Author: Anonymous

Find the area of the surface generated when the given curve is revolved about the x-axis.  y =   on  

Use a calculator to approximate the area of the surface generated when the given curve is revolved about the x-axis. Round to two decimal places when necessary.y = x8  on [0, 1]

Solve the problem.A cylindrical water tank has height 10 m and radius 2 m (see figure). If the tank is full of water, how much work is required to pump the water to the level of the top of the tank and out of the tank? Express the answer in terms of π. 

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines.y = 2x,y = x2; revolve about the y-axis

Write the integral that gives the surface area generated when the curve is revolved about the x-axis. Do not simplify.y = ln x4  on [1, ]

Find the volume of the described solid.The solid lies between planes perpendicular to the x-axis at  and . The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the parabola  to the parabola .

“The authors and promoters of this desperate conspiracy have…meant only to amuse, by vague expressions of attachment to the parent state, and the strongest protestations of loyalty to me, whilst they were preparing for a general revolt… The resolutions of Parliament breathed a spirit of moderation and forbearance; conciliatory propositions accompanied the measures taken to enforce authority… I have acted with the same temper, anxious to prevent, if it had been possible…the calamities which are inseparable from a state of war; still hoping that my people in America would have discerned the traitorous views of their leaders, and have been convinced, that to be a subject of Great Britain, with all its consequences, is to be the freest member of any civil society in the known world.”-King George III, Speech to Parliament, October 27, 1775Based on the excerpt, which of the following best describes King George’s view of the colonists?

“We hold…that on their separation from the Crown of Great Britain, the several colonies became free and independent States, each enjoying the separate and independent right of self-government; and that no authority can be exercised over them…but by their consent… It is equally true, that the States…that the government created by it is a joint agency of the States, appointed to execute the powers enumerated and granted by that instrument; that all its acts not intentionally authorized are of themselves essentially null and void, and that the States have the right… to pronounce, in the last resort, authoritative judgement on the usurpations of the Federal Government… Such we deem to be inherent rights of the States.”-John C. Calhoun, statement adopted by a convention in South Carolina, 1832As described in the excerpt, which individual or body makes the final decision on whether a law is valid in a state?

“Gov. Randolph observed that the confederation is incompetent to any one object for which it was instituted.  The framers of it wise and great men; but human rights were the chief knowledge of the times when it was framed so far as they applied to oppose Great Britain.  Requisitions for men and money had never offered their form to our assemblies.  None of those vices that have since discovered themselves were apprehended.”-Dr. James McHenryWhy was maintaining state power and preventing abuses by the national government a major concern for many Americans in the 18th century?

“We might feel a pride in the reflection, that our young country…was the first to adopt with any efficacy, the penitentiary system of prison discipline, and the first to attempt to prevent the commission of crimes, by seeking out the youthful and unprotected, who were in the way of temptation, and by religions and moral instruction, by imparting to them useful knowledge, and by giving them industrious and orderly habits, rescuing them from vice, and rendering them valuable members of society… To confine these youthful criminals…where no, or scarcely any, distinction can be made between the young and the old, or between the more or less vicious, where little can be learned but the ways of the wicked, and from whence they must be sent to encounter new wants, new temptation, and to commit new crimes, is to pursue a course, as little reconcilable with justice as humanity; yet, till the House of Refuge was established there was no alternative.”-Society for the Reformation of Juvenile Delinquents in the City of New York, Fourth Annual Report, 1829The above account best reflects what growing reform sentiment during the period 1820 to 1848?