A geometric progression has first term log2( 27) and common ratio log2(y). (i)Find the set of values of y for which the geometric progression has a sum to
infinity [2 marks]

(ii)Find the exact value of y for which the sum of infinity of the geometric progression is 3 [5marks]

The rows and columns of lattice points in a three-by-three square array are evenly spaced one unit apart. how many distinct triangles with at least one side of length 2 units can be drawn using three lattice points for the vertices?

Ben bowled 124 and 188 in his first two games. what must he bowl in his third game to have an average of at least 160?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?