Some ecologists divided a female bird population into three categories: juvenile left parenthesis up to 1 yr o l d right parenthesis comma subadult (1 to 2 yr old), and adult (over 2 yr old). They concluded that the change in the makeup of the bird population in successive years could be described by the matrix equation below. The numbers in the column matrices give the numbers of females in the three age groups after n years and n + 1 years.

Let f(x) = 3 − x . find the average rate of change of f(x) from x = a to x = a + h and simplify your answer so that no single factor of h is left in the denominator.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

Which of the following circles have their centers in the third quadrant?