document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142926>Question 1142926</A>: <I><SPAN STYLE=\"word-break: break-all;\">  If one throws a ball down from a high cliff, the distance it travels can be modeled by the equation: LaTeX: d = -9.8t^2-15t+100 d = − 9.8 t 2 − 15 t + 100  where t is the time in seconds and d is the distance in meters.\r<BR>\n" );
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document.write( "1. At what time will the ball hit the ground?<BR>\n" );
document.write( "2. You will get two answers because this is a quadratic equation. Do both make sense? (Explain in detail Why or Why not). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763657 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28t%29+=+-9.8t%5E2+-+15t+%2B+100+ ALIGN=MIDDLE  ALT=\"+d%28t%29+=+-9.8t%5E2+-+15t+%2B+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The ball is thrown downward at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t=0+ ALIGN=MIDDLE  ALT=\"+t=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%280%29+=+-9.8%2A0%5E2+-+15%2A0+%2B+100+ ALIGN=MIDDLE  ALT=\"+d%280%29+=+-9.8%2A0%5E2+-+15%2A0+%2B+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%280%29+=+100+ ALIGN=MIDDLE  ALT=\"+d%280%29+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so, the cliff is 100 m high<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
document.write( "What is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28t%29+=+0+ ALIGN=MIDDLE  ALT=\"+d%28t%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9.8t%5E2+-+15t+%2B+100+=+0+ ALIGN=MIDDLE  ALT=\"+-9.8t%5E2+-+15t+%2B+100+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-9.8+ ALIGN=MIDDLE  ALT=\"+a+=+-9.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-15+ ALIGN=MIDDLE  ALT=\"+b+=+-15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+100+ ALIGN=MIDDLE  ALT=\"+c+=+100+\"   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+=+%28-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2-4%2A%28-9.8%29%2A100+%29%29%2F%282%2A%28-9.8%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+15+%2B-+sqrt%28+225+%2B+3920+%29%29%2F%28-19.6%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+15+%2B-+sqrt%28+225+%2B+3920+%29%29%2F%28-19.6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+15+%2B-+sqrt%28+4145+%29%29%2F%28-19.6%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+15+%2B-+sqrt%28+4145+%29%29%2F%28-19.6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+15+%2B+64.3817+%29+%2F+%28-19.6+%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+15+%2B+64.3817+%29+%2F+%28-19.6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "can't use this result since the answer is negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++t+=+%28+15+-+64.3817+%29+%2F+%28-19.6+%29+ ALIGN=MIDDLE  ALT=\"++t+=+%28+15+-+64.3817+%29+%2F+%28-19.6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+-49.3817+%2F+%28+-19.6+%29+ ALIGN=MIDDLE  ALT=\"+t+=+-49.3817+%2F+%28+-19.6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+2.5195+ ALIGN=MIDDLE  ALT=\"+t+=+2.5195+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "The ball hits the ground in 2.52 sec ( rounded off )<BR>\n" );
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document.write( "Note that the problem is not stated correctly.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28t%29+ ALIGN=MIDDLE  ALT=\"+d%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not the distance that the ball travels,<BR>\n" );
document.write( "but it is the distance above ground from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+0+ ALIGN=MIDDLE  ALT=\"+t+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+2.52+ ALIGN=MIDDLE  ALT=\"+t+=+2.52+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "Does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28+2.52+%29+=+0+ ALIGN=MIDDLE  ALT=\"+d%28+2.52+%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28+2.52+%29+=+-9.8%2A2.52%5E2+-+15%2A2.52+%2B+100+ ALIGN=MIDDLE  ALT=\"+d%28+2.52+%29+=+-9.8%2A2.52%5E2+-+15%2A2.52+%2B+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28+2.52+%29+=+-62.234+-+37.8+%2B+100+ ALIGN=MIDDLE  ALT=\"+d%28+2.52+%29+=+-62.234+-+37.8+%2B+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28+2.52+%29+=+-100.034+%2B+100+ ALIGN=MIDDLE  ALT=\"+d%28+2.52+%29+=+-100.034+%2B+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%28+2.52+%29+=+-.034+ ALIGN=MIDDLE  ALT=\"+d%28+2.52+%29+=+-.034+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The error is due to rounding off<BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );