The equation for finding the length of an arc is L = rθ, where L represents the length of the arc, r represents the radius of the circle, and θ represents the angle of the arc in radians.
If the equation for the arc is given in terms of y, you can use the substitution method to rewrite the equation in terms of x. Once the equation is in terms of x, you can use the formula L = rθ to find the length of the arc.
The value of r represents the radius of the circle that the arc is a part of. This is a fixed value and can be measured or given in the problem.
The value of θ can be found by taking the derivative of the given equation and solving for θ. In this case, the derivative would be dθ/dx = 4/3y^(1/3) - 3/16y^(-1/3).
No, the length of the arc cannot be negative as it represents a physical distance. If the equation results in a negative value for L, it is likely that there is an error in the calculation or the problem is not applicable in that case.