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Home » \[ s = ut + \frac12at^2 \] - AMAZONAWS

\[ s = ut + \frac12at^2 \] - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Divide by 10:

📌 Thus, the value of \( x \) is \(\boxed{6.2}\).

📌 Question:** A soil scientist is modeling pH levels in a series of soil samples, where the values follow an arithmetic sequence starting at 2, with a common difference of 3. How many terms are there before the value exceeds 100?

📌 Solution:** The sequence is defined by:

📌 a_n = 2 + (n - 1) \cdot 3

📌 We want the largest integer \( n \) such that:

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\(n(n+1) = 10100\).
\(n^2 + n - 10100 = 0\).
Using quadratic formula: \(n = \frac{-1 \pm \sqrt{1 + 40400}}{2}\).
\(n = \frac{-1 \pm 201}{2}\).
\(n = \frac{200}{2} = 100\).
A bank offers an interest rate of 5% compounded annually. How much wil...
Future value: \(FV = P(1 + r)^t\).
\(FV = 1000(1 + 0.05)^3\).
\(= 1000 \times 1.157625 = 1157.63\).
A ladder 10 meters long leans against a wall, forming a 60-degree angl...

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