The curvature at a point P of a parametric curve x = x(t), y = y(t) is given below, where the dots indicate derivatives with respect to t, so ẋ = dx/dt. Use the formula to find the curvature of the cycloid x = θ − sin(θ), y = 1 − cos(θ) at the top of one of its arches. $ \kappa = \dfrac {\left| \dot{x} \ddot{y} - \ddot{x} \dot{y} \right|} {[\dot{x}^2 + \dot{y}^2]^{3/2}} $

Step-by-step explanation:

The first and second derivatives of the components of the parametric curve are:

and

and

After substitution, the equation of curvature is:

The correct answer is B. The number of rides and the total cost are both dependent variables, as both depend on the amount of money that Nia has.

Step-by-step explanation:

The total cost is dependent because it relies on how many rides Nia takes, and the $19.50 limit.

The number of rides is dependent on the limit of $19.50 because the $19.50 is the limit and the total amount of rides is locked by $19.50

I'm not sure, though.