SOLUTION: A railroad crosses a highway over an arch a cross section of which is an semi-ellipse 42 meters long and 12 meters high. there are vertical supports at interval of 7 meters.find th

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Question 1186849: A railroad crosses a highway over an arch a cross section of which is an semi-ellipse 42 meters long and 12 meters high. there are vertical supports at interval of 7 meters.find the heights and supports.

Answer by ikleyn(52798) About Me  (Show Source):
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A railroad crosses a highway over an arch a cross section of which is an semi-ellipse 42 meters long
and 12 meters high. there are vertical supports at interval of 7 meters. find the heights and supports.
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An equation of the ellipse is

    x%5E2%2F21%5E2 + y2%2F12%5E2 = 1.


From equation, express

    y = 12%2Asqrt%281-x%5E2%2F441%29.


The supports are at x = -14, -7, 0, 7, 14.


Therefore, what you need is to calculate this sum


    Sum = 12%2Asqrt%281-14%5E2%2F441%29 + 12%2Asqrt%281-7%5E2%2F441%29 + 12%2Asqrt%281-0%5E2%2F441%29 + 12%2Asqrt%281-14%5E2%2F441%29 + 12%2Asqrt%281-7%5E2%2F441%29.


The sum is  52.52  meters  (rounded).    ANSWER

Solved.