document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970145>Question 970145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need some help on the following, any help would be appreciated.\r<BR>\n" );
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document.write( "Finding the intersection of a line and a Parabola\r<BR>\n" );
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document.write( "A certain pump has a characteristic curve described by the right half of a parabola described by the equation \r<BR>\n" );
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document.write( "h(c) = -0.0025.q^2 + 25\r<BR>\n" );
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document.write( "NOTE: The c hangs low but wasn't sure how to type that out so I put it in parenthesis\r<BR>\n" );
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document.write( "where the vertical coordinate, h, is in units of feet, and the horizontal coordinate, q, the flow rate, is in gallons per minute.\r<BR>\n" );
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document.write( "a) In physics terms, what is maximum height of water that can be supported by this pump with zero flow rate?  In mathematical terms, what is the value of h(c) when q = 0?\r<BR>\n" );
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document.write( "b) At what value of q will the value of h(c) = 0?\r<BR>\n" );
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document.write( "-Shun<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 #592803 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C300%2C-5%2C100%2C-5%2C25%2C-0.0025x%5E2+%2B25%29 ALIGN=MIDDLE  ALT=\"graph+%28300%2C300%2C-5%2C100%2C-5%2C25%2C-0.0025x%5E2+%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The graph shows part of the parabola.  \r<BR>\n" );
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document.write( "When q=0, h(c)=25.  <BR>\n" );
document.write( "0=-0.0025q^2 +25\r<BR>\n" );
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document.write( "-25=-00025q^2\r<BR>\n" );
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document.write( "25=0.0025 q^2<BR>\n" );
document.write( "Take positive square root\r<BR>\n" );
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document.write( "5=.05 q\r<BR>\n" );
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document.write( "q=100\r<BR>\n" );
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document.write( "At q=100; q^2=10000; h(c)=0\r<BR>\n" );
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document.write( "The vertex is at (0,25)\r<BR>\n" );
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document.write( "I am not sure if this answers the full question, but the graph gives an idea of what is occurring. </SPAN>\n" );
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