The equation to the rate of increase of the radius in terms of the radius is:
[tex]R = \frac{14000}{r}[/tex]
Solution:
The rate of increase (R) of the radius (r) in meters per second is inversely proportional to the radius
Therefore,
[tex]R \propto \frac{1}{r}\\\\R = k \times \frac{!}{r} -------- eqn\ 1[/tex]
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
[tex]1400 = k \times \frac{1}{10}\\\\k = 14000[/tex]
Substitute k = 14000 in eqn 1
[tex]R = 14000 \times \frac{1}{r}\\\\R = \frac{14000}{r}[/tex]
Thus the equation is found
