Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } z = 6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right) \\ w = 12 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \end{array}\] Find $\frac { z } { w }$.

A) $\frac { 1 } { 6 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ B) $\frac { 1 } { 6 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ C) $\frac { 1 } { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ D) $\frac { 1 } { 2 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ A) $\frac { 1 } { 6 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ B) $\frac { 1 } { 6 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ C) $\frac { 1 } { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ D) $\frac { 1 } { 2 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } z = 8 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right) \\ w = 3 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right) \end{array}\] Find $\frac { Z } { w }$.

A) $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ B) $\frac { 8 } { 3 } \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ C) $5 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ D) $\frac { 8 } { 3 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ A) $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ B) $\frac { 8 } { 3 } \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ C) $5 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ D) $\frac { 8 } { 3 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } \left. z = 6 \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right) \\ w = 12 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \end{array}\] Find zw.

A) $36 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$ B) $72 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$ C) $36 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ D) $72 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ A) $36 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$ B) $72 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$ C) $36 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ D) $72 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Exam 8: Polar Coordinates; Vectors

Graph the polar equation. - $r = \theta , \theta \geq 0$ $Graph the polar equation. - r = \theta , \theta \geq 0 A) B) C) D)$ A) $Graph the polar equation. - r = \theta , \theta \geq 0 A) B) C) D)$ B) $Graph the polar equation. - r = \theta , \theta \geq 0 A) B) C) D)$ C) $Graph the polar equation. - r = \theta , \theta \geq 0 A) B) C) D)$ D) $Graph the polar equation. - r = \theta , \theta \geq 0 A) B) C) D)$

(Multiple Choice)

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Question 41

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $- 15 + 20 \mathrm { i }$

(Multiple Choice)

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Question 42

Use the figure below. Determine whether the given statement is true or false. -A + B + C + D + E = 0

(Multiple Choice)

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Question 43

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( 0,0,0 ) , \mathrm { P } _ { 2 } ( 4,2,1 ) , \mathrm { P } _ { 3 } ( - 2,3,1 )$

(Multiple Choice)

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Question 44

The polar coordinates of a point are given. Find the rectangular coordinates of the point. -(4, 70°) Round the rectangular coordinates to two decimal places.

(Multiple Choice)

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Question 45

Solve the problem. -If w = 3i + 3j, find 2w.

(Multiple Choice)

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Question 46

Solve the problem. -If $\mathbf { v } = - \mathbf { i } - \mathbf { j }$ , find $\| \mathbf { v } \|$ .

(Multiple Choice)

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Question 47

Describe the set of points (x, y, z) defined by the equation. -y = 0

(Multiple Choice)

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Question 48

Find the value of the determinant. - $\left| \begin{array} { r r } - 1 & 1 \\2 & 3\end{array} \right|$

(Multiple Choice)

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Question 49

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. -P = (0, 0); Q = (6, 4)

(Multiple Choice)

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Question 50

Use the figure below. Determine whether the given statement is true or false. -C + D + G + I + J = 0

(Multiple Choice)

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Question 51

Find $\| \mathbf { v } \|$ . - $v = - 5 i - 3 j + 4 k$

(Multiple Choice)

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Question 52

Find the dot product v · w. -v = -12i - 15j, w = -5i - 8j

(Multiple Choice)

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Question 53

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 3 \sin ( 3 \theta ) ;$ the line $\theta = \frac { \pi } { 2 }$

(Multiple Choice)

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Question 54

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find $\frac { z } { w }$ .

(Multiple Choice)

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Question 55

Solve the problem. Leave your answer in polar form. - z=8 +i w=3 +i Find $\frac { Z } { w }$ .

(Multiple Choice)

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Question 56

Solve the problem. Leave your answer in polar form. - z=6+i w=12 +i Find zw.

(Multiple Choice)

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Question 57

Find the requested vector. -w = 3i - 3j - k Find a vector orthogonal to both w and j + k.

(Multiple Choice)

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Question 58

Find the dot product v · w. -v = i + j and w = i + j - k

(Multiple Choice)

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Question 59

Solve the problem. -An airplane has an air speed of 550 miles per hour bearing N30°W. The wind velocity is 50 kilometers per hour in the direction N30°E. Find the resultant vector (with exact components) representing the path of the plane relative to the ground. To the nearest tenth, what is the ground speed of the plane? What is its direction?

(Essay)

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Question 60

Showing 41 - 60 of 270

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $- 15 + 20 \mathrm { i }$

Use the figure below. Determine whether the given statement is true or false. -A + B + C + D + E = 0

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( 0,0,0 ) , \mathrm { P } _ { 2 } ( 4,2,1 ) , \mathrm { P } _ { 3 } ( - 2,3,1 )$

The polar coordinates of a point are given. Find the rectangular coordinates of the point. -(4, 70°) Round the rectangular coordinates to two decimal places.

Solve the problem. -If w = 3i + 3j, find 2w.

Solve the problem. -If $\mathbf { v } = - \mathbf { i } - \mathbf { j }$ , find $\| \mathbf { v } \|$ .

Describe the set of points (x, y, z) defined by the equation. -y = 0

Find the value of the determinant. - $\left| \begin{array} { r r } - 1 & 1 \\2 & 3\end{array} \right|$

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. -P = (0, 0); Q = (6, 4)

Use the figure below. Determine whether the given statement is true or false. -C + D + G + I + J = 0

Find $\| \mathbf { v } \|$ . - $v = - 5 i - 3 j + 4 k$

Find the dot product v · w. -v = -12i - 15j, w = -5i - 8j

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 3 \sin ( 3 \theta ) ;$ the line $\theta = \frac { \pi } { 2 }$

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find $\frac { z } { w }$ .

Solve the problem. Leave your answer in polar form. - z=8 +i w=3 +i Find $\frac { Z } { w }$ .

Solve the problem. Leave your answer in polar form. - z=6+i w=12 +i Find zw.

Find the requested vector. -w = 3i - 3j - k Find a vector orthogonal to both w and j + k.

Find the dot product v · w. -v = i + j and w = i + j - k

Functions and Their Graphs

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A Preview of Calculus: the Limit, Derivative, and Integral of a Function

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Exam 8: Polar Coordinates; Vectors

Graph the polar equation. - r=θ,θ≥0r = \theta , \theta \geq 0r=θ,θ≥0 A) B) C) D)

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - −15+20i- 15 + 20 \mathrm { i }−15+20i

Use the figure below. Determine whether the given statement is true or false. -A + B + C + D + E = 0

Find the area of the parallelogram. - P1(0,0,0),P2(4,2,1),P3(−2,3,1)\mathrm { P } _ { 1 } ( 0,0,0 ) , \mathrm { P } _ { 2 } ( 4,2,1 ) , \mathrm { P } _ { 3 } ( - 2,3,1 )P1​(0,0,0),P2​(4,2,1),P3​(−2,3,1)

The polar coordinates of a point are given. Find the rectangular coordinates of the point. -(4, 70°) Round the rectangular coordinates to two decimal places.

Solve the problem. -If w = 3i + 3j, find 2w.

Solve the problem. -If v=−i−j\mathbf { v } = - \mathbf { i } - \mathbf { j }v=−i−j , find ∥v∥\| \mathbf { v } \|∥v∥ .

Describe the set of points (x, y, z) defined by the equation. -y = 0

Find the value of the determinant. - ∣−1123∣\left| \begin{array} { r r } - 1 & 1 \\2 & 3\end{array} \right|​−12​13​​

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. -P = (0, 0); Q = (6, 4)

Use the figure below. Determine whether the given statement is true or false. -C + D + G + I + J = 0

Find ∥v∥\| \mathbf { v } \|∥v∥ . - v=−5i−3j+4kv = - 5 i - 3 j + 4 kv=−5i−3j+4k

Find the dot product v · w. -v = -12i - 15j, w = -5i - 8j

Test the equation for symmetry with respect to the given axis, line, or pole. - r=3sin⁡(3θ);r = 3 \sin ( 3 \theta ) ;r=3sin(3θ); the line θ=π2\theta = \frac { \pi } { 2 }θ=2π​

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find zw\frac { z } { w }wz​ .

Solve the problem. Leave your answer in polar form. - z=8 +i w=3 +i Find Zw\frac { Z } { w }wZ​ .

Solve the problem. Leave your answer in polar form. - z=6+i w=12 +i Find zw.

Find the requested vector. -w = 3i - 3j - k Find a vector orthogonal to both w and j + k.

Find the dot product v · w. -v = i + j and w = i + j - k

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $- 15 + 20 \mathrm { i }$

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( 0,0,0 ) , \mathrm { P } _ { 2 } ( 4,2,1 ) , \mathrm { P } _ { 3 } ( - 2,3,1 )$

Solve the problem. -If $\mathbf { v } = - \mathbf { i } - \mathbf { j }$ , find $\| \mathbf { v } \|$ .

Find the value of the determinant. - $\left| \begin{array} { r r } - 1 & 1 \\2 & 3\end{array} \right|$

Find $\| \mathbf { v } \|$ . - $v = - 5 i - 3 j + 4 k$

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 3 \sin ( 3 \theta ) ;$ the line $\theta = \frac { \pi } { 2 }$

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find $\frac { z } { w }$ .

Solve the problem. Leave your answer in polar form. - z=8 +i w=3 +i Find $\frac { Z } { w }$ .