The lesson is about finding the equation of a circle given two points and another condition. The given is I should find the equation of the circle which passes through the points A(5, 0), B(3, 4) and has its center lying on the line 2y + x = 4. Can you help you guys answer it?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)