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c Math 151 WIR, Spring 2010, Benjamin Aurispa Math 151 Week in Review 1 Answer Key 1. − √115 2. − √521 √ 3. − 3 8 7 5π 7π 4. (a) x = π4 , 3π 4 , 4 , 4 4π (b) x = 0, 2π 3 , π, 3 , 2π 3π (c) x = π6 , 5π 6 , 2 5. Start with the graph of y = sin x, compress horizontally by 2 so that the new period is π, stretch vertically by 3 (amplitude is now 3), and reflect across the x-axis. See Full Solutions for graph. 6. Start with the graph of y = cos x, shift left by π 4 and shift down by 2. See Full Solutions for graph. 7. (a) (b) 2a+b b − 1/2 a b b a a 8. (a) < −3, −9 > √ (b) 74 (c) D (d) D (e) √5 , − √6 61 61 E E √12 , − √8 13 13 11 8 s = − 29 , t = 29 −− → 9. AB =< −5, 2 >, Direction from positive x-axis: ≈ 158.2◦ √ 10. < −6 3, −6 > √ 11. True velocity vector of boat: < 18 3 + 4, 18 >; True speed ≈ 39.5 km/s; True course: N 62.9◦ E 12. Plane should head in the direction N 1.24◦ E with an airspeed of ≈ 489.51 mph √ √ 13. (a) F =< −15 + 20 3, 15 3 − 20 >; |F| ≈ 20.53 N; Direction: 16.94◦ from positive x-axis √ √ (b) F3 = −F =< 15 − 20 3, −15 3 + 20 > 14. The magnitude of the tension in the wire that makes the 60◦ angle is 36.60 lbs; The magnitude of the tension in the wire that makes the 45◦ angle is 25.88 lbs 1