document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=13411>Question 13411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with this problem? It looks like Greek to me.\r<BR>\n" );
document.write( "\n" );
document.write( "The numberof parts per million of nitric oxide emissions y from a certain car engine is approximated by the model y=-5.05x^3+3857x-38411.25 (13<or equal to x<or equal to 18), where x is the air-fuel ratio. What air-fuel ratio produces 2400 parts per million of nitric oxide? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #6782 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=6782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WOW!!  What an intimidating problem!\r<BR>\n" );
document.write( "\n" );
document.write( "Let's try to simplify things a little bit.  First of all, you are given an incredibly intimidating formula:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-5.05x%5E3+%2B3857x+-+38411.25 ALIGN=MIDDLE  ALT=\"y=+-5.05x%5E3+%2B3857x+-+38411.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where y is 2400 and x is the unknown that you need to find:  the air-fuel ratio.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute the value of y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2400+=+-5.05x%5E3+%2B+3857x+-+38411.25+ ALIGN=MIDDLE  ALT=\"2400+=+-5.05x%5E3+%2B+3857x+-+38411.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract 2400 from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-5.05x%5E3+%2B+3857x+-+38411.25+-2400+ ALIGN=MIDDLE  ALT=\"0+=+-5.05x%5E3+%2B+3857x+-+38411.25+-2400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-5.05x%5E3+%2B+3857x+-+40811.25+ ALIGN=MIDDLE  ALT=\"+0+=+-5.05x%5E3+%2B+3857x+-+40811.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now you have a really ugly equation to solve, and it looks like a real-life problem, probably one that is not going to come out even--it probably won't factor!  So use a graphing calculator to solve it.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The problem is to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-5.05x%5E3+%2B+3857x+-+40811.25+ ALIGN=MIDDLE  ALT=\"y+=+-5.05x%5E3+%2B+3857x+-+40811.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and find the x intercept(s).  That will be the solution.  Also, in the problem, it says that we are looking for values of x that are between 13 and 18.  The graph should look like this between x = 10 and x= 20 and y between -1000 and 1000:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28+300%2C+300%2C+10%2C+20%2C+-1000%2C+1000%2C+-5.05x%5E3+%2B+3857x+-+40811.25+%29 ALIGN=MIDDLE  ALT=\"graph+%28+300%2C+300%2C+10%2C+20%2C+-1000%2C+1000%2C+-5.05x%5E3+%2B+3857x+-+40811.25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There appear to be two points where the graph crosses the x axis within this interval.  With further calculation it seems that the first point is exact at x= 15.  The second number looks like 17, but it turns out to be approximately 16.89.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Neat problem!!  Where did you get it?? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R^2 at SCC\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );