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mac1147_review_3_ans - Answers Review Unit III 1(a ln 33 ln...

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Answers – Review Unit III 1. (a) ln33 ln 2 ± (b) { } ln5 (c) ln 20 ln(5/ 4) (d) 3ln6 ln 4 2. (a) { } 1, 7 (b) 10 7 (c) { } 3 (d) { } 87 3. (a) 1 (b) 3 , 0 x x > (c) 2 2 x (d) 2 1 2 x e, f cannot be simplified 4. 1 5. 2 3 32 log y x 6. 6 6 6 1 3 1 log log 2log 2 2 x y z + + 7. (a) 1 ln 2 (b) 1 log 2 x (c) 3 2 8. (a) ln10 ln9 2.65 4ln1.01 t = years (b) ln10 ln9 2.63 0.04 t = years 9. 2 3 hours 10. (a) 2 2000 270.67 e grams (b) ln2 34.66 0.02 t = days 11. (a) 130 ° (b) 5 50 18 π α = ° = 12. 125 12 π sq. cm 13. 80 radians/min 14. 2 5 sin 5 θ = − 5 cos 5 θ = tan 2 θ = − 15. (a) 2 (b) 3 (c) 0 (d) 1 16. 3 4 A = , 2 3 T π = , 4 B = , 3 φ π ω = − 17. 18. 2sin 2 4 y x π π = − or 2cos 2 4 y x π π = + 19. (a) 4 2 x n π π = + , 0, 1, 2,... n = ± ± (b) 4 x n π π = + , 0, 1, 2,... n = ± ± (c) 0 y = and y π = (d) 2 y π =
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20. (a) 4 π (b) 5 6 π (c) 3 π (d) 2 3 π (e) 2 π 21. (a) 3 2 (b) 2 2 (c) 2 2 3 (d) 5 13 (e) 3 7 7 22. (a) 2 π (b) 6 7 π (c) 7 8 π (d) 4 π 23. 2 1 u 24. (a) 1 (b) 1 sin 2 θ (c) 2cot θ 26. (a) 6 2 7 12 + (b) 3 2 14 12 + (c) 7 9 (d) 3 7 27. 2 42 2 15 28. (a) 2 6 7 5 (b) 7 2 6 14 + (c) 7 2 6 14 29. (a) 2 3 4 (b) 2 2 30. (a) 4 n π θ π = + , 0, 1, 2... n = ± ± (b) 2 2 , 0, 1, 2... 3 n n π π ± + = ± ± (c) 5 2 , 2 , 0, 1, 2...
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