SOLUTION: The cable of a substanded deck bridge are in the shape of parabola. The pillars supporting the cables are 182.9 meters apart and rise 27.4 meters above the road. The lowest height

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The cable of a substanded deck bridge are in the shape of parabola. The pillars supporting the cables are 182.9 meters apart and rise 27.4 meters above the road. The lowest height       Log On


   

Question 1190089: The cable of a substanded deck bridge are in the shape of parabola. The pillars supporting the cables are 182.9 meters apart and rise 27.4 meters above the road. The lowest height of the cable which is 3.05 meters above the road, is reached half way between the pillars.
What is the height of the cable from the road at a point 45.7 meters ( horizontally) from the center of the bridge?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The cable of a substanded deck bridge are in the shape of parabola.
The pillars supporting the cables are 182.9 meters apart and rise 27.4 meters above the road.
The lowest height of the cable which is 3.05 meters above the road, is reached half way between the pillars.
:
using the form ax^2 +bx + c = y, we will have the parabola centered around 0 so we can ignore the b coefficient.
x = 182.9/2 = 91.45 and c = 3.05, y = 27.4
91.45^2a + 3.05 = 27.4
8363.1025a = 27.4 - 3.05
a = 24.35/8363.1025
a .00291
the equation y =.00291x^2 + 3.05
looks like, green line 27.4 m
+graph%28+300%2C+200%2C+-110%2C+110%2C+-10%2C+50%2C+.00291x%5E2%2B3.05%2C+27.4%29+
:
What is the height of the cable from the road at a point 45.7 meters ( horizontally) from the center of the bridge?
x = 45.7
y = .00291(45.7^2) + 3.05
y = 9.12 meters high at 45.7 meter from the center
graphically, green line is 9.12
+graph%28+300%2C+200%2C+-110%2C+110%2C+-10%2C+50%2C+.00291x%5E2%2B3.05%2C+9.12%29+