Question

The intensity i of light from a light bulb varies inversely as the square of the distance d from the light bulb. suppose i is 90 ​w/msquared when the distance is 5 m. how much farther would it be to a point where the intensity is 40 ​w/msquared​?

Answer 1

Let
x---------> the intensity i of light from a light bulb
y--------> the distance d from the light bulb

we know that
x*y²=k

step 1
find the constant of variation  k 
for x=90 w/m²   and y=5 m
k=90*5²------> k=2250

step 2
for x=40 w/m²
x*y²=k--------> y²=k/x--------> y²=2250/40----> y²=56.25
y=7.5 m

the answer is
 7.5 m