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=(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=(k)/(8^2) \\ 12=(k)/(64) \\ 12 * 64=k \\ k=768 \\ \Downarrow \\ y=(768)/(x^2)`

When the distance is x inches, the intensity is 3 lm.

`3=(768)/(x^2) \\ 3x^2=768 \\ x^2=(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.