Question 1

Use De Moivre's Theorem to verify z = -1 + i is a solution to z4 - 2z3 - z2 + 2z + 10 = 0.

Accepted Answer

Use the theorem to compute the

Question 2

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely.
side c = 27.5 mi
$\angle$A = 44°
side a = 10.1 mi

Accepted Answer

The answer of Solve using the law of sines and...

Question 3

Use the following to answer questions :
p =   ; q =  
-Compute the dot product p • q.

Accepted Answer

A)    
B)    
C)  -13 
D)  11 
A)    
B)    
C)  -13 
D)  11

Question 4

Two tractors are pulling at a stump in an effort to clear land for more crops. The Massey-Ferguson is pulling with a force of 200 N, while the John Deere is pulling with a force of 250 N. The chains attached to the stump and each tractor form a 28° angle. Represent this situation using geometric vectors.

Accepted Answer

The answer of Two tractors are pulling at a stump...

Question 5

v =   (a) Graph the vector.
(b) Write the vector as a linear combination of i and j.
(c) Compute the magnitude of the vector.

Accepted Answer

(a) @#IMG-DLM& (b) v

Question 6

A baby-sitter pulls some kids in a wagon on a level street. How much work is done if she pulls the wagon 200 feet at a constant force of 45 lbs with the wagon handle making an angle of 34° with the street? Round to the nearest whole number.

Accepted Answer

A)  approximately 4808 ft-lbs 
B)  approximately 5033 ft-lbs 
C)  approximately 6529 ft-lbs 
D)  approximately 7461 ft-lbs 
A)  approximately 4808 ft-lbs 
B)  approximately 5033 ft-lbs 
C)  approximately 6529 ft-lbs 
D)  approximately 7461 ft-lbs

Question 7

Two planes leave an airport at the same time. One travels due west (bearing 270°) with a cruising speed of 420 mph. The other travels at bearing 235° with a cruising speed of 440 mph. Approximate the distance between the planes after 3 hours of flight.

Accepted Answer

The answer of Two planes leave an airport at the...

Question 8

Use the following to answer questions :
zS1U1B11S1U1B0 = 3 - 4i
zS1U1B12S1U1B0 = -1 - 3i
zS1U1B13S1U1B0 = 4 - i
-Graph the complex numbers z1, z2, and z3 given.

Accepted Answer

A)   
(Gridlines are spaced one unit apart.) 
B)   
(Gridlines are spaced one unit apart.) 
C)   
(Gridlines are spaced one unit apart.) 
D)   
(Gridlines are spaced one unit apart.) 
A)   
(Gridlines are spaced one unit apart.) 
B)   
(Gridlines are spaced one unit apart.) 
C)   
(Gridlines are spaced one unit apart.) 
D)   
(Gridlines are spaced one unit apart.)

Question 9

Use De Moivre's Theorem to determine whether z =   is a solution to z4 - 4z2 + 16 = 0.

Accepted Answer

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

Question 10

Write the complex number in trigonometric form using degrees. -4 + 4i

Accepted Answer

A)  4   (cos 45° + i sin 45°) 
B)  32(cos 45° + i sin 45°) 
C)  4   (cos 135° + i sin 135°) 
D)  32(cos 135° + i sin 135°) 
A)  4   (cos 45° + i sin 45°) 
B)  32(cos 45° + i sin 45°) 
C)  4   (cos 135° + i sin 135°) 
D)  32(cos 135° + i sin 135°)

Question 11

Find a unit vector pointing in the same direction as the vector v = -2i - 5j.

Accepted Answer

The answer of Find a unit vector pointing in the...

Question 12

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely.
side c = 25.0 ft
$\angle$C = 62°
side b = 26.3 ft

Accepted Answer

B @#LAT-DLM& 68.3°
A @#LAT-DLM& 49.7°
a

Question 13

Use the following to answer questions :
Vector v =   has initial point (2, 5).
-Find the magnitude |v| of the vector.

Accepted Answer

A)  13 
B)  37 
C)    
D)    
A)  13 
B)  37 
C)    
D)

Question 14

Use the following to answer questions :
u = -2i + j; v = 4i + 3j
-Compute 2u + 5v.

Accepted Answer

A)  -17i + 7j 
B)  -16i + 8j 
C)  -17i + 8j 
D)  -16i + 7j 
A)  -17i + 7j 
B)  -16i + 8j 
C)  -17i + 8j 
D)  -16i + 7j

Question 15

Solve the triangle using the law of sines. Round sides to the nearest tenth. side a = 5 m
$\angle$A = 56°
$\angle$B = 41°

Accepted Answer

A) . $\angle$C = 83° b $\approx$3.3 m
C $\approx$ 5.4 m 
B) . $\angle$C = 83° b $\approx$ 3.8 m
C $\approx$ 6.4 m 
C) . $\angle$C = 83° b $\approx$ 4.0 m
C $\approx$6.0 m 
D) . $\angle$C = 83° b $\approx$ 4.5 m
C $\approx$ 5.8 m 
A) . $\angle$C = 83° b $\approx$3.3 m
C $\approx$ 5.4 m 
B) . $\angle$C = 83° b $\approx$ 3.8 m
C $\approx$ 6.4 m 
C) . $\angle$C = 83° b $\approx$ 4.0 m
C $\approx$6.0 m 
D) . $\angle$C = 83° b $\approx$ 4.5 m
C $\approx$ 5.8 m

Question 16

Determine whether the law of cosines can be used to begin the solution process for the triangle.

Accepted Answer

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

Question 17

Use the following to answer questions :
In   $\angle$A = 60°, and side c = 26 ft.
-How many triangles can be formed if side a = 10 ft?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  3 
A)  0 
B)  1 
C)  2 
D)  3

Question 18

Solve using the law of sines and a scaled drawing. If two triangles exist, solve both completely.
side a = 23.6 yd
$\angle$A = 30°
side c = 47.2 yd

Accepted Answer

B = 60°
C

Question 19

Assume the law of sines is being applied to solve a triangle. Solve for A (if possible), then determine if a second angle (0° <$\theta$ < 180°) exists that also satisfies the proportion. Round to the nearest tenth of a degree.

Accepted Answer

A)  41.1° 
B)  41.1°, 138.9° 
C)  41.7°, 138.3° 
D)  not possible 
A)  41.1° 
B)  41.1°, 138.9° 
C)  41.7°, 138.3° 
D)  not possible

Question 20

Use the following to answer questions :
u =   ; v =  
-Compute u - v.

Accepted Answer

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

Use De Moivre's Theorem to verify z = -1 + i is a solution to z⁴ - 2z³ - z² + 2z + 10 = 0.

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely. side c = 27.5 mi $\angle$ A = 44° side a = 10.1 mi

Use the following to answer questions : p = ; q = -Compute the dot product p • q.

v = (a) Graph the vector. (b) Write the vector as a linear combination of i and j. (c) Compute the magnitude of the vector.

A baby-sitter pulls some kids in a wagon on a level street. How much work is done if she pulls the wagon 200 feet at a constant force of 45 lbs with the wagon handle making an angle of 34° with the street? Round to the nearest whole number.

Two planes leave an airport at the same time. One travels due west (bearing 270°) with a cruising speed of 420 mph. The other travels at bearing 235° with a cruising speed of 440 mph. Approximate the distance between the planes after 3 hours of flight.

Use the following to answer questions : z₁ = 3 - 4i z₂ = -1 - 3i z₃ = 4 - i -Graph the complex numbers z₁, z₂, and z₃ given.

Use De Moivre's Theorem to determine whether z = is a solution to z⁴ - 4z² + 16 = 0.

Write the complex number in trigonometric form using degrees. -4 + 4i

Find a unit vector pointing in the same direction as the vector v = -2i - 5j.

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely. side c = 25.0 ft $\angle$ C = 62° side b = 26.3 ft

Use the following to answer questions : Vector v = has initial point (2, 5). -Find the magnitude |v| of the vector.

Use the following to answer questions : u = -2i + j; v = 4i + 3j -Compute 2u + 5v.

Solve the triangle using the law of sines. Round sides to the nearest tenth. side a = 5 m $\angle$ A = 56° $\angle$ B = 41°

Determine whether the law of cosines can be used to begin the solution process for the triangle.

Use the following to answer questions : In $Use the following to answer questions : In \angle A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 10 ft?$ $\angle$ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 10 ft?

Solve using the law of sines and a scaled drawing. If two triangles exist, solve both completely. side a = 23.6 yd $\angle$ A = 30° side c = 47.2 yd

Use the following to answer questions : u = ; v = -Compute u - v.

Equations and Inequalities

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Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

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Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

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Exam 7: Applications of Trigonometry

Use De Moivre's Theorem to verify z = -1 + i is a solution to z4 - 2z3 - z2 + 2z + 10 = 0.

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely. side c = 27.5 mi ∠\angle∠ A = 44° side a = 10.1 mi

Use the following to answer questions : p = ; q = -Compute the dot product p • q.

v = (a) Graph the vector. (b) Write the vector as a linear combination of i and j. (c) Compute the magnitude of the vector.

A baby-sitter pulls some kids in a wagon on a level street. How much work is done if she pulls the wagon 200 feet at a constant force of 45 lbs with the wagon handle making an angle of 34° with the street? Round to the nearest whole number.

Two planes leave an airport at the same time. One travels due west (bearing 270°) with a cruising speed of 420 mph. The other travels at bearing 235° with a cruising speed of 440 mph. Approximate the distance between the planes after 3 hours of flight.

Use the following to answer questions : z1 = 3 - 4i z2 = -1 - 3i z3 = 4 - i -Graph the complex numbers z1, z2, and z3 given.

Use De Moivre's Theorem to determine whether z = is a solution to z4 - 4z2 + 16 = 0.

Write the complex number in trigonometric form using degrees. -4 + 4i

Find a unit vector pointing in the same direction as the vector v = -2i - 5j.

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely. side c = 25.0 ft ∠\angle∠ C = 62° side b = 26.3 ft

Use the following to answer questions : Vector v = has initial point (2, 5). -Find the magnitude |v| of the vector.

Use the following to answer questions : u = -2i + j; v = 4i + 3j -Compute 2u + 5v.

Solve the triangle using the law of sines. Round sides to the nearest tenth. side a = 5 m ∠\angle∠ A = 56° ∠\angle∠ B = 41°

Determine whether the law of cosines can be used to begin the solution process for the triangle.

Use the following to answer questions : In ∠\angle∠ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 10 ft?

Solve using the law of sines and a scaled drawing. If two triangles exist, solve both completely. side a = 23.6 yd ∠\angle∠ A = 30° side c = 47.2 yd

Assume the law of sines is being applied to solve a triangle. Solve for A (if possible), then determine if a second angle (0° < θ\thetaθ < 180°) exists that also satisfies the proportion. Round to the nearest tenth of a degree.

Use the following to answer questions : u = ; v = -Compute u - v.

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

Use De Moivre's Theorem to verify z = -1 + i is a solution to z⁴ - 2z³ - z² + 2z + 10 = 0.

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely. side c = 27.5 mi $\angle$ A = 44° side a = 10.1 mi

Use the following to answer questions : z₁ = 3 - 4i z₂ = -1 - 3i z₃ = 4 - i -Graph the complex numbers z₁, z₂, and z₃ given.

Use De Moivre's Theorem to determine whether z = is a solution to z⁴ - 4z² + 16 = 0.

Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely. side c = 25.0 ft $\angle$ C = 62° side b = 26.3 ft

Solve the triangle using the law of sines. Round sides to the nearest tenth. side a = 5 m $\angle$ A = 56° $\angle$ B = 41°

Use the following to answer questions : In $Use the following to answer questions : In \angle A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 10 ft?$ $\angle$ A = 60°, and side c = 26 ft. -How many triangles can be formed if side a = 10 ft?

Solve using the law of sines and a scaled drawing. If two triangles exist, solve both completely. side a = 23.6 yd $\angle$ A = 30° side c = 47.2 yd