Related Rates Shadow

Let $y = \sin{(x)}$

Find $\frac{dy}{dt}$ when $x = \frac{\pi}{4}$ given $\frac{dx}{dt} = 2 \frac{cm}{sec}$

A 10 by 6 foot rectangular swimming pool is being filled. Find the rate at which the height of the water rises if the hose is pouring at $20 \frac{{ft}^3}{hour}$

A boat is pulled in by means of a winch on a dock 12 ft above the deck of the boat. If the winch pulls in rope at the rate of 4 ft/sec, determine the speed of the boat when 13 feet of rope is out.

A cylindrical water tank with a radius of 4 meters is being filled with water at a constant rate of 2 cubic meters per minute. Find the rate at which the water level is rising when the water is 3 meters deep.