To solve for \( k \) in the equation \( c = \frac{1}{2}kv \), we can follow these steps:
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Start with the original equation: \[ c = \frac{1}{2}kv \]
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Multiply both sides of the equation by 2 to eliminate the fraction: \[ 2c = kv \]
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Now, divide both sides by \( v \) to isolate \( k \): \[ k = \frac{2c}{v} \]
Thus, the solution for \( k \) is: \[ k = \frac{2c}{v} \]