Answer:
The length of the bridge is 126.492 feet.
Step-by-step explanation:
Let [tex]h(x) = 40-0.01\cdot x^{2}[/tex], where [tex]x[/tex] is the position from the middle of the bridge, measured in feet, and [tex]h(x)[/tex] is the height of the bridge at a location of x feet, measured in feet. In this case, the length of the bridge is represented by the distance between the x-intercepts of the parabola, which we now find by factorization:
[tex]40-0.01\cdot x^{2} = 0[/tex] (Eq. 1)
[tex]x^{2} = \frac{40}{0.01}[/tex]
[tex]x =\pm \sqrt{\frac{40}{0.01} }[/tex]
[tex]x = \pm 63.246\,ft[/tex]
Given that the parabola is symmetrical with respect to y-axis, then the length is two times the magnitude of the value found above, that is:
[tex]l = 2\cdot (63.246\,ft)[/tex]
[tex]l = 126.492\,ft[/tex]
The length of the bridge is 126.492 feet.
