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📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 #### 10**Question:

📌 A seismologist is modeling the intensity of ground shaking using the function \( I(t) = 5\sin(t) + 3\cos(t) \). Determine the maximum intensity of ground shaking.

📌 To find the maximum intensity of the function \( I(t) = 5\sin(t) + 3\cos(t) \), we can express it in the form \( R\sin(t + \alpha) \).

📌 First, find \( R \) using the formula:

📌 R = \sqrt{a^2 + b^2} = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}

📌 The maximum value of \( R\sin(t + \alpha) \) is \( R \). Therefore, the maximum intensity is:

📌 \boxed{\sqrt{34}}

📌 A statistics analyst is evaluating the performance of a player whose score over a series of games follows the pattern \( S(n) = 2n^2 + 3n + 1 \). Determine the score difference between the 5th and 3rd games.

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