El evento musical ha sido todo un exito, por lo que han decidido expandir su presentacion. El director de la escuela ha notado que la compra de boletos ha disminuido proporcionalmente con el precio, pues si cobra \( \$ 600 \), asistirian 300 personas y si cobra \( \$ 650 \), asistirian 200 personas. ¿Que precio le sugerirlas al director para maximizar los ingresos? La función de ingresos en fuincion del prech se expresa de la siguiente forma: \[ i(p)=1,500 p-2 p^{2} \]

Use L'Hopited nule to frin the Limit: \( \lim _{x \rightarrow 0}\left(\frac{1}{x}-\frac{1}{\sin x}\right) \)

5. A cross country runner jogged a distance of 400 meters in 180 seconds. What was their average speed?

18. Verifique se a matriz \( \left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 3 & 1 \\ -1 & 7 & 3\end{array}\right] \) é inversível.

1. The maximum number of individuals that an ecosystem can support. (Two words) 2. Population growh that is rapid because there are lots of resqurces, and very unstable; a "J-shaped" curve. 4. All the individuals of the same species living in the same area at the same time 6. Individuals live a specid distance from one another. 7. The movement of ind viduals out of a population. 10. These decrease the size of a population. 11. These cause a poputation to grow 12. Survivorship Type in wich there is equal chance of 13. Population growth that is stable and near carrying capacity, an "s-shaped" graph 14. Individuals are dispersed in an indiscriminate patterm.

\( F=\frac{r m_{1} m_{2}}{k^{2}} \) d) \( E=\frac{k q}{r^{2}} \)