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 = -0.000475×2 + 0.851x. where x and y are in feet. About how high above the river is the bridge at the top of the arch? About 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.
To find the height of the bridge at the top of the arch, we need to find the maximum value of the function y = -0.000475x^2 + 0.851x.
The function is a quadratic equation in the form of y = ax^2 + bx + c, where a = -0.000475, b = 0.851, and c = 0.
To find the maximum value of y, we can calculate the x-coordinate of the vertex using the formula x = -b/(2a).
x = -(0.851) / (2(-0.000475))
x ≈ 896.84
Plugging this value back into the function, we can find the corresponding y-coordinate.
y = -0.000475(896.84)^2 + 0.851(896.84)
y ≈ 1,791.58
Therefore, the bridge is about 1,791.58 ft above the river at the top of the arch.
To find the length of the section of bridge above the arch, we need to find the x-values where the function intersects with the x-axis.
Setting y = 0, we can solve for x:
0 = -0.000475x^2 + 0.851x
0.000475x^2 - 0.851x = 0
x(0.000475x - 0.851) = 0
x = 0 (one solution) or x ≈ 1784.21
Therefore, the length of the section of bridge above the arch is approximately 1784.21 ft.
However, none of the given options match this result.