document.write( "Question 1092324: Hi, this question is suppose to be solved using systems of equations but I'm not sure how to solve it.
\n" ); document.write( "As part of a fountain display, two jets of water travel from the surface of an upper pool and
\n" ); document.write( "meet at the surface of a lower pool. The paths of the two jets are
\n" ); document.write( "modelled by y=-x^2-4x and y=-3x^2-15x , where x and y are measured in feet. What is
\n" ); document.write( "the vertical height difference, d, of the pools? Round the answer to the nearest hundredth.
\n" ); document.write( "Thank you for your help
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Algebra.Com's Answer #706935 by ikleyn(53763) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Plot y = $\"-x%5E2-4x\"$ (red) and y = $\"-3x%5E2-15x\"$ (green)\r
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document.write( "This plot is to illustrate the problem.\r\n" );
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document.write( "You have two jets released from the origin (0,0).\r\n" );
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document.write( "They intersect somewhere. You need to find the intersection point.\r\n" );
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document.write( "For it, since \"y\"-s are equal, you can equate the right sides:\r\n" );
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document.write( "-x^2-4x = -3x^2-15x.\r\n" );
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document.write( "Which implies\r\n" );
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document.write( "2x^2 + 11x = 0  ====>  x*(2x + 11) = 0. ====>\r\n" );
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document.write( "====>  the only interesting root is 2x + 11 = 0,  i.e.  x = .\r\n" );
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document.write( "Then y =  = -8.25.\r\n" );
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document.write( "Answer.  The vertical height difference, d, of the pools is 8.25 ft.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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