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Home » Get Ready to Relive These NES Games Guaranteed to Top the Charts! - Leaselab

Get Ready to Relive These NES Games Guaranteed to Top the Charts! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 The vector is $ \boxed{\begin{bmatrix} 7 \\ -7 \end{bmatrix}} $.Question: A volcanologist models the amplitude of seismic waves using the function $ f(x) = \sin^2 x + 2\cos x $. Find the range of $ f(x) $ as $ x $ ranges over all real numbers.

📌 Solution: Start by using the identity $ \sin^2 x = 1 - \cos^2 x $ to rewrite $ f(x) $:

📌 f(x) = 1 - \cos^2 x + 2\cos x = -\cos^2 x + 2\cos x + 1.

📌 Let $ y = \cos x $, where $ y \in [-1, 1] $. The function becomes:

📌 f(y) = -y^2 + 2y + 1.

📌 This is a quadratic opening downward. Its maximum occurs at the vertex $ y = \frac{-b}{2a} = \frac{-2}{-2} = 1 $. Evaluating at $ y = 1 $:

📌 f(1) = -1 + 2 + 1 = 2.

📌 Evaluate at $ y = -1 $:

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