Applications Of Derivatives Question 264
Question: The volume V and depth x of water in a vessel are connected by the relation $ V=5x-\frac{x^{2}}{6} $ and the volume of water is increasing at the rate of $ 5cm^{3}/\sec $ , when $ x=2cm $ . The rate at which the depth of water is increasing, is
Options:
A) $ \frac{5}{18}cm/\sec $
B) $ \frac{1}{4}cm/\sec $
C) $ \frac{5}{16}cm/\sec $
D) None of these
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Answer:
Correct Answer: D
Solution:
$ V=5x-\frac{x^{2}}{6}\Rightarrow \frac{dV}{dt}=5\frac{dx}{dt}-\frac{x}{3}.\frac{dx}{dt} $
therefore $ \frac{dx}{dt}=\frac{\frac{dV}{dt}}{( 5-\frac{x}{3} )}\Rightarrow {{( \frac{dx}{dt} )} _{x=2}}=\frac{5}{5-\frac{2}{3}}=\frac{15}{13}cm/\sec $ .
BETA
