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Home » You Won’t Believe Where You Can Stream Pokémon Without Paying a Dime! - Carbonext

You Won’t Believe Where You Can Stream Pokémon Without Paying a Dime! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \boxed{36.00}

📌 Question: In a science experiment, a drone flies along the line $ \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 2 \\ -1 \end{pmatrix} + t \begin{pmatrix} 3 \\ 4 \end{pmatrix} $. Find the point on this line closest to $ (5, 7) $.

📌 Solution: The closest point occurs where the vector from $ (5, 7) $ to the line is perpendicular to the direction vector $ \begin{pmatrix} 3 \\ 4 \end{pmatrix} $. Let the point on the line be $ (2 + 3t, -1 + 4t) $. The vector from $ (5, 7) $ to this point is $ \begin{pmatrix} 2 + 3t - 5 \\ -1 + 4t - 7 \end{pmatrix} = \begin{pmatrix} -3 + 3t \\ -8 + 4t \end{pmatrix} $. Dot product with $ \begin{pmatrix} 3 \\ 4 \end{pmatrix} $ must be zero: $ 3(-3 + 3t) + 4(-8 + 4t) = 0 $. Simplify: $ -9 + 9t - 32 + 16t = 0 \Rightarrow 25t - 41 = 0 \Rightarrow t = \frac{41}{25} $. Substitute back: $ x = 2 + 3 \cdot \frac{41}{25} = \frac{173}{25} $, $ y = -1 + 4 \cdot \frac{41}{25} = \frac{156}{25} $.

📌 \boxed{\left( \dfrac{173}{25}, \dfrac{156}{25} \right)}

📌 Question: A medical imaging algorithm uses vectors $ \begin{pmatrix} x \\ 2 \end{pmatrix} $ and $ \begin{pmatrix} 3 \\ -1 \end{pmatrix} $ to detect anomalies. Find $ x $ so the vectors are orthogonal.

📌 Solution: Two vectors are orthogonal if their dot product is zero: $ x \cdot 3 + 2 \cdot (-1) = 0 $. Simplify: $ 3x - 2 = 0 \Rightarrow x = \frac{2}{3} $.

📌 \boxed{\dfrac{2}{3}}

📌 Question: A drug dosage model requires solving $ \log_2(x + 4) - \log_2(x - 1) = 3 $. Find the value of $ x $.

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