Question

A sound receiving dish used at outdoor sporting events is constructed in the shape of a paraboloid, with its focus 8 inches from the vertex. Determine the width of the dish if the depth is to be 3 feet. (Round your answer to two decimal places.)

Answer 1

Answer:

w≅8.46ft

Step-by-step explanation:

Data

focus=8

vertex=(0,0)

width=?

depth (y)=3ft

parabola equation: $(x-h)^{2}=4p(y-k)$; then for V=(0,0), $x^{2} =4py$, be focus(f)=8in;  $x^{2} =4*8*y=32y$ → $y=\frac{x^{2} }{32}$

we have that y=3ft then $3=\frac{x^{2} }{32}$; but 1in≅0.083ft so $x^{2} =3*32*0.083=7.968$ → x=±2.82, finally w=3*2.82≅8.46ft