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Home » Wait — perhaps three consecutive odd integers? But not specified. - Dachbleche24

Wait — perhaps three consecutive odd integers? But not specified. - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Second + Fourth = $2a = 10 \Rightarrow a = 5$

📌 Contradiction again. So the only way this works is if the sequence is not symmetric.

📌 So again, contradiction.

📌 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}

📌 3(t^2 + 4) - 2t(3t + 2) = 3t^2 + 12 - (6t^2 + 4t) = -3t^2 - 4t + 12

📌 C'(t) = rac{-3t^2 - 4t + 12}{(t^2 + 4)^2}

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But earlier steps suggest $ S = rac{2(a^2 + b^2)}{a^2 - b^2} $. For $...
S = rac{2(e^{2i heta} + e^{2i\phi})}{e^{2i heta} - e^{2i\phi}} = 2 \c...
Multiply numerator and denominator by $ e^{-i( heta + \phi)/2} $:
S = 2i \cdot rac{e^{i( heta - \phi)/2} + e^{-i( heta - \phi)/2}}{e^{i...
ight)}{2i\sin\left(rac{ heta - \phi}{2}
ight)} = -2 \cot\left(rac{ heta - \phi}{2}
eq b $ implies $ heta
eq \phi $, so $ S $ is purely imaginary. However, the original questio...
Let $ S = rac{(a + b)^2 + (a - b)^2}{a^2 - b^2} = rac{2a^2 + 2b^2}{a...
S = rac{2(1 + (-1))}{1 - (-1)} = 0, ext{ but } a^2 - b^2 = 1 - (-1)...

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