Advanced Math Archive: Questions from September 18, 2022
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5. Use a table to express the values of each of these Boolean functions. a) \( F(x, y, z)=\bar{x} y \) b) \( F(x, y, z)=x+y z \) c) \( F(x, y, z)=x \bar{y}+\overline{(x y z)} \) d) \( F(x, y, z)=x(y z1 answer -
\( y^{\prime \prime}+2 y^{\prime}+e^{y}=x \) \( 3 x^{2} y^{\prime \prime}+2 \ln (x) y^{\prime}+e^{x} y=3 x \cos x \) \( 4 y y^{\prime \prime}-x^{3} y^{\prime}+\cos y=e^{2 x} \) \( \frac{d^{2} y}{d x^{1 answer -
1 answer
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(1 point) Consider the following convergent series: ∑k=0∞811k≈8.8 Also, consider the partial sums: ∑k=0N811k S2= 1064/121 The true error of S2 as an approximation of the series is .00661157 Si
(1 point) Consideremos la siguiente serie convergente: \[ \sum_{k=0}^{\infty} \frac{8}{11^{k}} \approx 8.8 \] También, consideremos las sumas parciales: \[ \sum_{k=0}^{N} \frac{8}{11^{k}} \] - \( S_{1 answer -
1 answer
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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 -
just need to slove it using separable DE
\( \frac{d y}{d x}=\frac{\frac{x}{(2 x+1)^{3}}}{y \sin y \cos y} \)2 answers -
13. Maximize \( P=x+3 y \) subject to \[ \begin{array}{r} 2 x+y \leq 6 \\ x+y \leq 4 \\ x \leq 1 \\ x \geq 0, y \geq 0 \end{array} \]1 answer -
Find the solution to the differential equation (i) \( y^{\prime \prime \prime}+3 y^{\prime}-4 y=0, \quad y(0)=0, y^{\prime}(0)=3, y^{\prime \prime}(0)=6 \) (ii) \( y^{\prime \prime \prime}-y^{\prime \1 answer -
WA#3 4
4. Find the solution of the given IVP: \[ \begin{array}{l} y^{\prime \prime}+4 y=3 \sin (2 t) \\ y(0)=2 \\ y^{\prime}(0)=-1 \end{array} \]1 answer -
WA#3 8
8. Solve the following IVP: \[ y^{\prime \prime}-2 y^{\prime}+y=\frac{e^{t}}{t^{2}+1} \quad y(0)=5 \quad y^{\prime}(0)=-1 \]1 answer -
do 9, 11, 16
In Problems 9-20, graph each function. 9. \( y=4^{x} \quad \) 10. \( y=8^{x} \) 11. \( y=2\left(3^{x}\right) \) 12. \( y=3\left(2^{x}\right) \) 13. \( y=\left(\frac{4}{5}\right)^{x} \) 14. \( y=\left(1 answer -
2 answers
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Resuelva: \[ \begin{array}{l} 1 . y^{\prime}+6 t=e^{4 t}, y(0)=2 \\ 2 . y^{\prime \prime}+6 y^{\prime}+4 y=0, y(0)=1, y^{\prime}(0)=0 \\ 3 \cdot y^{\prime}+t=e^{5 t}, y(0)=1 \\ 4 . y^{\prime \prime}-51 answer -
Find \( (w \circ g)(x) \) and \( (g \circ w)(x) \) for \( w(x)=3 x-2 \) and \( g(x)=\sqrt{x} \). \[ (w \circ g)(x)= \] \[ (g \circ w)(x)= \]1 answer -
Answer should be
2) Solve the IVP. \[ y^{\prime}=2 x\left(2 e^{-x^{2}}-y\right) \quad y(0)=3 \] Linear Equations KEY 1. (a) \( y=\frac{1}{2} x-\frac{1}{8}+K e^{-4 x} \) (b) \( y=-\frac{1}{11} e^{-2 x}+\frac{5}{3}+K e1 answer