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Home » A circle's circumference is 31.4 cm. Find the area of the circle. - Appcentric

A circle's circumference is 31.4 cm. Find the area of the circle. - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 This formula arises from known results in triangular lattice geometry: the number of interior points in a triangle of side $n$ is $\frac{n(n-2)(n-1)}{6}$, or equivalently $\frac{(n-1)(n-2)}{2}$.

📌 Thus, the number of interior lattice points is $ \boxed{10} $.Question: Compute the sum of the roots of the equation

📌 u\sqrt{u} - 5u + 6\sqrt{u} = 0,

📌 given that all of the roots are real and nonnegative.

📌 Solution: Let us make the substitution $ x = \sqrt{u} $, so that $ u = x^2 $. Substituting into the equation gives:

📌 x^2 \cdot x - 5x^2 + 6x = 0 \quad \Rightarrow \quad x^3 - 5x^2 + 6x = 0.

📌 Factor out $ x $:

📌 x(x^2 - 5x + 6) = 0.

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