Solve the Problem $y = e ^ { - 2 x }$

question 91

Multiple Choice

Solve the problem.
-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve $y = e ^ { - 2 x }$ , and the line $x = 6$ about the $y$ -axis.

• A) \(\frac { 1 } { 2 } \pi \left( 1 - 13 \mathrm { e } ^ { - 12 } \right)\)
• B) \(- \frac { 1 } { 2 } \pi \left( 1 + 13 \mathrm { e } ^ { - 12 } \right)\)
• C) \(\frac { 1 } { 2 } \pi \left( 1 - 11 \mathrm { e } ^ { - 12 } \right)\)
• D) \(\frac { 1 } { 2 } \pi \left( 1 - 12 \mathrm { e } ^ { - 12 } \right)\)

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Definitions:

Retained Earnings

The segment of net profits that are not distributed as dividends, instead kept within the company for reinvestment in its main operations or for debt repayment.

Current Asset

A slightly different term for assets likely to be used or turned into cash within one fiscal year or operating cycle, emphasizing liquidity.

Land

An asset representing the earth's surface that a company owns, used for operations, development, or investment.

Liquidity

The ease with which an asset can be converted into cash without significantly affecting its price, reflecting a company's ability to meet short-term obligations.