Question 1

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]
$$2 u + v$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E)  none of these 
A) 
  
B) 
  
C) 
  
D) 
  
E)  none of these

Question 2

Write the complex number shown below in trigonometric form.

Accepted Answer

A)  $6 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$ 
B)  $6 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C)  $6 \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)$ 
D)  $6 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
E)  $6 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ 
A)  $6 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$ 
B)  $6 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C)  $6 \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)$ 
D)  $6 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
E)  $6 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$

Question 3

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
$B = 76 ^ { \circ } 30 ^ { \prime } , a = 8$, and $c = 13$

Accepted Answer

A)  $60.68$ sq. units 
B)  $45.51 \mathrm { sq }$. units 
C)  $40.45$ sq. units 
D)  $50.56 \mathrm { sq }$. units 
E)  $55.62$ sq. units 
A)  $60.68$ sq. units 
B)  $45.51 \mathrm { sq }$. units 
C)  $40.45$ sq. units 
D)  $50.56 \mathrm { sq }$. units 
E)  $55.62$ sq. units

Question 4

In the figure below, $a = 7 , c = 20$, and $d = 14$. Use this information to solve the parallelogram for $b$. The diagonals of the parallelogram are represented by $c$ and $d$. Round answer to two decimal places.

Accepted Answer

A)  7.14 
B)  13.62 
C)  15.78 
D)  12.00 
E)  11.46 
A)  7.14 
B)  13.62 
C)  15.78 
D)  12.00 
E)  11.46

Question 5

A plane flies 710 miles from City A to City B with a bearing of $28 ^ { \circ }$ (clockwise from north). Then it flies 672 miles from City B to City C with a bearing of $45 ^ { \circ }$. Find the straight-line distance from City C to City A. Round your answer to two decimals.

Accepted Answer

A)  $207.70$ miles 
B)  $1238.36$ miles 
C)  $1111.16$ miles 
D)  $955.99$ miles 
E)  $1366.83$ miles 
A)  $207.70$ miles 
B)  $1238.36$ miles 
C)  $1111.16$ miles 
D)  $955.99$ miles 
E)  $1366.83$ miles

Question 6

A triangular parcel of land has sides of lengths 900, 580, and 550 feet. Approximate the area of the land. Round answer to nearest foot.

Accepted Answer

A)  $154,345 \mathrm { ft } ^ { 2 }$ 
B)  $153,657 \mathrm { ft } ^ { 2 }$ 
C)  $152,972 \mathrm { ft } ^ { 2 }$ 
D)  $152,971 \mathrm { ft } ^ { 2 }$ 
E)  $153,656 \mathrm { ft } ^ { 2 }$ 
A)  $154,345 \mathrm { ft } ^ { 2 }$ 
B)  $153,657 \mathrm { ft } ^ { 2 }$ 
C)  $152,972 \mathrm { ft } ^ { 2 }$ 
D)  $152,971 \mathrm { ft } ^ { 2 }$ 
E)  $153,656 \mathrm { ft } ^ { 2 }$

Question 7

Plot the following complex number. $3 i$

Accepted Answer

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

Question 8

Given $A = 52 ^ { \circ } , B = 65 ^ { \circ }$, and $a = 7.1$, use the Law of Sines to solve the triangle for the value of $b$. Round answer to two decimal places.

Accepted Answer

A)  $b = 6.98$ 
B)  $b = 8.03$ 
C)  $b = 6.28$ 
D)  $b = 8.17$ 
E)  $b = 6.17$ 
A)  $b = 6.98$ 
B)  $b = 8.03$ 
C)  $b = 6.28$ 
D)  $b = 8.17$ 
E)  $b = 6.17$

Question 9

Let $\mathbf { u } = \langle 6,8 \rangle$ and $\mathbf { v } = \langle 14,10 \rangle$. Find $\mathbf { u } - \mathbf { v }$

Accepted Answer

A)  $\langle 16,22 \rangle$ 
B)  $\langle - 8 , - 2 \rangle$ 
C)  $\langle 20,18 \rangle$ 
D)  $\langle - 4 , - 6 \rangle$ 
E)  $\langle 22,16 \rangle$ 
A)  $\langle 16,22 \rangle$ 
B)  $\langle - 8 , - 2 \rangle$ 
C)  $\langle 20,18 \rangle$ 
D)  $\langle - 4 , - 6 \rangle$ 
E)  $\langle 22,16 \rangle$

Question 10

In the figure below, $a = 9 , b = 11$, and $c = 12$. Use this information to solve the parallelogram for $\theta$. The diagonals of the parallelogram are represented by $c$ and $d$. Round answer to two decimal places.

Accepted Answer

A)  $107.03 ^ { \circ }$ 
B)  $98.52$ 
C)  $90.00 ^ { \circ }$ 
D)  $92.13$ 
E)  $72.97 ^ { \circ }$ 
A)  $107.03 ^ { \circ }$ 
B)  $98.52$ 
C)  $90.00 ^ { \circ }$ 
D)  $92.13$ 
E)  $72.97 ^ { \circ }$

Question 11

A force of 50 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 43 feet. How much work has been Accomplished? Round answer to one decimal place.

Accepted Answer

A)  2,150.0 foot-pounds 
B)  2, 482.6 foot-pounds 
C)  2,006.0 foot-pounds 
D)  2, 244.3 foot-pounds 
E)  1,862.0 foot-pounds 
A)  2,150.0 foot-pounds 
B)  2, 482.6 foot-pounds 
C)  2,006.0 foot-pounds 
D)  2, 244.3 foot-pounds 
E)  1,862.0 foot-pounds

Question 12

Find the trigonometric form of the complex number shown below.
$$- 3 - 3 i$$

Accepted Answer

A)  $3 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
B)  $\sqrt { 3 } \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ 
C)  $9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$ 
D)  $3 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
E)  $\sqrt { 2 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
A)  $3 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
B)  $\sqrt { 3 } \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ 
C)  $9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$ 
D)  $3 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
E)  $\sqrt { 2 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$

Question 13

Determine whether $\mathbf { u }$ and $\mathbf { v }$ are orthogonal, parallel, or neither.
$$\mathbf { u } = \left\langle \frac { 7 } { 3 } , \frac { - 1 } { 2 } \right\rangle , \mathbf { v } = \langle 14 , - 3 \rangle$$

Accepted Answer

A)  orthogonal 
B)  parallel 
C)  neither 
A)  orthogonal 
B)  parallel 
C)  neither

Question 14

Find the vector $\mathbf { v }$ that has a magnitude of 8 and is in the same direction as $\mathbf { u }$, where $\mathbf { u } = \langle - 6 , - 4 \rangle$

Accepted Answer

A)  $\mathbf { v } = \left\langle \frac { - 24 } { \sqrt { 13 } } , \frac { - 16 } { \sqrt { 13 } } \right\rangle$ 
B)  $\mathbf { v } = \left\langle \frac { - 3 } { \sqrt { 13 } } , \frac { - 2 } { \sqrt { 13 } } \right\rangle$ 
C)  $\mathbf { v } = \left\langle \frac { - 8 } { \sqrt { 13 } } , \frac { - 4 } { \sqrt { 13 } } \right\rangle$ 
D)  $\mathbf { v } = \left\langle \frac { - 2 } { \sqrt { 13 } } , \frac { 2 } { \sqrt { 13 } } \right\rangle$ 
E)  $ \mathbf { v } = \left\langle \frac { 4 } { \sqrt { 13 } } , \frac { 6 } { \sqrt { 13 } } \right\rangle$ 
A)  $\mathbf { v } = \left\langle \frac { - 24 } { \sqrt { 13 } } , \frac { - 16 } { \sqrt { 13 } } \right\rangle$ 
B)  $\mathbf { v } = \left\langle \frac { - 3 } { \sqrt { 13 } } , \frac { - 2 } { \sqrt { 13 } } \right\rangle$ 
C)  $\mathbf { v } = \left\langle \frac { - 8 } { \sqrt { 13 } } , \frac { - 4 } { \sqrt { 13 } } \right\rangle$ 
D)  $\mathbf { v } = \left\langle \frac { - 2 } { \sqrt { 13 } } , \frac { 2 } { \sqrt { 13 } } \right\rangle$ 
E)  $ \mathbf { v } = \left\langle \frac { 4 } { \sqrt { 13 } } , \frac { 6 } { \sqrt { 13 } } \right\rangle$

Question 15

Determine whether $\mathbf { u }$ are $\mathbf { v }$ and orthogonal, parallel, or neither.
$$\mathbf { u } = \langle 6,4 \rangle , \mathbf { v } = \langle - 20,30 \rangle$$

Accepted Answer

A)  orthogonal 
B)  parallel 
C)  neither 
A)  orthogonal 
B)  parallel 
C)  neither

Question 16

Let $\mathbf { u } = \langle 10,6 \rangle$ and $\mathbf { v } = \langle 11,15 \rangle$. Find $\mathbf { u } - \mathbf { v }$

Accepted Answer

A)  $\langle 25,17 \rangle$ 
B)  $\langle - 1 , - 9 \rangle$ 
C)  $\langle 21,21 \rangle$ 
D)  $\langle - 5 , - 5 \rangle$ 
E)  $\langle 17,25 \rangle$ 
A)  $\langle 25,17 \rangle$ 
B)  $\langle - 1 , - 9 \rangle$ 
C)  $\langle 21,21 \rangle$ 
D)  $\langle - 5 , - 5 \rangle$ 
E)  $\langle 17,25 \rangle$

Question 17

A plane flies 450 kilometers with a bearing of $319 ^ { \circ }$ from City A to City B (see figure below). The plane then flies 730 kilometers from City B to City C, which is directly west of City A. Find the bearing of the flight from City B to City C. Round your answer to two decimals.

Accepted Answer

A)  $242.27 ^ { \circ }$ 
B)  $332.27 ^ { \circ }$ 
C)  $27.73 ^ { \circ }$ 
D)  $23.85 ^ { \circ }$ 
E)  $246.15 ^ { \circ }$ 
A)  $242.27 ^ { \circ }$ 
B)  $332.27 ^ { \circ }$ 
C)  $27.73 ^ { \circ }$ 
D)  $23.85 ^ { \circ }$ 
E)  $246.15 ^ { \circ }$

Question 18

Given $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ and $\mathbf { v } = - \mathbf { i } - 5 \mathbf { j }$, determine $- 9 \mathbf { u } + 6 \mathbf { v }$.

Accepted Answer

A)  $- 9 \mathbf { u } + 6 \mathbf { v } = 21 \mathbf { i } - 12 \mathbf { j }$ 
B)  $- 9 \mathbf { u } + 6 \mathbf { v } = 27 \mathbf { i } - 21 \mathbf { j }$ 
C)  $- 9 \mathbf { u } + 6 \mathbf { v } = - 9 \mathbf { i } - 3 \mathbf { j }$ 
D)  $- 9 \mathbf { u } + 6 \mathbf { v } = 12 \mathbf { i } - 3 \mathbf { j }$ 
E)  $- 9 \mathbf { u } + 6 \mathbf { v } = - 3 \mathbf { i } + 3 \mathbf { j }$ 
A)  $- 9 \mathbf { u } + 6 \mathbf { v } = 21 \mathbf { i } - 12 \mathbf { j }$ 
B)  $- 9 \mathbf { u } + 6 \mathbf { v } = 27 \mathbf { i } - 21 \mathbf { j }$ 
C)  $- 9 \mathbf { u } + 6 \mathbf { v } = - 9 \mathbf { i } - 3 \mathbf { j }$ 
D)  $- 9 \mathbf { u } + 6 \mathbf { v } = 12 \mathbf { i } - 3 \mathbf { j }$ 
E)  $- 9 \mathbf { u } + 6 \mathbf { v } = - 3 \mathbf { i } + 3 \mathbf { j }$

Question 19

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$. Write the roots in trigonometric form.

Accepted Answer

A) 
$$w _ { 1 } = \cos \left( 20 ^ { \circ } \right) + i \sin \left( 20 ^ { \circ } \right)$$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 110 ^ { \circ } \right) + i \sin \left( 110 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 200 ^ { \circ } \right) + i \sin \left( 200 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 290 ^ { \circ } \right) + i \sin \left( 290 ^ { \circ } \right)
\end{array}$$ 
B) 
$w _ { 1 } = \cos \left( 30 ^ { \circ } \right) + i \sin \left( 30 ^ { \circ } \right)$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 120 ^ { \circ } \right) + i \sin \left( 120 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 300 ^ { \circ } \right) + i \sin \left( 300 ^ { \circ } \right)
\end{array}$$ 
C) 
$$w _ { 1 } = \cos \left( 35 ^ { \circ } \right) + i \sin \left( 35 ^ { \circ } \right)$$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 125 ^ { \circ } \right) + i \sin \left( 125 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 215 ^ { \circ } \right) + i \sin \left( 215 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 305 ^ { \circ } \right) + i \sin \left( 305 ^ { \circ } \right)
\end{array}$$ 
D) 
$w _ { 1 } = \cos \left( 25 ^ { \circ } \right) + i \sin \left( 25 ^ { \circ } \right)$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 115 ^ { \circ } \right) + i \sin \left( 115 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 205 ^ { \circ } \right) + i \sin \left( 205 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 295 ^ { \circ } \right) + i \sin \left( 295 ^ { \circ } \right)
\end{array}$$ 
E) 
$$\begin{array} { l } 
w _ { 1 } = \cos \left( 40 ^ { \circ } \right) + i \sin \left( 40 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 130 ^ { \circ } \right) + i \sin \left( 130 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 220 ^ { \circ } \right) + i \sin \left( 220 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 310 ^ { \circ } \right) + i \sin \left( 310 ^ { \circ } \right)
\end{array}$$ 
A) 
$$w _ { 1 } = \cos \left( 20 ^ { \circ } \right) + i \sin \left( 20 ^ { \circ } \right)$$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 110 ^ { \circ } \right) + i \sin \left( 110 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 200 ^ { \circ } \right) + i \sin \left( 200 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 290 ^ { \circ } \right) + i \sin \left( 290 ^ { \circ } \right)
\end{array}$$ 
B) 
$w _ { 1 } = \cos \left( 30 ^ { \circ } \right) + i \sin \left( 30 ^ { \circ } \right)$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 120 ^ { \circ } \right) + i \sin \left( 120 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 300 ^ { \circ } \right) + i \sin \left( 300 ^ { \circ } \right)
\end{array}$$ 
C) 
$$w _ { 1 } = \cos \left( 35 ^ { \circ } \right) + i \sin \left( 35 ^ { \circ } \right)$$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 125 ^ { \circ } \right) + i \sin \left( 125 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 215 ^ { \circ } \right) + i \sin \left( 215 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 305 ^ { \circ } \right) + i \sin \left( 305 ^ { \circ } \right)
\end{array}$$ 
D) 
$w _ { 1 } = \cos \left( 25 ^ { \circ } \right) + i \sin \left( 25 ^ { \circ } \right)$
$$\begin{array} { l } 
w _ { 2 } = \cos \left( 115 ^ { \circ } \right) + i \sin \left( 115 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 205 ^ { \circ } \right) + i \sin \left( 205 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 295 ^ { \circ } \right) + i \sin \left( 295 ^ { \circ } \right)
\end{array}$$ 
E) 
$$\begin{array} { l } 
w _ { 1 } = \cos \left( 40 ^ { \circ } \right) + i \sin \left( 40 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 130 ^ { \circ } \right) + i \sin \left( 130 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 220 ^ { \circ } \right) + i \sin \left( 220 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 310 ^ { \circ } \right) + i \sin \left( 310 ^ { \circ } \right)
\end{array}$$

Question 20

Let $\mathbf { w }$ be a vector with initial point $( 2,1 )$ and terminal point $( 9 , - 3 )$. Write $\mathbf { w }$ as a linear combination of the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$.

Accepted Answer

A)  $\mathbf { w } = \mathbf { i } + 12 \mathbf { j }$ 
B)  $\mathbf { w } = - 5 \mathbf { i } + 8 \mathbf { j }$ 
C)  $\mathbf { w } = 7 \mathbf { i } - 4 \mathbf { j }$ 
D)  $\mathbf { w } = 11 \mathbf { i } + 4 \mathbf { j }$ 
E)  $\mathbf { w } = 3 \mathbf { i } - 12 \mathbf { j }$ 
A)  $\mathbf { w } = \mathbf { i } + 12 \mathbf { j }$ 
B)  $\mathbf { w } = - 5 \mathbf { i } + 8 \mathbf { j }$ 
C)  $\mathbf { w } = 7 \mathbf { i } - 4 \mathbf { j }$ 
D)  $\mathbf { w } = 11 \mathbf { i } + 4 \mathbf { j }$ 
E)  $\mathbf { w } = 3 \mathbf { i } - 12 \mathbf { j }$

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.] $2 u + v$

Write the complex number shown below in trigonometric form.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $B = 76 ^ { \circ } 30 ^ { \prime } , a = 8$ , and $c = 13$

In the figure below, $a = 7 , c = 20$ , and $d = 14$ . Use this information to solve the parallelogram for $b$ . The diagonals of the parallelogram are represented by $c$ and $d$ . Round answer to two decimal places.

A plane flies 710 miles from City A to City B with a bearing of $28 ^ { \circ }$ (clockwise from north). Then it flies 672 miles from City B to City C with a bearing of $45 ^ { \circ }$ . Find the straight-line distance from City C to City A. Round your answer to two decimals.

A triangular parcel of land has sides of lengths 900, 580, and 550 feet. Approximate the area of the land. Round answer to nearest foot.

Plot the following complex number. $3 i$

Let $\mathbf { u } = \langle 6,8 \rangle$ and $\mathbf { v } = \langle 14,10 \rangle$ . Find $\mathbf { u } - \mathbf { v }$

A force of 50 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 43 feet. How much work has been Accomplished? Round answer to one decimal place.

Find the trigonometric form of the complex number shown below. $- 3 - 3 i$

Determine whether $\mathbf { u }$ and $\mathbf { v }$ are orthogonal, parallel, or neither. $\mathbf { u } = \left\langle \frac { 7 } { 3 } , \frac { - 1 } { 2 } \right\rangle , \mathbf { v } = \langle 14 , - 3 \rangle$

Find the vector $\mathbf { v }$ that has a magnitude of 8 and is in the same direction as $\mathbf { u }$ , where $\mathbf { u } = \langle - 6 , - 4 \rangle$

Determine whether $\mathbf { u }$ are $\mathbf { v }$ and orthogonal, parallel, or neither. $\mathbf { u } = \langle 6,4 \rangle , \mathbf { v } = \langle - 20,30 \rangle$

Let $\mathbf { u } = \langle 10,6 \rangle$ and $\mathbf { v } = \langle 11,15 \rangle$ . Find $\mathbf { u } - \mathbf { v }$

Given $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ and $\mathbf { v } = - \mathbf { i } - 5 \mathbf { j }$ , determine $- 9 \mathbf { u } + 6 \mathbf { v }$ .

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$ . Write the roots in trigonometric form.

Let $\mathbf { w }$ be a vector with initial point $( 2,1 )$ and terminal point $( 9 , - 3 )$ . Write $\mathbf { w }$ as a linear combination of the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$ .

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 6: Additional Topics in Trigonometry

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.] 2u+v2 u + v2u+v

Write the complex number shown below in trigonometric form.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. B=76∘30′,a=8B = 76 ^ { \circ } 30 ^ { \prime } , a = 8B=76∘30′,a=8 , and c=13c = 13c=13

In the figure below, a=7,c=20a = 7 , c = 20a=7,c=20 , and d=14d = 14d=14 . Use this information to solve the parallelogram for bbb . The diagonals of the parallelogram are represented by ccc and ddd . Round answer to two decimal places.

A plane flies 710 miles from City A to City B with a bearing of 28∘28 ^ { \circ }28∘ (clockwise from north). Then it flies 672 miles from City B to City C with a bearing of 45∘45 ^ { \circ }45∘ . Find the straight-line distance from City C to City A. Round your answer to two decimals.

A triangular parcel of land has sides of lengths 900, 580, and 550 feet. Approximate the area of the land. Round answer to nearest foot.

Plot the following complex number. 3i3 i3i

Given A=52∘,B=65∘A = 52 ^ { \circ } , B = 65 ^ { \circ }A=52∘,B=65∘ , and a=7.1a = 7.1a=7.1 , use the Law of Sines to solve the triangle for the value of bbb . Round answer to two decimal places.

Let u=⟨6,8⟩\mathbf { u } = \langle 6,8 \rangleu=⟨6,8⟩ and v=⟨14,10⟩\mathbf { v } = \langle 14,10 \ranglev=⟨14,10⟩ . Find u−v\mathbf { u } - \mathbf { v }u−v

In the figure below, a=9,b=11a = 9 , b = 11a=9,b=11 , and c=12c = 12c=12 . Use this information to solve the parallelogram for θ\thetaθ . The diagonals of the parallelogram are represented by ccc and ddd . Round answer to two decimal places.

A force of 50 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 43 feet. How much work has been Accomplished? Round answer to one decimal place.

Find the trigonometric form of the complex number shown below. −3−3i- 3 - 3 i−3−3i

Determine whether u\mathbf { u }u and v\mathbf { v }v are orthogonal, parallel, or neither. u=⟨73,−12⟩,v=⟨14,−3⟩\mathbf { u } = \left\langle \frac { 7 } { 3 } , \frac { - 1 } { 2 } \right\rangle , \mathbf { v } = \langle 14 , - 3 \rangleu=⟨37​,2−1​⟩,v=⟨14,−3⟩

Find the vector v\mathbf { v }v that has a magnitude of 8 and is in the same direction as u\mathbf { u }u , where u=⟨−6,−4⟩\mathbf { u } = \langle - 6 , - 4 \rangleu=⟨−6,−4⟩

Determine whether u\mathbf { u }u are v\mathbf { v }v and orthogonal, parallel, or neither. u=⟨6,4⟩,v=⟨−20,30⟩\mathbf { u } = \langle 6,4 \rangle , \mathbf { v } = \langle - 20,30 \rangleu=⟨6,4⟩,v=⟨−20,30⟩

Let u=⟨10,6⟩\mathbf { u } = \langle 10,6 \rangleu=⟨10,6⟩ and v=⟨11,15⟩\mathbf { v } = \langle 11,15 \ranglev=⟨11,15⟩ . Find u−v\mathbf { u } - \mathbf { v }u−v

A plane flies 450 kilometers with a bearing of 319∘319 ^ { \circ }319∘ from City A to City B (see figure below). The plane then flies 730 kilometers from City B to City C, which is directly west of City A. Find the bearing of the flight from City B to City C. Round your answer to two decimals.

Given u=−3i−2j\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }u=−3i−2j and v=−i−5j\mathbf { v } = - \mathbf { i } - 5 \mathbf { j }v=−i−5j , determine −9u+6v- 9 \mathbf { u } + 6 \mathbf { v }−9u+6v .

Find the fourth roots of −12+32i- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i−21​+23​​i . Write the roots in trigonometric form.

Let w\mathbf { w }w be a vector with initial point (2,1)( 2,1 )(2,1) and terminal point (9,−3)( 9 , - 3 )(9,−3) . Write w\mathbf { w }w as a linear combination of the standard unit vectors i\mathbf { i }i and j\mathbf { j }j .

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.] $2 u + v$

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $B = 76 ^ { \circ } 30 ^ { \prime } , a = 8$ , and $c = 13$

In the figure below, $a = 7 , c = 20$ , and $d = 14$ . Use this information to solve the parallelogram for $b$ . The diagonals of the parallelogram are represented by $c$ and $d$ . Round answer to two decimal places.

A plane flies 710 miles from City A to City B with a bearing of $28 ^ { \circ }$ (clockwise from north). Then it flies 672 miles from City B to City C with a bearing of $45 ^ { \circ }$ . Find the straight-line distance from City C to City A. Round your answer to two decimals.

Plot the following complex number. $3 i$

Let $\mathbf { u } = \langle 6,8 \rangle$ and $\mathbf { v } = \langle 14,10 \rangle$ . Find $\mathbf { u } - \mathbf { v }$

Find the trigonometric form of the complex number shown below. $- 3 - 3 i$

Determine whether $\mathbf { u }$ and $\mathbf { v }$ are orthogonal, parallel, or neither. $\mathbf { u } = \left\langle \frac { 7 } { 3 } , \frac { - 1 } { 2 } \right\rangle , \mathbf { v } = \langle 14 , - 3 \rangle$

Find the vector $\mathbf { v }$ that has a magnitude of 8 and is in the same direction as $\mathbf { u }$ , where $\mathbf { u } = \langle - 6 , - 4 \rangle$

Determine whether $\mathbf { u }$ are $\mathbf { v }$ and orthogonal, parallel, or neither. $\mathbf { u } = \langle 6,4 \rangle , \mathbf { v } = \langle - 20,30 \rangle$

Let $\mathbf { u } = \langle 10,6 \rangle$ and $\mathbf { v } = \langle 11,15 \rangle$ . Find $\mathbf { u } - \mathbf { v }$

Given $\mathbf { u } = - 3 \mathbf { i } - 2 \mathbf { j }$ and $\mathbf { v } = - \mathbf { i } - 5 \mathbf { j }$ , determine $- 9 \mathbf { u } + 6 \mathbf { v }$ .

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$ . Write the roots in trigonometric form.

Let $\mathbf { w }$ be a vector with initial point $( 2,1 )$ and terminal point $( 9 , - 3 )$ . Write $\mathbf { w }$ as a linear combination of the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$ .