Asked by Net
A parabolic arch bridge has a 60ft base and a height of 24ft. Find the height of the arch at a distance of 5, 10, and 20 ft from the center
Answers
Answered by
Reiny
let the vertex of the parabola be (0,60)
its equation would be
y = ax^2 + 60 , but (30,0) and (-30,0) would also lie on it
0 = a(900) + 60
a = -60/900 = -1/15
equation of bridge is
y = (-1/15)x^2 + 60
so when x = 5
y = (-1/15)(25) + 60 = 175/3 ft
or 58 1/3 ft
or appr 58.33 ft
repeat for x = 10 and x = 20
its equation would be
y = ax^2 + 60 , but (30,0) and (-30,0) would also lie on it
0 = a(900) + 60
a = -60/900 = -1/15
equation of bridge is
y = (-1/15)x^2 + 60
so when x = 5
y = (-1/15)(25) + 60 = 175/3 ft
or 58 1/3 ft
or appr 58.33 ft
repeat for x = 10 and x = 20
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