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Advanced Math Archive: Questions from December 15, 2022

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  Solve \( F_{y y}+3 F_{x y}+2 F_{x x}=-2 x, F(x, 0)=-x, \partial_{y} F(x, 0)=0 \) \[ F(x, y)= \]
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  Find \( \frac{d^{2} y}{d x^{2}} \) if \( \cos ^{2} x+\sin ^{2} y=1 \) A. \( \quad \frac{2 \cos 2 x}{\sin 2 y}-\frac{2 \cos 2 y \sin ^{2} 2 x}{\sin ^{3} 2 y} \) B. \( \frac{2 \cos 2 x}{\sin 2 y}+\frac{
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  \( \log _{3}(x+10)-\log _{3} 36=2 \) Resuelva para \( x \). \[ \log 55+\log 55+\log 5 x=2 \] Si se invierten \( \$ 14,000 \) a una tasa anual de \( 8 \% \) compuesto cada hora, determine el valor de
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• Determine the surface area of ​​that portion of the cylinder x 2 # z 2 ! sixteen which is over the region in the first z!x2"y2 which is in the first octant first quadrant bounded by the graphs of
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  Resuelva para \( x \) \[ \log 55+\log 55+\log 5 x=2 \]
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  Encuentre el valor de \( x \) en: \( \log x=9 \). No incluya comas (.) en su contestación. \( x= \)
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  Si se invierten \( \$ 14,000 \) a una tasa anual de \( 8 \% \) compuesto cada hora, determine el valor de la inversión al final de 12 años. Redondee su contestación al centavo más cercano. No incl
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• 3. Determine the surface area of ​​that portion of the cylinder x^2 + z^2 = 16 that lies over the region in the first quadrant bounded by the graphs of x = 0, x = 2, y=0,y=5.
  Determine el área de la superficie de aquella porción del cilindro \( x^{2}+z^{2}=16 \) que está sobre la región en el primer cuadrante acotada por las gráficas de \( x=0, x=2 \), \( y=0, y=5 \)
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  Q4: Is \( Z_{10} \oplus Z_{12} \oplus Z_{6} \approx Z_{60} \oplus Z_{6} \oplus Z_{2} \) ? Is \( Z_{10} \oplus Z_{12} \oplus Z_{6} \approx Z_{15} \oplus \) \( Z_{4} \oplus Z_{12} \)
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  3 (5 pts.) Prove that if \( x, y \in \mathbb{R}, x>0 \) and \( y>0 \), then \( \sqrt{x+y} \neq \sqrt{x}+\sqrt{y} \).
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  \( y^{\prime \prime}+4 y=\left\{\begin{array}{ccc}\sin (t) & 0 \leq t
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  (a) Find the negation of each statement below. (i) \( (\forall x \in \mathbb{R})(\exists y \in \mathbb{R})(|x+y|=|x|+|y|) \) (ii) \( (\exists x \in \mathbb{R})(\forall y \in \mathbb{R})(|x \cdot y|0 \
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  Use the Laplace Transform to solve: \( \frac{1}{8} y^{\prime \prime}+4 y=0, y^{\prime}(0)=2, y^{\prime}(0)=0 \) (a) \( Y(s)= \) (b) \( y(t)= \)
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  48. \( \mathbf{a}=\langle 1,-1\rangle, \theta=2 \pi / 3 \)
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  Solve the given equation.. \[ \left(e^{2 x}+y-1\right) d x-d y=0 \] a. \( y=C e^{x}+e^{2 x}+x \) b. \( y=C e^{-x}+1+e^{2 x} \) c. \( y=C e^{x}+1+e^{2 x} \) d. \( y=C x e^{x}+e^{2 x} \) e. \( y=C e^{x}
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  Find all complementary functions of the equation \( y^{\prime \prime}-6 y^{\prime}+9 y=0 \). a. \( \cos 3 x, \sin 3 x \) b. \( e^{-3 x}, e^{3 x} \) c. \( e^{-3 x}, x e^{-3} \) d. \( e^{3 x}, x e^{3 x}
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  2. Solve: a. \( y^{\prime \prime}+6 y^{\prime}+10 y=0 \) b. \( y^{\prime \prime}-6 y^{\prime}+9 y=0 \) c. \( y^{\prime \prime}-5 y^{\prime}+6 y=0 \)
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  1. Solve: a. \[ y^{\prime}=\frac{(x+1) y}{1+x^{2}} \] b. \[ y^{\prime}-\frac{1}{x} y=x \sin x \]
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  suelve \( \left(y+x \cot \frac{y}{x}\right) d x-x d y=0 \) \( \ln \cos \frac{y}{x}|=\ln | x \mid+c \) \[ x \cos \frac{y}{x}=c \] \( \ln |x|=\sec ^{2}\left(\frac{y}{x}\right)+c \) Ninguna de las anteri
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