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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![**Title: Finding the Closest Points to the Origin on the Surface z² = xy + 100**
In this exercise, we aim to determine which points on the surface defined by the equation \( z^2 = xy + 100 \) are nearest to the origin (0, 0, 0).
**Given Points:**
1. (-4, -9, -8), (4, 9, 8)
2. (-10, 10, 0), (10, -10, 0)
3. (-2, 18, -8), (2, -18, 8)
4. (4, -9, 8), (-4, 9, -8)
5. (0, 0, -10), (0, 0, 10)
To solve this problem, calculate the distance of each point from the origin using the formula for Euclidean distance in three dimensions:
\[
d = \sqrt{x^2 + y^2 + z^2}
\]
Compare these distances to identify the points that are closest to the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2acbb8d8-ea7d-469f-beb1-443cebbd2d53%2Ffe0c00ae-b364-49a9-a995-830e76c6ba25%2Fy0o6k0o_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Finding the Closest Points to the Origin on the Surface z² = xy + 100**
In this exercise, we aim to determine which points on the surface defined by the equation \( z^2 = xy + 100 \) are nearest to the origin (0, 0, 0).
**Given Points:**
1. (-4, -9, -8), (4, 9, 8)
2. (-10, 10, 0), (10, -10, 0)
3. (-2, 18, -8), (2, -18, 8)
4. (4, -9, 8), (-4, 9, -8)
5. (0, 0, -10), (0, 0, 10)
To solve this problem, calculate the distance of each point from the origin using the formula for Euclidean distance in three dimensions:
\[
d = \sqrt{x^2 + y^2 + z^2}
\]
Compare these distances to identify the points that are closest to the origin.
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