Sunday, 17 August 2014

`int (x^2 - x^-2) dx` Find the general indefinite integral.

You need to evaluate the indefinite integral, such that:


`int f(x)dx = F(x) + c`


`int (x^2 - x^(-2))dx = int (x^2)dx - int x^(-2) dx `


Evaluating each definite integral, using the formula `int x^n dx = (x^(n+1))/(n+1) + c` , yields:


`int (x^2)dx= (x^3)/3 + c`


`int x^(-2) dx = (x^(-2+1))/(-2+1) + c = -1/x + c`


Gathering the results, yields:


`int (x^2 - x^(-2))dx = (x^3)/3 - (-1/x) + c = (x^3)/3...

You need to evaluate the indefinite integral, such that:


`int f(x)dx = F(x) + c`


`int (x^2 - x^(-2))dx = int (x^2)dx - int x^(-2) dx `


Evaluating each definite integral, using the formula `int x^n dx = (x^(n+1))/(n+1) + c` , yields:


`int (x^2)dx= (x^3)/3 + c`


`int x^(-2) dx = (x^(-2+1))/(-2+1) + c = -1/x + c`


Gathering the results, yields:


`int (x^2 - x^(-2))dx = (x^3)/3 - (-1/x) + c = (x^3)/3 + 1/x + c`


Hence, evaluating the indefinite integral yields `int (x^2 - x^(-2))dx = (x^3)/3 + 1/x + c.`

How did New Jersey's geography and population influence the outcome of events in the Revolutionary War?

New Jersey's geography and population were definite factors that influenced the outcome of events in the Revolutionary War.

In late August, 1776, the Continental Army suffered immense casualties after the Brooklyn Battle. Washington ordered his soldiers to retreat to Fort Lee, but the men did not linger at the fort. Instead, Washington led his men on a retreat march across New Jersey. The group of exhausted soldiers rested for two days in Hackensack, where foraging parties were able to amass abundant supplies from the surrounding countryside. The food refreshed the weary soldiers, and the short reprieve allowed Washington to make important logistical decisions.


The New Jersey population in the countryside was not especially supportive of Washington's troops, as many were Loyalists. These supporters of the English monarchy viewed Washington's bedraggled soldiers with a sense of inevitability; they believed that the war would end soon, with the British and Hessians as the victors. Washington made the decision to press on, ordering his sickest soldiers to march northwest to Morristown. The rest of the army marched south towards Brunswick, Trenton, and Princeton to join up with other militia members there. The author reports that the roads going south were "intolerable" and that the men suffered on the long trek. 


By the time the retreating soldiers arrived in Brunswick on November 29, 1776, there were only 3,000 men in the ranks. Many had already deserted the revolutionary cause along the way. So, New Jersey's unforgiving terrain and its largely Loyalist population led to mass desertions from Washington's army. Meanwhile, British forces pursued the Continental Army across New Jersey, and the cities of Trenton and Princeton hosted the English in large numbers. In these towns, British soldiers arrested Whigs loyal to the rebels and appropriated their farms and properties for their own use. Additionally, there was a large Tory presence in Monmouth county willing to sacrifice life and limb for the English king. 


Although much of the population in New Jersey consisted of Loyalists, there were some surprising holdouts. Many African-American slaves fought in support of the patriots. Additionally, some Quakers rejected their community's neutral stance and took up arms alongside the rebels. Meanwhile, some merchants and manufacturers chose to supply both sides of the conflict with ammunition, arms, and provisions. 


Despite the challenges, Washington decided to take Trenton and Princeton. He knew that Trenton itself had no walls or fortifications, a weakness that he could exploit. So, under cover of night, Washington and his men set sail across the icy Delaware River to ambush the Hessians and English soldiers stationed in Trenton. The river was unforgiving; the men had to cut their way through flat cakes of whirling flow-ice. Despite the treacherous river terrain, Washington managed to cross the river with his army largely intact.


So, New Jersey's geography and population greatly influenced how Washington fought the Revolutionary War. It is true that icy rivers, bad country roads, cold weather, and Loyalists made things more difficult for Washington and his men. However, the general was able to use these challenges to his advantage. For example, his bold decision to cross the icy Delaware River gave him the element of surprise he needed. Neither the British nor the Hessians expected such a maneuver in the thick of winter. Also, Washington found some surprising allies within the New Jersey population: African-American slaves, Quakers, and sympathetic businessmen who supplied the Continental Army with provisions, arms, and ammunition.

What are a few important central values of early Greek society which are expressed in the Homeric epics?

The first set of values one finds in these epics are heroic ones. In heroic culture, aristocrats are expected to demonstrate physical prowess in individual combat. Displaying certain types of courage is more important than winning. For example, killing an enemy by shooting him in the back is dishonorable, while losing a sword fight while displaying steadfast bravery is honorable.


The Homeric culture is one described as a "shame" rather than a "guilt" culture. In...

The first set of values one finds in these epics are heroic ones. In heroic culture, aristocrats are expected to demonstrate physical prowess in individual combat. Displaying certain types of courage is more important than winning. For example, killing an enemy by shooting him in the back is dishonorable, while losing a sword fight while displaying steadfast bravery is honorable.


The Homeric culture is one described as a "shame" rather than a "guilt" culture. In other words, reputation (Greek: kleos) is enormously important. The acts of an individual bring shame or honor to the entire family. Thus Menelaus' insistence on retrieving Helen or Achilles' anger over the distribution of war prizes has as much to do with honor or saving face as actual desire for the women.


Hospitality and the bonds of guest-friendship are extremely important. One can see this in the Iliad when Diomedes and Glaucus realize that they are linked by bonds of guest friendship and thus cannot fight each other. Polyphemus in the Odyssey, on the other hand, is considered extremely evil due to his violation of the code of guest-friendship. 


Saturday, 16 August 2014

Why is acid rain unevenly distributed across the world?

Acid rain is unevenly distributed around the world, and even across some countries, because this weather pattern is highly dependent upon environmental conditions. 


As an overriding factor, parts of the world where rain generally does not fall (such as deserts or the poles) are not likely to experience acid rain. More importantly, acid rain is a result of the environmental concentration of sulfur dioxide and nitrogen oxide. When these emissions are circulating in the air,...

Acid rain is unevenly distributed around the world, and even across some countries, because this weather pattern is highly dependent upon environmental conditions. 


As an overriding factor, parts of the world where rain generally does not fall (such as deserts or the poles) are not likely to experience acid rain. More importantly, acid rain is a result of the environmental concentration of sulfur dioxide and nitrogen oxide. When these emissions are circulating in the air, they react with water and oxygen to create acids. Sulfur dioxide and nitrogen oxide do occur naturally as a result of, respectively, volcanic eruptions and lightning strikes. Human activity and industrialization produce relatively large amounts of these emissions and contribute to greater concentrations of these basic ingredients for acid rain. 


Most of these emissions released into the environment are the result of burning fossil fuels for energy. In areas where many cars burn gasoline or factories use fossil fuels, there are likely to be higher environmental concentrations of sulfur dioxide and nitrogen oxide. These emissions alone aren't necessarily enough to cause acid rain; there must also be sufficient humidity in the air. When acid rain does fall, it isn't always right on top of the people and machines who provided the ingredients. Winds may push acid rain clouds far away from their point of origin, causing trouble for people who may not have contributed to the formation of acid rain at all.

1.What is the Green New Deal? Would it be helpful/necessary today? Pick 2 Pillars to help explain your answer (research terms/policies you don't...

The Green New Deal follows from initiatives put into place after the Great Depression and during President Franklin D. Roosevelt’s administration. The initiatives were targeted at improving the nation’s economy by creating jobs, reforming the financial sector and restoring the economy to acceptable secure and stable levels. The Green New Deal by the Green Party of the United States is based on four key pillars that are aimed at economic and social reforms.


The Green...

The Green New Deal follows from initiatives put into place after the Great Depression and during President Franklin D. Roosevelt’s administration. The initiatives were targeted at improving the nation’s economy by creating jobs, reforming the financial sector and restoring the economy to acceptable secure and stable levels. The Green New Deal by the Green Party of the United States is based on four key pillars that are aimed at economic and social reforms.


The Green New Deal seeks to establish an Economic Bill of Rights to ensure that all citizens have access to employment and to protect their rights as workers and as property owners. The deal also seeks to support locally based green businesses through accessible financing and research into sustainable sources of energy. The deal’s financial initiative seeks to reform the sector by imposing more stringent regulation and controls on Wall Street. Socially, the Green New Deal aimed at instituting democratic reforms by protecting the people’s right to vote


The Green New Deal is still relevant and would be useful today based on its agenda to secure the economy and social well-being of all people living in the United States. The fourth pillar on establishing a functioning democracy brought up the issue of the Patriot Act that was enacted and enforced to deal with terrorism. Although it was a noble idea, the Act also posed a threat to individual privacy as evident in the Snowden scandal. Such initiatives without controls pose a major threat to democracy and individual rights. The third pillar on real financial reforms is also currently relevant due to the enhanced financial protection outlined in the agenda. The pillar addresses the issue of bailouts and “too big to fail” financial institutions that hold the financial sector ransom. The pillar also provides an opportunity for further financial practice regulations that would be necessary for addressing issues such as the recent Wells Fargo scandal. 

Would a Kantian think that having unpaid internships as part of students’ courses of study is morally permissible? Why or why not?

One could make arguments based on a Kantian deontological system of ethics either for or against internships, but the strongest are probably against internships due to their narrowly vocational nature. The main issue you will need to address for writing your paper about this is that Kant's system of ethics is rule-based rather than consequentialist. In other words, Kant would not, as this excerpt does, look at the outcomes of internships, but rather look at...

One could make arguments based on a Kantian deontological system of ethics either for or against internships, but the strongest are probably against internships due to their narrowly vocational nature. The main issue you will need to address for writing your paper about this is that Kant's system of ethics is rule-based rather than consequentialist. In other words, Kant would not, as this excerpt does, look at the outcomes of internships, but rather look at whether their existence was compatible with an ethical system based on rules and duty. 


Kant would begin by looking at the ultimate end of internships within the context of education. A good starting point would be to look at Kant's book on education. Kant believes that the central problem of education is how to develop moral character in a child without constraining moral freedom. Equally important is developing habits of discipline and especially self-discipline. Students, for Kant, should be educated with a view to the progress of humanity in the future, not for simply immediate or proximate goals. Rather than pandering to the desires of students and parents for narrow job training or easy and palatable edutainment, educators, according to Kant, should consider what is best for society as a whole. Thus for Kant, the sort of vocational training implied in internships (of any sort, paid or unpaid) distracts from the main purpose of education as moral and cultural formation to act as narrow vocational training; this would would be problematic. 


You could examine this in light of his notion of universalizing one's moral maxims. If everyone simply trained for immediate vocational goals, our civilization would have no people capable of complex political and ethical thought, and would lack artists, scientists, social activists, and others whose education needs to be broader and more global rather than narrower and more focused on specific jobs (which may well become obsolete in a few years due to technological change anyway). Education should be done by " enlightened experts" rather than outsourced to for-profit interests according to Kant. 

`int_0^(pi/4)(sec^2 (t))dt` Evaluate the integral.

`int_0^(pi/4) sec^2(t) dt`


Take note that the derivative of tangent is d/(d theta) tan (theta)= sec^2 (theta).


So taking the integral of sec^2(t) result to:


`= tan (t) |_0^(pi/4)`


Plug-in the limits of integral as follows `F(x)=int_a^b f(x) dx= F(b)-F(a)` .


`=tan (pi/4)-tan(0)`


`=1-0`


`=1`


Therefore,  `int_0^(pi/4) sec^2(t) dt = 1` .

`int_0^(pi/4) sec^2(t) dt`


Take note that the derivative of tangent is d/(d theta) tan (theta)= sec^2 (theta).


So taking the integral of sec^2(t) result to:


`= tan (t) |_0^(pi/4)`


Plug-in the limits of integral as follows `F(x)=int_a^b f(x) dx= F(b)-F(a)` .


`=tan (pi/4)-tan(0)`


`=1-0`


`=1`


Therefore,  `int_0^(pi/4) sec^2(t) dt = 1` .

In "By the Waters of Babylon," under the leadership of John, what do you think the Hill People will do with their society?

The best place to look for evidence in regards to what John's plans are for his people is the final paragraphs of the story. John has re...