document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150467>Question 150467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward from a 100 foot tall building with an initial velocity of 14 feet per second.  Its height s(t) in feet is given by the function s(t)= -16t^2+14t+100.  Find the interval of time for which the height of the ball is greater than 103 feet.\r<BR>\n" );
document.write( "\n" );
document.write( "I don't even know where to start. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110437 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown upward from a 100 foot tall building with an initial velocity of 14 feet per second. Its height s(t) in feet is given by the function s(t)= -16t^2+14t+100. Find the interval of time for which the height of the ball is greater than 103 feet. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write the equation for s = 103 ft<BR>\n" );
document.write( "-16t^2 + 14t + 100 = 103<BR>\n" );
document.write( ":<BR>\n" );
document.write( "-16t^2 + 14t + 100 - 103 = 0<BR>\n" );
document.write( ";<BR>\n" );
document.write( "-16t^2 + 14t - 3 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the quadratic formula to find t:<BR>\n" );
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" );
document.write( "In this problem a=-16, b=14; c=-3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B-+sqrt%2814%5E2-4%2A-16%2A-3+%29%29%2F%282%2A-16%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B-+sqrt%2814%5E2-4%2A-16%2A-3+%29%29%2F%282%2A-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B-+sqrt%28196+-+192%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B-+sqrt%28196+-+192%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B-+sqrt%284%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B-+sqrt%284%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+%2B+2%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-14+%2B+2%29%2F%28-32%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+=+%28-12%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-12%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = .375 sec; (passes 103 ft on the way up)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-14+-+2%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-14+-+2%29%2F%28-32%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+=+%28-16%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28-16%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = .5 sec; (passes 103 ft on the way down)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "So the interval of time would be .5 - .375 = .125 sec above 103 ft<BR>\n" );
document.write( ";<BR>\n" );
document.write( "How about this? Does it make sense to you now? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );