document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39287>Question 39287</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073016020/algebrahomeworkh>beggining algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Original equation= h=-5t^2+25t+80\r<BR>\n" );
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document.write( "The only part of the height equation that we have not discussed is the constant. You have<BR>\n" );
document.write( "probably noticed that the constant is always equal to the initial height of the ball (80 m in<BR>\n" );
document.write( "our previous exercises). Now, let’s have you develop a height equation.<BR>\n" );
document.write( "A ball is thrown upward from the roof of a building 100 m tall with an initial velocity<BR>\n" );
document.write( "of 20 m/s. Use this information for exercises 35 to 38.\r<BR>\n" );
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document.write( "36. Science and medicine. When will the ball reach a height of 80 m? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24726 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  h=-5t^2+25t+100 <BR>\n" );
document.write( "Let h=80 and solve for \"t\" as follows:<BR>\n" );
document.write( "80=-5t^2+25t+100<BR>\n" );
document.write( "-5t^2+25t+20=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=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=-5t%5E2%2B25t%2B20+=+0 ALIGN=MIDDLE  ALT=\"-5t%5E2%2B25t%2B20+=+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=%2825%29%5E2-4%2A-5%2A20=1025 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2825%29%5E2-4%2A-5%2A20=1025\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1025 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+=+%28-25%2B-sqrt%28+1025+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-25%2B-sqrt%28+1025+%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-%2825%29%2Bsqrt%28+1025+%29%29%2F2%5C-5+=+-0.701562118716424 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%2825%29%2Bsqrt%28+1025+%29%29%2F2%5C-5+=+-0.701562118716424\"   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-%2825%29-sqrt%28+1025+%29%29%2F2%5C-5+=+5.70156211871642 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%2825%29-sqrt%28+1025+%29%29%2F2%5C-5+=+5.70156211871642\"   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=-5t%5E2%2B25t%2B20 ALIGN=MIDDLE  ALT=\"-5t%5E2%2B25t%2B20\"   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=-5t%5E2%2B25t%2B20+=+-5%28t--0.701562118716424%29%2A%28t-5.70156211871642%29 ALIGN=MIDDLE  ALT=\"-5t%5E2%2B25t%2B20+=+-5%28t--0.701562118716424%29%2A%28t-5.70156211871642%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.701562118716424, 5.70156211871642.\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%2B25%2Ax%2B20+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B25%2Ax%2B20+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t=5.7... seconds is the only practical answer.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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