Advanced Math Archive: Questions from August 16, 2022
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Simplify \( \frac{(\cos \theta-i \sin \theta)^{2}(\cos 7 \theta+i \sin 7 \theta)^{-3}}{(\cos 4 \theta+i \sin 4 \theta)^{2}(\cos \theta+i \sin \theta)^{5}} \) using De Movier's Theorem.1 answer -
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Q1. Simplify \( \frac{(\cos \theta-i \sin \theta)^{2}(\cos 7 \theta+i \sin 7 \theta)^{-3}}{(\cos 4 \theta+i \sin 4 \theta)^{2}(\cos \theta+i \sin \theta)^{5}} \) using De Movier's Theorem.1 answer -
1. Simplify \( \frac{(\cos \theta-i \sin \theta)^{2}(\cos 7 \theta+i \sin 7 \theta)^{-3}}{(\cos 4 \theta+i \sin 4 \theta)^{2}(\cos \theta+i \sin \theta)^{5}} \) using De Movier's Theorem.1 answer -
1 answer
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a and m, both the questions please
2. Find the Laplace transform. (a) \( \int_{0}^{t} \sin a \tau \cos b(t-\tau) d \tau \) (b) \( \int_{0}^{t} e^{\tau} \sin a(t-\tau) d \tau \) (c) \( \int_{0}^{t} \sinh a \tau \cosh a(t-\tau) d \tau \)1 answer -
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\( \begin{aligned} x_{1}-2 x_{2}-4 x_{3} &=19 \\-x_{1}+3 x_{2}+6 x_{3} &=-29 \\-3 x_{1}+6 x_{2}+13 x_{3} &=-62 \\ x_{1}=\\ x_{2}=\end{aligned} \)1 answer