Question 1021014
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 810 w/m^2 when the distance is 3 m.  How much farther would it be to a point where the intensity is 160 w/m^2.


the formula is i = k / d^2


i equals the intensity of the light in watts per square meter.
d equals the distances from the light bulb in meters.
k is the constant of variation.


i is 810 watts per square meter when d is 3 meters.


the formula if i = k / d^2 becomes 810 = k / 3^2.


this becomes 810 = k / 9.


solve for k to get k = 810 * 9 = 7290.


you are asked to determine how much farther away from the light bulb would a point be if the intensity of the light was 160 watts per square meter.


k is the constant of variation, so it stays the same.


the formula of i = k / d^2 becomes i = 7290 / d^2.


when i = 160, the formula becomes 160 = 7290 / d^2.


solve for d^2 to get d^2 = 7290 / 160 = 45.5625.


solve for d to get d = sqrt(45.5625) = 6.75 meters.


the intensity of light would be 160 watts per square meter when the distance from the light bulb is 6.75 meters.


that would be 6.75 - 3 = 3.75 meters further away.


that's your solution.