Chapter 3.3, Problem 43E

Related Rates Figure 7 shows a $10$- foot ladder leaning against a wall.

a. Use the Pythagorean theorem to find an equation relating $x$ and $y$.

b. If the foot of the ladder is being pulled along the ground at the rate of $3$ feet per second, how fast is the top end of the ladder sliding down the wall at the time when the foot of the ladder is $8$ feet from the wall? That is, what is $\frac{dy}{dt}$ at the time when $\frac{dx}{dt}=3$ and $x=8$?