Volume of a cube is \( 216 \mathrm{~cm}^{3} \), find its total surface area. Volume of a cube is \( 512 \mathrm{~cm}^{3} \), find its total surface area.

Determine if the following lines are parallel, perpendicular, or neither \[ \begin{array}{l}y=\frac{8 x}{7}-1 \\ -x+3 y=1\end{array} \]

Find the perpendicular d \( x^{2}+y^{2}-8 x+2 y+8 \) Hence, find the shortest

Find the equation of line perpendicular to \( 5 x-3 y+4=0 \) that passes through the point \( (-4,1) \).

BCD un carré et \( G= \) bary \( \{(A, 2) ;(B,-1) ;(C, 2) ;(D ; 1)\} \) oient \( I= \) bary \( \{(A, 2) ;(B,-1)\} \) et \( J= \) bary \( \{(C, 2) ;(D ; 1)\} \); Montrer que \( 2 \overrightarrow{G A}-\overrightarrow{G B}=\overrightarrow{G I} \) et \( 2 \overrightarrow{G C}+\overrightarrow{G D}=3 \overrightarrow{G j} \) En déduire que \( G=\operatorname{bary\{ }(I, 1) ;(1,3)\} \) Construire I et \( J \) puis \( G \) a) Vérifier que: \( \forall M \in(P): 2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}=4 \overrightarrow{M G} \) b) Déterminer l'ensemble des points M du plan \( (P) \) tel que : \[ \|2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}\|=4\|2 \overrightarrow{M A}-\overrightarrow{M B}\| \]

A ball bounces \( \frac{1}{2} \) of its previous height on each bounce. Find the total distance covered by the ball, until it comes to rest, if it is dropped from a height of 20 metres.