Pierre, the mountain climbing ant, moves along the x-axis so that at time t its position is given by x(t) = 2cos(π/2 t^2).

For values of t in the interval [-1,1]
(a)Find an expression for the velocity of the ant at any given time t.
(b) Find an expression for the acceleration at any given time t.
(c)Determine the values of t for which the ant is moving to the right.
Justify your answer.
(d) Determine the values of t for which the ant changes direction.
Justify your answers.

Exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on october 4. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (d) compute the probability that a randomly selected person was not born in january. (type an integer or a decimal rounded to three decimal places as needed.)