HCI P1 Q2

Solve the inequality

Hence find , leaving your answer in exact form.

Cultivating Champions, Moulding Success

VJC P1 Q9

(i) Sketch the graph with equation , where and

A hemispherical bowl of fixed radius cm is filled with water. Water drains out from a hole at the bottom of the bowl at a constant rate. When the depth of water if cm (where ).

(ii) Use your graph in (i) to show that the volume of water in the bowl is given by .

(iii) Find the rate of decrease of the depth of water in the bowl, given that a full bowl of water would become empty in 24 s,

(iv) without any differentiation, determine the slowest rate at which the depth of water is decreasing.

(i)

When

When

Using GC,

When

time interval between the first and second alarm.

(iii)

As which is impossible as the canal has only a fixed capacity of . Thus, the model is not valid for large values of

(iv)

Assume that the weather condition remain unchanged.

(a)(i)

Consider is a circle with centre Origin and radius .

Thus, required area is the area of a quadrant with radius

(ii)

(b)