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Last question on C2 Edexcel 2005 (urgent) watch

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    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.
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    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.
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    (Original post by 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.
    b) find dA/dx and set it to zero
    c) find d²A/dx² and it should be less than zero
    d) put value found from b) into A=80x-(2+pi/2)x²
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    Thanks samdavyson and widowmaker for ur help.
 
 
 
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