31. There are 150 students volunteering to help at a community fair. The students must be divided into groups of equal size. How many ways can
the students be divided into the groups?

To find the extreme values of a function f(x. y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x, y)=xy

Benito is selecting samples of five values from the table, which row will result in the greatest mean? population data row 1 4 2 2 3 3 row 2 3 3 4 3 2 row 3 2 4 3 4 3 row 4 3 4 4 7 3 row 1 row 2 r

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)