document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=303155>Question 303155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A typical car's stopping distance on dry pavement \"d\" in feet can be approximated by the function    <BR>\n" );
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document.write( "d= 0.034s2(squared)     + 0.56s - 17.11.      Where \"s\" is the speed in miles per hour, of the car before braking.\r<BR>\n" );
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document.write( "A.   How fast is the car going if it requires 100 feet for the car to stop after the brakes are applied?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217311 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=217311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A typical car's stopping distance on dry pavement \"d\" in feet can be approximated by the function\r<BR>\n" );
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document.write( "d= 0.034s2(squared) + 0.56s - 17.11. Where \"s\" is the speed in miles per hour, of the car before braking.\r<BR>\n" );
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document.write( "A. How fast is the car going if it requires 100 feet for the car to stop after the brakes are applied?<BR>\n" );
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document.write( "Replace d with 100 and solve for s:<BR>\n" );
document.write( "d= 0.034s^2 + 0.56s - 17.11<BR>\n" );
document.write( "100= 0.034s^2 + 0.56s - 17.11<BR>\n" );
document.write( "0= 0.034s^2 + 0.56s - 117.11<BR>\n" );
document.write( "Solve using the quadratic formula.  Doing so yields:<BR>\n" );
document.write( "s = {51.0, -67.5}<BR>\n" );
document.write( "Toss out the negative solution -- doesn't make sense.<BR>\n" );
document.write( "so, the car was moving at 51 mph.<BR>\n" );
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document.write( "Details of quadratic formula:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.034x%5E2%2B0.56x%2B-117.11+=+0 ALIGN=MIDDLE  ALT=\"0.034x%5E2%2B0.56x%2B-117.11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
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document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%280.56%29%5E2-4%2A0.034%2A-117.11=16.24056 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%280.56%29%5E2-4%2A0.034%2A-117.11=16.24056\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=16.24056 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-0.56%2B-sqrt%28+16.24056+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-0.56%2B-sqrt%28+16.24056+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%280.56%29%2Bsqrt%28+16.24056+%29%29%2F2%5C0.034+=+51.0287914140646 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%280.56%29%2Bsqrt%28+16.24056+%29%29%2F2%5C0.034+=+51.0287914140646\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%280.56%29-sqrt%28+16.24056+%29%29%2F2%5C0.034+=+-67.4993796493587 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%280.56%29-sqrt%28+16.24056+%29%29%2F2%5C0.034+=+-67.4993796493587\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.034x%5E2%2B0.56x%2B-117.11 ALIGN=MIDDLE  ALT=\"0.034x%5E2%2B0.56x%2B-117.11\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.034x%5E2%2B0.56x%2B-117.11+=+0.034%28x-51.0287914140646%29%2A%28x--67.4993796493587%29 ALIGN=MIDDLE  ALT=\"0.034x%5E2%2B0.56x%2B-117.11+=+0.034%28x-51.0287914140646%29%2A%28x--67.4993796493587%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 51.0287914140646, -67.4993796493587.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.034%2Ax%5E2%2B0.56%2Ax%2B-117.11+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.034%2Ax%5E2%2B0.56%2Ax%2B-117.11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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