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Math Help - Four Questions Need Help With

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    68

    Four Questions Need Help With

    1 . A farmer has rectangular garden plot surrounded by 200ft of fence. Find the length and width of the garden if its is 2400ft^2.

    2. Find the length of X if the shaded area is 160 in^2.
    ImageShack - Hosting :: 59310350aa9.png

    3. Find the length X if the shaded area is 1200cm^2
    ImageShack - Hosting :: 22151047zo3.png

    4. A cylindrical can has a volume of 40\pi cm^3 and is 10cm tall. What is the diameter?

    Thanks a lot!
    Nate
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  2. #2
    Member SengNee's Avatar
    Joined
    Jan 2008
    From
    Pangkor Island, Perak, Malaysia.
    Posts
    155
    1)

    2l+2w=200
    l+w=100
    l=100-w......i

    A=2400
    lw=2400......ii

    Substitute i into ii

    (100-w)w=2400[/tex]
    100w-w^2=2400
    w^2-100w+2400=0
    (w-40)(w-60)=0

    If w=40,
    Therefore, l=60.

    If w=60,
    Therefore, l=40.


    2) I can't see the shaded region.

    If all are shaded,

    A=160
    (x+13)(x+14)-(13)(14)=160
    x^2+27x+182-182=160
    x^2+27x-160=0
    (x+32)(x-5)=0

    x=-32
    x=5

    x>0
    Therefore, x=5.


    3) I can't see the shaded region.

    If all are shaded,

    A=0.5bh
    1200=0.5[(x+1)+(1)](x)
    2400=x^2+2x
    x^2+2x-2400=0
    (x-48)(x+50)=0

    x=48
    x=-50

    x>0
    Therefore, x=48.


    4)

    V=\pi r^2h
    40\pi=\pi r^2(10)
    r^2=4
    r=2

    r>0
    Therefore,
    r=2
    2r=4
    d=4
    Last edited by SengNee; January 10th 2008 at 08:51 PM.
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