Solve the Problem $y = 2 x ^ { 4 }$

question 10

Multiple Choice

Solve the problem.
-A water tank is formed by revolving the curve $y = 2 x ^ { 4 }$ about the $y$ -axis. Find the volume of water in the tank as a function of the water depth, $\mathrm { y }$ .

• A) \(V ( y ) = \frac { 2 \pi } { 3 \sqrt { 2 } } y ^ { 3 / 2 }\)
• B) \(V ( y ) = \frac { \pi } { 2 \sqrt { 2 } } y ^ { 1 / 2 }\)
• C) \(V ( y ) = \frac { 3 \pi } { 2 \sqrt { 2 } } y ^ { 3 / 2 }\)
• D) \(V ( y ) = \frac { \pi } { 9 } y ^ { 9 }\)

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Definitions:

Feedback Signal

A signal that is sent back to control a system by comparing the output with the input, thus allowing for adjustments to achieve desired performance.

Process

A continuous manufacturing operation.

SCADA System

Supervisory Control and Data Acquisition system, a computer system for gathering and analyzing real-time data to monitor and control processes.