[填空题]
The amount of water, A, in thousands of litres, av2ia31yns rei 3hin.jctx 8s .6aila-: )th,zf.b ll3nzuov:wo 7xjble in a water tank located on a farm fluctuatlx: .:johbw,z f-v )u7oz3lntes in a yearly cycle and can be modelled by the function
A(t)=asin(kt)+b,where t is the elapsed time, in weeks, since the start of the year.
The amount of water available in the tank on week 66 is 24 thousand litres and on week 31 is 9.2 thousand litres.
1.Find the value of k, in degrees, assuming there are 52 whole weeks in a year. ≈ $^{\circ}$
2.Set up a pair of equations to find the value of a and the value of b. Give your answers correct to the nearest integer. a ≈ b ≈
3.Hence find the amount of water available in the tank in week 42. thousands liters
4.Draw the graph of y=A(t) on the grid below, for one full year, indicating clearly the minimum and maximum points.
