Advanced Math Archive: Questions from October 24, 2022
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Solve \( \frac{d y}{d x}=\tan y \cot x-\sec y \cos x \), simple substitution [Hint: Express the functions first in terms of sine and cosine.] (A) \( \left|\frac{\sin x}{\sin y}\right|=c e^{\frac{1}{4}2 answers -
2 answers
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1. \( \int \frac{3 x+11}{x^{2}-x-6} d x \) \( 2 \cdot \int \frac{1}{x^{2}-1} d x \) 3. \( \int \frac{3 x-37}{x^{2}-3 x-4} d x \) 4. \( \int \frac{9-9 x}{2 x^{2}+7 x-4} d x \) 5. \( \int \frac{4 x^{2}}2 answers -
2 answers
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4. \( x y^{\prime}-y+2 \sqrt{y}=0 ; \quad y(2)=1 \) 5. \( \left(\cos (x+2 y)+2 e^{y}\right) d x+\left(2 \cos (x+2 y)+2 x e^{y}-2 y\right) d y=0 \)2 answers -
2 answers
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prove or disprove
If \( x \in \mathbb{Z}, y \in \mathbb{Z} \), and \( z \in \mathbb{Z} \), then \( \frac{x+y+z}{3} \geq \sqrt[3]{x \cdot y \cdot z} \)2 answers -
Determine cual o cuales de las siguientes ecuaciones es (son) Ecuaciones diferenciales: separables, exactas, lineales, homogéneas o ninguna de las anteriores: 1. Separable: _______________________ 2.
I. Determine cual o cuales de las siguientes ecuaciones es (son) Ecuaciones diferenciales: separables, exactas, lineales, homogéneas o ninguna de las anteriores: 1. Separable: 2. Exacta: 3. Lineal: 41 answer -
(1 point) Match the direction fields labeled A through D with the differential equation below. \( y^{\prime}=x y \sin y \) \( y^{\prime}=\frac{y^{2}}{2} \sin x \) \( y^{\prime}=2 \cos x \sin y \) \(2 answers -
Solve the initial value problems.
\( \begin{array}{ll}\text { a) } y y^{\prime}-x=0 & y(1)=-2 \\ \text { b) } y^{\prime}=-e^{x+y} & y(0)=-\ln 3 \\ \text { c) } y^{\prime}+y^{2} \sin x=0 & y(0)=1\end{array} \)2 answers -
2 answers
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\( \left\{\begin{aligned} 4 x+\frac{4 y-z}{3} &=\\ 3(6 z-3 x)+y-4 &=9 \\ x-(4+z) &=6 y \end{aligned}\right. \)2 answers -
Given the following matrices, if possible, determine \( 3 A-3 B \). If not, state "Not Possible". \[ A=\left[\begin{array}{cc} 7 & 4 \\ -7 & -5 \\ 5 & -5 \end{array}\right] \quad B=\left[\begin{array}2 answers -
I) Solve by undetermined coefficients \[ y^{\prime \prime}-3 y^{\prime}+2 y=x e^{2 x} \text {, } \] II) \( \quad y^{\prime \prime}-3 y^{\prime}=18 x+10 e^{2 x}, 0, \quad y^{\prime}(0)=2 \). Solution 32 answers -
(1 point) Solve the initial-value problem \( y^{\prime \prime}-2 y^{\prime}=x+2 e^{x}, y(0)=17, y^{\prime}(0)=\frac{39}{4} \). Answer: \( y(x)= \)2 answers -
Fill in the blanks
Self Assessment LLENE LOS BLANCOS MATH 2350 - ECUACIONES DIFERENCIALES ORDINARIA. 1. \( L^{-1}\left\{\frac{120}{s^{6}}\right\}= \) 2. \( L^{-1}\left\{\frac{s}{s^{2}+7}\right\}= \) \( e^{-6 t} \) 3. \(2 answers -
Identify the inicial entrance pivot
Dado la tabla inicial simplex, identifique el pivote de entrada inicial2 answers -
For each of the non-homogeneous differential equations below, find a particular solution. a. \( y^{\prime \prime}+y^{\prime}+2 y=5 e^{-3 t}+2 t^{2} \) b. \( y^{\prime \prime}+y^{\prime}+2 y=e^{2 i t}2 answers -
Determine el valor que maximiza \( z=x+y \) sujeto a las siguientes restricciones: \[ \begin{array}{l} 5 x+3 y \leq 38 \\ x+3 y \leq 10 \\ x \geq 0, y \geq 0 \end{array} \]2 answers -
Determine the value of Y
Determine el valor de \( y \) que maximiza \( z=x+y \) sujeto a las siguientes restricciones: \[ \begin{array}{l} 2 x+4 y \leq 26 \\ x+4 y \leq 13 \\ x \geq 0, y \geq 0 \end{array} \]2 answers -
Resuelva el par de congruencias lineales. \[ \begin{array}{l} 3 x+2 y \equiv 5(\bmod 7) \\ 2 x+3 y \equiv 6(\bmod 7) \end{array} \]2 answers -
show the expression factor the expression 1+z+z^2+ z^n-1 using the sin nth roots of unity, then evaluate at z = 1.
\( \frac{n}{2^{n-1}}=\prod_{k=1}^{n-1} \operatorname{sen}\left(\frac{\pi k}{n}\right) \) 3. Demuestre la expresión \[ \frac{n}{2^{n-1}}=\prod_{k=1}^{n-1} \operatorname{sen}\left(\frac{\pi k}{n}\righ0 answers -
Use polar coordinate substitution to find the value of the following double integral.
(a) \( \iint_{D} x d x d y, \quad D=\left\{(x, y) \in \mathbb{R}^{2} \mid x^{2}+y^{2} \leq 1, x \geq 0\right\} \). (b) \( \iint_{D} y d x d y, \quad D=\left\{(x, y) \in \mathbb{R}^{2}\left|x^{2}+y^{2}2 answers -
0 answers
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The expression \[ d f=\cos (x+y) d x+\cos (x+y) d y \] is a total differential. What is the function \( f(x, y) \) ? \[ \begin{array}{l} f(x, y)=\sin (x+y) \\ f(x, y)=2 \cos (x+y) \\ f(x, y)=\cos (x+y2 answers