A bridge is built in the shape of a parabolic arch. The bridge has a span of 50 meters and a maximum height of 40 meters. How do you find the height of the arch 10 meters from the center?

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Answer 1 · 2016-05-16T06:44:57

#33.6# meters.

Referring to the highest point as the origin O and the the altitude

from O as the x-axis, the equation of the parabola is #y^2=4ax#

From the data given, the ends of the bridge are at #(40, +-25)#.

So, #25^2=(4a)(40)#. This gives a = 125/32.

When, at 10 meters from the center, #y = +-10#. So, the height

there is #40-x#, when #y=+-10#.

From the equation of the parabola, #10^2=(4)(125/32)x#. So, x =

6.4. And so, the required height # = 40-32/5 = 33.6# meters.

The graph for the arch is in a befitting frame.

graph{(y-40+0.064x^2)(y)=0[-25 25 -40 40]}