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# Multi Choice Problems…

Question 1 of 200.0/ 5.0 PointsWrite the vector v in terms of i and j whose magnitude and direction angle θ are given.= 8, θ = 30°A. v = -4i + 4jB. v = 4i + 4jC. v = 4i + 4jD. v = 4i + 4jQuestion 2 of 200.0/ 5.0 PointsSelect the representation that does not change the location of the given point. (4, 110°)A. (4, 470)°B. (4, 290)°C. (-4, 200)°D. (-4, 470)°Question 3 of 200.0/ 5.0 PointsFind the quotient of the complex numbers. Leave answer in polar form.z1 =z2 =A.B.C.D.Question 4 of 200.0/ 5.0 PointsFind the unit vector that has the same direction as the vector v. v = 3i + jA. u = i + jB. u = i + jC. u = 3i + jD. u = i + jQuestion 5 of 205.0/ 5.0 PointsPolar coordinates of a point are given. Find the rectangular coordinates of the point.A. (-1.6, -1.3)B. (1.6, 1.3)C. (1.3, 1.6)D. (-1.3, -1.6)Question 6 of 200.0/ 5.0 PointsFind the work done by a force of 4 pounds acting in the direction of 41° to the horizontal in moving an object 5 feet from (0, 0) to (5, 0).A. 13.1 ft-lbB. 16.2 ft-lbC. 15.1 ft-lbD. 30.2 ft-lbQuestion 7 of 200.0/ 5.0 PointsSolve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 6, c = 11, B = 109°A. b = 14.1, A = 24°, C = 47°B. b = 19.9, A = 22°, C = 49°C. b = 17, A = 26°, C = 45°D. no triangleQuestion 8 of 200.0/ 5.0 PointsSolve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 15° C = 113° b = 49A. A = 50°, a = 176.3, c = 151.2B. A = 52°, a = 149.2, c = 174.3C. A = 52°, a = 151.2, c = 176.3D. A = 50°, a = 174.3, c = 149.2Question 9 of 200.0/ 5.0 PointsFind all the complex roots. Write the answer in the indicated form. The complex cube roots of 27(cos 234° + i sin 234°) (polar form)A. -3(cos 78° + i sin 78°), 3(cos 198° + i sin 198°), -3(cos 318° + i sin 318°)B. 3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), 3(cos 158° + i sin 158°)C. -3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), -3(cos 158° + i sin 158°)D. 3(cos 78° + i sin 78°), 3(cos198° + i sin 198°), 3(cos 318° + i sin 318°)Question 10 of 205.0/ 5.0 PointsFind the specified vector or scalar.u = -4i + 1j and v = 4i + 1j; Find .A.B. 8C. 5D. 2Question 11 of 205.0/ 5.0 PointsUse the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = j, w = 4iA. orthogonalB. parallelC. neitherQuestion 12 of 200.0/ 5.0 PointsWrite the complex number in polar form. Express the argument in degrees. 4iA. 4(cos 0° + i sin 0°)B. 4(cos 270° + i sin 270°)C. 4(cos 90° + i sin 90°)D. 4(cos 180° + i sin 180°)Question 13 of 200.0/ 5.0 PointsThe wind is blowing at 10 knots. Sailboat racers look for a sailing angle to the 10-knot wind that produces maximum sailing speed. This situation is now represented by the polar graph in the figure shown below. Each point (r, θ) on the graph gives the sailing speed, r, in knots, at an angle θ to the 10-knot wind. What is the speed to the nearest knot, of the sailboat sailing at 120° angle to the wind?A. 8 knotsB. 9 knotsC. 7 knotsD. 10 knotsQuestion 14 of 200.0/ 5.0 PointsSolve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 7, b = 7, c = 5A. A = 70°, B = 70°, C = 40°B. A = 69°, B = 69°, C = 42°C. A = 42°, B = 69°, C = 69°D. A = 69°, B = 42°, C = 69°Question 15 of 200.0/ 5.0 PointsPlot the complex number. 2 + iA.B.C.D.Question 16 of 200.0/ 5.0 PointsFind the magnitude and direction angle θ, to the nearest tenth of a degree, for the given vector v. v = -4i – 3jA. 5; 233.1°B. 7; 216.9°C. 5; 216.9°D. 5; 36.9°Question 17 of 200.0/ 5.0 PointsFind the quotient of the complex numbers. Leave answer in polar form.z1 =z2 =A.B.C.D.Question 18 of 200.0/ 5.0 PointsGraph the polar equation.r = 2 + 2sin θA.B.C.D.Question 19 of 200.0/ 5.0 PointsPolar coordinates of a point are given. Find the rectangular coordinates of the point. (-5, -180°)A. (-5, 0)B. (0, -5)C. (0, 5)D. (5, 0)Question 20 of 200.0/ 5.0 PointsPlot the complex number.-5- 5iA.B.C.D.