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Home » Substitute \(a = 2\) into the equation \(a(a+b) = 2a + 3b\): - go-checkin.com

Substitute \(a = 2\) into the equation \(a(a+b) = 2a + 3b\): - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Divide by 3:

📌 n - 1 < \frac{98}{3} \approx 32.666\ldots

📌 n < 33.666\ldots

📌 The largest integer \( n \) satisfying this is \( n = 33 \). Verify:

📌 a_{33} = 2 + 32 \cdot 3 = 2 + 96 = 98 < 100

📌 a_{34} = 2 + 33 \cdot 3 = 101 > 100

📌 Thus, there are \(\boxed{33}\) terms before the value exceeds 100.

📌 Question:** The mechanical engineer is calibrating sensors placed at positions \( y \) such that \( y \) is a positive multiple of 5 and \( y^3 < 12000 \). What is the largest possible value of \( y \)?

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