Subjects algebra

Piecewise Function E08691

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Piecewise Function E08691


1. **Stating the problem:** We have a piecewise function $$f(x) = \begin{cases} x & 0 < x < 2.5 \\ 5 - x & 2.5 < x < 5 \end{cases}$$ and some variables: $$49\cdot4x = u +$$ (incomplete), with $$u = ?$$, $$l = 5$$, $$x = 2$$, $$t = 20$$, and $$n = 4$$. 2. **Interpreting the problem:** Since the equation $$49\cdot4x = u +$$ is incomplete, we focus on evaluating $$u$$ using the given values and the function. 3. **Evaluating the function at $$x=2$$:** Since $$0 < 2 < 2.5$$, we use $$f(x) = x$$. 4. **Calculate $$f(2)$$:** $$f(2) = 2$$. 5. **Calculate $$49 \cdot 4x$$ at $$x=2$$:** $$49 \cdot 4 \cdot 2 = 49 \cdot 8 = 392$$. 6. **Assuming $$u$$ is the sum of $$49 \cdot 4x$$ and $$f(x)$$ at $$x=2$$:** $$u = 392 + 2 = 394$$. 7. **Summary:** Given the incomplete equation, the best interpretation is $$u = 394$$ when $$x=2$$. **Final answer:** $$u = 394$$