The spherical balloon is inflated at the rate of 10 m³/sec. find the rate at which the surface area is increasing when the radius of the sphere is 3m?

The balloon has a volume dependent on its radius :

Differentiating with respect to time gives

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

The surface area of the balloon is

and differentiating gives

so that at the moment the radius is 3 m, its area is increasing at a rate of

step-by-step explanation: a reaction is first order. if the initial reactant concentration is 0.0200 m, and 25.0 days later the concentration is 6.25 x 10-4 m, then its half-life is:

-4

step-by-step explanation: