document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987005>Question 987005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small rock sits on the edge of a tall building. A strong wind blows the rock off the edge. The distance, in feet, between the rock and the ground tseconds after the rock leaves the edge is given by d=&#8722;16t2&#8722;5t+470.<BR>\n" );
document.write( "If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth<BR>\n" );
document.write( "How many seconds after the rock leaves the edge is it 446feet from the ground?How many seconds after the rock leaves the edge does it hit the ground?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #607854 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=607854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2-5t%2B470=d ALIGN=MIDDLE  ALT=\"-16t%5E2-5t%2B470=d\"   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=-16t%5E2-5t%2B470=446 ALIGN=MIDDLE  ALT=\"-16t%5E2-5t%2B470=446\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2-5t%2B24=0 ALIGN=MIDDLE  ALT=\"-16t%5E2-5t%2B24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=-16t%5E2%2B-5t%2B24+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B-5t%2B24+=+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=%28-5%29%5E2-4%2A-16%2A24=1561 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5%29%5E2-4%2A-16%2A24=1561\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1561 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+1561+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5%2B-sqrt%28+1561+%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-%28-5%29%2Bsqrt%28+1561+%29%29%2F2%5C-16+=+-1.39092164157115 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+1561+%29%29%2F2%5C-16+=+-1.39092164157115\"   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-%28-5%29-sqrt%28+1561+%29%29%2F2%5C-16+=+1.07842164157115 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%28-5%29-sqrt%28+1561+%29%29%2F2%5C-16+=+1.07842164157115\"   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=-16t%5E2%2B-5t%2B24 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B-5t%2B24\"   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=-16t%5E2%2B-5t%2B24+=+-16%28t--1.39092164157115%29%2A%28t-1.07842164157115%29 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B-5t%2B24+=+-16%28t--1.39092164157115%29%2A%28t-1.07842164157115%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.39092164157115, 1.07842164157115.\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-5%2Ax%2B24+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B-5%2Ax%2B24+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( "t=1.08 seconds<BR>\n" );
document.write( "ANSWER:The rock is 446 feet from the ground after 1.08 seconds.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Rock hits ground when d-0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2-5t%2B470=0 ALIGN=MIDDLE  ALT=\"-16t%5E2-5t%2B470=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=-16t%5E2%2B-5t%2B470+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B-5t%2B470+=+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=%28-5%29%5E2-4%2A-16%2A470=30105 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5%29%5E2-4%2A-16%2A470=30105\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=30105 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+30105+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5%2B-sqrt%28+30105+%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-%28-5%29%2Bsqrt%28+30105+%29%29%2F2%5C-16+=+-5.57837265284547 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+30105+%29%29%2F2%5C-16+=+-5.57837265284547\"   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-%28-5%29-sqrt%28+30105+%29%29%2F2%5C-16+=+5.26587265284547 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%28-5%29-sqrt%28+30105+%29%29%2F2%5C-16+=+5.26587265284547\"   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=-16t%5E2%2B-5t%2B470 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B-5t%2B470\"   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=-16t%5E2%2B-5t%2B470+=+-16%28t--5.57837265284547%29%2A%28t-5.26587265284547%29 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B-5t%2B470+=+-16%28t--5.57837265284547%29%2A%28t-5.26587265284547%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -5.57837265284547, 5.26587265284547.\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-5%2Ax%2B470+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B-5%2Ax%2B470+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( "t=5.27 seconds<BR>\n" );
document.write( "ANSWER: The rock hits the ground after 5.27 seconds. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );