Question

Because a stadium will be used at night, lights have been installed. The brightness (B) of a light varies directly with the intensity (I) of the light and inversely as the square of the distance (D) from the light. Brightness (B) is measured in light energy per unit and intensity (I) is measured in candle power. At a distance of 40 feet, a light meter gives a reading if 12 light energy units for a 160-candle power lamp

Part A: Write an equation that can be used to determine the constant of variation (k), then solve it for k.

Part B: Find the reading of a 90 candle power lamp at the distance of 60 feet.

Answer 1

B = something * I
B = something / D^2
so
B = k I / D^2
the question is what is k?
12 = k *160 / (40*40)
so k = 12 * 40 * 40 / 160
k = 120 in these units
B = 120 * 90 / (60*60) = 2 * 3 / 2 = 3