Advanced Math Archive: Questions from November 12, 2022
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EVALUATE THE FOLLOWING ALGEBRAIC EXPRESSIONS. 1. \( 2 x^{2}+x y^{2} \), where \( x=-1, y=2 \) 2. \( 2\left(x^{2}-y^{2}\right) \), where \( x=2, y=-2 \) 3. \( \frac{2 x+2 y}{x^{2}+10} \) if \( x=-1, y=2 answers -
SIMPLIFY ALGEBRAIC EXPRESSIONS. 5. \( 5 x^{2}-2 x+3-3 x^{2}-3 x-8 \) 6. \( -2 x^{2}+3 x+1-2 x^{2}-3 x-3 \)2 answers -
2 answers
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(40 points) Solve the initial value problem \[ y^{\prime \prime}+4 x y^{\prime}-16 y=0, y(0)=2, y^{\prime}(0)=0 \text {. } \] \[ y= \]2 answers -
\( \mathbf{y}^{\prime}=\left[\begin{array}{lll}4 & 0 & 0 \\ 2 & 1 & 0 \\ 2 & 0 & 1\end{array}\right] \mathbf{y} \)2 answers -
2 answers
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1. Solve the initial value problem \[ \mathbf{y}^{\prime}=\left[\begin{array}{ccc} -1 & 4 & 2 \\ -2 & 5 & 2 \\ 1 & -2 & 0 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c} 7 \\2 answers -
4. Let \( \mathbf{F}=\left(-y, 0, x^{2}+y^{2}\right) \), and \( \mathbf{S}=\left\{(x, y, s): 4 x^{2}+y^{2} \leq \frac{\pi}{2}, z=\sin \left(4 x^{2}+y^{2}\right)\right\} \). Compute \[ \iint_{\mathbf{S2 answers