document.write( "Question 1185272: A school is building a new track for cycling teams. The track is to be elliptical,
\n" ); document.write( "with the ratio between the lengths of the major and minor axes to be 4:3. If the available
\n" ); document.write( "land is 200 yd long and 100 yd wide, what are the maximum lengths of the axes? Sketch
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Algebra.Com's Answer #816079 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "A school is building a new track for cycling teams. The track is to be elliptical,
\n" ); document.write( "with the ratio between the lengths of the major and minor axes to be 4:3. If the available
\n" ); document.write( "land is 200 yd long and 100 yd wide, what are the maximum lengths of the axes? Sketch
\n" ); document.write( "a graph of the track and indicate the location of the foci.
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document.write( "Let  \"a\"  be the major semi-axis of the ellipse;  \"b\"  be the minor semi-axis.\r\n" );
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document.write( "From the condition, we have \r\n" );
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document.write( "   a = 4x;  b = 3x,   where x is the common factor\r\n" );
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document.write( "   4x <= 100 yards    (one half of 200 yards);    (1)\r\n" );
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document.write( "   3x <=  50 yards    (one half of 100 yards).    (2)\r\n" );
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document.write( "From restrictions (1) and (2)\r\n" );
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document.write( "   \r\n" );
document.write( "    x <= 25  yards;  \r\n" );
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document.write( "    x <= 16  yards.\r\n" );
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document.write( "According to the meaning of the variables, we must take the minimum value of (3) and (4) for  x;  so, we take\r\n" );
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document.write( "    x = 16   yards.\r\n" );
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document.write( "Thus  a = 4x = 64  = 66  yards.\r\n" );
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document.write( "      b = 3x = 50 yards.\r\n" );
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document.write( "The distance from the center of the ellipse to the foci is\r\n" );
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document.write( "     c =  =  = 44.095 yards.\r\n" );
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