Question

The intensity of illumination from the light source varies inversely with the square of the distance from the light source when photoelectric sale is placed 8 inches from a light source intensity is 12 lm then it is moved so that it is receives only three loans how far is it from the light source

Answer 1

Inverse variation:
$y=\frac{k}{x^2}$
y - the intensity of illumination, x - the distance from the light source

When the distance is 8 inches, the intensity is 12 lm.
$12=\frac{k}{8^2} \\ 12=\frac{k}{64} \\ 12 \times 64=k \\ k=768 \\ \Downarrow \\ y=\frac{768}{x^2}$

When the distance is x inches, the intensity is 3 lm.
$3=\frac{768}{x^2} \\ 3x^2=768 \\ x^2=\frac{768}{3} \\ x^2=256 \\ x=-16 \hbox{ or } x=16$
The distance can't be a negative number, so x=16.

The photoelectric cell is 16 inches from the light source.