Other Math Archive: Questions from January 04, 2023
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Find the truth table T = T (E) for the Boolean expression E = E(x, y, z) where (a) E1=xyz′+x′yz+x′yz′+x′y′z; (b) E2=x′yz+x′yz′;
Find the truth table \( T=T(E) \) for the Boolean expression \( E=E(x, y, z) \) where (a) \( E_{1}=x y z^{\prime}+x^{\prime} y z+x^{\prime} y z^{\prime}+x^{\prime} y^{\prime} z \); (b) \( \mathrm{E}_{2 answers -
solve this Cauchy problems
\( \alpha) \) \[ \begin{array}{c} x u_{x}-y u_{y}=u, x>0, y>0 \\ u(x, x)=x^{2}, x>0 \end{array} \] B) \[ \begin{array}{c} -2 y u_{x}+u_{y}+2 y u=2 y, x>0, y \in \mathbb{R}^{*} \\ u(1, y)=1+e^{-1-2 y^{2 answers -
Example Solve the initial value problem \( y^{\prime}+\frac{2}{x} y=\frac{3 x^{2} y^{2}+6 x y+2}{x^{2}(2 x y+3)}, \quad y(2)=2 \).2 answers -
Let \( T: R^{3} \rightarrow R^{3} \). Which of the following functions is a linear transformation? a) \( T(x, y, z)=(x, 2, z+y) \) b) \( T(x, y, z)=(0, x+y, z) \) c) \( T(x, y, z)=\left(x, x^{2}+y, y-2 answers -
7. \( \sin ^{-1} \frac{1}{\sqrt{2}}+\sin ^{-1} \frac{\sqrt{2}-1}{\sqrt{6}}+\sin ^{-1} \frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+\sin ^{-1} \frac{2-\sqrt{3}}{\sqrt{20}}+\sin ^{-1} \frac{\sqrt{5}-2}{\sqrt{30}2 answers