Aballoon is blowing up at a constant rate of 9 cubic centimeters per second. when the volume of the balloon is 2048/3 pi cubic centimeters, what is the rate of change of the radius?

Step-by-step explanation:

Rates of Change as Derivatives

If some variable V is a function of another variable r, we can compute the rate of change of one with respect to the other as the first derivative of V, or

The volume of a sphere of radius r is

The volume of the balloon is growing at a rate of . This can be written as

We need to compute the rate of change of the radius. Note that both the volume and the radius are functions of time, so we need to use the chain rule. Differentiating the volume with respect to t, we get

solving for

We need to find the value of r, which can be obtained by using the condition that in that exact time

Simplifying and isolating r

Replacing in the rate of change

answer: huh

step-by-step explanation:

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

u also answered this so i think u would know but i am here to

put in or use mine