A rental car agency charges \( \$ 240 \) per week plus \( \$ 0.25 \) per mile to rent a car. The charge for a minivan is \( \$ 180 \) per week plus \( \$ 0.40 \) per mile. After how many miles is the total charge for each vehicle the same?

Find the value of \( k \) that makes \( f(x) \) continuous at \( x=-1 \) \[ f(x)=\left\{\begin{array}{ll}\frac{x+1}{x^{2}+3 x+2} & \text { if } x \neq- \\ k & \text { if } x=-\end{array}\right. \] \( k=\square \)

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 4 feet per second. Find the rate at which the area is changing at the instant the radius is 13 feet. When the radius is 13 feet, the area is changing at approximately \( \square \) square feet per second. (Round to the nearest thousandth as needed.)

27. Treinta obreros fueron contratados para construir un pozo 5 m de radio y 10 metros de altura en 30 dias, pero luego dueño decide aumentar en un metro el radio para lo cual contrez a otros 18 obreros, ¿en cuánto tiempo estos obreros termina de completar la obra?

Raise each factor within parentheses to the third power. \[ \left(\frac{1}{y}\right)^{3}=\frac{1}{\square} \]

1. \( \frac{5}{6}+\left[\left(-\frac{1}{3}+\frac{3}{2}\right) \times \frac{5}{4}\right] \)