SOLUTION: A field microphone has a parabolic cross section. It is 20 in wide at the opening and its focus is 2 in from the vertex. How deep is the microphone at the vertex?

Question 868779: A field microphone has a parabolic cross section. It is 20 in wide at the opening and its focus is 2 in from the vertex. How deep is the microphone at the vertex?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A field microphone has a parabolic cross section. It is 20 in wide at the opening and its focus is 2 in from the vertex. How deep is the microphone at the vertex?
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representing the parabolic cross section of the microphone, consider a parabola that opens upwards with vertex at the origin.
Its basic form of equation: x^2=4py
For given parabola:
p=2 (distance from focus to vertex on the axis of symmetry
4p=8
equation:x^2=8y
solve for y with x=10
y=x^2/8=100/8=12.5
How deep is the microphone at the vertex? 12.5 in
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