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Math 151 WIR, Spring 2014, Benjamin
Aurispa
Math 151 Week in Review 1
Appendix D and Section 1.1
1. Find the domain of the function f (x) = √
√
4
x2
x+3
.
− 3x − 4
2. Given that cos θ = − 41 and that π < θ < 2π, find csc θ.
3. If cot x = − 35 where π < x < 2π, find sin 2x.
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Math 151 WIR, Spring 2014, Benjamin
Aurispa
4. Solve the following equations on the interval [0, 2π].
(a) 2 cos2 x = 1
(b) sin 2x = − sin x
(c) 2 sin2 x + sin x − 1 = 0
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Math 151 WIR, Spring 2014, Benjamin
Aurispa
5. Using the figures below, sketch the following vectors.
(b) b − 21 a
(a)2a + b
b
b
a
a
6. Consider the vectors a =< 5, −6 >, b = −4i − j, and c =< −3, 2 >. Calculate the following.
(a) a + 2b − j
(b) |b − 3c|
(c) A unit vector in the direction of a.
(d) A vector with length 4 in the opposite direction of c.
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Math 151 WIR, Spring 2014, Benjamin
Aurispa
(e) Find constants s and t so that sa + tb = c.
−
−→
7. Find the vector AB with initial point A(−3, 7) and terminal point B(2, 5). What is the direction of
this vector from the positive x-axis?
8. Find a vector with length 12 and direction 210◦ from the positive x-axis.
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Math 151 WIR, Spring 2014, Benjamin
Aurispa
9. A plane heads in the direction N 60◦ E with an airspeed of 500 mph. The wind is blowing due west
with speed 10 mph. Find the true speed and direction of the plane relative to the ground.
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Math 151 WIR, Spring 2014, Benjamin
Aurispa
10. Two forces are acting on an object. F1 has a magnitude of 30 Newtons and is applied in a direction
of 120◦ from the positive x-axis. F2 has a magnitude of 40 Newtons and is applied in a direction of
−30◦ from the positive x-axis. What is the resultant force F as well as its magnitude and direction?
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Math 151 WIR, Spring 2014, Benjamin
Aurispa
11. A 50-lb piñata is being held up between two buildings by two wires. The two wires make angles of
30◦ and 45◦ with the horizontal. Determine the magnitudes of the tension in each wire.
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