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A parabolic satellite dish is 40 inches wide and 6 inches deep. What is the focal distance of the satellite dish?

A) 16.67 inches
B) 20 inches
C) 12.5 inches
D) 25.33 inches

1 Answer

4 votes

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).

User Gongdo Gong
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