Answer to Question #283734 in Calculus for Yuyu

Question

the intensity (I) of illumination given by a projector varies inversely as the square of the distance(d) of its lamp from the screen if the projector is 20m from the screen when the intensity is 2.5 find the distance when the intensity is 62.5 a if r varies inversity as the aquare of h and r =6 when h = 4 

Answer 1

$I \propto \frac{1}{{{d^2}}} \\ \Rightarrow I = \frac{k}{{{d^2}}} \text{ where k is constant of proportionality} \\ k = I{d^2} \text{ so if } I = 2.5, d=20 \\ \text{Then } k=2.5\times 20^2=1000. \\ \text{If } I=62.5, ~d = \sqrt {\frac{{1000}}{I}} = \sqrt {\frac{{1000}}{{62.5}}} = 4$