document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98246>Question 98246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this word problem. \r<BR>\n" );
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document.write( "If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 80 ft/s, its height h after t s is given by h=-16t^2 + 80t + 5. How long does it take the ball to return to the ground?\r<BR>\n" );
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document.write( "thak you very much for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71394 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=71394\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find when it hits the ground, let h=0\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+80t+%2B+5 ALIGN=MIDDLE  ALT=\"0=-16t%5E2+%2B+80t+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=0=-16%2At%5E2%2B80%2At%2B5 ALIGN=MIDDLE  ALT=\"0=-16%2At%5E2%2B80%2At%2B5\"   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=80 ALIGN=MIDDLE  ALT=\"b=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   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+=+%28-80+%2B-+sqrt%28+%2880%29%5E2-4%2A-16%2A5+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+%2880%29%5E2-4%2A-16%2A5+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=80, and c=5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+%2B-+sqrt%28+6400-4%2A-16%2A5+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+6400-4%2A-16%2A5+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 80 to get 6400  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+%2B-+sqrt%28+6400%2B320+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+6400%2B320+%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%2A5%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A5%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320 ALIGN=MIDDLE  ALT=\"320\"   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+=+%28-80+%2B-+sqrt%28+6720+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+sqrt%28+6720+%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+=+%28-80+%2B-+8%2Asqrt%28105%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+8%2Asqrt%28105%29%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+=+%28-80+%2B-+8%2Asqrt%28105%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B-+8%2Asqrt%28105%29%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+=+%28-80+%2B+8%2Asqrt%28105%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-80+%2B+8%2Asqrt%28105%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-80+-+8%2Asqrt%28105%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-80+-+8%2Asqrt%28105%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-80%2F-32%2B8%2Asqrt%28105%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-80%2F-32%2B8%2Asqrt%28105%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-80%2F-32-8%2Asqrt%28105%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-80%2F-32-8%2Asqrt%28105%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5+%2F+2-sqrt%28105%29%2F4 ALIGN=MIDDLE  ALT=\"t=5+%2F+2-sqrt%28105%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5+%2F+2%2Bsqrt%28105%29%2F4 ALIGN=MIDDLE  ALT=\"t=5+%2F+2%2Bsqrt%28105%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-0.0617376914898995 ALIGN=MIDDLE  ALT=\"t=-0.0617376914898995\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5.0617376914899 ALIGN=MIDDLE  ALT=\"t=5.0617376914899\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-0.0617376914898995 ALIGN=MIDDLE  ALT=\"t=-0.0617376914898995\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5.0617376914899 ALIGN=MIDDLE  ALT=\"t=5.0617376914899\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, since a negative time doesn't make sense, our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5.0617376914899 ALIGN=MIDDLE  ALT=\"t=5.0617376914899\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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