document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=373946>Question 373946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "     Please can somebody help with this problem\r<BR>\n" );
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document.write( "i) The variables x and y are given in terms of the parameter t as x = 3t(1 + t^3) and y = 3t^2(1 + t^3). Prove<BR>\n" );
document.write( "that\r<BR>\n" );
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document.write( "dy/dx = t(2 + 5t^3)/1 + 4t^3 \r<BR>\n" );
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document.write( "ii) A cycloid is a curve traced out by a point on the rim of a wheel as it rolls along the ground. Its curve may<BR>\n" );
document.write( "be given parametrically by x = a(t - sin t) and y = a(1 - cos t), where a is a constant. Show that<BR>\n" );
document.write( "dy/dx = cot(t/2)\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266189 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i) The variables x and y are given in terms of the parameter t as x = 3t(1 + t^3) and y = 3t^2(1 + t^3). Prove<BR>\n" );
document.write( "that\r<BR>\n" );
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document.write( "dy/dx = t(2 + 5t^3)/1 + 4t^3<BR>\n" );
document.write( "Find dy/dt and dx/dt<BR>\n" );
document.write( "Divide dy/dt by dx/dt, you'll see that's what it is.<BR>\n" );
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document.write( "ii) A cycloid is a curve traced out by a point on the rim of a wheel as it rolls along the ground. Its curve may<BR>\n" );
document.write( "be given parametrically by x = a(t - sin t) and y = a(1 - cos t), where a is a constant. Show that<BR>\n" );
document.write( "dy/dx = cot(t/2)<BR>\n" );
document.write( "dy/dt = asin(t)<BR>\n" );
document.write( "dx/dt = a(1 - cos(t))<BR>\n" );
document.write( "dy/dx = sin(t)/(1 - cos(t))<BR>\n" );
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document.write( "Use half-angle formula for cot(t/2)<BR>\n" );
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