document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=603039>Question 603039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boy is standing next to the chimney on top of the roof of a house, which is located on the top of a cliff. The chimney runs straight down into the fireplace at the floor of the basement of the house. The cliff on which the house is built rises 50 feet above the ocean below. The roof of the house is 18 feet above the ground on which it is built, and the floor of the basement is 9 feet below ground. He throws a ball straight upward with an initial velocity of 80 feet per second. At the moment the ball is released, the boy's hand is level with the top of the chimney 5 feet above the roof. From this information, it can be shown that the height h of the ball t seconds after it is released from the boy's hand is modeled by the following equation:\r<BR>\n" );
document.write( "\n" );
document.write( "       h(t)= -16t2 + 80t +73\r<BR>\n" );
document.write( "\n" );
document.write( "to the nearest tenth of a second, determine the amount of time after the ball is released from the boy'y hand at which it lands in the fireplace in the basement of the house.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380551 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=380551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given equation:<BR>\n" );
document.write( "h(t)= -16t2 + 80t +73 <BR>\n" );
document.write( ".<BR>\n" );
document.write( "The basement floor (relative to sea level) is 50-9 = 41 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Set h(t) to 41 and solve for t:<BR>\n" );
document.write( "h(t)= -16t2 + 80t +73 <BR>\n" );
document.write( "41 = -16t2 + 80t +73 <BR>\n" );
document.write( "0 = -16t2 + 80t + 114<BR>\n" );
document.write( "0 = -8t2 + 40t + 57<BR>\n" );
document.write( "0 = 8t2 - 40t - 57<BR>\n" );
document.write( "Solve by the \"quadratic formula\" to get:<BR>\n" );
document.write( "x = {6.2, -1.2}<BR>\n" );
document.write( "throw out the negative solution (extraneous) leaving:<BR>\n" );
document.write( "x = 6.2 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "details of quadratic formula:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=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-40x%2B-57+=+0 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-40x%2B-57+=+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=%28-40%29%5E2-4%2A8%2A-57=3424 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-40%29%5E2-4%2A8%2A-57=3424\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3424 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--40%2B-sqrt%28+3424+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--40%2B-sqrt%28+3424+%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-%28-40%29%2Bsqrt%28+3424+%29%29%2F2%5C8+=+6.15718470958195 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+3424+%29%29%2F2%5C8+=+6.15718470958195\"   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-%28-40%29-sqrt%28+3424+%29%29%2F2%5C8+=+-1.15718470958195 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-40%29-sqrt%28+3424+%29%29%2F2%5C8+=+-1.15718470958195\"   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-40x%2B-57 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-40x%2B-57\"   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-40x%2B-57+=+8%28x-6.15718470958195%29%2A%28x--1.15718470958195%29 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-40x%2B-57+=+8%28x-6.15718470958195%29%2A%28x--1.15718470958195%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.15718470958195, -1.15718470958195.\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-40%2Ax%2B-57+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-40%2Ax%2B-57+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );