Let n be a natural number such that n + 1, n + 3, n + 7, and n + 9 are prime numbers. Additionally, the numbers n + 31, n + 33, n + 37 and n + 39 are also prime numbers. Determine the remainder after dividing n by 210.

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.