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Home » Longest piece: \( 5 \times 1.5 = 7.5 \) - Silent Sales Machine

Longest piece: \( 5 \times 1.5 = 7.5 \) - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Solution: Let $ y = x^2 - 1 $. Then $ x^2 = y + 1 $. Substitute into $...
x^4 = (x^2)^2 = (y + 1)^2 = y^2 + 2y + 1.
g(y) = 2(y^2 + 2y + 1) - 5(y + 1) + 1 = 2y^2 + 4y + 2 - 5y - 5 + 1 = 2...
Now, substitute $ y = x^2 + 1 $ to find $ g(x^2 + 1) $:
g(x^2 + 1) = 2(x^2 + 1)^2 - (x^2 + 1) - 2 = 2x^4 + 4x^2 + 2 - x^2 - 1...
The final answer is $ \boxed{2x^4 + 3x^2 - 1} $.
Question: An angel investor analyzes a medical startup's growth, model...
Solution: Let $ y = x^2 + 2 $. Then $ x^2 = y - 2 $. Express $ g(y) $...
g(y) = 3x^6 - 4x^4 + 5x^2 - 2 = 3(x^2)^3 - 4(x^2)^2 + 5x^2 - 2 = 3(y -...
3(y^3 - 6y^2 + 12y - 8) - 4(y^2 - 4y + 4) + 5y - 10 - 2 = 3y^3 - 18y^2...

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