document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93461>Question 93461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. Suppose that a ball is thrown upward with an initial velocity of 22 ft/sec. If the ball is released at a height of 5 ft., the height equation may be written as h=-16t^2+22t+5 When, to the nearest thousandth of a sec., will the ball be at a height of 9ft. on the way up? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68043 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=68043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "To find the time the ball is in the air at 9 ft, simply let h=9 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=-16t%5E2%2B22t%2B5+ ALIGN=MIDDLE  ALT=\"9=-16t%5E2%2B22t%2B5+\"   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=0=-16t%5E2%2B22t-4+ ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B22t-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 9 from both sides\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%2B22%2At-4=0 ALIGN=MIDDLE  ALT=\"-16%2At%5E2%2B22%2At-4=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=22 ALIGN=MIDDLE  ALT=\"b=22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4 ALIGN=MIDDLE  ALT=\"c=-4\"   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+=+%28-22+%2B-+sqrt%28+%2822%29%5E2-4%2A-16%2A-4+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-22+%2B-+sqrt%28+%2822%29%5E2-4%2A-16%2A-4+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=22, and c=-4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-22+%2B-+sqrt%28+484-4%2A-16%2A-4+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-22+%2B-+sqrt%28+484-4%2A-16%2A-4+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 22 to get 484  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-22+%2B-+sqrt%28+484%2B-256+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-22+%2B-+sqrt%28+484%2B-256+%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%2A-4%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A-4%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-256 ALIGN=MIDDLE  ALT=\"-256\"   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+=+%28-22+%2B-+sqrt%28+228+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-22+%2B-+sqrt%28+228+%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+=+%28-22+%2B-+2%2Asqrt%2857%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-22+%2B-+2%2Asqrt%2857%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+=+%28-22+%2B-+2%2Asqrt%2857%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-22+%2B-+2%2Asqrt%2857%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+=+%28-22+%2B+2%2Asqrt%2857%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-22+%2B+2%2Asqrt%2857%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+=+%28-22+-+2%2Asqrt%2857%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-22+-+2%2Asqrt%2857%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=-22%2F-32%2B2%2Asqrt%2857%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-22%2F-32%2B2%2Asqrt%2857%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-22%2F-32-2%2Asqrt%2857%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-22%2F-32-2%2Asqrt%2857%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=11+%2F+16-sqrt%2857%29%2F16 ALIGN=MIDDLE  ALT=\"t=11+%2F+16-sqrt%2857%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=11+%2F+16%2Bsqrt%2857%29%2F16 ALIGN=MIDDLE  ALT=\"t=11+%2F+16%2Bsqrt%2857%29%2F16\"   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=0.215635347795578 ALIGN=MIDDLE  ALT=\"t=0.215635347795578\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.15936465220442 ALIGN=MIDDLE  ALT=\"t=1.15936465220442\"   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=0.215635347795578 ALIGN=MIDDLE  ALT=\"t=0.215635347795578\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.15936465220442 ALIGN=MIDDLE  ALT=\"t=1.15936465220442\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But since we only want the height when the ball is going up, we only care about the first solution.\r<BR>\n" );
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document.write( "So our solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.215635347795578 ALIGN=MIDDLE  ALT=\"t=0.215635347795578\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is 0.216 to the nearest thousandth </SPAN>\n" );
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