Other Math Archive: Questions from September 25, 2022
-
2 answers
-
10. Which of the following are true in the universe of all real numbers? * (a) \( (\forall x)(\exists y)(x+y=0) \). (b) \( (\exists x)(\forall y)(x+y=0) \). (c) \( (\exists x)(\exists y)\left(x^{2}+y^1 answer -
2 answers
-
4. Suppose \( x \in \mathbb{R} \). If \( x^{7}+3 x^{3}+5 x \geq x^{6}+x^{4}+6 \), then \( x \geq 0 \)2 answers -
Solve the following IVP: \[ \begin{array}{c} y^{\prime \prime \prime}-9 y^{\prime \prime}-y^{\prime}+9 y=0 \\ y(0)=8, \quad y^{\prime}(0)=-2, \quad y^{\prime \prime}(0)=328 \end{array} \] Enter the an1 answer -
5. Solve the initial value problem \[ y^{\prime}-y=2 t e^{2 t}, \quad y(0)=1 . \] 6. Solve \[ \frac{d y}{d x}=-\frac{x}{y} \]1 answer -
2 answers
-
2. Find \( x \) and \( y \) if \[ \left[\begin{array}{cc} 1 & 3 \\ x & x+y \end{array}\right]=\left[\begin{array}{ll} 1 & 3 \\ 2 & 6 \end{array}\right] \]2 answers -
Which one of the following is the negation of the statement: \( \exists x, y \in \mathbb{Z} \) such that if \( 1 \geq x^{2} \geq y^{2} \), then \( x \geq y \) \[ \begin{array}{l} \forall x, y \in \mat3 answers -
6. From the given harmonic function, find the corresponding analytic function \( f(z)=u+i v \) : (1) \( u=e^{x}(x \cos y-y \sin y), f(0)=0 \); (2) \( v=\frac{y}{x^{2}+y^{2}}, f(2)=0 \).2 answers