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

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."