The polar coordinates of a point are given. Find the rectangular coordinates of the point. 1) 7, 2 3 D) - 7 2, A) - 7 2, 7 3

Transcription

1 Ch 9. Assignment Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The polar coordinates of a point are given. Find the rectangular coordinates of the point. 1) 7, 3 1) A) - 7, 7 3 B) 7, C) 7, 7 3 D) - 7, Graph the polar equation. ) r = ) A) B) C) D) 1

2 Write the expression in the standard form a + bi. 3) ( 3 + i) 5 3) A) i B) i C) i D) i Solve the problem. 4) Two forces, F1 of magnitude 60 newtons (N) and F of magnitude 70 newtons, act on an object at 4) angles of 40 and 130 (respectively) with the positive x-axis. Find the direction and magnitude of the resultant force; that is, find F1 + F. Round the direction and magnitude to two decimal places. A) Direction: ; magnitude: N B) Direction: ; magnitude: 9.0 N C) Direction: ; magnitude: N D) Direction: ; magnitude: 9.0 N 5) Which of the following vectors is orthogonal to 0i - 8j? 5) A) w = 4i + 3j B) w = -10i - 5j C) w = 15i - 6j D) w = 0i + 4j 6) Which of the following vectors is parallel to v = i + j? 6) A) w = 1 i + j B) w = i - 1 j C) w = i + j D) w = i + j Solve the problem. Round your answer to the nearest tenth. 7) Find the work done by a force of 00 pounds acting in the direction -i + j in moving an object 75 7) feet from (0, 0) to (-75, 0). A) 13,416.1 ft-lb B) 15,000.0 ft-lb C) ft-lb D) ft-lb 8) Find the work done by a force of 9 pounds acting in the direction of 4 to the horizontal in moving 8) an object 5 feet from (0, 0) to (5, 0). A) 30.1 ft-lb B) 33.4 ft-lb C) 66.9 ft-lb D) 35.9 ft-lb Solve the problem. 9) An SUV weighing 5800 pounds is parked on a street which has an incline of 9. Find the force 9) required to keep the SUV from rolling down the hill and the force of the SUV perpendicular to the hill. Round the forces to the nearest hundredth. A) lb and lb B) lb and lb C) lb and lb D) lb and lb The vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. 10) P = (0, 0); Q = (6, 4) 10) A) v = -6i - 4j B) v = 4i + 4j C) v = 6i + 4j D) v = -4i - 6j

3 Solve the problem. 11) v = 13, = 45 11) A) v = - i - 13 j B) v = i j C) v = 13 i + 13 j D) v = 13 3 i + 13 j Find the indicated quantity. 1) If w = 5i + j, find w. 1) A) 7i + 4j B) 10i + 4j C) 7i + j D) 10i + j 13) If v = -i - j, find v. 13) A) B) 0 C) D) 1 14) If v = 3i - 5j and w = -7i + 4j, find 3v - 4w. 14) A) 37i - 31j B) 17i - 10j C) -19i + j D) -4i - j 3

4 Use the vectors in the figure below to graph the following vector. 15) u - z - w 15) A) B) C) D) 4

5 Solve the problem. 16) An audio speaker that weighs 50 pounds hangs from the ceiling of a restaurant from two cables as 16) shown in the figure. To two decimal places, what is the tension in the two cables? A) Tension in right cable: lb; tension in left cable: lb B) Tension in right cable: lb; tension in left cable: lb C) Tension in right cable: lb; tension in left cable: lb D) Tension in right cable: lb; tension in left cable: lb 17) Two forces, F1 of magnitude 35 newtons (N) and F of magnitude 55 newtons, act on an object at 17) angles of 45 and -60 (respectively) with the positive x-axis. Find the direction and magnitude of the resultant force; that is, find F1 + F. Round the direction and magnitude to two decimal places. A) Direction: ; magnitude: 8.67 N B) Direction: ; magnitude: N C) Direction: ; magnitude: N D) Direction: ; magnitude: N 18) v = 6, = ) A) v = 6j B) v = -6j C) v = -6i D) v = -6i - 6j Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. 19) i 19) A) 0(cos i sin 33.1 ) B) 0(cos i sin ) C) 0(cos i sin 53.1 ) D) 0(cos i sin 16.9 ) 5

6 Find all the complex roots. Leave your answers in polar form with the argument in degrees. 0) The complex fifth roots of 3 + i 0) A) 3(cos 6 + i sin 6 ), 3(cos 78 + i sin 78 ), 3(cos i sin 150 ), 3(cos + i sin ), 3(cos 94 + i sin 94 ) B) 5 (cos 30 + i sin 30 ), 5 (cos 10 + i sin 10 ), 5 (cos i sin 174 ), 5 (cos 46 + i sin 46 ), 5 (cos i sin 318 ) C) 3(cos 30 + i sin 30 ), 3(cos 10 + i sin 10 ), 3(cos i sin 174 ), 3(cos 46 + i sin 46 ), 3(cos i sin 318 ) D) 5 (cos 6 + i sin 6 ), 5 (cos 78 + i sin 78 ), 5 (cos i sin 150 ), 5 (cos + i sin ), 5 (cos 94 + i sin 94 ) Write the complex number in rectangular form. 1) 8 cos 6 + i sin 6 1) A) i B) i C) i D) i 4 ) 9(cos i sin 180 ) ) A) -9 B) 9 C) 9i D) -9i The polar equation of the graph is either r = a + b cos or r = a + b sin, a > 0, b > 0. Match the graph to one of the equations. 3) 3) A) r = 4 + sin B) r = 4 + cos C) r = + 4 cos D) r = + 4 sin Use a graphing utility to graph the polar equation. 6

7 4) r = - 4 sin 4) A) B) C)

8 D) The polar equation of the graph is either r = a + b cos or r = a + b sin, a > 0, b > 0. Match the graph to one of the equations. 5) 5) A) r = cos B) r = sin C) r = sin D) r = cos Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. 6) r = sin 6) 8

9 A) B) x + (y - 1) = 1; circle, radius 1, center at (0, 1) in rectangular coordinates C) (x + 1) + y = 1; circle, radius 1, center at (-1, 0) in rectangular coordinates x + (y + 1) = 1; circle, radius 1, center at (0, -1) in rectangular coordinates 9

10 D) (x - 1) + y = 1; circle, radius 1, center at (1, 0) in rectangular coordinates The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, ). 7) x + y = 4x 7) A) r = 4 cos B) r sin = 4 cos C) r cos = 4 sin D) r = 4 sin Plot the point given in polar coordinates. 8) (, 360 ) 8) A) B) 10

11 C) D) The polar coordinates of a point are given. Find the rectangular coordinates of the point. 9) (-3, 10 ) 9) A) - 3, B) 3, 3 3 C) 3, D) - 3, 3 3 The letters r and represent polar coordinates. Write the equation using rectangular coordinates (x, y). 5 30) r = 1 + cos 30) A) x = 5-10y B) y = 5-10x C) x = 10y - 5 D) y = 10x