The cross-section of a 10 metre long tank is an isosceles triangle, as shown in the diagram. The top of the tank is horizontal.
When the tank is full, the depth of water is 3 m. The depth of water at time `t` days is `h` metres.
- Find the volume, `V`, of water in the tank when the depth of water is `h` metres. (1 mark)
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- Show that the area, `A`, of the top surface of the water is given by `A = 20 sqrt3 h`. (1 mark)
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- The rate of evaporation of the water is given by `(dV)/(dt) = - kA`, where `k` is a positive constant.
Find the rate at which the depth of water is changing at time `t`. (2 marks)
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- It takes 100 days for the depth to fall from 3 m to 2 m. Find the time taken for the depth to fall from 2 m to 1 m. (1 mark)
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