Question 1

Determine m such that the two vectors are orthogonal.   and

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 2

A straight road makes an angle of   with the horizontal. When the angle of elevation of the sun is   , a vertical pole at the side of the road casts a shadow   feet long directly down the road, as shown in the figure.   Approximate the length of the pole.

Accepted Answer

A) 94.60 ft 
B) 94.90 ft 
C) 62.67 ft 
D) 94.00 ft 
E) 95.50 ft 
A) 94.60 ft 
B) 94.90 ft 
C) 62.67 ft 
D) 94.00 ft 
E) 95.50 ft A

Question 3

Find the four fourth roots of   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    D

Question 4

Express in the form   , where a and b are real numbers.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Use De Moivre's theorem to change the given complex number to the form   , where   and   are real numbers.

Accepted Answer

A) -24+24i 
B) 2,048 
C) 4,096 
D) -2,048i 
E) -4,096i 
A) -24+24i 
B) 2,048 
C) 4,096 
D) -2,048i 
E) -4,096i

Question 6

Two tugboats are towing a large ship into port, as shown in the figure. The larger tug exerts a force of 4,500 pounds on its cable, and the smaller tug exerts a force of 3,300 pounds on its cable.   If the ship is to travel on a straight line l, approximate the angle   that the larger tug must make with l.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Shown in the figure is a plan for the top of a wing of a jet fighter, where   feet and   feet.   Approximate angle   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the two square roots of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Find || a ||. a = -

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Find the absolute value.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle   , as shown in the figure.   If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector   .

Accepted Answer

A) 24.74 
B) 26.99 
C) 25.50 
D) 26.28 
E) 0 
A) 24.74 
B) 26.99 
C) 25.50 
D) 26.28 
E) 0

Question 12

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Represent the complex number geometrically.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Find the two square roots of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is   . Approximate the unknown quantity, and express the answer in rectangular form to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Solve

Accepted Answer

A)    
B)    
C)    
D)    
E) No triangle exists 
A)    
B)    
C)    
D)    
E) No triangle exists

Question 17

Express in the form   , where a and b are real numbers.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

A straight road makes an angle of   with the horizontal. When the angle of elevation of the sun is   , a vertical pole at the side of the road casts a shadow   feet long directly down the road, as shown in the figure.   Approximate the length of the pole.

Accepted Answer

A) 94.60 ft 
B) 94.90 ft 
C) 62.67 ft 
D) 94.00 ft 
E) 95.50 ft 
A) 94.60 ft 
B) 94.90 ft 
C) 62.67 ft 
D) 94.00 ft 
E) 95.50 ft

Question 19

A jet airplane approaches a runway at an angle of   with the horizontal, traveling at a speed of 165 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Accepted Answer

A) vertical = 21.76 mi/hr, horizontal = 163.39 mi/hr 
B) vertical = 163.39 mi/hr , horizontal = 163.39 mi/hr 
C) vertical = 22.96 mi/hr, horizontal = 163.39 mi/hr 
D) vertical = 21.76 mi/hr, horizontal = 21.76 mi/hr 
E) vertical = 26.56 mi/hr, horizontal = 163.39 mi/hr 
A) vertical = 21.76 mi/hr, horizontal = 163.39 mi/hr 
B) vertical = 163.39 mi/hr , horizontal = 163.39 mi/hr 
C) vertical = 22.96 mi/hr, horizontal = 163.39 mi/hr 
D) vertical = 21.76 mi/hr, horizontal = 21.76 mi/hr 
E) vertical = 26.56 mi/hr, horizontal = 163.39 mi/hr

Question 20

The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is   . Approximate the unknown quantity, and express the answer in rectangular form to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Determine m such that the two vectors are orthogonal. and

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

Find the four fourth roots of .

Express in the form , where a and b are real numbers.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate angle .

Find the two square roots of

Find || a ||. a = - < 3, - 9 >

Find the absolute value.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Represent the complex number geometrically.

Find the two square roots of

Solve

Express in the form , where a and b are real numbers.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 165 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

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Exam 8: Applications of Trigonometry

Determine m such that the two vectors are orthogonal. and

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

Find the four fourth roots of .

Express in the form , where a and b are real numbers.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate angle .

Find the two square roots of

Find || a ||. a = - < 3, - 9 >

Find the absolute value.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Represent the complex number geometrically.

Find the two square roots of

Solve

Express in the form , where a and b are real numbers.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 165 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters