2. for each of the following statements, determine whether the statement is true or false. for a true statement, give a proof. for a false statement, write out its negation and prove that. (a) for all rational numbers a, there is a positive integer n so that na is an integer. (b) there is a positive integer n so that for all rational numbers a, nz is an integer. (c) for all integers a, b and c, if a b + 2c and a | 2b+3c then a | b and a | c (d) for all integers a, b and c, if a l b + 2c and a l 3b + 2c then a | b and a l c.

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)