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.

\[ \sin 2 x+\cos x=0 \] Dentro del intervalo dado por: \( 0 \leq x \leq 360^{\circ} \)

Se construyó una caja con forma cúbica en la cual caben exactamente 27 cubos de chocolate de 3 cm de arista. Para proteger los chocolates, se debe cubrir la base de la caja con papel foil. ¿Cuantos centimetros cuadrados de papel foil se deben poner para cubrir exactamente la base de la caja?

Actividades: Hallar dominio, imagen, vértice, intersección con cada cje, cje de simetria, concavidad, intervalos de crecimientos y decrecimientos y luego graficar las siguientes funciones: \( \begin{array}{lll}\text { a) } y=(x-1)(x+2) & \text { b) } y=-(x+3)(x-3) & \text { c) } y=3 \cdot\left(x+\frac{1}{2}\right) \cdot(x-4) \\ \text { d) } y=-2(x+2)(x-1) & \text { c) } y=-\frac{1}{2}(x+6)(x-6) & \text { f) } y=\frac{3}{2}(x+1)\left(x-\frac{1}{2}\right)\end{array} \)

Give a fully simplified expression for \( \cos \left(\tan ^{-1}\left(\frac{t}{5}\right)\right) \)

Refer to functions \( m \) and \( n \). Find the function \( (m \circ n)(x) \) and write the domain in interval notation. Write any number in the intervals as an integer or a simplified fraction. \( m(x)=\sqrt{x+9} \quad n(x)=x+2 \) Part: \( 0 / 2 \) Part 1 of 2 \( (m \circ n)(x)= \)