document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=375015>Question 375015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi Totally Bewildered, Please Help?\r<BR>\n" );
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document.write( "The path of a point is given parametrically by x = a cos t, y = b sin t. Show that the point travels<BR>\n" );
document.write( "around the ellipse<BR>\n" );
document.write( "x^2/a^2 +y^2/b^2 = 1\r<BR>\n" );
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document.write( "Express dy=dx in terms of t. Suppose that t represents time. Express the speed as a function of t.\r<BR>\n" );
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document.write( "ii) A closed hollow vessel is in the form of a right-circular cone, together with its base, and is made of sheet<BR>\n" );
document.write( "metal of negligible thickness.<BR>\n" );
document.write( "Express the total surface area S in terms of the volume V and the semi-vertical angle 'theta' of the cone.<BR>\n" );
document.write( "Show that for a given volume, the total area of the surface is a minimum if sin 'theta' = 1/3 . With this value of 'theta', find<BR>\n" );
document.write( "the value of S if V = 8/3'pie' a^3 where a is a constant.\r<BR>\n" );
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document.write( "Sorry didnt know how to get symbols on this, so typed the names\r<BR>\n" );
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document.write( "Kind Regards<BR>\n" );
document.write( "John </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266711 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=266711\">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( "Given\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ a\cos(t)\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ b\sin(t)\">\r<BR>\n" );
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document.write( "Square both parametric equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ =\ a^2\cos^2(t)\ \Rightarrow\ \ \frac{x^2}{a^2}\ =\ \cos^2(t)\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y^2\ = b^2\sin^2(t)\ \Rightarrow\ \ \frac{y^2}{b^2}\ =\ \sin^2(t)\">\r<BR>\n" );
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document.write( "Recall the Pythagorean Identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\varphi\ +\ \sin^2\varphi\ =\ 1\">\r<BR>\n" );
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document.write( "hence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y^2}{b^2}\ =\ 1\ -\ \cos^2(t)\">\r<BR>\n" );
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document.write( "Then substitute:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{y^2}{b^2}\ =\ 1\ -\ \frac{x^2}{a^2}\">\r<BR>\n" );
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document.write( "And finally:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2}{a^2}\ +\ \frac{y^2}{b^2}\ =\ 1\">\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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