Question

The illumination provided by a car's headlight varies inversely as the square of the distance from the headlight. A car's headlight produces an illumination of 3.75 footcandles at a distance of 40 feet. What is the illumination when the distance is 50 feet?

Answer 1

The illumination should be represented by y, while the distance from the headlight should be represented by x, therefore the inverse relationship between both variables is shown as;

`\begin{gathered} y=(k)/(x^2) \\ \text{When y=3.75, then x=40. Therefore;} \\ 3.75=(k)/(40^2) \\ 3.75=(k)/(1600) \\ 3.75*1600=k \\ k=6000 \\ \text{Hence, when the distance (x) is 50 feet} \\ y=(k)/(x^2) \\ y=(6000)/(50^2) \\ y=(6000)/(2500) \\ y=2.4 \end{gathered}`

The illumination at a distance of 50 feet is therefore 2.4 footcandles