Select all the correct answers. Imagine a car as a model that represents the human body, with its parts performing various functions similar to human body systems. Which two statements are correct analogies? The gas in the car is the digestive system that provides the necessary energy. The frame of the car is the digestive system that provides structure and support to the body. The engine of the car is the digestive system that circulates nutrients to the rest of the body. The oil in the car is the excretory system that protects and coats the body.

1) Express the complex number \( 1-\sqrt{3} i \) in polar form. Hence express \( (1-\sqrt{3} i)^{5} \) in the form \( a+b i \).

\( \begin{array}{ll}\text { 7. } F(x)=\left(x^{4}+3 x^{2}-2\right)^{5} & \text { 8. } F(x)=\left(4 x-x^{2}\right)^{100} \\ \text { 9. } F(x)=\sqrt{1-2 x} & \text { 10. } f(x)=\frac{1}{(1+\sec x)^{2}} \\ \text { 11. } f(z)=\frac{1}{z^{2}+1} & \text { 12. } f(t)=\operatorname{sen}\left(e^{t}\right)+e^{\operatorname{sen} t} \\ \text { 13. } y=\cos \left(a^{3}+x^{3}\right) & \text { 14. } y=a^{3}+\cos ^{3} x \\ \text { 15. } y=x e^{-k x} & \text { 16. } y=e^{-2 t} \cos 4 t \\ \text { 17. } f(x)=(2 x-3)^{4}\left(x^{2}+x+1\right)^{5} & \\ \text { 18. } g(x)=\left(x^{2}+1\right)^{3}\left(x^{2}+2\right)^{6} & \\ \text { 19. } f(t)=(t+1)^{2 / 3}\left(2 t^{2}-1\right)^{3} & \\ \text { 2n } F(t)=(3 t-1)^{4}(2 t+1)^{-3} & \end{array} \)

2. \( f(x)=x^{3} \) en \( a=1 \)

Los matrisekvationen \( \operatorname{sar} \quad A=\left(\begin{array}{ccc}1 & 0 & 2 \\ -2 & 1 & 0 \\ 0 & 1 & 1\end{array}\right) \quad \) och \( B=\left(\begin{array}{ccc}1 & 3 & 0 \\ -1 & -2 & 0 \\ 0 & -1 & -1\end{array}\right) \)

3. Si m representa a un número entero par positivo. ¿cuál de las siguientes afirmaciones es siempre verdadera? A) \( (3 m+12) \) es divisible por 4 . B) \( (4 m+3 m) \) es divisible por 14 . C) \( (2+5 m) \) es divisible por 7 . D) \( (m+3) \) es divisible por 6 .