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This gives two potential solutions:\[ t = \frac{-3 + 282.8}{2} \approx 139.9 \]\[ t = \frac{-3 - 282.8}{2} \approx -142.9 \]Since time cannot be negative, the valid solution is:\(\boxed{139.9}\)A programmer is optimizing a neural network and models the loss function as \( L(x) = 2x^2 - 8x + k \). Find \( k \) if the minimum loss occurs at \( x = 2 \) and the loss there is 4.The vertex form of a quadratic function \( ax^2 + bx + c \) occurs at \( x = -\frac{b}{2a} \). For \( L(x) = 2x^2 - 8x + k \),\[ a = 2, \, b = -8 \]\[ x_{vertex} = -\frac{-8}{2 \times 2} = 2 \]The minimum loss occurs at \( x = 2 \), and \( L(2) = 4 \). Substitute \( x = 2 \) into \( L(x) \):