Consider the following sets: a = {84n23 | n e z}, в 3 (12п — 1| пе z}, an с [14п + 9|n€ z). a) show that a is a proper subset of b b) show that a is a proper subset of c c) show that there is no containment relation between b and c

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

15 liters is approximately how many gallons

Two numbers have a sum of 93. if one number is p, express the other number in terms of p.