Advanced Math Archive: Questions from September 22, 2022
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43. Solve the initial value problem: \[ \begin{array}{l} y^{\prime \prime \prime}-y^{\prime}=0 ; \quad y(0)=2, \\ y^{\prime}(0)=3, \quad y^{\prime \prime}(0)=-1 . \end{array} \]2 answers -
Determine el vector posición del punto \( \mathrm{P} \) con respecto al punto \( \mathrm{A} \) \( \mathrm{r}_{\mathrm{PA}}=( \) \( \mathbf{i}+ \) \( \mathbf{j}+ \)1 answer -
Determine el vector unitario en dirección de la fuerza F. \[ \mathrm{u}=( \] \( \mathbf{i}+\quad \mathbf{j}+ \) Escriba tres decimales en sus resultados.1 answer -
1) If \( f(x, y)=4 x^{3}-x y^{2} \), find \( \frac{\partial^{2} f}{\partial x \partial y}= \) \( \frac{\partial^{2} f}{\partial y^{2}}= \) 2) If \( z=x^{2} y+3 x y^{4} \), where \( x=\sin 2 t \) and \1 answer -
Find the degree and order of the following Differential Equation. Type or paste question here
1. \( \sin \left(\frac{d y}{d x}\right) \cdot \frac{d^{3} y}{d x^{3}}-\log y=x^{2} \) 2. \( y^{\prime \prime}+9 y=e^{2 x} \) 3. \( \left(\frac{d^{2} x}{d w^{2}}\right)^{3}-\left(\frac{d x}{d w}\right)2 answers -
Tarcara par.e: Tooria dal grod̀uctor E. srcicio sumarico Imazina que axiste una emprosa productora dis hamburzusias denominzan HHE Hambarger Heaven y cuy fumcitn is groduccion os it siguiente: Kambur0 answers -
Q36: Let \( h(x)=\sqrt{x+2}, g(x)=\sin x-3 \), then find the value of \( \frac{(g o h)^{\prime}(2)}{(h o g)^{\prime}(2)} \). (a) \( \frac{\sqrt{(\sin 2)+1}}{2} \) (b) \( \frac{\sqrt{(\sin 4)-1}}{2} \)1 answer -
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Solve the following equations for \( y \). (a) \( y^{\prime}+y \tan x=\sec x \) (b) \( 2 y \frac{d y}{d x}-x=x y^{2} \), where \( y(0)=-2 \) (c) \( x^{2} y^{\prime}+1=y^{2} \)1 answer -
Find the product if possible. \[ \left[\begin{array}{ccc} 3 & 2 & 5 \\ -1 & 3 & 1 \end{array}\right]\left[\begin{array}{lll} 4 & 5 & 0 \\ 1 & 2 & 7 \end{array}\right] \] \( \left[\begin{array}{l}22 \\1 answer -
For the following functions, describe the level surface for \( k=36 \). (a) \( f(x, y, z)=3 x+4 y+2 z \) (b) \( g(x, y, z)=(3 x+4 y+2 z)^{2} \) (c) \( h(x, y, z)=3 x^{2}+4 y^{2}+2 z^{2} \)1 answer -
1 answer
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Use the Chain Rule to find \( d w / d t \). \[ w=x e^{y / z}, \quad x=t^{3}, \quad y=3-t, \quad z=2+5 t \] \( \frac{d w}{d t}= \)1 answer -
1 answer