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c Math 151 WIR, Fall 2013, 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. 1 c Math 151 WIR, Fall 2013, 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 2 c Math 151 WIR, Fall 2013, 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. 3 c Math 151 WIR, Fall 2013, Benjamin Aurispa (e) Find constants s and t so that sa + tb = c. − −→ 7. Find the vector AB with initial point A(2, 7) and terminal point B(−3, 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. 4 c Math 151 WIR, Fall 2013, Benjamin Aurispa 9. A plane heads in the direction N 60◦ E with an airspeed of 500 mph. The wind is blowing due east with speed 10 mph. Find the true speed and direction of the plane relative to the ground. 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. (a) What is the resultant force F as well as its magnitude and direction? (b) What third force F3 would be required to keep the object from moving? 5 c Math 151 WIR, Fall 2013, Benjamin Aurispa 11. A boat heads in the direction S 45◦ E with a speed of 36 km/hr relative to the water. However, the current of the water pushes the boat so that it is traveling due south with a speed of 30 km/hr relative to the shore. What are the velocity and speed of the current? 12. 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. 6