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Answer:
38.27775 feet
Step-by-step explanation:
The bridge has been shown in the figure.
Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, in the cartesian coordinate system.
As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is
where is an arbitrary constant (distance between focus and vertex of the parabola).
The span of the bridge = 166 feet and
Maximum height of the bridge= 40 feet.
The coordinate where the bridge meets the base is and
There is only one constant in the equation of the parabola, so, use either of one point to find the value of .
Putting in the equation (i) we have
So, on putting the value of in the equation (i), the equation of bridge is
From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, feet, put this value in equation (i) to get the value of y.
feet.
The point and
represent the point on the bridge at a distance of 10 feet from its center.
The distance of these points from the x-axis is feet and the distance of the base of the bridge from the x-axis is
feet.
Hence, height from the base of the bridge at 10 feet from its center
feet.
