A light is to be placed atop a pole of height h feet to illuminate a busy traffic circle, which has a radius of 40 ft. The intensity of illumination I at any point P on the circle
is directly proportional to the cosine of the angle ‑ (seethe figure) and inversely proportional to the square of the distance d from the source.
(a) How tall should the light pole be to maximize I?
(b) Suppose that the light pole is h feet tall and that a woman is walking away from the base of the pole at the rate of 4 ftys. At what rate is the intensity of the light at the point on her back 4 ft above the ground decreasing when she reaches the outer edge of the
traffic circle?

Question

A light is to be placed atop a pole of height h feet to illuminate a busy traffic circle, which has a radius of 40 ft. The intensity of illumination I at any point P on the circle

is directly proportional to the cosine of the angle ‑ (seethe figure) and inversely proportional to the square of the distance d from the source.

(a) How tall should the light pole be to maximize I?

(b) Suppose that the light pole is h feet tall and that a woman is walking away from the base of the pole at the rate of 4 ftys. At what rate is the intensity of the light at the point on her back 4 ft above the ground decreasing when she reaches the outer edge of the

traffic circle?

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