document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90368>Question 90368</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073016020/algebrahomeworkh>Beginning Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward from the roof a building 100 m tall with an initial velocity of 20 m/s - when will the ball reach a height of 80 m?\r<BR>\n" );
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document.write( "80 = -16t^2 + 20t + 100<BR>\n" );
document.write( "16t^2 -20t -20 = 0<BR>\n" );
document.write( "4t^2 - 5t - 5 = 0<BR>\n" );
document.write( "t = -(-5) +/- radical (-5)^2 - 4(4)(-5) over 2(4)<BR>\n" );
document.write( "t = 5 +/- radical 25 + 80 over 8<BR>\n" );
document.write( "t = 5 + 10.247 over 8<BR>\n" );
document.write( "t = 15.247 over 8<BR>\n" );
document.write( "t = 1.906 seconds\r<BR>\n" );
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document.write( "Please confirm if I'm doing this correctly - thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65579 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=65579\">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=80+=+-16t%5E2+%2B+20t+%2B+100 ALIGN=MIDDLE  ALT=\"80+=+-16t%5E2+%2B+20t+%2B+100\"   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+20t+%2B+20 ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2+%2B+20t+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 80 from both sides\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+20t+%2B+20 ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2+%2B+20t+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 80 from both sides\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%2B20%2At%2B20=0 ALIGN=MIDDLE  ALT=\"-16%2At%5E2%2B20%2At%2B20=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=20 ALIGN=MIDDLE  ALT=\"b=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=20 ALIGN=MIDDLE  ALT=\"c=20\"   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+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-16%2A20+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+%2820%29%5E2-4%2A-16%2A20+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-16, b=20, and c=20\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+400-4%2A-16%2A20+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+400-4%2A-16%2A20+%29%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 20 to get 400  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-20+%2B-+sqrt%28+400%2B1280+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+400%2B1280+%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%2A20%2A-16 ALIGN=MIDDLE  ALT=\"-4%2A20%2A-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1280 ALIGN=MIDDLE  ALT=\"1280\"   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+=+%28-20+%2B-+sqrt%28+1680+%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+sqrt%28+1680+%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+=+%28-20+%2B-+4%2Asqrt%28105%29%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+4%2Asqrt%28105%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+=+%28-20+%2B-+4%2Asqrt%28105%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B-+4%2Asqrt%28105%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+=+%28-20+%2B+4%2Asqrt%28105%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-20+%2B+4%2Asqrt%28105%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+=+%28-20+-+4%2Asqrt%28105%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-20+-+4%2Asqrt%28105%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=-20%2F-32%2B4%2Asqrt%28105%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-20%2F-32%2B4%2Asqrt%28105%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-20%2F-32-4%2Asqrt%28105%29%2F-32 ALIGN=MIDDLE  ALT=\"t=-20%2F-32-4%2Asqrt%28105%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=5+%2F+8-sqrt%28105%29%2F8 ALIGN=MIDDLE  ALT=\"t=5+%2F+8-sqrt%28105%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5+%2F+8%2Bsqrt%28105%29%2F8 ALIGN=MIDDLE  ALT=\"t=5+%2F+8%2Bsqrt%28105%29%2F8\"   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=-0.65586884574495 ALIGN=MIDDLE  ALT=\"t=-0.65586884574495\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.90586884574495 ALIGN=MIDDLE  ALT=\"t=1.90586884574495\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since a negative time doesn't make sense, our only solution is:\r<BR>\n" );
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document.write( "So you are correct </SPAN>\n" );
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