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Home » We have the quadratic model \( R(T) = aT^2 + bT + c \) with the conditions: - AMAZONAWS

We have the quadratic model \( R(T) = aT^2 + bT + c \) with the conditions: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 An oceanographer is studying the impacts of climate change on ocean currents and models the velocity \( v \) of a particular current in meters per second as a function of depth \( d \) in meters with the equation \( v(d) = ad + b \), where \( a \) and \( b \) are constants. Given that at a depth of 5 meters, the velocity is 3 m/s, and at 20 meters, it is 8 m/s, solve for \( a \) and \( b \).

📌 To solve for \( a \) and \( b \), we use the given conditions in the linear equation \( v(d) = ad + b \).

📌 Substitute \( d = 5 \) and \( v = 3 \) into the equation:

📌 Substitute \( d = 20 \) and \( v = 8 \) into the equation:

📌 5a + b &= 3 \quad \text{(Equation 1)} \\

📌 20a + b &= 8 \quad \text{(Equation 2)}

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