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Question 640618: A gigantic gate to the entrance of a theme park in the shape of a parabola is constructed on a level ground. The horizontal distance between the end points to the gigantic gate is 20 meters. The maximum height of the gigantic gate from the ground is 5 meters. Calculate the height of the gigantic gate at a horizontal distance of 4 meters from one of the end points.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A gigantic gate to the entrance of a theme park in the shape of a parabola is constructed on a level ground. The horizontal distance between the end points to the gigantic gate is 20 meters. The maximum height of the gigantic gate from the ground is 5 meters. Calculate the height of the gigantic gate at a horizontal distance of 4 meters from one of the end points.
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Standard form of a parabola that opens downwards: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex.
Set origin (0,0) midway between end points of the gate at ground level.
vertex: (h,k)=(0,5)
coordinates of end points at ground level: (-10,0) (left end) and (10,0) (right end)
Solving for A:
Using given (x,y) coordinates of right end point,(10,0) and height (5 m)
y=A(x-h)^2+k
0=A(10-0)^2+5
0=100A+5
A=-5/100=-1/20
Equation of parabolic gate:
y=-x^2/20+5
..
4 m from end points or 6 m from origin:
y=-36/20+5=-9/5+25/5=16/5=3.2 m
height of the gigantic gate at a horizontal distance of 4 meters from one of the end points=3.2 m
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