document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764112>Question 764112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> help please!!! Can you explain this step by step?\r<BR>\n" );
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document.write( "if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time is given by: <BR>\n" );
document.write( "h=-16t^2+vt+s (where h and s are in ft, t is in seconds, and v is in ft/sec)<BR>\n" );
document.write( "if a rock is thrown upward from a height of 100ft, with an initial velocity of 32ft/sec, solve for the time that it takes for it to hit the ground. (when h=0) <BR>\n" );
document.write( "answer in seconds. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #465198 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=465198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time is given by: <BR>\n" );
document.write( "h=-16t^2+vt+s (where h and s are in ft, t is in seconds, and v is in ft/sec)<BR>\n" );
document.write( "if a rock is thrown upward from a height of 100ft, with an initial velocity of 32ft/sec, solve for the time that it takes for it to hit the ground. (when h=0) <BR>\n" );
document.write( "answer in seconds. <BR>\n" );
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document.write( "h=-16t^2+vt+s<BR>\n" );
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document.write( "h(t) = -16t^2 + 32t + 100<BR>\n" );
document.write( "-16t^2 + 32t + 100 = 0<BR>\n" );
document.write( "Solve for t<BR>\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=-16x%5E2%2B32x%2B100+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B32x%2B100+=+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%2A-16%2A100=7424 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2832%29%5E2-4%2A-16%2A100=7424\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=7424 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+7424+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-32%2B-sqrt%28+7424+%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+7424+%29%29%2F2%5C-16+=+-1.69258240356725 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+7424+%29%29%2F2%5C-16+=+-1.69258240356725\"   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+7424+%29%29%2F2%5C-16+=+3.69258240356725 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2832%29-sqrt%28+7424+%29%29%2F2%5C-16+=+3.69258240356725\"   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%2B100 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B32x%2B100\"   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%2B100+=+%28x--1.69258240356725%29%2A%28x-3.69258240356725%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B32x%2B100+=+%28x--1.69258240356725%29%2A%28x-3.69258240356725%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.69258240356725, 3.69258240356725.\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%2B100+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B32%2Ax%2B100+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t =~ 3.6926 seconds<BR>\n" );
document.write( "Ignore the negative solution<BR>\n" );
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