document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122875>Question 122875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve.\r<BR>\n" );
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document.write( "The equation h = -16t squared + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90194 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=90194\">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=h+=+-16t%5E2+%2B+112t ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+112t\"   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=180+=+-16t%5E2+%2B+112t ALIGN=MIDDLE  ALT=\"180+=+-16t%5E2+%2B+112t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=180 ALIGN=MIDDLE  ALT=\"h=180\"   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%5E2-112t%2B180=0 ALIGN=MIDDLE  ALT=\"16t%5E2-112t%2B180=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to the left side\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%5E2-112%2At%2B180=0 ALIGN=MIDDLE  ALT=\"16%2At%5E2-112%2At%2B180=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=-112 ALIGN=MIDDLE  ALT=\"b=-112\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=180 ALIGN=MIDDLE  ALT=\"c=180\"   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--112+%2B-+sqrt%28+%28-112%29%5E2-4%2A16%2A180+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%28--112+%2B-+sqrt%28+%28-112%29%5E2-4%2A16%2A180+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=16, b=-112, and c=180\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28112+%2B-+sqrt%28+%28-112%29%5E2-4%2A16%2A180+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%28112+%2B-+sqrt%28+%28-112%29%5E2-4%2A16%2A180+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -112 to get 112\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28112+%2B-+sqrt%28+12544-4%2A16%2A180+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%28112+%2B-+sqrt%28+12544-4%2A16%2A180+%29%29%2F%282%2A16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -112 to get 12544  (note: remember when you square -112, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-112%29%5E2=-112%2A-112=12544 ALIGN=MIDDLE  ALT=\"%28-112%29%5E2=-112%2A-112=12544\"   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+=+%28112+%2B-+sqrt%28+12544%2B-11520+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%28112+%2B-+sqrt%28+12544%2B-11520+%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%2A180%2A16 ALIGN=MIDDLE  ALT=\"-4%2A180%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11520 ALIGN=MIDDLE  ALT=\"-11520\"   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+=+%28112+%2B-+sqrt%28+1024+%29%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%28112+%2B-+sqrt%28+1024+%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=t+=+%28112+%2B-+32%29%2F%282%2A16%29 ALIGN=MIDDLE  ALT=\"t+=+%28112+%2B-+32%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=t+=+%28112+%2B-+32%29%2F32 ALIGN=MIDDLE  ALT=\"t+=+%28112+%2B-+32%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=t+=+%28112+%2B+32%29%2F32 ALIGN=MIDDLE  ALT=\"t+=+%28112+%2B+32%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28112+-+32%29%2F32 ALIGN=MIDDLE  ALT=\"t+=+%28112+-+32%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=%28112+%2B+32%29%2F32 ALIGN=MIDDLE  ALT=\"x=%28112+%2B+32%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=t=144%2F32 ALIGN=MIDDLE  ALT=\"t=144%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=t=9%2F2 ALIGN=MIDDLE  ALT=\"t=9%2F2\"   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=9%2F2 ALIGN=MIDDLE  ALT=\"t=9%2F2\"   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=%28112+-+32%29%2F32 ALIGN=MIDDLE  ALT=\"x=%28112+-+32%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=t=80%2F32 ALIGN=MIDDLE  ALT=\"t=80%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=t=5%2F2 ALIGN=MIDDLE  ALT=\"t=5%2F2\"   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%2F2 ALIGN=MIDDLE  ALT=\"t=5%2F2\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=9%2F2 ALIGN=MIDDLE  ALT=\"t=9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5%2F2 ALIGN=MIDDLE  ALT=\"t=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4.5 ALIGN=MIDDLE  ALT=\"t=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.5 ALIGN=MIDDLE  ALT=\"t=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively in decimal form)\r<BR>\n" );
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document.write( "So it takes 2.5 seconds for the arrow to climb to 180 ft and then 4.5 seconds for the arrow to fall back to 180 ft<BR>\n" );
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