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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13.1.3 With the attached image, please help me find 4u + 7v =
![**Problem Statement:**
Given vectors \( u = \langle 6, 6 \rangle \) and \( v = \langle 5, 6 \rangle \), express \( 4u + 7v \) in the form \( \langle a, b \rangle \).
**Solution:**
First, we need to calculate \( 4u \) and \( 7v \):
\[ 4u = 4 \times \langle 6, 6 \rangle = \langle 24, 24 \rangle \]
\[ 7v = 7 \times \langle 5, 6 \rangle = \langle 35, 42 \rangle \]
Now, add the vectors \( 4u \) and \( 7v \):
\[ 4u + 7v = \langle 24, 24 \rangle + \langle 35, 42 \rangle = \langle 24 + 35, 24 + 42 \rangle \]
\[ 4u + 7v = \langle 59, 66 \rangle \]
Thus, the expression \( 4u + 7v \) in the form \( \langle a, b \rangle \) is \(\langle 59, 66 \rangle \).
(Simplify your answers.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabd5e741-0235-409f-80de-883f5f0e5da7%2Fb5615bbd-62c6-4d0f-8130-201628164365%2Fckqluhq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given vectors \( u = \langle 6, 6 \rangle \) and \( v = \langle 5, 6 \rangle \), express \( 4u + 7v \) in the form \( \langle a, b \rangle \).
**Solution:**
First, we need to calculate \( 4u \) and \( 7v \):
\[ 4u = 4 \times \langle 6, 6 \rangle = \langle 24, 24 \rangle \]
\[ 7v = 7 \times \langle 5, 6 \rangle = \langle 35, 42 \rangle \]
Now, add the vectors \( 4u \) and \( 7v \):
\[ 4u + 7v = \langle 24, 24 \rangle + \langle 35, 42 \rangle = \langle 24 + 35, 24 + 42 \rangle \]
\[ 4u + 7v = \langle 59, 66 \rangle \]
Thus, the expression \( 4u + 7v \) in the form \( \langle a, b \rangle \) is \(\langle 59, 66 \rangle \).
(Simplify your answers.)
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