Advanced Math Archive: Questions from October 09, 2022
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Use the double integral to check that the moments of inertia in the region with respect to the axes are those illustrated in the figure. Then calculate the turning radius with respect to each axis ...
1. Utilice la integral doble para comprobar que los momentos de inercia en la región con respecto a los ejes son los que se ilustran en la figura. Luego calcule los radios de giro con respecto a cada1 answer -
For particles with spin 3/2, the matrix representation of the operator S_x in the S_z basis is given by: [Here goes the equation showed in the image] For each eigenstate, check whether they are eigens
Para partículas de espín \( 3 / 2 \), la representación matricial del operador \( \hat{S}_{x} \) en la base de \( \hat{S}_{z} \) está dado por \[ \hat{S}_{x} \rightarrow \frac{\hbar}{2}\left(\begi2 answers -
4.4. Find the domain for each of the following functions: a) \( y=\sqrt{x-5}-\sqrt{8-x} \) b) \( y=\frac{x+2}{(x-5)(3-x)} \) c) \( y=\frac{1}{\lg x} \) d) \( y=\frac{\log _{7} x}{\sqrt[5]{x-3}} \) e)2 answers -
Find \( \frac{d^{2} y}{d x^{2}} \) for the follo \[ y=8 x \cos \left(x^{2}\right) \] \[ \frac{d^{2} y}{d x^{2}}= \] Evaluate and simplify \( y^{\prime} \) \[ y=\left(\tan \left(3 x^{3}+5 x+9\right)\r1 answer -
Prove or disprove the propositions: (a) \( \forall x \in \mathbb{R}, \exists y \in \mathbb{R} \cdot x=y^{3} \) (b) \( \exists y \in \mathbb{Z} . \forall x \in \mathbb{N}, x>y \) (c) \( \forall x \in[02 answers -
plz show each step answer is cos(y/x)=-x!!!!!
5. Solve the initial value problem, \[ x \tan \left(\frac{y}{x}\right) y^{\prime}+x=y \tan \left(\frac{y}{x}\right), \quad y(1)=\pi \]2 answers -
22.19. Find the general solution for each. (a) \( y^{\prime \prime}+2 y^{\prime}=4 x^{2} \) (b) \( y^{\prime \prime}+2 y^{\prime}+y=c 0 \) (c) \( \ddot{x}+c \dot{x}=f(t) \) (d) \( \left(D^{4}-20 D^{2}2 answers -
Find \( y \) as a function of \( t \) if \[ 4 y^{\prime \prime}+36 y^{\prime}+117 y=0 \] \[ y(2)=3, \quad y^{\prime}(2)=6 \]2 answers -
solve initial value problem
Solve the initial value problems 1. \( y^{\prime \prime}+4 y^{\prime}+4 y=4 \cos 2 t \) \( y(0)=0, \quad y^{\prime}(0)=1 \) 2. \( y^{\prime \prime}+4 y^{\prime}+4 y=16 t \sin 2 t \) \( y(0)=1, \quad y2 answers -
2 answers
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true or false
Cierto o Falso: 1). \( x^{2} y^{\prime \prime}-2 y^{\prime}-4 y=0 \) 2). \( x^{2} y^{\prime \prime}-x y^{\prime}+y=x^{3} \) 3). \( x^{2} y^{\prime \prime}-4 x y^{\prime}+6 y=2 x^{4}+x^{2} \) 4). \( y^1 answer -
Prove "cancellation" for fields (without looking up the proofs): (a) For all \( x, y, z \in \mathbb{F} \), if \( x+z=y+z \), then \( x=y \). (b) For all \( x, y, z \in \mathbb{F} \backslash\{0\} \), i2 answers -
For all n ∈ N we define 10.1 Calculate I0. 10.2 utilizing integration by parts show that 10.3 Find a non-recursive expression for In and prove by induction that the expression found is correct.
Ejercicio 10. Para todo \( n \in \mathbb{N} \) se define \[ I_{n}=\int_{0}^{x} \frac{t^{n}}{n !} e^{1-t} \mathrm{dt} . \] P-10.1 Calcule \( I_{0} \). P-10.2 Utilizando integración por partes muestre2 answers -
Let (x)=x cos(x) be a solution of the differential equation -3x+5y=0. find one second solution
Sea \( y_{1}(x)=x^{2} \cos (\ln x) \) una solución de la ecuación diferencial \( x^{2} y^{\prime \prime}-3 x y^{\prime}+5 y=0 \). Encuentre una segunda solución. \[ y_{2}(x)=x^{2} \tan (\ln x) \] \2 answers -
Find the general solution of the differential equation
Encuentre la solución general de la ecuación diferencial \( \frac{d^{2} t}{d s^{3}}+5 \frac{d^{2} t}{d s^{4}}-2 \frac{d^{2} t}{d s^{3}}-10 \frac{d^{2} t}{d s^{2}}+\frac{d t}{d s}+5 t=0 \). \[ t=c_{12 answers -
Solve the initial value problems 1. \( y^{\prime \prime}+4 y^{\prime}+4 y=4 \cos 2 t \) \[ y(0)=0, \quad y^{\prime}(0)=1 \] 2. \( y^{\prime \prime}+4 y^{\prime}+4 y=16 t \sin 2 t \) \[ y(0)=1, \quad y2 answers -
Find the general solution of the differential eqns 5. \( y^{\prime \prime}+3 y^{\prime}-4 y=e^{2 t} \) 6. \( y^{\prime \prime}+y=2 \sin t \) 7. \( y^{\prime \prime}+6 y^{\prime}+9 y=25 t e^{-3 t} \)2 answers -
2 answers
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2 answers
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4. Solve following \( \operatorname{ODE}(\mathrm{u}=\mathrm{y} / \mathrm{x}) \) (1) \( y^{\prime}=\frac{y}{x+y} \) (2) \( x y^{\prime}=x^{2} e^{y / x}+y \) (3) \( x y^{\prime}=\frac{y^{2}}{x}+y \) (4)2 answers -
2. Solve following questions (Separation variables) (1) \( e^{x+y} y^{\prime}=3 x \) (2) \( y=x y^{\prime}+\frac{y}{1+y} \) (3) \( \sin 3 x d x+2 y \cos ^{3} 3 x d y=0 \) (4) \( \left(e^{x}+e^{-x}\rig2 answers -
Diga si la ecuación diferencial dada es lineal en \( y \) o en \( x \). En caso de serlo determine su solución ceneral. 5. \( y d x+\left(x y+2 x-y e^{y}\right) d y=0 \)2 answers -
Q7: (2 point) Without directly evaluating the determinant, show that \[ \left|\begin{array}{lll} \sin \alpha & \cos \alpha & \sin (\alpha+\delta) \\ \sin \beta & \cos \beta & \sin (\beta+\delta) \\ \s2 answers -
2 answers