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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Question
![**Problem:**
If \( \mathbf{v} = 9\mathbf{i} - 5\mathbf{j} \), find \( -2\|\mathbf{v}\|^2 \). Round your answer to the nearest tenth, if necessary.
**Options:**
- (A) -20.6
- (B) -212
- (C) 20.6
- (D) 212
**Explanation:**
1. First, calculate the magnitude \( \|\mathbf{v}\| \) of the vector \( \mathbf{v} \).
\[
\|\mathbf{v}\| = \sqrt{(9^2) + (-5^2)} = \sqrt{81 + 25} = \sqrt{106}
\]
2. Then, find \( \|\mathbf{v}\|^2 \):
\[
\|\mathbf{v}\|^2 = 106
\]
3. Next, calculate \( -2\|\mathbf{v}\|^2 \):
\[
-2 \|\mathbf{v}\|^2 = -2 \times 106 = -212
\]
The correct answer is \( \boxed{-212} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb65d250f-ce79-4155-be29-8b1588e7e3e2%2Fe76320ad-f896-4f18-9448-91278bcadb8d%2F765i2ej_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
If \( \mathbf{v} = 9\mathbf{i} - 5\mathbf{j} \), find \( -2\|\mathbf{v}\|^2 \). Round your answer to the nearest tenth, if necessary.
**Options:**
- (A) -20.6
- (B) -212
- (C) 20.6
- (D) 212
**Explanation:**
1. First, calculate the magnitude \( \|\mathbf{v}\| \) of the vector \( \mathbf{v} \).
\[
\|\mathbf{v}\| = \sqrt{(9^2) + (-5^2)} = \sqrt{81 + 25} = \sqrt{106}
\]
2. Then, find \( \|\mathbf{v}\|^2 \):
\[
\|\mathbf{v}\|^2 = 106
\]
3. Next, calculate \( -2\|\mathbf{v}\|^2 \):
\[
-2 \|\mathbf{v}\|^2 = -2 \times 106 = -212
\]
The correct answer is \( \boxed{-212} \).
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