Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } z = 10 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) \\ w = 5 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right) \end{array}\] Find zw.

A) $50 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ B) $15 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ C) $15 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$ D) $50 \left( \cos 300 ^ { \circ } + \mathrm { i } \sin 300 ^ { \circ } \right)$ A) $50 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ B) $15 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ C) $15 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$ D) $50 \left( \cos 300 ^ { \circ } + \mathrm { i } \sin 300 ^ { \circ } \right)$

Exam 8: Polar Coordinates; Vectors

Plot the point given in polar coordinates. - $\left( 2 , \frac { 9 \pi } { 4 } \right)$ $Plot the point given in polar coordinates. - \left( 2 , \frac { 9 \pi } { 4 } \right) A) B) C) D)$ A) $Plot the point given in polar coordinates. - \left( 2 , \frac { 9 \pi } { 4 } \right) A) B) C) D)$ B) $Plot the point given in polar coordinates. - \left( 2 , \frac { 9 \pi } { 4 } \right) A) B) C) D)$ C) $Plot the point given in polar coordinates. - \left( 2 , \frac { 9 \pi } { 4 } \right) A) B) C) D)$ D) $Plot the point given in polar coordinates. - \left( 2 , \frac { 9 \pi } { 4 } \right) A) B) C) D)$

(Multiple Choice)

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Question 161

Solve the problem. -If $\mathbf { v } = - 3 \mathrm { i } + 2 \mathrm { j }$ , find $\| v \|$ .

(Multiple Choice)

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Question 162

The rectangular coordinates of a point are given. Find polar coordinates for the point. -(-3, 3) A) $\left( 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$ B) $\left( - 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$ C) $\left( - 3 \sqrt { 2 } , \frac { \pi } { 4 } \right)$ D) $\left( 3 \sqrt { 2 } , \frac { 3 \pi } { 4 } \right)$

(Multiple Choice)

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Question 163

Find the direction angles of the vector. Round to the nearest degree, if necessary. - $\mathbf { v } = \mathbf { i } - \mathbf { j } + 2 \mathbf { k }$

(Multiple Choice)

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Question 164

Match the graph to one of the polar equations. - $Match the graph to one of the polar equations. - A) r = 3 + \sin \theta B) r = 6 \sin \theta C) r = 3 + \cos \theta D) r = 6 \cos \theta$ A) $r = 3 + \sin \theta$ B) $r = 6 \sin \theta$ C) $r = 3 + \cos \theta$ D) $r = 6 \cos \theta$

(Multiple Choice)

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Question 165

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $\sqrt { 3 } - \mathrm { i }$

(Multiple Choice)

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Question 166

Plot the complex number in the complex plane. - $-6+i$ A) B) C) D)

(Multiple Choice)

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Question 167

Solve the problem. -A sail on a sailboat is supported by a mast and a boom. The length and direction of the mast and boom can be described by the vectors m = i - 4j + 5k and b = -2i + 3j + k, respectively, where the components are in meters. Find the angle (to the nearest tenth of a degree) between the mast and boom.

(Essay)

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Question 168

Write the expression in the standard form a + bi. - $\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }$

(Multiple Choice)

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Question 169

Use the figure below. Determine whether the given statement is true or false. -G + H = F

(Multiple Choice)

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Question 170

Use the vectors in the figure below to graph the following vector. - $z = v$

(Multiple Choice)

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Question 171

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

(Multiple Choice)

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Question 172

Plot the point given in polar coordinates. - $\left( 2,0 ^ { \circ } \right)$ $Plot the point given in polar coordinates. - \left( 2,0 ^ { \circ } \right) A) B) C) D)$ A) $Plot the point given in polar coordinates. - \left( 2,0 ^ { \circ } \right) A) B) C) D)$ B) $Plot the point given in polar coordinates. - \left( 2,0 ^ { \circ } \right) A) B) C) D)$ C) $Plot the point given in polar coordinates. - \left( 2,0 ^ { \circ } \right) A) B) C) D)$ D) $Plot the point given in polar coordinates. - \left( 2,0 ^ { \circ } \right) A) B) C) D)$

(Multiple Choice)

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Question 173

Solve the problem. Leave your answer in polar form. - z=10 3+i3 w=5 1+i1 Find zw.

(Multiple Choice)

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Question 174

Find the position vector for the vector having initial point P and terminal point Q. -P = (0, 0, 0) and Q = (-3, 3, 4)

(Multiple Choice)

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Question 175

Graph the polar equation. - r= $Graph the polar equation. - \begin{array}{l} r = \frac { 5 } { 1 - 5 \sin \theta }\\ \end{array} A) B) C) D)$ A) $Graph the polar equation. - \begin{array}{l} r = \frac { 5 } { 1 - 5 \sin \theta }\\ \end{array} A) B) C) D)$ B) $Graph the polar equation. - \begin{array}{l} r = \frac { 5 } { 1 - 5 \sin \theta }\\ \end{array} A) B) C) D)$ C) $Graph the polar equation. - \begin{array}{l} r = \frac { 5 } { 1 - 5 \sin \theta }\\ \end{array} A) B) C) D)$ D) $Graph the polar equation. - \begin{array}{l} r = \frac { 5 } { 1 - 5 \sin \theta }\\ \end{array} A) B) C) D)$

(Multiple Choice)

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Question 176

Find the indicated cross product. -v = 4i - 5j + k, w = 2i - 2j - k Find w × v.

(Multiple Choice)

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Question 177

Find the angle between v and w. Round to one decimal place, if necessary. -v = 3i + 2j + k and w = 4i + 5j + 2k

(Multiple Choice)

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Question 178

Find the value of the determinant. - $\left| \begin{array} { r r } 12 & - 7 \\- 4 & 3\end{array} \right|$

(Multiple Choice)

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Question 179

Find the quantity if v = 5i - 7j and w = 3i + 2j. - $\| \mathbf { v } - \mathbf { w } \|$

(Multiple Choice)

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Question 180

Showing 161 - 180 of 270

Solve the problem. -If $\mathbf { v } = - 3 \mathrm { i } + 2 \mathrm { j }$ , find $\| v \|$ .

Find the direction angles of the vector. Round to the nearest degree, if necessary. - $\mathbf { v } = \mathbf { i } - \mathbf { j } + 2 \mathbf { k }$

Match the graph to one of the polar equations. - $Match the graph to one of the polar equations. - A) r = 3 + \sin \theta B) r = 6 \sin \theta C) r = 3 + \cos \theta D) r = 6 \cos \theta$ A) $r = 3 + \sin \theta$ B) $r = 6 \sin \theta$ C) $r = 3 + \cos \theta$ D) $r = 6 \cos \theta$

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $\sqrt { 3 } - \mathrm { i }$

Plot the complex number in the complex plane. - $-6+i$ A) B) C) D)

Write the expression in the standard form a + bi. - $\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }$

Use the figure below. Determine whether the given statement is true or false. -G + H = F

Use the vectors in the figure below to graph the following vector. - $z = v$

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

Solve the problem. Leave your answer in polar form. - z=10 3+i3 w=5 1+i1 Find zw.

Find the position vector for the vector having initial point P and terminal point Q. -P = (0, 0, 0) and Q = (-3, 3, 4)

Find the indicated cross product. -v = 4i - 5j + k, w = 2i - 2j - k Find w × v.

Find the angle between v and w. Round to one decimal place, if necessary. -v = 3i + 2j + k and w = 4i + 5j + 2k

Find the value of the determinant. - $\left| \begin{array} { r r } 12 & - 7 \\- 4 & 3\end{array} \right|$

Find the quantity if v = 5i - 7j and w = 3i + 2j. - $\| \mathbf { v } - \mathbf { w } \|$

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

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Exam 8: Polar Coordinates; Vectors

Plot the point given in polar coordinates. - (2,9π4)\left( 2 , \frac { 9 \pi } { 4 } \right)(2,49π​) A) B) C) D)

Solve the problem. -If v=−3i+2j\mathbf { v } = - 3 \mathrm { i } + 2 \mathrm { j }v=−3i+2j , find ∥v∥\| v \|∥v∥ .

Find the direction angles of the vector. Round to the nearest degree, if necessary. - v=i−j+2k\mathbf { v } = \mathbf { i } - \mathbf { j } + 2 \mathbf { k }v=i−j+2k

Match the graph to one of the polar equations. - A) r=3+sin⁡θr = 3 + \sin \thetar=3+sinθ B) r=6sin⁡θr = 6 \sin \thetar=6sinθ C) r=3+cos⁡θr = 3 + \cos \thetar=3+cosθ D) r=6cos⁡θr = 6 \cos \thetar=6cosθ

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - 3−i\sqrt { 3 } - \mathrm { i }3​−i

Plot the complex number in the complex plane. - −6+i-6+i−6+i A) B) C) D)

Write the expression in the standard form a + bi. - (−12−32i)10\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }(−21​−23​​i)10

Use the figure below. Determine whether the given statement is true or false. -G + H = F

Use the vectors in the figure below to graph the following vector. - z=vz = vz=v

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

Plot the point given in polar coordinates. - (2,0∘)\left( 2,0 ^ { \circ } \right)(2,0∘) A) B) C) D)

Solve the problem. Leave your answer in polar form. - z=10 3+i3 w=5 1+i1 Find zw.

Find the position vector for the vector having initial point P and terminal point Q. -P = (0, 0, 0) and Q = (-3, 3, 4)

Graph the polar equation. - r= A) B) C) D)

Find the indicated cross product. -v = 4i - 5j + k, w = 2i - 2j - k Find w × v.

Find the angle between v and w. Round to one decimal place, if necessary. -v = 3i + 2j + k and w = 4i + 5j + 2k

Find the value of the determinant. - ∣12−7−43∣\left| \begin{array} { r r } 12 & - 7 \\- 4 & 3\end{array} \right|​12−4​−73​​

Find the quantity if v = 5i - 7j and w = 3i + 2j. - ∥v−w∥\| \mathbf { v } - \mathbf { w } \|∥v−w∥

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

Solve the problem. -If $\mathbf { v } = - 3 \mathrm { i } + 2 \mathrm { j }$ , find $\| v \|$ .

Find the direction angles of the vector. Round to the nearest degree, if necessary. - $\mathbf { v } = \mathbf { i } - \mathbf { j } + 2 \mathbf { k }$

Match the graph to one of the polar equations. - $Match the graph to one of the polar equations. - A) r = 3 + \sin \theta B) r = 6 \sin \theta C) r = 3 + \cos \theta D) r = 6 \cos \theta$ A) $r = 3 + \sin \theta$ B) $r = 6 \sin \theta$ C) $r = 3 + \cos \theta$ D) $r = 6 \cos \theta$

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $\sqrt { 3 } - \mathrm { i }$

Plot the complex number in the complex plane. - $-6+i$ A) B) C) D)

Write the expression in the standard form a + bi. - $\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }$

Use the vectors in the figure below to graph the following vector. - $z = v$

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

Find the value of the determinant. - $\left| \begin{array} { r r } 12 & - 7 \\- 4 & 3\end{array} \right|$

Find the quantity if v = 5i - 7j and w = 3i + 2j. - $\| \mathbf { v } - \mathbf { w } \|$