document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118286>Question 118286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> jessie kicked a soccer ball into the air with an initial upward velocity of 40 feet per second. The hieght (h) in feet of the ball above the ground can be modeled by h=-16t2+40t,where t is the time in seconds after jessie kicked the ball. find the time it takes the ball to reach 25 feet above the grond. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86408 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=86408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we're finding the time it takes for the ball to reach 25 feet, this means h is 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B40t ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B40t\"   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=25=-16t%5E2%2B40t ALIGN=MIDDLE  ALT=\"25=-16t%5E2%2B40t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=25 ALIGN=MIDDLE  ALT=\"h=25\"   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=16t%5E2-40t%2B25=0 ALIGN=MIDDLE  ALT=\"16t%5E2-40t%2B25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2 ALIGN=MIDDLE  ALT=\"16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides. Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40t ALIGN=MIDDLE  ALT=\"40t\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x:\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=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%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=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%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%2Ax%5E2-40%2Ax%2B25=0 ALIGN=MIDDLE  ALT=\"16%2Ax%5E2-40%2Ax%2B25=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=-40 ALIGN=MIDDLE  ALT=\"b=-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=25 ALIGN=MIDDLE  ALT=\"c=25\"   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=x+=+%28--40+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%28--40+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=16, b=-40, and c=25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2840+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%2840+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -40 to get 40\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2840+%2B-+sqrt%28+1600-4%2A16%2A25+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%2840+%2B-+sqrt%28+1600-4%2A16%2A25+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -40 to get 1600  (note: remember when you square -40, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-40%29%5E2=-40%2A-40=1600 ALIGN=MIDDLE  ALT=\"%28-40%29%5E2=-40%2A-40=1600\"   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=x+=+%2840+%2B-+sqrt%28+1600%2B-1600+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%2840+%2B-+sqrt%28+1600%2B-1600+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A25%2A16 ALIGN=MIDDLE  ALT=\"-4%2A25%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1600 ALIGN=MIDDLE  ALT=\"-1600\"   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=x+=+%2840+%2B-+sqrt%28+0+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%2840+%2B-+sqrt%28+0+%29%29%2F%282%2A16%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=x+=+%2840+%2B-+0%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"x+=+%2840+%2B-+0%29%2F%282%2A16%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=x+=+%2840+%2B-+0%29%2F32 ALIGN=MIDDLE  ALT=\"x+=+%2840+%2B-+0%29%2F32\"   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=x+=+%2840+%2B+0%29%2F32 ALIGN=MIDDLE  ALT=\"x+=+%2840+%2B+0%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2840+-+0%29%2F32 ALIGN=MIDDLE  ALT=\"x+=+%2840+-+0%29%2F32\"   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=%2840+%2B+0%29%2F32 ALIGN=MIDDLE  ALT=\"x=%2840+%2B+0%29%2F32\"   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=x=40%2F32 ALIGN=MIDDLE  ALT=\"x=40%2F32\"   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=x=5%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4\"   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=x=5%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4\"   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=%2840+-+0%29%2F32 ALIGN=MIDDLE  ALT=\"x=%2840+-+0%29%2F32\"   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=x=40%2F32 ALIGN=MIDDLE  ALT=\"x=40%2F32\"   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=x=5%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4\"   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=x=5%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So 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=x=5%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.25 ALIGN=MIDDLE  ALT=\"x=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form)\r<BR>\n" );
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document.write( "So at 1.25 seconds, the ball is 25 feet high.<BR>\n" );
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