Confused on this for calc.

a particle moves along the x-axis with position function s(t) = e^sin(x). how many times in the interval [0, 2π] is the velocity equal to 0?

2 times

Step-by-step explanation:

If S(x) is the position, the derivative S'(x) is the velocity.

Take the derivative using the chain rule:

Now, if the velocity = 0 then S'(x) = 0, and cos(x) must be 0 because the exponential is always different to 0.

In the interval [0, 2π] cos(x) = 0 when x= π/2 (90°) or x = 3π/2 (270°)

So the velocity equals 0 only 2 times in the interval [0, 2π]

number of green ÷ total number of marbles

times by

number of red ÷ total number of marbles left

so

(3/9) × (2/8) = (1/12)