Question 1013457
a parabolic arch has a width of 18 m across the bottom. at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters?
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Plot the points (-9,0) and (9,0) for the bottom.
2 other points are (-6,3) and (6,3)
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The form is y = -ax^2 + c
0 = -a*81 + c
3 = -a*36 + c
----------------- Subtract
-3 = -45a
a = 1/15
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0 = -81/15 + c
c = 5.4
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--> {{{y = -x^2/15 + 5.4}}}
Height of the arch at the center = 5.4 meters