Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to \( t \). \[ \begin{aligned} 2 x^{\prime}+y^{\prime}-9 x-9 y & =e^{-4 t} \\ x^{\prime}+y^{\prime}+8 x+4 y & =e^{9 t}\end{aligned} \]

9. The energ temperature o cal/g \( \cdot C^{*} \) is: A) 0.50

Solve for \( |A=| \) \[ \begin{array}{l}x+2 y+2 z=4 ; 3 x-y+4 z=25 ; 3 x+2 y-z=-4 \\ \text { Select one: } \\ \text { a. } 41 \\ \text { b. } 164 \\ \text { c. } 182 \\ \text { d. }-123\end{array} \]

Доказати идентитете: а) \( \frac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}-x^{-\frac{1}{3}}}+\frac{x^{\frac{4}{3}}}{x^{\frac{4}{3}}-x^{\frac{1}{3}}}-\frac{2 x^{\frac{1}{3}}}{x^{\frac{1}{3}}-x^{-\frac{2}{3}}}=0, x \neq 0, x \)

2. How did Enlightenment Ideas challenge political absolutism? 3. Who are the most prominent Enlightenment thinkers, what were their most important intellectual contributions to the Enlightenment, and what were some long term effects of these contributions? 4. What were the immediate effects of the Enlightenment? 5. How did the abolitionist movement in Britain begin? 5. What is "Enlightened Despotism"? Provide and example and a list of accomplishments of this monarch that are consistent with Enlightenment ideals.

(1.) 5