Math141HWAnswers5

# Math141HWAnswers5 - (Answers for Chapter 7 Systems and...

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(Answers for Chapter 7: Systems and Inequalities) A.7.1 CHAPTER 7: Systems and Inequalities SECTIONS 7.1-7.3: SYSTEMS OF EQUATIONS 1) a) 1 b) ± 1, 6 () {} . Hint: If the first equation is solved for y in terms of x , we eventually obtain 5 x ± 35 ± x = ± 23 . c) ± . Hint: If we multiply both sides of the first equation by 3, we obtain 3 x + 3 y = 15 5 x ± 3 y = ± 23 ² ³ ´ 2) a) ± 1, 1 b) 3) a) a circle and a parabola [that opens upward], respectively b) 2 c) 1, 2 2 ± ² ³ ´ µ , · 2 ± ² ³ ´ µ ¸ ¹ º » º ¼ ½ º ¾ º . Warning: ‘ ± ’ notation could be considered ambiguous.

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(Answers for Chapter 7: Systems and Inequalities) A.7.2 4) a) a parabola [that opens to the right] and a parabola [that opens to the left], respectively b) 2 c) 2, 2 () ,2 , ± 2 {} . Warning: ‘ ± ’ notation could be considered ambiguous. 5) a) Hint: Rewrite x 2 + y = 0 as y = ± x 2 . Rewrite y ± x 2 = 1 as y = x 2 + 1 . b) ± . (Observe that the two graphs in a) do not intersect.) c) ± . You may obtain the equation x 2 = ± 1 2 , which has no real solutions for x . 6) a) ± 4, 52 , 1 0 b) ± 7 5 , ± 1 10 ² ³ ´ µ · , ± 1, 1 2 ² ³ ´ µ · ¸ ¹ º » ¼ ½ c) ± . You may obtain the equation x 2 = 5 2 , but then there are no corresponding real values for y . 7) ±
(Answers for Chapter 7: Systems and Inequalities) A.7.3 SECTION 7.4: PARTIAL FRACTIONS 1) a) A x + 4 + B x ± 3 + Cx + D x 2 + 1 b) A x + B x 2 + C x 3 + D x ± 1 + E x ± 1 () 2 + Fx + G x 2 + 3 + Hx + I x 2 + 3 2 c) A t + B t 2 + C 2 t + 5 + D 2 t + 5 2 + E 2 t + 5 3 + Ft + G 2 t 2 + 5 + Ht + I t 2 + t + 1 2) a) 4 x ± 3 ± 1 x ± 2 b) 3 x + 5 ± 2 x + 1 + 1 x ± 2 c) 2 x + 6 x 2 + 5 2 x + 1 d) 1 x ± 4 + 5 x ± 4 2 e) 6 x + 2 + 2 x + 3 x 2 + 1 f) 4 x ± 5 + x x 2 + 3 g) ± 3 x + ± 2 x ± 5 x 2 + x + 1 , or, equivalently, ± 3 x ± 2 x + 5 x 2 + x + 1 h) 5 t ± 1 t 2 + 4 ± 4 t 2 + 4 2 3) No, because the rational expression on the left-hand side is improper. (The student should multiply out the denominator and then perform Long Division; the idea of using repeated Synthetic Division can be confusing.)

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(Answers for Chapter 8: Matrices and Determinants) A.8.1 CHAPTER 8: Matrices and Determinants SECTION 8.1: MATRICES and SYSTEMS OF EQUATIONS 1) a) 3 ± 2 , 6 entries; b) 4 ± 5 , 20 entries; c) 3 ± 3 (order 3 square), 9 entries 2) a) 3 ± 1 12 18 ± 1 ² ³ ´ µ · b) 2 ± 2 (order 2 square) c) 2 ± 1 d) 3 ± 1 ± 1 18 ² ³ ´ µ · e) 0 ± 7 ± 1 21 ² ³ ´ µ · f) 01 ± 1 ± 3 ² ³ ´ µ · g) x + 2 y = ± 1 y = ± 3 ² ³ ´ h) 5, ± 3 () {} i) 35 ±± 3 = 18 5 () + 2 ± 3 = ± 1 ² ³ ´ µ ´
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Math141HWAnswers5 - (Answers for Chapter 7 Systems and...

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