document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092324>Question 1092324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, this question is suppose to be solved using systems of equations but I'm not sure how to solve it. <BR>\n" );
document.write( "As part of a fountain display, two jets of water travel from the surface of an upper pool and<BR>\n" );
document.write( "meet at the surface of a lower pool. The paths of the two jets are<BR>\n" );
document.write( "modelled by y=-x^2-4x and y=-3x^2-15x , where x and y are measured in feet. What is<BR>\n" );
document.write( "the vertical height difference, d, of the pools? Round the answer to the nearest hundredth. <BR>\n" );
document.write( "Thank you for your help<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706936 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=706936\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> both of these equations are parabolas that curve downward<BR>\n" );
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document.write( "we want the intersection point/s of the two parabolas<BR>\n" );
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document.write( "-x^2 -4x = -3x^2 -15x<BR>\n" );
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document.write( "2x^2 +11x = 0<BR>\n" );
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document.write( "x^2 +11x/2 = 0<BR>\n" );
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document.write( "complete the square<BR>\n" );
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document.write( "(x +11/4)^2 = 121/16<BR>\n" );
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document.write( "take square root of both sides of =<BR>\n" );
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document.write( "x +11/4 = + or - 11/4<BR>\n" );
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document.write( "x = 0 or x = -11/2<BR>\n" );
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document.write( "we have two intersection points<BR>\n" );
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document.write( "x = 0, y = 0 and x = -11/2, y = -33/4<BR>\n" );
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document.write( "the point (0,0) is where the two jets begin at the upper pool(y = 0 at this time)<BR>\n" );
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document.write( "y = -33/4 is the height of the upper pool above the lower pool where the jets meet<BR>\n" );
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document.write( "33/4 = 8.25<BR>\n" );
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document.write( "the vertical height difference is 8.25 feet<BR>\n" );
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document.write( "here is the graph of the two jets, y = -x^2 -4x(red line), y = -3x^2 -15x(green line)<BR>\n" );
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