Homework Help is Here – Start Your Trial Now!
Math
Calculus
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...
See similar textbooks
icon
Related questions
Question
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS