document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=914483>Question 914483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need help solving this math word problem please.\r<BR>\n" );
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document.write( "The average number of vehicles waiting in line to enter a sports arena parking lot is modeled by the function w(x)=x^2/2(1-x), where x is a number between 0 and 1 and known as the traffic intensity. Find the average number of vehicles waiting if the traffic intensity is 0.63.\r<BR>\n" );
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document.write( "According to my professor, the answer is: 0.54 -average number of vehicles waiting (rounded to nearest hundreth)\r<BR>\n" );
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document.write( "Would you please show me the steps on how my professor got this answer please. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555148 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By w(x)=x^2/2(1-x), your professor must mean w(x)=x^2/[2(1-x)]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F2%281-x%29 ALIGN=MIDDLE  ALT=\"x%5E2%2F2%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "where the 2 and the (1-x) are both in the denominator.<BR>\n" );
document.write( "It is not be the same as w(x)=x^2/2*(1-x)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F2%29%281-x%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F2%29%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.63 ALIGN=MIDDLE  ALT=\"x=0.63\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%280.63%29=0.63%5E2%2F2%281-0.63%29=0.3969%2F%282%2A0.37%29=0.3969%2F0.74=%220.536351352352351...%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "NOTES:\r<BR>\n" );
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document.write( "That long horizontal line/fraction bar in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28x%29=x%5E2%2F2%281-x%29 ALIGN=MIDDLE  ALT=\"w%28x%29=x%5E2%2F2%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a grouping symbol, just like the parentheses.\r<BR>\n" );
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document.write( "If I had to write that in one line, I would write<BR>\n" );
document.write( "w(x)=x^2/[2(1-x)], or w(x)=x^2/2/(1-x), to make it perfectly clear that both, x and (1-x) are dividing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "You have to be careful about those \"undercover grouping symbols\" when entering calculations into a calculator.<BR>\n" );
document.write( "Doing calculations one at a time as I showed above may be safer.<BR>\n" );
document.write( "To enter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%280.63%29=0.63%5E2%2F2%281-0.63%29 ALIGN=MIDDLE  ALT=\"w%280.63%29=0.63%5E2%2F2%281-0.63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into a calculator as one calculation I would enter<BR>\n" );
document.write( "0.63 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%2F%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%2F%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 2 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28X%29 ALIGN=MIDDLE  ALT=\"highlight%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 1 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22-%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22-%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 0.63 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22=%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22=%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "0.63 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%2F%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%2F%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 2 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%2F%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%2F%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 1 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22-%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22-%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 0.63 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22=%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22=%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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