1. Dados los vectores \( \vec{u}=\left(-4 k ; 1 ; 2 k^{2}\right) \) y \( \vec{v}=(1 ; 2 ; 1) \), vectores no nulos de \( \mathbb{R}^{3} \), se pide: a) Hallar el/los valores reales de \( k \), de manera que \( \vec{u} \) y \( \vec{v} \) resulten perpendiculares. Indicar \( \vec{u} \). b) Para \( k=-2 \) y dado \( \vec{w}=(1 ; 2 ;-2) \), encontrar el volumen del paralelepípedo que determi- nan \( \vec{u}, \vec{v} \) y . c) Encontrar todos los vectores paralelos a proy \( _{\vec{w}} \vec{v} \) que tienen norma 6

47. The measure, in degrees, of each interior angle of a regular polygon with \( n \) sides is given by \( \frac{(n-2) \mid 80}{n} \). What is the sum of the measures of the interior angles of a regular octagon?

Calcola la lunghezza di una circoner tro 8 cm , approssimando \( \pi \) ai centesimi.

50. Ten distinct lines lie in the same plane. No pair of these lines is parallel to each other, and no more than two of the lines intersect at any one point. How many poins lie on more than one of these ten lines? (A) 10 (B) 36 (D) 45 (D) 55 (E) 100

lunghezza della circonferenza di raggio maggiore? \[ [\approx 38,81 \mathrm{~m}] \] La somma dei raggi di due circonferenze misura 15 cm e uno è i \( \frac{2}{3} \) dell'altro. Determina la lunghez- za delle due circonferenze. \[ [12 \pi \mathrm{~cm} \approx 37,68 \mathrm{~cm} \text { e } 18 \pi \mathrm{~cm} \approx 56,52 \mathrm{~cm}] \]

3] (a) If the distance between the point \( (a, 7) \) and the point \( (0,-5) \) equals 13 length units find the value of a