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Math Help - Confused on finding a function with multiple variables (Pizzabox)

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    Confused on finding a function with multiple variables (Pizzabox) (still confused)

    Confused on finding a function with multiple variables (Pizzabox)-pizzabox.png
    Well the problem is this
    1) Find a polynomial function p(x) that computes the volume of the box in terms of x. What is the degree of p?

    2) Find a polynomial function q(x) that computes the exposed surface area of the closed box in terms of x. What is the degree of q? What are the explicit dimensions if the exposed surface of the area is 600 square inches?

    I was having trouble with this, because there is 'x' in 2 sides.
    At first I was thinking 50 + 20, but I don't know where that came from.
    I was thinking that there was 3 'x' in one side, and 3 'x' in the other half
    So it was like 2x^3? But I'm confused if that makes any sense at all.
    May anyone help me start this off and explain the steps?

    SOLVED
    I understand the steps now and where the 600 came from
    Thanks for all your help
    Last edited by Chaim; October 22nd 2011 at 07:52 PM.
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    Re: Confused on finding a function with multiple variables (Pizzabox)



    folded box length = 20-2x

    folded box width = \frac{50-2x}{2} = 25-x

    folded box height = x
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    Re: Confused on finding a function with multiple variables (Pizzabox)

    Quote Originally Posted by skeeter View Post


    folded box length = 20-2x

    folded box width = \frac{50-2x}{2} = 25-x

    folded box height = x
    Oh.... I see now
    Thanks
    So to find the volume, would be multiplying the length, width, and height together right? (Since it's a rectangle?)
    So (20-2x) * (25 - x) * (x), I think
    500 - 20x - 50x + 2x^2
    =500-70x+2x^2
    Which, in order would be 2x^2 - 70x + 500
    Though I am confused with to 'find the degree of 'p'
    (70 +- sqrt 4900 - 40000)/2
    Though that is wrong cause I can't get the square root of a negative number
    I am confused on what is the 'degree'?
    I thought it was like 90 degree, as in right angle, but that makes no sense, and I'm assuming it's not that type of degree.
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    Re: Confused on finding a function with multiple variables (Pizzabox)

    V = (20-2x)(25-x)(x)

    you forgot to multiply by the last x, the height

    the degree of a polynomial is the highest power of x in the polynomial
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    Re: Confused on finding a function with multiple variables (Pizzabox)

    Quote Originally Posted by skeeter View Post
    V = (20-2x)(25-x)(x)

    you forgot to multiply by the last x, the height

    the degree of a polynomial is the highest power of x in the polynomial
    Oh I get it now, thank you very much
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    Re: Confused on finding a function with multiple variables (Pizzabox)

    So the second part is the surface area of a rectangle which is what I am on right now
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    Re: Confused on finding a function with multiple variables (Pizzabox)

    Quote Originally Posted by skeeter View Post


    folded box length = 20-2x

    folded box width = \frac{50-2x}{2} = 25-x

    folded box height = x
    So I'm on the second part right now to find the surface area of the rectangle which is
    2ab + 2bc + 2ac right?
    a = 20-2x
    b = 25-x
    c = x
    2(20-2x)(25-x) + 2(25-x)(x) + 2(20-2x)(2x)
    =2(500-20x-50x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
    =2(500-70x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
    =1000-140x+4x^2+50x+2x^2+80x-8x^2
    =1000-60x-2x^2
    Though I think I messed up, it's suppose to be -50x instead of -60x, but I don't know how did I do it wrong
    And how would you do "What are the explicit dimensions if the exposed surface of the area is 600 square inches?"

    Also, how did you get (50-2x)/2
    I understand the 50-2x, but all over the 2, how did you get that?
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    Re: Confused on finding a function with multiple variables (Pizzabox)

    Quote Originally Posted by Chaim View Post
    So I'm on the second part right now to find the surface area of the rectangle which is
    2ab + 2bc + 2ac right?
    a = 20-2x
    b = 25-x
    c = x
    2(20-2x)(25-x) + 2(25-x)(x) + 2(20-2x)(2x)
    =2(500-20x-50x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
    =2(500-70x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
    =1000-140x+4x^2+50x+2x^2+80x-8x^2
    =1000-60x-2x^2
    Though I think I messed up, it's suppose to be -50x instead of -60x, but I don't know how did I do it wrong
    And how would you do "What are the explicit dimensions if the exposed surface of the area is 600 square inches?"

    Also, how did you get (50-2x)/2
    I understand the 50-2x, but all over the 2, how did you get that?
    This is the part I am still confused with, help please?
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    Re: Confused on finding a function with multiple variables (Pizzabox)

    Quote Originally Posted by Chaim View Post
    So I'm on the second part right now to find the surface area of the rectangle which is
    2ab + 2bc + 2ac right?
    a = 20-2x
    b = 25-x
    c = x
    2(20-2x)(25-x) + 2(25-x)(x) + 2(20-2x)(2x)
    =2(500-20x-50x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
    That middle term should be 25x- x^2.

    =2(500-70x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
    =1000-140x+4x^2+50x+2x^2+80x-8x^2
    =1000-60x-2x^2
    Though I think I messed up, it's suppose to be -50x instead of -60x, but I don't know how did I do it wrong
    No, neither -50x nor -60 x. (-140+ 50+ 80)x= -10x. And with that "-x^2" in the middle term, you have (4- 2- 8)x^2= -6x^2. it should be 1000- 10x- 6x^2.

    [quote] And how would you do "What are the explicit dimensions if the exposed surface of the area is 600 square inches?"
    Solve 1000- 10x- 6x^2= 600 and use that value of x to find the three lengths.

    Also, how did you get (50-2x)/2
    I understand the 50-2x, but all over the 2, how did you get that?
    The long side of the original rectangle was 50 and there are two sections of length x taken out so that leaves 50-2x. And both top and bottom are cut from that: each has length (50-2x)/2= 25- x.
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