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Home » Differentiate \(y = \sin(3x)\) with respect to \(x\). - DNSFLEX

Differentiate \(y = \sin(3x)\) with respect to \(x\). - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Common difference $ d = 2 $

📌 Last term $ l = 1099 $

📌 n = \frac{1099 - 1001}{2} + 1 = \frac{98}{2} + 1 = 49 + 1 = 50

📌 Sum of arithmetic series:

📌 S = \frac{n}{2}(a + l) = \frac{50}{2}(1001 + 1099) = 25 \cdot 2100 = 52500

📌 Now compute $ 52500 \mod 16 $.

📌 Note that $ 16 = 2^4 $. We can compute $ 52500 \div 16 $, or use modular arithmetic:

📌 First, $ 1000 \equiv 8 \pmod{16} $, so $ 5000 = 5 \cdot 1000 \equiv 5 \cdot 8 = 40 \equiv 8 \pmod{16} $ (since $ 40 - 2 \cdot 16 = 8 $)

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