document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80866>Question 80866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, Can anyone help with this word problem? The height h in feet of an object after t seconds is given by the function h = –16t2 + 20t + 5.  How long will it take the object to hit the ground?  Round your answer to the nearest thousandth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58039 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=58039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find when it will hit the ground, set h equal to zero \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16t%5E2+%2B+20t+%2B+5 ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2+%2B+20t+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use the quadratic formula to solve for t\r<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=-16t%5E2%2B20t%2B5+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B20t%2B5+=+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" );
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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=%2820%29%5E2-4%2A-16%2A5=720 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2820%29%5E2-4%2A-16%2A5=720\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=720 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+=+%28-20%2B-sqrt%28+720+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-20%2B-sqrt%28+720+%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=t%5B1%5D+=+%28-%2820%29%2Bsqrt%28+720+%29%29%2F2%5C-16+=+-0.213525491562421 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%2820%29%2Bsqrt%28+720+%29%29%2F2%5C-16+=+-0.213525491562421\"   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-%2820%29-sqrt%28+720+%29%29%2F2%5C-16+=+1.46352549156242 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%2820%29-sqrt%28+720+%29%29%2F2%5C-16+=+1.46352549156242\"   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=-16t%5E2%2B20t%2B5 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B20t%2B5\"   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=-16t%5E2%2B20t%2B5+=+-16%28t--0.213525491562421%29%2A%28t-1.46352549156242%29 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B20t%2B5+=+-16%28t--0.213525491562421%29%2A%28t-1.46352549156242%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.213525491562421, 1.46352549156242.\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+-16%2Ax%5E2%2B20%2Ax%2B5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B20%2Ax%2B5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignoring the negative answer, the answer is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.46352549156242 ALIGN=MIDDLE  ALT=\"t=1.46352549156242\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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