To evaluate the expression \( u^2 + v - 6.7 \) for \( u = 6 \) and \( v = 2 \), we start by substituting the values of \( u \) and \( v \) into the expression.
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Calculate \( u^2 \): \[ u^2 = 6^2 = 36 \]
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Substitute \( u^2 \) and \( v \) into the expression: \[ u^2 + v - 6.7 = 36 + 2 - 6.7 \]
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Now perform the addition and subtraction: \[ 36 + 2 = 38 \] \[ 38 - 6.7 = 31.3 \]
Thus, the value of the expression is \( \boxed{31.3} \).