Answer:
Step-by-step explanation:
Given
span of bridge [tex]L=1270\ ft[/tex]
height of span [tex]h=157\ ft[/tex]
Equation of Parabola
[tex]y=0.00039x^2[/tex]
[tex]|x|<635[/tex] i.e.
[tex]-635<x<635[/tex]
[tex]\frac{dy}{dx}=2\times 0.00039[/tex]
length of Arc[tex]=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}[/tex]
[tex]=\int_{-635}^{635}\sqrt{1+(\frac{dy}{dx})^2}[/tex]
[tex]=\int_{-635}^{635}\sqrt{1+(0.00078x)^2}[/tex]
[tex]=2\times \int_{0}^{635}\sqrt{1+(0.00078x)^2}[/tex]
[tex]=2\times (660.08)[/tex]
[tex]=1320.16\ ft[/tex]