document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136159>Question 136159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please, help mw with this\r<BR>\n" );
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document.write( " A ball is thrown upward at a velocity of 12 feet per second from a height that is 40 feet above the ground. The height A (in feet) of the ball at time t (in seconds), after it is thrown, can be found by the formula h = -12t2 + 14t + 40   <BR>\n" );
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document.write( "Find the time, in seconds, when the ball is again 40 feet above the ground.<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 #99721 by </B><A HREF=/tutors/aboutme.mpl?userid=JSmall><B>JSmall(7)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JSmall><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=99721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since you are interested in when the height is 40, set h to 40:<BR>\n" );
document.write( "  h = -12t2 + 14t + 40<BR>\n" );
document.write( "  40 = -12t2 + 14t + 40<BR>\n" );
document.write( "Now solve this equation for t by<BR>\n" );
document.write( "1) Getting one side equal of the equation to zero; and then<BR>\n" );
document.write( "2) Using factoring or the quadratic formula to solve for t\r<BR>\n" );
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document.write( "To get one side equal to zero, subtract 40 from each side:<BR>\n" );
document.write( "  40 - 40 = -12t2 + 14t + 40 - 40<BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "  0       = -12t2 + 14t + 0<BR>\n" );
document.write( "or<BR>\n" );
document.write( "  0       = -12t2 + 14t\r<BR>\n" );
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document.write( "Since the expression on the right is easily factored, factoring will be used in this solution. (The quadratic formula can also be used.)\r<BR>\n" );
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document.write( "Always start factoring with the greatest common factor (GCF). In this case the GCF is 2t.<BR>\n" );
document.write( "  0       = 2t (-6t + 7)<BR>\n" );
document.write( "This is all the factoring that can be done.\r<BR>\n" );
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document.write( "In order for this product (multiplication) to be zero, one of the factors must be zero. So<BR>\n" );
document.write( "  2t = 0<BR>\n" );
document.write( "or<BR>\n" );
document.write( "  -6t + 7 = 0\r<BR>\n" );
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document.write( "Solve each of these equations for t. Divide both sides of<BR>\n" );
document.write( "  2t = 0<BR>\n" );
document.write( "by 2 and get<BR>\n" );
document.write( "  2t/2 = 0/2<BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "  t = 0<BR>\n" );
document.write( "This says the ball was at height 40 at t = 0, the start (which we already knew).\r<BR>\n" );
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document.write( "For the other equation, subtract 7 from each side:<BR>\n" );
document.write( "  -6t + 7 - 7 = 0 - 7<BR>\n" );
document.write( "giving<BR>\n" );
document.write( "  -6t + 0 = -7<BR>\n" );
document.write( "or<BR>\n" );
document.write( "  -6t = -7<BR>\n" );
document.write( "Now divide both sides of the equation by -6:<BR>\n" );
document.write( "  -6t/-6 = -7/-6<BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "  t = 7/6<BR>\n" );
document.write( "or, writing 7/6 as a mixed number:<BR>\n" );
document.write( "  t = 1 1/6<BR>\n" );
document.write( "So the ball must return to a height of 40 after 1 1/6 seconds.\r<BR>\n" );
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