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A. $ \sigma(x)(1 - \sigma(x)) $ - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Thus, the ratio of the volume of the sphere to the volume of the cube is \(\boxed{\frac{\pi}{6}}\).

📌 An equilateral triangle has a side length of \( s \) units. The triangle is circumscribed about a circle. What is the ratio of the area of the circle to the area of the triangle?

📌 The area \( A_{\text{triangle}} \) of an equilateral triangle with side length \( s \) is:

📌 A_{\text{triangle}} = \frac{\sqrt{3}}{4} s^2

📌 For an equilateral triangle, the radius \( r \) of the inscribed circle is given by:

📌 r = \frac{s \sqrt{3}}{6}

📌 The area \( A_{\text{circle}} \) of the circle is:

📌 A_{\text{circle}} = \pi r^2 = \pi \left(\frac{s \sqrt{3}}{6}\right)^2 = \pi \frac{3s^2}{36} = \frac{\pi s^2}{12}

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