Notes

There was unrest in the Thirteen Colonies for many years before the Revolutionary War.  New taxes, such as the Sugar Act and the Stamp Act, were considered unfair.  The Colonists were not represented in Parliament, and because of this they had no one to speak on their behalf.  The Townshend Revenue Act of 1967 taxed tea and other common commodities.  All of the taxes were eventually repealed except for the one on tea.  Protests in Boston led to British troops occupying the city.  The unrest continued, and led to the Boston Massacre. The Tea Act was made to benefit the East India Company, which was having financial difficulties.  They had an overstock of tea, which was to be sold cheaply in Boston.  Concern that this would have a negative impact on local merchants combined with the unrest led to the Boston Tea Party.  Tea from ships in the Boston Harbor were thrown into the water in protest.   Troops were quartered in private homes and buildings, which led to further dissatisfaction wit...

In the forest primeval, Young Goodman Brown suffers a fall from innocence that is not unlike that of Adam. When Brown ventures into the forest in order to test his faith, he loses this faith after witnessing the black mass and seeing his wife Faith there. As the pink ribbons of his once innocent wife "flutter lightly down through the air," Goodman cries, "My Faith is gone!" and he learns the terrible significance of this loss. Goodman Brown experiences such a dramatic change in his character because he is initially so confident in his faith. But, this faith is challenged as one by one the seemingly saintly members of his community demonstrate that they are in league with the devil. For instance, when Brown happens upon Goody Cloyse, who has taught him his catechism and who he recognizes as "a very pious and exemplary dame," he is surprised to see her in the forest. Then, he is shocked when this "pious old lady" notices the traveler "put fort...

`int1/(4+4x^2+x^4)dx` Let's rewrite the integrand as : `=int1/((x^2)^2+2(2)(x^2)+2^2)dx` `=int1/(x^2+2)^2dx` Apply integral substitution:`x=sqrt(2)tan(u),u=arctan(x/sqrt(2))` `dx=sqrt(2)sec^2(u)du` `=int(sqrt(2)sec^2(u))/((sqrt(2)tan(u))^2+2)^2du` `=int(sqrt(2)sec^2(u))/(2tan^2(u)+2)^2du` `=int(sqrt(2)sec^2(u))/(2^2(tan^2(u)+1)^2)du` Take the constant out, `=sqrt(2)/2^2int(sec^2(u))/(tan^2(u)+1)^2du` Use the identity:`1+tan^2(x)=sec^2(x)` `=sqrt(2)/4int(sec^2(u))/(sec^2(u))^2du` `=sqrt(2)/4int1/(sec^2(u))du` `=sqrt(2)/4intcos^2(u)du` Use the trigonometric identity:`cos^2(x)=(1+cos(2x))/2` `=sqrt(2)/4int1/2(1+cos(2u))du` Take the constant out, `=sqrt(2)/8int(1+cos(2u))du` Apply the sum rule, `=sqrt(2)/8{int1du+intcos(2u)du}` Apply the common integral:`intcos(x)dx=sin(x)` `=sqrt(2)/8{u+1/2sin(2u)}` Substitute back `u=arctan(x/sqrt(2))` `=sqrt(2)/8{arctan(x/sqrt(2))+1/2sin(2arctan(x/sqrt(2)))}` `=sqrt(2)/8{arctan(x/sqrt(2))+1/2(2sin(arctan(x/sqrt(2)))cos(arctan(x/sqrt(2))))}` `=sqrt(2...

Poe actually never has Montresor state the specific reasons behind his wanting revenge, though he hints at several possibilities. Although he does mention injuries and insults, he never reveals details. First, Montresor seems vindictive and almost paranoid. It could well be that the wrongs for which he is obtaining revenge never actually happened and are products of Montresor's imagination.  Another possibility is that Montresor comes from a wealthy family now on hard times. He may blame Fortunato for the change in his family's fortunes or may simply resent Fortunato for being a nouveau riche . Both men are wine connoisseurs and possibly merchants. There appears to be some rivalry concerning expertise in wines, or perhaps there was some sort of commercial rivalry in the past. Part of the point of of this vagueness is to convey the idea that the desire for vengeance has become so overwhelming that the original cause no longer matters; instead, the vengeance and its planning have...

The main problem confronting France in the late eighteenth century (at least as regards taxation) was that the first two estates--the clergy and the nobility, respectively--were not really taxed at all. The complex network of privileges that undergirded Bourbon society placed the tax burden most heavily on the Third Estate. This presented a major problem as the French Crown faced a severe fiscal crisis in the wake of its participation in the wars of the American Revolution. Louis XVI attempted, through his ministers, to secure at least moderate tax reforms, but the nobles, who had control of the French courts, blocked these measures. By the time Louis XVI called the Estates General to address the crisis, his kingdom was basically insolvent as a result of the unbalanced tax system. As to how this system affected the people of each of the orders, ordinary Frenchmen found the gabelle , a tax on salt, to be particularly odious. The bourgeoisie, a growing class of merchants and professional...

Human Papillomavirus, or HPV, is a common sexually transmitted disease. The infection caused by the virus is responsible for two illnesses: genital warts, and various types of cancer, including cervical cancer. There are over 120 strains of Human Papillomavirus. All of these strains are similar: they are all sexually transmitted and cause genital infection. Strains that cause genital warts but not cancer are considered low-risk, while strains that cause cervical cancer are considered high-risk. Certain strains are more likely to cause infections that lead to cervical cancer. The HPV strains linked to cervical cancer are HPV 16 and HPV 18. These two strains are responsible for 70% of cervical cancer caused by HPV infections. At this time, these two strains are the known HPV strains that cause cervical cancer, but medical research may reveal others in the future.

Despite using distances that are big, this question is using a basic equation.  Speed = Distance/Time.  That equation can be reordered to read Time = Distance/Speed.   The distance in this case is 34 astronomical units.  I'll leave it in that unit.  Converting to miles or kilometers will make these numbers huge.  The speed of light is 300,000,000 m/s.  It is going to work best to convert the speed of light into astronomical units per second.  That number is 0.00200399 AU/sec. We can now use the initial equation.   Time = Distance/Speed Time = 34 / 0.00200399 Time = 16966.1525257 seconds Let's round that to 16,966 seconds.  Divide by 60 to get minutes.   That's about 282.767 minutes.  Divide by 60 again to get hours.     That's roughly 4.713 hours. In hours, minutes, and seconds, that comes out to be 4 hours, 42 minutes, and 46 seconds.