Last question on C2 Edexcel 2005 (urgent)

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.

Reply 1

samd

I don't want to have to write out the full solution (sorry!)

But bascially the method is:

(a) Show that the area, A m², of stage is given by A=80x-(2+pi/2)x²

--> You know.

(b) Use calculus to find the value of x at which A is a stationary point.

--> Differentiate and set equal to zero. Then solve for x.

(c) Prove that the value of x you found in part (b) gives the maximum value of A.

--> Find 2nd derivative, and sub in x from (b) show it comes out negative => therefore maximum.

(d) Calculate, to the nearest m², the maximum area of the stage.

--> Put value of x from (b) in equation from (a).

If you send me your email address (by PM) I'll send you the mark scheme.

Reply 2

Christophicus

goku999

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.