document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60892>Question 60892</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need help with this question. \r<BR>\n" );
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document.write( "When a ball is thrown vertically upward, its height (h, in feet)above the ground after t seconds is described by the mathematical formula <BR>\n" );
document.write( "h=12t^2 + 96t +80. At what times is the ball 103 feet above the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41949 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=41949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for expressing the height, h, at time, t, of an object thrown upwards with an initial velocity of Vo from an initial height of Ho, is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28h%29+=+-16t%5E2+%2BVot+%2B+Ho ALIGN=MIDDLE  ALT=\"f%28h%29+=+-16t%5E2+%2BVot+%2B+Ho\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Notice that the coefficient of t^2 is negative to account for the doward (negative) effect of gravity.\r<BR>\n" );
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document.write( "In your problem, the initial upward velocity, Vo = 96 and the initial height, Ho = 80.<BR>\n" );
document.write( "You want to find at what time, t, will f(h) = 103, so we'll set the equation = 103 and solve for t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B96t%2B80+=+103 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B96t%2B80+=+103\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 103 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B96t-23+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B96t-23+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve this quadratic equation using the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: a = -16, b = 96, and c = -23, and because you are solve a quadratic equation, you can expect to get two answers for t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B96t-23+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B96t-23+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-96%2B-sqrt%2896%5E2-4%28-16%29%28-23%29%29%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-96%2B-sqrt%2896%5E2-4%28-16%29%28-23%29%29%29%2F2%28-16%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+=+%28-96%2B-sqrt%289216-1472%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-96%2B-sqrt%289216-1472%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-96%2B-sqrt%287744%29%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-96%2B-sqrt%287744%29%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-96%2Bor-88%29%2F-32 ALIGN=MIDDLE  ALT=\"t+=+%28-96%2Bor-88%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3%2B%28-2.75%29 ALIGN=MIDDLE  ALT=\"t+=+3%2B%28-2.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+3-%28-2.75%29 ALIGN=MIDDLE  ALT=\"t+=+3-%28-2.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5.75\r<BR>\n" );
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document.write( "The answers are:<BR>\n" );
document.write( "t = 5.75 seconds. The ball is at 103 feet on the way down.<BR>\n" );
document.write( "t = 0.25 seconds. The ball is at 103 feet on the way up. </SPAN>\n" );
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