Final answer:
The focal distance of a parabolic satellite dish that is 40 inches wide and 6 inches deep is 16.67 inches, which corresponds to option A).
Step-by-step explanation:
To determine the focal distance of a parabolic satellite dish, we can use the formula for the focus of a parabola in the shape of y = ax^2, where 4a is the depth of the dish, and the width is the distance from one side of the parabola to the other at the vertex's level. Given that a parabolic satellite dish is 40 inches wide and 6 inches deep, we can set up the following equation based on the shape's vertex being at the origin (0,0):
(40/2)^2 = 4a(6)
20^2 = 24a
400 = 24a
a = 400 / 24
a = 16.67 inches
Therefore, the focal distance of the satellite dish is 16.67 inches, which corresponds to option A).