A special box designed to hold an antique artifact is shaped like a triangular prism. The height of the base triangle is 4.3 inches, each side of the base triangle is 5 inches long, and the height of box is 14 in. What is the surface area of box?

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.

The nth term of a sequence in 2n-1 the nth term of a different sequence is 3n+1 work out 3 numbers that are in bothe sequences and are between 20 and 40

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. 1^2 + 4^2 + 7^2 + + (3n - 2)^2 = [n(6n^2-3n-1)/2]