A concrete bridge over a river has an underside in the shape of a parabolic arch. At the water level, the arch is 30 m wide. It has a maximum height of 10 m. the minimum vertical thickness of the concrete is 1.5 m.
a)Find an algebraic relation that represents the shape of the arch.
b)What is the vertical thickness of the concrete 3 m from the centre of the arch?
c)If the water level rises 2 m, how wide will the arch be at this new level?
15:))a question about math
2009-06-23 3:46 pm
回答 (1)
2009-06-23 6:57 pm
✔ 最佳答案
a) Let the vertical bisector of the parabolic arch be the y-axis and let the water level be the x-axis.Then, the algebraic relation that represents the shape of the arch is
y = 10 - (2/45) x^2
b) At x = 3 or -3, y = 10 - (2/45) (9) = 9.6(m)
The vertical thickness of the concrete = 10 + 1.5 - 9.6 = 1.9(m)
c) At y = 2, 2 = 10 - (2/45) x^2 ==> x = 6*sqrt(5) or - 6*sqrt(5)
So, the new width of the arch = 6*sqrt(5) - [- 6*sqrt(5)] = 12*sqrt(5)
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