CarsonYarbrough CarsonYarbrough

30-04-2017
Mathematics

contestada

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?

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BlueSky06 BlueSky06

13-05-2017

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.

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