document.write( "Question 771842: how high is a semi elliptical arch of height 20 ft. and span 80 feet at a distance of 15 ft from the end? \n" ); document.write( "

Algebra.Com's Answer #471031 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "To make it easy, let's change feet to \"dekafeet\".\r\n" );
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document.write( "1 dekafoot = 10 feet, the length of one of those measuring chains\r\n" );
document.write( "used at a football game to see if a first down was made.  So 1\r\n" );
document.write( "of those chains is 1 dekafoot long. \r\n" );
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document.write( "So the problem is:\r\n" );
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document.write( "how high is a semi elliptical arch of height 2 dekafeet. and span \r\n" );
document.write( "8 dekafeet at a distance of 1.5 dekafeet from the end?  So we'll \r\n" );
document.write( "draw the arch:\r\n" );
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document.write( "We'll let 4 of the 8 dekafeet be on the left of the origin, and 4 on\r\n" );
document.write( "the right, making the vertices (-4,0) and (4,0)\r\n" );
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document.write( "The whole ellipse looks like this:\r\n" );
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document.write( "Since a=4 and b=2, the equation\r\n" );
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document.write( "  1\r\n" );
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document.write( "  1\r\n" );
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document.write( "  1\r\n" );
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document.write( "Let's solve for y, so we can find the height 1.5 dekafeet\r\n" );
document.write( "from the the end.\r\n" );
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document.write( "Clear of fractions by multiplying every term by 16\r\n" );
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document.write( "x² + 4y² = 16\r\n" );
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document.write( "     4y² = 16 - x²\r\n" );
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document.write( "      y² = \r\n" );
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document.write( "       y = \r\n" );
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document.write( "The + is the arch, the - is the dotted line lower part, below\r\n" );
document.write( "the ground.\r\n" );
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document.write( "1.5 dekafeet from the right end is 4-1.5 = 2.5 dekafeet from the\r\n" );
document.write( "origin, see the green line\r\n" );
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document.write( "  \r\n" );
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document.write( "So we substitute x=2.5in\r\n" );
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document.write( "       y = \r\n" );
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document.write( "       y = \r\n" );
document.write( "      \r\n" );
document.write( "       y =  = 1.5612495 dekafeet.\r\n" );
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document.write( "So the answer in feet is 15.612495.\r\n" );
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document.write( "Edwin

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