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70s color palette - Sourci

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📝 Recent Posts

5Question: Find the point on the line \(y = 2x + 3\) that is closest t...
Solution: To find the point on the line \(y = 2x + 3\) closest to \((1...
D = (x - 1)^2 + (2x + 3 + 1)^2 = (x - 1)^2 + (2x + 4)^2
Expanding:
D = (x^2 - 2x + 1) + (4x^2 + 16x + 16) = 5x^2 + 14x + 17
\(D' = 10x + 14\). Set to zero:
\(10x + 14 = 0 \Rightarrow x = -rac{7}{5}\)
Then \(y = 2(-rac{7}{5}) + 3 = -rac{14}{5} + rac{15}{5} = rac{1}{5...
Thus, the closest point is \(\left(-rac{7}{5}, rac{1}{5}
ight)\)

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