document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=599432>Question 599432</A>: <I><SPAN STYLE=\"word-break: break-all;\">  If a stone is thrown upward from a height of 8.25 feet with an initial velocity of 64 feet per second, how long does it take for the stone to fall to the ground?  Give answer to the nearest one-hundredth. (Formulas:   ; where h represents final height,   is initial velocity, t is time and   is the initial height) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378955 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=378955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a stone is thrown upward from a height of 8.25 feet with an initial velocity of 64 feet per second, how long does it take for the stone to fall to the ground? Give answer to the nearest one-hundredth. (Formulas: ; where h represents final height, is initial velocity, t is time and is the initial height)<BR>\n" );
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document.write( "General formula:<BR>\n" );
document.write( "h(t) = -32t^2 + vt + Ho<BR>\n" );
document.write( "where<BR>\n" );
document.write( "h(t) is height at time t<BR>\n" );
document.write( "t is time (secs)<BR>\n" );
document.write( "v is initial velocity<BR>\n" );
document.write( "Ho is the initial height<BR>\n" );
document.write( ".<BR>\n" );
document.write( "From stated problem, then, we have:<BR>\n" );
document.write( "h(t) = -32t^2 + 64t + 8.25  (formula)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "how long does it take for the stone to fall to the ground?<BR>\n" );
document.write( "set h(t) to zero and solve for t:<BR>\n" );
document.write( "h(t) = -32t^2 + 64t + 8.25<BR>\n" );
document.write( "0 = -32t^2 + 64t + 8.25<BR>\n" );
document.write( "applying the quadratic formula, we get<BR>\n" );
document.write( "t = {-0.12, 2.12}<BR>\n" );
document.write( "we can throw out the negative solution (extraneous) leaving:<BR>\n" );
document.write( "t = 2.12 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic to follow:<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=-32x%5E2%2B64x%2B8.25+=+0 ALIGN=MIDDLE  ALT=\"-32x%5E2%2B64x%2B8.25+=+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=%2864%29%5E2-4%2A-32%2A8.25=5152 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2864%29%5E2-4%2A-32%2A8.25=5152\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5152 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+=+%28-64%2B-sqrt%28+5152+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-64%2B-sqrt%28+5152+%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-%2864%29%2Bsqrt%28+5152+%29%29%2F2%5C-32+=+-0.121522402807898 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2864%29%2Bsqrt%28+5152+%29%29%2F2%5C-32+=+-0.121522402807898\"   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-%2864%29-sqrt%28+5152+%29%29%2F2%5C-32+=+2.1215224028079 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2864%29-sqrt%28+5152+%29%29%2F2%5C-32+=+2.1215224028079\"   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=-32x%5E2%2B64x%2B8.25 ALIGN=MIDDLE  ALT=\"-32x%5E2%2B64x%2B8.25\"   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=-32x%5E2%2B64x%2B8.25+=+-32%28x--0.121522402807898%29%2A%28x-2.1215224028079%29 ALIGN=MIDDLE  ALT=\"-32x%5E2%2B64x%2B8.25+=+-32%28x--0.121522402807898%29%2A%28x-2.1215224028079%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.121522402807898, 2.1215224028079.\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+-32%2Ax%5E2%2B64%2Ax%2B8.25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-32%2Ax%5E2%2B64%2Ax%2B8.25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );