document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=344463>Question 344463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a toy rocket is launched from a 2.1 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= -4.9t^2 + 14.0t + 2.1. How long will it take for the rocket to hit the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246414 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=246414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set h to zero and solve for t:<BR>\n" );
document.write( "h= -4.9t^2 + 14.0t + 2.1<BR>\n" );
document.write( "0= -4.9t^2 + 14.0t + 2.1<BR>\n" );
document.write( "Apply quadratic formula to get:<BR>\n" );
document.write( "t = {-0.143, 3}<BR>\n" );
document.write( "You can toss out the negative solution leaving:<BR>\n" );
document.write( "t = 3 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic to follow:<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=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9t%5E2%2B14t%2B2.1+=+0 ALIGN=MIDDLE  ALT=\"-4.9t%5E2%2B14t%2B2.1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
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=%2814%29%5E2-4%2A-4.9%2A2.1=237.16 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2814%29%5E2-4%2A-4.9%2A2.1=237.16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=237.16 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+=+%28-14%2B-sqrt%28+237.16+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-14%2B-sqrt%28+237.16+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+%28-%2814%29%2Bsqrt%28+237.16+%29%29%2F2%5C-4.9+=+-0.142857142857143 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%2814%29%2Bsqrt%28+237.16+%29%29%2F2%5C-4.9+=+-0.142857142857143\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+%28-%2814%29-sqrt%28+237.16+%29%29%2F2%5C-4.9+=+3 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%2814%29-sqrt%28+237.16+%29%29%2F2%5C-4.9+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9t%5E2%2B14t%2B2.1 ALIGN=MIDDLE  ALT=\"-4.9t%5E2%2B14t%2B2.1\"   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=-4.9t%5E2%2B14t%2B2.1+=+-4.9%28t--0.142857142857143%29%2A%28t-3%29 ALIGN=MIDDLE  ALT=\"-4.9t%5E2%2B14t%2B2.1+=+-4.9%28t--0.142857142857143%29%2A%28t-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.142857142857143, 3.\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+-4.9%2Ax%5E2%2B14%2Ax%2B2.1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B14%2Ax%2B2.1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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