Bài 3. (I diêm) Có ba chiếc họp hình vuông: Hộp màu đỏ cao 8 cm , hộp màu xanh cao 7 cm , hộp màu vàng a) 12 cm . Người ta xếp thành ba chồng bằng nhau, mỗi chồng một màu. Hỏi chiều cao nhỏ nhất của chồng hộp đô.

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

EXERCISE 15.1 (in the figure, seg OP \( \perp \mathrm{seg} S T \). Chord LM \( \| \) chord ST. O is the centre of the circle. \( \mathrm{ON}=6 \mathrm{~cm}, \mathrm{LM}=16 \mathrm{~cm} \). Find the length of the longest chord that can be drawn in the circle. (2018) \( \begin{array}{llll}\text { (1) } 32 \mathrm{~cm} & \text { (2) } 20 \mathrm{~cm} & \text { (3) } 12 \mathrm{~cm} & \text { (4) } 22 \mathrm{~cm}\end{array} \)

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.