Question

The height in feet of the curved arch support for a bridge can be modeled by f(x) =

-0.0009x2 + 1.24x + 1.65. You are standing on a platform 2 feet above the maximum height ofthe arch. If you bungee from this point, and your bungee will stretch to 420 feet before retracting;are you safe to jump?
A) Yes you are totally safe!
B) No, you will hit the ground before your bungee retracts

SHow steps please!

Answer 1

A) Yes you are totally safe

Explanation:

The function that models the height of the curved arch in feet, f(x) = -0.0009·x² + 1.24·x + 1.65

The height of the platform = 2 feet + The maximum height of the arch

The amount of stretch of the bungee before retracting = 420 feet

The vertex of the parabola is the point x = (-b/2·a), from which we get;

At the maximum height of the arch, x = -1.24/(2 × -0.0009) = 6,200/9 = 688.
`\overline 8`

The maximum height of the arch = f(688.
`\overline 8`), therefore, we have;

f(688.
`\overline 8`) = -0.0009×(688.
`\overline 8`)² + 1.24 × (688.
`\overline 8`) + 1.65 = 428.76
`\overline 1`

The maximum height of the arch = 428.76
`\overline 1` feet

The height of the platform above the ground = 2 ft. + 428.76
`\overline 1` ft. = 430.76
`\overline 1` ft.

Therefore;

The height of the platform above the ground = 430.76
`\overline 1` feet > The amount the bungee will stretch before retracting = 420 ft.

430.76
`\overline 1` ft, > 420 ft.

Therefore, the jumper is totally safe.