document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103591>Question 103591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height h in feet of an object after t seconds is given by the function <BR>\n" );
document.write( "	h = –16t^2 + 40t + 10.  <BR>\n" );
document.write( "How long will it take the object to hit the ground?  Round your answer to the nearest thousandth<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75337 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=75337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find when the object will hit the ground, let h=0 and solve for t\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+40t+%2B+10 ALIGN=MIDDLE  ALT=\"0=-16t%5E2+%2B+40t+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for t:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<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;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<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;\" ><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%2B40%2At%2B10=0 ALIGN=MIDDLE  ALT=\"-16%2At%5E2%2B40%2At%2B10=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=10 ALIGN=MIDDLE  ALT=\"c=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40+%2B-+sqrt%28+%2840%29%5E2-4%2A-16%2A10+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-40+%2B-+sqrt%28+%2840%29%5E2-4%2A-16%2A10+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=40, and c=10<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40+%2B-+sqrt%28+1600-4%2A-16%2A10+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-40+%2B-+sqrt%28+1600-4%2A-16%2A10+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 40 to get 1600  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40+%2B-+sqrt%28+1600%2B640+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-40+%2B-+sqrt%28+1600%2B640+%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%2A10%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A10%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=640 ALIGN=MIDDLE  ALT=\"640\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40+%2B-+sqrt%28+2240+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-40+%2B-+sqrt%28+2240+%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)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40+%2B-+8%2Asqrt%2835%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-40+%2B-+8%2Asqrt%2835%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>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40+%2B-+8%2Asqrt%2835%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-40+%2B-+8%2Asqrt%2835%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -16 to get -32<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40+%2B+8%2Asqrt%2835%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-40+%2B+8%2Asqrt%2835%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+=+%28-40+-+8%2Asqrt%2835%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-40+-+8%2Asqrt%2835%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now break up the fraction<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-40%2F-32%2B8%2Asqrt%2835%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-40%2F-32%2B8%2Asqrt%2835%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-40%2F-32-8%2Asqrt%2835%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-40%2F-32-8%2Asqrt%2835%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Simplify<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5%2F4-sqrt%2835%29%2F4 ALIGN=MIDDLE  ALT=\"t=5%2F4-sqrt%2835%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5%2F4%2Bsqrt%2835%29%2F4 ALIGN=MIDDLE  ALT=\"t=5%2F4%2Bsqrt%2835%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5%2F4-sqrt%2835%29%2F4 ALIGN=MIDDLE  ALT=\"t=5%2F4-sqrt%2835%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5%2F4%2Bsqrt%2835%29%2F4 ALIGN=MIDDLE  ALT=\"t=5%2F4%2Bsqrt%2835%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since a negative time doesn't make any sense, the only solution is approximately \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.729 ALIGN=MIDDLE  ALT=\"t=2.729\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So it will take about 2.729 seconds for the object to hit the ground </SPAN>\n" );
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