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