(Solved): help The figure shows a 12 -foot ladder leaning against a wall. (a) Use the Pythagorean theorem to f ...

The figure shows a 12 -foot ladder leaning against a wall. (a) Use the Pythagorean theorem to find an equation relating \( x \) and \( y \). (b) Suppose that the foot of the ladder is being pulled along the ground at the rate of 5 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 \( \frac{d y}{d t} \) at the time when \( \frac{d x}{d t}=5 \) and \( x=8 \) ? (a) The equation is (b) \( \frac{d y}{d t}= \) (Type an exact answer, using radicals as needed)