Advanced Math Archive: Questions from November 08, 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 -
\( \begin{array}{ll}(\sin x)^{\prime}=\cos x & (\cos x)^{\prime}=-\sin x \\ (\tan x)^{\prime}=\sec ^{2} x & (\cot x)^{\prime}=-\csc ^{2} x \\ (\sec x)^{\prime}=\sec x \cdot \tan x & (\csc x)^{\prime}=0 answers -
LAPLACE Transform
e) \( y^{\prime \prime}+10 y=\delta(t-2 \pi) \quad y(0)=0 \quad y^{\prime}(0)=1 \) g) \( y^{\prime \prime}+9 y=3 \delta(t-4)+9 u_{7}(t) \quad y(0)=0 \quad y^{\prime}(0)=7 \)2 answers -
(1 point) Calculate all four second-order partial derivatives of \( f(x, y)=(4 x+4 y) e^{y} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y) \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y) \]2 answers -
Sea \( X_{1}, X_{2}, \ldots, X_{n} \) una muestra aleatoria de una distribución \( \operatorname{Ber}(\theta) \), \( \operatorname{con} \theta \) desconocido. Se define la función parametral \( h(\t0 answers -
10, 43, 52, 54 please.
1-54 Use the guidelines of this section to sketch the curve. 1. \( y=x^{3}+3 x^{2} \) 2. \( y=2+3 x^{2}-x^{3} \) 11. \( y=\frac{x-x^{2}}{2-3 x+x^{2}} \) 12. \( y=1+\frac{1}{x}+\frac{1}{x^{2}} \) 3. \(2 answers -
Solve: \[ \begin{array}{l} y^{\prime \prime}+2 y^{\prime}-3 y=-9 t+18 \\ y(0)=-9, y^{\prime}(0)=2 \end{array} \]2 answers -
Problem 6. Find \( d x d z d y \) and \( d y d z d x \). \[ \int_{0}^{2} \int_{0}^{-3 z+12} \int_{0}^{4-y^{2}} f(x, y, z) d x d y d z \]2 answers -
Considering the block diagram, determine the arrangement of the Routh-Huwirtz Criterion and the value of the gain K that it locates at the closed-loop poles as shown in the complex plane S
Considerando el diagrama a bloques, determine el arreglo del Criterio de Routh-Hurwitz y el valor de la ganancia k que ubique los polos de lazo cerrado como se muestra en el plano complejo 5 \( s^{\we0 answers -
Decide which of the following maps are linear:
E.1 Decidir cuáles de las siguientes aplicaciones son lineales: (a) \( M_{B}: \mathcal{M}_{2 \times 2}(\mathbb{R}) \rightarrow \mathcal{M}_{2 \times 1}(\mathbb{R}) \) dada por \( M_{B}(A)=A B \) con2 answers -
6.2.3 La banda lateral superior de una señal de AM (DSB-LC) con modulación senoidal e indice de modulación \( m \) se maltiplica por un factor \( \alpha \), donde: \( 0 \leq \alpha \leq 1 \). Deriv0 answers -
find the corresponding values
\( \left[\begin{array}{ccccccc|c}x_{1} & x_{2} & x_{3} & s_{1} & s_{2} & s_{3} & P & \\ -2 & 0 & 1 & 5 & 4 & 0 & 0 & 21 \\ 0 & 1 & 0 & -2 & 0 & 0 & 0 & 26 \\ -3 & 0 & 0 & 5 & 4 & 1 & 0 & 29 \\ \hline2 answers -
2 answers
-
7 please
In Problems \( 1-18 \) solve each differential equation by variation of parameters. 1. \( y^{\prime \prime}+y=\sec x \) 2. \( y^{\prime \prime}+y=\tan x \) 3. \( y^{\prime \prime}+y=\sin x \) 4. \( y^1 answer -
11 please
EXERCISES \( 4.6 \) Answers to selected add-numbered problems begin on page ANS-5. In Problems 1-18 solve each differential equation by variation of parameters. 11. \( y^{\prime \prime}+3 y^{\prime}+22 answers -
17 please
EXERCISES \( 4.6 \) Answers to selected add-numbered problems begin on page ANS-5. In Problems I - 18 solve each differential equation by variation of parameters. 11. \( y^{\prime \prime}+3 y^{\prime}2 answers -
IQuestion 1. (2.5 marks) Solve the following D.E.: \[ \left\{\begin{array}{l} \sqrt{y} y^{\prime}+y^{\frac{3}{2}}=1 \\ y(0)=4 \end{array}\right. \]2 answers -
93. Solve \( 2 \frac{\partial U}{\partial y}+\frac{\partial^{2} U}{\partial y \partial x}=4 e^{2 y}+4 e^{2 x+y} \) Given boundary conditions: \( U(0, y)=e^{2 y}+e^{y} \quad, \quad \frac{\partial U}{\p2 answers -
derivative
4. Evaluate: (1) \( y=x^{4} \); (2) \( y=\sqrt[3]{x^{2}} \); (3) \( y=x^{1.6} \); (4) \( y=\frac{1}{\sqrt{x}} \); (5) \( y=\frac{1}{x^{2}} \); (6) \( y=x^{3} \sqrt[5]{x} \); (7) \( y=\frac{x^{2} \sqrt2 answers