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Home » The area \(A\) of a semicircle with radius \(R\) is half the area of a circle: - 500apps

The area \(A\) of a semicircle with radius \(R\) is half the area of a circle: - 500apps

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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From $ B = (6, 0) $:
d_B^2 = (3 - 6)^2 + (2 - 0)^2 = 9 + 4 = 13
From $ C = (3, 6) $:
d_C^2 = (3 - 3)^2 + (2 - 6)^2 = 0 + 16 = 16
Let the influence from each village be proportional to $ \frac{1}{d^2}...
I_{\text{total}} = \frac{1}{13} + \frac{1}{13} + \frac{1}{16} = \frac{...
Find a common denominator:
\frac{2}{13} + \frac{1}{16} = \frac{32 + 13}{208} = \frac{45}{208}
Since total influence is normalized to 1, the influence from village $...
\frac{\frac{1}{13}}{\frac{45}{208}} = \frac{1}{13} \cdot \frac{208}{45...

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