Question

3. Bunyip reservoir is 1km long, 100m wide and 25m deep, with a uniform cross-section that is modelled by a curve of the form f(x) ax2 bx +c as shown in Figure 1. 100m (0,0) (100,0) 25m (50,-25) Figure 1: Cross-section of Bunyip Reservoir (a) Find the values of a, b and c, given that the points (0, 0), (50, -25) and (100, 0) lie of the curve. (b) When full, how much water d oes Bunyip reservoir hold (c) On Sunday the water is 9 metres deep at the deepest point. What percentage of the reservoir's capacity is being used? (d) At midnight on Sunday, rain starts falling in the catchment for the reservoir. From that point on, water enters the reservoir at a rate of e-*t2 gigalitres per day, where the parameter t measures the time in days since midnight on Sunday. Use the Product Rule to show that - (t2 2t 2)e-t is an antiderivative of e *t2 reservoir will start to overflow at some point on Thursday morning. before the rain starts falling (e) Use the result from the previous part to show that if no water is released, then the (f) Write down a relation that describes all the points (x, y) in Figure 1 that are underwater (g) Write down a relation that describes all the points (x, y) in Figure 1 that would be underwater when the reservoir is full.

Answer 1

tToD) a) ( o -f ,勿 丹一1( -thun 4 Α.yoooofet(CJ-o广ー1e9,

e td 2 수은 | the anhdrivative