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Given vector u with components square root three comma negative one and vector v with components three comma negative four , what is vector u times vector v ?

A
negative 4 square root of 3 minus 3
B
3 square root of 3 plus 4
C
negative 4 square root of 3 plus 3
D
3 square root of 3 minus 4
25

Which equation represents a hyperbola with a center at open paren 0 comma 0 close paren , a vertex at open paren 0 comma 60 close paren , and a focus at open paren 0 comma negative 65 close paren ?

A
the fraction with numerator y squared and denominator 60 squared minus the fraction with numerator x squared and denominator 25 squared is equal to 1
B
the fraction with numerator x squared and denominator 60 squared minus the fraction with numerator y squared and denominator 65 squared is equal to 1
C
the fraction with numerator x squared and denominator 60 squared minus the fraction with numerator y squared and denominator 25 squared is equal to 1
D
the fraction with numerator y squared and denominator 60 squared minus the fraction with numerator x squared and denominator 65 squared is equal to 1
26

Given the vector the 2 by 1 column matrix 4 3 and the transformation matrix the 2 by 2 matrix, row 1, column 1, 0 column 2, 1 row 2, column 1, negative 1 column 2, 0 , which vector is the image after applying the transformation to the 2 by 1 column matrix 4 3 ?

A
the 2 by 1 column matrix row 1 3 row 2 negative 4
B
the 2 by 1 column matrix row 1 negative 4 row 2 3
C
the 2 by 1 column matrix row 1 4 row 2 negative 3
D
the 2 by 1 column matrix row 1 negative 3 row 2 4
27

Which graph represents the polar curve r is equal to 1 plus sine of theta ?

A
Image with description On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, 2). It has a cardioid at (0, 0).
B
Image with description On a polar coordinate plane, a circle crosses the y-axis at (0, 0) and (0, negative 2). It has a cardioid at (0, 0).
C
Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (2, 0). It has a cardioid at (0, 0).
D
Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (negative 2, 0). It has a cardioid at (0, 0).
28

An ellipse has a center at the origin, a vertex along the major axis at open paren 0 comma 17 close paren , and a focus at open paren 0 comma negative 8 close paren Which equation represents this ellipse?

A
the fraction with numerator y squared and denominator 17 squared plus the fraction with numerator x squared and denominator 15 squared is equal to 1
B
the fraction with numerator x squared and denominator 17 squared plus the fraction with numerator y squared and denominator 15 squared is equal to 1
C
the fraction with numerator y squared and denominator 17 squared plus the fraction with numerator x squared and denominator 8 squared is equal to 1
D
the fraction with numerator x squared and denominator 17 squared plus the fraction with numerator y squared and denominator 8 squared is equal to 1
31

Consider the sequence 1 third comma 1 ninth comma 1 over 27 comma 1 over 81 comma dot dot dot Which statement describes the sequence?

A
The sequence converges to a limit of infinity .
B
The sequence converges to a limit of negative infinity .
C
The sequence diverges.
D
The sequence converges to a limit of 0 .
32

Sam takes a job with a starting salary of 50 dollars comma 000 for the first year. He earns a 4 percent increase each year. Which expression gives the partial sum, cap s sub 3 , (in thousands)?

A
cap s sub 3 is equal to the sum from n is equal to 1 to 3 of 50
B
cap s sub 3 is equal to the sum from n is equal to 1 to 3 of 50
C
cap s sub 3 is equal to the sum from n is equal to 1 to 3 of 50
D
cap s sub 3 is equal to the sum from n is equal to 1 to 3 of 50
34

What is the approximate angle measure for angle cap w in the triangle?

A
77.6 degrees
B
48.5 degrees
C
89.8 degrees
D
53.9 degrees
35

Which is an equation of an asymptote of the hyperbola?

A
y is equal to 1 third x plus 2
B
y is equal to negative 1 third x
C
y is equal to 3 x plus 10
D
y is equal to negative 3 x plus 8
36

What mistake did Aaron make?

A
He should have subtracted components 7 comma negative 21 rather than add.
B
He did not correctly distribute 4 to both components of vector s .
C
He did not correctly distribute the negative when subtracting 7 vector t .
D
He added components 10 comma negative 2 plus components 24 comma 0 plus components 7 comma negative 21 incorrectly.
37

Which point is a vertex of the hyperbola?

A
open paren 1 comma 11 close paren
B
open paren 1 comma negative 15 close paren
C
open paren 1 comma 3 close paren
D
open paren 1 comma negative 2 close paren
38

Given transformation matrix cap t is equal to the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 0 row 2, column 1, 0 column 2, 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 1 to 5 in increments of 1, and the y-axis ranges from negative 5 to 1 in increments of 1. A vector v prime has origin (0, 0) and terminal point (5, negative 1).
B
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 1 in increments of 1, and the y-axis ranges from negative 3 to 4 in increments of 1. A vector v prime has origin (0, 0) and terminal point (negative 5, 1).
C
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 1 in increments of 1, and the y-axis ranges from negative 1 to 5 in increments of 1. A vector v prime has origin (0, 0) and terminal point (negative 1, 5).
D
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 5 to 1 in increments of 1. A vector v prime has origin (0, 0) and terminal point (1, negative 5).
39

What is the unknown side length x ? Round the answer to the nearest tenth.

A
40 point 5 ft
B
6 point 4 ft
C
31 point 5 ft
D
5 point 6 ft
40

A plane is located on radar by an air traffic controller. What are the magnitude and the direction angle of the vector from the airport to the plane?

A
The magnitude is 7 point 9 4 , and the direction angle is cap n 49.09 degrees cap e .
B
The magnitude is 7 point 9 4 , and the direction angle is cap n 40.91 degrees cap e .
C
The magnitude is 11 point 2 , and the direction angle is cap e 49.09 degrees cap n .
D
The magnitude is 11 point 2 , and the direction angle is cap e 40.91 degrees cap n .

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N/A — Exam Answers — Precalculus