document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168549>Question 168549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the number of mosquitoes M(x)in millions, in a certain area depends on the june rainfall x, in inches, according to the function M(x) =12x-x^2 What rainfall produces the maximum number of mosquitoes\r<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 #124243 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=124243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> looks like m(x) = 12x - x^2 is a quadratic equation which is equivalent to:<BR>\n" );
document.write( "m(x) = -x^2 + 12x + 0<BR>\n" );
document.write( "since this is a quadratic, the max/min point is given by the formula -b/2a.<BR>\n" );
document.write( "standard form of quadratic is:<BR>\n" );
document.write( "ax^2 + bx + c<BR>\n" );
document.write( "in your equation, b = 12, and a = -1.<BR>\n" );
document.write( "-b/2a = -12/-2 = 6.<BR>\n" );
document.write( "max/min point should be when x = 6.<BR>\n" );
document.write( "since the coefficient of x^2 (represented by a in the standard form) is minus, this graph has it's head pointing upwards and it's tails pointing downwards, so x = 6 leads to a maximum point.<BR>\n" );
document.write( "when x = 6, the equation becomes:<BR>\n" );
document.write( "-x^2 + 12x + 0 = -(6)^2 + 12(6) = -36 + 72 = 36.<BR>\n" );
document.write( "the maximum point on the graph is (6,36).<BR>\n" );
document.write( "what this says is that m(6) = 36 which means when the rainfall is 6 inches in june, 36 million mosquitoes are produced, and that is the maximum number of mosquitoes that will be produced in that area.<BR>\n" );
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document.write( "graph of this equation shows up as follows:<BR>\n" );
document.write( "x axis is in inches.<BR>\n" );
document.write( "y axis is in millions of mosquitors.<BR>\n" );
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