Question 1036410: A railway bridge over a ravine is supported by arches. The function that describes the arches is h(x)= -0.03x square + 2.2056x, where h(x) is the height, in meters, of the arch above the ravine at any distance, x, in metres, from one end of the bridge. A) determine the distance between the bases of the arch. round to the nearest hundredth of a Metre.
B) determine the maximum height of the arch, to the nearest tenth of a metre
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A railway bridge over a ravine is supported by arches.
The function that describes the arches is h(x)= -0.03x square + 2.2056x, where h(x) is the height, in meters, of the arch above the ravine at any distance, x, in metres, from one end of the bridge.
A) determine the distance between the bases of the arch. round to the nearest hundredth of a Metre.
We assume the first base is at the origin, the 2nd base when y = 0
-.03x^2 + 2.2056x = 0
factor out -x
-x(.03x - 2.2056) = 0
.03x = 2.2056
x = 2.2056/.03
x = 73.52 meters is the distance between the braces
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B) determine the maximum height of the arch, to the nearest tenth of a metre
We know that max occurs half the distance between the bases or 36.76
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Find the max height, replace x with 36.76
h(x) = -.03(36.76^2) + 2.2056(36.76)
h(x) = -.03(13.2976) + 81.078
h(x) = -40.539 + 81.078
h(x) = 40.5 meters is the height of the arches
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looks like this
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