# Answer_to_problems - ME 130 Applied Engineering Analysis...

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1 ME 130 Applied Engineering Analysis Answers to Selected Problems Instructor: Dr. Tai-Ran Hsu Chapter 2: Homework on applications of differentiation and integration Problem 2.7: (a) 3 2 x ? (b) x 2 1 1 ? (c) 3 ) 2 ( 2 1 x ? ? Problem 2.8: (a) 4 r y ave ? ? (b) 3 8 ? ave y Problem 2.9: (a) 32 5 9 ? ? C F (b) - 40 o Problem 2.10: r(x) = -0.1 x + 10 Problem 2.11: V = 9158 cm 3 Problem 2.12: dt t dX t V ) ( ) ( ? Problem 2.13: ) ( ) ( ) ( 3 2 3 x u W x u W x W L o L o ? ? 0 < x < 8 Problem 2.14: ) ( 2 1 2 1 ) ( 2 x u x L W x L W x W L o o ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 0 < x < 8 Problem 2.15: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3 2 3 ) ( L x P L x P x P o o ? ? 0 < x < 8 Problem 2.16:

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2 Area A = pab 4 b a dy y a y a b 4 I 3 2 2 a 0 2 x ? ? ? ? ? Problem 2.17: ? ? x L 2 Cos P x P o ? ? Problem 2.18: Total area = 24 unit square units 166 . 2 y ; units 33 . 4 x ? ? Chapter 3 First Order Ordinary Differential Equations Problem 3.1: u(x) = K e 10x with K = constant Problem 3.2: x e K x u 2 2 3 ) ( ? ? ? with K = constant Problem 3.3: ? ? x Cos e Cos K x u 1 ) ( ? ? with K = constant Problem 3.4: 2 2 ) ( ? ? ? x Cx n x u ? with C = constant Problem 3.5: Kx n x x u ? 2 ) ( ? ? with K = constant Problem 3.6: ? ? 3 / 1 3 ) ( Kx n x x u ? ? with K = constant Problem 3.7: K x x x x u ? ? ? ) ( with K = constant Problem 3.8: ? ? 1 5 2 1 ) ( 2 ? ? x e x u Problem 3.9: x x x u 9 ) ( ? ? Problem 3.10: ? ? ? ? e e x x u x x u x 2 ) ( 1 ) ( 2 2 2 ? ? ? ?
3 Problem 3.11: 35.89 seconds to empty the tank. Problem 3.12: (a) ) ( 4 2 ) ( 2 t H LW d g dt t dH ? ? ? ? ? ? ? ? ? ? ? (b) 2 2 4 2 ) ( ? ? ? ? ? ? ? ? ? ? ? D t LW d g t H ? (c) LW d g D t e 4 2 2 ? ? t e = 45164 seconds or 12.55 hrs to empty the pool. Problem 3.13: t g 2 12 d H y 5 2 2 2 5 2 5 ? ? ? ? ? ? ? ? ? ? ? t

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## Answer_to_problems - ME 130 Applied Engineering Analysis...

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