In una circonferenza un arco misura \( 15,7 \mathrm{~cm} \) e l'angolo al centro che gli corrisponde è ampio \( 60^{\circ} \). Calcola la misura del diametro della cir- conferenza. [ 30 cm\( ] \)

WJEC June 2017 Q6 The coordinates of the points \( F \) and \( G \) are \( (8,20) \) and \( (-4,10) \) respectively. (a) Calculate the length of the line FG. Express your answer as a surd in its simplest form, \( n \sqrt{m} \).

7. En cada ítem, estudiar la posición relativa entre las dos rectas dadas y graficar ambas en un mismo sistema de coordenadas cartesianas. a) \( \left\{\begin{array}{l}x=1-5 \lambda \\ y=2+3 \lambda \\ z=-5+\lambda\end{array}\left\{\begin{array}{l}x=1 \\ y=1 \\ z=\mu\end{array}(\lambda, \mu \in \mathbb{R})\right.\right. \) b) \( \left\{\begin{array}{l}x=3+2 \alpha \\ y=1-\alpha \\ z=5\end{array}\left\{\begin{array}{l}x=-1-6 \beta \\ y=3+3 \beta \\ z=5\end{array} \quad(\alpha, \beta \in \mathbb{R})\right.\right. \)

What is the formula for calculating the volume of a cone?

Find the equation of the straight line perpendicular to FG that passes through the mid point of \( F G \). Express your answer in the form \( a x+b y+c=0 \), where \( a, b \) and \( c \) are integers. Give your answer in its simplest form.

\[ g: \vec{x}=\left(\begin{array}{l}3 \\ 1 \\ 4\end{array}\right)+t\left(\begin{array}{c}2 \\ -7 \\ 5\end{array}\right) \quad h: \vec{x}=\left(\begin{array}{c}5 \\ -6 \\ 9\end{array}\right)+k\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right) \] (1) Zeigen Sie, das die Geraden sich schneiden. (2) Geben Sie den Schnittpunkt an. (3) Prüfen Sie, ob sie senkrecht aufeinander stehen. b) Formulieren Sie in mathematischer Schreibweise mithilfe des