The intensity I of light received from a source varies inversely as the square of the distance d from the source. If the light intensity is 5 foot-candles at 17 feet, find the light intensity at 16 feet.
(17/16)^2 * 5
To find the light intensity at 16 feet, we can use the inverse square law formula:
I = k/d^2
where I is the light intensity, k is the constant of variation, and d is the distance from the source.
Given that the light intensity is 5 foot-candles at 17 feet, we can substitute these values into the formula to solve for k:
5 = k/17^2
To find the value of k, we can multiply both sides of the equation by 17^2:
5 * 17^2 = k
k = 5 * 289
k = 1445
Now we have the value of k, we can use it to find the light intensity at 16 feet. Substituting the values into the formula:
I = 1445/16^2
I = 1445/256
I ≈ 5.65 foot-candles
Therefore, the light intensity at 16 feet is approximately 5.65 foot-candles.