Answer:
The correct option is D.
Step-by-step explanation:
The underside of the bridge is an arch that can be modeled with the function
[tex]y=-0.000475x^2+0.851x[/tex]
Where, x is the horizontal distance from one end of the bridge (in feet) and y is height of the bridge above the river (in feet).
The leading coefficient is negative so it is a downward parabola.
If a function is [tex]y=ax^2+bx+c[/tex], then its vertex is
[tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]
In the given function a=-0.000475 and b=0.851.
[tex]\frac{-b}{2a}=\frac{-0.851}{2(-0.000475)}=895.789[/tex]
[tex]f(\frac{-b}{2a})=f(895.789)=-0.000475(895.789)^2+0.851(895.789)=381.158\approx 381.16[/tex]
The vertex of the downward parabola is the point of maxima. The vertex of the function is (895.79,381.16).
Therefore the bridge is about 381.16 ft. above the river.
Substitute y=0 in the given function, to find the x-intercepts of the function.
[tex]0=-0.000475x^2+0.851x[/tex]
[tex]0=x(-0.000475x+0.851)[/tex]
Using zero product product property,
[tex]x=0[/tex]
[tex]-0.000475x+0.851=0[/tex]
[tex]-0.000475x=-0.851[/tex]
[tex]x=\frac{-0.851}{-0.000475}\approx 1791.58[/tex]
The x-intercepts of the function are 0 and 1791.58.
The time in which the section of bridge above the arch is the difference of x-intercepts because it is an downward parabola.
[tex]1791.58-0=1791.58[/tex]
The time in which the section of bridge above the arch is 1791.58 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.
Therefore the correct option is D.
