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Home » We are to partition 7 distinguishable species into 3 - Crankk.io

We are to partition 7 distinguishable species into 3 - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \( \log_2(x(x - 2)) = 3 \) → \( x(x - 2) = 2^3 = 8 \).

📌 \( x^2 - 2x - 8 = 0 \) → \( (x - 4)(x + 2) = 0 \).

📌 \( x = 4 \) (since \( x > 2 \) for log to be defined).

📌 The graph of \( y = a \cdot 2^x \) passes through the points $ (0, 3) $ and $ (2, 12) $. Find \( a \).

📌 At \( x = 0 \): \( y = a \cdot 2^0 = a = 3 \).

📌 Check with \( x = 2 \): \( y = 3 \cdot 2^2 = 12 \), which matches.

📌 So \( a = 3 \).

📌 What is the remainder when \( x^4 - 3x^2 + 2x + 5 \) is divided by \( x - 1 \)?

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