Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 14 inches and a depth of 4 inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

Question

Mathematics

Alessandra Perkins

18 March, 05:46

Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 14 inches and a depth of 4 inches. If the receiver of the microphone is located at the focus of the reflector dish, how far from the vertex should the receiver be positioned?

+5

Answers (1)

Know the Answer?

Terry Houston · Answer 1

Given:

diameter = 14 inches

depth = 4 inches

radius = 14 / 2 = 7 inches

(x, y) → (7,4)

y = 1/4c * x²

4 = 1/4c * 7²

4 * 4c = 49

16c = 49

c = 49/16

c = 3.0625 inches

The receiver should be positioned 3.0625 inches from the vertex.