Calculate the volume in \( \mathrm{dm}^{3} \) of 16.22 g of sulfur hexafluoride, \( S F_{6} \). ( \( A \), values: \( F=19 \), \( S=32 \) )

(a) An angle measures \( 52^{\circ} \). What is the measure of its complement? (b) An angle measures \( 105^{\circ} \). What is the measure of its supplement? measure of the complement:

6. \( \left(4 x^{2}\right)^{\frac{3}{2}} \)

Four explorers wish to get one of their number as far as possible into the wilderness from their base. Each explorer can carry supplies for up to 10 days. At any time supplies can be transferred between explorers and individual explorers can return to base, provided they have sufficient supplies for the retum journey. Supplies cannot be left unattended in the wilderness. What is the greatest number of days the lead explorer can travel from the base so that all return safely?

\( 6.3 \quad \) If \( \sin 76^{\circ}=x \) and \( \cos 76^{\circ}=y \), show that \( x^{2}-y^{2}=\sin 62^{\circ} \)

Determina la derivada de cada función y calcula la derivada en los puntos que se indican. \( \begin{array}{ll}\text { a. } f(x)=-12 x^{7} & (0,0) y(-1,12) \\ \text { b. } g(x)=9 \sqrt[6]{x^{5}} & (1,9) y(4,2 \sqrt[6]{16}) \\ \text { c. } f(x)=\frac{2}{5 \sqrt[4]{x^{5}}} & \left(1, \frac{2}{5}\right) \text { y }(2,2 \sqrt{2}) \\ \text { d. } g(x)=\frac{3 \pi}{2} & \text { en } x=0 y x=2 \\ \text { e. } h(x)=\frac{2}{3} x^{-2} & \text { en } x=-1 y x=1\end{array} \)