document.write( "Question 1089467: hi! I'm not sure how to do this word problem of a parabola. The question is: An arch is the shape of a parabola. If an arch is 200 feet high and 80 feet wide, how tall is the arch at 20 feet away from the center. Thank you! \n" ); document.write( "

Algebra.Com's Answer #703812 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "For simplicity, let assume that the origin of the coordinate system is placed on the ground EXACTLY at the symmetry line of the parabola.\r\n" );
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document.write( "Then the equation of the parabola in this coordinate system is \r\n" );
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document.write( "y = a*(x+40)*(x-40) =  = ,\r\n" );
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document.write( "where 40 is half the distance between the arc's foots, and \"a\" is some unknown coefficient.\r\n" );
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document.write( "You need to choose the value of \"a\" in a way to provide its arc height 200 ft at x = 0. So, your equation for \"a\" is\r\n" );
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document.write( "200 =  = -a*1600,\r\n" );
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document.write( "which gives you  a =  = .\r\n" );
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document.write( "Thus your parabola is  y = .     (1)\r\n" );
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document.write( "Now to find the height at x = 20 ft, you need simply substitute x= 20 into the formula (1).  You will get\r\n" );
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document.write( "    The height of the arc at x= 20  is  y =  =  =  = 100 ft.\r\n" );
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document.write( "Answer.  The height of the arc at x= 20  is  100 ft.\r\n" );
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