Advanced Math Archive: Questions from April 24, 2023
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\( \left.\begin{array}{c}u+v^{2}-2 x+5 y^{2}=0 \\ u-v+x+y^{3}=0\end{array}\right\} \quad u_{x}=? \quad v_{y}=? \)2 answers -
16. Y MX + B1 Y = MX + B2 (3 points) a.Perpendicular straight lines b.lines are parallel c.lines overlap d.All of the above e.None of the above 17.Y MX + B Y = MX + B (3 points) a.lines intersect b.P
16. \( \begin{aligned} Y & =M X+B 1 \\ Y & =M X+B 2\end{aligned} \) (3 puntos) Rectas Perpendiculares Rectas son paralelas Rectas se superponen Todas las anteriores Ninguna de las anteriores 17. \( \b2 answers -
18. If m=0 (3 points) a.Increasing graph b.Decreasing graph c.vertical graph d.diagonal graph e.Horizontal graph 19. If a > 0 (3 points) a.Increasing Graph b.Decreasing graph c.vertical graph d.di
18. Si \( m=0 \) G (3 puntos) Gráfica Creciente Gráfica Decreciente Gráfica Vertical Gráfica Diagonal Gráfica Horizontal 19. Si \( a>0 \) (3 puntos) Gráfica Creciente Gráfica Decreciente Gráfi2 answers -
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22. If a = 0 (3 points) a.Increasing graph b.Decreasing graph c.vertical graph d.diagonal graph e.Horizontal graph
22. Si \( a=0 \) (3 puntos) Gráfica Creciente Gráfica Decreciente Gráfica Vertical Gráfica Diagonal Gráfica Horizontal2 answers -
1) Differentiate the following with respect to \( x \) : a. \( y=5 x^{4}+2 x^{2}+x+15 \) b. \( y=4 x^{6}+3 x^{2}-4 x-10 \) c. \( y=3 \operatorname{Sin}(5 x) \) d. \( y=3 \operatorname{Cos}(3 x) \) e.2 answers -
4) Integrate the following expressions with respect to \( x \) : a. \( y=5 x^{3}-\frac{x^{2}}{4}+5 \) b. \( y=\frac{1}{4 x^{3}} \) c. \( y=3 \sin \sin 4 x \) d. \( y=3 e^{3 x} \)2 answers -
Find \( y^{\prime \prime} \) if \( y=-7 \cos x \) A. \( y^{\prime \prime}=7 \cos x \) B. \( y^{\prime \prime}=-7 \cos x \) C. \( y^{\prime \prime}=-7 \sin x \) D. \( y^{\prime \prime}=7 \sin \mathrm{x2 answers -
Rewrite the system in matrix form. Let \( \mathbf{y}=\left[\begin{array}{l}y_{1} \\ y_{2}\end{array}\right] \) and \( \mathbf{y}^{\prime}=\left[\begin{array}{l}y_{1}^{\prime} \\ y_{2}^{\prime}\end{arr2 answers -
Solve. \[ \left[\begin{array}{l} x^{\prime} \\ y^{\prime} \end{array}\right]=\left[\begin{array}{cc} 1 & 1 \\ -41 & -9 \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right], x(0)=-2, y(0)2 answers -
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\[ \begin{array}{l} y=b o+/-b 1 x \\ y=700-75 x \\ y=640 \quad-80 x \\ \end{array} \] Find SSE Find TSS Find SSR Find \( R^{\wedge} 2 \) \begin{tabular}{cc} \( x \) & \( y \) \\ \hline 2 & 500 \\ 3 &2 answers -
Calculate \( I=\iint_{S} f(x, y, z) d S \) for the surface \[ x^{2}+y^{2}=5^{2}, 0 \leq z \leq 3 \] for the function \( f(x, y, z)=e^{-z} \). \[ I=( \]2 answers -
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Solve (Mathematical Physics : Discussion : Laurent Series)
\( B=\int_{0}^{2 \pi} \frac{d \theta}{\cos \theta+\sin \theta} \)2 answers -
Compute the following improper integrals (a) (b) ∫∫ dxdy 2 2 2 3 whereD:={(x,y)∈R :y≥0} D (1+x +y )2 ∫ ∫ ∫ D dxdydz (1 + x + y + z) √ 7 , where D:={(x,y,z):x≥0, y≥0, z≥0}
Problem 4: Compute the following improper integrals (a) \( \iint_{D} \frac{d x d y}{\left(1+x^{2}+y^{2}\right)^{\frac{3}{2}}} \) where \( D:=\left\{(x, y) \in \mathbb{R}^{2}: y \geq 0\right\} \) (b) \2 answers -
Find all triples of real numbers \( (x, y, z) \) that satisfy the system of equations \[ \begin{array}{l} x^{2}+5 y^{2}+6 z^{2}+8(x y+y z+z x)=36 \\ 6 x^{2}+y^{2}+5 z^{2}+8(x y+y z+z x)=36 \\ 5 x^{2}+2 answers -
Express the solution of the given initial value problem in terms of a convolution integral. \[ y^{\prime \prime}+4 y^{\prime}+29 y=\sin \alpha t, \quad y(0)=0, \quad y^{\prime}(0)=0 \] \[ \begin{array2 answers -
Encuentre el valor de la integral \( \int_{C}\left(x^{2}+i y^{2}\right) d z \) donce \( C \) es el contorno que se muestra en la figura \( [A=(1+2 i) \quad D=(1+3 i)] \) Responda en el archivo de proc2 answers -
es cierto,?
La función \( f(z)=e^{x}(\operatorname{Cos} y+i \) Sen \( y) \) no satisfacen las escuaciones de Cauchy-Riemman Verdadero Falso2 answers -
(1 point) Solve the initial value problem \[ y^{\prime \prime}+3 x y^{\prime}-12 y=0, y(0)=1, y^{\prime}(0)=0 \text {. } \] \[ y= \]1 answer -
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I need help with this one, please show me all the steps, and thank you in advance. Original picture :
5. Consider the vector field \( F(x, y)=\left(4 x^{\wedge} 3^{*} y^{\wedge} 3+1 / x\right) \mathbf{i}+\left(3 x^{\wedge} 4^{*} y^{\wedge} 2-1 / y\right) \mathbf{j} \) : to. a) Is \( F \) conservative?2 answers -
Show all the steps to solve this and thank you! Compute (integral in the picture) where C is given by the parametrization x = 1+ 3t, y = 2+ t^2, z = t^4, for -1<= t <= 1.
6. Calcule \( \int_{C} z \ln (x+y) d s \), donde \( C \) está dada por la parametrización \[ \begin{array}{l} x=1+3 t \\ y=2+t^{2} \\ z=t^{4} \end{array} \] para \( -1 \leq t \leq 1 \).2 answers -
Variación de variables con método de Cramer
\( x^{2} y^{\prime \prime}-x y^{\prime}+y=4 x \ln (x) \) si sabemos que las soluciones de la EDO homogénea son \[ y_{1}(x)=x \text { у } y_{2}(x)=x \ln x \]2 answers -
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Variación de Parámetros con método de Cramer
\( x^{2} y^{\prime \prime}-x y^{\prime}-3 y=-30 \sqrt{x} \) si sabemos que las soluciones a la EDO homogénea son \[ y_{1}(x)=x^{3} \text { y } y_{2}(x)=\frac{1}{x} \text {. } \]2 answers -
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12. \( P=4 y-x \) \[ \left\{\begin{array}{l} x \leq 2 \\ y \geq 0 \\ x+y \geq 1 \\ 2 y-x \leq 1 \end{array}\right. \]0 answers -
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2. \( y=x(1-2 x)-(x+1)^{2}+5 x-1 \) a) \( x \in \mathbb{R}, y \leq 2 / 3 \) b) \( x \in \mathbb{R}, y \leq-2 / 3 \) c) \( x \in \mathbb{R}, y \geq-1 / 8 \) d) \( x \in \mathbb{R}, y \leq 4 / 3 \)2 answers -
3. \( y=3+2 \sqrt{-5+2 x} \) a) \( x \geq 2.5, y \geq 3 \) b) \( x \leq 2.5, y \geq 3 \) c) \( x \geq 2.5, y \leq 3 \) d) \( x \leq 2.5, y \leq 3 \)2 answers -
4. \( y=1-3|2-x| \) a) \( x \in \mathbb{R}, y \leq 3 \) b) \( x \in \mathbb{R}, y \leq-4 \) c) \( x \in \mathbb{R}, y \leq 1 \) d) \( x \in \mathbb{R}, y \leq 2 \)2 answers -
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(d) (e) D r92(y) phz(y,z) O (f) 91(y) b = 2004 91 (y) 92(y) = h₁(y, z) =h₂(y, z) = O J b1(3,2) 2(2) ph₂(2,3) So Song Sale $(2, 3, 2) dydzia f(x, y, Q (3) hi(z,e) b= = (2 ft)'પ્ 91(x) = 92(x)
\( \begin{array}{l}\text { (d) } \int_{a}^{0} \int_{g_{1}(y)}^{g_{2}(y)} \int_{h_{1}(y, z)}^{h_{2}(y, z)} f(x, y, z) d x d z d y \\ a=b= \\ g_{1}(y)=g_{2}(y)= \\ h_{1}(y, z)=h_{2}(y, z)= \\ \text { (e0 answers -
Using the Routh-Hurwitz criterion, determine if the following system is stable.
\( \begin{array}{l}\text { 1. Utilizando el criterio de Routh-Hurwitz, determinar si el siguiente } \\ \text { sistema es estable. } \\ \qquad G(s)=\frac{1}{s^{5}+s^{4}+10 s^{3}+72 s^{2}+152 s+240}\en2 answers -
1) Find the Laplace transform Y(s) = £{y}(s) Y_1 (s) = ? Y_2 (s) = ?
\( \mathbf{y}^{\prime}=\left[\begin{array}{cc}3 & 0 \\ 4 & -3\end{array}\right] \cdot \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c}3 \\ -3\end{array}\right] \) \( \mathbf{y}(t)=\left[\begin{a2 answers -
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Problem 4: Compute the following improper integrals (a) \( \iint_{D} \frac{d x d y}{\left(1+x^{2}+y^{2}\right)^{\frac{3}{2}}} \) where \( D:=\left\{(x, y) \in \mathbb{R}^{2}: y \geq 0\right\} \) (b) \2 answers -
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\[ c_{1} e^{m x}+c_{2} m e^{m x} . \] Matching type (5 pts each). Match the solution in \( B \) to the given problem in \( \mathrm{A} \). 1. \( y^{\prime \prime \prime}-9 y^{\prime \prime}+15 y^{\prim2 answers -
Solve: \[ \begin{array}{l} y^{(4)}+32 y^{\prime \prime}+256 y=0 \\ y(0)=1, y^{\prime}(0)=1, y^{\prime \prime}(0)=-48, y^{\prime \prime \prime}(0)=80 \end{array} \]2 answers -
Diagonalize the matrix, if possible
\( \left[\begin{array}{lll}4 & 0 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5\end{array}\right] \)2 answers