\( \frac { d } { d t } \vec { x } = \left( \begin{array} { c c c } { - 25 } & { 12 } & { 24 } \\ { - 12 } & { 5 } & { 12 } \\ { - 24 } & { 12 } & { 23 } \end{array} \right) \vec { x } , \quad \vec { x } ( 0 ) = \left( \begin{array} { l } { 7 } \\ { 5 } \\ { 5 } \end{array} \right) \)

7. c) \( \frac{1}{1+x}-\frac{2}{x^{2}-1} \)

2) La ecuación del movimiento de una particula está dada por: \( s(t)=t^{3}-3 t \) Encontrar: a) La velocidad como función de \( t \) b) La aceleración después de 4 segundos. c) la aceleración cuando la velocidad es cero.

1. \( y=\frac{x}{\sqrt[4]{25-x^{2}}} \)

A national fast food company has just analyzed the effect of the latest sales promotion. It has determined that the sales decay for its milkshakes is given by \( S=285,000 e^{-0.7 x} \), where \( S \) is the weekly sales and \( x \) is the number of weeks that have passes since the end of the sales promotion. a) Determine the sales 2 weeks after the end of the promotion: Round answer to 2 decimal places. Sales \( =\$ \) b) If no new campaign is started, how many weeks after the end of the promotion will sales drop below 30,000 ? Round answer to 1 decimal place. Num. weeks =

Find the average rate of change of \( h(x)=-2 x^{2}-5 x \) from \( x=-4 \) to \( x=1 \). Simplify your answer as much as possible.