document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124287>Question 124287</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 + 30t + 3.  How long will it take the object to hit the ground?  Round your answer to the nearest thousandth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91088 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=91088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The object will hit the ground when h=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16t%5E2+%2B+30t+%2B+3 ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+30t+%2B+3\"   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=0+=+-16t%5E2+%2B+30t+%2B+3 ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2+%2B+30t+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in h=0\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( "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%2B30%2At%2B3=0 ALIGN=MIDDLE  ALT=\"-16%2At%5E2%2B30%2At%2B3=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=30 ALIGN=MIDDLE  ALT=\"b=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   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+=+%28-30+%2B-+sqrt%28+%2830%29%5E2-4%2A-16%2A3+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-30+%2B-+sqrt%28+%2830%29%5E2-4%2A-16%2A3+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=30, and c=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-30+%2B-+sqrt%28+900-4%2A-16%2A3+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-30+%2B-+sqrt%28+900-4%2A-16%2A3+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 30 to get 900  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-30+%2B-+sqrt%28+900%2B192+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-30+%2B-+sqrt%28+900%2B192+%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%2A3%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A3%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=192 ALIGN=MIDDLE  ALT=\"192\"   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+=+%28-30+%2B-+sqrt%28+1092+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-30+%2B-+sqrt%28+1092+%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+=+%28-30+%2B-+2%2Asqrt%28273%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-30+%2B-+2%2Asqrt%28273%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+=+%28-30+%2B-+2%2Asqrt%28273%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-30+%2B-+2%2Asqrt%28273%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+=+%28-30+%2B+2%2Asqrt%28273%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-30+%2B+2%2Asqrt%28273%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+=+%28-30+-+2%2Asqrt%28273%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-30+-+2%2Asqrt%28273%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=-30%2F-32%2B2%2Asqrt%28273%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-30%2F-32%2B2%2Asqrt%28273%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-30%2F-32-2%2Asqrt%28273%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-30%2F-32-2%2Asqrt%28273%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=15+%2F+16-sqrt%28273%29%2F16 ALIGN=MIDDLE  ALT=\"t=15+%2F+16-sqrt%28273%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=15+%2F+16%2Bsqrt%28273%29%2F16 ALIGN=MIDDLE  ALT=\"t=15+%2F+16%2Bsqrt%28273%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=-0.095169477616144 ALIGN=MIDDLE  ALT=\"t=-0.095169477616144\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.97016947761614 ALIGN=MIDDLE  ALT=\"t=1.97016947761614\"   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( "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=1.97016947761614 ALIGN=MIDDLE  ALT=\"t=1.97016947761614\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the object will hit the ground at about 1.970 seconds <BR>\n" );
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