SOLUTION: center oA suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road surface. The cables are parabolic in shape and are suspended from t

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Question 169281: center oA suspension bridge has twin towers that are 1300 feet apart. Each tower extends 180 feet above the road surface. 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 cable at a point 200 feet from the f the bridge.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A suspension bridge has twin towers that are 1300 feet apart. Each tower extends
180 feet above the road surface. 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 cable at a point 200 feet
from the from the center of the bridge.
:
Find the equation for this:
Three coordinates:
0, 180; the vertical suspension point on the left
650, 0; the center point that touches the road
1300, 180; vertical suspension point on the right
:
Using: ax^2 + bx + c = y
:
0,180, we know c = 180
:
write equation from coordinates;
(650^2)a + 650b + 180 = 0
and
(1300^2)a + 1300b + 180 = 180
:
422500a + 650b + 180 = 0
1690000a + 1300b + 180 = 180
:
Multiply the 1st equation by 2, subtract from the 2nd equation
1690000a + 1300b + 180 = 180
845000a + 1300b + 360 = 0
------------------------------
845000a - 180 = 180
845000a = 180 + 180
845000a = 360
a = 360%2F845000
a = .000426

find b:
.000426(650^2) + 650b + 180 = 0
180 + 650b = -180
650b = -180 - 180
b = %28-360%29%2F650
b = -.5538
:
The equation; y = .000426x^2 - .5538x + 180
:
Looks something like this:
+graph%28+300%2C+200%2C+-500%2C+1500%2C+-100%2C+500%2C+.000426x%5E2-.5538x%2B180%29+
:
"Find the height of the cable at a point 200 feet
from the from the center of the bridge."
:
200' before the midpoint of 650': x = 450
and
200' after the midpoint of 650': x = 850
:
Substitute these values for x and find y:
y = .000426(450)^2 - .5538(450) + 180
y = 86.265 - 249.21 + 180
y = 17.055 ft
:
You can do the same for x = 850; it is 17.055 ft as you would expect.