Let \( \mathbf{v}=-8 \mathbf{i}-15 \mathbf{j} \), find \( \|\mathbf{v}\| \)

2. Calcula el volumen del sólido que se obtiene al hacer girar la región limitada por la curva \( f(x)=\sqrt{x-2} \) y las rectas \( x=2, x=11 \), alrededor del eje \( X \). 3. Obtén el volumen del sólido que se genera al hacer girar la región limitada por la curva \( f(x)=x^{2} y \) las rectas

5. Suppose the govemment increases the tax on tobacco products, and suppose the demand for these products is inelastic. How should this be analysed on the multiplier model? Which of the following statements is true? A The planned expenditure line will shift upwards, because people will pay more in the shops on tobacco products. B The planned expenditure line will shift downwards, because people will buy fewer cigarettes, so their spending on tobacco after allowing for the tax will be lower. C The withdrawals line will end up shifting downwards, because the rise in the tax will cause people to save less. D The injections line will shift downwards, because this includes all govemment spending net of taxes.

The equation of a direct variation relationship is given as \( y = kx \). If \( k = 5 \), write the corresponding equation.

8) Una persona tarda 3 días en pintar una casa trabajando 8 horas diarias. ¿Qué parte de la casa pinta en \( \frac{x}{2} \) horas? A) \( \frac{48}{x} \) B) \( \frac{3 x}{2} \) C) \( \frac{6}{x} \) D) \( \frac{x}{6} \) E) \( \frac{x}{48} \)

Calculez en détaillant les étapes: \[ 1 . \frac{-3}{8}-\left(\frac{12}{2^{3}}-2^{-1}\right)^{3} \]