document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=644717>Question 644717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the height, h, of the rocket after t seconds is given by the equation h=-16t^2+120t+30. how long after the rocket is launched will it be 20 feet from 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 #405232 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=405232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the height, h, of the rocket after t seconds is given by the equation h=-16t^2+120t+30. how long after the rocket is launched will it be 20 feet from the ground.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Set h to 20 and solve for t:<BR>\n" );
document.write( "h=-16t^2+120t+30<BR>\n" );
document.write( "20=-16t^2+120t+30<BR>\n" );
document.write( "0=-16t^2+120t+10<BR>\n" );
document.write( "0=-8t^2+60t+5<BR>\n" );
document.write( "0=8t^2-60t-5<BR>\n" );
document.write( "solving for t using the quadratic formula yields:<BR>\n" );
document.write( "t = {7.58, -0.08}<BR>\n" );
document.write( "throw out the negative solution (extraneous) leaving:<BR>\n" );
document.write( "t = 7.58 secs<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic formula 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=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=8x%5E2%2B-60x%2B-5+=+0 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-60x%2B-5+=+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=%28-60%29%5E2-4%2A8%2A-5=3760 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-60%29%5E2-4%2A8%2A-5=3760\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3760 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--60%2B-sqrt%28+3760+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--60%2B-sqrt%28+3760+%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-%28-60%29%2Bsqrt%28+3760+%29%29%2F2%5C8+=+7.58242742918897 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-60%29%2Bsqrt%28+3760+%29%29%2F2%5C8+=+7.58242742918897\"   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-%28-60%29-sqrt%28+3760+%29%29%2F2%5C8+=+-0.0824274291889728 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-60%29-sqrt%28+3760+%29%29%2F2%5C8+=+-0.0824274291889728\"   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=8x%5E2%2B-60x%2B-5 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-60x%2B-5\"   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=8x%5E2%2B-60x%2B-5+=+8%28x-7.58242742918897%29%2A%28x--0.0824274291889728%29 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-60x%2B-5+=+8%28x-7.58242742918897%29%2A%28x--0.0824274291889728%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 7.58242742918897, -0.0824274291889728.\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+8%2Ax%5E2%2B-60%2Ax%2B-5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-60%2Ax%2B-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );