Question 1

The volume V of the right triangular prism shown in the figure is   where B is the area of the base and h is the height of the prism.   Approximate h, if   .

Accepted Answer

A) 4.9 
B) 18.8 
C) 18.4 
D) 18.0 
E) 17.6 
A) 4.9 
B) 18.8 
C) 18.4 
D) 18.0 
E) 17.6

Question 2

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 3

A helicopter hovers at an altitude that is   feet above a mountain peak of altitude 5,847 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is   , and from the mountaintop, the angle of elevation is   .   Approximate the altitude of the taller peak.

Accepted Answer

A) 5,578 ft 
B) 6,118 ft 
C) 6,112 ft 
D) 6,116 ft 
E) 6,110 ft 
A) 5,578 ft 
B) 6,118 ft 
C) 6,112 ft 
D) 6,116 ft 
E) 6,110 ft

Question 4

Express the complex number in trigonometric form with   .

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

The volume V of the right triangular prism shown in the figure is   where B is the area of the base and h is the height of the prism.   Approximate h, if   .

Accepted Answer

A) 15.6 
B) 15.2 
C) 4.3 
D) 16.0 
E) 14.0 
A) 15.6 
B) 15.2 
C) 4.3 
D) 16.0 
E) 14.0

Question 7

Determine whether the given pair of vectors are orthogonal or not.   and

Accepted Answer

A) yes 
B) no 
A) yes 
B) no

Question 8

Express the complex number in trigonometric form with   .

Accepted Answer

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

Question 9

The volume V of the right triangular prism shown in the figure is   where B is the area of the base and h is the height of the prism.   Approximate h, if   .

Accepted Answer

A) 6.2 
B) 22.6 
C) 23.0 
D) 22.2 
E) 21.0 
A) 6.2 
B) 22.6 
C) 23.0 
D) 22.2 
E) 21.0

Question 10

Represent the complex number geometrically.

Accepted Answer

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

Question 11

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure   .

Accepted Answer

A) 95.2 
B) 110.3 
C) 89.3 
D) 88.4 
E) 92.6 
A) 95.2 
B) 110.3 
C) 89.3 
D) 88.4 
E) 92.6

Question 12

Find the two square roots of

Accepted Answer

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

Question 13

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) 101.34 ft 
B) 99.84 ft 
C) 100.74 ft 
D) 100.44 ft 
E) 66.74 ft 
A) 101.34 ft 
B) 99.84 ft 
C) 100.74 ft 
D) 100.44 ft 
E) 66.74 ft

Question 14

The volume V of the right triangular prism shown in the figure is   where B is the area of the base and h is the height of the prism.   Approximate h, if   .

Accepted Answer

A) 17.0 
B) 17.4 
C) 16.2 
D) 4.9 
E) 16.6 
A) 17.0 
B) 17.4 
C) 16.2 
D) 4.9 
E) 16.6

Question 15

Represent the complex number geometrically.

Accepted Answer

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

Question 16

Represent the complex number geometrically.

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q.   and

Accepted Answer

A) 34 
B) 30 
C) -10 
D) 10 
E) 17 
A) 34 
B) 30 
C) -10 
D) 10 
E) 17

Question 19

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   . The real part of I represents the actual current delivered to an electrical appliance in amps. Approximate this current when   and   , and express the answer in rectangular form to two decimal places.

Accepted Answer

A) 2.76 amps 
B) 1.33 amps 
C) 1.23 amps 
D) 1.38 amps 
E) 1.45 amps 
A) 2.76 amps 
B) 1.33 amps 
C) 1.23 amps 
D) 1.38 amps 
E) 1.45 amps

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)

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

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

Express the complex number in trigonometric form with .

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

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

Determine whether the given pair of vectors are orthogonal or not. and

Express the complex number in trigonometric form with .

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

Represent the complex number geometrically.

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure .

Find the two square roots of

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.

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

Represent the complex number geometrically.

Represent the complex number geometrically.

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

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and

Fundamental Concepts of Algebra

Equations and Inequalities

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Polynomial and Rational Functions

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Exam 8: Applications of Trigonometry

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

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

Express the complex number in trigonometric form with .

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

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

Determine whether the given pair of vectors are orthogonal or not. and

Express the complex number in trigonometric form with .

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

Represent the complex number geometrically.

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure .

Find the two square roots of

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.

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

Represent the complex number geometrically.

Represent the complex number geometrically.

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

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and

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