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Home » Since \( x \) is in the first quadrant, \( \cos(x) = \frac45 \). - Nelissen Grade advocaten

Since \( x \) is in the first quadrant, \( \cos(x) = \frac45 \). - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 We observe that the values increase linearly: $ f(x) = 15x $ fits all given points.

📌 Since $ f(x) $ is a cubic polynomial and agrees with a linear function at four points, and a cubic can only differ from a linear function by a cubic term that vanishes at those points, define:

📌 f(x) = 15x + k(x - 1)(x - 2)(x - 3)(x - 4)

📌 But since $ f(x) $ is only cubic, the quartic term must vanish, so $ k = 0 $. Therefore:

📌 f(x) = 15x

📌 f(5) = 15 \cdot 5 = \boxed{75}

📌 Question: A cartographer is analyzing a terrain modeled by the function $ h(x) = x^3 - 3x^2 + 2x $, and wants to find the sum of all $ x $-coordinates where the terrain has horizontal slope.

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