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Home » Stop Settling—You’re The Best at Achieving Unstoppable Success! - Decision Point

Stop Settling—You’re The Best at Achieving Unstoppable Success! - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Question: A right triangle has legs of lengths $ a $ and $ b $, and hypotenuse $ c $. If the inradius is $ r $, express the ratio of the area of the inscribed circle to the area of the triangle in terms of $ r $ and $ c $.

📌 The inradius $ r $ of a right triangle is:

📌 We now express this in terms of $ r $ and $ c $.

📌 New side length is $ s = 12 - 2 = 10 $ cm.

📌 Using the cosine angle addition identity:

📌 Solution: Let $ S = E_1 + E_2 $, $ P = E_1 E_2 $. From the equations:

📌 Now compute $ h(3) = g(f(3)) = g(0) $:

📌 ---Question: The ratio of plankton to algae in a samples is $5:7$. If there are 35 plankton, how many algae are present?

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