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...
Related questions
Question
![The image contains handwritten mathematical text with the following content, formatted appropriately for an educational website:
---
**Problem Statement:**
Find the shortest distance, \( d \), from the point \( (3, 1, -8) \) to the plane given by the equation \( x + y + z = 8 \).
**Solution:**
The distance \( d \) from a point \((x_1, y_1, z_1)\) to a plane defined by \( Ax + By + Cz + D = 0 \) can be calculated using the formula:
\[
d = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}}
\]
In this problem:
- The point is \( (x_1, y_1, z_1) = (3, 1, -8) \)
- The plane is \( x + y + z - 8 = 0 \), so \( A = 1 \), \( B = 1 \), \( C = 1 \), and \( D = -8 \)
Plug the values into the formula to find \( d \).
---
*Note: This is a transcription and explanation based on the image and is intended for educational purposes.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe040b111-4b10-4c24-8337-c45ed461242d%2Fea73cd98-ff0d-41f3-8bb0-3c0b50d4ea78%2Fsy3j0d9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains handwritten mathematical text with the following content, formatted appropriately for an educational website:
---
**Problem Statement:**
Find the shortest distance, \( d \), from the point \( (3, 1, -8) \) to the plane given by the equation \( x + y + z = 8 \).
**Solution:**
The distance \( d \) from a point \((x_1, y_1, z_1)\) to a plane defined by \( Ax + By + Cz + D = 0 \) can be calculated using the formula:
\[
d = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}}
\]
In this problem:
- The point is \( (x_1, y_1, z_1) = (3, 1, -8) \)
- The plane is \( x + y + z - 8 = 0 \), so \( A = 1 \), \( B = 1 \), \( C = 1 \), and \( D = -8 \)
Plug the values into the formula to find \( d \).
---
*Note: This is a transcription and explanation based on the image and is intended for educational purposes.*
Expert Solution
Step 1
Let's find.
Step by step
Solved in 2 steps
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning