document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=324748>Question 324748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me work through this word problem?\r<BR>\n" );
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document.write( "A flare is fired directly upward into the air from a boat that is experiencing engine problems. The height of the flare (in feet) above the water, t seconds after being fired, is given by the formula h = -16t2 + 128t + 15. If the flare is designed to explode when it reaches its highest point, at what height will this occur?\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Alberto<BR>\n" );
document.write( "beto@san.rr.com </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #232463 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=232463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(t)\ =\ -16t^2\ +\ 128t\ +\ 15\">\r<BR>\n" );
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document.write( "Note that the graph of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\"> is a parabola.  It opens downward because the lead coefficient is negative, hence the vertex is a maximum.  The value of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex of a parabola which equation is in standard form is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_v\ =\ \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "for this problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_v\ =\ \frac{-128}{2(-16)}\ =\ 4\">\r<BR>\n" );
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document.write( "hence the maximum height is reached 4 seconds after the flare is fired.  The maximum height reached is therefore <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h(4)\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(4)\ =\ -16(4)^2\ +\ 128(4)\ +\ 15\">\r<BR>\n" );
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document.write( "You can do your own arithmetic.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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