Question

A satellite dish has a parabolic surface that can be defined by the equation 1/12 x². When the height from the vertex is 0.75 feet, the width of the dish is ____ feet. If the receiver is at the focus, it will be at the point _____.

Answer 1

The width of the dish when the height from the vertex is 0.75 feet is 3 feet. The focus of the dish is at the point (0,0).

Step-by-step explanation:

The equation for the parabolic surface of the satellite dish is given by 1/12 x², where x represents the distance from the vertex. To find the width of the dish when the height from the vertex is 0.75 feet, we can substitute 0.75 into the equation and solve for x.

1/12 x² = 0.75
Multiply both sides by 12 to eliminate the fraction:
x² = 9
Take the square root of both sides:
x = 3 feet

Therefore, when the height from the vertex is 0.75 feet, the width of the dish is 3 feet.

If the receiver is at the focus, it will be at the point (0,0). The focus of a parabolic dish is located at the vertex of the parabola.