A school laboratory tank initially contains water at a height of 7cm. After the outlet tap is opened, the height of the water (in centimetres) after t minutes is given by the linear polynomial h(t)=7−0.6t.
a. (i) Find the time when the tank becomes empty.
b. (ii) The flow rate is changed so that the water level now follows H(t)=7−kt and the tank is required to become empty exactly after 9 minutes. Determine the value of k.
c. (iii) For the value of k obtained in part (ii), verify by direct substitution that H(t)=0 when t=9 minutes.