In Exercises 8284, sketch each vector as a position vector and fi nd its magnitude v = -3i - 4j
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0
P.3
P.4
P.5
P.6
P.7
P.8
P.9
1.1
Graphs and Graphing Utilities
1.10
Graphs and Graphing Utilities
1.2
Basics of Functions and Their Graphs
1.3
More on Functions and Their Graphs
1.4
Linear Functions and Slope
1.5
More on Slope
1.6
Transformations of Functions
1.7
Combinations of Functions; Composite Functions
1.8
Inverse Functions
1.9
Distance and Midpoint Formulas; Circles
2
Polynomial and Rational Functions
2.1
Complex Numbers
2.2
Quadratic Functions
2.3
Polynomial Functions and Their Graphs
2.4
Dividing Polynomials; Remainder and Factor Theorems
2.5
Zeros of Polynomial Functions
2.6
Rational Functions and Their Graphs
2.7
Polynomial and Rational Inequalities
2.8
Modeling Using Variation
3
Exponential and Logarithmic Functions
3.1
Exponential Functions
3.2
Logarithmic Functions
3.3
Properties of Logarithms
3.4
Exponential and Logarithmic Equations
3.5
Exponential Growth and Decay; Modeling Data
4.1
Angles and Radian Measure
4.2
Trigonometric Functions: The Unit Circle
4.3
Right Triangle Trigonometry
4.4
Trigonometric Functions of Any Angle
4.5
Graphs of Sine and Cosine Functions
4.6
Graphs of Other Trigonometric Functions
4.7
Inverse Trigonometric Functions
4.8
Applications of Trigonometric Functions
5.1
Verifying Trigonometric Identities
5.2 and 5.3
5.4
Product-to-Sum and Sum-to-Product Formulas
5.5
Trigonometric Equations
6.1 and 6.2
6.3 and 6.4
6.5
Complex Numbers in Polar Form; DeMoivre’s Theorem
6.6
Vectors
6.7
The Dot Product
7.1
Systems of Linear Equations in Two Variables
7.2
Systems of Linear Equations in Three Variables
7.3
Partial Fractions
7.4
Systems of Nonlinear Equations in Two Variables
7.5
Systems of Inequalities
7.6
Linear Programming
8.1
Matrix Solutions to Linear Systems
8.2
Inconsistent and Dependent Systems and Their Applications
8.3
Matrix Operations and Their Applications
8.4
Multiplicative Inverses of Matrices and Matrix Equations
8.5
Determinants and Cramer’s Rule
9.1
The Ellipse
9.2
The Hyperbola
9.3
The Parabola
9.4
Rotation of Axes
9.5
Parametric Equations
9.6
Conic Sections in Polar Coordinates
10.1
Sequences and Summation Notation
10.2
Arithmetic Sequences
10.3
Geometric Sequences and Series
10.4
Mathematical Induction
10.5
The Binomial Theorem
10.6
Counting Principles, Permutations, and Combinations
10.7
Probability
11.1
Finding Limits Using Tables and Graphs
11.2
Finding Limits Using Properties of Limits
11.3
Limits and Continuity
11.4
Introduction to Derivatives
Textbook Solutions for Precalculus
Chapter 6.6 Problem 95
Question
Your boat is moving at a speed of 15 miles per hour at an angle of 25 upstream on a river fl owing at 4 miles per hour. The situation is illustrated in the fi gure below. v w x y 25 Boats speed: 15 miles per hour Boats velocity relative to the ground Waters speed: 4 miles per hour a. Find the vector representing your boats velocity relative to the ground. b. What is the speed of your boat, to the nearest mile per hour, relative to the ground? c. What is the boats direction angle, to the nearest tenth of a degree, relative to the ground?
Solution
The first step in solving 6.6 problem number 95 trying to solve the problem we have to refer to the textbook question: Your boat is moving at a speed of 15 miles per hour at an angle of 25 upstream on a river fl owing at 4 miles per hour. The situation is illustrated in the fi gure below. v w x y 25 Boats speed: 15 miles per hour Boats velocity relative to the ground Waters speed: 4 miles per hour a. Find the vector representing your boats velocity relative to the ground. b. What is the speed of your boat, to the nearest mile per hour, relative to the ground? c. What is the boats direction angle, to the nearest tenth of a degree, relative to the ground?
From the textbook chapter Vectors you will find a few key concepts needed to solve this.
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full solution
Title
Precalculus 5
Author
Rober F. Blitzer
ISBN
9780321837349
Your boat is moving at a speed of 15 miles per hour at an
Chapter 6.6 textbook questions
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Chapter 6: Problem 82 Precalculus 5
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Chapter 6: Problem 83 Precalculus 5
In Exercises 8284, sketch each vector as a position vector and fi nd its magnitude v = 5i - 2j
Read more -
Chapter 6: Problem 84 Precalculus 5
In Exercises 8284, sketch each vector as a position vector and fi nd its magnitude v = -3j
Read more -
Chapter 6: Problem 85 Precalculus 5
In Exercises 8586, let v be the vector from initial point P1 to terminal point P2. Write v in terms of i and j P1 = (2, -1), P2 = (5, -3)
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Chapter 6: Problem 86 Precalculus 5
In Exercises 8586, let v be the vector from initial point P1 to terminal point P2. Write v in terms of i and j P1 = (-3, 0), P2 = (-2,-2)
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Chapter 6: Problem 87 Precalculus 5
In Exercises 8790, let v = i - 5j and w = -2i + 7j. Find each specifi ed vector or scalar. v + w
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Chapter 6: Problem 88 Precalculus 5
In Exercises 8790, let v = i - 5j and w = -2i + 7j. Find each specifi ed vector or scalar. w - v
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Chapter 6: Problem 89 Precalculus 5
In Exercises 8790, let v = i - 5j and w = -2i + 7j. Find each specifi ed vector or scalar. 6v - 3w
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Chapter 6: Problem 90 Precalculus 5
In Exercises 8790, let v = i - 5j and w = -2i + 7j. Find each specifi ed vector or scalar. 7 -2v 7
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Chapter 6: Problem 91 Precalculus 5
In Exercises 9192, fi nd the unit vector that has the same direction as the vector v = 8i - 6j
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Chapter 6: Problem 92 Precalculus 5
In Exercises 9192, fi nd the unit vector that has the same direction as the vector v v = -i + 2j
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Chapter 6: Problem 93 Precalculus 5
The magnitude and direction angle of v are 7 v 7 = 12 and u = 60. Express v in terms of i and j .
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Chapter 6: Problem 94 Precalculus 5
The magnitude and direction of two forces acting on an object are 100 pounds, N25E, and 200 pounds, N80E, respectively. Find the magnitude, to the nearest pound, and the direction angle, to the nearest tenth of a degree, of the resultant force.
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Chapter 6: Problem 95 Precalculus 5
Your boat is moving at a speed of 15 miles per hour at an angle of 25 upstream on a river fl owing at 4 miles per hour. The situation is illustrated in the fi gure below. v w x y 25 Boats speed: 15 miles per hour Boats velocity relative to the ground Waters speed: 4 miles per hour a. Find the vector representing your boats velocity relative to the ground. b. What is the speed of your boat, to the nearest mile per hour, relative to the ground? c. What is the boats direction angle, to the nearest tenth of a degree, relative to the ground?
Read more