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document.write( "A roll of tape is on a spool with diameter 3.6 cm. The diameter of the spool plus the diameter
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document.write( "of the tape is 5.4 cm. The tape is 25.4 m long. The number of layers on the tape is closest to
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document.write( "a) 160
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document.write( "b) 180
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document.write( "c) 215
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document.write( "d) 230
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document.write( "e) 1773
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document.write( "The minimum diameter (the diameter of the first layer) is d = 3.6 cm; \r\n" );
document.write( "the circumference (the length) of the first layer is 
= 3.14159*3.6 = 11.309724 cm.\r\n" );
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document.write( "The maximum diameter (the diameter of the last layer) is D = 5.4 cm; \r\n" );
document.write( "the circumference (the length) of the last layer is 
= 3.14159*5.4 = 16.964586 cm.\r\n" );
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document.write( "The lengths of consecutive layers make an arithmetic progression with the common difference 
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document.write( "where 
is the thickness of the tape. Therefore, the number of layers n can be found from \r\n" );
document.write( "the formula of the sum of an arithmetic progression\r\n" );
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document.write( " 2540 = 
= 
= 14.137155*n,\r\n" );
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document.write( " n = 
= 179.67 (approximately).\r\n" );
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document.write( "ANSWER. The number of layers on the tape (approximately 180), is closest to option b).\r\n" );
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document.write( "Solved.\r
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
