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)

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

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

divide both sides by 40

vertex to focus= 9 in approx

they will manufacture 8496 cars