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A horse runs around a circular track (as the following figure shows) at 12 revolutions per hour. Find the linear speed in miles per minute the horse runs. __π miles/minute

A horse runs around a circular track (as the following figure shows) at 12 revolutions per hour. Find the linear speed in miles per minute the horse runs. __π miles/minute

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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A horse runs around a circular track (as the following figure shows) at 12 revolutions per hour. Find the linear speed in miles per minute the horse runs. __π miles/minute
### Circle and Motion Illustration **Diagram Description:** The image shows a circle with a diameter labeled as "D=6 miles." There is an arrow indicating the direction of motion along the circle's circumference. Below the circle, there is a silhouette of a horse in motion. **Speed Calculation:** The text beneath the diagram is "_____π miles/minute," indicating a placeholder for calculating the speed of an object moving along the circle's circumference in terms of π. ### Explanation: - **Diameter:** The straight-line distance across the circle, passing through the center, is 6 miles. - **Circumference Formula:** The circumference \( C \) of a circle is calculated using the formula \( C = \pi \times D \). - For this circle, \( C = \pi \times 6 \) miles. - **Speed Placeholder:** The speed of the object (horse) moving along the path is expressed as a multiple of π, to be determined in context (e.g., time taken to complete one revolution). Understanding this setup is crucial for applying concepts of circular motion in mathematics and physics, such as calculating speeds and understanding rotational dynamics.
Transcribed Image Text:### Circle and Motion Illustration **Diagram Description:** The image shows a circle with a diameter labeled as "D=6 miles." There is an arrow indicating the direction of motion along the circle's circumference. Below the circle, there is a silhouette of a horse in motion. **Speed Calculation:** The text beneath the diagram is "_____π miles/minute," indicating a placeholder for calculating the speed of an object moving along the circle's circumference in terms of π. ### Explanation: - **Diameter:** The straight-line distance across the circle, passing through the center, is 6 miles. - **Circumference Formula:** The circumference \( C \) of a circle is calculated using the formula \( C = \pi \times D \). - For this circle, \( C = \pi \times 6 \) miles. - **Speed Placeholder:** The speed of the object (horse) moving along the path is expressed as a multiple of π, to be determined in context (e.g., time taken to complete one revolution). Understanding this setup is crucial for applying concepts of circular motion in mathematics and physics, such as calculating speeds and understanding rotational dynamics.
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