document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332089>Question 332089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a ball is thrown, its height in feet h after t seconds is given by the equation vt-16t^2 where v is the initial upwards velocity in feet per second. If v=35 feet per second, find all values of t for which h=18 feet </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238024 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=238024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a ball is thrown, its height in feet h after t seconds is given by the equation vt-16t^2 where v is the initial upwards velocity in feet per second. If v=35 feet per second, find all values of t for which h=18 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The problem gives us:<BR>\n" );
document.write( "h = vt-16t^2<BR>\n" );
document.write( "and v=35<BR>\n" );
document.write( "h = 35t-16t^2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now, when h=18<BR>\n" );
document.write( "18 = 35t-16t^2<BR>\n" );
document.write( "Solving for t:<BR>\n" );
document.write( "18 = 35t-16t^2<BR>\n" );
document.write( "16t^2+18 = 35t<BR>\n" );
document.write( "16t^2-35t+18 = 0<BR>\n" );
document.write( "Applying the \"quadratic formula\" we find that:<BR>\n" );
document.write( "t = {0.83, 1.36} seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of 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=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%2B-35x%2B18+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-35x%2B18+=+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=%28-35%29%5E2-4%2A16%2A18=73 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-35%29%5E2-4%2A16%2A18=73\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=73 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--35%2B-sqrt%28+73+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--35%2B-sqrt%28+73+%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-%28-35%29%2Bsqrt%28+73+%29%29%2F2%5C16+=+1.36075011704117 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+73+%29%29%2F2%5C16+=+1.36075011704117\"   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-%28-35%29-sqrt%28+73+%29%29%2F2%5C16+=+0.826749882958827 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-35%29-sqrt%28+73+%29%29%2F2%5C16+=+0.826749882958827\"   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%2B-35x%2B18 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-35x%2B18\"   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%2B-35x%2B18+=+16%28x-1.36075011704117%29%2A%28x-0.826749882958827%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-35x%2B18+=+16%28x-1.36075011704117%29%2A%28x-0.826749882958827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.36075011704117, 0.826749882958827.\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%2B-35%2Ax%2B18+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-35%2Ax%2B18+%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" );