Answer: -1/8 or -0.125
Explanation:
Given that the suspension bridge has twin towers that are 600 meters apart
.Each tower extends 50 meters 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.
So, we need to find the height of the cable at a point 225 meters from the center of the bridge.
The equation of a parabola is of the form: y = a(x - h)² + k where (h, k) is the vertex of the parabola.
To find the equation of the cable, we need to find its vertex and a value of "a".The vertex of the parabola is at the center of the bridge.
The road surface is the x-axis and the vertex is the point (0, 50).
Since the cables touch the road surface at the center of the bridge, the two points on the cable that are on the x-axis are at (-300, 0) and (300, 0).
Using the three points, we can find the equation of the parabola:y = a(x + 300)(x - 300)
Expanding the equation, we get y = a (x² - 90000)
To find "a", we use the fact that the cables extend 50 meters above the road surface at the towers. The y-coordinate of the vertex is 50.
So, substituting (0, 50) into the equation of the parabola, we get: 50 = a(0² - 90000) => a = -1/1800
Substituting "a" into the equation of the parabola, we get:y = -(1/1800)x² + 50
The height of the cable at a point 225 meters from the center of the bridge is: y = -(1/1800)(225)² + 50y = -1/8 meters
The height of the cable at a point 225 meters from the center of the bridge is -1/8 meters or -0.125 meters.