Both x and y denote functions of t that are related by the given equation. Use this equation and the given derivative information to find the specified derivative. Equation: x+7y=7

(a)Given that dx/dt=5, find dy/dt when x=6.

(b)Given that dy/dt=10, find dx/dt when x=7.

Suppose that f(0) = −3 and f '(x) ≤ 8 for all values of x. how large can f(4) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 4] . there exists a number c such that

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

The sum of the reciprocal of a positive number and the reciprocal of 2 more than the number is 3/4 equation: the number is