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The conversion factor from cylindrical to rectangular coordinates is

Question : The conversion factor from cylindrical to rectangular coordinates is : 2151583

Solve the problem by writing an appropriate system of equations and using the inverse of the coefficient matrix to solve the system.

92) The conversion factor from cylindrical to rectangular coordinates is

When θ = 60°, find the inverse of A.

A)

B)

93) The currents in an unbalanced Wheatstone bridge are given by the following system

of equations.

1400I1 - 2600I2 + 5600I3 = 0

-2600I1 + 4000I2 + 2900I3 = 0

5600I1 - 2900I2 + 1100I3 = 10

Write this system as a matrix equation.

A)   =

B)  =

C)   =

94) The sum of the angles of a triangle is 180°. The largest angle is the sum of the smaller two angles and is 30° more than twice the smallest angle. What is the measure of the smallest angle?

A) 17°

B) 45°

C) 30°

D) 90°

95) The sum of three numbers is 13. The first, plus three times the second, plus the third, is 1. Two times the first, minus the second, plus the third, is 15. Which of the numbers are odd numbers?

A) -7

B) 29

C) 29 and 7

D) -7 and -29

96) The sum of three numbers is 5. The sum of the first and second numbers is 3, and the first number is one more than three times the third number. How many of the numbers are even numbers?

A) 1

B) 3

C) None

D) 2

97) The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal and Cal is 1 year younger than Ben. Which of these people were teenagers 7 years ago?

A) Ben

B) Art

C) Art, Ben, and Cal

D) Art and Ben

98) The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other angle. Find the measure of the smallest angle.

A) 20°

B) 40°

C) 30°

D) 10°

99) A grain dealer sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $39.60; to another, 2 of wheat, 3 of corn, and 5 of rye, for $34.80; and to a third, 3 of wheat, 5 of corn, and 2 of rye, for $33.60. Which of the grains was the cheapest?

A) Wheat and rye (tie)

B) Corn

C) Corn and rye (tie)

D) Wheat

100) A $100,000 trust is to be invested in bonds paying 8%, CDs paying 7%, and mortgages paying 10%. The bond and CD investment must be triple the mortgage investment. To earn an $8000 annual income from the investments, how much should the bank invest in bonds?

A) $25,000

B) $50,000

C) $30,000

D) $15,000

Solve the system of equations by Gaussian elimination. If there is an unlimited number of solutions, find two of them.

101) x + y = 2

x - y = -3

A) x = - 1/2, y = - 1/2

B) x = - 1/2, y = 5/2

C) Inconsistent

D) x = 5/2, y = - 3/2

102) 4x + y = 6

3x + 2y = 2

A) Inconsistent

B) x = -2, y =-2

C) x = -2, y = 2

D) x = 2, y = -2

103) 3x + 2y = 2

5x + 4y = 6

A) Unlimited: x = -2, y = 4; x = -2, y = -4

B) Inconsistent

C) x = -2, y = 4

D) x = -2, y = -4

104) 6x - 7y = -63

-2x - 2y = -18

A) Inconsistent

B) x = 0, y = 10

C) x = 0, y = 9

D) x = -1, y = 10

105) 9x + 8y = 9

-2x + 6y = -2

A) x = 1, y = 1

B) x = 0, y = 1

C) Inconsistent

D) x = 1, y = 0

106) 6x - 5y = 8

-6x + 5y = -1

A) x = -1, y = -1

B) x = 8, y = -1

C) Inconsistent

D) x = 0, y = 0

107) 9x + 5y = -25

3x + 2y = -10

-8x + 5y = -25

A) x = -1, y = -4

B) Inconsistent

C) x = 0, y = -5

D) Unlimited: x = -1, y = -4; x = 0, y = -5

108) x - y + 4z = 2

-x + y - 4z = -4

A) Inconsistent

B) x = 0, y = 0, z = -2

C) x = 4, y = -2, z = 0

D) x = 0, y = -2, z = 0

109) 4x + y + z = 12

8x + 2y + 4z = 24

A) Unlimited: x = 0, y = 12, z = 0; x = 5, y = -8, z = 0

B) Inconsistent

C) x = 5, y = -8, z = 0

D) x = 0, y = 12, z = 0

110) 9x + 7y - z = 42

x + 7y - 2z = 2

3x + y + z = 22

A) Inconsistent

B) x = 4, y = 2, z = 8

C) x = 4, y = 8, z = 2

D) x = -4, y = 2, z = 8

111) 3x - y + 3z = 19

9x + 4y - 7z = 7

-6x - 7y + z = -28

A) x = 3, y = 2, z = 4

B) Unlimited: x = 3, y = 2, z = 4, x = 3, y = 4, z = 2

C) x = 3, y = 4, z = 2

D) Inconsistent

112) 6x - y + 5z = 19

3x + 2z = 11

4y + z = 32

A) x = -1, y = 7, z = 2

B) x = 1, y = 4, z = 7

C) x = 1, y = 7, z = 4

D) Inconsistent

113) -4x - 6y - 8z = 4

7x + 6y + 9z = 4

-20x - 30y - 40z = 6

A) Inconsistent

B) x = 4, y = 4, z = 6

C) x = 5, y = 5, z = -1

D) x = 0, y = 0, z = 0

114) x - z = 5

y + z = 5

x + z = 2

A) x = - 3/2, y = 23/2, z = - 13/2

B) x = 5, y = 5, z = 0

C) x = 7/2, y = 13/2, z = - 3/2

D) x = 7, y = 13, z = -3

115) 2x - 2y + 3z = -10

x + 2y - z = 8

2y + z = -2

A) x = 2, y = 1, z = -4

B) x = -2, y = 6, z = -8

C) x = -2, y = 1, z = 4

D) Inconsistent

116) x + 3y - 2z - w = 19

4x + y + z + 2w = 22

-3x - y - 3z - 2w = -8

x - y - 3z -2w = 8

A) Inconsistent

B) x = 3, y = 5, z = -9, w = 6

C) x = 19, y = 22, z = -8, w = 8

D) x = 4, y = 3, z = -5, w = 4

Solve the problem using Gaussian elimination.

117) The voltage across an electric resistor equals the current (in A) times the resistance (in Ω). If a current of

4 A passes through each of two resistors, the sum of the voltages is 44. If 5 A passes through the first resistor and 9 A passes through the second resistor, the sum of the voltages is 83 V. Find the resistances.

A) resistance 1 = 7 Ω and resistance 2 = 7 Ω

B) resistance 1 = 4 Ω and resistance 2 = 4 Ω

C) resistance 1 = 4 Ω and resistance 2 = 7 Ω

D) resistance 1 = 7 Ω and resistance 2 = 4 Ω

118) Three machines together produce 155 parts each hour. Twice the production of the second machine is 25 parts/h more than the sum of the production of the other two machines. If the first machine operates for 2 hours and the others operate for 7 hours, 985 parts are produced. Find the production rate of each machine.

A) 75 parts/h, 20 parts/h, 60 parts/h

B) 75 parts/h, 60 parts/h, 20 parts/h

C) 60 parts/h, 75 parts/h, 20 parts/h

D) 20 parts/h, 75 parts/h, 60 parts/h

119) A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 100 black, 110 white and 90 red wires. How many of each cable were made?

A) 10 cable A

103 cable B

20 cable C

B) 10 cable A

30 cable B

93 cable C

C) 10 cable A

30 cable B

20 cable C

D) 20 cable A

30 cable B

10 cable C

120) A $156,000 trust is to be invested in bonds paying 6%, CDs paying 5%, and mortgages paying 8%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $10,620 annual interest from the investments, how much should the bank invest in bonds?

A) $46,000

B) $48,000

C) $30,000

D) $78,000

Evaluate the determinant by inspection.

121)

A) 270

B) 246

C) -294

D) -270

122)

A) 162

B) -162

C) 138

D) -186

123)

A) -7

B) -14

C) -805

D) 0

124)

A) -69

B) -42

C) 0

D) 240

Solution
5 (1 Ratings )

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