document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41055>Question 41055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to understand each step in the procedure to show and explain EACH step in setting up and solving the following application problems. Give answers to the nearest thousandth. <BR>\n" );
document.write( "a. The equation h = -16t^2 - 32t + 320 gives the height of a ball, thrown downward from the top of a 320-ft building with an initial velocity of 32ft/s. Find the time it takes for the ball to reach a height of 64ft. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26474 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h = -16t^2 - 32t + 320<BR>\n" );
document.write( "64 = -16t^2 - 32t + 320<BR>\n" );
document.write( "0 = -t^2 - 2t + 16<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=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=-1t%5E2%2B-2t%2B16+=+0 ALIGN=MIDDLE  ALT=\"-1t%5E2%2B-2t%2B16+=+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=%28-2%29%5E2-4%2A-1%2A16=68 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A-1%2A16=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=68 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--2%2B-sqrt%28+68+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+68+%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-%28-2%29%2Bsqrt%28+68+%29%29%2F2%5C-1+=+-5.12310562561766 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+68+%29%29%2F2%5C-1+=+-5.12310562561766\"   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-%28-2%29-sqrt%28+68+%29%29%2F2%5C-1+=+3.12310562561766 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%28-2%29-sqrt%28+68+%29%29%2F2%5C-1+=+3.12310562561766\"   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=-1t%5E2%2B-2t%2B16 ALIGN=MIDDLE  ALT=\"-1t%5E2%2B-2t%2B16\"   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=-1t%5E2%2B-2t%2B16+=+-1%28t--5.12310562561766%29%2A%28t-3.12310562561766%29 ALIGN=MIDDLE  ALT=\"-1t%5E2%2B-2t%2B16+=+-1%28t--5.12310562561766%29%2A%28t-3.12310562561766%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -5.12310562561766, 3.12310562561766.\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+-1%2Ax%5E2%2B-2%2Ax%2B16+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-2%2Ax%2B16+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "About 3.123 seconds<BR>\n" );
document.write( "Pretty Self-Explanatory </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );