11. Let the equations of two adjacent sides of a parallelogram \( A B C D \) be \( 2 x-3 y=-23 \) and \( 5 x+4 y=23 \). If the equation of its one diagonal \( A C \) is \( 3 x+7 y=23 \) and the distance of \( A \) from the other diagonal is \( d \), then \( 50 d^{2} \) is equal to

Soit \( A B C \) un triangle. Eet \( F \) deux points tel que: \( \overrightarrow{B E}=2 \overrightarrow{A C} \quad \) et \( \overrightarrow{C F}=\frac{1}{2} \overrightarrow{A B} \) 1) Construire les points \( E \) et \( F \). 2) Montrer que : \( \overrightarrow{A E}=\overrightarrow{A B}+2 \overrightarrow{A C} \quad \) et \( \overrightarrow{A F}=\frac{1}{2} \overrightarrow{A B}+\overrightarrow{A C} \)

Find equation of straight line through \( (-1,4) \) and perpendicular to the line passing through \( (3,0) \) and \( (1,-2) \).

12. G'ildirak aylanasining uzunligi 1,5 m . G'ildirak 20,5 marta aylanganda qancha masofani bosib o'tadi? G'ildirak 231 m masofani bosib o'tganda necha marta aylanadi?

Explain the relationship between the area of cross-sections of a three-dimensional shape and its total volume.

In the figure below, the chord \( E F \) subtends angle of \( 114^{\circ} \) at the centre \( O \). Calculate (a) the length of the chord \( E F \),