document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350709>Question 350709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a ball is thrown, its height in feet h after t seconds is given by the equation\r<BR>\n" );
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document.write( " h=vt-16t^2\r<BR>\n" );
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document.write( "where v is the initial upwards velocity in feet per second. If v=9  feet per second, find all values of t for which h=1 foot. Do not round any intermediate steps. Round your answer to 2 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250695 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=250695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a ball is thrown, its height in feet h after t seconds is given by the equation <BR>\n" );
document.write( "h=vt-16t^2 <BR>\n" );
document.write( "where v is the initial upwards velocity in feet per second. If v=9 feet per second, find all values of t for which h=1 foot. Do not round any intermediate steps. Round your answer to 2 decimal places.<BR>\n" );
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document.write( "h=vt-16t^2 <BR>\n" );
document.write( "Substitute in the value for v:<BR>\n" );
document.write( "h=9t-16t^2 <BR>\n" );
document.write( "Substitute in the value for h:<BR>\n" );
document.write( "1=9t-16t^2 <BR>\n" );
document.write( "Solving for t:<BR>\n" );
document.write( "1=9t-16t^2 <BR>\n" );
document.write( "16t^2+1=9t <BR>\n" );
document.write( "16t^2-9t+1=0<BR>\n" );
document.write( "Solve using the quadratic formula.  Doing so yields<BR>\n" );
document.write( "t = {0.41, 0.15} seconds<BR>\n" );
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document.write( "Detail of quadratic follows:<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=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=16t%5E2%2B-9t%2B1+=+0 ALIGN=MIDDLE  ALT=\"16t%5E2%2B-9t%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=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=%28-9%29%5E2-4%2A16%2A1=17 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-9%29%5E2-4%2A16%2A1=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=17 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--9%2B-sqrt%28+17+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--9%2B-sqrt%28+17+%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-%28-9%29%2Bsqrt%28+17+%29%29%2F2%5C16+=+0.410097050800552 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+17+%29%29%2F2%5C16+=+0.410097050800552\"   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-%28-9%29-sqrt%28+17+%29%29%2F2%5C16+=+0.152402949199448 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%28-9%29-sqrt%28+17+%29%29%2F2%5C16+=+0.152402949199448\"   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=16t%5E2%2B-9t%2B1 ALIGN=MIDDLE  ALT=\"16t%5E2%2B-9t%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=16t%5E2%2B-9t%2B1+=+16%28t-0.410097050800552%29%2A%28t-0.152402949199448%29 ALIGN=MIDDLE  ALT=\"16t%5E2%2B-9t%2B1+=+16%28t-0.410097050800552%29%2A%28t-0.152402949199448%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.410097050800552, 0.152402949199448.\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-9%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-9%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );