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The bearing of a lighthouse from a ship was found to be N 37° E. After the ship sailed 2.5 mi due south, the new bearing was N 25° E. Find the distance between the ship and the lighthouse at each location.
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Ch. 7 - Applications of Trigonometry and Vectors
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 8, Problema 38
Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.
- 2u + 4v
Guida verificata passo dopo passo1
Identify the given vectors: \( \mathbf{u} = \langle -2, 5 \rangle \) and \( \mathbf{v} = \langle 4, 3 \rangle \).
Understand that scalar multiplication means multiplying each component of the vector by the scalar. For example, \( 2\mathbf{u} = \langle 2 \times (-2), 2 \times 5 \rangle \).
Calculate \( 2\mathbf{u} \) by multiplying each component of \( \mathbf{u} \) by 2: \( 2\mathbf{u} = \langle -4, 10 \rangle \).
Calculate \( 4\mathbf{v} \) by multiplying each component of \( \mathbf{v} \) by 4: \( 4\mathbf{v} = \langle 16, 12 \rangle \).
Add the resulting vectors component-wise: \( 2\mathbf{u} + 4\mathbf{v} = \langle -4 + 16, 10 + 12 \rangle \).
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Vector Addition and Scalar Multiplication
Vector addition involves adding corresponding components of two vectors to form a new vector. Scalar multiplication means multiplying each component of a vector by a scalar (a real number). These operations allow combining and scaling vectors, essential for expressions like 2u + 4v.
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Percorso guidato
05:05
Multiplying Vectors By Scalars
Component-wise Operations
Vectors in two dimensions are represented by ordered pairs. Operations such as addition and scalar multiplication are performed component-wise, meaning each x-component and y-component is handled separately. This simplifies calculations and helps visualize vector results.
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04:12Algebraic Operations on Vectors
Notation and Vector Representation
Vectors are often denoted by angle brackets, e.g., 〈x, y〉, representing their components along the x and y axes. Understanding this notation is crucial for interpreting and manipulating vectors in problems involving vector arithmetic.
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06:01i & j Notation
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Domanda del libro di testo
To build the pyramids in Egypt, it is believed that giant causeways were constructed to transport the building materials to the site. One such causeway is said to have been 3000 ft long, with a slope of about 2.3°. How much force would be required to hold a 60-ton monolith on this causeway?
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Use the law of sines to prove that each statement is true for any triangle ABC, with corresponding sides a, b, and c.
(a - b)/(a + b) = (sin A - sin B)/(sin A + sin B)
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Domanda del libro di testo
A balloonist is directly above a straight road 1.5 mi long that joins two villages. She finds that the town closer to her is at an angle of depression of 35°, and the farther town is at an angle of depression of 31°. How high above the ground is the balloon?
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Domanda del libro di testo
Standing on one bank of a river flowing north, Mark notices a tree on the opposite bank at a bearing of 115.45°. Lisa is on the same bank as Mark, but 428.3 m away. She notices that the bearing of the tree is 45.47°. The two banks are parallel. What is the distance across the river?
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Domanda del libro di testo
Find the force required to keep a 3000-lb car parked on a hill that makes an angle of 15° with the horizontal.
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