Advanced Math Archive: Questions from September 17, 2022
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all questions please
10. Which of the following are true in the universe of all real numbers? * (a) \( (\forall x)(\exists y)(x+y=0) \). (b) \( (\exists x)(\forall y)(x+y=0) \). (c) \( (\exists x)(\exists y)\left(x^{2}+y^1 answer -
Homework 2.6. Find the general solution of the following homogeneous problems 1. \( y^{\prime \prime}+4 y^{\prime}+4 y=0 \) 2. \( y^{\prime \prime}+2 y^{\prime}-15 y=0 \) 3. \( y^{\prime \prime}+4 y=01 answer -
Homework 2.7. Find the solution of the following initial value problems 1. \( y^{\prime \prime}-y^{\prime}-2 y=0, y(0)=y^{\prime}(0)=1 \) 2. \( y^{\prime \prime}-4 y^{\prime}-21 y=0, y(0)=y^{\prime}(2 answers -
Solve the differential equation. \[ \begin{array}{c} \mathrm{e}^{\mathrm{x}} \frac{\mathrm{dy}}{\mathrm{dx}}+4 \mathrm{e}^{\mathrm{x}} \mathrm{y}=3, \mathrm{x}>0 \\ \mathrm{y}=\mathrm{e}^{-4 \mathrm{x1 answer -
Solve the differential equation. \[ \begin{array}{c} \mathrm{e}^{\mathrm{x}} \frac{\mathrm{dy}}{\mathrm{dx}}+4 \mathrm{e}^{\mathrm{x}} \mathrm{y}=3, \mathrm{x}>0 \\ \mathrm{y}=\mathrm{e}^{-4 \mathrm{x1 answer -
2 answers
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Para la funcion \( f(x)=5 x^{2}+4 \), encuentre \( \frac{f(a+h)-f(a)}{h}, h \neq 0 \) a. \( \frac{f(a+h)-f(a)}{h}=5 h+10 a \) b. \( \frac{f(a+h)-f(a)}{h}=5 h+5 a \) c. \( \frac{f(a+h)-f(a)}{h}=10 h+51 answer -
1 answer
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1. En los siguientes ejercicios, estime: a) \( A+B \) b) \( B-A \) c) \( 2 A+3 B \) d) \( 5 \mathrm{~A}-4 \mathrm{~B} \) \( A=\left|\begin{array}{cc}1 & 2 \\ 3 & 4 \\ -1 & 0\end{array}\right| \quad B=1 answer -
1 answer
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Una fuerza electromotriz de 200 voltios es aplicada a un circuito en series RC en el cual la resistencia es de 1000 ohms y la capacitancia es de \( 5 \times 10^{-6} \) farad. Encuentre la carga y la c1 answer -
Una solución particular para \( y^{\prime \prime}+4 y^{\prime}+4 y=e^{2 x} \) es: \[ \begin{array}{l} y_{p}=2 x+1 \\ y_{p}=8 x+2 \\ y_{p}=2 x-1 \\ y_{p}=x^{2}+3 x \\ y_{p}=2 x-3 \end{array} \]2 answers -
1 answer
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SELECCIONE LA RESPUESTA CORRECTA Una solución particular para \( y^{\prime \prime}+2 y^{\prime}+y=e^{-x} \) es: \[ \begin{array}{l} y_{p}=\frac{1}{2} x^{2} e^{-x} \\ y_{p}=\frac{1}{2} x e^{-x} \\ y_{0 answers -
Determine si el método de coeficientes indeterminados es aplicable. Conteste "si" o "no". \[ y^{\prime \prime}+4 y^{\prime}-5 y=x^{-2} e^{x} \] \[ y^{\prime \prime}+4 y^{\prime}-5 y=x^{2} e^{x}+1 \]0 answers -
2 answers
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esuelva \( 3 y^{\prime \prime}-6 y^{\prime}+6 y=e^{x} \sec x \) \( y=c_{1} e^{x} \cos x+c_{2} e^{x} \sin x+\frac{1}{3} e^{x} \cos x \ln (\cos x)+\frac{1}{3} x e^{x} \sin x \) \( y=c_{1} e^{x} \cos x+c1 answer -
1 answer
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LLENE LOS BLANCOS 1. \( L\left\{e^{-7 t}\right\}= \) \( \frac{\sqrt{3}}{s^{2}+3} \quad \frac{1}{s+4} \) 2. \( L\{\sin 2 t\}= \) \( \frac{2}{s^{2}+4} \) 3. \( L\left\{t^{5}\right\}= \) \( \frac{120}{s^1 answer -
1 answer
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\( h(X)=X^{4}+X+1 \in Z_{2}[X], g(X)=X^{4}+X^{3}+X^{2}+X+1 \in Z_{2}[X] \) 2-2. Find an explicit (field) isomorphism \( \psi \) between two finite fields of \( 2^{4} \) elements; \[ \psi: Z_{2}[X] /\1 answer