Consider using a circle's radius as the unit for measuring its circle's circumference. If you were to measure any circle's circumference, C, using its radius, r, as the unit of measure, the measurement would be . As the circle's radius and circumference vary together the circle's circumference C is always times as large as the circle's radius, r. Determine if the following statement is true or false: Since a circle's circumference C is proportional to its radius r, it follows that C is changing at a constant rate of change with r. For any change in a circle's radius, Δr, the circle' circumference changes by . Since a circle's diameter is 2 times as long as its radius, we can also define a circle's circumference in terms of its diameter, d, by writing, C= . Think about the meaning of the formula for circumference in terms of diameter you wrote above. The circumference, C, of any circle is always times as large as its diameter, d If we measure a circle's circumference using its diameter as the unit of measurement, the answer will always be: Since Cd=π, we know that π (or about 3.14) is the constant that represents the relative size, or how many times as large, a circle's circumference is compared to its diameter.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter12: Quadratic Functions

Section12.8: Joint And Combined Variation

Problem 11OE

See similar textbooks

Related questions

Concept explainers

Question

Consider using a circle's radius as the unit for measuring its circle's circumference.

If you were to measure any circle's circumference, C, using its radius, r, as the unit of measure, the measurement would be .
As the circle's radius and circumference vary together the circle's circumference C is always times as large as the circle's radius, r.
Determine if the following statement is true or false:

Since a circle's circumference C is proportional to its radius r, it follows that C is changing at a constant rate of change with r.
For any change in a circle's radius, Δr, the circle' circumference changes by .
Since a circle's diameter is 2 times as long as its radius, we can also define a circle's circumference in terms of its diameter, d, by writing, C= .
Think about the meaning of the formula for circumference in terms of diameter you wrote above.
- The circumference, C, of any circle is always times as large as its diameter, d
- If we measure a circle's circumference using its diameter as the unit of measurement, the answer will always be:
- Since Cd=π, we know that π (or about 3.14) is the constant that represents the relative size, or how many times as large, a circle's circumference is compared to its diameter.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 6 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions