[填空题]
The amount of water, A, in thousands of litres, available i 6tj+ix /rr /l*6pwjppn a water tankym fsnnj;6w .yhr 6d e.zf616bp(dfp, located on a farm fluctuates in a yearly cyclepff,nhn(yfm6jbr ed. 6;616d szp .yw 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 6 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. k ≈ $^{\circ}$
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. A = thousand litres
4.Draw the graph of y=A(t) on the grid below, for one full year, indicating clearly the minimum and maximum points.
