This problem illustrates a typical approach for creating a model. Use lower case letters. We want to express the area of a circle, A, as a function of its circumference, c. (a) Because we want a formula for area, start with the basic formula we know for the area of a circle in terms of its radius. (b) Because we want the area formula in terms of circumference and not radius, we need another formula that will allow us to replace r in terms of c. The formula that has both r and c in it is the circumference formula for a circle. Write out the circumference formula and then solve the formula for r. (c) Now substitute r in terms of c into your area formula in part (a). A(c) =

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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This problem illustrates a typical approach for creating a model. Use lower case letters.
We want to express the area of a circle, A, as a function of its circumference, c.
(a) Because we want a formula for area, start with the basic formula we know for the area of a circle in terms of its radius.
A =
(b) Because we want the area formula in terms of circumference and not radius, we need another formula that will allow us to replace r in terms of c. The formula that has both r and c in it is the circumference formula for a circle. Write out the circumference formula and then solve the formula for r.
C =
r =
(c) Now substitute r in terms of c into your area formula in part (a).
A(c) =
Transcribed Image Text:This problem illustrates a typical approach for creating a model. Use lower case letters. We want to express the area of a circle, A, as a function of its circumference, c. (a) Because we want a formula for area, start with the basic formula we know for the area of a circle in terms of its radius. A = (b) Because we want the area formula in terms of circumference and not radius, we need another formula that will allow us to replace r in terms of c. The formula that has both r and c in it is the circumference formula for a circle. Write out the circumference formula and then solve the formula for r. C = r = (c) Now substitute r in terms of c into your area formula in part (a). A(c) =
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