document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198727>Question 198727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please HELP!! \r<BR>\n" );
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document.write( "A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as it falls can be represented by the function h(t)= -16t^2 + 30, where t is time in seconds. To catch the crab as it falls, a gull flies along a path represented by the function<BR>\n" );
document.write( " g(t)= -8t + 15. Can the gull catch the crab before the crab hits the water? \r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149228 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=149228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simply set the height equations equal to each other 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=-16t%5E2+%2B+30=-8t+%2B+15 ALIGN=MIDDLE  ALT=\"-16t%5E2+%2B+30=-8t+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the two right sides equal to each other.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B30%2B8t-15=0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B30%2B8t-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B8t%2B15=0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B8t%2B15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%5E2%2BBt%2BC ALIGN=MIDDLE  ALT=\"At%5E2%2BBt%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <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=8 ALIGN=MIDDLE  ALT=\"B=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=15 ALIGN=MIDDLE  ALT=\"C=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%28-16%29%2815%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%28-16%29%2815%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <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=8 ALIGN=MIDDLE  ALT=\"B=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=15 ALIGN=MIDDLE  ALT=\"C=15\"   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+=+%28-8+%2B-+sqrt%28+64-4%28-16%29%2815%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+%2B-+sqrt%28+64-4%28-16%29%2815%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   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+=+%28-8+%2B-+sqrt%28+64--960+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+%2B-+sqrt%28+64--960+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-16%29%2815%29 ALIGN=MIDDLE  ALT=\"4%28-16%29%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-960 ALIGN=MIDDLE  ALT=\"-960\"   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+=+%28-8+%2B-+sqrt%28+64%2B960+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+%2B-+sqrt%28+64%2B960+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864--960%29 ALIGN=MIDDLE  ALT=\"sqrt%2864--960%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%2B960%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%2B960%29\"   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+=+%28-8+%2B-+sqrt%28+1024+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+%2B-+sqrt%28+1024+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=960 ALIGN=MIDDLE  ALT=\"960\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024 ALIGN=MIDDLE  ALT=\"1024\"   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+=+%28-8+%2B-+sqrt%28+1024+%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+%2B-+sqrt%28+1024+%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   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+=+%28-8+%2B-+32%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+%2B-+32%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024 ALIGN=MIDDLE  ALT=\"1024\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   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+=+%28-8+%2B+32%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+%2B+32%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-8+-+32%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-8+-+32%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2824%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%2824%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=++%28-40%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=++%28-40%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-3%2F4 ALIGN=MIDDLE  ALT=\"t+=+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5%2F4 ALIGN=MIDDLE  ALT=\"t+=+5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So <i>possible</i> the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-3%2F4 ALIGN=MIDDLE  ALT=\"t+=+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5%2F4 ALIGN=MIDDLE  ALT=\"t+=+5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "Since a negative time doesn't make sense, this means that the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5%2F4 ALIGN=MIDDLE  ALT=\"t+=+5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.25 ALIGN=MIDDLE  ALT=\"t=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the pelican will catch the crab in 1.25 seconds. \r<BR>\n" );
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document.write( "Notice how if we plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.25 ALIGN=MIDDLE  ALT=\"t=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > into either equation, we get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%281.25%29=-8%281.25%29%2B15=-10%2B15=5 ALIGN=MIDDLE  ALT=\"g%281.25%29=-8%281.25%29%2B15=-10%2B15=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the pelican will meet with the crab 5 feet in the air. \r<BR>\n" );
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document.write( "So the gull will catch the crab before the crab hits the water. </SPAN>\n" );
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