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Home » Volibear Counters Exposed: The Shocking Truth Behind This Hidden Feline Phenomenon! - Leaselab

Volibear Counters Exposed: The Shocking Truth Behind This Hidden Feline Phenomenon! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: In a city map, vectors $ \overrightarrow{OA} = \begin{bmatrix} 2 \\ 1 \end{bmatrix} $ and $ \overrightarrow{OB} = \begin{bmatrix} -1 \\ 3 \end{bmatrix} $ represent street segments. Find $ \overrightarrow{OC} $ such that $ \overrightarrow{OC} = 2\overrightarrow{OA} - 3\overrightarrow{OB} $.

📌 Solution: Compute $ 2\overrightarrow{OA} = \begin{bmatrix} 4 \\ 2 \end{bmatrix} $ and $ 3\overrightarrow{OB} = \begin{bmatrix} -3 \\ 9 \end{bmatrix} $. Subtract:

📌 \overrightarrow{OC} = \begin{bmatrix} 4 - (-3) \\ 2 - 9 \end{bmatrix} = \begin{bmatrix} 7 \\ -7 \end{bmatrix}.

📌 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.

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