Question 1

Find the standard form of the complex number shown below. $3 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$

Accepted Answer

A)  $- \frac { 3 \sqrt { 3 } } { 4 } - \frac { 3 } { 4 } i$ 
B)   $- \frac { 2 } { 3 } - \frac { 2 \sqrt { 3 } } { 3 } i$ 
C)   $- \frac { 4 \sqrt { 3 } } { 3 } - \frac { 4 } { 3 } i$ 
D)   $- \frac { 3 \sqrt { 3 } } { 2 } - \frac { 3 } { 2 } i$ 
E)   $- \frac { 3 } { 2 } - \frac { 3 \sqrt { 3 } } { 2 } i$ 
A)  $- \frac { 3 \sqrt { 3 } } { 4 } - \frac { 3 } { 4 } i$ 
B)   $- \frac { 2 } { 3 } - \frac { 2 \sqrt { 3 } } { 3 } i$ 
C)   $- \frac { 4 \sqrt { 3 } } { 3 } - \frac { 4 } { 3 } i$ 
D)   $- \frac { 3 \sqrt { 3 } } { 2 } - \frac { 3 } { 2 } i$ 
E)   $- \frac { 3 } { 2 } - \frac { 3 \sqrt { 3 } } { 2 } i$

Question 2

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form.

Accepted Answer

A)   $\mathbf { v } = \langle - 4 , - 9 \rangle$ 
B)   $\mathbf { v } = \langle - 4,9 \rangle$ 
C)  $\mathbf { v } = \langle 4,9 \rangle$ 
D)  $\mathbf { v } = \langle 4 , - 9 \rangle$ 
E)   $\mathbf { v } = \langle 9,4 \rangle$ 
A)   $\mathbf { v } = \langle - 4 , - 9 \rangle$ 
B)   $\mathbf { v } = \langle - 4,9 \rangle$ 
C)  $\mathbf { v } = \langle 4,9 \rangle$ 
D)  $\mathbf { v } = \langle 4 , - 9 \rangle$ 
E)   $\mathbf { v } = \langle 9,4 \rangle$

Question 3

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 50°, b = 4, c = 15
​

Accepted Answer

A) a ≈ 15, B ≈ 13.85°, C ≈ 116.15° 
B) a ≈ 12.80, B ≈ 116.15°, C ≈ 13.85° 
C) a ≈ 4, B ≈ 13.85°, C ≈ 116.15° 
D) a ≈ 15, B ≈ 15.85°, C ≈ 114.15° 
E) a ≈ 12.80, B ≈ 13.85°, C ≈ 116.15° 
A) a ≈ 15, B ≈ 13.85°, C ≈ 116.15° 
B) a ≈ 12.80, B ≈ 116.15°, C ≈ 13.85° 
C) a ≈ 4, B ≈ 13.85°, C ≈ 116.15° 
D) a ≈ 15, B ≈ 15.85°, C ≈ 114.15° 
E) a ≈ 12.80, B ≈ 13.85°, C ≈ 116.15°

Question 4

Find 2u - 3v. 
 $\mathbf { u } = 6 \mathbf { i } , \mathbf { v } = \mathbf { j }$

Accepted Answer

A)  $12 \mathbf { i } - 3 \mathbf { j }$ 
B)   $- 12 \mathbf { i } - 3 \mathbf { j }$ 
C)   $6 \mathbf { i } - 3 \mathbf { j }$ 
D)   $12 \mathbf { i } + 3 \mathbf { j }$ 
E)   $6 i - j$ 
A)  $12 \mathbf { i } - 3 \mathbf { j }$ 
B)   $- 12 \mathbf { i } - 3 \mathbf { j }$ 
C)   $6 \mathbf { i } - 3 \mathbf { j }$ 
D)   $12 \mathbf { i } + 3 \mathbf { j }$ 
E)   $6 i - j$

Question 5

Find the angle between the vectors u and v.   $\mathbf { u } = \cos \left( \frac { \pi } { 3 } \right) \mathbf { i } + \sin \left( \frac { \pi } { 3 } \right) \mathbf { j }$ , $\mathbf { v } = \cos \left( \frac { 5 \pi } { 4 } \right) \mathbf { i } + \sin \left( \frac { 5 \pi } { 4 } \right) \mathbf { j }$

Accepted Answer

A)  $40 ^ { \circ }$ 
B)  $75 ^ { \circ }$ 
C)  $105 ^ { \circ }$ 
D)  $165 ^ { \circ }$ 
E)  $175 ^ { \circ }$ 
A)  $40 ^ { \circ }$ 
B)  $75 ^ { \circ }$ 
C)  $105 ^ { \circ }$ 
D)  $165 ^ { \circ }$ 
E)  $175 ^ { \circ }$

Question 6

Perform the operation shown below and leave the result in trigonometric form.  
  $\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }$

Accepted Answer

A)  $6 ( \cos 0.4 + i \sin 0.4 )$ 
B)   $6 ( \cos 1.1 + i \sin 1.1 )$ 
C)   $2 ( \cos 0.4 + i \sin 0.4 )$ 
D)   $2 ( \cos 8.37 + i \sin 8.37 )$ 
E)   $2 ( \cos 5.8 + i \sin 5.8 )$ 
A)  $6 ( \cos 0.4 + i \sin 0.4 )$ 
B)   $6 ( \cos 1.1 + i \sin 1.1 )$ 
C)   $2 ( \cos 0.4 + i \sin 0.4 )$ 
D)   $2 ( \cos 8.37 + i \sin 8.37 )$ 
E)   $2 ( \cos 5.8 + i \sin 5.8 )$

Question 7

Find the trigonometric form of the complex number shown below. $- 10 i$

Accepted Answer

A)  $10 ( \cos 0 + i \sin 0 )$ 
B)  $10 ( \cos \pi + i \sin \pi )$ 
C)  $10 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D)  $10 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $10 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
A)  $10 ( \cos 0 + i \sin 0 )$ 
B)  $10 ( \cos \pi + i \sin \pi )$ 
C)  $10 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D)  $10 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $10 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

Question 8

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.   $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Accepted Answer

A) 4.3301 + 2.5i 
B) 2.5 + 4.3301i 
C) 2.5 - 4.3301i 
D) 4.3301 - 2.5i 
E) None of the above 
A) 4.3301 + 2.5i 
B) 2.5 + 4.3301i 
C) 2.5 - 4.3301i 
D) 4.3301 - 2.5i 
E) None of the above

Question 9

Perform the indicated operation using trigonometric form.Leave the answer in trigonometric forms. $( 2 + 2 i ) ( - 1 - i )$

Accepted Answer

A)  $- 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
B)   $4 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$ 
C)   $4 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D)   $- 2 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$ 
E)   $2 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
A)  $- 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
B)   $4 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$ 
C)   $4 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D)   $- 2 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$ 
E)   $2 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

Question 10

Plot the complex number and find its absolute value.  -2

Accepted Answer

A)       $| - 2 | = - 3$ 
B)       $| - 2 | = 2$ 
C)        $| - 2 | = - 4$ 
D)       $| - 2 | = 4$ 
E)       $| - 2 | = 3$ 
A)       $| - 2 | = - 3$ 
B)       $| - 2 | = 2$ 
C)        $| - 2 | = - 4$ 
D)       $| - 2 | = 4$ 
E)       $| - 2 | = 3$

Question 11

Given $\mathbf { u } = - \mathbf { i } + 3 \mathbf { j }$ and $\mathbf { v } = 5 \mathbf { i } + 4 \mathbf { j }$ , find $\text { u v }$

Accepted Answer

A) 7 
B) -5 
C) -17 
D) 11 
E) -19 
A) 7 
B) -5 
C) -17 
D) 11 
E) -19

Question 12

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. $\begin{array}{lr}\text { Magnitude}&\text { Angle }\\|\mathbf{v}\|=4&0^o
\end{array}$

Accepted Answer

A)  $\langle 0,0 \rangle$ 
B)   $\langle 4,4 \rangle$ 
C)   $\langle 0,4 \rangle$ 
D)   $\langle 4,0 \rangle$ 
E)   $\langle - 4,0 \rangle$ 
A)  $\langle 0,0 \rangle$ 
B)   $\langle 4,4 \rangle$ 
C)   $\langle 0,4 \rangle$ 
D)   $\langle 4,0 \rangle$ 
E)   $\langle - 4,0 \rangle$

Question 13

Find values for b such that the triangle has no solutions.  
A = 64°, a = 340.2

Accepted Answer

A)  $b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
B)  $b = \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
C)  $b \geq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
D)  $b  \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
A)  $b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
B)  $b = \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
C)  $b \geq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
D)  $b  \frac { 340.2 } { \sin 64 ^ { \circ } }$

Question 14

Use the dot product to find the magnitude of u.   $\mathbf { u } = 24 \mathbf { i } - 28 \mathbf { j }$

Accepted Answer

A)  $4 \sqrt { 85 }$ 
B)  $\sqrt { 1358 }$ 
C)  $2 \sqrt { 339 }$ 
D)  $\sqrt { 1362 }$ 
E)  $2 \sqrt { 341 }$ 
A)  $4 \sqrt { 85 }$ 
B)  $\sqrt { 1358 }$ 
C)  $2 \sqrt { 339 }$ 
D)  $\sqrt { 1362 }$ 
E)  $2 \sqrt { 341 }$

Question 15

Plot the following complex number. -3

Accepted Answer

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

Question 16

Given $\mathbf { u } = \langle 3 , - 2 \rangle$ and $\mathbf { v } = \langle - 3,2 \rangle$ , determine $- 4 \mathbf { u } - \mathbf { v }$ .

Accepted Answer

A)   $- 4 \mathbf { u } - \mathbf { v } = \langle 9 , - 14 \rangle$ 
B)  $- 4 \mathbf { u } - \mathbf { v } = \langle - 9,6 \rangle$ 
C)   $- 4 \mathbf { u } - \mathbf { v } = \langle - 14 , - 14 \rangle$ 
D)   $- 4 \mathbf { u } - \mathbf { v } = \langle 11 , - 14 \rangle$ 
E)   $- 4 \mathbf { u } - \mathbf { v } = \langle - 11,10 \rangle$ 
A)   $- 4 \mathbf { u } - \mathbf { v } = \langle 9 , - 14 \rangle$ 
B)  $- 4 \mathbf { u } - \mathbf { v } = \langle - 9,6 \rangle$ 
C)   $- 4 \mathbf { u } - \mathbf { v } = \langle - 14 , - 14 \rangle$ 
D)   $- 4 \mathbf { u } - \mathbf { v } = \langle 11 , - 14 \rangle$ 
E)   $- 4 \mathbf { u } - \mathbf { v } = \langle - 11,10 \rangle$

Question 17

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 75.4, b = 52, c = 52
​
​

Accepted Answer

A) A ≈ 43.53°, B ≈ 92.94°, C ≈ 43.53° 
B) A ≈ 43.53°, B ≈ 97.94°, C ≈ 38.53° 
C) A ≈ 43.53°, B ≈ 38.53°, C ≈ 97.94° 
D) A ≈ 92.94°, B ≈ 43.53°, C ≈ 43.53° 
E) A ≈ 97.94°, B ≈ 38.53°, C ≈ 43.53° 
A) A ≈ 43.53°, B ≈ 92.94°, C ≈ 43.53° 
B) A ≈ 43.53°, B ≈ 97.94°, C ≈ 38.53° 
C) A ≈ 43.53°, B ≈ 38.53°, C ≈ 97.94° 
D) A ≈ 92.94°, B ≈ 43.53°, C ≈ 43.53° 
E) A ≈ 97.94°, B ≈ 38.53°, C ≈ 43.53°

Question 18

Find the projection of u onto v if $\mathbf { u } = \langle 5 , - 3 \rangle$ , $\mathbf { v } = \langle - 1,4 \rangle$ .

Accepted Answer

A)   $\left\langle \frac { - 17 \sqrt { 17 } } { 17 } , \frac { 51 \sqrt { 17 } } { 17 } \right\rangle$ 
B)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { 68 \sqrt { 17 } } { 17 } \right\rangle$ 
C)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { 17 \sqrt { 17 } } { 17 } \right\rangle$ 
D)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { - 68 \sqrt { 17 } } { 17 } \right\rangle$ 
E)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { 51 \sqrt { 17 } } { 17 } \right\rangle$ 
A)   $\left\langle \frac { - 17 \sqrt { 17 } } { 17 } , \frac { 51 \sqrt { 17 } } { 17 } \right\rangle$ 
B)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { 68 \sqrt { 17 } } { 17 } \right\rangle$ 
C)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { 17 \sqrt { 17 } } { 17 } \right\rangle$ 
D)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { - 68 \sqrt { 17 } } { 17 } \right\rangle$ 
E)   $\left\langle \frac { 17 \sqrt { 17 } } { 17 } , \frac { 51 \sqrt { 17 } } { 17 } \right\rangle$

Question 19

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet)
​

Accepted Answer

A) $63,450.91 
B) $63,300.91 
C) $63,400.91 
D) $63,200.91 
E) $63,320.91 
A) $63,450.91 
B) $63,300.91 
C) $63,400.91 
D) $63,200.91 
E) $63,320.91

Question 20

Plot the complex number and find its absolute value. 
-5 + 10i

Accepted Answer

A)      -5 + 10i| = $\sqrt { 95 }$ 
B)      |-5 + 10i| = $2 \sqrt { 7 }$ 
C)     |-5 + 10i| = $5 \sqrt { 5 }$ 
D)     |-5 + 10i| = $\sqrt { 22 }$ 
E)      |-5 + 10i| = $\sqrt { 105 }$ 
A)      -5 + 10i| = $\sqrt { 95 }$ 
B)      |-5 + 10i| = $2 \sqrt { 7 }$ 
C)     |-5 + 10i| = $5 \sqrt { 5 }$ 
D)     |-5 + 10i| = $\sqrt { 22 }$ 
E)      |-5 + 10i| = $\sqrt { 105 }$

Find the standard form of the complex number shown below. $3 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 50°, b = 4, c = 15

Find 2u - 3v. $\mathbf { u } = 6 \mathbf { i } , \mathbf { v } = \mathbf { j }$

Perform the operation shown below and leave the result in trigonometric form. $\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }$

Find the trigonometric form of the complex number shown below. $- 10 i$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Perform the indicated operation using trigonometric form.Leave the answer in trigonometric forms. $( 2 + 2 i ) ( - 1 - i )$

Plot the complex number and find its absolute value. -2

Given $\mathbf { u } = - \mathbf { i } + 3 \mathbf { j }$ and $\mathbf { v } = 5 \mathbf { i } + 4 \mathbf { j }$ , find $\text { u v }$

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle \|\|=4

Find values for b such that the triangle has no solutions. A = 64°, a = 340.2

Use the dot product to find the magnitude of u. $\mathbf { u } = 24 \mathbf { i } - 28 \mathbf { j }$

Plot the following complex number. -3

Given $\mathbf { u } = \langle 3 , - 2 \rangle$ and $\mathbf { v } = \langle - 3,2 \rangle$ , determine $- 4 \mathbf { u } - \mathbf { v }$ .

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 75.4, b = 52, c = 52

Find the projection of u onto v if $\mathbf { u } = \langle 5 , - 3 \rangle$ , $\mathbf { v } = \langle - 1,4 \rangle$ .

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet)

Plot the complex number and find its absolute value. -5 + 10i

Functions and Their Graphs

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Exponential and Logarithmic Functions

Trigonometry

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Systems Of Equations and Inequalities

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Exam 6: Additional Topics In Trigonometery

Find the standard form of the complex number shown below. 3(cos⁡7π6+isin⁡7π6)3 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)3(cos67π​+isin67π​)

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 50°, b = 4, c = 15 ​

Find 2u - 3v. u=6i,v=j\mathbf { u } = 6 \mathbf { i } , \mathbf { v } = \mathbf { j }u=6i,v=j

Perform the operation shown below and leave the result in trigonometric form. 12(cos⁡3.1+isin⁡3.1)6(cos⁡2.7+isin⁡2.7)\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }6(cos2.7+isin2.7)12(cos3.1+isin3.1)​

Find the trigonometric form of the complex number shown below. −10i- 10 i−10i

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. 5(cos⁡π3+isin⁡π3)5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)5(cos3π​+isin3π​)

Perform the indicated operation using trigonometric form.Leave the answer in trigonometric forms. (2+2i)(−1−i)( 2 + 2 i ) ( - 1 - i )(2+2i)(−1−i)

Plot the complex number and find its absolute value. -2

Given u=−i+3j\mathbf { u } = - \mathbf { i } + 3 \mathbf { j }u=−i+3j and v=5i+4j\mathbf { v } = 5 \mathbf { i } + 4 \mathbf { j }v=5i+4j , find u v \text { u v } u v

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle \|\|=4

Find values for b such that the triangle has no solutions. A = 64°, a = 340.2

Use the dot product to find the magnitude of u. u=24i−28j\mathbf { u } = 24 \mathbf { i } - 28 \mathbf { j }u=24i−28j

Plot the following complex number. -3

Given u=⟨3,−2⟩\mathbf { u } = \langle 3 , - 2 \rangleu=⟨3,−2⟩ and v=⟨−3,2⟩\mathbf { v } = \langle - 3,2 \ranglev=⟨−3,2⟩ , determine −4u−v- 4 \mathbf { u } - \mathbf { v }−4u−v .

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 75.4, b = 52, c = 52 ​ ​

Find the projection of u onto v if u=⟨5,−3⟩\mathbf { u } = \langle 5 , - 3 \rangleu=⟨5,−3⟩ , v=⟨−1,4⟩\mathbf { v } = \langle - 1,4 \ranglev=⟨−1,4⟩ .

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet) ​

Plot the complex number and find its absolute value. -5 + 10i

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Find the standard form of the complex number shown below. $3 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 50°, b = 4, c = 15

Find 2u - 3v. $\mathbf { u } = 6 \mathbf { i } , \mathbf { v } = \mathbf { j }$

Perform the operation shown below and leave the result in trigonometric form. $\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }$

Find the trigonometric form of the complex number shown below. $- 10 i$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Perform the indicated operation using trigonometric form.Leave the answer in trigonometric forms. $( 2 + 2 i ) ( - 1 - i )$

Given $\mathbf { u } = - \mathbf { i } + 3 \mathbf { j }$ and $\mathbf { v } = 5 \mathbf { i } + 4 \mathbf { j }$ , find $\text { u v }$

Use the dot product to find the magnitude of u. $\mathbf { u } = 24 \mathbf { i } - 28 \mathbf { j }$

Given $\mathbf { u } = \langle 3 , - 2 \rangle$ and $\mathbf { v } = \langle - 3,2 \rangle$ , determine $- 4 \mathbf { u } - \mathbf { v }$ .

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. A = 75.4, b = 52, c = 52

Find the projection of u onto v if $\mathbf { u } = \langle 5 , - 3 \rangle$ , $\mathbf { v } = \langle - 1,4 \rangle$ .

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet)