A spherical balloon is inflated at a rate of two cubic feet per minute. How quickly is the radius expanding when there is already 4π/3 cubic feet of air in the balloon?

2/π feet per minute

Step-by-step explanation:

V = (4/3)π×r³

dV/dr = 4π×r²

When V = 4π/3, r = 1

dV/dr = 4π

dr/dt = dr/dV × dV/dt

= 1/4π × 2

= 2/π feet per minute

We are given the area of the region under the curve of the function f(x) = 5x + 7 with an interval [1, b] which is 88 square units where b > 1 

We need to find the integral of the function f(x) = 5x + 7 with the limits 1 and b 

5/2 x^2 + 7x (limits: 1, b)

substitute the limits:

5/2 (1^2) + 7 (1) - 5/2 b^2 + 7b = 0

solve for b

Then after solving for b, this would be your interval input with 1: [1, b].