Advanced Math Archive: Questions from November 18, 2022
-
1. Solve the initial value problem \[ \mathbf{y}^{\prime}=\left[\begin{array}{ccc} -1 & 4 & 2 \\ -2 & 5 & 2 \\ 1 & -2 & 0 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c} 7 \\2 answers -
Simplify the expressions
\( \sin ^{2} x+\cos ^{2} x+1= \) \( 1-\left(\sec ^{2} x-\tan ^{2} x\right)= \) \( \csc ^{2} x-1= \) \( 1-\sin ^{2} x= \) \( \frac{\tan ^{2} x}{\sec x-1}= \) \( \frac{\tan ^{2} x}{\sec x+1}= \) \( -\le2 answers -
Simplify the expressions
\( \frac{\sin ^{2}}{1+\cos x}= \) \( 1+\tan ^{2} x= \) \( \csc ^{2} x-\cot ^{2} x= \) \( \frac{\cos ^{2} x}{1+\sin x}= \) \( \frac{\sin x+\cos x}{\sin x \cos x}= \) \( \frac{\cot ^{2} x}{\csc x-1}= \)2 answers -
\( y=\frac{8 x^{3}-5}{2 x^{2}-7 x+6} \) \( y=\frac{7 x^{3}-2}{4 x^{3}-4 x^{2}+x} \) \( y=\frac{9-x}{x^{3}-x} \) 1. \( [6 \) points each] Find all asymptotes (horizontal, vertical, and oblique) of the1 answer -
Solve the initial value problem \[ \mathbf{y}^{\prime}=\left[\begin{array}{ccc} -1 & 4 & 2 \\ -2 & 5 & 2 \\ 1 & -2 & 0 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c} 7 \\ 51 answer -
For the circuit in the figure, determine the Zi input impedance, the Zo output impedance and the Ay voltage gain for the next circuit. Consider ß = 140 and ro = 30k.
2.- Para el circuito de la figura, determinar la impedancia de entrada \( Z_{i} \), la impedancia de salida \( Z_{o} \) y la ganancia de voltaje \( A_{V} \) para el siguiente circuito. Considere \( \b0 answers -
1.- Para el circuito de la figura determinar \( V_{C}, I_{E} \) considere que \( I_{E} \approx I_{C} \). (20 puntos)2 answers -
2. (a) Solve the DE \( y^{\prime \prime}=2 y y^{\prime} \). (b) Solve the IVP \( y y^{\prime \prime}+3\left(y^{\prime}\right)^{2}=0, y(0)=1, y^{\prime}(0)=6 \). (c) Solve the system of linear DEs \( x2 answers -
i need help for all
Evalúe las siguientes integrales: 1. \( \int \frac{d x}{x^{2} \sqrt{9-x^{2}}} \) 2. \( \int \frac{\sqrt{x^{2}-3}}{x} d x \) 3. \( \int_{0}^{3} \frac{x^{3}}{\sqrt{x^{2}+9}} d x \) 4. \( \int \frac{d x2 answers -
\[ S=\left\{(x, y) / x \leq 1,0 \leq y \leq e^{x}\right\} \] Explique en sus propias palabras su procedimiento para resolver la integral impropia. Comparta sus resultados con sus compañeros de clases2 answers -
Maximize \( p=8 x_{1}+2 x_{2}-x_{3} \) Subsect \( x_{1}+x_{2}-x_{3} \leq 5 \) \[ \text { to } \begin{array}{l} 2 x_{1}+4 x_{2}+3 x_{3} \leq 15 \\ \quad x_{1}, x_{2}, x_{3} \geq 0 \end{array} \]2 answers -
Help please urgent
3. Demuestre las dos siguientes afirmaciones usando diferentes métodos de demostración. El universo son los números enteros. For every \( x>0 \) there exists an even number \( m \), such that \( m>2 answers -
Solve the following initial value problems
Resuelve los siguientes Problemas de Valor Inicial a) [7 pts.] \( x^{2} \frac{d y}{d x}=y(1-x) ; y(-1)=-1 \). b) \( [\mathbf{1 1} \mathbf{p t s}] x \frac{d y}{d x}+y=4 x+1 ; y(1)=8 \).2 answers -
check if the D.E. is exact, and if it is solve it
2. [9 pts.] Verifica si la E.D. \( \left(y^{2} \cos x-3 x^{2} y-2 x\right) d x+\left(2 y \sin x-x^{3}+\ln y\right) d y=0 \) es exacta, y de ser así resuélvela.2 answers -
Let \( \vec{x}=\left[\begin{array}{c}2 \\ -3 \\ -5\end{array}\right] \) and \( \vec{y}=\left[\begin{array}{c}-2 \\ 5 \\ -3\end{array}\right] \). Then \( \vec{x} \cdot \vec{y}= \)2 answers -
Find the solution to the following diferential ecuation
[8 pts.] Halla la solución de las siguientes ecuación diferencial \( \frac{d y}{d x}=1+e^{y-x+5} \).2 answers -
Multiply \( \left[\begin{array}{c}-2 \\ 7\end{array}\right]\left[\begin{array}{ll}-3 & 2\end{array}\right] \) if possible. If not possible, enter DNE.2 answers -
\( x^{\prime}-y^{\prime}=\operatorname{sen}(t) u(t-\pi),-x=y^{\prime} ; x(0)=y(0)=1 \) \( u(t-\pi)=\left\{\begin{array}{l}0,0 \leq t \leq \pi \\ 1, t>1\end{array}\right. \)2 answers -
(a) Determine whether \( (x-y) \mid\left(x^{n}-y^{n}\right), \forall n \in \mathbf{Z}^{+} \)and \( x, y \in \mathbf{Z}, x \neq y \). (b) Determine whether \( 6 \mid\left(n^{3}-n\right) \), for each in2 answers -
a. Let the set \( A, B, C \) and \( D \) be: \[ \begin{array}{l} A=\left\{(x, y) \in \mathbb{Q}^{2} \mid y=x^{2}\right\} \\ B=\left\{(x, y) \in \mathbb{Q}^{2} \mid y=x+2\right\} \\ C=\left\{(x, y) \in2 answers -
1 (e and g) and 2b
1. Use the Laplace transform to find the solution of the IVP. a) \( 2 y^{\prime}+y=1, \quad y(0)=2 \) b) \( 3 y^{\prime}=-y+e^{-t}, \quad y(0)=\frac{1}{2} \) c) \( y^{\prime \prime}+y^{\prime}-2 y=0,2 answers -
2 answers