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how many cups are in a liter - IQnection

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Lets define $ d(x) = h(x+1) - h(x) = px + q $. Since $ h $ is quadratic, $ d(x) $ is linear. We know $ d(2024) = h(2025) - h(2024) = 2025 - 2024 = 1 $. Also, $ d(2025) = h(2026) - h(2025) $.

📌 Now, since $ d(x) $ is linear, we need another condition. But we only have two point evaluations and the form. However, we can express $ h(x) $ in terms of finite differences. For a quadratic polynomial, the second difference is constant:

📌 But we only have $ h(2024) = 2024 $, $ h(2025) = 2025 $. Compute $ h(2026) = h(2025) + d(2025) = 2025 + (2a(2025) + a + b) $

📌 But from $ d(x) = 2a x + (a + b) $, and $ d(2024) = 1 $. We need $ d(2025) = 2a(2025) + a + b $. Express in terms of knowns.

📌 Then $ d(2025) = 2a(2025) + a + (1 - 4049a) = 4050a + a + 1 - 4049a = (4050a + a - 4049a) + 1 = 2a + 1 $

📌 So $ h(2026) = h(2025) + d(2025) = 2025 + (2a + 1) = 2026 + 2a $

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