Let p (n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 5-cent stamps. the parts of this exercise outline a strong induction proof that p (n) is true for n ≥ 8.

(a) show that the statements p(8), p(9), and p(10) are true, completing the basis step of the proof.

(b) what is the inductive hypothesis of the proof?

(c) what do you need to prove in the inductive step?

(d) complete the inductive step for k ≥ 10.

(e) is p(n) true for n ≥ 8 if you have only one 5-cent stamp? only two 5-cent stamps?

Write 5(6x+4)-2(5x-2) in the form a(bx+c) where a,b and c integers and a> 1

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.

Atown has a population of 17000 and grows at 2.5% every year. to the nearest year, how long will it be until the population will reach 19600?