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Home » Since $ abc = 1 $, we can assume $ a = racxy $, $ b = racyz $, $ c = raczx $, and by AM-GM, - Crosslake

Since $ abc = 1 $, we can assume $ a = racxy $, $ b = racyz $, $ c = raczx $, and by AM-GM, - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \boxed{k = 15, \, m = -15, \, n = 120}

📌 Question:** In a machine learning model, the cost function is given by \( C(w) = pw^2 + qw + r \). If \( C(1) = 10 \), \( C(2) = 18 \), and \( C(3) = 30 \), find the parameters \( p \), \( q \), and \( r \).

📌 We have the equations:

📌 \( p(1)^2 + q(1) + r = 10 \implies p + q + r = 10 \)

📌 \( p(2)^2 + q(2) + r = 18 \implies 4p + 2q + r = 18 \)

📌 \( p(3)^2 + q(3) + r = 30 \implies 9p + 3q + r = 30 \)

📌 p + q + r &= 10 \quad \text{(1)}\\

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