document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062615>Question 1062615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.\r<BR>\n" );
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document.write( "Thank you. I would like to know how to obtain the answer. as well as the correct answer if you please.<BR>\n" );
document.write( "I sincerely appreciate your assistance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677570 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) h(t) = -t^2 +3t +10<BR>\n" );
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document.write( "The graph of h(t) is a parabola that curves downward<BR>\n" );
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document.write( "at t = 0, h(t) = 10, I assume this is the height of the platform above the ground<BR>\n" );
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document.write( "The max height of the rocket is determined from the first derivative<BR>\n" );
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document.write( "dh/dt = -2t + 3<BR>\n" );
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document.write( "-2t + 3 = 0<BR>\n" );
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document.write( "t = 3/2 = 1.5 seconds<BR>\n" );
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document.write( "substitute for t in h(t)<BR>\n" );
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document.write( "h(1.5) = -(1.5)^2 +3(1.5) + 10 = 12.25<BR>\n" );
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document.write( "here is a graph of the parabola<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+0%2C+10%2C+0%2C+15%2C+-x%5E2+%2B+3%2Ax+%2B10%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+0%2C+10%2C+0%2C+15%2C+-x%5E2+%2B+3%2Ax+%2B10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the rocket reaches the platform when<BR>\n" );
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document.write( "x^2 = 3x<BR>\n" );
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document.write( "x = 3<BR>\n" );
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document.write( "to check this, substitute in equation 1)<BR>\n" );
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document.write( "h(3) = -(3^2) +3(3) + 10 = 10<BR>\n" );
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document.write( "the rocket reaches the platform when t = 3 seconds<BR>\n" );
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