I can do the first part from the question showing that the rea of the stage is this.
But i dont know how to do the rest of the question.
Sorry i do not have a scanner and if anyone has the link to this paper, the rest can see it.
The plan of a stage in the shape of a rectangle joined to a semicircle. The length of the rectangular part is 2x metres and the width is y metres. The diameter of the semicircle part is 2x metres. The perimeter of the stage is 80m.
(a) Show that the area, A m², of stage is given by
A=80x-(2+pi/2)x²
(b) Use calculus to find the value of x at which A is a stationary point.
(c) Prove that the value of x you found in part (b) gives the maximum value of A.
(d) Calculate, to the nearest m², the maximum area of the stage.
My exam is on monday so its urgent and i havent revised C3 yet.
Thanks.