The Rao of North American butterflies to South American butterflies at a butterfly park is 5 : 3. The Rao of South American butterflies to European butterflies is 3: 2. There are 30 North American butterflies at the butterfly park.

Ben is three times as old as samantha, who is two years older than half of michel's age. if michel is 12. how old is ben?

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 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)

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis.y = 7ex, y = 7e^-x, x = 1; about the y-axis