Exam 8: Polar Coordinates; Vectors

Graph the polar equation. - $r = \frac { 4 } { 4 - 2 \sin \theta }$ $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \sin \theta } A) B) C) D)$ A) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \sin \theta } A) B) C) D)$ B) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \sin \theta } A) B) C) D)$ C) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \sin \theta } A) B) C) D)$ D) $Graph the polar equation. - r = \frac { 4 } { 4 - 2 \sin \theta } A) B) C) D)$

(Multiple Choice)

4.9/5

(37)

Question 61

State whether the vectors are parallel, orthogonal, or neither. -v = 4i + 2j, w = 2i - 4j

(Multiple Choice)

4.7/5

(31)

Question 62

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - $x y = 1$

(Multiple Choice)

4.9/5

(35)

Question 63

Find the position vector for the vector having initial point P and terminal point Q. -P = (-1, -1, 0) and Q = (-3, 3, -4)

(Multiple Choice)

4.9/5

(38)

Question 64

Identify and graph the polar equation. - $r=5-4 \cos \theta$ $Identify and graph the polar equation. - r=5-4 \cos \theta A) limacon without inner loop B) limacon without inner loop C) limacon with inner loop D) limacon with inner loop$ A) $Identify and graph the polar equation. - r=5-4 \cos \theta A) limacon without inner loop B) limacon without inner loop C) limacon with inner loop D) limacon with inner loop$ limacon without inner loop B) $Identify and graph the polar equation. - r=5-4 \cos \theta A) limacon without inner loop B) limacon without inner loop C) limacon with inner loop D) limacon with inner loop$ limacon without inner loop C) $Identify and graph the polar equation. - r=5-4 \cos \theta A) limacon without inner loop B) limacon without inner loop C) limacon with inner loop D) limacon with inner loop$ limacon with inner loop D) $Identify and graph the polar equation. - r=5-4 \cos \theta A) limacon without inner loop B) limacon without inner loop C) limacon with inner loop D) limacon with inner loop$ limacon with inner loop

(Multiple Choice)

4.8/5

(40)

Question 65

Identify and graph the polar equation. - $r=4 \sin (2 \theta)$ $Identify and graph the polar equation. - r=4 \sin (2 \theta) A) circle B) rose with four petals C) rose with two petals D) lemniscate$ A) $Identify and graph the polar equation. - r=4 \sin (2 \theta) A) circle B) rose with four petals C) rose with two petals D) lemniscate$ circle B) $Identify and graph the polar equation. - r=4 \sin (2 \theta) A) circle B) rose with four petals C) rose with two petals D) lemniscate$ rose with four petals C) $Identify and graph the polar equation. - r=4 \sin (2 \theta) A) circle B) rose with four petals C) rose with two petals D) lemniscate$ rose with two petals D) $Identify and graph the polar equation. - r=4 \sin (2 \theta) A) circle B) rose with four petals C) rose with two petals D) lemniscate$ lemniscate

(Multiple Choice)

4.8/5

(36)

Question 66

The rectangular coordinates of a point are given. Find polar coordinates for the point. - $( \sqrt { 3 } , - 1 )$

(Multiple Choice)

4.7/5

(44)

Question 67

Solve the problem. -A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 130 pounds, how much tension is in each part of the rope? Round your answers to the nearest Tenth.

(Multiple Choice)

4.9/5

(32)

Question 68

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

(Multiple Choice)

4.9/5

(36)

Question 69

Graph the polar equation. - $\mathrm { r } = \tan \theta , - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ $Graph the polar equation. - \mathrm { r } = \tan \theta , - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } A) B) C) D)$ A) $Graph the polar equation. - \mathrm { r } = \tan \theta , - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } A) B) C) D)$ B) $Graph the polar equation. - \mathrm { r } = \tan \theta , - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } A) B) C) D)$ C) $Graph the polar equation. - \mathrm { r } = \tan \theta , - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } A) B) C) D)$ D) $Graph the polar equation. - \mathrm { r } = \tan \theta , - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 } A) B) C) D)$

(Multiple Choice)

4.8/5

(36)

Question 70

Plot the complex number in the complex plane. - $- 3 - i$ A) B) C) D)

(Multiple Choice)

4.9/5

(38)

Question 71

Find the dot product v · w. -v = -15i + 5j, w = 4i - 4j

(Multiple Choice)

4.8/5

(39)

Question 72

Match the point in polar coordinates with either A, B, C, or D on the graph. - $\left( - 3 , - \frac { \pi } { 3 } \right)$ $Match the point in polar coordinates with either A, B, C, or D on the graph. - \left( - 3 , - \frac { \pi } { 3 } \right)$

(Multiple Choice)

4.9/5

(38)

Question 73

Solve the problem. -A DC-10 jumbo jet maintains an airspeed of 600 miles per hour in a southeasterly direction. The velocity of the jet stream is a constant 50 miles per hour from the west. Find the actual speed and direction of the aircraft. (Round the speed and direction to the nearest tenth.)

(Short Answer)

4.8/5

(38)

Question 74

Use the given vectors to find the indicated expression. -v = -3i - 4j + 4k, w = 2i + 2j - 3k Find v × (2w).

(Multiple Choice)

4.8/5

(30)

Question 75

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

(Multiple Choice)

4.8/5

(44)

Question 76

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( - 5,120 ^ { \circ } \right)$

(Multiple Choice)

4.9/5

(29)

Question 77

Find the indicated cross product. -v = i + 2j - 3k, w = 5i - 5j - k Find w × v.

(Multiple Choice)

4.8/5

(33)

Question 78

Write the expression in the standard form a + bi. - $( 1 + i ) ^ { 20 }$

(Multiple Choice)

4.9/5

(43)

Question 79

Solve the problem. - $\text { If } \mathbf { v } = 3 \mathbf { i } + 4 \mathbf { j } \text {, find } \| \mathbf { v } \|$

(Multiple Choice)

4.8/5

(39)

Question 80

Showing 61 - 80 of 270

State whether the vectors are parallel, orthogonal, or neither. -v = 4i + 2j, w = 2i - 4j

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - $x y = 1$

Find the position vector for the vector having initial point P and terminal point Q. -P = (-1, -1, 0) and Q = (-3, 3, -4)

The rectangular coordinates of a point are given. Find polar coordinates for the point. - $( \sqrt { 3 } , - 1 )$

Solve the problem. -A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 130 pounds, how much tension is in each part of the rope? Round your answers to the nearest Tenth.

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

Plot the complex number in the complex plane. - $- 3 - i$ A) B) C) D)

Find the dot product v · w. -v = -15i + 5j, w = 4i - 4j

Match the point in polar coordinates with either A, B, C, or D on the graph. - $\left( - 3 , - \frac { \pi } { 3 } \right)$ $Match the point in polar coordinates with either A, B, C, or D on the graph. - \left( - 3 , - \frac { \pi } { 3 } \right)$

Solve the problem. -A DC-10 jumbo jet maintains an airspeed of 600 miles per hour in a southeasterly direction. The velocity of the jet stream is a constant 50 miles per hour from the west. Find the actual speed and direction of the aircraft. (Round the speed and direction to the nearest tenth.)

Use the given vectors to find the indicated expression. -v = -3i - 4j + 4k, w = 2i + 2j - 3k Find v × (2w).

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

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( - 5,120 ^ { \circ } \right)$

Find the indicated cross product. -v = i + 2j - 3k, w = 5i - 5j - k Find w × v.

Write the expression in the standard form a + bi. - $( 1 + i ) ^ { 20 }$

Solve the problem. - $\text { If } \mathbf { v } = 3 \mathbf { i } + 4 \mathbf { j } \text {, find } \| \mathbf { v } \|$

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

Graph the polar equation. - r=44−2sin⁡θr = \frac { 4 } { 4 - 2 \sin \theta }r=4−2sinθ4​ A) B) C) D)

State whether the vectors are parallel, orthogonal, or neither. -v = 4i + 2j, w = 2i - 4j

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - xy=1x y = 1xy=1

Find the position vector for the vector having initial point P and terminal point Q. -P = (-1, -1, 0) and Q = (-3, 3, -4)

Identify and graph the polar equation. - r=5−4cos⁡θr=5-4 \cos \thetar=5−4cosθ A) limacon without inner loop B) limacon without inner loop C) limacon with inner loop D) limacon with inner loop

Identify and graph the polar equation. - r=4sin⁡(2θ)r=4 \sin (2 \theta)r=4sin(2θ) A) circle B) rose with four petals C) rose with two petals D) lemniscate

The rectangular coordinates of a point are given. Find polar coordinates for the point. - (3,−1)( \sqrt { 3 } , - 1 )(3​,−1)

Solve the problem. -A tightrope walker located at a certain point deflects the rope as indicated in the figure. If the weight of the tightrope walker is 130 pounds, how much tension is in each part of the rope? Round your answers to the nearest Tenth.

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

Graph the polar equation. - r=tan⁡θ,−π2<θ<π2\mathrm { r } = \tan \theta , - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }r=tanθ,−2π​<θ<2π​ A) B) C) D)

Plot the complex number in the complex plane. - −3−i- 3 - i−3−i A) B) C) D)

Find the dot product v · w. -v = -15i + 5j, w = 4i - 4j

Match the point in polar coordinates with either A, B, C, or D on the graph. - (−3,−π3)\left( - 3 , - \frac { \pi } { 3 } \right)(−3,−3π​)

Solve the problem. -A DC-10 jumbo jet maintains an airspeed of 600 miles per hour in a southeasterly direction. The velocity of the jet stream is a constant 50 miles per hour from the west. Find the actual speed and direction of the aircraft. (Round the speed and direction to the nearest tenth.)

Use the given vectors to find the indicated expression. -v = -3i - 4j + 4k, w = 2i + 2j - 3k Find v × (2w).

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

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - (−5,120∘)\left( - 5,120 ^ { \circ } \right)(−5,120∘)

Find the indicated cross product. -v = i + 2j - 3k, w = 5i - 5j - k Find w × v.

Write the expression in the standard form a + bi. - (1+i)20( 1 + i ) ^ { 20 }(1+i)20

Solve the problem. - If v=3i+4j, find ∥v∥\text { If } \mathbf { v } = 3 \mathbf { i } + 4 \mathbf { j } \text {, find } \| \mathbf { v } \| If v=3i+4j, find ∥v∥

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

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - $x y = 1$

The rectangular coordinates of a point are given. Find polar coordinates for the point. - $( \sqrt { 3 } , - 1 )$

Plot the complex number in the complex plane. - $- 3 - i$ A) B) C) D)

Match the point in polar coordinates with either A, B, C, or D on the graph. - $\left( - 3 , - \frac { \pi } { 3 } \right)$ $Match the point in polar coordinates with either A, B, C, or D on the graph. - \left( - 3 , - \frac { \pi } { 3 } \right)$

The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( - 5,120 ^ { \circ } \right)$

Write the expression in the standard form a + bi. - $( 1 + i ) ^ { 20 }$

Solve the problem. - $\text { If } \mathbf { v } = 3 \mathbf { i } + 4 \mathbf { j } \text {, find } \| \mathbf { v } \|$