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7) Find the average distance from (0, 0) of the points that lie in the region X² + y² ≤ (10.5)²

7) Find the average distance from (0, 0) of the points that lie in the region X² + y² ≤ (10.5)²

Calculus: Early Transcendentals
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 7:** Find the average distance from the origin \((0, 0)\) of the points that lie in the region defined by the inequality \(X^2 + Y^2 \leq (10.5)^2\). ### Explanation: The problem requires calculating the average distance from the origin for all points located within or on the circle centered at the origin with a radius of 10.5. The inequality \(X^2 + Y^2 \leq (10.5)^2\) describes a circular region with radius 10.5 units in a Cartesian plane. The distance from a point \((X, Y)\) to the origin is given by \(\sqrt{X^2 + Y^2}\). The task is to find the mean of these distances over the area of the circle.
Transcribed Image Text:**Problem 7:** Find the average distance from the origin \((0, 0)\) of the points that lie in the region defined by the inequality \(X^2 + Y^2 \leq (10.5)^2\). ### Explanation: The problem requires calculating the average distance from the origin for all points located within or on the circle centered at the origin with a radius of 10.5. The inequality \(X^2 + Y^2 \leq (10.5)^2\) describes a circular region with radius 10.5 units in a Cartesian plane. The distance from a point \((X, Y)\) to the origin is given by \(\sqrt{X^2 + Y^2}\). The task is to find the mean of these distances over the area of the circle.
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