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;
[tex]\begin{gathered} y=\frac{k}{x^2} \\ \text{When y=3.75, then x=40. Therefore;} \\ 3.75=\frac{k}{40^2} \\ 3.75=\frac{k}{1600} \\ 3.75\times1600=k \\ k=6000 \\ \text{Hence, when the distance (x) is 50 feet} \\ y=\frac{k}{x^2} \\ y=\frac{6000}{50^2} \\ y=\frac{6000}{2500} \\ y=2.4 \end{gathered}[/tex]The illumination at a distance of 50 feet is therefore 2.4 footcandles
