Advanced Math Archive: Questions from September 13, 2022
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e the gradient of \( f(x, y, z)=1 / \sqrt{ }\left(x^{4}+y^{4}+z^{4}\right) \) \[ -2\left(x^{3} i+y^{3} j+z^{3} k\right) /\left(x^{4}+y^{4}+z^{4}\right)^{3 / 2} \] \[ \left.-4 x^{3} i+4 y^{3} j+4 z^{3}2 answers -
3.- calculate complex square root from z polynomium:
3. Calcular las raíces complejas \( z \) del polinomio : \[ p(z)=z^{5}-1 \]1 answer -
4.- find solutions for C from equation
Encontrar las soluciones en \( \mathbb{C} \) de la ecuación : \[ z^{3}=\frac{1}{4}(-1+i) \]1 answer -
Determine the \( x-, y \) - and \( z \)-components of the vector \( F_{2} \). \[ \begin{array}{l} \mathbf{F}_{2}=300 \cos 30^{0} \sin 40^{0} \mathbf{i}+300 \cos 30^{\circ} \cos 40^{\circ} \mathbf{j}-31 answer -
A 5kg block is in recess in a plane. Determine the force along the length of the unstretched spring.
Un bloque de \( 5 \mathrm{~kg} \) se encuentra en receso en un plano. Determine la fuerza el largo del resorte sin estirar.1 answer -
The solution of the linear differential equation
La solución de la ecuación diferencial lineal, \( x \frac{d y}{d x}+3 y=\frac{\sin x}{x^{2}}, \operatorname{si} y(\pi / 2)=0, x \neq 0 \) es: a. \( y=\frac{-\cos x}{x^{3}}+\frac{\pi^{3}}{8} \) b. \(1 answer -
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ANSWER OPTIONS: - AB & BA both are possible - AB is possible but BA is not possible - BA is possible, but AB is not possible - You can not multiply the matrixs A & B in any order
\[ \begin{array}{l} A=\left[\begin{array}{ll} 2 & 1 \\ 4 & 3 \\ 5 & 6 \end{array}\right] \\ B=\left[\begin{array}{ll} 2 & 1 \\ 0 & 1 \\ -4 & 7 \end{array}\right] \end{array} \] \( \mathrm{AB} \) y \(2 answers -
1. \( \frac{d y}{d x}=12 x y \) 2. \( \frac{d y}{d x}=7 y \) A. \( y=C e^{-7 x^{3}}+1 \) 3. \( \frac{d^{2} y}{d x^{2}}+14 \frac{d y}{d x}+49 y=0 \) B. \( y=A e^{6 x^{2}} \) C. \( y=C e^{7 x} \) 4. \(2 answers -
Find the general solution of the following equations: 1. \( x \sin (y) y^{\prime}=\cos y \) 2. \( [\cos (x+y)+\sin (x-y)] y^{\prime}=\cos 2 x \) 3. \( \frac{1}{x}+y+\left(3 y^{2}+x\right) y^{\prime}=01 answer -
1. Suppose that \( f(x, y)=g\left(\frac{x+y^{2}}{x y^{2}}\right) \), and compute \( f_{x}(x, y)+f_{y}(x, y) \).1 answer -
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