Advanced Math Archive: Questions from July 14, 2022
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\( y^{\prime \prime \prime}+2 y^{\prime \prime}=32 e^{2 x}+24 x, y(0)=6, y^{\prime}(0)=0, y^{\prime \prime}(0)=14 \)1 answer -
\[ z=x^{2}+x y+\frac{1}{2} y^{2}-8 x+y \] relative minimum \( (x, y, z)= \) relative maximum \( (x, y, z)= \) saddle point \( (x, y, z)= \)3 answers -
En el triángulo \( \mathrm{ABC}, \angle \mathrm{B}=29^{\circ}, \angle \mathrm{C}=48^{\circ}, \& \mathrm{a}=13 \). Halla la medida de \( \mathrm{c} \) en redondeado a 1 lugar decimal. QUESTION 4 En el1 answer -
Hay dos fuerzas actuando simultaneamente sobre un objeto. La primera fuerza es de \( 20 \mathrm{lbs} \) a un ángulo de \( 150^{\circ} \) y la segunda fuerza es de \( 16 \mathrm{Ibs} \) a un ángulo d1 answer -
Solve the initial value problem: \[ y^{\prime \prime}+y=u_{3}(t), \quad y(0)=0, \quad y^{\prime}(0)=1 \]3 answers -
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Solve sec^2y dy/dx+1/2sqrt(x+1)tany=1/2sqrt(x+1)
Extra Credit 1: Solve \( \sec ^{2} y \frac{d y}{d x}+\frac{1}{2 \sqrt{x+1}} \tan y=\frac{1}{2 \sqrt{x+1}} \)3 answers -
Section 8.1 Arc Length 1. Define arc length. How is it calculated? 2. Find the length of the line segment from the point A=(0,1) to the point B= (5.13). graph. Check using the distance formula. Find t
Sección 8.1 Longitud de arco 1. Define longitud de arco. ¿Cómo se calcula? 2. Encuentra la longitud del segmento de recta desde el punto \( A=(0,1) \) hasta el punto \( B=(5,13) \). Graficar. Verif1 answer -
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Solve the following initial value problems. \( y^{\prime \prime}+y=\frac{2}{\cos x}, y(0)=y^{\prime}(0)=2 \) \( x^{3} y^{\prime \prime \prime}-6 x y^{\prime}+12 y=20 x^{4}, x>0, y(1)=\frac{8}{3}, y^3 answers -
Solve using elimination. \[ \left\{\begin{array}{l} 2 x^{2}+x y-y^{2}=3 \\ x^{2}+2 x y+y^{2}=3 \end{array}\right. \] \[ x=\frac{-2}{3}, y=\frac{1}{3} ; x=\frac{2 \sqrt{3}}{3}, y=-\frac{1}{3} \] or \(1 answer -
\[ \begin{array}{l} 1 y^{\prime}+6 t=e^{4 t}, y(0)=2 \\ 2 y^{\prime \prime}+6 y^{\prime}+4 y=0, y(0)=1, y^{\prime}(0)=0 \\ 3 \cdot y^{\prime}+t=e^{5 t}, y(0)=1 \\ 4 \cdot y^{\prime \prime}-5 y^{\prime1 answer -
use Laplace method to solve differential equations
\[ \begin{array}{l} 2 \cdot y^{\prime \prime}+6 y^{\prime}+4 y=0, y(0)=1, y^{\prime}(0)=0 \\ 3 \cdot y^{\prime}+t=e^{5 t}, y(0)=1 \\ \text { 4. } y^{\prime \prime}-5 y^{\prime}+6 y=e^{4 t}, y(0)=1, y^1 answer -
Use the method of separable variables to determine the general solution of the simple transport PDE in fluids: aut+bux=0 where a,b∈R∖{0} constants.c
Utilice el método de variables separables para determinar la solución general de la EDP de transporte simple en fluidos: \[ a u_{t}+b u_{x}=0 \] donde \( a, b \in \mathbb{R} \backslash\{0\} \) const1 answer -
Use separable variables to solve the Laplace PDE subject to the following conditions:
Utilice variables separables para resolver la EDP de Laplace sujeta a las siguientes condiciones: \[ \left\{\begin{array}{llll} \Delta u=0 & 01 answer -
Solve using Laplace Transforms \[ y^{\prime \prime}+9 y=2 \sin (2 t), \quad y(0)=0, y^{\prime}(0)=-1 \] \( y=\frac{2}{3} \sin 2 t-\frac{3}{5} \sin 3 t \) \( y=\frac{2}{5} \sin 2 t+\frac{3}{5} \sin 3 t1 answer -
Find \( Y(s) \) for the initial value problem \[ y^{\prime \prime}+6 y=4 t^{2}-3, y(0)=0, y^{\prime}(0)=-7 \] \[ \begin{array}{l} \frac{-7 s^{3}-3 s^{2}-8}{s^{3}\left(s^{2}+6\right)} \\ \frac{-7 s^{3}1 answer -
\[ y^{\prime \prime}-y=x+\sin x, y(0)=3, y^{\prime}(0)=4 \] \[ y=\frac{17}{4} e^{x}-\frac{1}{4} e^{-x}-x-\frac{1}{2} \sin (x) \] Solve the given differential equation subject to the indicated conditio1 answer -
Q36: Let \( h(x)=\sqrt{x+2}, g(x)=\sin x-3 \), then find the value of \( \frac{(g \circ h)^{\prime}(2)}{(h o g)^{\prime}(2)} \). (a) \( \frac{\sqrt{(\sin 2)+1}}{2} \) (b) \( \frac{\sqrt{(\sin 4)-1}}{23 answers -
\( \sin \left(\frac{\pi}{2}-x\right)+\sin (\pi-x)+\sin \left(\frac{3 \pi}{2}-x\right)+\sin (2 \pi-x) \)1 answer