The rate of change of the radius of a sphere is $0.1 \ cm/s$. Find the rate of change of its surface area when its radius is $200 \ cm$.

For what values of $x$ does the rate of change of $x^3 - 5x^2 + 5x + 8$ become twice the rate of change of $x$?

$A$ balloon,which always remains spherical,has a variable diameter $\frac{3}{2}(2x+1)$. Find the rate of change of its volume with respect to $x$.

The rate of change of the volume of a sphere with respect to its surface area,when its radius is $2 \text{ cm}$,is

From a balloon rising vertically with a uniform velocity of $v \ ft/sec$, a stone is dropped. If the stone reaches the ground after $4 \ sec$, what is the height of the balloon above the ground at that moment (in $ft$)? (Take $g = 32 \ ft/sec^2$)

The distance $s$ in meters covered by a particle in $t$ seconds is given by $s = 2 + 27t - t^3$. The particle will stop after covering a distance of: