document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121556>Question 121556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. May I have some help with the following problem?\r<BR>\n" );
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document.write( "For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the following formula, where d is measured in feet. Kerry wants her stopping distance not to exceed d = 400 ft. At what range of speeds can she travel?\r<BR>\n" );
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document.write( "d=v+(v^2)/20  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89225 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First thing is to realize what 'not to exceed' means.  More than 400 feet exceeds 400 feet, but exactly 400 feet or anything less does not.  So you want to determine v such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%3C=400 ALIGN=MIDDLE  ALT=\"d%3C=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=v%2B%28v%5E2%29%2F20 ALIGN=MIDDLE  ALT=\"d=v%2B%28v%5E2%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the given model.  This is a reasonably good model presuming you have a better than average reaction time, dry pavement, new tires, etc.  Be that as it may, you need to determine v such that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%2B%28v%5E2%29%2F20%3C=400 ALIGN=MIDDLE  ALT=\"v%2B%28v%5E2%29%2F20%3C=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by 20\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20v+%2B+v%5E2%3C=8000 ALIGN=MIDDLE  ALT=\"20v+%2B+v%5E2%3C=8000\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (Since you multiplied by a positive number, the sense of the inequality remains the same)\r<BR>\n" );
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document.write( "Add -8000 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5E2%2B20v-8000%3C=0 ALIGN=MIDDLE  ALT=\"v%5E2%2B20v-8000%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28v-80%29%28v%2B100%29%3C=0 ALIGN=MIDDLE  ALT=\"%28v-80%29%28v%2B100%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%3C=80 ALIGN=MIDDLE  ALT=\"v%3C=80\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%3C=-100 ALIGN=MIDDLE  ALT=\"v%3C=-100\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100%3C80 ALIGN=MIDDLE  ALT=\"-100%3C80\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can exclude this root as redundant.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=80+%2B+%2880%5E2%29%2F20=80%2B320=400 ALIGN=MIDDLE  ALT=\"d=80+%2B+%2880%5E2%29%2F20=80%2B320=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2B%2890%5E2%29%2F20=495%3E400 ALIGN=MIDDLE  ALT=\"90%2B%2890%5E2%29%2F20=495%3E400\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2B%2870%5E2%29%2F20=315%3C400 ALIGN=MIDDLE  ALT=\"70%2B%2870%5E2%29%2F20=315%3C400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Answer checks.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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