Working together, Bill and Tom painted a fence in 6 hours. Last year, Tom painted the fence by himself. The year before, Bill painted it by himself, but took three
times longer than Tom took. How long did Bill take when painting the fence alone?

If f(x) = x+8 and g(x) = 4x- 3, find (f+g)(x)

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

The serenity and the mystic are sail boats. the serenity and the mystic start at the same point and travel away from each other in opposite directions. the serenity travels at 16 mph and the mystic travels at 19 mph. how far apart will they be in 3 hours?