The rate of change of the volume of a sphere of radius $r$ with respect to its surface area is:

$A$ point moves in a straight line during the time $t = 0$ to $t = 3$ according to the law $s = 15t - 2t^2$. The average velocity is

$A$ ladder is resting against a wall at an angle of $30^\circ$ with the wall. $A$ man is ascending the ladder at the rate of $3 \, ft/sec$. His rate of approaching the wall is:

$A$ particle moves along the curve $y=x^2+2x$. Then, the point on the curve such that the $x$ and $y$ coordinates of the particle change with the same rate is

$A$ kind of bacteria grows by $t^3$ in $t \ s$. The time taken for the rate of growth of the bacteria to become $1200 \ \text{per } s$ is: (in $s$)

The length $x$ of a rectangle is decreasing at the rate of $5 \text{ cm/min}$ and the width $y$ is increasing at the rate of $4 \text{ cm/min}$. When $x = 8 \text{ cm}$ and $y = 6 \text{ cm}$,find the rate of change of the perimeter.