SOLUTION: A laboratory designed a radio telescope with a diameter of 300 feet and a maximum depth of 44 feet. The graph depicts a cross section of this telescope. Find the equation of this p
Question 1109014: A laboratory designed a radio telescope with a diameter of 300 feet and a maximum depth of 44 feet. The graph depicts a cross section of this telescope. Find the equation of this parabola. Found 2 solutions by ankor@dixie-net.com, josgarithmetic:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A laboratory designed a radio telescope with a diameter of 300 feet and a maximum depth of 44 feet.
The graph depicts a cross section of this telescope. Find the equation of this parabola
:
Using the form y = ax^2 + bx + c, our parabola crosses the origin so c=0
x = 300 y = 0
300^2a + 300b = 0
and
x = 150, y = 44
150^2a + 150b = 44
:
90000a + 300b = 0
22500a + 155b = 44
use elimination, multiply the 2nd equation by 2
90000a + 300b = 0
45000a + 300b = 44
---------------------subtraction eliminates b, find a
45000a = -44
a = -44/45000
a = -.00195
Find b
90000(-.001955) + 300b = 0
-176 + 300b = 0
300b = 176
b = 176/300
b = .5867
the equation: y = -.00195x^2 + .5867x
looks like this
green line y = 44, x = 150
Imagine a cross section through the middle, so that if graphed on Cartesian coordinate system, parabola opens upward, vertex is placed on the origin, and two other points on the parabola are (-150, 44) and (150, 44).
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Other possible equation arrangements are possible.
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