Suppose a finite number of players play a round-robin tournament, with everyone playing everyone else exactlyonce. each match has a winner and a loser (no ties). we say that the tournament has acycle of length mif there exist m players {p_1,p_2, . . ,p_m} such that p_1 beats p_2, who beats p_3, who beats p_m, who beats p_1. clearly this is possible only form ≥ 3.using mathematical induction, prove that if such a tournament has a cycle of length m, for some m≥3, then ithas a cycle of length 3.

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. the function below shows the relationship between f(x) and x: f(x) = 10(1.3)xwhich of the following graphs best represents the function? graph of f of x equals 1.3 multiplied by 10 to the power of x graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity graph of f of x equals 10 multiplied by 1.3 to the power of x graph of f of x equals 1.3 to the power of x