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C2 - Applications of Differentiation watch

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    Q:This diagram represents the end view of the outer cover of a match box, AB and EF being gummed together, and assumed to be the same length.

    If the total length of edge (ABCDEF) is 12 cm, calculate the lengths of AB and BC which will give the maximum possible cross-section area.

    So, I'm struggling a lot on this question. Help would really be appreciated.
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    start by labelling the sides as x and y
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    (Original post by TarotOfMagic)
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    Q:This diagram represents the end view of the outer cover of a match box, AB and EF being gummed together, and assumed to be the same length.

    If the total length of edge (ABCDEF) is 12 cm, calculate the lengths of AB and BC which will give the maximum possible cross-section area.

    So, I'm struggling a lot on this question. Help would really be appreciated.
    Always start by giving variables to stuff. Let's call AB =x the length of AB. Let's call DC=y, the length of DC.

    You know it's a rectangle (but we're counting that weird double edge thing) so 3x+2y = 12 \Rightarrow y = \frac{12-3x}{2} = 6 - \frac{3x}{2}.

    Now you have one equations in two variables, but that will not do at all. You need to have a one variable equation. Let's see what other geometric-based formula we can use... hmmm, I can't think of any OH WAIT! It says it right in the question. We want to maximise the area which is given by A=xy.

    So we will want to compute \frac{\mathrm{d}A}{\mathrm{d}x} find what value of x makes that 0 since that will then be a maximum.

    Oh damn! A is in terms of x AND y and I don't know any multivariable calculus or lagrange multipliers. Time to start crying, methinks... the saga continues... :cry:
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    HA! I got you! A=xy, yes. But we also know that y = 6-\frac{3x}{2}, so really, we can just write A = xy = x\left((6-\frac{3x}{x}\right) = 6x - \frac{3x^2}{2}. HALLELUJAH, IT'S ALL IN ONE VARIABLE IN X and it's an easy quadratic! Why'd I cry? Things are good in life again. :yep:

    So, what'd \frac{\mathrm{d}A}{\mathrm{d}x}? What value of x makes it zero? What's the corresponding value of y? (hint: y = 6-\frac{3x}{2}, don't tell the maths fairy I told you that! )
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    (Original post by Zacken)
    ...
    Dramatic much?
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    (Original post by tinkerbella~)
    Dramatic much?
    Don't hate because I make maths fun.
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    (Original post by Zacken)
    Don't hate because I make maths fun.
    "Fun", yeah... :rolleyes:
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    6 minutes too late >.>
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    (Original post by Zacken)
    HA! I got you! A=xy, yes. But we also know that x+y = 6 \Rightarrow y = 6-x, so really, we can just write A = xy = x(6-x) = 6x - x^2. HALLELUJAH, IT'S ALL IN ONE VARIABLE IN X and it's an easy quadratic! Why'd I cry? Things are good in life again. :yep:

    So, what'd \frac{\mathrm{d}A}{\mathrm{d}x}? What value of x makes it zero? What's the corresponding value of y? (hint: y = 6-x, don't tell the maths fairy I told you that! )
    are you on drugs? :laugh: this made me laugh a lot
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    (Original post by tinkerbella~)
    "Fun", yeah... :rolleyes:
    (Original post by DylanJ42)
    are you on drugs? :laugh: this made me laugh a lot
    Drugs are not cool, kids.

    Spoiler:
    Show
    #smokinglyfe #defostonedrn #youneedtobehightodomaths
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    (Original post by DylanJ42)
    are you on drugs? :laugh: this made me laugh a lot
    LOOOL that was f***ing brilliant to read :rofl:
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    (Original post by Zacken)
    Drugs are not cool, kids.
    Spoiler:
    Show
    #smokinglyfe #defostonedrn #youneedtobehightodomaths
    you've gone from "full solutions are against forum guidelines" to this :laugh:
    Spoiler:
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    in all seriousness, clearly you're not on drugs, that y=6-x substitution was crazy :adore:
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    (Original post by dylanj42)
    you've gone from "full solutions are against forum guidelines" to this :laugh:
    Spoiler:
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    in all seriousness, clearly you're not on drugs, that y=6-x substitution was crazy :adore:
    zacken you are a wizard!

    no hagrid, i am just zacken

    no just zacken, you are a wizard
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    (Original post by DylanJ42)
    you've gone from "full solutions are against forum guidelines" to this :laugh:
    Spoiler:
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    in all seriousness, clearly you're not on drugs, that y=6-x substitution was crazy :adore:
    D you think I gave away too much information and should have hinted more? In hindsight, I probably should have, sorry OP!

    I'm clearly not on drugs, I'm on subs. :cool: #Koolkid
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    (Original post by Zacken)
    HA! I got you! A=xy, yes. But we also know that x+y = 6 \Rightarrow y = 6-x, so really, we can just write A = xy = x(6-x) = 6x - x^2. HALLELUJAH, IT'S ALL IN ONE VARIABLE IN X and it's an easy quadratic! Why'd I cry? Things are good in life again. :yep:

    So, what'd \frac{\mathrm{d}A}{\mathrm{d}x}? What value of x makes it zero? What's the corresponding value of y? (hint: y = 6-x, don't tell the maths fairy I told you that! )
    So much passion! :ahee: Lovely to see
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    (Original post by student403)
    zacken you are a wizard!

    no hagrid, i am just zacken

    no just zacken, you are a wizard
    i'm not a ****ing wizard hagrid im just zacken

    EDIT: why did TSR take my all caps away
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    (Original post by Student403)
    zacken you are a wizard!

    no hagrid, i am just zacken

    no just zacken, you are a wizard
    :rofl: what a video that was, back in the day, I think ill actually go watch it again, someone should do a zacken edit
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    (Original post by aymanzayedmannan)
    i'm not a ****ing wizard hagrid im just zacken

    EDIT: why did TSR take my all caps away
    If you type everything in caps, TSR makes everything lowercase for you. You need to do all caps and then add in a small lowercase letter somewhere like 'x' at the end.
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    (Original post by DylanJ42)
    :rofl: what a video that was, back in the day, I think ill actually go watch it again, someone should do a zacken edit
    OMG NO :rofl: :rofl: :rofl:
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    (Original post by Zacken)
    Drugs are not cool, kids.
    Spoiler:
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    #smokinglyfe #defostonedrn #youneedtobehightodomaths
    Lol, thanks for your help. For dA/dx I got 6-2x. And then when dA/dx = 0, x= 3, y=3. But I checked the answers and it said 2 cm and 3 cm which im assuming means that x=2?
 
 
 
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