find the length of the curve(r=2+4*cos(t))

Identify each of the following statements as true or false in relation to confidence intervals (CIs). 
Note: 0.5 marks will be taken away for each incorrect answer. The minimum score is 0.

discrete math 
functions pegeonhole principle
How many multiples of 6 are in the set $\{171,172,173,..,286\}$ ?

At t=0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by 𝜃(𝑡) = (250 𝑟𝑎𝑑/𝑠 )𝑡 − (20.0 𝑟𝑎𝑑/𝑠 2 )𝑡 2 − (1.50 𝑟𝑎𝑑/𝑠 3 ) 𝑡 3 . (a) At what time is the angular velocity of the motor shaft zero? (b) Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity. (c) How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero? (d) How fast was the motor shaft rotating at t=0 when the current was reversed? (e) Calculate the average angular velocity for the time period from t=0 to the time calculated in part (a). A

Let a and b be coprime integers, and let m be an integer such that a | m and b | m. Prove that ab | m

 How many strings are there of lowercase letters of length four or less, not counting the empty string?

5) Find the least integer n such that f (x) is O(n^x) for each of these functions.

c. f(x) = (x4 + x2 + 1)/(x3 + 1)