Math6

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1.   Use the given vectors below to find the specified scalar: u = 9i – 6j, v = –8i – 9j, w = –10i + 5j; Find u(v + w). 

    

A. –120

B. –18

C. 72

D. –138

2.   Which graph represents the polar equation r = 2 – cos θ? 

    

A. 

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B. 

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C. 

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D. 

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3.   The rectangular coordinates of a point are given. Find polar coordinates of the point. Express θ in radians. (–1, 0) 

    

A. 

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B. 

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C. 

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D. 

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4.   The graph of a polar equation is given below. Select the polar equation for the graph.

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A.  r = 2 sin(2θ)

B.  r = 2 + cos(2θ)

C.  r = 2 cos(2θ)

D.  r = 2

 

5.   Convert the rectangular equation to a polar equation that expresses r in terms of θ x = 4 

    

A. 

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B. 

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C. 

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D. 

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6.   Convert the polar equation r = 4 csc θ to a rectangular equation. 

    

A.  x2 + y2 = 4

B.  x = 4

C.  y = 4

D.  y2 = 4

7.   A force of 5 pounds acts in the direction of 5° to the horizontal. The force moves an object along a straight line from the point (5, 4) to the point (18, 13), with distance measured in feet. Find the work done by the force. Round the answer to one decimal place, if necessary. 

    

A. 78.8 ft-lb

B. 15.8 ft-lb

C. 109.6 ft-lb

D. 79.1 ft-lb

8.   Find the absolute value of the complex number z = –12 – 8i 

    

A. 

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B. 

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C. 

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D. 

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9.   Find all the complex roots of 144(cos 210° + i sin 210°) in polar form. 

    

A. 12(cos 210° + i sin 210°), 12(cos 195° + i sin 195°)

B. 12(cos 105° + i sin 105°), 12(cos 285° + i sin 285°)

C. 12(cos 105° + i sin 105°), 195(cos 285° + i sin 285°)

D. 12(cos 210° + i sin 210°), – 12(cos 195° + i sin 195°)

10.   Use the given vectors below to find the specified scalar: u = 13i – 13j and v = –15 i + 4j; Find uv. 

    

A. –143

B. –247

C. –195

D. –52

11.   Solve the following triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.

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A. A = 51°, B = 42°, C = 87°

B. A = 42°, B = 51°, C = 87°

C. A = 51°, B = 87°, C = 42°

D. A = 42°, B = 87°, C = 51°

12.   Which graph represents the polar equation r = 3 cos θ + 4 sin θ? 

    

A. 

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B. 

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C. 

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D. 

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13.   A person is pulling a freight cart with a force of 49 pounds. How much work is done in moving the cart 30 feet if the cart's handle makes an angle of 32° with the ground? 

    

A. 77.9 ft-lb.

B. 1246.6 ft-lb.

C. 1309.8 ft-lb.

D. 779 ft-lb.

14.   Which graph represents the plotted complex number 3 + 6i? 

    

A. 

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B. 

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C. 

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D. 

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15.   Solve the following triangle.

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A. B = 60°, a = 4.32, c = 6.01

B. B = 55°, a = 4.32, c = 6.01

C. B = 55°, a = 6.01, c = 4.32

D. B = 50°, a = 6.01, c = 4.32

16.   Find another representation, (r, &theta), for the point under the given conditions.

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A. 

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B. 

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C. 

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D. 

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17.   The distance from home plate to dead center field in Sun Devil Stadium is 402 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center field? 

    

A. 32,702 feet

B. 470 feet

C. 379.6 feet

D. 344.3 feet

18.   Which graph represents the polar equation r = 3 + sin θ? 

    

A. 

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B. 

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C. 

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D. 

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19.   Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i + j, w = i – 4j 

    

A. Neither orthogonal nor parallel

B. Parallel

C. Not enough information

D. Orthogonal

20.   Write the complex number 6 in polar form. Express the argument in degrees. 

    

A. 6(cos 270° + i sin 270°)

B. 6(cos 0° + i sin 0°)

C. 6(cos 90° + i sin 90°)

D. 6(cos 180° + i sin 180°)