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Coordinate geometry 一條,英文好的高手來

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The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between the two towers is 150m, the points of support of the cable are 22m above the roadway, and the lowest point on the cable is 7m above the roadway. Find the vertical distance to... 顯示更多 The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between the two towers is 150m, the points of support of the cable are 22m above the roadway, and the lowest point on the cable is 7m above the roadway. Find the vertical distance to the cable from a point in the roadway 15m from the foot of the tower. 更新: 請問一下爲什麽你數學那麼厲害?有沒有什麽訣竅可以變得這麼神?

最佳解答:

Imposing an xy-coordinate system into the scenario and supposing that one of the towers aligns with the y-axis, then we have: Coordinates of the points of support are: (0, 22) and (150, 22) Lowest point is at (75, 7) Then let the equation of the parabola be y = ax2 + bx + c Sub x = 0, y = 22 and hence c = 22 Sub x = 150, y = 22 and hence 150a + b = 0 ... (1) Sub x = 75, y = 7 and hence: 5625a + 75b + 22 = 7 5625a + 75b = -15 375a + 5b = -1 ... (2) Solving (1) and (2), we have a = 1/375 and b = -2/5 So the equation of parabola is y = x2/375 - 2x/5 + 22 So at a distance of 15 m from the foot of tower along the roadway, sub x = 15, then y = 225/375 - 30/5 + 22 = 16.6 m 2010-05-10 09:11:52 補充： 沒什麼特別的, 只是勤於練習反覆思考. 吾乃平常人, 並無過人之處.

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