ANSWERS GIVEN. PLEASE COMPLETE BOTH PROBLEMS. Show all work, formulas used, and

Question

ANSWERS GIVEN. PLEASE COMPLETE BOTH PROBLEMS. Show all work, formulas used, and simple math calculated.
I. Parabolas 1. A satellite dish has a diameter of 20 ft. If the receiver (focus) is to be placed 6 ft from the base (vertex), how deep (h) is the dish? 20 ft AIUSWER (0,6) (0,0) A parabolic arch bridge above a river is 50 ft above the water at its center and 200 ft wide at its base. What is the maximum height of a boat that can pass through the arch 40 ft from the center? 2. { 12 fl (0,0) BOAT 200 ft

Explanation / Answer

1)This is an up-opening parabola:
      y = a(x-h)² + k
      vertex (h, k)
      a > 0
      focal length p = 1/(4a)
      focus (h, k+p)

"The parabola is positioned with its vertex at the origin."
h = k = 0
The equation becomes
y = ax²

"The [parabola] has a diameter of 20 feet and a depth of 6 feet"
(-10, 6) and (10, 6) are points on the parabola.
6 = a10²
a = 6/100 = 3/50 =
The equation becomes
y = (3/50)x²

p = 1/(4a) = 1/4 *(3/50) = 25/6 =4 1/6 ft
focus (0, 3)

The receiver should be placed 25/6 feet above the base.

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