Question 1

Solve the following equation for a. Round to the nearest hundredth.

Accepted Answer

A)  a$\approx$ 6.01 
B)  a $\approx$ 6.96 
C)  a $\approx$ 7.67 
D)  a$\approx$ 8.09 
A)  a$\approx$ 6.01 
B)  a $\approx$ 6.96 
C)  a $\approx$ 7.67 
D)  a$\approx$ 8.09 B

Question 2

The force vectors F1 = -5i + j and F2 = -4i - 5j are acting on a common point P. Find an additional force vector so that equilibrium takes place.

Accepted Answer

9i + 4j

Question 3

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 A

Question 4

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

Accepted Answer

A)  (-7, 9) 
B)  (1, 7) 
C)  (-1, -7) 
D)  (-7, 7) 
A)  (-7, 9) 
B)  (1, 7) 
C)  (-1, -7) 
D)  (-7, 7)

Question 5

For the complex numbers z1 = 1 -   i and z2 = -5 + 0i
(a) Find the moduli r1 and r2 and the arguments $\theta$1 and $\theta$2.
(b) Compute the quotient in rectangular form.
(c) Find the modulus r and argument $\theta$ of the quotient.
(d) Verify that   = r and $\theta$1 - $\theta$2 = $\theta$.

Accepted Answer

(a) r₁ = 2, r₂

Question 6

Solve the triangle using the law of cosines. Round to tenths.

Accepted Answer

A @#LAT-DLM& 15.9°
B

Question 7

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

Accepted Answer

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

Question 8

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 9

For the complex numbers z1 = 3 + 3i and z2 = -2 - 2i
(a) Find the moduli r1 and r2 and the arguments $\theta$1 and $\theta$2.
(b) Compute their product in rectangular form.
(c) Find the modulus r and argument $\theta$of the product.
(d) Verify that r1r2 = r and$\theta$1 + $\theta$2 = $\theta$.

Accepted Answer

(a) r₁ = @#IMG-DLM& , r₂ = @#IMG-DLM&

Question 10

Use the following to answer questions :
p =   ; q =  
-Find the angle between the vectors to the nearest tenth of a degree.

Accepted Answer

A)  165.5° 
B)  166.3° 
C)  166.7° 
D)  168.0° 
A)  165.5° 
B)  166.3° 
C)  166.7° 
D)  168.0°

Question 11

Use the following to answer questions :  
-Compute the product   and the quotient   using the trigonometric form. Write your answer in rectangular form. Round to two decimal places as necessary.   = 15(cos 72° + i sin 72°),   = 2.5(cos 36° + i sin 36°)

Accepted Answer

@#IMG-DLM& = -11.59

Question 12

Solve the triangle using the law of cosines. Round to tenths.

Accepted Answer

A)  A $\approx$ 22.0° C $\approx$ 138.0°
B $\approx$ 80.7 cm 
B)  A $\approx$ 158.0° C $\approx$ 2.0°
B $\approx$ 80.7 cm 
C)  A $\approx$ 56.0° C $\approx$ 104.0°
B $\approx$ 36.4 cm 
D)  A $\approx$ 124.0° C $\approx$ 36.0°
B $\approx$ 36.4 cm 
A)  A $\approx$ 22.0° C $\approx$ 138.0°
B $\approx$ 80.7 cm 
B)  A $\approx$ 158.0° C $\approx$ 2.0°
B $\approx$ 80.7 cm 
C)  A $\approx$ 56.0° C $\approx$ 104.0°
B $\approx$ 36.4 cm 
D)  A $\approx$ 124.0° C $\approx$ 36.0°
B $\approx$ 36.4 cm

Question 13

Solve for the unknown part. Round to one decimal place. 52 = (9)2 + (10)2 - 2(9)(10)cos(A)

Accepted Answer

A)  A $\approx$ 29.4° 
B)  A $\approx$ 29.6° 
C)  A $\approx$29.9° 
D)  A $\approx$ 30.2° 
A)  A $\approx$ 29.4° 
B)  A $\approx$ 29.6° 
C)  A $\approx$29.9° 
D)  A $\approx$ 30.2°

Question 14

Use the following to answer questions :
For a certain AC circuit, R = 35 $\Omega$, XS1U1B1LS1U1B0 = 20  $\Omega$ and XS1U1B1CS1U1B0 = 8  $\Omega$, with I = 2 A.  
-Find the total voltage across the circuit.

Accepted Answer

A)  74V 
B)  75V 
C)  76V 
D)  77V 
A)  74V 
B)  75V 
C)  76V 
D)  77V

Question 15

u =   ; v =   (a) Compute u + v.
(b) Illustrate u + v graphically.

Accepted Answer

The answer of u =   ; v =...

Question 16

Use the following to answer questions :
u =   ; v =  
-Resolve u into vectors u1 and u2 where u1 || v and u2 $\bot$ v. Round to the nearest hundredth as necessary.

Accepted Answer

A)  u1 =   , u2 =
  
B)  u1 =   , u2 =
  
C)  u1 =   , u2 =
  
D)  u1 =   , u2 =
  
A)  u1 =   , u2 =
  
B)  u1 =   , u2 =
  
C)  u1 =   , u2 =
  
D)  u1 =   , u2 =

Question 17

Use De Moivre's Theorem to compute (4 + 4i)4.

Accepted Answer

A)  1024 
B)  -1024 
C)  1024i 
D)  -1024i 
A)  1024 
B)  -1024 
C)  1024i 
D)  -1024i

Question 18

Solve using the nth roots theorem. Approximate answers to four decimal places.

Accepted Answer

A)  1.0506 + 1.7018i, -0.1327 + 1.9956i, -1.2667 + 1.5477i 
B)  1.8435 - 0.7756i, 1.9512 + 0.4389i, 1.3338 + 1.4903i 
C)  -0.5176 + 1.9319i, -1.4142 - 1.4142i, 1.9319 - 0.5176i 
D)  -1.5194 + 1.3006i, -1.9922 + 0.1767i, -1.7246 - 1.0128i 
A)  1.0506 + 1.7018i, -0.1327 + 1.9956i, -1.2667 + 1.5477i 
B)  1.8435 - 0.7756i, 1.9512 + 0.4389i, 1.3338 + 1.4903i 
C)  -0.5176 + 1.9319i, -1.4142 - 1.4142i, 1.9319 - 0.5176i 
D)  -1.5194 + 1.3006i, -1.9922 + 0.1767i, -1.7246 - 1.0128i

Question 19

Use the nth roots theorem to find the four fourth roots of   . Answer in exact form.

Accepted Answer

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

Question 20

Hal pushes a box full of books 40 ft. If he uses a constant force of 75 pounds, how much work did he do?

Accepted Answer

The answer of Hal pushes a box full of books...

Solve the following equation for a. Round to the nearest hundredth.

The force vectors F₁ = -5i + j and F₂ = -4i - 5j are acting on a common point P. Find an additional force vector so that equilibrium takes place.

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

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

Solve the triangle using the law of cosines. Round to tenths.

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

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

Use the following to answer questions : p = ; q = -Find the angle between the vectors to the nearest tenth of a degree.

Use the following to answer questions : -Compute the product and the quotient using the trigonometric form. Write your answer in rectangular form. Round to two decimal places as necessary. = 15(cos 72° + i sin 72°), = 2.5(cos 36° + i sin 36°)

Solve the triangle using the law of cosines. Round to tenths.

Solve for the unknown part. Round to one decimal place. 5² = (9)² + (10)² - 2(9)(10)cos(A)

u = ; v = (a) Compute u + v. (b) Illustrate u + v graphically.

Use De Moivre's Theorem to compute (4 + 4i)⁴.

Solve using the nth roots theorem. Approximate answers to four decimal places.

Use the nth roots theorem to find the four fourth roots of . Answer in exact form.

Hal pushes a box full of books 40 ft. If he uses a constant force of 75 pounds, how much work did he do?

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

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Analytical Geometry

Additional Topics in Algebra

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

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Exam 7: Applications of Trigonometry

Solve the following equation for a. Round to the nearest hundredth.

The force vectors F1 = -5i + j and F2 = -4i - 5j are acting on a common point P. Find an additional force vector so that equilibrium takes place.

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

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

Solve the triangle using the law of cosines. Round to tenths.

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

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

Use the following to answer questions : p = ; q = -Find the angle between the vectors to the nearest tenth of a degree.

Use the following to answer questions : -Compute the product and the quotient using the trigonometric form. Write your answer in rectangular form. Round to two decimal places as necessary. = 15(cos 72° + i sin 72°), = 2.5(cos 36° + i sin 36°)

Solve the triangle using the law of cosines. Round to tenths.

Solve for the unknown part. Round to one decimal place. 52 = (9)2 + (10)2 - 2(9)(10)cos(A)

Use the following to answer questions : For a certain AC circuit, R = 35 Ω\OmegaΩ , XL = 20 Ω\OmegaΩ and XC = 8 Ω\OmegaΩ , with I = 2 A. -Find the total voltage across the circuit.

u = ; v = (a) Compute u + v. (b) Illustrate u + v graphically.

Use the following to answer questions : u = ; v = -Resolve u into vectors u1 and u2 where u1 || v and u2 ⊥\bot⊥ v. Round to the nearest hundredth as necessary.

Use De Moivre's Theorem to compute (4 + 4i)4.

Solve using the nth roots theorem. Approximate answers to four decimal places.

Use the nth roots theorem to find the four fourth roots of . Answer in exact form.

Hal pushes a box full of books 40 ft. If he uses a constant force of 75 pounds, how much work did he do?

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

The force vectors F₁ = -5i + j and F₂ = -4i - 5j are acting on a common point P. Find an additional force vector so that equilibrium takes place.

Solve for the unknown part. Round to one decimal place. 5² = (9)² + (10)² - 2(9)(10)cos(A)

Use De Moivre's Theorem to compute (4 + 4i)⁴.