The sides of an equilateral triangle are increasing at the rate of $2 \ cm/s$. Find the rate at which its area is increasing when each side is $10 \ cm$.

Coffee is draining from a conical filter,with both height and diameter equal to $15 \, cm$,into a cylindrical coffee pot with a diameter of $15 \, cm$. The rate at which coffee drains from the filter into the pot is $100 \, cm^3/min$. The rate in $cm/min$ at which the level in the pot is rising at the instant when the coffee in the pot is $10 \, cm$ deep,is:

If displacement $s = 5 \sin(2t)$,then the velocity at the end of $t = \frac{\pi}{3} \text{ s}$ is

The ordinate of a point describing the circle $x^2 + y^2 = 25$ decreases at the rate of $1 \, cm/sec$. Find the rate of change of the abscissa of the point when the ordinate is equal to $3 \, cm$ (Given $x > 0, y > 0$).

The equation of motion of a stone thrown vertically upward from the surface of a planet is given by $s = 10t - 3t^2$,where the units of $s$ and $t$ are $cm$ and $sec$ respectively. The stone will return to the surface of the planet after:

$A$ stone is dropped into a quiet lake and waves move in circles at a speed of $4 \text{ cm/s}$. At the instant when the radius of the circular wave is $10 \text{ cm}$,how fast is the enclosed area increasing?