SOLUTION: A suspension bridge with weight uniformly distributed along its length has twin towers that extend 80 meters above the road surface and are 1600 meters apart. The cables are parabo

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Question 1146321: A suspension bridge with weight uniformly distributed along its length has twin towers that extend 80 meters above the road surface and are 1600 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 400 meters from the center.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A suspension bridge with weight uniformly distributed along its length has twin towers that extend 80 meters above the road surface and are 1600 meters apart.
The cables are parabolic in shape and are suspended from the tops of the towers.
The cables touch the road surface at the center of the bridge.
:
Let center of the bridge surface be at the origin
the form ax^2 + bx + c = y (c=0)
the two coordinates are
x=-800, y=80
640000a - 800b + 0 = 80
and
x=+800, y=80
640000a + 800b + 0 = 80
Add these two equations (elimnates b)
1280000a = 160
a = 160/1280000
a = .0001
The equation: y = .0001x^2
Graphically
+graph%28+300%2C+200%2C+-1000%2C+1000%2C+-10%2C+100%2C+.0001x%5E2%2C+80%2C+16%29+
"Find the height of the cables at a point 400 meters from the center."
y = .0001(400^2)
y = 16 meters
:
Green line 80m, blue 16m