Find the dot product of u and v. $\begin{array} { l } \mathbf { u } = \langle - 4,9 \rangle \\ \mathbf { v } = \langle - 2 , - 5 \rangle \end{array}$

A) -41 B) -33 C) -37 D) -35 E) -39 A) -41 B) -33 C) -37 D) -35 E) -39

Find the projection of u onto v. $\begin{array} { l } \mathbf { u } = \langle 3,6 \rangle \\ \mathbf { v } = \langle 4,6 \rangle \end{array}$

A) $13 \langle 72,48 \rangle$ B) $\frac { 1 } { 13 } \langle 3,4 \rangle$ C) $\frac { 13 } { 12 } \langle 48,72 \rangle$ D) $\frac { 1 } { 13 } \langle 48,72 \rangle$ E) $\frac { 12 } { 13 } \langle 48,72 \rangle$ A) $13 \langle 72,48 \rangle$ B) $\frac { 1 } { 13 } \langle 3,4 \rangle$ C) $\frac { 13 } { 12 } \langle 48,72 \rangle$ D) $\frac { 1 } { 13 } \langle 48,72 \rangle$ E) $\frac { 12 } { 13 } \langle 48,72 \rangle$

Exam 6: Additional Topics In Trigonometery

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.

(Multiple Choice)

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Question 281

Given vectors $\mathbf { u } = \langle - 1,3 \rangle$ and $\mathbf { v } = \langle 1,4 \rangle$ determine the quantity indicated below. $- 2 \mathbf { u }^. - 4 \mathbf { v }$

(Multiple Choice)

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Question 282

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal.The crate is moved 31 feet horizontally.How much work has been accomplished $\theta$ Round your answer to one decimal place.

(Multiple Choice)

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Question 283

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel.

(Multiple Choice)

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Question 284

Find u + v. $\mathbf { u } = \langle 4,5 \rangle , \mathbf { v } = \langle 6,0 \rangle$

(Multiple Choice)

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Question 285

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. a = 8, b = 10, c = 14

(Multiple Choice)

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Question 286

Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle 0 , - 4 \rangle$

(Multiple Choice)

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Question 287

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle 2 , - 9 \rangle$

(Multiple Choice)

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Question 288

Multiply the complex numbers.Write the answer in trigonometric form. $9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right) 4 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right)$

(Multiple Choice)

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Question 289

Find the area of the triangle having the indicated angle and sides. B = 123°, a = 64, c = 28 (Round your answer to one decimal place.)

(Multiple Choice)

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Question 290

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 33, b = 36, c = 25

(Multiple Choice)

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Question 291

Find the area of the triangle having the indicated angle and sides. $C = 102 ^ { \circ } , a = 6 , b = 2$ (Round your answer to one decimal place.)

(Multiple Choice)

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Question 292

Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 7 \left( \cos \frac { 6 \pi } { 7 } + i \sin \frac { 6 \pi } { 7 } \right) \right] \left[ 2 \left( \cos \frac { 4 \pi } { 9 } + i \sin \frac { 4 \pi } { 9 } \right) \right]$

(Multiple Choice)

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Question 293

Find the magnitude and direction angle of $\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)$ .

(Multiple Choice)

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Question 294

Use the dot product to find the magnitude of u. $\mathbf { u } = 4 \mathbf { j }$

(Multiple Choice)

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Question 295

Find the dot product of u and v. =\langle-4,9\rangle =\langle-2,-5\rangle

(Multiple Choice)

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Question 296

Find the projection of u onto v. =\langle3,6\rangle =\langle4,6\rangle

(Multiple Choice)

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Question 297

Find values for b such that the triangle has two solutions. A = 46°, a = 10

(Multiple Choice)

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Question 298

Find the standard form of the complex number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$ .

(Multiple Choice)

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Question 299

If $\| \mathbf { u } \| = 4$ and $\| \mathbf { v } \| = 6$ , and the vectors make angles of 140° and 20° with the x-axis respectively, find the component form of the sum of u and v.Round answers to two decimal places.

(Multiple Choice)

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Question 300

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.

Given vectors $\mathbf { u } = \langle - 1,3 \rangle$ and $\mathbf { v } = \langle 1,4 \rangle$ determine the quantity indicated below. $- 2 \mathbf { u }^. - 4 \mathbf { v }$

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal.The crate is moved 31 feet horizontally.How much work has been accomplished $\theta$ Round your answer to one decimal place.

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel.

Find u + v. $\mathbf { u } = \langle 4,5 \rangle , \mathbf { v } = \langle 6,0 \rangle$

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. a = 8, b = 10, c = 14

Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle 0 , - 4 \rangle$

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle 2 , - 9 \rangle$

Multiply the complex numbers.Write the answer in trigonometric form. $9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right) 4 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right)$

Find the area of the triangle having the indicated angle and sides. B = 123°, a = 64, c = 28 (Round your answer to one decimal place.)

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 33, b = 36, c = 25

Find the area of the triangle having the indicated angle and sides. $C = 102 ^ { \circ } , a = 6 , b = 2$ (Round your answer to one decimal place.)

Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 7 \left( \cos \frac { 6 \pi } { 7 } + i \sin \frac { 6 \pi } { 7 } \right) \right] \left[ 2 \left( \cos \frac { 4 \pi } { 9 } + i \sin \frac { 4 \pi } { 9 } \right) \right]$

Find the magnitude and direction angle of $\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)$ .

Use the dot product to find the magnitude of u. $\mathbf { u } = 4 \mathbf { j }$

Find the dot product of u and v. =\langle-4,9\rangle =\langle-2,-5\rangle

Find the projection of u onto v. =\langle3,6\rangle =\langle4,6\rangle

Find values for b such that the triangle has two solutions. A = 46°, a = 10

Find the standard form of the complex number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$ .

If $\| \mathbf { u } \| = 4$ and $\| \mathbf { v } \| = 6$ , and the vectors make angles of 140° and 20° with the x-axis respectively, find the component form of the sum of u and v.Round answers to two decimal places.

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

Exam 6: Additional Topics In Trigonometery

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place. ​

Given vectors u=⟨−1,3⟩\mathbf { u } = \langle - 1,3 \rangleu=⟨−1,3⟩ and v=⟨1,4⟩\mathbf { v } = \langle 1,4 \ranglev=⟨1,4⟩ determine the quantity indicated below. −2u.−4v- 2 \mathbf { u }^. - 4 \mathbf { v }−2u.−4v

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal.The crate is moved 31 feet horizontally.How much work has been accomplished θ\thetaθ Round your answer to one decimal place.

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel. ​

Find u + v. u=⟨4,5⟩,v=⟨6,0⟩\mathbf { u } = \langle 4,5 \rangle , \mathbf { v } = \langle 6,0 \rangleu=⟨4,5⟩,v=⟨6,0⟩

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ a = 8, b = 10, c = 14 ​

Find a unit vector in the direction of the given vector. u=⟨0,−4⟩\mathbf { u } = \langle 0 , - 4 \rangleu=⟨0,−4⟩

Use the dot product to find the magnitude of u. u=⟨2,−9⟩\mathbf { u } = \langle 2 , - 9 \rangleu=⟨2,−9⟩

Find the area of the triangle having the indicated angle and sides. ​ B = 123°, a = 64, c = 28 ​ (Round your answer to one decimal place.) ​

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​ A = 33, b = 36, c = 25 ​

Find the area of the triangle having the indicated angle and sides. C=102∘,a=6,b=2C = 102 ^ { \circ } , a = 6 , b = 2C=102∘,a=6,b=2 (Round your answer to one decimal place.)

Find the magnitude and direction angle of v=6(cos⁡80∘i+sin⁡80∘j)\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)v=6(cos80∘i+sin80∘j) .

Use the dot product to find the magnitude of u. u=4j\mathbf { u } = 4 \mathbf { j }u=4j

Find the dot product of u and v. =\langle-4,9\rangle =\langle-2,-5\rangle

Find the projection of u onto v. =\langle3,6\rangle =\langle4,6\rangle

Find values for b such that the triangle has two solutions. A = 46°, a = 10

Find the standard form of the complex number 8(cos⁡330∘)+isin⁡330∘8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }8(cos330∘)+isin330∘ .

If ∥u∥=4\| \mathbf { u } \| = 4∥u∥=4 and ∥v∥=6\| \mathbf { v } \| = 6∥v∥=6 , and the vectors make angles of 140° and 20° with the x-axis respectively, find the component form of the sum of u and v.Round answers to two decimal places.

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

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.

Given vectors $\mathbf { u } = \langle - 1,3 \rangle$ and $\mathbf { v } = \langle 1,4 \rangle$ determine the quantity indicated below. $- 2 \mathbf { u }^. - 4 \mathbf { v }$

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal.The crate is moved 31 feet horizontally.How much work has been accomplished $\theta$ Round your answer to one decimal place.

The lengths of the sides of a triangular parcel of land are approximately 400 feet, 700 feet, and 800 feet.Approximate the area of the parcel.

Find u + v. $\mathbf { u } = \langle 4,5 \rangle , \mathbf { v } = \langle 6,0 \rangle$

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. a = 8, b = 10, c = 14

Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle 0 , - 4 \rangle$

Use the dot product to find the magnitude of u. $\mathbf { u } = \langle 2 , - 9 \rangle$

Find the area of the triangle having the indicated angle and sides. B = 123°, a = 64, c = 28 (Round your answer to one decimal place.)

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 33, b = 36, c = 25

Find the area of the triangle having the indicated angle and sides. $C = 102 ^ { \circ } , a = 6 , b = 2$ (Round your answer to one decimal place.)

Find the magnitude and direction angle of $\mathbf { v } = 6 \left( \cos 80 ^ { \circ } \mathbf { i } + \sin 80 ^ { \circ } \mathbf { j } \right)$ .

Use the dot product to find the magnitude of u. $\mathbf { u } = 4 \mathbf { j }$

Find the standard form of the complex number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$ .

If $\| \mathbf { u } \| = 4$ and $\| \mathbf { v } \| = 6$ , and the vectors make angles of 140° and 20° with the x-axis respectively, find the component form of the sum of u and v.Round answers to two decimal places.