# AP Calc

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The picture to the right shows the Ben Franklin Bridge which stretches across the Delaware River joining Pennsylvania and New Jersey. The center span of the bridge is about 4200 feet long. The suspension cables hang in parabolic arcs from towers 750 feet above the surface of the water. These cables come as close as 220 feet to the water at the center of each span. Use this information to write an equation of the quadratic function expressing the height of the cables from the water as a function of the horizontal distance from the center span. Use the equation to calculate the length of one parabolic cable span.

I have no clue how to get the equation! I can probably get the rest of it on my own! Thanks!

• AP Calc -

let the center of the cable be at (0,220). That becomes the vertex of the parabola, so the equation is

y = ax^2+220
Since y(2100) = 750, that means that

a*2100^2 + 220 = 750
a = 530/2100^2 = 0.00012

So, we now know that the height

y = 0.00012x^2 + 220
Now, we know
y' = 0.00024x

To find the length of one side of the cable, just take

∫[0,2100] √(1+(0.00024x)^2) dx = 2186 ft