document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4263>Question 4263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula h=50t-5t^2 can be used to find the height in meters of a object shot upward at an initial velocity of 50 meters per second after t seconds. When will the height be 100 meters (on its way down) from when it was shot? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1931 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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/cgi-bin/show-face.mpl?user=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+50+t+-+5t%5E2 ALIGN=MIDDLE  ALT=\"h+=+50+t+-+5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the question is when will h=100 meters.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+=+50t+-+5t%5E2 ALIGN=MIDDLE  ALT=\"100+=+50t+-+5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since this is a quadratic equation, you must set it equal to zero by moving everything either to the left side or the right side.  My preference, in order to eliminate the negative coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is to move everything to the left side.  In other words, add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B5t%5E2 ALIGN=MIDDLE  ALT=\"%2B5t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-50t ALIGN=MIDDLE  ALT=\"-50t\"   DISABLED_style= \"max-width:90%; height:auto;\" > to each side. \r<BR>\n" );
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document.write( "Writing this with the highest powers of x first, it gives you <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5t%5E2+-+50t+%2B+100+=+0 ALIGN=MIDDLE  ALT=\"5t%5E2+-+50t+%2B+100+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides of the equation by 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-+10t+%2B+20+=+0 ALIGN=MIDDLE  ALT=\"t%5E2+-+10t+%2B+20+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve by completing the square or quadratic formula.  Completing the square is easier in this case.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-+10t+%2B+_____+=+-20+%2B+______ ALIGN=MIDDLE  ALT=\"t%5E2+-+10t+%2B+_____+=+-20+%2B+______\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take half of the -10 (which is -5) and square (which is 25), so you must add 25 to each side of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+-+10t+%2B+25++=+-20+%2B+25 ALIGN=MIDDLE  ALT=\"t%5E2+-+10t+%2B+25++=+-20+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28t-5%29%5E2+=+5+ ALIGN=MIDDLE  ALT=\"++%28t-5%29%5E2+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the square root of each side of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28t+-+5%29+=+0+%2B-+sqrt+%285%29+ ALIGN=MIDDLE  ALT=\"+%28t+-+5%29+=+0+%2B-+sqrt+%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add +5 to each side of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+5+%2B+5++=+0+%2B+5+%2B-+sqrt+%285%29+ ALIGN=MIDDLE  ALT=\"+t+-+5+%2B+5++=+0+%2B+5+%2B-+sqrt+%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+5+%2B-+sqrt+%285%29+ ALIGN=MIDDLE  ALT=\"+t+=+5+%2B-+sqrt+%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Of course the smaller of these values is the time to reach 100 meters going up, and the larger of these values is the time required to reach 100 meters coming back down.   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5+-+sqrt+%285%29+ ALIGN=MIDDLE  ALT=\"t+=+5+-+sqrt+%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the time required to get UP to 100 meters, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5+%2B+sqrt+%285%29+ ALIGN=MIDDLE  ALT=\"t+=+5+%2B+sqrt+%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is about 7.2 seconds) is the time required to reach 100 meters on the way down.  \r<BR>\n" );
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