Mathematics, 25.01.2020 21:31 ramosramos142

Aparabolic 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?

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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 from: joshbolaadebawore

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:

y^2=4ax .... (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).

(8)^2=4a(4)

64=16a

Divide both sides by 16.

4=a

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

Aparabolic microphone used on the sidelines of a professional football game uses a reflective dish 1

Answer from: Quest

40%=2/550=1/230=3/1056=14/25

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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