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    a)
    I get 40 m² as well.


    b)
    The bits of fence labelled as x would be replaced on one side by the existing (permanent) fence, thus doubling the value of x an the other side of the pen. i.e the area doubles!
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    can u explain it more please?
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    i understand part b) but i dont quite know how to calculate part a)....
    can you show me please? cheers
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    (Original post by ronnie)
    can u explain it more please?
    Let L be the length of fencing.
    Let A be the area of all the pens together.
    let a be the area of a single pen.
    Then,
    a)
    L = 80
    A = 4xy
    a = xy

    L = 5 lots of y plus 2*(4 lots of x)
    L = 5y + 8x
    5y + 8x = 80
    y = 16 - 1.6x

    A = 4x(16 - 1.6x)
    A = 64x - 6.4x²
    dA/dx = 64 - 12.8x = 0 for max or min
    64 - 12.8x = 0
    :. x = 5
    ======
    & y = 8
    ======
    a = 5*8 = 40 m²
    ============
    b)
    When the permanent fence is used, The fencing is only used on the 5 lots of y and on only 4 lots of x, not 8 lots like in part a).
    So,
    L = 5y + 4x
    5y + 4x = 80
    y = 16 - 0.8x
    A = 4x(16 - 0.8x)
    A = 64x - 3.2x²
    dA/dx = 64 - 6.4x = 0 for max or min
    64 - 6.4x = 0
    :. x = 10
    =======
    & y = 8
    ======
    a = 10*8 = 80 m²
    =============
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    cheers fermat! unfortunately part a) came to me in my sleep. but thanks anyway! tis a rather easy question in the end.
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    maybe if i put it like this, would be better to understand.

    Let L be the length of fencing.
    Let A be the area of all the pens together.
    Then,
    a)
    L = 80
    A = 4.x.y


    L = 5 y's plus 2 rows of 4 x's
    therefore, L = 5y + 8x
    and total length is 80 so
    5y + 8x = 80
    make it y equals
    y = 16 - 1.6x

    them put y=16-1.6x into the A=4.x.y
    A = 4x(16 - 1.6x)
    A = 64x - 6.4x²
    differentiating and get
    A'=64 - 12.8x
    make it equal 0 for max or min
    64 - 12.8x = 0
    then find x
    :. x = 5
    ======
    then u put it into this equation that u found earlier, y = 16 - 1.6x
    y=8
    ======
    then u put it into the equation u got in first step
    A = 4.x.y
    A=4x5x8
    =160 (which is the area of all 4 boxes/pens)
    do u divide 160 by 4 =40


    read mine and fermats and keep looking at the diagram and good luck !


    cheers !
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    (Original post by ronnie)
    maybe if i put it like this, would be better to understand.

    Let L be the length of fencing.
    Let A be the area of all the pens together.
    Then,
    a)
    L = 80
    A = 4.x.y


    L = 5 y's plus 2 rows of 4 x's
    therefore, L = 5y + 8x
    and total length is 80 so
    5y + 8x = 80
    make it y equals
    y = 16 - 1.6x

    them put y=16-1.6x into the A=4.x.y
    A = 4x(16 - 1.6x)
    A = 64x - 6.4x²
    differentiating and get
    A'=64 - 12.8x
    make it equal 0 for max or min
    64 - 12.8x = 0
    then find x
    :. x = 5
    ======
    then u put it into this equation that u found earlier, y = 16 - 1.6x
    y=8
    ======
    then u put it into the equation u got in first step
    A = 4.x.y
    A=4x5x8
    =160 (which is the area of all 4 boxes/pens)
    do u divide 160 by 4 =40


    read mine and fermats and keep looking at the diagram and good luck !
    thanks! but as i said (in post6), i already got it. thanks anyway.
    and part b) is 80 as x is doubled (so x=10, y remains 8, so A=80).
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    i know how to do part b now but don't really understand, why is the answer doubled ?(lol, math is not really my thing)
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    ronnie send me your email add and i will send you an explanation. i have it written on Word (which is much easier to explain on!)
 
 
 
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