Question 1186849
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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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<pre>
An equation of the ellipse is

    {{{x^2/21^2}}} + {{{y2/12^2}}} = 1.


From equation, express

    y = {{{12*sqrt(1-x^2/441)}}}.


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


Therefore, what you need is to calculate this sum


    Sum = {{{12*sqrt(1-14^2/441)}}} + {{{12*sqrt(1-7^2/441)}}} + {{{12*sqrt(1-0^2/441)}}} + {{{12*sqrt(1-14^2/441)}}} + {{{12*sqrt(1-7^2/441)}}}.


The sum is  52.52  meters  (rounded).    <U>ANSWER</U>
</pre>

Solved.