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📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📝 Recent Posts

oxed{ ext{A sphere of radius } \dfrac{3c}{2} ext{ centered at } \lef...
Question: Find the point on the line \(y = 2x + 1\) in the plane that...
Solution: We minimize the distance from a point \((x, 2x+1)\) on the l...
D = (x - 4)^2 + (2x + 1 - 3)^2 = (x - 4)^2 + (2x - 2)^2.
D = (x^2 - 8x + 16) + (4x^2 - 8x + 4) = 5x^2 - 16x + 20.
rac{dD}{dx} = 10x - 16 = 0 \Rightarrow x = rac{8}{5}.
Then $y = 2\left(rac{8}{5}
ight) + 1 = rac{16}{5} + rac{5}{5} = rac{21}{5}$.
Thus, the closest point is $\left(rac{8}{5}, rac{21}{5}
oxed{\left( \dfrac{8}{5},\ \dfrac{21}{5}

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