3_ch 01 Mechanical Design budynas_SM_ch01

3_ch 01 Mechanical Design budynas_SM_ch01 - Ans(b X 1 = 2...

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Chapter 1 3 1-7 (a) x 1 + x 2 = X 1 + e 1 + X 2 + e 2 error = e = ( x 1 + x 2 ) ( X 1 + X 2 ) = e 1 + e 2 Ans. (b) x 1 x 2 = X 1 + e 1 ( X 2 + e 2 ) e = ( x 1 x 2 ) ( X 1 X 2 ) = e 1 e 2 Ans. (c) x 1 x 2 = ( X 1 + e 1 )( X 2 + e 2 ) e = x 1 x 2 X 1 X 2 = X 1 e 2 + X 2 e 1 + e 1 e 2 . = X 1 e 2 + X 2 e 1 = X 1 X 2 µ e 1 X 1 + e 2 X 2 Ans. (d) x 1 x 2 = X 1 + e 1 X 2 + e 2 = X 1 X 2 µ 1 + e 1 / X 1 1 + e 2 / X 2 µ 1 + e 2 X 2 1 . = 1 e 2 X 2 and µ 1 + e 1 X 1 ¶µ 1 e 2 X 2 . = 1 + e 1 X 1 e 2 X 2 e = x 1 x 2 X 1 X 2 . = X 1 X 2 µ e 1 X 1 e 2 X 2 Ans. 1-8 (a) x 1 = 5 = 2 . 236 067 977 5 X 1 = 2 . 23 3-correct digits x 2 = 6 = 2 . 449 487 742 78 X 2 = 2 . 44 3-correct digits x 1 + x 2 = 5 + 6 = 4 . 685 557 720 28 e 1 = x 1 X 1 = 5 2 . 23 = 0.006 067 977 5 e 2 = x 2 X 2 = 6 2 . 44 = 0.009 489 742 78 e = e 1 + e 2 = 5 2 . 23 + 6 2 . 44 = 0.015 557 720 28 Sum = x 1 + x 2 = X 1 + X 2 + e = 2 . 23 + 2 . 44 + 0 . 015 557 720 28 = 4.685 557 720 28 (Checks)
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Unformatted text preview: Ans. (b) X 1 = 2 . 24, X 2 = 2 . 45 e 1 = √ 5 − 2 . 24 = − . 003 932 022 50 e 2 = √ 6 − 2 . 45 = − . 000 510 257 22 e = e 1 + e 2 = − . 004 442 279 72 Sum = X 1 + X 2 + e = 2 . 24 + 2 . 45 + ( − . 004 442 279 72) = 4 . 685 557 720 28 Ans....
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