document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117153>Question 117153</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013062568x/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have to simplify each expression. # 11 is: (2+3i)(8-5i). <BR>\n" );
document.write( "And # 14 is: Physics<BR>\n" );
document.write( "For a model rocket, the altitude h, in meters, as a function of time t, in seconds, is given by h=68t-8t(squared). Find the maximum height of the rocket. How long does it take to reach the maximum height? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86590 by </B><A HREF=/tutors/aboutme.mpl?userid=wgunther><B>wgunther(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=wgunther><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=86590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2(8-5i)+3i(8-5i)=16-10i+24i+15=31+14i\r<BR>\n" );
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document.write( "So, the maximum height is when h is at it's maximum in h=68t-8t^2. There's a lot of ways to find this out.\r<BR>\n" );
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document.write( "One could, for example, take the first derivative, which would be 68-16t which is 0 when t=17/4, so the maximum is 68(17/4)-8(17/4)=255. \r<BR>\n" );
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document.write( "Another way would be to take advantage of the symmetry of quadratics, and say that the two zeros of 68t-8t^2 are 0 and 17/2, so the maximum occurs halfway in between them, or at 17/4. \r<BR>\n" );
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document.write( "Another way is the generalization you may have learned that the vertex is at the x value -b/2a, which is this case is -68/-16=17/4. Lots of ways. </SPAN>\n" );
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