Discussion Forum

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 5 cm³/sec, when x=2 cm. The rate at which the depth of water is increasing is

Answer:

Explanation:

$V=5x-\frac{x^{2}}{6}\Rightarrow\frac{dV}{dt}=5\frac{dx}{dt}\frac{x}{3}\frac{dx}{dt}$ 

$\Rightarrow\frac{dx}{dt}=\frac{\frac{dV}{dt}}{(5-\frac{x}{3})}$

$\Rightarrow(\frac{dx}{dt})_{x=2}=\frac{5}{5-\frac{2}{3}}= \frac{15}{13}cm/sec$