A Water Tank Is Formed by Revolving the Curve $y = 2 x ^ { 4 }$

question 43

Multiple Choice

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, $y$ .

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

Learn the differences between subjective and objective probabilities and their impact on decision-making.

Distinguish between conditions of certainty, risk, and uncertainty in the decision-making process.

Grasp the importance of environmental factors, such as economic crises, in creating uncertainty and risk in decision-making.

Recognize the steps involved in the decision-making process, including problem identification and alternative generation.

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Definitions:

Serous Fluid

A clear, pale yellow fluid that fills the space between membranes lining the body cavities and surrounding the internal organs.

Urine Stream

The flow of urine out of the body during urination.

Hesitancy

A delay or pause before initiating an action or speech, often due to uncertainty or anxiety.

Urgency

A sudden, compelling need to urinate, which is difficult to delay, often a symptom of a urinary tract condition.