document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=410027>Question 410027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP  PLEASE!!!!!<BR>\n" );
document.write( "If a stone is tossed from the top of a 170 meter building, the height of the stone as a function of time is given by h(t) = -9.8t^2 – 10t + 170, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288445 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=288445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> simply set h(t) to zero and solve for t:<BR>\n" );
document.write( "h(t) = -9.8t^2 – 10t + 170<BR>\n" );
document.write( "0 = -9.8t^2 – 10t + 170<BR>\n" );
document.write( "0 = 9.8t^2 + 10t - 170<BR>\n" );
document.write( "0 = 4.9t^2 + 5t - 85<BR>\n" );
document.write( "applying the quadratic formula gives you:<BR>\n" );
document.write( "t = {3.69, -4.71}<BR>\n" );
document.write( "we can throw out the negative solution leaving:<BR>\n" );
document.write( "t = 3.69 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of the quadratic follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%2B5t%2B-85+=+0 ALIGN=MIDDLE  ALT=\"4.9t%5E2%2B5t%2B-85+=+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=%285%29%5E2-4%2A4.9%2A-85=1691 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%285%29%5E2-4%2A4.9%2A-85=1691\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1691 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+=+%28-5%2B-sqrt%28+1691+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-5%2B-sqrt%28+1691+%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-%285%29%2Bsqrt%28+1691+%29%29%2F2%5C4.9+=+3.68589493774532 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%285%29%2Bsqrt%28+1691+%29%29%2F2%5C4.9+=+3.68589493774532\"   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-%285%29-sqrt%28+1691+%29%29%2F2%5C4.9+=+-4.70630310101063 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%285%29-sqrt%28+1691+%29%29%2F2%5C4.9+=+-4.70630310101063\"   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%2B5t%2B-85 ALIGN=MIDDLE  ALT=\"4.9t%5E2%2B5t%2B-85\"   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%2B5t%2B-85+=+4.9%28t-3.68589493774532%29%2A%28t--4.70630310101063%29 ALIGN=MIDDLE  ALT=\"4.9t%5E2%2B5t%2B-85+=+4.9%28t-3.68589493774532%29%2A%28t--4.70630310101063%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.68589493774532, -4.70630310101063.\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%2B5%2Ax%2B-85+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4.9%2Ax%5E2%2B5%2Ax%2B-85+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " = 0\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );