document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473190>Question 473190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown<BR>\n" );
document.write( "downward from the top of a 250-ft building with an initial velocity of 64 ft/s.<BR>\n" );
document.write( "Find the time it takes for the ball to reach a height of 100 ft. Round your answer<BR>\n" );
document.write( "to the nearest thousandth. \r<BR>\n" );
document.write( "\n" );
document.write( "Thank you in advance for your hardwork.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324510 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=324510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown<BR>\n" );
document.write( "downward from the top of a 250-ft building with an initial velocity of 64 ft/s.<BR>\n" );
document.write( "Find the time it takes for the ball to reach a height of 100 ft. Round your answer<BR>\n" );
document.write( "to the nearest thousandth.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Use ^2 for squared, ^3 for cubed, etc.<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "h(t) = -16t^2-64t+250 = 100<BR>\n" );
document.write( "8t^2 + 32t - 75 = 0<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=8x%5E2%2B32x%2B-75+=+0 ALIGN=MIDDLE  ALT=\"8x%5E2%2B32x%2B-75+=+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=%2832%29%5E2-4%2A8%2A-75=3424 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2832%29%5E2-4%2A8%2A-75=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+=+%28-32%2B-sqrt%28+3424+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-32%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-%2832%29%2Bsqrt%28+3424+%29%29%2F2%5C8+=+1.65718470958195 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+3424+%29%29%2F2%5C8+=+1.65718470958195\"   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-%2832%29-sqrt%28+3424+%29%29%2F2%5C8+=+-5.65718470958195 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2832%29-sqrt%28+3424+%29%29%2F2%5C8+=+-5.65718470958195\"   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%2B32x%2B-75 ALIGN=MIDDLE  ALT=\"8x%5E2%2B32x%2B-75\"   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%2B32x%2B-75+=+%28x-1.65718470958195%29%2A%28x--5.65718470958195%29 ALIGN=MIDDLE  ALT=\"8x%5E2%2B32x%2B-75+=+%28x-1.65718470958195%29%2A%28x--5.65718470958195%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.65718470958195, -5.65718470958195.\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%2B32%2Ax%2B-75+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B32%2Ax%2B-75+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t = 1.657 seconds<BR>\n" );
document.write( "Ignore the negative answer.<BR>\n" );
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