Question

The rate of increase (R) of the radius (r) in meters per second is inversely proportional to the radius. If the radius is increasing at 1400 meters per second when the radius is 10 meters . find an equation to the rate of increase of the radius in terms of the radius

Answer 1

The equation to the rate of increase of the radius in terms of the radius is:

$R = \frac{14000}{r}$

Solution:

The rate of increase (R) of the radius (r) in meters per second is inversely proportional to the radius

Therefore,

$R \propto \frac{1}{r}\\\\R = k \times \frac{!}{r} -------- eqn\ 1$

The radius is increasing at 1400 meters per second when the radius is 10 meters

r = 10 m

R = 1400 meter per second

Substitute in eqn 1

$1400 = k \times \frac{1}{10}\\\\k = 14000$

Substitute k = 14000 in eqn 1

$R = 14000 \times \frac{1}{r}\\\\R = \frac{14000}{r}$

Thus the equation is found