document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189307>Question 189307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you please help me with this equation???\r<BR>\n" );
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document.write( "For problems 11 through 13, a projectile is fired upward with an initial speed of 800 feet per second. It is given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h=-16t%5E2%2B800t+ ALIGN=MIDDLE  ALT=\"+h=-16t%5E2%2B800t+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (h is the height of the ball).\r<BR>\n" );
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document.write( " What will you set h equal to in the equation to find how many seconds it takes for the projectile to hit the ground? \r<BR>\n" );
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document.write( "a. h = 0<BR>\n" );
document.write( "b. h = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142018 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=142018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h=-16t%5E2%2B800t+ ALIGN=MIDDLE  ALT=\"+h=-16t%5E2%2B800t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a. h = 0<BR>\n" );
document.write( "Set h to zero and solve for t:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h=-16t%5E2%2B800t+ ALIGN=MIDDLE  ALT=\"+h=-16t%5E2%2B800t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=-16t%5E2%2B800t+ ALIGN=MIDDLE  ALT=\"+0=-16t%5E2%2B800t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=-16t%282t-50%29+ ALIGN=MIDDLE  ALT=\"+0=-16t%282t-50%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Two possible answers:<BR>\n" );
document.write( "-16t = 0<BR>\n" );
document.write( "t = 0 seconds (this is at the start)<BR>\n" );
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document.write( "OR<BR>\n" );
document.write( "2t-50 = 0<BR>\n" );
document.write( "2t = 50<BR>\n" );
document.write( "t = 25 seconds (this is at the end)<BR>\n" );
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document.write( "For this problem, the solution would be 50 seconds.<BR>\n" );
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document.write( "b. h = 1<BR>\n" );
document.write( "Set h to one and solve for t:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h=-16t%5E2%2B800t+ ALIGN=MIDDLE  ALT=\"+h=-16t%5E2%2B800t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1=-16t%5E2%2B800t+ ALIGN=MIDDLE  ALT=\"+1=-16t%5E2%2B800t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=-16t%5E2%2B800t-1+ ALIGN=MIDDLE  ALT=\"+0=-16t%5E2%2B800t-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=16t%5E2-800t%2B1+ ALIGN=MIDDLE  ALT=\"+0=16t%5E2-800t%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Can't factor so you must resort to the quadratic equation.<BR>\n" );
document.write( "Doing so will yield two solutions:<BR>\n" );
document.write( "x = {49.9987 secs, 0.0013 secs}<BR>\n" );
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document.write( "Details of quadratic solution follows:<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=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-800x%2B1+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-800x%2B1+=+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=%28-800%29%5E2-4%2A16%2A1=639936 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-800%29%5E2-4%2A16%2A1=639936\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=639936 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--800%2B-sqrt%28+639936+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--800%2B-sqrt%28+639936+%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-%28-800%29%2Bsqrt%28+639936+%29%29%2F2%5C16+=+49.9987499687484 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-800%29%2Bsqrt%28+639936+%29%29%2F2%5C16+=+49.9987499687484\"   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-%28-800%29-sqrt%28+639936+%29%29%2F2%5C16+=+0.00125003125156198 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-800%29-sqrt%28+639936+%29%29%2F2%5C16+=+0.00125003125156198\"   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-800x%2B1 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-800x%2B1\"   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-800x%2B1+=+16%28x-49.9987499687484%29%2A%28x-0.00125003125156198%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-800x%2B1+=+16%28x-49.9987499687484%29%2A%28x-0.00125003125156198%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 49.9987499687484, 0.00125003125156198.\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-800%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-800%2Ax%2B1+%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" );