document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=372800>Question 372800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of miles, M, that a car can travel on a gallon of gas during a trip depends on the average speed, v, of the car on the trip according to the model M = -.011v^2 + 1.3v.  Find the average speed that will minimize the costs for a trip.  A person wants to take a 1900 mile trip in the car and wants to spend less than $55 for gas.  If gas costs $1.10, how fast can the person drive? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #265578 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=265578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of miles, M, that a car can travel on a gallon of gas during a trip<BR>\n" );
document.write( " depends on the average speed, v, of the car on the trip according to the model<BR>\n" );
document.write( " M = -.011v^2 + 1.3v.<BR>\n" );
document.write( " Find the average speed that will minimize the costs for a trip.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Minimum cost will be at Maximum mpg, which occurs at the axis of symmetry.<BR>\n" );
document.write( "Find the axis of symmetry of the equation M = -.011v^2 + 1.3v<BR>\n" );
document.write( "v = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.3%29%2F%282%2A-.011%29 ALIGN=MIDDLE  ALT=\"%28-1.3%29%2F%282%2A-.011%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "v = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.3%29%2F%28-.022%29 ALIGN=MIDDLE  ALT=\"%28-1.3%29%2F%28-.022%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "v = +59.1 mph gives max mpg (M)<BR>\n" );
document.write( ";<BR>\n" );
document.write( ";<BR>\n" );
document.write( " A person wants to take a 1900 mile trip in the car and wants to spend less than $55 for gas.<BR>\n" );
document.write( " If gas costs $1.10, how fast can the person drive?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Solve for M<BR>\n" );
document.write( "1.10(1900/M) < $55<BR>\n" );
document.write( "Divide both sides by 1.10, results<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1900%2FM ALIGN=MIDDLE  ALT=\"1900%2FM\"   DISABLED_style= \"max-width:90%; height:auto;\" > < 50<BR>\n" );
document.write( "M > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1900%2F50 ALIGN=MIDDLE  ALT=\"1900%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "M > 38 mpg  (More than 38 mpg to spend under $55)<BR>\n" );
document.write( ":\r<BR>\n" );
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document.write( "Find the speed (v) which gives > 38 mpg. Let's use 38.1 mph <BR>\n" );
document.write( "-.011v^2 + 1.3v = 38.1<BR>\n" );
document.write( "-.011v^2 + 1.3v - 38.1 = 0<BR>\n" );
document.write( "Solve this using the quadratic formula, a=-.011; b=1.3; c=-38.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+%28-1.3+%2B-+sqrt%281.3%5E2-4%2A-.011%2A-38.1+%29%29%2F%282%2A-.011%29+ ALIGN=MIDDLE  ALT=\"v+=+%28-1.3+%2B-+sqrt%281.3%5E2-4%2A-.011%2A-38.1+%29%29%2F%282%2A-.011%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "do the math, you will get two solutions of<BR>\n" );
document.write( "53.8 mph and 64.4 mph<BR>\n" );
document.write( "Perhaps we can say if he drives between these two speeds he will spend <$55 </SPAN>\n" );
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