$A$ stone is dropped into a quiet lake and waves move in circles at a speed of $8 \,cm/sec$. At the instant when the radius of the circular wave is $12 \,cm$, how fast is the enclosed area increasing?

$A$ particle is fired straight up from the ground. Its height in feet after $t$ seconds is given by $s(t) = 128t - 16t^2$. The velocity of the particle when it hits the ground is...

The displacement of a particle at the time $t$ is given by $s = \sqrt{1+t}$. Then its acceleration $a$ is proportional to:

$A$ water tank has the shape of an inverted right circular cone,whose semi-vertical angle is $\tan^{-1}(1/2)$. Water is poured in at a constant rate of $5 \ m^3/min$. Then the rate (in $m/min$) at which the level of water is rising at the instant when the depth of water in the tank is $10 \ m$ is:

If $f(x) = 2x^{2}$,find $\frac{f(3.8) - f(4)}{3.8 - 4}$.

If a particle moves in a straight line according to the law $x = a \sin (\sqrt{\lambda} t + b)$, then the particle will come to rest at two points whose distance is [symbols have their usual meaning]