Ahorizontal pedestrian bridge is supported from a parabolic arch. the bridge goes
above a roadway that is 40 feet wide. at ground level, the main span of the bridge
is 90 feet wide. at the edge of the roadway, 25 feet from where the arch touches the
ground, the arch is 16 feet high. how tall is the arch at its tallest point?

  about 19.94 ft

Step-by-step explanation:

It is convenient to start with a parabola that opens downward and has a width of ±1 and a height of 1. Its equation is ...

  f(x) = 1 - x²

To make it have a horizontal width of ±45 feet, we need to use a horizontal expansion factor. The equation is then ...

  g(x) = f(x/45) = 1 - (x/45)²

To make it have a height of 16 when x=20, we need a vertical expansion factor.

  h(x) = a·g(x) = a(1 -(x/45)²)

Filling in the given values, we can find the value of the vertical expansion factor, a:

  16 = a(1 -(20/45)²) = a(1 -(4/9)²)

  16 = a(65/81)

  16(81/65) = a = 19 61/65 ≈ 19.94 . . . . . . . . divide by the coefficient of "a"

This makes the equation of the arch be ...

  h(x) = 19.94(1 -(x/45)²)

At the tallest point, x = 0, so the arch is ...

  h(0) = 19.94(1 -0) = 19.94 . . . . feet high

step-by-step explanation:

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