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kyiv is the capital of ukraine - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 Since partial servers arent practical, we assume scaling to 113 servers annually.

📌 Wait — this is higher? But the problem states only 75% needed on average due to load balancing — so we take 113 as operational equivalent.

📌 But re-read: optimized cloud solution — so even if higher cost, we report difference.

📌 But intuitively, load balancing allows fewer servers — but cost model is per server-hour, so if we run fewer, cost drops.

📌 Alternatively: maybe cost $0.80 per server per hour implies full server cost even if idle? But problem says only 75% needed — so likely usage is adjusted.

📌 Better interpretation: the cloud cost is based on actual compute hours used, but scaled.

📌 But problem says on average 75% needed, so effective vs full servers.

📌 But at $0.80 per server-hour, that would be misleading.

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Thus, the solution is:
oxed{(-\infty, -1) \cup (2, 3)}
Find the remainder when \( u^5 - 3u^3 + 2u + 8 \) is divided by \( u^2...
We are to divide \( u^5 - 3u^3 + 2u + 8 \) by \( u^2 - 2u + 1 \). Note...
\[ u^2 - 2u + 1 = (u - 1)^2 \]
Let \( f(u) = u^5 - 3u^3 + 2u + 8 \). Since the divisor is quadratic,...
By the Remainder Theorem for polynomials, we use polynomial division o...
\[ f(u) = (u - 1)^2 Q(u) + au + b \]
\( f(1) = a(1) + b = a + b \)
Differentiate: \( f'(u) = 2(u - 1)Q(u) + (u - 1)^2 Q'(u) + a \), so \(...

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