(Solved): 1. A water wheel has a radius of 10 metres. 3 metres of the wheel is submerged under water. If the ...

1. A water wheel has a radius of 10 metres. 3 metres of the wheel is submerged under water. If the wheel makes one full revolution every 40 seconds and you start observing the water bucket at the axis: a) Determine the height of the bucket after 32 seconds. b) Determine when the height of the bucket is 11 metres. 2. The population of prey in a predator-prey relation is shown in the graph below. Time is in years since 1985. a) Determine the maximum and minimum values of the population. b) Determine an equation to represent the situation. c) Determine the population in 2019. d) Determine when the population was 400 prey for the first and second times. 3. The population, \( P(t) \), of a lakeside town with a large number of seasonal residents can be modeled using the function \( P(t)=5000 \sin (30(t-7))+8000 \) where \( t \) is the number of months after New Year's Day. a) Determine the maximum and minimum population for the year. b) When is the population at a maximum? A minimum? c) What is the population on September 30th?