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Other Math Archive: Questions from December 27, 2022

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  10) Find \( y_{p}(0) \) for the equation \( y^{(4)}-y^{\prime \prime}-2 y^{\prime}+2 y=3 x e^{x}+\cos x \) a) \( 6 / 25 \) b) \( 1 / 5 \) c) \( 1 / 10 \) d) \( 3 / 5 \) e) \( -1 / 25 \)
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  Verify that each given function is a solution of the differential equation: 5. \( 2 y^{\prime}+y=0 ; y=e^{-\frac{x}{2}} \) 6. \( y^{\prime \prime}+y=0 ; \quad y=C_{1} \sin x+C_{2} \cos x \) 7. \( \fra
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  2. \( y^{\prime \prime}-y^{\prime}-12 y=0, y(0)=3, y^{\prime}(0)=5 \) 3. \( y^{\prime \prime}-3 y^{\prime}+2 y=4 x^{2} \) 4. \( y^{\prime \prime}+2 y^{\prime}+2 y=10 \sin 4 x \) 5. \( y^{\prime \prime
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  1. Given \( g(x)=\frac{3 x+7}{x-1} \), determine \( g(g(-5)) \). (1 mark)
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• (1 point) The equation y=αx2β+x2 is equivalent to the equation 1y=βα⋅1x2+1α. Using this, fit the following data to the model using regression via least squares. xy 1.1 0.45 2.9 1.72 1.85 0.88 5
  (1 point) La ecuación \[ y=\frac{\alpha x^{2}}{\beta+x^{2}} \] es equivalente a la ecuación \[ \frac{1}{y}=\frac{\beta}{\alpha} \cdot \frac{1}{x^{2}}+\frac{1}{\alpha} \] Usando esto, ajustar los sig
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• The equation y=αxeβx is equivalent to the equation ln(yx)=βx+lnα. Using this, fit the following data to the model using regression via least squares. xy 3.9 2.88 2.05 1.32 1.1 0.68 3.15 1.94 4.85
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• (1 point) Fit the following data to a parabola using regression via squares. xy −1.15 −9.28 2.1 28.26 −0.05 −7.34 −1.85 −2.84 1.15 7.66 Then the curve fitted to the data is y=
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• (1 point) Coefficient of Determination The coefficient of determination, which is denoted by R2 or r2, is a parameter that is used as a criterion to verify if the regression model is adequate. To def
  (1 point) Coeficiente de Determinación El coeficiente de determinación, que se denota por \( R^{2} \) o \( r^{2} \), es un parámetro que se usa como criterio para verificar si el modelo de regresiÃ
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• (1 point) Fit the following data to a plane using squares. X and Z −2.05 −2.2 −2.68 −0.1 −0.2 −8.93 1.8 2.05 −13.41 0.85 1.15 −11.54 −1.1 0.9 −10.19 Then the plane fitted to the d
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• (1 point) In a test to measure wear on a certain brand of tires, the following data was obtained: Mileage Wear (mm) 5000 0.2 12000 0.9 15000 1.2 18000 2 25000 2.3 32000 3 37000 3.1 40000 3.7 47000 4
  (1 point) En una prueba para medir el desgaste en cierta marca de neumáticos se obtuvieron los siguientes datos: Se pretende utilizar un modelo lineal para explicar la relación entre el kilometraje
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