= 5a + b

February 22, 2026

= 5a + b

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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:
= 20a + b
5a + b &= 3 \quad \text{(Equation 1)} \\

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