A Water Tank Is Formed by Revolving the Curve $y = 3 x ^ { 4 }$

question 51

Multiple Choice

A water tank is formed by revolving the curve $y = 3 x ^ { 4 }$ about the $y$ -axis. Water drains from the tank through a small hole in the bottom of the tank. At what constant rate does the water level, $y$ , fall? (Use Torricelli's Law: $\mathrm { dV } / \mathrm { dt } = - \mathrm { m } \sqrt { \mathrm { y } }$ .)

• A) \(\frac { d y } { d t } = \frac { - m \pi } { \sqrt { 3 } }\)
• B) \(\frac { d y } { d t } = \frac { - \sqrt { 3 } } { m \pi }\)
• C) \(\frac { \mathrm { dy } } { \mathrm { dt } } = \frac { - \pi } { \mathrm { m } \sqrt { 3 } }\)
• D) \(\frac { \mathrm { dy } } { \mathrm { dt } } = \frac { - \mathrm { m } \sqrt { 3 } } { \pi }\)

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Definitions:

Reaction Measurement

The process of quantifying the progress, rate, or yield of a chemical reaction using various methods like spectroscopy, calorimetry, or chromatography.

H2S

Hydrogen sulfide, a toxic, colorless gas with a characteristic odor of rotten eggs, widely found in nature and industrial processes.

Cl2

The chemical symbol for chlorine gas, a diatomic molecule consisting of two chlorine atoms, used in water purification and as a bleaching agent.

Rate Comparison

The analysis or measurement of the speed or velocity at which certain processes or reactions occur, often in a comparative context.