Assignment Bonus 2

Name___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the triangle.

1) 1)

635° 105°

A) C = 45°, a = 10.1, c = 6.72 B) C = 40°, a = 6.72, c = 10.1

C) C = 35°, a = 6.72, c = 10.1 D) C = 40°, a = 10.1, c = 6.72

Find the area of the triangle having the given measurements. Round to the nearest square unit.

2) 2)A = 20°, b = 13 meters, c = 10 meters

A) 44 square meters B) 46 square meters

C) 22 square meters D) 11 square meters

Solve the problem.

3) 3)Two tracking stations are on the equator 127 miles apart. A weather balloon is located on a bearingof N36°E from the western station and on a bearing of N13°W from the eastern station. How far isthe balloon from the western station? Round to the nearest mile.

A) 173 miles B) 136 miles C) 127 miles D) 164 miles

Find the area of the triangle having the given measurements. Round to the nearest square unit.

4) 4)C = 115°, a = 5 yards, b = 7 yards

A) 63 square yards B) 7 square yards C) 32 square yards D) 16 square yards

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

5) 5)A = 38°B = 32°a = 42.1

A) C = 110°, b = 36.2, c = 64.3 B) C = 111°, b = 64.3, c = 36.2

C) C = 111°, b = 36.2, c = 64.3 D) C = 110°, b = 64.3, c = 36.2

Use Heron's formula to find the area of the triangle. Round to the nearest square unit.

6) 6)a = 10 yards, b = 11 yards, c = 15 yards

A) 58 square yards B) 55 square yards C) 64 square yards D) 61 square yards

1

Solve the problem.

7) 7)Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 25 mph in adirection 320°. The second sails at 30 mph in a direction 200°. Assuming that both boats maintainspeed and heading, after 4 hours, how far apart are the boats?

A) 184 miles B) 116.3 miles C) 190.8 miles D) 134.5 miles

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

8) 8)

7 6

8

A) A = 58°, B = 75°, C = 47° B) A = 47°, B = 58°, C = 75°

C) A = 58°, B = 47°, C = 75° D) A = 47°, B = 75°, C = 58°

9) 9)a = 9, b = 6, c = 4

A) A = 32°, B = 127°, C = 21° B) A = 32°, B = 21°, C = 127°

C) A = 127°, B = 21°, C = 32° D) A = 127°, B = 32°, C = 21°

Solve the problem.

10) 10)A painter needs to cover a triangular region 60 meters by 68 meters by 71 meters. A can of paintcovers 70 square meters. How many cans will be needed?

A) 27 cans B) 308 cans C) 3 cans D) 14 cans

The rectangular coordinates of a point are given. Find polar coordinates of the point. Express in radians.

11) 11)(2 3, 2)

A) 4,6 B) 2,

3 C) 2,6 D) 4,

3

Polar coordinates of a point are given. Find the rectangular coordinates of the point.

12) 12)(-3, 120°)

A) 32

, -3 32

B) -32

, 3 32

C) -32

, -3 32

D) 32

, 3 32

2

Convert the polar equation to a rectangular equation. Then determine the graph's slope and y-intercept.

13) r sin -4

= 2 13)

A) y = x + 2 2; slope: 1; y-intercept: 2 2

B) y = -x + 2 2; slope: -1; y-intercept: 2 2

C) y = -x - 2 2; slope: -1; y-intercept: - 2 2

D) y = x - 2 2; slope: 1; y-intercept: - 2 2

Use a polar coordinate system to plot the point with the given polar coordinates.

14) 14)(2, -135°)

A) B)

3

C) D)

15) -4, 94 15)

A) B)

4

C) D)

Test the equation for symmetry with respect to the given axis, line, or pole.

16) r = 2 sin 3 ; the line =2 16)

A) has symmetry with respect to the line =2

B) may or may not have symmetry with respect to the line =2

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

17) 17)

A) r = 3 B) r = 3 cos(3 ) C) r = 3 + cos(3 ) D) r = 3 sin(3 )

Test the equation for symmetry with respect to the given axis, line, or pole.

18) 18)r = 3 + 6 sin ; the polar axis

A) has symmetry with respect to the polar axis

B) may or may not have symmetry with respect to the polar axis

5

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

19) 19)

A) r = 8 cos B) r = 8 sin C) r = 4 + sin D) r = 4 + cos

Graph the polar equation.

20) 20)r cos = -2

A) B)

6

C) D)

Find the quotientz1z2

of the complex numbers. Leave answer in polar form.

21) z1 = 8 cos2

+ i sin2

z2 = 3 cos6

+ i sin6

21)

A) 83

cos 23

+ i sin 23 B) 8

3cos

3- i sin

3

C) 83

cos3

+ i sin3 D) 8

3sin

3+ i cos

3

Find all the complex roots. Write the answer in the indicated form.

22) 22)The complex square roots of i (rectangular form)

A) -1, 1 B) -i, i

C) 22

-2

2i, -

22

+2

2i D) 2

2+

22

i, -2

2-

22

i

23) 23)The complex cube roots of 8i (rectangular form)

A) 2i, 3 - i, - 3 - i B) 2i, 3 + i, - 3 + i

C) -2i, 3 + i, - 3 + i D) -2i, - 3 - i, 3 - i

24) 24)The complex square roots of 4 + 4 3i (rectangular form)

A) 6 - 2i, - 6 + 2i B) 22

+6

2i, -

22

-6

2i

C) - 6 - 2i, 6 - 2i D) 6 + 2i, - 6 - 2i

7

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.

25) 2 2 (cos 74

+ i sin 74

)5

25)

A) -128 + 128i B) -64 2 + 64 2i C) - 2 + 2i D) -64 + 64i

Use the vectors v, u, w, and z to draw the indicated vector.

26) 26)-2v

A) B)

8

C) D)

Solve the problem.

27) 27)The magnitude and direction of two forces acting on an object are 35 pounds, N45°E, and 55pounds, S30°E, respectively. Find the magnitude, to the nearest hundredth of a pound, and thedirection angle, to the nearest tenth of a degree, of the resultant force.

A) F = 43.30; = 2.7° B) F = 49.17; = -11.3°

C) F = 65.19; = -7.5° D) F = 57.04; = -23.6°

9

Use the vectors v, u, w, and z to draw the indicated vector.

28) 28)v - w

A) B)

C) D)

10

Find the unit vector that has the same direction as the vector v.

29) 29)v = 4i

A) u = i B) u =14

i C) u = 16i D) u = 4i

11

Use the vectors v, u, w, and z to draw the indicated vector.

30) 30)3w

A) B)

C) D)

12

Find projwv.

31) 31)v = -3i - 3j; w = 3i + j

A) -95

(3i + j) B) 110

(3i + j) C) -43

(3i + j) D) -65

(3i + j)

Use the dot product to determine whether the vectors are parallel, orthogonal, or neither.

32) 32)v = 2i, w = -3i

A) orthogonal B) parallel C) neither

Use the given vectors to find the specified scalar.

33) 33)u = 3i - 7j, v = -5i - 9j; Find (-2u) · v.

A) 36 B) -20 C) -96 D) -16

Find the angle between the given vectors. Round to the nearest tenth of a degree.

34) 34)u = -2i + 5j, v = 4i - 6j

A) 84.1° B) 168.1° C) 74.1° D) 178.1°

Solve the problem.

35) 35)A force of 6 pounds acts in the direction of 6° to the horizontal. The force moves an object along astraight line from the point (6, 8) to the point (15, 12), with distance measured in feet. Find the workdone by the force. Round the answer to one decimal place, if necessary.

A) 59.1 ft-lb B) 9.8 ft-lb C) 58.8 ft-lb D) 77.6 ft-lb

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