The volume V of a right circular cylinder of radius r and height h is V=πr2h. (a)

Step-by-step explanation:

Given that the  volume V of a right circular cylinder of radius r and height h is

To find rate of change of V with respect to rate of change of radius

Here given that h is constant

So differentiation with respect to t gives

This would be dv/dt i.e. rate of change of volume with respect to time in terms of dr/dt

This varies whenever r varies

The probability is 0.97682

Step-by-step explanation:

We start by finding the z-values of the runner times given.

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 13 seconds and SD = 0.3 seconds

So for 12.4 seconds, we have;

z = (12.4-13)/0.3 = -0.6/0.3 = -2

For 14 seconds, we have;

z = (14-13)/0.3= 1/0.3 = 3.33

So the probability we want to calculate is;

P(-2<z<3.33)

We can find this using the standard normal distribution table

Mathematically;

P(-2<z<3.33) = P(z<3.33) - P(z < -2)

Using the standard normal distribution table, the value of this is;

P(-2<z<3.33) = 0.97682