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Audio Amplifier Circuit Input: A sinusoidal input with $ =100 \mathrm{mV} $ and a frequency of $ 100 \mathrm{~Hz} $ - Calculate the gain $ (\mathrm{Vo} / \mathrm{Vin}) $ of this circuit. - Explain the working principle of the circuit. - Explain the reason why we use the capacitor $ \mathrm{C} 1 $ and resistor $ \mathrm{R} 1 $ at the output.

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Breanna Ollech

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Find a unit vector in the direction of the given vector. [ left[egin{array}{r} -12 \ 12 \ -6 end{array} ight] ] A. ( left[egin{array}{c}frac{2}{3} \ frac{2}{3} \ frac{1}{3}end{array} ight] ) B. ( left[egin{array}{r}-frac{2}{3} \ frac{2}{3} \ -frac{1}{3}end{array} ight] ) C. ( left[egin{array}{r}-frac{2}{sqrt{5}} \ frac{2}{sqrt{5}} \ -frac{1}{sqrt{5}}end{array} ight] ) D. ( left[egin{array}{r}-frac{2}{9} \ frac{2}{9} \ -frac{1}{9}end{array} ight] )

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Breanna Ollech

Numerade educator

Determine if the following vectors are orthogonal. [ mathbf{u}=left[egin{array}{r} 12 \ 5 \ 1 end{array} ight], mathbf{v}=left[egin{array}{r} 2 \ -5 \ 1 end{array} ight] ] Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a simplified fraction.) A. The vectors ( mathbf{u} ) and ( mathbf{v} ) are orthogonal because ( mathbf{u}+mathbf{v}=square ). B. The vectors ( mathbf{u} ) and ( mathbf{v} ) are orthogonal because ( mathbf{u} cdot mathbf{v}=square ). C. The vectors ( mathbf{u} ) and ( mathbf{v} ) are not orthogonal because ( mathbf{u}+mathbf{v}=square ). D. The vectors ( mathbf{u} ) and ( mathbf{v} ) are not orthogonal because ( mathbf{u} cdot mathbf{v}=square ).

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need help pleas.e

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Diagonalize the matrix $ A $, if possible. That is, find an invertible matrix $ P $ and a diagonal matrix $ D $ such that $ A=P D P^{-1} $. \[ A=\left[\begin{array}{rrr} 1 & 1 & 4 \\ 0 & -4 & 0 \\ -5 & -1 & -8 \end{array}\right] \] A. Not diagonalizable $ P=\left[\begin{array}{rrr}1 & 0 & -1 \\ 0 & -4 & 0 \\ 1 & 1 & 1\end{array}\right], D=\left[\begin{array}{rrr}-4 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -3\end{array}\right] $ $ P=\left[\begin{array}{rrr}-4 & -1 & -1 \\ 0 & 5 & 0 \\ 5 & 0 & 1\end{array}\right], D=\left[\begin{array}{rrr}-4 & 0 & 0 \\ 0 & -4 & 0 \\ 0 & 0 & -3\end{array}\right] $ $ P=\left[\begin{array}{rrr}1 & -9 & -1 \\ -9 & -4 & 0 \\ 1 & -4 & 1\end{array}\right], D=\left[\begin{array}{rrr}-4 & 1 & 0 \\ 0 & -4 & 0 \\ 0 & 0 & -3\end{array}\right] $

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Breanna Ollech

Numerade educator

Find the eigenvalues of the given matrix. [ left[egin{array}{rr} -78 & -20 \ 300 & 77 end{array} ight] ] A. 3 B. ( -3,2 ) C. ( 3,-2 ) D. 2

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For the given matrix $ \mathrm{A} $, find a basis for the corresponding eigenspace for the given eigenvalue. \[ A=\left[\begin{array}{rrr} 25 & 16 & 16 \\ -32 & -23 & -16 \\ -16 & -8 & -15 \end{array}\right], \lambda=-7 \] A. $ \left\{\left[\begin{array}{r}0 \\ 1 \\ -1\end{array}\right]\right\} $ B. $ \left\{\left[\begin{array}{l}1 \\ 0 \\ 2\end{array}\right],\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]\right\} $ c. $ \left\{\left[\begin{array}{l}1 \\ 0 \\ 2\end{array}\right]\right\} $ D. $ \left\{\left[\begin{array}{r}1 \\ -2 \\ 0\end{array}\right],\left[\begin{array}{r}1 \\ 0 \\ -2\end{array}\right]\right\} $

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Audio Amplifier Circuit Input: A sinusoidal input with $ =100 \mathrm{mV} $ and a frequency of $ 100 \mathrm{~Hz} $ Project Report - Calculate the gain $ (\mathrm{Vo} / \mathrm{Vin}) $ of this circuit. - Explain the working principle of the circuit. - Explain the reason why we use the capacitor $ \mathrm{C} 1 $ and resistor $ \mathrm{R} 1 $ at the output. - Provide your PCB layout for this circuit on $ \mathrm{KiCAD} $.

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Breanna Ollech

Numerade educator

7. (4.24) A man is planning to retire in 20 years. He can deposit money for his retirement at 8% compounded monthly. It is estimated that the future general inflation (f?) rate will be 3% compounded monthly. What deposit, in terms of constant dollars, must be made each month until the man retires so that he can make annual withdrawals of $20,000, in terms of actual dollars, over the 15 years following his retirement? (Assume that his first withdrawal occurs at the end of the first year after his retirement.)

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ahmet