A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 3 feet per second. Find the rate at which the area is changing at the instant the radius is 14 feet. When the radius is 14 feet, the area is changing at approximately \( \square \) square feet per second. (Round to the nearest thousandth as needed.)

Find the solution of the equation \( x^{2}+24 x+144=9 \) by completing the square. \( \begin{array}{l}x=-15 \text { or } x=9 \\ x=15 \text { or } x=-9 \\ x=-15 \text { or } x=-9 \\ x=15 \text { or } x=9\end{array} \) \( \begin{array}{l}x\end{array} \)

Solve using the Quadratic Formula. \( \begin{array}{l}3 x^{2}+4 x+5=0 \\ x=\frac{-2 \pm \sqrt{11}}{3} \\ x=\frac{-4 \pm 2 i \sqrt{11}}{2} \\ x=\frac{-4 \pm i \sqrt{11}}{6} \\ x=\frac{-2 \pm i \sqrt{11}}{3}\end{array} \)

10.) \( 36 x^{2}+48 x+16=12 \)

Determine the number and type of solutions of \( -x^{2}-2 x-4=0 \). one real and one imaginary solution two imaginary solutions two real solutions one real solutions

Una fábrica de producción de agua embotellada, cuenta con una máquina de envasado tomático, la cual vierte en cada botella una cierta cantidad de agua que sigue una distribución rmal con media de 500 mililitros y una varianza de 25 mililitros. ¿Qué porcentaje de las botellas Ilenan con agua entre 490 y 507 mililitros?