**Problem Statement:**A wire 57 inches long is cut into two pieces, with the first piece bent into a square and the second piece bent into a circle.**Diagram Explanation:**- The wire is depicted as a straight line labeled with a total length of 57 inches.- The line is divided into two segments: - The first segment is marked as "x" inches long and is designated for forming a square. - The remainder of the wire, labeled as "57 - x," is used for forming a circle. - Underneath the line, there are two geometric shapes: - A square, representing the area formed by the first piece of wire. - A circle, representing the area formed by the second piece of wire.**Task:**- Express $ A $, the combined area of the shapes (in $\text{in}^2$), as a function of $ x $, the length of the first piece (in inches). - Determine the value of $ x $ that minimizes the total area of the two shapes combined. Provide the answer to at least 3 decimal places, where necessary.**Solution:**- **Minimum Area $ A $:** $\_\_\_\_\_\_\_\_\_) \, \text{in}^2$- **Value of $ x $ for Minimum Area:** $ x = \_\_\_\_\_\_\_\_\_$ inches

A wire 57 inches long is cut into two pieces, with the first piece bent into a square and the second piece bent into a circle. 57- Express A, the combined area of the shapes (in in"), inches). What should z be so that the total Area of the two shapes combined is Minimized? Give at least 3 decimal places, when necessary. ), as a function of r, the length of the first piece (in Minimum Area A = in? when I = inches

A wire 57 inches long is cut into two pieces, with the first piece bent into a square and the second piece bent into a circle. 57- Express A, the combined area of the shapes (in in"), inches). What should z be so that the total Area of the two shapes combined is Minimized? Give at least 3 decimal places, when necessary. ), as a function of r, the length of the first piece (in Minimum Area A = in? when I = inches

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem Statement:**

A wire 57 inches long is cut into two pieces, with the first piece bent into a square and the second piece bent into a circle.

**Diagram Explanation:**

- The wire is depicted as a straight line labeled with a total length of 57 inches.
- The line is divided into two segments:
- The first segment is marked as "x" inches long and is designated for forming a square.
- The remainder of the wire, labeled as "57 - x," is used for forming a circle.

- Underneath the line, there are two geometric shapes:
- A square, representing the area formed by the first piece of wire.
- A circle, representing the area formed by the second piece of wire.

**Task:**

- Express $ A $, the combined area of the shapes (in $\text{in}^2$), as a function of $ x $, the length of the first piece (in inches).

- Determine the value of $ x $ that minimizes the total area of the two shapes combined. Provide the answer to at least 3 decimal places, where necessary.

**Solution:**

- **Minimum Area $ A $:** $\_\_\_\_\_\_\_\_\_) \, \text{in}^2$

- **Value of $ x $ for Minimum Area:** $ x = \_\_\_\_\_\_\_\_\_$ inches

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