Created by T Madas Question 249 (****+) y y = x + px + 10 B y = x+q A x O The figure above shows the graphs of a quadratic curve and a straight line with respective equations y = x + px + 10 and y = x+q, where p and q are constants The curve and the straight line intersect at the points A and B , whose x coordinates are and , respectively Determine the area of the finite region bounded by the curve and the straight line, shown shaded in the figure area = Created by T Madas Created by T Madas Question 250 (****+) The volume, V cm3 , of a soap bubble is modelled by the formula V = ( p − qt ) , t ≥ , where p and q are positive constants, and t is the time in seconds, measured after a certain instant When t = the volume of a soap bubble is cm3 and at that instant its volume is decreasing at the rate of cm3 per second Determine the value of p and the value of q C1Z , p = , q = Created by T Madas Created by T Madas Question 251 (****+) y y = 36 − x − x y=x x O The figure above shows the graph of the curve with equation y = 36 − x − x and its reflection about the straight line with equation y = x a) Write down the equation of the curve which is the reflection of the curve with equation y = 36 − x − x about the straight line with equation y = x b) Determine an exact value for the area of the finite region bounded by the curve with equation y = 36 − x − x , its reflection about the straight line with equation y = x , and the positive x and y axes This region is shown shaded in the figure above MP1-I , x = 36 − y − y , AREA = 496 = 165 3 Created by T Madas