Question 1

Given a = 4.6, b = 6.1, and c = 9.1, use Heron's Area Formula to find the area of ΔABC.Round your answer to two decimal places. ​

Accepted Answer

A) 10.79 
B) 9.89 
C) 12.60 
D) 8.58 
E) 12.09 
A) 10.79 
B) 9.89 
C) 12.60 
D) 8.58 
E) 12.09

Question 2

Find values for b such that the triangle has no solutions. ​
A = 24°, a = 5
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Use the vectors   ,   to find the indicated quantity.State whether the result is a vector or a scalar. ​   ​

Accepted Answer

A)    ; vector 
B) -2; scalar 
C) 2; scalar 
D)    ; vector 
E) 0; scalar 
A)    ; vector 
B) -2; scalar 
C) 2; scalar 
D)    ; vector 
E) 0; scalar

Question 4

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​
A = 76°, a = 7, b = 5
​

Accepted Answer

A) B ≈ 43.87°, C ≈ 43.87°, c ≈ 7.96 
B) B ≈ 48.87°, C ≈ 60.13°, c ≈ 6.26 
C) B ≈ 43.87°, C ≈ 60.13°, c ≈ 6.26 
D) B ≈ 48.87°, C ≈ 65.13°, c ≈ 7.96 
E) No Solution 
A) B ≈ 43.87°, C ≈ 43.87°, c ≈ 7.96 
B) B ≈ 48.87°, C ≈ 60.13°, c ≈ 6.26 
C) B ≈ 43.87°, C ≈ 60.13°, c ≈ 6.26 
D) B ≈ 48.87°, C ≈ 65.13°, c ≈ 7.96 
E) No Solution

Question 5

Find u - v. ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 6

Use the vectors   ,   and   to find the indicated quantity.State whether the result is a vector or a scalar.
​   ​

Accepted Answer

A) 16; scalar 
B)    ; vector 
C)    ; vector 
D) 22; scalar 
E) 20; scalar 
A) 16; scalar 
B)    ; vector 
C)    ; vector 
D) 22; scalar 
E) 20; scalar

Question 7

​Find a unit vector in the direction of   . ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 8

Use the vectors   ,   , and   to find the indicated quantity.State whether the result is a vector or a scalar.
​   ​

Accepted Answer

A)    ; vector 
B)    ; vector 
C) -58; scalar 
D) -56; scalar 
E)    ; vector 
A)    ; vector 
B)    ; vector 
C) -58; scalar 
D) -56; scalar 
E)    ; vector

Question 9

Determine the work done by a crane lifting a 2,800-pound car 7 feet.

Accepted Answer

A) 19,600 ft-lb 
B) 19,620 ft-lb 
C) 19,610 ft-lb 
D) 19,640 ft-lb 
E) 19,630 ft-lb 
A) 19,600 ft-lb 
B) 19,620 ft-lb 
C) 19,610 ft-lb 
D) 19,640 ft-lb 
E) 19,630 ft-lb

Question 10

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places.   A = 29°, b = 14, c = 29 ​

Accepted Answer

A) a ≈ 18.08, B ≈ 22.05°, C ≈ 128.95° 
B) a ≈ 29, B ≈ 24.05°, C ≈ 126.95° 
C) a ≈ 18.08, B ≈ 128.95°, C ≈ 22.05° 
D) a ≈ 14, B ≈ 22.05°, C ≈ 128.95° 
E) a ≈ 29, B ≈ 22.05°, C ≈ 128.95° 
A) a ≈ 18.08, B ≈ 22.05°, C ≈ 128.95° 
B) a ≈ 29, B ≈ 24.05°, C ≈ 126.95° 
C) a ≈ 18.08, B ≈ 128.95°, C ≈ 22.05° 
D) a ≈ 14, B ≈ 22.05°, C ≈ 128.95° 
E) a ≈ 29, B ≈ 22.05°, C ≈ 128.95°

Question 11

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.) ​

Accepted Answer

A) Vertical ≈ 118.6 ft/sec, Horisontal ≈ 1,695.9 ft/sec. 
B) ​Vertical ≈ 119.6 ft/sec, Horisontal ≈ 1,696.9 ft/sec. 
C) ​Vertical ≈ 1,695.9 ft/sec, Horisontal ≈ 1,695.9 ft/sec. 
D) ​Vertical ≈ 1,695.9 ft/sec, Horisontal ≈ 118.6 ft/sec. 
E) ​Vertical ≈ 118.6 ft/sec, Horisontal ≈ 118.6 ft/sec. 
A) Vertical ≈ 118.6 ft/sec, Horisontal ≈ 1,695.9 ft/sec. 
B) ​Vertical ≈ 119.6 ft/sec, Horisontal ≈ 1,696.9 ft/sec. 
C) ​Vertical ≈ 1,695.9 ft/sec, Horisontal ≈ 1,695.9 ft/sec. 
D) ​Vertical ≈ 1,695.9 ft/sec, Horisontal ≈ 118.6 ft/sec. 
E) ​Vertical ≈ 118.6 ft/sec, Horisontal ≈ 118.6 ft/sec.

Question 12

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 13, b = 17, c = 23
​

Accepted Answer

A) A ≈ 46.85°, B ≈ 46.85°, C ≈ 86.3° 
B) A ≈ 33.91°, B ≈ 99.24°, C ≈ 46.85° 
C) A ≈ 46.85°, B ≈ 33.91°, C ≈ 99.24° 
D) A ≈ 33.91°, B ≈ 46.85°, C ≈ 99.24° 
E) A ≈ 99.24°, B ≈ 46.85°, C ≈ 33.91° 
A) A ≈ 46.85°, B ≈ 46.85°, C ≈ 86.3° 
B) A ≈ 33.91°, B ≈ 99.24°, C ≈ 46.85° 
C) A ≈ 46.85°, B ≈ 33.91°, C ≈ 99.24° 
D) A ≈ 33.91°, B ≈ 46.85°, C ≈ 99.24° 
E) A ≈ 99.24°, B ≈ 46.85°, C ≈ 33.91°

Question 13

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution. ​

Accepted Answer

A) b = 16 
B) b = 17 
C) b = 11 
D) b = 15 
E) b = 24 
A) b = 16 
B) b = 17 
C) b = 11 
D) b = 15 
E) b = 24

Question 14

Find the angle between the vectors u and v if   , and   Round answer to two decimal places.

Accepted Answer

A) 167.77° 
B) 168.46° 
C) 169.70° 
D) 170.66° 
E) 171.11° 
A) 167.77° 
B) 168.46° 
C) 169.70° 
D) 170.66° 
E) 171.11°

Question 15

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​
Magnitude
Angle     ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 16

Find the component form of v if   and the angle it makes with the x-axis is 30°.

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 17

The vector   gives the number of units of two models of laptops produced by a company.The vector   gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 6%.

Accepted Answer

A) $7,664,400 
B) $7,791,300 
C) $7,918,200 
D) $7,723,800 
E) $7,768,800 
A) $7,664,400 
B) $7,791,300 
C) $7,918,200 
D) $7,723,800 
E) $7,768,800

Question 18

Find 2u - 3v. ​   ​

Accepted Answer

A) ​   
B)    
C)    ​ 
D)    
E)    ​ 
A) ​   
B)    
C)    ​ 
D)    
E)    ​

Question 19

63​ Find the projection of u onto v if ,   ,   .
​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 20

The baseball player in center field is playing approximately 310 feet from the television camera that is behind home plate.A batter hits a fly ball that goes to the wall 400 feet from the camera (see figure).The camera turns 10° to follow the play.Approximately how far does the center fielder have to run to make the catch? ​   ​

Accepted Answer

A) 102.9 ft 
B) 114.9 ft 
C) 108.9 ft 
D) 113.9 ft 
E) 103.9 ft 
A) 102.9 ft 
B) 114.9 ft 
C) 108.9 ft 
D) 113.9 ft 
E) 103.9 ft

Given a = 4.6, b = 6.1, and c = 9.1, use Heron's Area Formula to find the area of ΔABC.Round your answer to two decimal places.

Find values for b such that the triangle has no solutions. A = 24°, a = 5

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar.

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 76°, a = 7, b = 5

Find u - v.

Use the vectors , and to find the indicated quantity.State whether the result is a vector or a scalar.

Find a unit vector in the direction of .

Use the vectors , , and to find the indicated quantity.State whether the result is a vector or a scalar.

Determine the work done by a crane lifting a 2,800-pound car 7 feet.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 29°, b = 14, c = 29

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.)

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 13, b = 17, c = 23

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution.

Find the angle between the vectors u and v if , and Round answer to two decimal places.

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle

Find the component form of v if and the angle it makes with the x-axis is 30°.

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 6%.

Find 2u - 3v.

63 Find the projection of u onto v if , , .

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

Given a = 4.6, b = 6.1, and c = 9.1, use Heron's Area Formula to find the area of ΔABC.Round your answer to two decimal places. ​

Find values for b such that the triangle has no solutions. ​ A = 24°, a = 5 ​

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​ A = 76°, a = 7, b = 5 ​

Find u - v. ​ ​

Use the vectors , and to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

​Find a unit vector in the direction of . ​

Use the vectors , , and to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

Determine the work done by a crane lifting a 2,800-pound car 7 feet.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 29°, b = 14, c = 29 ​

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.) ​

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 13, b = 17, c = 23 ​

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution. ​

Find the angle between the vectors u and v if , and Round answer to two decimal places.

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​ Magnitude Angle ​

Find the component form of v if and the angle it makes with the x-axis is 30°.

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 6%.

Find 2u - 3v. ​ ​

63​ Find the projection of u onto v if , , . ​

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Given a = 4.6, b = 6.1, and c = 9.1, use Heron's Area Formula to find the area of ΔABC.Round your answer to two decimal places.

Find values for b such that the triangle has no solutions. A = 24°, a = 5

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar.

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. A = 76°, a = 7, b = 5

Find u - v.

Use the vectors , and to find the indicated quantity.State whether the result is a vector or a scalar.

Find a unit vector in the direction of .

Use the vectors , , and to find the indicated quantity.State whether the result is a vector or a scalar.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 29°, b = 14, c = 29

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.)

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 13, b = 17, c = 23

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution.

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle

Find 2u - 3v.

63 Find the projection of u onto v if , , .