ANSWERS GIVEN. PLEASE COMPLETE BOTH PROBLEMS. Show all work, formulas used, and
ID: 3017003 • Letter: A
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.