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Home » Wildcat DC: The Untamed Truth Behind This Mysterious Urban Legend! - AMAZONAWS

Wildcat DC: The Untamed Truth Behind This Mysterious Urban Legend! - AMAZONAWS

Wildcat DC: The Untamed Truth Behind This Mysterious Urban Legend

📅 March 6, 2026 👤 scraface

Mar 06, 2026

Wildcat DC: The Untamed Truth Behind This Mysterious Urban Legend!

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📌 Let \(d\) be a positive divisor of 100. Then \(x = d\) and \(y = \frac{100}{d}\) is an integer. Since \(xy = 100\), both \((d, 100/d)\) and \((-d, -100/d)\) are solutions.

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📌 Solution: Assume $f$ is quadratic. Let $f(x) = px^2 + qx + r$. Substitute into the equation: $p(a + b)^2 + q(a + b) + r = pa^2 + qa + r + pb^2 + qb + r + ab$. Expand and equate coefficients: $p(a^2 + 2ab + b^2) + q(a + b) + r = pa^2 + pb^2 + q(a + b) + 2r + ab$. Simplify: $2pab = ab + 2r$. For this to hold for all $a, b$, we require $2p = 1$ and $2r = 0$, so $p = rac{1}{2}$, $r = 0$. The linear term $q$ cancels out, so $f(x) = rac{1}{2}x^2 + qx$. Verifying, $f(a + b) = rac{1}{2}(a + b)^2 + q(a + b) = rac{1}{2}a^2 + ab + rac{1}{2}b^2 + q(a + b)$, and $f(a) + f(b) + ab = rac{1}{2}a^2 + qa + rac{1}{2}b^2 + qb + ab$. The results match. Thus, all solutions are $f(x) = oxed{\dfrac{1}{2}x^2 + cx}$ for some constant $c \in \mathbb{R}$.Question: A conservation educator observes that the population of a rare bird species increases by a periodic pattern modeled by $ P(n) = n^2 + 3n + 5 $, where $ n $ is the year modulo 10. What is the remainder when $ P(1) + P(2) + \dots + P(10) $ is divided by 7?

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📌 So, the volume removed is \( 50\pi \) cubic meters, or approximately \( 157.08 \) cubic meters.

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