document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109956>Question 109956</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0074711571/algebrahomeworkh>Mathematics for Technicians</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hi everyone.<BR>\n" );
document.write( "I am stuck on another problem which I have been working on since yesterday morning, and although I have the answer from the text. I have absolutely no idea how they have came about it, any assistance would be greatly appreciated. Cheers D<BR>\n" );
document.write( "The question is as follows:-<BR>\n" );
document.write( "The frequency of revolution, n (i.e. the number of orbits per unit of time), of a satellite above the earth varies inversely as sqrt r^3, where r is the radius of orbit. Given that a satellite whose radius of orbit is 5080 km orbits the earth each hour, find:<BR>\n" );
document.write( "The radius of orbit for a satellite that orbits the earth once per day (correct to the nearest 100 km)<BR>\n" );
document.write( "It gives me an answer of 42,300 km. This is however how I have gone about trying to solve this problem: ((sqrt5080^3)*(1/24))/(24/1)= 628.598. I have tried various different combinations but am still struggling to get the correct answer.<BR>\n" );
document.write( "Again your help and assistance would be greatly appreciated. Thank you. Cheers D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80122 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=80122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The given information is on a satellite that makes an orbit an hour. This means that it <BR>\n" );
document.write( "has a frequency of 24 orbits per day.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since it's frequency (f) varies inversely as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28r%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%28r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where r is the radius of the orbit, <BR>\n" );
document.write( "you can write the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+k%2F%28sqrt%28r%5E3%29%29 ALIGN=MIDDLE  ALT=\"f+=+k%2F%28sqrt%28r%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "where k is a constant of proportionality that adjusts for the units used etc.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since for the given satellite you know that its frequency is 24 orbits per day and its radius<BR>\n" );
document.write( "is 5080 km, you can substitute these values to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+=+k%2F%28sqrt%285080%5E3%29%29 ALIGN=MIDDLE  ALT=\"24+=+k%2F%28sqrt%285080%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve this for k by multiplying both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285080%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%285080%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to eliminate the denominator.<BR>\n" );
document.write( "With this multiplication you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Asqrt%285080%5E3%29+=+k ALIGN=MIDDLE  ALT=\"24%2Asqrt%285080%5E3%29+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "When you calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285080%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%285080%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get 362072.5231. Multiplying this by 24 results<BR>\n" );
document.write( "in this equation becoming:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8689740.555+=+k ALIGN=MIDDLE  ALT=\"8689740.555+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now that we know the value of k we can substitute it into the equation for the frequency to<BR>\n" );
document.write( "make it:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+k%2F%28sqrt%28r%5E3%29%29=+8689740.555%2F%28sqrt%28r%5E3%29%29 ALIGN=MIDDLE  ALT=\"f+=+k%2F%28sqrt%28r%5E3%29%29=+8689740.555%2F%28sqrt%28r%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that the way k was calculated requires that the frequency be specified in units of<BR>\n" );
document.write( "orbits per day and the radius be specified in km in order for the equation to work.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So now you have the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+8689740.555%2F%28sqrt%28r%5E3%29%29 ALIGN=MIDDLE  ALT=\"f+=+8689740.555%2F%28sqrt%28r%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You are given that a satellite makes 1 orbit per day and are asked to find the radius <BR>\n" );
document.write( "of its orbit. Substitute 1 for f and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+8689740.555%2F%28sqrt%28r%5E3%29%29 ALIGN=MIDDLE  ALT=\"1+=+8689740.555%2F%28sqrt%28r%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the denominator by multiplying both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28r%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%28r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "When you do that the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28r%5E3%29+=+8689740.555 ALIGN=MIDDLE  ALT=\"sqrt%28r%5E3%29+=+8689740.555\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Square both sides of this equation to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3+=+8689740.555%5E2+=+7.551159091%2A10%5E13 ALIGN=MIDDLE  ALT=\"r%5E3+=+8689740.555%5E2+=+7.551159091%2A10%5E13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for r by taking the cube root of both sides:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+root%283%2C7.551159091%2A10%5E13%29+=+42267.30328 ALIGN=MIDDLE  ALT=\"r+=+root%283%2C7.551159091%2A10%5E13%29+=+42267.30328\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "That rounds off to 42,300 km which is the answer you were given.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to see how to do the problem and aids you to identify the stuff that<BR>\n" );
document.write( "gave you the difficulty.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );