document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=876382>Question 876382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The time a planet takes to revolve once around the sun relates directly to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > power of the planet's average distance from the sun in millions of kilometres. Thus: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=f%28d%29=kd%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"t=f%28d%29=kd%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) if it takes the earth on year to revolve around the sun at an average distance of 150 000 000 km, determine the value of k. Write the equation for f(d). \r<BR>\n" );
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document.write( "b) Use f(d) to find how many earth years it takes Mercury to revolve once around the sun, if its average distance from the sun is 58 000 000km. \r<BR>\n" );
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document.write( "c) Is this an irrational function? Does it have a restricted domain?\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 #528813 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=528813\">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=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= time a planet takes to revolve once around the sun (in Earth years).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= distance from the sun to the planet (in millions of km).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=f%28d%29=kd%5E%28%223+%2F+2%22%29 ALIGN=MIDDLE  ALT=\"t=f%28d%29=kd%5E%28%223+%2F+2%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a) For Earth, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=150 ALIGN=MIDDLE  ALT=\"d=150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=k%2A150%5E%28%223+%2F+2%22%29 ALIGN=MIDDLE  ALT=\"1=k%2A150%5E%28%223+%2F+2%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F150%5E%28%223+%2F+2%22%29=k ALIGN=MIDDLE  ALT=\"1%2F150%5E%28%223+%2F+2%22%29=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=1%2F750sqrt%286%29 ALIGN=MIDDLE  ALT=\"k=1%2F750sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=sqrt%286%29%2F4500%29 ALIGN=MIDDLE  ALT=\"highlight%28k=sqrt%286%29%2F4500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The approximate value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=0.00054433%29 ALIGN=MIDDLE  ALT=\"highlight%28k=0.00054433%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%28t=f%28d%29=0.00054433d%5E%28%223+%2F+2%22%29%29 ALIGN=MIDDLE  ALT=\"highlight%28t=f%28d%29=0.00054433d%5E%28%223+%2F+2%22%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "b) For Mercury, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=58 ALIGN=MIDDLE  ALT=\"d=58\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=f%2858%29=0.00054433%2A58%5E%28%223+%2F+2%22%29=0.240 ALIGN=MIDDLE  ALT=\"t=f%2858%29=0.00054433%2A58%5E%28%223+%2F+2%22%29=0.240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It takes Mercury <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.240%29 ALIGN=MIDDLE  ALT=\"highlight%280.240%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Earth years to revolve once around the sun.<BR>\n" );
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document.write( "c) I had not heard the term \"irrational function\" before, but then again, I am not a fan of calling anything names.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=f%28d%29=0.00054433d%5E%28%223+%2F+2%22%29 ALIGN=MIDDLE  ALT=\"t=f%28d%29=0.00054433d%5E%28%223+%2F+2%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a rational function,<BR>\n" );
document.write( "because rational functions are quotients of polynomials, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=f%28d%29=0.00054433d%5E%28%223+%2F+2%22%29 ALIGN=MIDDLE  ALT=\"t=f%28d%29=0.00054433d%5E%28%223+%2F+2%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an exponential function.<BR>\n" );
document.write( "It does have a restricted domain because we expect <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%3E0 ALIGN=MIDDLE  ALT=\"d%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%3C0 ALIGN=MIDDLE  ALT=\"d%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E%28%223+%2F+2%22%29=sqrt%28d%5E3%29 ALIGN=MIDDLE  ALT=\"d%5E%28%223+%2F+2%22%29=sqrt%28d%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > undefined. </SPAN>\n" );
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