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Math Help - [SOLVED] Confusing Functions

  1. #1
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    Cool [SOLVED] Confusing Functions

    I've tried to do the following questions with the help of provided examples but can't seem to get a right answer. I don't think I am solving them with the right method.

    1) A piece of wire 24 cm long has the shape of a rectangle. Given that the width is w cm, show that the area, A cm^2, of the rectangle is given by the function A = 36-(6-w)^2. Find the greatest possible domain and the corresponding range of this function in this context.

    2) Sketch the graph of y = x(8-2x)(22-2x)

    Given that y cm^3 is the volume of a cuboid with height x cm, length (22-2x) cm and width (8-2x) cm, state an appropriate domain for the function given above.

    Can you also please tell me how would I go on about sketching these kind of graphs.

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by unstopabl3 View Post
    I've tried to do the following questions with the help of provided examples but can't seem to get a right answer. I don't think I am solving them with the right method.

    1) A piece of wire 24 cm long has the shape of a rectangle. Given that the width is w cm, show that the area, A cm^2, of the rectangle is given by the function A = 36-(6-w)^2. Find the greatest possible domain and the corresponding range of this function in this context.

    2) Sketch the graph of y = x(8-2x)(22-2x)

    Given that y cm^3 is the volume of a cuboid with height x cm, length (22-2x) cm and width (8-2x) cm, state an appropriate domain for the function given above.

    Can you also please tell me how would I go on about sketching these kind of graphs.

    Thanks in advance!

    HI

    (1) The width is w , then let the other side be x .

    2x+2w=24 .... x+w=12

    A=wx

    A=w(12-w)

    A=12w-w^2

    A-36=12w-w^2-36

    A-36=-(36-12w+w^2)

    A-36=-(6-w)^2

    A=36-(6-w)^2

    When you graph this , it has an 'n' shape so w=6 and the correspoinding range would be 36 .
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  3. #3
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    Can you please explain why did you add -36?
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  4. #4
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    Talking

    Quote Originally Posted by unstopabl3 View Post
    Can you please explain why did you add -36?
    It was to complete the square. To learn that process, try here.
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