Advanced Math Archive: Questions from April 13, 2023
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For \( x, y \in \mathbb{R} \) define \[ d(x, y):=\left|\frac{x}{1+|x|}-\frac{y}{1+|y|}\right| \] Is \( (\mathbb{R}, d) \) complete ?2 answers -
Evaluate the triple integral \( \iiint_{Q} f(x, y, z) d V \). \[ f(x, y, z)=9 x+10 y-4 z, Q=\{(x, y, z) \mid 1 \leq x \leq 9,-5 \leq y \leq 5,0 \leq z \leq 8\} \] \[ \iiint_{Q} f(x, y, z) d V= \]2 answers -
2. Determine whether the following functions are homogeneous. If so, of what 'degree'? (a) \( \mathrm{h}(\mathrm{x}, \mathrm{y}, \mathrm{w})=\frac{\mathrm{x}^{2}}{\mathrm{y}}+\frac{2 \mathrm{w}^{2}}{\2 answers -
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\( \left.\begin{array}{l}F(t)-\left(t^{2}+3\right) i+\cos t J+t^{3} k \\ G(t)=\sin t i+\left(t^{2}+2\right) J-(t+1) k\end{array}\right\} \quad\langle F, 2 G\rangle(0)= \) ?2 answers -
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[6 pts.] Halla la solución general de la ecuación diferencial \( 4 x^{2} y^{\prime \prime}+y=0 \) dado que \( y_{1}(x)=x^{1 / 2} \ln x \) es también una solución. [6 pts.] Halla una ecuación dife2 answers -
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Considera una lÃnea de carga infinita con densidad de carga \( 2.5 \times 10^{-4} \mathrm{C} / \mathrm{m} \), suponga que se tiene una carga \( 1.5 \times 10^{-5} \mathrm{C} \) a una distancia perpen2 answers -
Considera una lÃnea de carga \( q=1.4 \times 10^{-4} \mathrm{C} \) y una carga \( \mathrm{Q}=6.6 \times 10^{\wedge-5} \mathrm{C} \). Considera que la longitud de la lÃnea es 1.9 metros y la distanci2 answers -
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Considera una lÃnea de carga \( \mathrm{q}=2 \times 10^{-4} \mathrm{C} \) y una carga \( \mathrm{Q}=2.6 \times 10^{\wedge-5} \mathrm{C} \). Considera que la longitud de la lÃnea es 1 metros y que la2 answers -
Solve the following systems: 1. \[ \begin{array}{l} 5 x^{\prime}+y^{\prime}-3 x+y=0 \\ 4 x^{\prime}+y^{\prime}-3 x=-t \end{array} \] 2. \[ \begin{array}{l} x^{\prime}-2 x+y=e^{t} \\ x^{\prime}+y-2 y^{2 answers -
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Problem #1 For the network shown below, use the path augmentation algorithm to find the flow pattern that gives the maximum flow from source to sink. The arcs show the capabilities from node i to node
Para la red de trabajo que se muestra abajo utiliza el algoritmo de aumento de ruta para encontrar el patrón de flujo que da el flujo máximo desde el "source" hasta el "sink". Los arcos muestran las2 answers -
Problem #3 Use the Shortest Path Method to find the shortest path of the source to destination in the following network.
Problema \#3 Utilice el método de Ruta más Corta ("Shortest Path Method") para encontrar la ruta más corta del origen al destino en la siguiente red.2 answers -
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Given \( f(x, y)=-5 x^{4}+3 x^{2} y^{6}-6 y^{2} \), fi \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
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Sean A y B matrices de nxn. Demuestre que si AB es invertible, entonces A y B son ambos invertibles.1 answer