L'altezza di una scatola è 18 cm , le dimensioni interne sono 20 cm e 40 cm . La scatola viene riempita con alcuni dadi a forma di cubo. Lo spigolo di un dado misura 2 cm . - Calcola il volume della scatola e del dado in \( \mathrm{cm}^{3} \). Quanti dadi entrano dentro la scatola? [14400 \( \left.\mathrm{cm}^{3}, 8 \mathrm{~cm}^{3} ; 1800\right] \)

Multiplica \( 7.2 \times 10^{6} \) por \( 1.5 \times 10^{-4} \).

(30 points) Solve the system of linear equations using Ganss-Jordan method. Find the rank of the matrix of this system. Indicate dependent and independent uariables. Find the fundamental solution set (write the answer as a linear combination of particular vectors) \[ \left\{\begin{array}{l}-2 x_{1}+x_{2}+8 x_{3}=0 \\ 7 x_{1}-2 x_{2}-22 x_{3}=0 \\ 3 x_{1}-x_{2}-10 x_{3}=0\end{array}\right. \]

5. Diketahui jarak kedua titik pusat lingkaran adalah 15 cm . Panjang garis singgung persekutuan dalam kedua lingkaran tersebut adalah 12 cm . Jika salah satu lingkaran berjari- jari 7 cm , panjang jari-jari lingkaran lainnya adalah... \( \begin{array}{ll}\text { A. } 2 \mathrm{~cm} & \text { D. } 5 \mathrm{~cm} \\ \text { B. } 3 \mathrm{~cm} & \text { E. } 6 \mathrm{~cm} \\ \text { C. } 4 \mathrm{~cm} & \end{array} \)

1. Resuelvan los siguientes sistemas por el metodo de Gauss Jordan. \( \left\{\begin{array}{l}x+2 y+3 z=2 \\ x+3 y-z=-2 \\ 3 x+4 y+3 z=0\end{array}\right. \)

(e) Si \( m(\angle \alpha)=\frac{7 \pi}{6} \) y \( m(\angle \beta)=-30^{\circ} \). entonces \( \alpha \) y \( \beta \) son ángulos suplementarios \( F= \)