# The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of 6 miles?

Oct 7, 2016

$\left(A p p r .\right) 888.89 \text{unit.}$

#### Explanation:

Let $I , \mathmr{and} d$ resp. denote the intensity of radio signal and the

distance in mile) of the place from the radio station.

We are given that, $I \propto \frac{1}{d} ^ 2 \Rightarrow I = \frac{k}{d} ^ 2 , \mathmr{and} , I {d}^{2} = k , k \ne 0.$

When $I = 8000 , d = 2 \therefore k = 8000 {\left(2\right)}^{2} = 32000.$

Hence, $I {d}^{2} = k = 32000$

Now, to find $I \text{, when } d = 6$

$\therefore I = \frac{32000}{d} ^ 2 = \frac{32000}{36} \approx 888.89 \text{unit} .$