document.write( "Question 77349: A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 28 feet from the center is to be 6 feet. Find the height of the arch at its center. \n" ); document.write( "
Algebra.Com's Answer #55482 by stanbon(75887)\"\" \"About 
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A bridge is built in the shape of a semielliptical arch. It has a span of 94 feet. The height of the arch 28 feet from the center is to be 6 feet. Find the height of the arch at its center.
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\n" ); document.write( "Draw the picture putting the width of 94 on the x-axis centered
\n" ); document.write( "at the origin.
\n" ); document.write( "The vertices are then (-47,0) and (47,0)------
\n" ); document.write( "Then x^2/47^2 + y^2/b^2 = 1
\n" ); document.write( "The ellipse passes thru the point (28,6)
\n" ); document.write( "Substitute those values in the equation to solve for \"b\".
\n" ); document.write( "--------
\n" ); document.write( "28^2/47^2 + 6^2/b^2 = 1
\n" ); document.write( "0.3549117248 + 36/b^2 = 1
\n" ); document.write( "36/b^2 = 0.6450882752..
\n" ); document.write( "b^2/36=1.550175439
\n" ); document.write( "b^2=55.806
\n" ); document.write( "------
\n" ); document.write( "At the center the height is b=7.47 feet
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\n" ); document.write( "EQUATION of the ellipse
\n" ); document.write( "x^2/47^2 + y^2/55.806 = 1\r
\n" ); document.write( "\n" ); document.write( "==========
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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