AnswersPrecalculusModeling with Vector Quantities

Modeling with Vector Quantities — Test Answers

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Given transformation matrix cap t is equal to the 2 by 2 matrix, row 1, column 1, 1 column 2, 0 row 2, column 1, 0 column 2, negative 1 , which diagram shows the application of cap t to v ?

A
Image with description On a coordinate plane, the x-axis ranges from negative 4 to 2 in increments of 1, and the y-axis ranges from negative 4 to 2 in increments of 1. A vector v prime has origin (0, 0) and terminal point (negative 2, negative 4).
B
Image with description On a coordinate plane, the x-axis ranges from negative 2 to 4 in increments of 1, and the y-axis ranges from negative 2 to 4 in increments of 1. A vector v prime has origin (0, 0) and terminal point (2, 4).
C
Image with description On a coordinate plane, the x-axis ranges from negative 1 to 5 in increments of 1, and the y-axis ranges from negative 4 to 2 in increments of 1. A vector v prime has origin (0, 0) and terminal point (4, negative 2).
D
Image with description On a coordinate plane, the x-axis ranges from negative 4 to 2 in increments of 1, and the y-axis ranges from negative 2 to 4 in increments of 1. A vector v prime has origin (0, 0) and terminal point (negative 4, 2).
2
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Which transformation is applied to the figure?

A
rotate 90 degrees counterclockwise about the origin
B
rotate 180 degrees counterclockwise about the origin
C
reflect across y is equal to negative x
D
reflect across the y -axis
3

Which statement accurately describes the vector shown?

A
magnitude of square root of 61 and direction angle equal to approximately 40 degrees
B
magnitude of square root of 11 and direction angle equal to approximately 40 degrees
C
magnitude of square root of 11 and direction angle equal to approximately 50 degrees
D
magnitude of square root of 61 and direction angle equal to approximately 50 degrees
4

A wagon is being pulled by a 300 -pound force that makes a 30 degrees angle with the ground. What are the horizontal and vertical components of the force vector?

A
The horizontal is 346 pounds, and the vertical is 600 pounds.
B
The horizontal is 600 pounds, and the vertical is 346 pounds.
C
The horizontal is 150 pounds, and the vertical is 260 pounds.
D
The horizontal is 260 pounds, and the vertical is 150 pounds.
5

Let magnitude of vector u is equal to 4 at an angle of 210 degrees and magnitude of vector v is equal to 9 at an angle of 315 degrees , and vector w is equal to vector u minus vector v What is the magnitude and direction angle of vector w ?

A
magnitude of vector w is equal to 10 point 8 ; theta is equal to 156.1 degrees
B
magnitude of vector w is equal to 5 point 5 ; theta is equal to 156.1 degrees
C
magnitude of vector w is equal to 5 point 5 ; theta is equal to 203.9 degrees
D
magnitude of vector w is equal to 10 point 8 ; theta is equal to 203.9 degrees
6

Which diagram shows the parallelogram method for vector addition?

A
Image with description Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right and is double the size of vectors v and u.
B
Image with description Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the terminal point of vector u, and shares a terminal point with the terminal point of vector v.
C
Image with description Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares a terminal point with the terminal point of vector u, and shares an origin with the terminal point of vector v.
D
Image with description Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right.
10

A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction cap n 20 degrees cap e Which diagram represents the boat’s current distance, x , from the pier?

A
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by vector 15 miles and the x-axis is 20 degrees.
B
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by a vertical line and vector 15 miles is 20 degrees.
C
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with a vertical line and vector 15 miles is 20 degrees.
D
Image with description On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with the x-axis and vector 15 miles is 20 degrees.
13

A vector has initial point at open paren 3 comma negative 5 close paren and terminal point at open paren negative 2 comma 3 close paren What are the characteristics of this vector?

A
The magnitude is square root of 13 , and the direction angle is about 122 degrees .
B
The magnitude is square root of 89 , and the direction angle is about 122 degrees .
C
The magnitude is square root of 13 , and the direction angle is about 58 degrees .
D
The magnitude is square root of 89 , and the direction angle is about 58 degrees .
16

Which rectangular equation represents the parametric equations x is equal to 3 t raised to the 1 half power and y is equal to 6 t ?

A
y is equal to 54 x squared , for x is greater than or equal to 0
B
y is equal to 2 thirds x squared , for x is greater than or equal to 0
C
y is equal to 2 x squared , for x is greater than or equal to 0
D
y is equal to 1 over 54 x squared , for x is greater than or equal to 0
19

A bicycle path starts 5 miles due east of an intersection, and continues in a straight line to finish 8 miles due north of the same intersection. Let the intersection be represented by the point open paren 0 comma 0 close paren Suppose a cyclist rides the path from start to finish in 2 hours. Which parametric equations model the path of the rider?

A
x times t is equal to negative 5 halves t plus 5 and y times t is equal to 4 t plus 8
B
x times t is equal to negative 5 halves t plus 5 and y times t is equal to 4 t
C
x times t is equal to 5 t and y times t is equal to 8 t plus 2
D
x times t is equal to 5 t plus 2 and y times t is equal to 8 t
20

Let magnitude of vector r is equal to 6 at an angle of 30 degrees and magnitude of vector s is equal to 11 at an angle of 225 degrees Which expression represents magnitude of vector r minus vector s ?

A
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 165 degrees close paren end root
B
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 45 degrees close paren end root
C
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 255 degrees close paren end root
D
square root of 6 squared plus 11 squared minus 2 6 11 cosine open paren 15 degrees close paren end root

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