Lea detenidamente la siguiente oración: El nin̄o jugando en el parque se trompesó al subir en la res baladera. ¿A cuál de los siguientes metaplasmos hace referencia la palabra subrayad: a Metátesis b. Apócope c Aféresis d. Epéntesis

(b) Find the exact values of the following trigonometric expre: i. \( 2 \sin \left(75^{\circ}\right) \cos \left(75^{\circ}\right) \)

Simplify \( 5 a b c \times 5 a b c \times 5 a b c \) \( 15 a^{3} b^{3} c^{3} \quad 125 a^{3} b^{3} c^{3} \quad 125 a b c \)

4. A machine has a flywheel with a diameter of 1,2 metres. When the machine is started it takes 2,5 seconds to reach the operating speed of \( 600 \mathrm{r} / \mathrm{min} \). The engine then malfunctions and the machine is switched off \( 11 / 2 \) minutes after reaching the operating speed, and it takes a further 40 seconds to come to rest. 4.1 Draw a graph of angular velocity vs time, that shows the motion of this flywheel. All relevant velocity and time values must be indicated. Determine: 4.2 the angular acceleration of the machine 4.3 the number of revolutions through which it turned while in motion 4.4 the speed in rpm (ie: the rotational frequency) of the wheel 2 minutes after starting and 4.5 the linear velocity of a point on the rim of the flywheel at operating speed.

Realizar paso a paso la transformada de Laplace de: \( \mathcal{L}\left[\frac{-3}{4}\right] \)

4. Desarrolla cada uno de los siguientes binomios. a. \( \left(5 a^{4}+4 b^{3}\right)^{6} \) b. \( (3 x-2 y)^{4} \) c. \( (2 x y-3 z)^{7} \) d. \( (7 x+10 y)^{3} \)