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Thread: Four Questions Need Help With

  1. #1
    Junior Member
    Joined
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    Four Questions Need Help With

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

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

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

    4. A cylindrical can has a volume of $\displaystyle 40\pi cm^3$ 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)

    $\displaystyle 2l+2w=200$
    $\displaystyle l+w=100$
    $\displaystyle l=100-w$......i

    $\displaystyle A=2400$
    $\displaystyle lw=2400$......ii

    Substitute i into ii

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

    If $\displaystyle w=40$,
    Therefore, $\displaystyle l=60$.

    If $\displaystyle w=60,$
    Therefore, $\displaystyle l=40$.


    2) I can't see the shaded region.

    If all are shaded,

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

    $\displaystyle x=-32$
    $\displaystyle x=5$

    $\displaystyle x>0$
    Therefore, $\displaystyle x=5$.


    3) I can't see the shaded region.

    If all are shaded,

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

    $\displaystyle x=48$
    $\displaystyle x=-50$

    $\displaystyle x>0$
    Therefore, $\displaystyle x=48$.


    4)

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

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