document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=375008>Question 375008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HiPlease can somebody help with this problem 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). Provethat dy/dx = t(2 + 5t^3)/1 + 4t^3  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 maybe given parametrically by x = a(t - sin t) and y = a(1 - cos t), where a is a constant. Show thatdy/dx = cot(t/2) Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266696 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3t%281+%2B+t%5E3%29=3t%2B3t%5E4 ALIGN=MIDDLE  ALT=\"x+=+3t%281+%2B+t%5E3%29=3t%2B3t%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dx%2Fdt=3%2B12t%5E3 ALIGN=MIDDLE  ALT=\"dx%2Fdt=3%2B12t%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdt=6t%2B15t%5E4 ALIGN=MIDDLE  ALT=\"dy%2Fdt=6t%2B15t%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=%286t%2B15t%5E4%29%2F%283%2B12t%5E3%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=%286t%2B15t%5E4%29%2F%283%2B12t%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=%283t%282%2B5t%5E3%29%29%2F%283%281%2B4t%5E3%29%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=%283t%282%2B5t%5E3%29%29%2F%283%281%2B4t%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=%28t%282%2B5t%5E3%29%29%2F%28%281%2B4t%5E3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use the same method.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a%28t+-+sin+t%29 ALIGN=MIDDLE  ALT=\"x+=+a%28t+-+sin+t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%281+-+cos+t%29 ALIGN=MIDDLE  ALT=\"y+=+a%281+-+cos+t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dx%2Fdt=a%281-cos%28t%29%29 ALIGN=MIDDLE  ALT=\"dx%2Fdt=a%281-cos%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdt=a%28sin%28t%29%29 ALIGN=MIDDLE  ALT=\"dy%2Fdt=a%28sin%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=%28a%28sin%28t%29%29%29%2F%28a%281-cos%28t%29%29%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=%28a%28sin%28t%29%29%29%2F%28a%281-cos%28t%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=1%2F%281%2Fsin%28t%29-1%2Ftan%28t%29%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=1%2F%281%2Fsin%28t%29-1%2Ftan%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=1%2F%28csc%28t%29-cot%28t%29%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=1%2F%28csc%28t%29-cot%28t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=1%2Ftan%28t%2F2%29 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=1%2Ftan%28t%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=cot%28t%2F2%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28dy%2Fdx=%28dy%2Fdt%29%2F%28dx%2Fdt%29=cot%28t%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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