Advanced Math Archive: Questions from October 27, 2022
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4. If possible, construct a 1-4-2-3 weighted code for decimal digits. If not possible, explain why. If possible, express 673 decimals in the \( 1-4-2-3 \) code. ( 10 points)2 answers -
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Determine the derivative \( \frac{d y}{d x} \) for each of the following: a. \( y=e^{-2 x^{2}} \) d. \( y=2 \sin x-3 \cos 5 x \) b. \( y=3^{x^{2}+3 x} \) e. \( y=\sin ^{3}\left(x^{2}\right) \) c. \( y2 answers -
1. Verificar que la ecuación es exacta y resolverla. \[ x^{2} y^{3} d x+x^{3} y^{2} d y=0 J \] 2. Verificar que la ecuación diferencial es homogénea y resolverla. \[ (x-y) d x+x d y=0 \] 3. Resolve2 answers -
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find the slope in the directionv of axis y in the points given (translation)
1. Hallar las pendientes en la dirección del eje \( x \) y en la dirección del eje \( y \) en el punto dado: \[ \begin{array}{ll} g(x, y)=4-x^{2}-y^{2} & z=e^{-x} \cos y \\ (1,1,2) & (0,0,1) \end{ar2 answers -
Find the values of x and y ... simultaniously
2. Hallar todos los valores de \( \mathbf{x} \) y y tal que \( \frac{\partial f}{\partial x}=0 \) y \( \frac{\partial f}{\partial y}=0 \) simultáneamente. a. \[ f(x, y)=3 x^{3}-12 x y+y^{3} \] b. \[2 answers -
Find the directional derivative of the function in point P in the direction of v
5. Hallar la derivada direccional de la función en el punto \( P \) en la dirección de v a. \( h(x, y, z)=\frac{1}{2} x^{2} y z, P(2,1,1) \) v \( =\langle 2,1,2> \)2 answers -
Find the following Laplace transform or inverse Laplace transform.
Parte 1: Encuentre las siguientes transformadas de Laplace o transformada inversa de Laplace. (10 puntos cada uno) 8) \( L\left\{\int_{0}^{t} \sin 2(t-\tau) \cos 3 \tau d \tau\right\} \)2 answers -
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For \( f(x, y, z)=x^{2} y-z \) and \( \vec{F}(x, y, z)=x \hat{\imath}-x y \hat{\jmath}+z^{2} \hat{k} \) calculate \( \nabla f+\nabla \times F \).2 answers -
Use the Laplace Transform to solve the following initial value problems. 2. \( y^{\prime \prime}-y=\left\{\begin{array}{ll}\mathrm{t}, & t2 answers -
Solve the problem of initial value using the Laplace method.
Parte 2: Resuelve el problema de valor inicial usando el método de transformada de Laplace.(10 ptos) 1) \( y^{\prime \prime}+6 y^{\prime}+4 y=0, y(0)=1, y^{\prime}(0)=0 \)2 answers -
Find the Laplace of
2) Hallar la transformada de Laplace de \( \mathrm{f}(\mathrm{t})=\left\{\begin{array}{cc}-1,0 \leq t2 answers -
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Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-7 x \) and \( y=14 \). 1. \( \int_{a2 answers -
Suppose that \( P_{1}=6 \mathrm{kN}, P_{2}=8 \mathrm{kN} \), and \( P_{3}=12 \mathrm{kN} \). (Figure 1) Determine the force in member \( B C \) of the bridge truss. Express your answer to three signi2 answers -
Find the absolute extreme values of \( h(x, y)=x^{2}+2 x y \) when \( -\sqrt{5 / 2} \leq x \leq \sqrt{5 / 2}, x^{2}-2 \leq y \leq 3-x^{2} \).2 answers -
Problem#01: Solve the initial value problem. \[ \begin{array}{l} y^{\prime \prime}-y^{\prime}-12 y=3-\frac{x}{2} \\ y(0)=1 \quad, \quad y^{\prime}(0)=0 \end{array} \]2 answers -
Considere \( \frac{d y}{d x}-y=e^{2 x} y^{3} \) como una ecuación de Bernoulli. (1 pt) Identifique: \( v, P(x), Q(x) \) (1 pt) Indique la ecuación lineal estándar en la que se reduce la ecuación o2 answers -
Use el método discutido bajo la Ecuación Homogéneas para \( \frac{d y}{d x}=\frac{x \sec (y / x)+y}{x} \) (1 pt) Demuestre es homogénea (1 pt) Muestre su proceso para re-escribir \( \frac{d y}{d x2 answers -
(10 points) Solve the IVP \[ y^{\prime \prime}-y^{\prime}-2 y=5 \sin (x), \quad y(0)=1, \quad y^{\prime}(0)=-1 \]2 answers -
Calculate \( \frac{d^{2} y}{d x^{2}} \) \[ \begin{array}{l} y=-2 x^{2}+6 x \\ \frac{d^{2} y}{d x^{2}}= \end{array} \]2 answers -
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Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=7 y \) and \( x^{2}=9-y \). 1. \( \int_{a}^2 answers