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Home » CorrectQuestion: In propositional logic, which of the following is a tautology? - Sterling Industries

CorrectQuestion: In propositional logic, which of the following is a tautology? - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Average value over one period:

📌 The average value of a sine function \( a \sin(bx + c) + d \) over one period is \( d \), so:

📌 \[ d = 3 \]

📌 Substitute \( d = 3 \) into the equations:

📌 \[ a \sin(c) + 3 = 2 \quad \Rightarrow \quad a \sin(c) = -1 \]

📌 \[ a \cos(c) + 3 = 4 \quad \Rightarrow \quad a \cos(c) = 1 \]

📌 Square and add the equations:

📌 \[ (a \sin(c))^2 + (a \cos(c))^2 = (-1)^2 + 1^2 \]

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Same as before.
\( x = 240 / 6.1051 \approx 39.32 \)
Since the model allows decimals in intermediate steps, but gestures ar...
#### 39.32
But to match format, report precise value as per calculation.
Wait — better: use exact fraction.
\( 1.1 = 11/10 \), so \( r = 11/10 \)
\( r^5 = (11/10)^5 = 161051 / 100000 = 1.61051 \)
Sum = \( \frac{1 - 1.61051}{1 - 1.1} = \frac{-0.61051}{-0.1} = 6.1051...
So \( x = 240 / 6.1051 = 24000000 / 610510 ≈ 3932 / 100.051 ≈ 39.32 \)...

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