document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=308557>Question 308557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.\r<BR>\n" );
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document.write( "A. substitute the values into the vertical motion formula h=-16t^2+vt+c.Let h=0.\r<BR>\n" );
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document.write( "B. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched.Round to the nearest tenth of a second. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #220652 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=220652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.<BR>\n" );
document.write( "A. substitute the values into the vertical motion formula h=-16t^2+vt+c.Let h=0.<BR>\n" );
document.write( "h=-16t^2 + 116t + 101<BR>\n" );
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document.write( "B. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched.Round to the nearest tenth of a second.<BR>\n" );
document.write( "0=-16t^2 + 116t + 101<BR>\n" );
document.write( "Applying the quadratic formula yields:<BR>\n" );
document.write( "t = {-0.8, 8.0}<BR>\n" );
document.write( "We can toss out the negative solution leaving:<BR>\n" );
document.write( "t = 8.0 seconds<BR>\n" );
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document.write( "Details of quadratic formula follows:<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=-16x%5E2%2B116x%2B101+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B116x%2B101+=+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=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" );
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=%28116%29%5E2-4%2A-16%2A101=19920 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28116%29%5E2-4%2A-16%2A101=19920\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=19920 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+=+%28-116%2B-sqrt%28+19920+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-116%2B-sqrt%28+19920+%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=x%5B1%5D+=+%28-%28116%29%2Bsqrt%28+19920+%29%29%2F2%5C-16+=+-0.785569691094338 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28116%29%2Bsqrt%28+19920+%29%29%2F2%5C-16+=+-0.785569691094338\"   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-%28116%29-sqrt%28+19920+%29%29%2F2%5C-16+=+8.03556969109434 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28116%29-sqrt%28+19920+%29%29%2F2%5C-16+=+8.03556969109434\"   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=-16x%5E2%2B116x%2B101 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B116x%2B101\"   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=-16x%5E2%2B116x%2B101+=+-16%28x--0.785569691094338%29%2A%28x-8.03556969109434%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B116x%2B101+=+-16%28x--0.785569691094338%29%2A%28x-8.03556969109434%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.785569691094338, 8.03556969109434.\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%2B116%2Ax%2B101+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B116%2Ax%2B101+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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