MATH SOLVE

3 months ago

Q:
# 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 = β0.000475x2 + 0.851x, where x and y are 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)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 381.16 ft.The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft.

Accepted Solution

A:

The height of bridge will be found as follows:

y=-0.000475x^2+0.851x

at maximum height, dy/dx=0

thus

dy/dx=-0.00095x+0.851=0

thus x=895.7895 =895.79 ft

at this point the maximum height will be:

h(x)=895.79 ft

The length of the section will be given by:

y=-0.000475x^2+0.851x

solving for the x-intercept we get:

-0.000475x^2+0.851x

thus x=0 or x=1791.58 ft

thus the correct answer is D

y=-0.000475x^2+0.851x

at maximum height, dy/dx=0

thus

dy/dx=-0.00095x+0.851=0

thus x=895.7895 =895.79 ft

at this point the maximum height will be:

h(x)=895.79 ft

The length of the section will be given by:

y=-0.000475x^2+0.851x

solving for the x-intercept we get:

-0.000475x^2+0.851x

thus x=0 or x=1791.58 ft

thus the correct answer is D