document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166463>Question 166463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The speed of a car was tracked by radar in a police helicopter over a period of 10 minutes. The police found that the car's speed could be represented by the equation: s = 3t squared - 30t + 135 <BR>\n" );
document.write( "where s is the speed of the car in kilometers per hour after t minutes have passed.<BR>\n" );
document.write( "a. When was the car travelling at 80km/h?<BR>\n" );
document.write( "b. When was the car travelling at 120km/h? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122693 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=122693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first part to get you started\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+3t%5E2+-+30t+%2B+135 ALIGN=MIDDLE  ALT=\"s+=+3t%5E2+-+30t+%2B+135\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80+=+3t%5E2+-+30t+%2B+135 ALIGN=MIDDLE  ALT=\"80+=+3t%5E2+-+30t+%2B+135\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=80 ALIGN=MIDDLE  ALT=\"s=80\"   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=0+=+3t%5E2+-+30t+%2B+135-80 ALIGN=MIDDLE  ALT=\"0+=+3t%5E2+-+30t+%2B+135-80\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 80 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+3t%5E2+-+30t+%2B+55 ALIGN=MIDDLE  ALT=\"0+=+3t%5E2+-+30t+%2B+55\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-30 ALIGN=MIDDLE  ALT=\"b=-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=55 ALIGN=MIDDLE  ALT=\"c=55\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%283%29%2855%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%28-30%29+%2B-+sqrt%28+%28-30%29%5E2-4%283%29%2855%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-30 ALIGN=MIDDLE  ALT=\"b=-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=55 ALIGN=MIDDLE  ALT=\"c=55\"   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=t+=+%2830+%2B-+sqrt%28+%28-30%29%5E2-4%283%29%2855%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2830+%2B-+sqrt%28+%28-30%29%5E2-4%283%29%2855%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30 ALIGN=MIDDLE  ALT=\"-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   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=t+=+%2830+%2B-+sqrt%28+900-4%283%29%2855%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2830+%2B-+sqrt%28+900-4%283%29%2855%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-30 ALIGN=MIDDLE  ALT=\"-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900 ALIGN=MIDDLE  ALT=\"900\"   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=t+=+%2830+%2B-+sqrt%28+900-660+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2830+%2B-+sqrt%28+900-660+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%283%29%2855%29 ALIGN=MIDDLE  ALT=\"4%283%29%2855%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=660 ALIGN=MIDDLE  ALT=\"660\"   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=t+=+%2830+%2B-+sqrt%28+240+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2830+%2B-+sqrt%28+240+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=660 ALIGN=MIDDLE  ALT=\"660\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900 ALIGN=MIDDLE  ALT=\"900\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240 ALIGN=MIDDLE  ALT=\"240\"   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=t+=+%2830+%2B-+sqrt%28+240+%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"t+=+%2830+%2B-+sqrt%28+240+%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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=t+=+%2830+%2B-+4%2Asqrt%2815%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"t+=+%2830+%2B-+4%2Asqrt%2815%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2830%2B4%2Asqrt%2815%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"t+=+%2830%2B4%2Asqrt%2815%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2830-4%2Asqrt%2815%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"t+=+%2830-4%2Asqrt%2815%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2830%2B4%2Asqrt%2815%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"t+=+%2830%2B4%2Asqrt%2815%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2830-4%2Asqrt%2815%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"t+=+%2830-4%2Asqrt%2815%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=7.582 ALIGN=MIDDLE  ALT=\"t=7.582\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.418 ALIGN=MIDDLE  ALT=\"t=2.418\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the this means that at 2.418 seconds or at 7.582 seconds, the car was traveling at 80 km/h </SPAN>\n" );
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