document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=721213>Question 721213</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 functions M(x) =19x-x^2.What rainfall produces the maximum number of mosquitoes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #442277 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=442277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> M(x) =19x-x^2<BR>\n" );
document.write( "since the coefficient associated with the x^2 is NEGATIVE we know it is a parabola that opens downwards.  Therefore, the vertex is the maximum.<BR>\n" );
document.write( "x-value of vertex:<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -19/(2(-1))<BR>\n" );
document.write( "x = -19/(-2)<BR>\n" );
document.write( "x = 9.5 inches (answer) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );