Question 17 (3 marks) Archaeologists are excavating a square plot ABCD measuring 50 metres by 50 metres. The plot is divided into four sections of equal width as shown in the diagram below. At the end of the first phase of digging, the shaded area has been excavated. Measurements made to the edges of the excavated area are also shown on the diagram. D NOT TO SCALE 19 m 22 m 18 m 21 m 32 m A B 50 m (a) Use the trapezoidal rule with each of the measurements given to estimate the shaded 2 area. .... (b) Express the shaded area as a percentage of the total area. Give your answer correct to two decimal places. ........Question 20 {3 marks) A scientist is modelling a locust plague that is swarming in Uganda. The area affected by locusts is given by A = 800x025)" hectares, where n is the number of weeks after the initial observation. (a) Find the affected area after four weeks. Give your answer to the nearest hectare. ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ....................................................................................................... ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo (b) Find the smallest number of weeks until the locust plague overtakes Uganda, given Uganda is approximately 24.1 million hectares. 2 Question 21 (4 marks) A fountain is designed so that the water projected from it forms a parabolic are over a walkway. If x metres represents the horizontal distance in metres from the base of the fountain and y metres the vertical height of the water above the ground, the path of the water can be modelled by the equation y = x(6x), where 0 s x S 6. The average person is 1.71 m tall. If safety engineers stipulate that the average person needs 1.3 111 Width to walk comfortably, determine the maximum number of average-sized people that can comfortably walk under the fountain, side-by-side, without getting wet