document.write( "Question 1210336: (a) The eighth term of an Arithmetic Progression (A.P) is 46 and the sum of the first eight terms is 200. Find the:
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document.write( "(i) first term;
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document.write( "(ii) sum of the first 12 terms. \r
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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.
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document.write( "(i) Illustrate the information in a diagram.
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document.write( "(ii) Find the distance between X and Y along the meridian.
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document.write( "[Take л = 22/7 and R = 6,400 km] \n" );
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Algebra.Com's Answer #851921 by ikleyn(52776)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( "(b) The points X(70°S, 60°E) and Y(7°S, 60°E) lies on the surface of the earth. \n" ); document.write( "(i) Illustrate the information in a diagram. \n" ); document.write( "(ii) Find the distance between X and Y along the meridian. \n" ); document.write( "[Take л = 22/7 and R = 6,400 km] \n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " Calculations in the post by @greenestamps, giving the answer of 3520 km, are erroneous.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "From the school, we know that the Earth circumference along the equator \n" ); document.write( "is about 40,000 kilometers.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "In this problem, we consider the Earth as spherical; so, its circumference \n" ); document.write( "in any meridional section is the same 40,000 km.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Hence, under this assumption, the distance from the South pole to the North pole \n" ); document.write( "along any meridian is half of 40,000 km, i.e. 20,000 km.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "In this problem, the distance between the given points is 70° - 7° = 63°, measured as the difference of altitudes.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "It is about one third of 180°, which represents the distance between the poles, expressed in degrees.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So, we can expect, that the distance between the given points is at least one third of 20,000 km. \n" ); document.write( "i.e., at least 6666 km.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If you want to derive the value using the formula, you should write\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "It is the precise answer (under the given values and assumptions), \n" ); document.write( "and it is consistent with my crude evaluation above.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "---------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Solved, with explanations.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |