Advanced Math Archive: Questions from January 02, 2023
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Simplify the following algebra
(i) \( 2 w \times 3 w^{2} \times w \times 2 v \times v^{2} \times 2 w \times 4 v \) (ii) \( (2 w)^{2} \times\left(3 w^{2}\right)^{3} \) (i) \( \frac{\left(a^{3} b^{-2}\right)^{4}}{\left(a^{2} b^{2}\ri2 answers -
Simplify the following algebra
\[ x-3(x+2)-(3 x-2) \] \[ \text { (b) } a \times b \times a \times\left(a^{2} b\right)^{3} \] (c) \( (2 x-3)(3 x+2)-(x+2) \) (e) \( \left(a^{3} \times b^{2}\right)^{3} \times a^{2} \div b \) (f) \( 82 answers -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}+64 y^{\prime}=0 \] \[ \begin{array}{l} y(0)=-4, y^{\prime}(0)=64, y^{\prime \prime}(0)=256 . \\ y(x)= \end{array} \]2 answers -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-11 y^{\prime \prime}+24 y^{\prime}=42 e^{x} \] \[ \begin{array}{l} y(0)=23, \quad y^{\prime}(0)=15, \quad y^{\prime \prim2 answers -
need in 15 min
Compute \( \left(T_{3} \circ T_{2} \circ T_{1}\right)(x, y) . T_{1}(x, y)=(-2 y, 3 x, x-2 y) \), \[ T_{2}(x, y, z)=(y, z, x), T_{3}(x, y, z)=(x+z, y-z) \text {. } \] \[ \left(T_{3} \circ T_{2} \circ T2 answers