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Home » First, compute the dot product $\mathbfu \cdot \mathbfv$: - Coaching Toolbox

First, compute the dot product $\mathbfu \cdot \mathbfv$: - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A programmer is optimizing an AI algorithm's performance. Given two functions representing processing time: \( f(x) = 4x - 5 \) and \( g(x) = x^2 + 2 \), find \( g(f(3)) \).

📌 f(3) = 4(3) - 5 = 12 - 5 = 7

📌 Now substitute into \( g(x) \):

📌 g(f(3)) = g(7) = 7^2 + 2 = 49 + 2 = 51

📌 An ethics researcher is modeling AI decision accuracy. Find the \( y \)-intercept of the line passing through the points \( (2, 5) \) and \( (4, 9) \).

📌 First, find the slope \( m \):

📌 m = rac{9 - 5}{4 - 2} = rac{4}{2} = 2

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