document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906770>Question 906770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey! Huge thanks to anyone that can help! Pretty Confused!!\r<BR>\n" );
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document.write( "The height of a ball above the ground when the ball is thrown up from the bottom of a 64m building can be modelled by the equation h(t) = -4.9^2 + 35t + 1.2. How long is the ball visible to someone looking out of a fifth floor or higher window? Assume the fifth floor window is 15m above the ground. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550068 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plug in 15 for h(t)<BR>\n" );
document.write( "There should be two times all the time between the ball would be visible\r<BR>\n" );
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document.write( "15 = -4.9^2 + 35t + 1.2.<BR>\n" );
document.write( "0=-4.9^2 + 35t + -13.8<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=-49t%5E2%2B350t%2B-138+=+0 ALIGN=MIDDLE  ALT=\"-49t%5E2%2B350t%2B-138+=+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=%28350%29%5E2-4%2A-49%2A-138=95452 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28350%29%5E2-4%2A-49%2A-138=95452\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=95452 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+=+%28-350%2B-sqrt%28+95452+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-350%2B-sqrt%28+95452+%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-%28350%29%2Bsqrt%28+95452+%29%29%2F2%5C-49+=+0.418846215612299 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%28350%29%2Bsqrt%28+95452+%29%29%2F2%5C-49+=+0.418846215612299\"   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-%28350%29-sqrt%28+95452+%29%29%2F2%5C-49+=+6.72401092724484 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%28350%29-sqrt%28+95452+%29%29%2F2%5C-49+=+6.72401092724484\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-49t%5E2%2B350t%2B-138 ALIGN=MIDDLE  ALT=\"-49t%5E2%2B350t%2B-138\"   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=-49t%5E2%2B350t%2B-138+=+-49%28t-0.418846215612299%29%2A%28t-6.72401092724484%29 ALIGN=MIDDLE  ALT=\"-49t%5E2%2B350t%2B-138+=+-49%28t-0.418846215612299%29%2A%28t-6.72401092724484%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.418846215612299, 6.72401092724484.\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+-49%2Ax%5E2%2B350%2Ax%2B-138+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-49%2Ax%5E2%2B350%2Ax%2B-138+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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