Question

A satellite dish is the shape of a paraboloid. The dish is 38 inches wide, and 10 inches deep. How many inches should the receiver be located from the vertex for optimal reception? (round to the nearest thousandth)

Answer 1

Answer:

9 in approx

Step-by-step explanation:

Step one:

given data

the shape of the satellite dish takes the form of a paraboloid.

the diameter of the dish is 38in wide

and 10 inches deep.

step two:

The expression for the paraboloid is

$4ay=x^2$

where y is the vertical axis of the  paraboloid

a is vertex to focus.

and x is the radius of the dish

x= 38/2= 19in

substituting we have

$4a10 =19^2\\\\40a=361$

divide both sides by 40

$a=361/40\\\\a=9.025$

vertex to focus= 9 in approx