Advanced Math Archive: Questions from November 03, 2022
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In Problems 31-40 use the Laplace transform to solve the given initial-value problem. 31. \( \frac{d y}{d t}-y=1, \quad y(0)=0 \) 32. \( 2 \frac{d y}{d t}+y=0, \quad y(0)=-3 \) 33. \( y^{\prime}+6 y=e2 answers -
1) \( \left(x+y e^{y}\right) \cdot y^{\prime}=1 \) 2) \( \left(x^{2}+1\right) y^{\prime}+4 x y=x, y(2)=1 \) 3) \( y^{\prime}-2 x y=e^{x^{2}} \) 4) \( \frac{d y}{d x}=3 x^{2}\left(y^{2}+1\right) \cdot0 answers -
13. Prove (1) \( \left|\sin ^{2} x-\sin ^{2} y\right| \leq|x-y| \) for all \( x, y \in \mathbb{R} \). (2) \( \cos x \geq 1-\frac{x^{2}}{2} \). (3) \( 3 \arccos x-\arccos \left(3 x-4 x^{3}\right)=\pi,|2 answers -
5. Evaluate the following limits. (1) \( \lim _{x \rightarrow 0} \frac{\tan x-x}{x-\sin x} \); (2) \( \lim _{x \rightarrow 0^{+}} x^{x} \); (3) \( \lim _{x \rightarrow 0}\left(\frac{1}{x}-\frac{1}{e^{2 answers -
Q5) Simplify the following Boolean expression using Karnaugh map: a) \( F(x, y, z)=x^{\prime} y z+x y^{\prime} z^{\prime}+x y z+x y z^{\prime} \) b) \( F(x, y, z)=x^{\prime} y^{\prime} z^{\prime}+x^{\2 answers -
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1. (25\%) La población de pechn en un erisdero es dencrith con la ED \[ \frac{d P}{d t}=k H^{-h} \] donde \( k=0.5 y \) la conatante \( h=100 \) represebte la coencha diaria de peces. Consideria cada2 answers -
2. (25\%) BI perrito Chems entí practiendo oómo golpent con un bate. El bate de 1 kig de mana enth́ concetado a un cerorte de constanite \( k=2 y \) a ia amorthguador de consatante \( b=3 \) para h0 answers -
The following electrical circuit was connected to a voltage source, at time t = 0 Cheems removes the voltage source to change the capacitor for a larger one, at the time Cheems removed the source the
3. \( (25 \%) \) El golpe con of bate del problems anterioe hiso que Cheems dejarn sii sueno de ser beishotista \( y \) siguió el consejo de su mamń para graduarse cotno clectricista. El siguliente2 answers -
4. (25\%) Dos tanques con 21 litros de agua contaminadin calit umo están interconectsdos por dos tubes. Hay una entrada de agua limpin en el tanque \( \mathrm{A} \) con un thejo de \( 12 \mathrm{~L}2 answers -
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\( f(x, y)=y^{2} \cos (x)-x^{3} \ln (y) \), find \( \frac{\partial^{2} f}{\partial x \partial y} \) \[ \begin{array}{l} 2 y \cos (x)-\frac{3 x^{2}}{y} \\ -y^{2} \sin (x)-3 x^{2} \ln (y) \\ -2 y \sin (2 answers -
8. Caculate following determinant \[ \operatorname{det}\left(\left[\begin{array}{ccc} 1 & x & y z \\ 1 & y & x z \\ 1 & z & x y \end{array}\right]\left[\begin{array}{lll} 1 & x & x^{2} \\ 1 & y & y^{21 answer -
5.- Solve the initial value problem: \[ y^{\prime \prime \prime}-y^{\prime \prime}+y^{\prime}-y=0 ; \quad y(0)=2, \quad y^{\prime}(0)=-1, \quad y^{\prime \prime}(0)=-2 \]2 answers -
Giiven \( F_{1}(w, x, y, z)=\sum(0,1,3,5,9,13) \) and \( F_{2}(w, x, y, z)=\sum(0,3,6,14) \) a) Express \( G(w, x, y, z)=F_{1} \cdot F_{2} \) in sum of minterms0 answers -
Find and graph the solution for the following differential equation using Laplace's transformation tool:
\( \frac{d^{2} y(t)}{\lambda t^{2}}+4 y(t)=\psi(t) ; \) condiciones iniciales: \( \left.\quad \frac{d y}{d t}\right|_{t=0}=-1, y \) \[ D(t)=\left\{\begin{array}{l} 4 t, \\ 4, \\ 0 \end{array}\right. \2 answers -
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Evaluate \( \iiint_{\mathcal{W}} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=48(x+y) \quad \mathcal{W}: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x2 answers -
differential equations
Resuelve las siguientes ED's y de ser posible expresa la solución en forma explícita: a) ED lineal: \( (x \ln x) y^{\prime}+(1+\ln x) y+\frac{1}{2} \sqrt{x}(2+\ln x)=0 \)1 answer -
3) \( y^{\prime \prime}+2 y^{\prime}+2 y=(\cosh x)(\sin x) \quad \) Note: \( \cosh x=\frac{e^{x}+e^{-x}}{2} \) 4) \( y^{\prime \prime}-8 y^{\prime}+4 y=\cos (3 x) \)2 answers -
(1 point) Solve the equation \( y^{\prime \prime}+64 y=\exp (2 x) \) where \( y(0)=y^{\prime}(0)=0 \) \( y(x)= \)2 answers -
number 23-27 step by step please
Finding Local Exuema Find all the local maxime, local minima, and saddle points of the functions in Exercises 1-j0. 1. \( f(x, y)=x^{2}+x y+y^{2}+3 x-3 y+4 \) 2. \( f(x, y)=2 x y-5 x^{2}-2 y^{2}+4 x+41 answer -
Solve the equation or IVP. 1) \( y^{\prime \prime}+4 y^{\prime}+3 y=e^{x}, \quad y(1)=1, \quad y^{\prime}(1)=2 \) 2) \( y^{\prime \prime}-4 y=32 x, \quad y(0)=0, \quad y^{\prime}(0)=6 \)2 answers -
2. Solve the following initial value problems. (a) \( y^{\prime \prime}-\frac{1}{4} y=0, \quad y(2)=1, y^{\prime}(2)=0 \) (b) \( 25 y^{\prime \prime}+20 y^{\prime}+4 y=0, \quad y(5)=4 e^{-2}, y^{\prim2 answers -
Solve using Laplace Transforms \[ \begin{array}{l} y^{\prime \prime}+9 y=2 \sin (2 t), y(0)=0, y^{\prime}(0)=-1 \\ y=\frac{2}{5} \sin 2 t-\frac{5}{3} \sin 3 t \\ y=\frac{2}{5} \sin 2 t-\frac{3}{5} \si2 answers -
Find \( Y(s) \) for the initial value problem \[ \begin{array}{l} y^{\prime \prime}+6 y=4 t^{2}-3, y(0)=0, y^{\prime}(0)=-7 \\ \frac{-7 s^{3}-4 s^{2}+8}{s^{3}\left(s^{2}+6\right)} \\ \frac{-7 s^{3}-32 answers -
Solve using Separation of Variables
\( \frac{\mathrm{d}}{\mathrm{d} x}\left[x \frac{\mathrm{d} y}{\mathrm{~d} x}\right]+\frac{\mathrm{d}}{\mathrm{d} x} \frac{x^{2}}{2} y=0 \)2 answers -
The path S traveled by a body during time t. If its speed is proportional to the distance, if the body travels 100 meters in 10 minutes and 200 meters in 15 minutes. Determine: the differential equati
El camino S recorrido por un cuerpo durante el tiempo t. Si su velocidad es proporcional al trayecto, si el cuerpo recorre 100 metros en 10 minutos y 200 metros en 15 minutos. Determine: La solución2 answers -
Solve the initial value problem \[ y^{\prime \prime}+y=\delta(t-2 \pi) \cos (t), \quad y(0)=0, \quad y^{\prime}(0)=1 \]2 answers -
ASAP PLS HELP WILL UPVOTE 5:
Solve using Laplace Transforms \[ \begin{array}{l} y^{\prime \prime}+9 y=2 \sin (2 t), y(0)=0, y^{\prime}(0)=-1 \\ y=\frac{2}{5} \sin 2 t-\frac{3}{5} \cos 3 t \\ y=\frac{2}{5} \sin 2 t+\frac{3}{5} \si2 answers -
Use the order reduction method to solve x2y′′ + 3xy′ − y = x1 if y1 = x1/2, express as integrals the expressions for u1 and u2 , respectively, of the particular solution.
(e) (13 puntos) Use el método de reducción de orden para resolver \( x^{2} y^{\prime \prime}+ \) \( 3 x y^{\prime}-y=\frac{1}{x} \) si \( y_{1}=x^{1 / 2} \), exprese como integrales las expresiones0 answers