SOLUTION: The cabels of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at the height of 10 feet ,
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Question 582407: The cabels of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at the height of 10 feet ,idway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The cables of a suspension bridge are in the shape of a parabola.
The towers supporting the cable are 400 feet apart and 100 feet high.
If the cables are at the height of 10 feet midway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge?
:
Use the given information to create a quadratic equation to represent this bridge
Using the form: ax^2 + bx + c = y
left side
x=0, y=100, therefore c=100
:
Midway
x=200, y=10
200^2a + 200b + 100 = 10
40000a + 200b = 10 - 100
40000a + 200b = -90
:
right end
x=400, y=100
400^2a + 400b + 100 = 100
160000a + 400b = 0
:
Multiply the midway equation by 2, subtract from the above
160000a + 400b = 0
80000a + 400b = -180
-----------------------subtraction eliminates b, find a
80000a = 180
a = 180/80000
a = .00225
find b
160000(.00225) + 400b = 0
360 + 400b = 0
400b = -360
b = -360/400
b = -.9
:
The equation: y = .00225x^2 - .9x + 100
looks like this
:
"what is the height of the cable at the point 50 feet from the center of the bridge?"
x = 200-50
x = 150
y = .00225(150^2) - .9(150) + 100
y = 15.625 ft above 0
:
x = 200 + 50
x = 250
do the same as we did above
