What did Thomas Jefferson say that leads us to believe he thought very highly of John Locke?

Well for one thing, some of Jefferson's writings are so closely paraphrased from John Locke it borders on plagiarism. Indeed, the two documents are so similar that it's not hard to imagine Jefferson looking over his annotated copy of "Two Treatises of Government" as he drafted the Declaration of Independence.

Where Locke said we had "insuperable rights" of "life, liberty and property", Jefferson said we had "inalienable rights" of "life, liberty, and the pursuit of happiness".

Locke also appears to have been the source of many of Jefferson's core principles, such as "consent of the governed" and the role of revolutions as a last resort---but a necessary option to have---against tyranny.

Oddly, Jefferson did not actually speak or write about Locke specifically all that often, but he seemed to deeply internalize most of Locke's ideas on political philosophy. It could be what is called "the anxiety of influence"; perhaps Jefferson knew that he was so influenced by Locke that if he talked about Locke too much people would think he had no new ideas of his own!

What role did African slavery play in the development of north and South America and the Caribbean in the sixteenth and seventeenth centuries?

The want and need for slave labor to work sugar cane, cotton, and tobacco plantations prevalent in the Americas set up the Triangular Trade route in the 16th and 17th centuries. From England, Spain, and other countries like Portugal, slave traders would make the voyage to Africa to pick up slaves as the first leg of the route. The second leg of the trade route started in Africa with the capturing and enslavement of Africans where they were taken onboard ships and transferred to islands in the Caribbean and to countries in South America.  This is historically called the Middle Passage in the trade route.  From there, slaves were sold and forced to work in sugar cane plantations (and later cotton plantations) to make rum and other goods to be shipped to England and other European countries (the 3rd leg of the Triangular Trade route).

As slave trade continued in the 1600’s, it wasn’t long before the demand for slave labor included the newly settled North American continent.  Tobacco and cotton soon became the “cash crops” that demanded slaves to cultivate them. Unable to enslave Native Americans, the United States quickly turned to the slave trade to fill its plantations with free labor.  The majority of slaves brought to the United States originated from the Caribbean Islands and the Middle Passage in the Triangular Trade route. 

The slave trade developed many countries of today into the economical powers they are.  The statement that many countries were built on the backs of slaves rings true.  

`y = root(3)(x), y = 0, x = 1` Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given...

The shell has the radius `x` , the cricumference is `2pi*x ` and the height is `root(3)(x)` , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

`V = 2pi*int_(x_1)^(x_2) x*(6x - 3x^2) dx`

You need to evaluate the endpoints `x_1` and `x_2` , such that:

`root(3) x = 0 => x = 0^3 =>x = 0`

`V = 2pi*int_0^1 x*(root(3) x) dx`

`V = 2pi*(int_0^1 x^(1/3) dx`

Using the formula `int x^n dx = (x^(n+1))/(n+1)` yields:

`V = 2pi*(3/4)*(x^(4/3))|_0^1`

`V = (3pi/2)*(1^(4/3) - 0^(4/3))`

`V = (3pi)/2`

Hence, evaluating the volume, using the method of cylindrical shells, yields `V = (3pi)/2.`

Why did Numa initially turn down the kingship of Rome?

According to Plutarch's The Life of Numa, after the death of Romulus (the first king of Rome), the feuding supporters of Romulus and Tatius eventually agreed to crown Numa king.

However, Numa initially turned down the offer of kingship for a few reasons:

1) He was happy living a quiet life.

2) He was greatly devoted to academic pursuits.

3) He appreciated a peaceful existence, one in which his acquaintances came together to worship deity or to engage in friendly conversation.

4) He reasoned that the people were much accustomed to having a war-like king, such as Romulus was. He argued that he would have a hard time living up to Romulus' strong reputation for war and conquest. Additionally, he felt that he would become a laughing-stock among his subjects if he were to preach against the violence and war that has accorded Rome all its manifest power.

5) He asserted that the fortunes of a king seem to be predicated on the political winds of change. Numa gives the example of Romulus, who was accused of plotting against his colleague, Tatius, king of the Sabines. Yet, Romulus was greatly believed to be a 'child of the gods.' Indeed, Numa believed a king's position and power to be tenuous at best.

Moreover, the very traits in my disposition which are to be commended, are far from marking a man destined to be a king, namely, my great love of retirement, my devotion to studies inconsistent with the usual activities of men, and my well-known strong and inveterate love of peace, of unwarlike occupations...

Besides, the people has become much accustomed to war, and eager for it because of their successes, and no one is blind to their desire for growth by conquest. I should therefore become a laughing-stock if I sought to serve the gods, and taught men to honour justice and hate violence and war, in a city which desires a leader of its armies rather than a king.

In The Boy in the Striped Pajamas, how is Bruno's father presented and what is his personality like?

Bruno's father is depicted as a proud Nazi, who is determined to climb the ranks in the German Army. He makes significant sacrifices, like moving his family from Berlin to Auschwitz because of his job. Bruno describes his father a strict man who has many rules. If Bruno breaks these rules, he must endure a "serious talking to." Bruno's father treats the maids and housekeepers with contempt. The other soldiers at Auschwitz look up to Bruno's father and are continually trying to find favor with him. He is rather controversial throughout the novel and is always fighting with his wife and arguing with his mother. Although he is proud of his position as Commandant and all of his military accomplishments, he is scared to say "no" to Hitler, which is why he moves his family to Auschwitz. He is stressed out most of the time and even finds out his wife has been cheating on him. He struggles with his personal life and loses his mind after Bruno disappears. Bruno's father is a tragic character throughout the novel The Boy in The Striped Pajamas.

How old was Frost when he made his momentous decisions?

It is generally agreed that Frost (speaker of the poem) is a young man when he chooses one of the two roads. The final stanza makes this clear: 

I shall be telling this with a sigh 

Somewhere ages and ages hence: 

Two roads diverged in a wood, and I— 

I took the one less traveled by, 

And that has made all the difference. 

He says that he will be retelling the story of his choice years later. So, he is attempting to foresee how he will view his choice as an older man. It is not overtly clear exactly how old he is when he chooses this path. But considering that this idea of choosing a path is metaphoric, it could refer to any significant life choice at any time during his life. Since he is contemplating how his older self will judge his choice, we might suppose that he chooses during his twenties or thirties, a time when many people make significant life choices such as careers, marriage, and children. 

Note that in that final stanza, he says he will be telling the story of his choice "with a sigh." This is the key to the poem. The two roads looked the same: "the passing there / Had worn them really about the same." The "sigh" indicates that he might regret his choice and just pretend that he took the less traveled road. In other words, he hopes he will have taken the road less traveled. He can not know for sure at the time because both roads look "about the same." 

What were the similarities between World War I and World War II?

There were many similarities between World War I and World War II. One similarity was the causes of both of these wars. In both wars, imperialism was a factor. In both wars, countries that had no or few colonies wanted to get control of more land. Another similarity was nationalism. In both wars, countries believed that they were supreme and that their way of life should be spread to other areas. A third cause was militarism. In both wars, countries were building up their military forces before going to war.

There are a few other similarities in both world wars. In both wars, the United States was neutral when the conflicts began. We eventually joined the Allies in both world wars. The United States was very influential in helping the Allies win in both wars. We provided many supplies to the Allies in each conflict. The people in the United States made many sacrifices to help our military be successful in both conflicts. People limited their consumption of food and bought victory bonds. The government also assumed more control over our economy in both conflicts.