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ninja turtles movie april o'neil - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 A computational evolutionary ecology AI researcher is analyzing the growth patterns of circular plant colonies in Patagonia. One colony grows to form a circle with radius \( x \), while another expands to form an octagon with each side equal to \( x \). What is the ratio of the area of the circle to the area of the octagon?

📌 To find the ratio of the area of the circle to the area of the octagon, we calculate both areas separately.

📌 The formula for the area of a circle is:

📌 A_{\text{circle}} = \pi x^2

📌 Area of the Octagon:

📌 For a regular octagon with side length \( s = x \), the area \( A \) is given by:

📌 A_{\text{octagon}} = 2(1 + \sqrt{2})s^2 = 2(1 + \sqrt{2})x^2

📌 A_{\text{octagon}} = 2(1 + \sqrt{2})x^2

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