Julie will build a rectangular pen for her dog against a barn. a wall from the barn will from one side of the pen. she has 32m of fencing to form the other three sides. she plans to build the pen so that it has its maximum possible area. what will be the dimensions of julie's pen?

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.