EvenProblemSolutions

# EvenProblemSolutions - Answers to even-numbered problems in...

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Answers to even-numbered problems in Mathematics for Economic Analysis Knut Sydsæter Peter Hammond

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CHAPTER 1 INTRODUCTION 1 Chapter 1 Introduction 1.3 2. (a) Put p/ 100 = x . Then the given expression becomes a + ax (a + ax)x = a( 1 x 2 ) , as required. (b) \$2000 · 1 . 05 · 0 . 95 = \$1995. (c) The result is precisely the formula in (a). (d) With the notation used in the answer to (a), a + (a = 1 x 2 ) , which is the same expression as in (a). 4. (a) F = 32 yields C = 0; C = 100 yields F = 212. (b) F = 9 5 C + 32 (c) F = 40 for C 4 . 4, F = 80 for C 26 . 7. The assertion is meaningless. 6. x = R( 1 p) S( 1 q) (p q)( 1 p , y = pS qR (p 1 p if (p 1 p 6= 0. (Use, for example, (A.39) in Section A.9.) 1.4 2. (a) Correct. (b) Incorrect. (c) Incorrect. (d) Correct. (e) Incorrect. (f) Incorrect. (“Usually” the sum of two irrationals is irrational, but not always. For example, π and π are both irrationals, but π + ( π) = 0, which is rational.) 4. (a) y 3 3 4 x (b) y> 3 2 z (c) y (m px)/q 6. | 2 · 0 3 |=|− 3 |= 3, | 2 · 1 2 3 2 2, | 2 · 7 2 3 |=| 4 4 8. (a) 3 2 x = 5o r3 2 x =− 5, so 2 x = 2o r 8. Hence x 1o r x = 4. (b) 2 x 2 (c) 1 x 3 (d) 1 / 4 x 1 (e) x> 2or x< 2 (f) 1 x 2 3, and so 1 x 3o r 3 x ≤− 1 1.5 2. (a) right, wrong (b) wrong, right (c) right, wrong (d) and both right (e) wrong (0 · 5 = 0 · 4, but 5 4), right (f) right, wrong 4. x = 2. ( x 1, 0 or 1 make the equation meaningless. Multiplying each term by the common de- nominator x(x 1 )(x + 1 ) yields (x + 1 ) 3 + (x 1 ) 3 2 x( 3 x + 1 ) = 0. Expanding and simplifying, 2 x 3 6 x 2 + 4 x = 0, or 2 2 3 x + 2 ) = 0, or 2 1 )(x 2 ) = 0. Hence, x = 2 is the only solution.) 6. (a) No solutions. (Squaring each side yields x 4 = x + 5 18 x + 5 +

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EvenProblemSolutions - Answers to even-numbered problems in...

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