Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to \( t \). \( x^{\prime}=5 x-6 y+\sin t \) \( y^{\prime}=3 x-y-\cos t \) Eliminate \( x \) and solve the remaining differential equation for \( y \). Choose the correct answer below. A. \( y(t)=C_{1} e^{2 t}+C_{2} t e^{2 t}+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) B. \( y(t)=C_{1} e^{-2 t} \cos 3 t+C_{2} e^{-2 t} \sin 3 t+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) C. \( y(t)=C_{1} e^{-2 t}+C_{2} t e^{-2 t}+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) D. \( y(t)=C_{1} e^{2 t} \cos 3 t+C_{2} e^{2 t} \sin 3 t+\frac{19}{40} \cos t+\frac{7}{40} \sin t \) E. The system is degenerate.

21 Ao saltar de um avião, um Paraquedista aterrissou exatamente na metade do percurso entre uma árvore representada pelo ponto \( \mathrm{A}(2,3) \) e um rochedo representado pelo ponto \( \mathrm{B}(4,-5) \). Utili- zando os conhecimentos de geometria analítica, calcule o ponto médio \( \mathrm{M}(\mathrm{Xm} \), Ym) onde o Para- quedista aterrissou. (A) \( \mathrm{M}(3,-1) \) (B) \( \mathrm{M}(3,4) \) (C) \( \mathrm{M}(5,-1) \) (D) \( \mathrm{M}(3,-4) \)

11. Resuelve el sistema lineal por medio de la inversa \( X-3 Y=-5 \) \( Y+3 Z=-1 \) \( Z-10 Y+2 Z=-20 \)

a su profesor. 1. Determinen la ecuación de la recta que pasa por los siguientes puntos. Tracen una recta y ubiquen la ecuación en el plano. a. \( (-4,1) \) y \( (-6,2) \) b. \( (6,7) \) y \( (-4,-5) \)

Multiple Select Questlon Select all that apply Uses of sensors to control manufacturing processes include (More than one answer may be correct) \( \square \) handcrafting a pair of shoes \( \square \) the measurement of the thickness of material \( \square \) framing a house \( \square \) measuring humidity

3. \( \frac{x^{2}-x-12}{x^{2}+5 x+6} \)