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Suppose that at some future time every telephone in the world is assigned a number that contains a country code, 1 to 3 digits long, that is, of the form X, XX , XXX or followed by a ten-digit telephone number of the form NXX-NXX-XXXX. A telephone number consists of ten digits, which are split into a three-digit area code, a three-digit office code, and a four-digit station code. Because of signaling considerations, there are certain restrictions on some of these digits.
To specify the allowable format, let denote a digit that can take any of the values 0 through 9 and let denote a digit that can take any of the values 2 through 9.
How many different telephone numbers would be available worldwide under this numbering plan?
sin (cot -1 {cos (tan -1 x)}) tan -1 x = A => tan A =x sec A = √(1+x 2 ) ==> cos A = 1/√(1+x 2 ) so A = cos -1 (1/√(1+x 2 )) sin (cot -1 {cos (tan -1 x)}) = s
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