document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161256>Question 161256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:\r<BR>\n" );
document.write( "\n" );
document.write( "A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t^2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 175 feet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118848 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=118848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem gives you the equation:<BR>\n" );
document.write( "s = 16t^2 + 32t<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And, it gives you 's', the distance 175 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "175 = 16t^2 + 32t<BR>\n" );
document.write( "0 = 16t^2 + 32t + 175<BR>\n" );
document.write( "Since we can't factor, we must apply the quadratic equation.<BR>\n" );
document.write( "It will produce two numbers:<BR>\n" );
document.write( "t = (2.5, -4.5)<BR>\n" );
document.write( "We can toss out the negative answer (since it doesn't make sense)<BR>\n" );
document.write( "Solution: 2.5 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Below is the quadratic equation solved:<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%2B32x%2B-175+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B32x%2B-175+=+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=%2832%29%5E2-4%2A16%2A-175=12224 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2832%29%5E2-4%2A16%2A-175=12224\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=12224 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+=+%28-32%2B-sqrt%28+12224+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-32%2B-sqrt%28+12224+%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-%2832%29%2Bsqrt%28+12224+%29%29%2F2%5C16+=+2.45506874027131 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+12224+%29%29%2F2%5C16+=+2.45506874027131\"   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-%2832%29-sqrt%28+12224+%29%29%2F2%5C16+=+-4.45506874027131 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2832%29-sqrt%28+12224+%29%29%2F2%5C16+=+-4.45506874027131\"   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%2B32x%2B-175 ALIGN=MIDDLE  ALT=\"16x%5E2%2B32x%2B-175\"   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%2B32x%2B-175+=+16%28x-2.45506874027131%29%2A%28x--4.45506874027131%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B32x%2B-175+=+16%28x-2.45506874027131%29%2A%28x--4.45506874027131%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.45506874027131, -4.45506874027131.\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%2B32%2Ax%2B-175+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B32%2Ax%2B-175+%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" );