document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130410>Question 1130410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a stopper is removed from the bottom of a barrel filled with water, the depth d, in centimeters, of a liquid in the barrel can be approximated by d=0.039t^2-5.816t+200, where t is the time since stopper was removed from the hole. When will the depth be 125 cm? Round to the nearest tenth of a second. <BR>\n" );
document.write( "So far I have:<BR>\n" );
document.write( "125=0.039t^2-5.816t+200 then I subtracted 125 from both sides so the equation is equal to 0 which will make it 0=0.039t^2-5.816t+75 I know I need to factor it but I'm not sure how to go about that. Please help. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747069 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a stopper is removed from the bottom of a barrel filled with water, the depth d, in centimeters, of a liquid in the barrel can be approximated by d=0.039t^2-5.816t+200, where t is the time since stopper was removed from the hole. When will the depth be 125 cm? Round to the nearest tenth of a second. <BR>\n" );
document.write( "So far I have:<BR>\n" );
document.write( "125=0.039t^2-5.816t+200 then I subtracted 125 from both sides so the equation is equal to 0 which will make it 0=0.039t^2-5.816t+75 I know I need to factor it but I'm not sure how to go about that. <BR>\n" );
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document.write( "0.039t^2-5.816t+75 = 0<BR>\n" );
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document.write( "It might be factorable, might not.<BR>\n" );
document.write( "Use the quadratic equation:<BR>\n" );
document.write( "---<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=0.039x%5E2%2B-5.816x%2B75+=+0 ALIGN=MIDDLE  ALT=\"0.039x%5E2%2B-5.816x%2B75+=+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=%28-5.816%29%5E2-4%2A0.039%2A75=22.125856 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-5.816%29%5E2-4%2A0.039%2A75=22.125856\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=22.125856 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--5.816%2B-sqrt%28+22.125856+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--5.816%2B-sqrt%28+22.125856+%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-%28-5.816%29%2Bsqrt%28+22.125856+%29%29%2F2%5C0.039+=+134.869396428846 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-5.816%29%2Bsqrt%28+22.125856+%29%29%2F2%5C0.039+=+134.869396428846\"   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-%28-5.816%29-sqrt%28+22.125856+%29%29%2F2%5C0.039+=+14.258808699359 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-5.816%29-sqrt%28+22.125856+%29%29%2F2%5C0.039+=+14.258808699359\"   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=0.039x%5E2%2B-5.816x%2B75 ALIGN=MIDDLE  ALT=\"0.039x%5E2%2B-5.816x%2B75\"   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=0.039x%5E2%2B-5.816x%2B75+=+%28x-134.869396428846%29%2A%28x-14.258808699359%29 ALIGN=MIDDLE  ALT=\"0.039x%5E2%2B-5.816x%2B75+=+%28x-134.869396428846%29%2A%28x-14.258808699359%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 134.869396428846, 14.258808699359.\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+0.039%2Ax%5E2%2B-5.816%2Ax%2B75+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.039%2Ax%5E2%2B-5.816%2Ax%2B75+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "It cannot be factored, but there's another problem.<BR>\n" );
document.write( "It's a parabola that opens upward, giving 2 solutions for t.<BR>\n" );
document.write( "Check your equation for d.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );