In a suspension bridge,the shape of the suspension cables is parabolic.The bridge shown in the figure has towers that are 1000 m apart,and the lowest point of the suspension cables is 200 m below the top of the towers.Find the equation of the parabolic part of the cables,placing the origin of the coordinate system at the lowest point of the cable.
NOTE: This equation is used to find the length of the cable needed in the construction of the bridge.

Question

Quizplus · Accepted Answer

We can use the given information to set up a coordinate system with the origin at the lowest point of the cable. Let (0,0) be this point, and let the towers be located at (-500,200) and (500,200). Since the shape of the cable is parabolic, we know that it can be modeled by an equation of the form y = ax^2. We just need to find the value of a. To do this, we can use the fact that the cable passes through the points (-500,200) and (500,200), which gives us two equations: 200 = a(-500)^2 200 = a(500)^2 Solving for a, we get a = 0.00008. Therefore, the equation of the parabolic part of the cable is y = 0.00008x^2. Multiplying both sides by 1250 (the distance between the towers in meters), we get the equation x² = 1250y, which corresponds to choice C.

In a Suspension Bridge,the Shape of the Suspension Cables Is