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In the figure, a steel wire of a bridge is hanging in the shape of a parabola between two main poles. The two main poles with height of 85m each are 450m apart. The wire is 10m above the ground at the centre of the bridge. If the distances from the wire to A and B are 37m and 58m respectively, find the distance between A and B.
””F.4 quadratic function””
2010-01-07 6:58 am
回答 (2)
2010-01-07 7:31 am
✔ 最佳答案
設拋物線最低點座標為(0 , 10)於是可設拋物線方程為 y = ax^2 + 10
則85 = a(450/2)^2 + 10
a = 1/675
拋物線方程為 y = x^2 / 675 + 10
37 = x^2 / 675 + 10
x = - 135 or 135(rejected) ;
58 = x^2 / 675 + 10
x = 180 or - 180(rejected)
AB = 180 - (-135) = 315m
2010-01-07 7:04 am
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100106000051KK01864