document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122530>Question 122530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16)    a ball projected vertically upward from the top of a tower has height (in feet) \r<BR>\n" );
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document.write( "h(t) = -16t^2 + 64t + 80 after t seconds.  At what time will the ball hit the ground?\r<BR>\n" );
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document.write( "a)       t=2\r<BR>\n" );
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document.write( "b)       t=5\r<BR>\n" );
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document.write( "c)       t=4\r<BR>\n" );
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document.write( "d)       t=1\r<BR>\n" );
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document.write( "e)       none of these<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89940 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=89940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When the ball hits the ground, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29=0 ALIGN=MIDDLE  ALT=\"h%28t%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in other words, the height is zero)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+64t+%2B+80+ ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+64t+%2B+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-16t%5E2+%2B+64t+%2B+80+ ALIGN=MIDDLE  ALT=\"0=+-16t%5E2+%2B+64t+%2B+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29=0 ALIGN=MIDDLE  ALT=\"h%28t%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace h(t) with 0\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for t:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2At%5E2%2B64%2At%2B80=0 ALIGN=MIDDLE  ALT=\"-16%2At%5E2%2B64%2At%2B80=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16 ALIGN=MIDDLE  ALT=\"a=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=64 ALIGN=MIDDLE  ALT=\"b=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=80 ALIGN=MIDDLE  ALT=\"c=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+%2B-+sqrt%28+%2864%29%5E2-4%2A-16%2A80+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-64+%2B-+sqrt%28+%2864%29%5E2-4%2A-16%2A80+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=64, and c=80\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+%2B-+sqrt%28+4096-4%2A-16%2A80+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-64+%2B-+sqrt%28+4096-4%2A-16%2A80+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 64 to get 4096  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+%2B-+sqrt%28+4096%2B5120+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-64+%2B-+sqrt%28+4096%2B5120+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A80%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A80%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5120 ALIGN=MIDDLE  ALT=\"5120\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+%2B-+sqrt%28+9216+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-64+%2B-+sqrt%28+9216+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+%2B-+96%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-64+%2B-+96%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+%2B-+96%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-64+%2B-+96%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -16 to get -32\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+%2B+96%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-64+%2B+96%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-64+-+96%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-64+-+96%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-64+%2B+96%29%2F-32 ALIGN=MIDDLE  ALT=\"x=%28-64+%2B+96%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=32%2F-32 ALIGN=MIDDLE  ALT=\"t=32%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-1 ALIGN=MIDDLE  ALT=\"t=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So one answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-1 ALIGN=MIDDLE  ALT=\"t=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-64+-+96%29%2F-32 ALIGN=MIDDLE  ALT=\"x=%28-64+-+96%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-160%2F-32 ALIGN=MIDDLE  ALT=\"t=-160%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5 ALIGN=MIDDLE  ALT=\"t=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So another answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5 ALIGN=MIDDLE  ALT=\"t=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "However, since a negative time doesn't make sense, our only solution is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5 ALIGN=MIDDLE  ALT=\"t=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------------------\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So at 5 seconds, the ball will hit the ground. </SPAN>\n" );
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