document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204163>Question 204163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi I am confused by this question, it relates to a cork being released from a champagne bottle. The height in meters of the cork above the level ground at time t seconds is modelled into the equaiton. h= 1+8t-5t^2<BR>\n" );
document.write( "h stands for height t stands for time.<BR>\n" );
document.write( "I answered some eairler questions relating to this but am stuck on this next part.\r<BR>\n" );
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document.write( "Substitute h=1.65 into the equation h= 1+8t-5t^2, and rearrange this to the quadratic equation t^2-1.6t+0.13=0\r<BR>\n" );
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document.write( "I do not understand the question.<BR>\n" );
document.write( "Thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154104 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=154104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The height in meters of the cork above the level ground at time t seconds is modelled into the equaiton. h= 1+8t-5t^2<BR>\n" );
document.write( "h stands for height t stands for time.<BR>\n" );
document.write( "I answered some eairler questions relating to this but am stuck on this next part. <BR>\n" );
document.write( "Substitute h=1.65 into the equation h= 1+8t-5t^2, and rearrange this to the quadratic equation t^2-1.6t+0.13=0 <BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "1.65 = 1+8t-5t^2 gives the time that the cork is 1.65 meters above ground.<BR>\n" );
document.write( "1.65 = 1+8t-5t^2<BR>\n" );
document.write( "5t^2 - 8t + 0.65 = 0<BR>\n" );
document.write( "You can solve for t.<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=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=5x%5E2%2B-8x%2B0.65+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-8x%2B0.65+=+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=%28-8%29%5E2-4%2A5%2A0.65=51 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-8%29%5E2-4%2A5%2A0.65=51\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=51 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--8%2B-sqrt%28+51+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--8%2B-sqrt%28+51+%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-%28-8%29%2Bsqrt%28+51+%29%29%2F2%5C5+=+1.51414284285429 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+51+%29%29%2F2%5C5+=+1.51414284285429\"   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-%28-8%29-sqrt%28+51+%29%29%2F2%5C5+=+0.085857157145715 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-8%29-sqrt%28+51+%29%29%2F2%5C5+=+0.085857157145715\"   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=5x%5E2%2B-8x%2B0.65 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-8x%2B0.65\"   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=5x%5E2%2B-8x%2B0.65+=+%28x-1.51414284285429%29%2A%28x-0.085857157145715%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-8x%2B0.65+=+%28x-1.51414284285429%29%2A%28x-0.085857157145715%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.51414284285429, 0.085857157145715.\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+5%2Ax%5E2%2B-8%2Ax%2B0.65+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-8%2Ax%2B0.65+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "There are 2 values for t (the solver uses x) that the cork is 1.65 meters above ground.  It passes 1.65 meters going up, then again going down.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );