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The Brooklyn Bridge in New York City is a suspension bridge that crosses the East River and connects Brooklyn to the island of Manhattan. If the origin is placed at the top of one of the cable suport towers, as shown, the shape of a cable that supports the main span can be modelled by the equation

h=0.0008d^2-0.384d were h metres represents the height and d metres represents the horizontal distance.

a) What is the vertical distance from the top of a support tower to the lowest point on a cable, to the nearest metre?
b)What is the length of the main span?
c) At a horizontal distance of 50m from one end of the cable, how far is the cable below the top of the support towers, to the nearest metre?

h = .0008(d^2-480d)
= .0008(d^2-480d+240^2 - 240^2)
= .0008(d-240)^2 - 46.08
So, the vertex is at (240,-46.08)
That means the drop is 46 m

h = .0008d(d-480)
h=0 at d=0,480
The main span is 480 m

h(50) = .0008*50(-430) = -17.2
The point is 17 m below the top

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