Related Rates Angle Problem

Let $y = 2(x^2 - 3x)$

a. Find $\frac{dy}{dt}$ when $x = 3$ given $\frac{dx}{dt} = 2$

b. Find $\frac{dx}{dt}$ when $x = 1$ given $\frac{dy}{dt} = 5$

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 $20 \frac{{ft}^3}{hour}$

An airplane is flying at an altitude of 7 miles and passes directly over a radar antenna as shown in the figure. When the plane is 10 miles from the antenna, the radar detects that the distance between the plane and the tower is changing at the rate of 300 mph. What is the speed of the airplane at that moment?