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📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 \[ r = rac{31.4159}{2 imes 3.14159} = rac{31.4159}{6.28318} pprox 5 \]

📌 Calculate the derivative of the function \(f(x) = 4x^3 - 5x^2 + 2x - 7\).

📌 Derivative:

📌 \[ f'(x) = 12x^2 - 10x + 2 \]

📌 If a geometric sequence has a first term of 5 and a common ratio of 3, what is the 4th term?

📌 The \(n\)-th term of a geometric sequence is given by \(a_n = a \cdot r^{n-1}\).

📌 Substitute \(a = 5\), \(r = 3\), and \(n = 4\):

📌 \[ a_4 = 5 \cdot 3^{4-1} = 5 \cdot 3^3 = 5 \cdot 27 = 135 \]

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