To find the height of the bridge (the top of the arch), you need to determine the maximum value of the function y = –0.000475x^2 + 0.851x. This can be done by taking the derivative of the function with respect to x, setting it equal to zero, and solving for x.
The derivative of y with respect to x is dy/dx = (-0.00095x + 0.851). Setting dy/dx equal to zero, we get:
-0.00095x + 0.851 = 0
-0.00095x = -0.851
x = -0.851 / -0.00095
x ≈ 895.79
Now, plug this value of x back into the function to find the corresponding y-coordinate:
y = -0.000475(895.79)^2 + 0.851(895.79)
y ≈ -0.000475(802284.0841) + 762.83129
y ≈ -381.16 + 762.83129
y ≈ 381.67129
Therefore, the bridge is about 381.16 ft above the river.
To find the length of the section of the bridge above the arch, you need to calculate the x-values where the function y = –0.000475x^2 + 0.851x intersects the x-axis. This can be done by setting y equal to zero and solving for x.
-0.000475x^2 + 0.851x = 0
x(-0.000475x + 0.851) = 0
From this, we get two solutions:
x = 0 (which does not correspond to the section of the bridge above the arch)
and
-0.000475x + 0.851 = 0
-0.000475x = -0.851
x = -0.851 / -0.000475
x ≈ 1780
Therefore, the length of the section of the bridge above the arch is about 1780 ft.
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 = –0.000475x2 + 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)
Responses
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 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 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 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.
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.
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