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Home » Thus, the number of distinct seating arrangements is: - DNSFLEX

Thus, the number of distinct seating arrangements is: - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 A mammalogist is studying the diving behavior of a species of dolphin. The depth \( D(t) \) in meters that a dolphin reaches after \( t \) seconds is modeled by \( D(t) = pt^3 + qt^2 + rt + s \). Given \( D(1) = 3 \), \( D(2) = 14 \), \( D(3) = 39 \), and \( D(4) = 84 \), find the coefficients \( p \), \( q \), \( r \), and \( s \).

📌 We are given \( D(t) = pt^3 + qt^2 + rt + s \) with:

📌 \( D(1) = p + q + r + s = 3 \)

📌 \( D(2) = 8p + 4q + 2r + s = 14 \)

📌 \( D(3) = 27p + 9q + 3r + s = 39 \)

📌 \( D(4) = 64p + 16q + 4r + s = 84 \)

📌 We solve this system step by step.

📌 Subtract equation (1) from (2):

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