Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
Find the angle \( \theta \) between the lines:
1. \( 2x + 3y = 6 \)
2. \( x - y = 5 \)
**Instructions:**
To find the angle between two lines, you can use the formula involving their slopes:
\[
\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 \cdot m_2} \right|
\]
where \( m_1 \) and \( m_2 \) are the slopes of the two lines. First, convert each line to the slope-intercept form, \( y = mx + b \), to identify the slopes. Then, apply the formula to find \( \theta \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ebccba1-7761-4d01-83f7-9d6baa9c91e8%2Fcbebb14f-dd88-4efa-ad8c-aa40a131dd95%2Fu2das6d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the angle \( \theta \) between the lines:
1. \( 2x + 3y = 6 \)
2. \( x - y = 5 \)
**Instructions:**
To find the angle between two lines, you can use the formula involving their slopes:
\[
\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 \cdot m_2} \right|
\]
where \( m_1 \) and \( m_2 \) are the slopes of the two lines. First, convert each line to the slope-intercept form, \( y = mx + b \), to identify the slopes. Then, apply the formula to find \( \theta \).
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