assets—such as crops or appliances; however, they also may be speaking about financial assets, like those found in investments.

Others may speak about capital in ways in which they are referring to the money that a company has invested into the process of buying assets. In this instance, an organization might raise capital if they receive donations or other contributions.

How is satire used in "The Devil and Tom Walker"?

Satire is the use of hyperbole, irony, and humor to critique people, institutions, and even social norms. The purpose of satire is to alert people to crucial problems in society and to encourage specific changes.

In The Devil and Tom Walker, Washington Irving uses satire to criticize greedy moneylenders, shrewish women, hypocritical leaders, and biased historians.

Tom's wife is described as "a tall termagant, fierce of temper, loud of tongue, and strong of arm. Her voice was often heard in wordy warfare with her husband." In the 18th century, it was believed that shrewish women exhibited traits antithetical to those expected of a refined woman. When Tom shares the story of his encounter with Old Scratch, Tom's wife demands that he "comply with the black man's terms and secure what would make them wealthy for life." For her part, Tom's wife decides to take things into her own hands when her husband perversely refuses to comply with her demands.

She goes and meets with Old Scratch himself, taking with her "the silver teapot and spoons and every portable article of value." Washington Irving uses situational irony to critique the actions of an overbearing and shrewish wife; her actions reward her with the opposite of what she's hoped for. Instead of reaping great rewards from her efforts, she becomes the victim of Old Scratch and is "never heard of more."

The narrator tells us that "What was her real fate nobody knows, in consequence of so many pretending to know. It is one of those facts that have become confounded by a variety of historians." Here, Washington Irving is critiquing the problem of biased historians corrupting the truth about historical events. In the story, some say Tom's wife had "eloped with the household booty"; still others imagine that Old Scratch had decoyed her into a dismal quagmire." Meanwhile, there are those who support the theory that she had "lost her way among the tangled mazes of the swamp and sunk into some pit or slough." So, there's a variety of stories about the fate of Tom's wife, all suppositions engendered from the imaginations and biased perceptions of various parties.

In the story, Washington Irving also satirizes corrupt moneylenders and hypocritical leaders. Ministers and great men of the colony are portrayed as evil and untrustworthy men. Old Scratch pronounces judgment on these influential men, and they are burned up as firewood in the story: "Since the red men have been exterminated by you white savages, I amuse myself by presiding at the persecutions of quakers and anabaptists; I am the great patron and prompter of slave dealers, and the grand master of the Salem witches." Instead of God presiding over the judgment of these men, the author has the Devil do the honors, an irony.

Later, in the story, the author uses humor and hyperbole to highlight Tom Walker's hypocrisy. After enriching himself at the expense of his clients, Tom becomes religious because he's afraid for his chances in the afterlife: "He became, therefore, all of a sudden, a violent church goer. He prayed loudly and strenuously as if heaven were to be taken by force of lungs. Indeed, one might always tell when he had sinned most during the week, by the clamour of his Sunday devotion." Basically, Tom becomes religious, not for altruistic purposes, but so that he can cheat the Devil out of the bargain he's made with him.

As can be seen, the author uses satire as a sort of social commentary about life in New England in the 18th century.

`f(x) = |x + 2|, [-2, oo)` Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

We are asked to show that `f(x)=|x+2|,[-2,oo) ` has an inverse by showing that the function is monotonic on the interval using the derivative:

By definition, ` f(x)=|x+2|={[x+2,x+2 >=0],[-x-2,x+2<0]}`

x+2>0 ==> x>-2 which is the interval we wish so on the interval f(x)=x+2.

f'(x)=1 which is positive for all x in the interval so the function is monotonic (strictly increasing) on the interval. Thus the function has an inverse.

The graph:

How does the past Oceania differ from the present Oceania in 1984?

In 1984, it is very difficult to compare the past Oceania with the present. While we can state that there were no telescreens or ministries, for instance, it is almost impossible to make any other comparisons because the Party has rewritten the official history in a way which glorifies Big Brother and the revolution which brought him to power. Here's one example from a history book which Winston reads in Part One, Chapter Seven:

"In the old days (it ran), before the glorious Revolution, London was not the beautiful city that we know today. It was a dark, dirty, miserable place where hardly anybody had enough to eat and where hundreds and thousands of poor people had no boots on their feet and not even a roof to sleep under."

Winston tries to confirm this view by speaking to an old man in the Prole district but he soon realises that he is wasting his time since the old man remembers nothing of any real importance. Moreover, to exacerbate the problem, Winston's own memories of the past Oceania are distorted and fragmentary. In one flashback, for instance, he remembers spending the night in a tube station because of an air raid. In another, he remembers the last time that he saw his mother.

By making it impossible to obtain accurate information about the past, the Party demonstrates that it is powerful enough to rewrite history while also controlling the present and the future.

The normalized wave function for a hydrogen atom in the 1s state is given by `psi(r)=1/(sqrt(sqrt(pi) alpha0))*e^(-r/(alpha0))` where a0 is the...

(Note: This problem has been edited from its original version, to correct an obvious error in the units of measurement and the normalization of the wavefunction that made it unsolvable.)

We are given this wavefunction:

`psi(r) = 1/sqrt(alpha_0 sqrt(pi)) e^{-r/alpha_0}`

The probability density of finding the atom at a given point is given by the absolute square of the wavefunction at that point:

`p(r) = abs(psi(r))^2 = 1/(sqrt(pi) alpha_0) e^{-r^2/alpha_0^2}`

Normally, to get the overall probability of it being at or further than a particular point x, we would integrate that probability density from x to infinity:
` P(x gt= r) = int_{x}^{infty} p(r) dr = int_{x}^{infty} 1/(sqrt(pi) alpha_0) e^{-r^2/alpha_0^2}`
But in this case, that integral is not possible to solve exactly. Fortunately, there's a trick we can use. We can recognize that it is in fact a Gaussian function (also called a normal distribution or bell curve).
` N(mu, sigma) = 1/(sigma sqrt(2 pi)) e^{-(x-mu)^2/(2 sigma^2)}`

`mu = 0` is fairly easy to see. But what about `sigma` ?

We want `sigma sqrt(2pi) = sqrt(pi) alpha_0` , so` sigma = alpha/sqrt(2)`

That had better work in the other part of the equation, and indeed it does:

`1/(2 sigma^2) = 1/alpha_0^2`

From here, we can just look up the result in a table, because Gaussian functions have well-documented numerical solutions written in statistical tables. To be 3.9 a0 from the origin, we need to be 5.5 standard deviations from zero. The probability of that can be read off the table, as 2*10^-8.

What do you think of the fashion industry's approach to target young consumers at Fashion Week? Should designers be creating brands aimed at this...

Fashion Week (which is held London, Paris, Milan, and New York) and fashion labels target young consumers in several ways. First, Fashion Week uses social media, including Instagram, to capture images of the models on the runways. They also feature photos of the models behind the scenes, and they make the life of a fashion model seem glamorous and festive, like a party teens would want to attend. Fashion labels like Prada use celebrities, such as Kim Kardashian, to pose for ads. In these ads, Kardashian appeared semi-nude or nude and in very suggestive poses. By targeting teenagers, Fashion Week and fashion labels suggest teens are ready for the suggestive clothing and adult lifestyle they are marketing. They are marketing a lifestyle that is based on expensive, revealing clothing that many would argue is more appropriate for adults who have the money and discretion to choose what they want to wear. While fashion labels are trying to cultivate teenage followers so these young consumers will be faithful to their brand in the coming years, I believe what they are doing is not in the best interest of teenagers.