If $pv = 81$,then $\frac{dp}{dv}$ at $v = 9$ is equal to

The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.

Find the rate of change of the area of a circle with respect to its radius $r$ when $r=5 \text{ cm}$.

$A$ particle moves in a straight line in such a way that its velocity at any point is given by $v^2 = 2 - 3x$,where $x$ is measured from a fixed point. The acceleration is

$A$ water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is $\tan ^{-1}(0.5)$. Water is poured into it at a constant rate of $5 \ m^3/h$. Find the rate at which the level of the water is rising at the instant when the depth of the water in the tank is $4 \ m$.