SOLUTION: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft apart. If the bridge is tangent to the cables at its center, find the length of one
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-> SOLUTION: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft apart. If the bridge is tangent to the cables at its center, find the length of one
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Question 1186623: The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft apart. If the bridge is tangent to the cables at its center, find the length of one of its vertical support 30 ft from one of the towers. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The cables of a horizontal suspension bridge are supported from two towers 40 ft high and 150 ft apart.
If the bridge is tangent to the cables at its center, find the length of one of its vertical support 30 ft from one of the towers.
:
Write two equations to come up with up with a parabola with minimum at the origin 0,0.
The bridge is the x axis and the cable kisses the bridge at the origin
x=-75, y=40 and x=+75, y= 40
-75^2(a) - 75b = 40
5625a - 75b = 40
and
75^2(a) + 75b = 40
5625a + 75b = 40
Use elimination with these two equations
5625a - 75b = 40
5625a + 75b = 40
-------------------Addition eliminates b, find a
11250a + 0 = 80
a = 80/11250
a = .0071111
:
b cancels so we come up with a simple equation
y = .0071111x^2
looks like this
Green line is the 40 ft height of the towers
:
"find the length of one of its vertical support 30 ft from one of the towers."
75 - 30 = 45 ft and
find y when x=45
y = 0071111(45^2)
y = 14.4 is the height to the cable at x = 45 ft, represented by the blue line
