Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } \mathrm { z } = \sqrt { 3 } \left( \cos \frac { 7 \pi } { 4 } + \mathrm { i } \sin \frac { 7 \pi } { 4 } \right) \\ \mathrm { W } = \sqrt { 6 } \left( \cos \frac { 9 \pi } { 4 } + \mathrm { i } \sin \frac { 9 \pi } { 4 } \right) \end{array}\] Find $\frac { z } { w }$.

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

Exam 8: Polar Coordinates; Vectors

Solve the problem. -A truck pushes a load of 45 tons up a hill with an inclination of 35°. Express the force vector F in terms of i and j. Round the components of F to two decimal places.

(Short Answer)

4.8/5

(34)

Question 21

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

(Multiple Choice)

4.9/5

(31)

Question 22

Use the vectors in the figure below to graph the following vector. - $2 u - z - w$

(Multiple Choice)

4.7/5

(38)

Question 23

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

(Multiple Choice)

4.8/5

(34)

Question 24

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

(Multiple Choice)

4.9/5

(34)

Question 25

Identify and graph the polar equation. - $r^{2}=4 \cos (2 \theta)$ $Identify and graph the polar equation. - r^{2}=4 \cos (2 \theta) A) rose with four petals B) lemniscate C) lemniscate D) rose with four petals$ A) $Identify and graph the polar equation. - r^{2}=4 \cos (2 \theta) A) rose with four petals B) lemniscate C) lemniscate D) rose with four petals$ rose with four petals B) $Identify and graph the polar equation. - r^{2}=4 \cos (2 \theta) A) rose with four petals B) lemniscate C) lemniscate D) rose with four petals$ lemniscate C) $Identify and graph the polar equation. - r^{2}=4 \cos (2 \theta) A) rose with four petals B) lemniscate C) lemniscate D) rose with four petals$ lemniscate D) $Identify and graph the polar equation. - r^{2}=4 \cos (2 \theta) A) rose with four petals B) lemniscate C) lemniscate D) rose with four petals$ rose with four petals

(Multiple Choice)

4.8/5

(33)

Question 26

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - $x ^ { 2 } = 4 y$

(Multiple Choice)

4.8/5

(38)

Question 27

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( 5 , - \frac { 4 \pi } { 3 } \right)$

(Multiple Choice)

4.7/5

(27)

Question 28

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( - 5 , - 360 ^ { \circ } \right)$

(Multiple Choice)

4.8/5

(25)

Question 29

Find the indicated cross product. -v = i + 2j + 2k, w = 6i + 5j - k Find v × w.

(Multiple Choice)

4.8/5

(34)

Question 30

Graph the polar equation. - $\mathbf { r } = \frac { 3 } { \theta }$ $Graph the polar equation. - \mathbf { r } = \frac { 3 } { \theta } A) B) C) D)$ A) $Graph the polar equation. - \mathbf { r } = \frac { 3 } { \theta } A) B) C) D)$ B) $Graph the polar equation. - \mathbf { r } = \frac { 3 } { \theta } A) B) C) D)$ C) $Graph the polar equation. - \mathbf { r } = \frac { 3 } { \theta } A) B) C) D)$ D) $Graph the polar equation. - \mathbf { r } = \frac { 3 } { \theta } A) B) C) D)$

(Multiple Choice)

4.9/5

(36)

Question 31

Plot the point given in polar coordinates. - $\left( 2,45 ^ { \circ } \right)$ $Plot the point given in polar coordinates. - \left( 2,45 ^ { \circ } \right) A) B) C) D)$ A) $Plot the point given in polar coordinates. - \left( 2,45 ^ { \circ } \right) A) B) C) D)$ B) $Plot the point given in polar coordinates. - \left( 2,45 ^ { \circ } \right) A) B) C) D)$ C) $Plot the point given in polar coordinates. - \left( 2,45 ^ { \circ } \right) A) B) C) D)$ D) $Plot the point given in polar coordinates. - \left( 2,45 ^ { \circ } \right) A) B) C) D)$

(Multiple Choice)

4.9/5

(35)

Question 32

State whether the vectors are parallel, orthogonal, or neither. - $\mathbf { v } = \mathbf { i } + 5 \mathbf { j } , \quad \mathbf { w } = - 2 \mathbf { i } + \mathbf { j }$

(Multiple Choice)

4.7/5

(25)

Question 33

Solve the problem. -Find a unit vector normal to the plane containing u = -i + 3j - 5k and v = 2i - j + 6k.

(Essay)

4.8/5

(39)

Question 34

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - $r \sin \theta = 4$ $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r \sin \theta = 4 A) x = - 4 ; vertical line 4 units to the left of the pole B) x = 4 ; vertical line 4 units to the right of the pole C) y = - 4 ; horizontal line 4 units below the pole D) y = 4 ; horizontal line 4 units above the pole$ A) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r \sin \theta = 4 A) x = - 4 ; vertical line 4 units to the left of the pole B) x = 4 ; vertical line 4 units to the right of the pole C) y = - 4 ; horizontal line 4 units below the pole D) y = 4 ; horizontal line 4 units above the pole$ $x = - 4$ ; vertical line 4 units to the left of the pole B) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r \sin \theta = 4 A) x = - 4 ; vertical line 4 units to the left of the pole B) x = 4 ; vertical line 4 units to the right of the pole C) y = - 4 ; horizontal line 4 units below the pole D) y = 4 ; horizontal line 4 units above the pole$ $x = 4$ ; vertical line 4 units to the right of the pole C) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r \sin \theta = 4 A) x = - 4 ; vertical line 4 units to the left of the pole B) x = 4 ; vertical line 4 units to the right of the pole C) y = - 4 ; horizontal line 4 units below the pole D) y = 4 ; horizontal line 4 units above the pole$ $y = - 4$ ; horizontal line 4 units below the pole D) $Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - r \sin \theta = 4 A) x = - 4 ; vertical line 4 units to the left of the pole B) x = 4 ; vertical line 4 units to the right of the pole C) y = - 4 ; horizontal line 4 units below the pole D) y = 4 ; horizontal line 4 units above the pole$ $y = 4$ ; horizontal line 4 units above the pole

(Multiple Choice)

4.9/5

(34)

Question 35

Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with the positive x-axis. - $\| v \| = 7 , \alpha = 60 ^ { \circ }$

(Multiple Choice)

4.9/5

(36)

Question 36

Find the distance from $\mathrm { P } _ { 1 } \text { to } \mathrm { P } _ { 2 }$ - $\mathrm { P } _ { 1 } = ( - 3,1,1 )$ and $\mathrm { P } _ { 2 } = ( 1,0 , - 3 )$

(Multiple Choice)

4.7/5

(32)

Question 37

The rectangular coordinates of a point are given. Find polar coordinates for the point. -(0, 9) A) $( 9,0 )$ B) $\left( 9 , - \frac { \pi } { 2 } \right)$ C) $( 9 , \pi )$ D) $\left( 9 , \frac { \pi } { 2 } \right)$

(Multiple Choice)

4.9/5

(34)

Question 38

Find the requested vector. -v = 4i + 4j + k Find a vector orthogonal to both v and i + k.

(Multiple Choice)

4.9/5

(32)

Question 39

Solve the problem. -If $\mathbf { v } = 5 \mathbf { i } + \mathbf { j }$ and $\mathbf { w } = 9 \mathbf { i } + \mathbf { j }$ , find $\| \mathbf { v } + \mathbf { w } \|$ .

(Multiple Choice)

4.7/5

(32)

Question 40

Showing 21 - 40 of 270

Solve the problem. -A truck pushes a load of 45 tons up a hill with an inclination of 35°. Express the force vector F in terms of i and j. Round the components of F to two decimal places.

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

Use the vectors in the figure below to graph the following vector. - $2 u - z - w$

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

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

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - $x ^ { 2 } = 4 y$

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( 5 , - \frac { 4 \pi } { 3 } \right)$

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( - 5 , - 360 ^ { \circ } \right)$

Find the indicated cross product. -v = i + 2j + 2k, w = 6i + 5j - k Find v × w.

State whether the vectors are parallel, orthogonal, or neither. - $\mathbf { v } = \mathbf { i } + 5 \mathbf { j } , \quad \mathbf { w } = - 2 \mathbf { i } + \mathbf { j }$

Solve the problem. -Find a unit vector normal to the plane containing u = -i + 3j - 5k and v = 2i - j + 6k.

Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with the positive x-axis. - $\| v \| = 7 , \alpha = 60 ^ { \circ }$

Find the distance from $\mathrm { P } _ { 1 } \text { to } \mathrm { P } _ { 2 }$ - $\mathrm { P } _ { 1 } = ( - 3,1,1 )$ and $\mathrm { P } _ { 2 } = ( 1,0 , - 3 )$

The rectangular coordinates of a point are given. Find polar coordinates for the point. -(0, 9) A) $( 9,0 )$ B) $\left( 9 , - \frac { \pi } { 2 } \right)$ C) $( 9 , \pi )$ D) $\left( 9 , \frac { \pi } { 2 } \right)$

Find the requested vector. -v = 4i + 4j + k Find a vector orthogonal to both v and i + k.

Solve the problem. -If $\mathbf { v } = 5 \mathbf { i } + \mathbf { j }$ and $\mathbf { w } = 9 \mathbf { i } + \mathbf { j }$ , find $\| \mathbf { v } + \mathbf { w } \|$ .

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

Review

Filters

Exam 8: Polar Coordinates; Vectors

Solve the problem. -A truck pushes a load of 45 tons up a hill with an inclination of 35°. Express the force vector F in terms of i and j. Round the components of F to two decimal places.

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

Use the vectors in the figure below to graph the following vector. - 2u−z−w2 u - z - w2u−z−w

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

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

Identify and graph the polar equation. - r2=4cos⁡(2θ)r^{2}=4 \cos (2 \theta)r2=4cos(2θ) A) rose with four petals B) lemniscate C) lemniscate D) rose with four petals

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - x2=4yx ^ { 2 } = 4 yx2=4y

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - (5,−4π3)\left( 5 , - \frac { 4 \pi } { 3 } \right)(5,−34π​)

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - (−5,−360∘)\left( - 5 , - 360 ^ { \circ } \right)(−5,−360∘)

Find the indicated cross product. -v = i + 2j + 2k, w = 6i + 5j - k Find v × w.

Graph the polar equation. - r=3θ\mathbf { r } = \frac { 3 } { \theta }r=θ3​ A) B) C) D)

Plot the point given in polar coordinates. - (2,45∘)\left( 2,45 ^ { \circ } \right)(2,45∘) A) B) C) D)

State whether the vectors are parallel, orthogonal, or neither. - v=i+5j,w=−2i+j\mathbf { v } = \mathbf { i } + 5 \mathbf { j } , \quad \mathbf { w } = - 2 \mathbf { i } + \mathbf { j }v=i+5j,w=−2i+j

Solve the problem. -Find a unit vector normal to the plane containing u = -i + 3j - 5k and v = 2i - j + 6k.

Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with the positive x-axis. - ∥v∥=7,α=60∘\| v \| = 7 , \alpha = 60 ^ { \circ }∥v∥=7,α=60∘

Find the distance from P1 to P2\mathrm { P } _ { 1 } \text { to } \mathrm { P } _ { 2 }P1​ to P2​ - P1=(−3,1,1)\mathrm { P } _ { 1 } = ( - 3,1,1 )P1​=(−3,1,1) and P2=(1,0,−3)\mathrm { P } _ { 2 } = ( 1,0 , - 3 )P2​=(1,0,−3)

The rectangular coordinates of a point are given. Find polar coordinates for the point. -(0, 9) A) (9,0)( 9,0 )(9,0) B) (9,−π2)\left( 9 , - \frac { \pi } { 2 } \right)(9,−2π​) C) (9,π)( 9 , \pi )(9,π) D) (9,π2)\left( 9 , \frac { \pi } { 2 } \right)(9,2π​)

Find the requested vector. -v = 4i + 4j + k Find a vector orthogonal to both v and i + k.

Solve the problem. -If v=5i+j\mathbf { v } = 5 \mathbf { i } + \mathbf { j }v=5i+j and w=9i+j\mathbf { w } = 9 \mathbf { i } + \mathbf { j }w=9i+j , find ∥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

Use the vectors in the figure below to graph the following vector. - $2 u - z - w$

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

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

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - $x ^ { 2 } = 4 y$

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( 5 , - \frac { 4 \pi } { 3 } \right)$

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( - 5 , - 360 ^ { \circ } \right)$

State whether the vectors are parallel, orthogonal, or neither. - $\mathbf { v } = \mathbf { i } + 5 \mathbf { j } , \quad \mathbf { w } = - 2 \mathbf { i } + \mathbf { j }$

Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with the positive x-axis. - $\| v \| = 7 , \alpha = 60 ^ { \circ }$

Find the distance from $\mathrm { P } _ { 1 } \text { to } \mathrm { P } _ { 2 }$ - $\mathrm { P } _ { 1 } = ( - 3,1,1 )$ and $\mathrm { P } _ { 2 } = ( 1,0 , - 3 )$

The rectangular coordinates of a point are given. Find polar coordinates for the point. -(0, 9) A) $( 9,0 )$ B) $\left( 9 , - \frac { \pi } { 2 } \right)$ C) $( 9 , \pi )$ D) $\left( 9 , \frac { \pi } { 2 } \right)$

Solve the problem. -If $\mathbf { v } = 5 \mathbf { i } + \mathbf { j }$ and $\mathbf { w } = 9 \mathbf { i } + \mathbf { j }$ , find $\| \mathbf { v } + \mathbf { w } \|$ .