SOLUTION: the towers of a parabolic suspension bridges 200 meter long are 40 meter high. If the lowest point of the cable is 10 meter above the roadway.find the: a) standard equation of the

Question 1165726: the towers of a parabolic suspension bridges 200 meter long are 40 meter high. If the lowest point of the cable is 10 meter above the roadway.find the:
a) standard equation of the parabola
b) vertical distance from the roadway to the cable at 50 meter from the center.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the towers of a parabolic suspension bridges 200 meter long are 40 meter high. If the lowest point of the cable is 10 meter above the roadway.
find the:
a) standard equation of the parabola
let the center of the bridge be at the origin 0,0 then when x=0 and y=10
using the form ax^2 + bx + c = y, we know c=10
x=-100, y=200
10000a - 100b + 10 = 200
and
x=100, y=200
10000a, + 100b + 10 = 200
use elimination with these two equations
10000a - 100b + 10 = 200
10000a + 100b + 10 = 200
----------------------------Addition eliminates b, find a
20000a + 20 = 400
20000a = 400 - 20
20000a = 380
a = 380/20000
a = .019
therefore our equation is simple (b=0)
y = .019x^2 + 10

green line is 200 meters
:
b) vertical distance from the roadway to the cable at 50 meter from the center.
x = 50
y = .019(50)^2 + 10
y = 57.5 vertical dist at 50 meters (blue line)
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