A semicircular arched window has the curved shape modelled by the function w:[-4,4]- R,w(x)= \ -x' +c where r > 0 and cER* (0). Let x be the horizontal distance in decimetres from the origin and let y be the vertical distance, in decimetres, from the x-axis. The shape of the window is shown below, where the coordinates of the y-intercept are (0, 5) and the coordinates of the extremes of the window are (-b,c) and (b, c). (-b,c) b.c) a. State the radius of the semicircle. b. Hence find the rule for w. A team of specialised glaziers are brought in to insert a rectangular section of stained coloured glass that will sit inside the semicircular shape as shown below. The rectangular section touches the semicircle curve at the points (x,, ), ) and (-x,, );) . The glaziers will put the stained glass in the rectangle that has the maximum area. (0.5) (-b,c) b.c) c. Show that the area of the rectangle, A, , in terms of x, is A, = 2x, 16-x,?. d. Hence find the maximum possible area of the rectangle, in dm', that will fit inside the semicircular shape. Justify that this area is a maximum. The glaziers will fill the rest of the semicircular window with plain glass. Find the proportion of the semicircular window that is stained glass