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Advanced Math Archive: Questions from January 28, 2023

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  2. Si las bases están dadas por \( B=\{(1,0,0),(0,1,0),(0,0,1)\} \) y \( B^{\prime}=\{(1,0,0),(0,2,6),(6,0 \), 12)\}, halle una matriz de transición de \( B \) a \( B \) '.
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• solve and graph
  \( y^{\prime \prime \prime}+4 y^{\prime \prime}+5 y^{\prime}+2 y=6 \delta(t) ; y(0)=y^{\prime}(0) \) \( =y^{\prime \prime}(0)=0 \)
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  Express \( \frac{1}{8^{3}} \) using a negative exponent.
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  Differentiate \( y=-6 \sin (\tan \sqrt{\sin x}) \). \( y^{\prime} \)
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• please show all steps.
  \( \left\{\begin{array}{l}16 x-24 y-6 z=-58 \\ -18 x+29 y+9 z=60 \\ -6 x+9 y+3 z=18\end{array}\right. \)
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• please do problem (c) and (h), and show all steps.
  3. Find all of the equation. (a) \( y^{\prime}=-x \) (b) \( y^{\prime}=-x \sin x \) (c) \( y^{\prime}=x \ln x \) (d) \( y^{\prime \prime}=x \cos x \) (e) \( y^{\prime \prime}=2 x e^{x} \) (f) \( y^{\p
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  Ejercicios de Práctica: 1. Utilizando los vectores \( \mathbf{u}=(8,1,-8) \) y \( \mathbf{v}=(2,5,2) \) halle el producto interno \( \langle u, v\rangle=2 u_{1}{ }_{1}+3 u_{2} v_{2}+u_{3} v_{3} \) (1
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  (11) \( y^{\prime}=(x+1)^{4} \quad y(0)=1 \quad O D E 1^{\text {St corder }} \) \( y= \) ? \( y(1)=? \)
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• Suppose 0<x<1, and n is a positive integer.​​​​​​​ Please find the closed form for the series $\sum_{k=0}^{\infty}\binom{n+3k-1}{3k}x^{3k}$. (On Latex, it is ​​​​​​​)
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• General solution of the ODE y''' - 2y'' + y' = x2 + 3ex
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• Using the following information Use a=0.01 Ho: p1=18 Ha: p1>18 Sample N=36 S=5 X=20 a Test the following hypothesis presented above b. Find a 99% confidence interval for the true value of the mean
  Jtilizando la siguiente información Utilice \( \alpha=0.01 \) Ho: \( \mu_{1}=18 \) Ha: \( \mu_{1}>18 \) \[ \begin{array}{l} \text { Muestral } \\ N_{1}=36 \\ S_{1}=5 \\ X_{\text {barral }}=20 \end{ar
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