So again, contradiction.
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- Therefore, the only consistent assumption is that the sequence is symmetric: $a - 2d, a - d, a, a + d, a + 2d$
- Second + Fourth = $2a = 10 \Rightarrow a = 5$
- Contradiction again. So the only way this works is if the sequence is not symmetric.
- So the only way to resolve this is to define theQuestion: A chemical engineer models the concentration of a reactant in a reactor over time with the function $ C(t) = rac{3t + 2}{t^2 + 4} $. For what values of $ t $ is the concentration increasing?
- Solution: To determine when the concentration is increasing, we analyze the derivative of $ C(t) $. Using the quotient rule:
- C'(t) = rac{(3)(t^2 + 4) - (3t + 2)(2t)}{(t^2 + 4)^2}
