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Proceed as in Example 1. Translate the words into an appropriate function. A wire of length L is cut x units from its left end. As shown in the figure below, the piece of wire of length x (blue in the figure) is bent into the shape of a circle, whereas the remaining piece of wire of length L-x (red in the figure) is bent into the shape of a square. Express the sum of the areas, A, as a function of x. A(x) = Give the domain of the function. (Enter your answer using interval notation.) Wire (a) Wire of length L CircleO Square L-X (b) Wire cut r units from left end

Proceed as in Example 1. Translate the words into an appropriate function. A wire of length L is cut x units from its left end. As shown in the figure below, the piece of wire of length x (blue in the figure) is bent into the shape of a circle, whereas the remaining piece of wire of length L-x (red in the figure) is bent into the shape of a square. Express the sum of the areas, A, as a function of x. A(x) = Give the domain of the function. (Enter your answer using interval notation.) Wire (a) Wire of length L CircleO Square L-X (b) Wire cut r units from left end

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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Proceed as in Example 1. Translate the words into an appropriate function. A wire of length \( L \) is cut \( x \) units from its left end. As shown in the figure below, the piece of wire of length \( x \) (blue in the figure) is bent into the shape of a circle, whereas the remaining piece of wire of length \( L - x \) (red in the figure) is bent into the shape of a square. Express the sum of the areas, \( A \), as a function of \( x \). \[ A(x) = \] Give the domain of the function. (Enter your answer using interval notation.) --- **Diagrams Explanation:** - **(a) Wire of length \( L \):** This is a straight horizontal line indicating the total length \( L \). - **(b) Wire cut \( x \) units from left end:** - **Circle:** The section in blue, representing the length \( x \), is formed into a circle. - **Square:** The section in red, representing the length \( L - x \), is formed into a square. The diagram illustrates the division of the wire into two parts, one forming a circle and the other a square, based on the variable \( x \).
Transcribed Image Text:Proceed as in Example 1. Translate the words into an appropriate function. A wire of length \( L \) is cut \( x \) units from its left end. As shown in the figure below, the piece of wire of length \( x \) (blue in the figure) is bent into the shape of a circle, whereas the remaining piece of wire of length \( L - x \) (red in the figure) is bent into the shape of a square. Express the sum of the areas, \( A \), as a function of \( x \). \[ A(x) = \] Give the domain of the function. (Enter your answer using interval notation.) --- **Diagrams Explanation:** - **(a) Wire of length \( L \):** This is a straight horizontal line indicating the total length \( L \). - **(b) Wire cut \( x \) units from left end:** - **Circle:** The section in blue, representing the length \( x \), is formed into a circle. - **Square:** The section in red, representing the length \( L - x \), is formed into a square. The diagram illustrates the division of the wire into two parts, one forming a circle and the other a square, based on the variable \( x \).
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