Question

You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y = –0.000471x² + .837x, where x and y are measured in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? (1 point)

Answer 1

A. The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft.

B.The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft.

C. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 888.54 ft.

D. The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 371.85 ft.

Answer 2

@linn99123 @wyattjohnson can you help with this one as well?

Answer 3

I think B is the correct option

Answer 4

I hope your correct thanks @annas

Answer 5

yup B is correct for sure :) btw thanks for medal

Answer 6

no problem

Answer 7

the proof
y = –0.000471x² + .837x
the top of arch occurs when the slope of the curve is zero
i.e
dy/dx = 0.
dy/dx = -0.000942x + 0.837
equating this to zero

0.000942x = 0.837 : x = 0.837 / 0.000942 = 888.535 ft
y coord. determine the height of the arch
y = -0.000471 * 888.535² + 0.837 * 888.535
= 371.856 ft
if this means the span of the bridge
then this is the difference between the two points
where the y coordinate is zero i.e
when 0 = –0.000471x² + .837x = x(0.837 - 0.000471x)
So we have the trivial point where
x = 0 and the second point is the solution to the equation,
0.000471x = 0.837 : x = 0.837 / 0.000471 = 1777.070 ft
:D enjoy