A 16 -foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 4 feet from the wall? The top of the ladder is moving down at a rate of \( \square \) feet/second when the foot of the ladder is 4 feet from the wall. (Round to the nearest thousandth as needed.)

6. Evaluate th a) \( \frac{5}{8}+\frac{1}{4} \)

Which of the following is equal to \( \sqrt{-10} \) ? \( \begin{array}{l}-i \sqrt{10} \\ i \sqrt{10} \\ -\sqrt{10} \\ \sqrt{10 i}\end{array} \)

Use the quadratic formula to solve the equation \( 2 x^{2}-3 x-5=0 \). \( \begin{array}{l}x=-5, x=2 \\ x=-1, x=\frac{5}{2} \\ x=-\frac{5}{2}, x=1 \\ x=-2, x=5\end{array} \)

Jolene invests her savings in two bank accounts, one paying 3 percent and the other paying 10 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 7456 dollars. How much did she invest at each rate? Amount invested at 3 percent interest is \( \$ \) Amount invested at 10 percent interest is \( \$ \)

\( f(x)=x^{2}-x-1 \). On pose \( x_{0}=2 \). a. Résoudre l'équation \( x^{2}-x-1=0 \). On note \( \Phi \) la solution positive de cette équation. b. Montrer que pour tout entier naturel \( n \), on a: \( x_{n+1}=\frac{x_{n}^{2}+1}{2 x_{n}-1} \). c. Soit \( g \) la fonction définie sur \( [1 ;+\infty[ \) par \( g(x)=\frac{x^{2}+1}{2 x-1} \). Étudier les variations de la fonction \( g \).