SOLUTION: The towers supporting the cable of suspension bridge are 1200m apart and 170m above the bridge it supports.Suppose the cable hangs,following the shape of parabola,with its lowest p

Question 1042719: The towers supporting the cable of suspension bridge are 1200m apart and 170m above the bridge it supports.Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.How high is the cable 120m away from a tower? Sketch the graph.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The towers supporting the cable of suspension bridge are 1200m apart and 170m above the bridge it supports.
Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.
How high is the cable 120m away from a tower? Sketch the graph.
:
lets have the bridged centered at the origin
Three points are needed on the parabola
x = 0, y = 20
x = -600, y = 170
x = +600, y = 170
using the form ax^2 + bx + c = y, we know that c=20
x=-600, y = 170 and x =+600, y = 170; write two equations
-600^2a - 600b + 20 = 170
+600^2a + 600 + 20 = 170
use elimination
360000a - 600b + 20 = 170
360000a + 600b + 20 = 170
------------------------------addition eliminates b
720000a + 40 = 340
720000a = 300
a = 300/720000
a = .0004167
Now we can write the equation
y = .0004167x^2 + 20
Graphically

:
"How high is the cable 120m away from a tower? "
600 - 120 = 480
Solve for x=480
y = .0004167(480^2) + 20
y = 96 + 20
y = 116 m high (blue line)
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