Define el circuncentro de un triángulo. ¿Qué propiedades tiene?

Find the equations of the vertical and horizontal tangent lines of the following ellipse \( 4 x^{2}+y^{2}-8 x+4 y+4=0 \)

A. Illustrates whether the two ratios are equal or not using cross the products. Write your answer on the attached activity sheets. \( \begin{array}{ll}\text { 1. } \frac{8}{10}, \frac{4}{6} & \text { 2. } \frac{12}{15}, \frac{4}{5}\end{array} \)

1. Desarrolla las siguientes integrales por sustitución trigonométrica: a) \( \int \frac{2 x}{\sqrt[3]{x^{2}-9}} \)

23. \( f(x)=\frac{\sqrt{x-6}}{\sqrt{x-4}} \)

C. Solve the following probiems on compound interest. 13. Cian lends P45,000 for 3 years at \( 5 \% \) compounded semi-annually. Find the future value and interest of this amount. 14. Tenten deposited P10,000 in bank which gives \( 1 \% \) compounded quarterty and let it stay there for 5 years. Find the maturity value and interest. 15. How much should you set aside and invest in a fund earning \( 9 \% \) compounded quaterly if you want to accumulate P200,000 in 3 years and 3 months?