document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209449>Question 209449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a penny is thrown downward at 30 ft/sec<BR>\n" );
document.write( "from the bridge at Royal Gorge, Colorado, how long does it<BR>\n" );
document.write( "take to reach the Arkansas River 1000 ft below?\r<BR>\n" );
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document.write( "It says to use the quadratic equation.\r<BR>\n" );
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document.write( "x^2-&#12310;30&#12311;^2=&#12310;1000&#12311;^2 \r<BR>\n" );
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document.write( "I have work started but it's not pasting into here. \r<BR>\n" );
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document.write( "It's from my online textbook, I cannot find the ISBN.<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 #158366 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=158366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a penny is thrown downward at 30 ft/sec<BR>\n" );
document.write( "from the bridge at Royal Gorge, Colorado, how long does it<BR>\n" );
document.write( "take to reach the Arkansas River 1000 ft below? <BR>\n" );
document.write( "It says to use the quadratic equation. <BR>\n" );
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document.write( "The height of an object (neglecting air friction) is<BR>\n" );
document.write( "h(t) = -16t^2 + vt + h0 Where v is the starting speed and h0 is the initial height.  t is in seconds, h in feet.<BR>\n" );
document.write( "In this case h0 = 1000 ft, and v = -30 ft/sec (-30 since it's thrown downward)<BR>\n" );
document.write( "Find when h(t) = 0<BR>\n" );
document.write( "0 = -16t^2 - 30t + 1000<BR>\n" );
document.write( "-8t^2 - 15t + 500 = 0<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=-8x%5E2%2B-15x%2B500+=+0 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B-15x%2B500+=+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=%28-15%29%5E2-4%2A-8%2A500=16225 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-15%29%5E2-4%2A-8%2A500=16225\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=16225 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--15%2B-sqrt%28+16225+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--15%2B-sqrt%28+16225+%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-%28-15%29%2Bsqrt%28+16225+%29%29%2F2%5C-8+=+-8.89858700178562 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+16225+%29%29%2F2%5C-8+=+-8.89858700178562\"   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-%28-15%29-sqrt%28+16225+%29%29%2F2%5C-8+=+7.02358700178562 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-15%29-sqrt%28+16225+%29%29%2F2%5C-8+=+7.02358700178562\"   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=-8x%5E2%2B-15x%2B500 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B-15x%2B500\"   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=-8x%5E2%2B-15x%2B500+=+%28x--8.89858700178562%29%2A%28x-7.02358700178562%29 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B-15x%2B500+=+%28x--8.89858700178562%29%2A%28x-7.02358700178562%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -8.89858700178562, 7.02358700178562.\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+-8%2Ax%5E2%2B-15%2Ax%2B500+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B-15%2Ax%2B500+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Use the positive value for t (it says x2)<BR>\n" );
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