**Text Transcription for Educational Purpose:**---**1. Design Task:**You would like to design a rug created from a semicircle and sector. Point C represents the center of the circle that is associated with the sector, and point A is located at the midpoint of the diameter of the semicircle. a. You have 180 inches of decorative trim that you would like to add to the perimeter of the rug. Do you have enough material? The angle of the sector is $ \theta = 70^\circ $.**Diagram Explanation:**The diagram displays a composite shape consisting of a semicircle and a sector. - The semicircle is labeled with points A and C, where A is at the midpoint of the diameter of the semicircle, and C is the center of the circle.- The sector is shown adjoining the semicircle, with angle $ \theta = 70^\circ $.- The curved and straight edges outline the total perimeter that requires trimming.This configuration guides the calculation of the perimeter to determine if the available 180 inches of trim is sufficient.---

You would like to design a rug created from a semicircle and sector. Point C represents the center of the circle that is associated with the sector and point A is located at the midpoint of the diameter of the semicircle. a. You have 180 in. of decorative trim that you would like to add to the perimeter of the rug. Do you have enough material? The angle of the sector is 0 70°.

You would like to design a rug created from a semicircle and sector. Point C represents the center of the circle that is associated with the sector and point A is located at the midpoint of the diameter of the semicircle. a. You have 180 in. of decorative trim that you would like to add to the perimeter of the rug. Do you have enough material? The angle of the sector is 0 70°.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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**Text Transcription for Educational Purpose:**

---

**1. Design Task:**

You would like to design a rug created from a semicircle and sector. Point C represents the center of the circle that is associated with the sector, and point A is located at the midpoint of the diameter of the semicircle.

a. You have 180 inches of decorative trim that you would like to add to the perimeter of the rug. Do you have enough material? The angle of the sector is $ \theta = 70^\circ $.

**Diagram Explanation:**

The diagram displays a composite shape consisting of a semicircle and a sector.

- The semicircle is labeled with points A and C, where A is at the midpoint of the diameter of the semicircle, and C is the center of the circle.
- The sector is shown adjoining the semicircle, with angle $ \theta = 70^\circ $.
- The curved and straight edges outline the total perimeter that requires trimming.

This configuration guides the calculation of the perimeter to determine if the available 180 inches of trim is sufficient.

---

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