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callaway gardens christmas lights - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Utiliser \(\sin^2 \theta + \cos^2 \theta = 1\):

📌 \(\left(\frac{3}{5}\right)^2 + \cos^2 \theta = 1\)

📌 \(\frac{9}{25} + \cos^2 \theta = 1\)

📌 \(\cos^2 \theta = 1 - \frac{9}{25} = \frac{16}{25}\)

📌 \(\cos \theta = \sqrt{\frac{16}{25}} = \frac{4}{5}\) (positif dans le premier quadrant)

📌 #### \(\frac{4}{5}\)Question: An angel investor models the growth of two startups' valuations with $ f(x) = x^2 - 3x + m $ and $ g(x) = x^2 - 3x + 5m $. If $ f(2) = g(2) $, determine $ m $.

📌 Solution: Set $ f(2) = g(2) $. Compute $ f(2) = 4 - 6 + m = -2 + m $ and $ g(2) = 4 - 6 + 5m = -2 + 5m $. Equate: $ -2 + m = -2 + 5m $. Simplify: $ 0 = 4m $, so $ m = \boxed{0} $.

📌 Question: A chemist designs a catalyst where the reaction efficiency is modeled by $ h(x) = x^2 - 4x + m $. If the efficiency at $ x = 3 $ equals the efficiency of a second catalyst $ k(x) = x^2 - 4x + 2m $ at $ x = 1 $, find $ m $.

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