The displacement of a particle at time $t$ is given by $x = At^2 + Bt + C$,where $A, B$ and $C$ are constants. If $v$ is the velocity,then $4Ax - v^2 = ....$

$A$ spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to its surface area. Prove that the radius is decreasing at a constant rate.

$A$ spherical iron ball of radius $10 \, cm$ is coated with a layer of ice of uniform thickness that melts at a rate of $50 \, cm^3/min$. When the thickness of the ice is $5 \, cm$,then the rate at which the thickness (in $cm/min$) of ice decreases is

The radius of a circle is increasing at a rate of $0.7 \text{ cm/s}$. The rate at which the circumference of the circle is increasing is . . . . . . .

The surface area of a spherical balloon is increasing at the rate of $2 \text{ cm}^2/\text{sec}$. Find the rate of increase in the volume of the balloon when the radius of the balloon is $6 \text{ cm}$.

The rate of change of volume of a sphere with respect to its surface area when the radius is $4 \text{ cm}$ is