Answers PrecalculusDot Product and Work

Dot Product and Work — Unit test Answers

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Given vectors u = ⟨–2, 3⟩ and v = ⟨–6, 9⟩, what is the measure of the angle between u and v?

0°

86°

91°

180°

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Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.Trigonometric area formula: Area =

17 feet

33 feet

40 feet

50 feet

Review the graph.

(StartFraction 25 Over 2 EndFraction, StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

(StartFraction 25 Over 2 EndFraction, negative StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

(negative StartFraction 25 Over 2 EndFraction, StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

(negative StartFraction 25 Over 2 EndFraction, negative StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)

A force of 50 pounds acts in a direction 60° above horizontal, moving an object 100 feet from (0, 0) to (100, 0). How much work is done by the force?

25 foot-pounds

50 foot-pounds

2,500 foot-pounds

5,000 foot-pounds

Review the graph.

magnitude of and direction angle equal to approximately 40°

magnitude of and direction angle equal to approximately 50°

magnitude of and direction angle equal to approximately 40°

magnitude of and direction angle equal to approximately 50°

Triangle XYZ has vertices X(–1, –1), Y(–2, 1), and Z(1, 2). What is the approximate measure of angle Z?

37.2°

61.5°

78.5°

81.3°

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components . After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station.What are the characteristics of the vector representing the path of the ship?

components:, magnitude: 13.46

components:, magnitude: 53.85

components:, magnitude: 13.46

components:, magnitude: 53.85

Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45° angle to see a hot air balloon. Emily looks up at a 60° angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?

44.3 yd.

63.4 yd.

73.2 yd.

89.7 yd.

Trigonometric area formula: Area =

70.5 square units

111.3 square units

185.4 square units

222.5 square units

A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?

StartFraction 10 over cosine 30 degree EndFraction.

StartRoot 800 minus 800 cosine 30 degree EndRoot.

40 cosine 30 degree.

StartRoot 400 minus 40 cosine 30 degree EndRoot.

After a windstorm, a leaning pole makes a 75° angle with the road surface. The pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. About how long is the pole?

11.0 ft.

12.2 ft.

16.7 ft.

20.5 ft.

Let a = 2i + 9j, b = –4i + 5j, c = i – 3j, and d = 14j where i and j are unit vectors. What is (a – b) – (2d – c) in terms of i and j?

5i – 27j

5i + 35j

7i – 27j

7i + 39j

Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (15 degrees) EndRoot

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (45 degrees) EndRoot

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (165 degrees) EndRoot

StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (255 degrees) EndRoot

A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?

On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with a vertical line and vector 15 miles is 20 degrees.

On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by a vertical line and vector 15 miles is 20 degrees.

Let |u| = 4 at an angle of 210° and |v| = 9 at an angle of 315°, and w = u – v. What is the magnitude and direction angle of w?

|w| = 5.5; θ = 156.1°

|w| = 5.5; θ = 203.9°

|w| = 10.8; θ = 156.1°

|w| = 10.8; θ = 203.9°

In triangle ABC, AB = 90 in., BC = 80 in., and angle B measures 50°. What is the approximate perimeter of the triangle?

242.4 in.

265.3 in.

308.3 in.

324.1 in.

What are the possible remaining angle measures in triangle ABC with ?

and

m angle B similar to 121 degrees, m angle C similar to 19 degrees

m angle B similar to 59 degrees, m angle C similar to 81 degrees

No triangle can be formed with these measures.

Which diagram shows the parallelogram method for vector addition?

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the terminal point of vector u, and shares a terminal point with the terminal point of vector v.

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares a terminal point with the terminal point of vector u, and shares an origin with the terminal point of vector v.

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right.

Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right and is double the size of vectors v and u.