a parabolic microphone used on the sidelines of a professional football game uses a reflective dish 16 inch wide and 4 inch deep how far from the bottom of the disk should the microphone be placed?

If we put the parabola in a coordinate system with vertex at the origin and facing the positive x axis. We have the following points lying on the curve:
(4, 8), (4, -8)

For parabola facing right:
y2 = 4ax

Substituting either coordinates to solve for a:
a = 4

Therefore, the microphone should be placed 4 inches from the bottom of the disk.

Answer Link

DelcieRiveria DelcieRiveria · Answer 2 · 2019-01-11T11:12:35+01:00

Answer:

The microphone should be placed 4 inches far from the bottom of the disk.

Step-by-step explanation:

If we put the parabolic microphone into the coordinate system with the vertex at the origin and facing to the right, then the equation of the parabola would have the form:

[tex]y^2=4ax[/tex] .... (1)

Where, a is the distance between focus and vertex.

The microphone to be placed at focus.

The parabolic microphone used on the sidelines of a professional football game uses a reflective dish 16 inch wide and 4 inch deep. It means the parabola passing through the points (4,8) and (4,-8).

Put x=4 and y=8 in equation (1).

[tex](8)^2=4a(4)[/tex]

[tex]64=16a[/tex]

Divide both sides by 16.

[tex]4=a[/tex]

Therefore, the microphone should be placed 4 inches far from the bottom of the disk.