document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210336>Question 1210336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) The eighth term of an Arithmetic Progression (A.P) is 46 and the sum of the first eight terms is 200. Find the:<BR>\n" );
document.write( "(i) first term; <BR>\n" );
document.write( "(ii) sum of the first 12 terms. \r<BR>\n" );
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document.write( "(b) The points X(70°S, 60°E) and Y(7°S, 60°E) lies on the surface of the earth. <BR>\n" );
document.write( "(i) Illustrate the information in a diagram. <BR>\n" );
document.write( "(ii) Find the distance between X and Y along the meridian. <BR>\n" );
document.write( "[Take л = 22/7 and R = 6,400 km] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851921 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "(b) The points X(70°S, 60°E) and Y(7°S, 60°E) lies on the surface of the earth.<BR>\n" );
document.write( "(i) Illustrate the information in a diagram.<BR>\n" );
document.write( "(ii) Find the distance between X and Y along the meridian.<BR>\n" );
document.write( "[Take л = 22/7 and R = 6,400 km]<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculations in the post by @greenestamps, giving the answer of 3520 km,  are erroneous.\r<BR>\n" );
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document.write( "From the school, we know that the Earth circumference along the equator <BR>\n" );
document.write( "is about 40,000 kilometers.\r<BR>\n" );
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document.write( "In this problem, we consider the Earth as spherical; so, its circumference <BR>\n" );
document.write( "in any meridional section is the same 40,000 km.\r<BR>\n" );
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document.write( "Hence, under this assumption, the distance from the South pole to the North pole <BR>\n" );
document.write( "along any meridian is half of 40,000 km, i.e. 20,000 km.\r<BR>\n" );
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document.write( "In this problem, the distance between the given points is 70° - 7° = 63°, measured as the difference of altitudes.\r<BR>\n" );
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document.write( "It is about one third of 180°, which represents the distance between the poles, expressed in degrees.\r<BR>\n" );
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document.write( "So, we can expect, that the distance between the given points is at least one third of 20,000 km.<BR>\n" );
document.write( "i.e., at least  6666 km.\r<BR>\n" );
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document.write( "If you want to derive the value using the formula, you should write\r<BR>\n" );
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document.write( "  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2870-7%29%2F360%29%2A%282%2Api%2AR%29 ALIGN=MIDDLE  ALT=\"%28%2870-7%29%2F360%29%2A%282%2Api%2AR%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2870-7%29%2F180%29%2A%2822%2F7%29%2A6400 ALIGN=MIDDLE  ALT=\"%28%2870-7%29%2F180%29%2A%2822%2F7%29%2A6400\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2863%2F180%29%2A%2822%2F7%29%2A6400 ALIGN=MIDDLE  ALT=\"%2863%2F180%29%2A%2822%2F7%29%2A6400\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F20%29%2A%2822%2F7%29%2A6400 ALIGN=MIDDLE  ALT=\"%287%2F20%29%2A%2822%2F7%29%2A6400\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2822%2F20%29%2A6400 ALIGN=MIDDLE  ALT=\"%2822%2F20%29%2A6400\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 22*320 = 7040 kilometers.\r<BR>\n" );
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document.write( "It is the precise answer (under the given values and assumptions), <BR>\n" );
document.write( "and it is consistent with my crude evaluation above.\r<BR>\n" );
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document.write( "Solved, with explanations.\r<BR>\n" );
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