document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981452>Question 981452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface water will the dolphin reach 25 feet to get the fish from the trainer's hand? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602434 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=602434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface water will the dolphin reach 25 feet to get the fish from the trainer's hand?<BR>\n" );
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document.write( "h(t) = -4t^2 - 20t = 25<BR>\n" );
document.write( "That won't work.<BR>\n" );
document.write( "It's h(t) = -4t^2 + 20t = 25<BR>\n" );
document.write( "The 20 is its vertical speed when it leaves the water and becomes a projectile.<BR>\n" );
document.write( "-4t^2 = 20t - 25 = 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=-4x%5E2%2B20x%2B-25+=+0 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B20x%2B-25+=+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=%2820%29%5E2-4%2A-4%2A-25=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2820%29%5E2-4%2A-4%2A-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=0 is zero! That means that there is only one solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2820%29%29%2F2%5C-4 ALIGN=MIDDLE  ALT=\"x+=+%28-%2820%29%29%2F2%5C-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "      Expression can be factored: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B20x%2B-25+=+%28x-2.5%29%2A%28x-2.5%29 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B20x%2B-25+=+%28x-2.5%29%2A%28x-2.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Again, the answer is: 2.5, 2.5.\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+-4%2Ax%5E2%2B20%2Ax%2B-25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B20%2Ax%2B-25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t = 2.5 seconds.<BR>\n" );
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