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

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.
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Quizplus · Accepted Answer

Since the shape of suspension cables is parabolic, we can assume that the equation of the cable will be of the form y = ax^2. We can then use the given information about the bridge to find the value of a. Since the lowest point of the cable is 200 m below the top of the towers, the y-intercept of the parabola is -200. Also, since the towers are 1000 m apart, the length of the cable between them is 1000 m. To find the value of a, we substitute the two points (0, -200) and (500, 0) into the equation y = ax^2, since the midpoint between the towers is at x = 500. -200 = a(0)^2 0 = a(500)^2 Solving for a, we get a = -0.0008. Therefore, the equation of the parabolic part of the cables is y = -0.0008x^2 - 200. Multiplying both sides by -1250 gives us the equation in the form given in the answer choices: x ² = 1,250y

In a Suspension Bridge, the Shape of the Suspension Cables