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Home » Drumroll, Please: You’re About to Learn Exactly How Many Calories Are in a Donut! - Carbonext

Drumroll, Please: You’re About to Learn Exactly How Many Calories Are in a Donut! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📝 Recent Posts

\boxed{\dfrac{5}{3}x^6 - 5x^4 + \dfrac{50}{3}x^2 - 18}.
$$Question: A particle physicist models the trajectory of a neutrino t...
Solution: To find the point on the line $ y = \frac{3}{4}x + 2 $ close...
D(x) = x^2 + \left( \frac{3}{4}x + 2 \right)^2
D(x) = x^2 + \frac{9}{16}x^2 + 3x + 4 = \frac{25}{16}x^2 + 3x + 4
D'(x) = \frac{50}{16}x + 3 = \frac{25}{8}x + 3 = 0 \Rightarrow x = -\f...
Substitute into the line equation to find $ y $:
y = \frac{3}{4} \cdot \left( -\frac{24}{25} \right) + 2 = -\frac{18}{2...
Thus, the closest point is $ \left( -\frac{24}{25}, \frac{32}{25} \rig...
\boxed{\left( -\frac{24}{25}, \frac{32}{25} \right)}

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