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Math Help - Need some help with a few questions that have been annoying me

  1. #1
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    Thumbs down Need some help with a few questions that have been annoying me

    1) Make s the subject of the formula below

    v= s (w+x) (thats "S" over "3")
    --
    3


    2)Simplify Fully

    12s squared t squared
    OVER
    16st cubed

    3) Solve the simultaneous equasion

    3p+q=11.25
    p-2q=7.25

    4)Show that a solution of the equation
    x Cubed- 10x=35
    Lies between 4.2 and 4.3

    5)Marks jigsaw puzzle contains 3 types of pieces
    >Corner pieces-- 0.008
    >Straight edge pieces--0.164
    >Middle pieces-- unknown

    Mark picks a piece out at random. The probability's of picking a corner or straight edge piece are shows above

    There are 500 pieces in marks jigsaw puzzle
    How many middle pieces are there?

    Thanks in advance to anyone who helps in and if you can will you please show me some formula so i can learn from my mistakes

    :>:>
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    1) \displaystyle v=\frac{s}{3}(w+x)\Rightarrow s=\frac{3v}{w+x}

    2) \displaystyle\frac{12s^2t^2}{16st^3}=\frac{3s}{4t}

    3) \left\{\begin{array}{ll}3p+q=11.25\\p-2q=7.25\end{array}\right.
    Multiply the first equation by 2, then add the equations.
    We have 7p=29.75\Rightarrow p=4.25.
    Now, plug p in any equation and find q.

    4) Plug x=4.2 and x=4.3 in equation and probably you'll obtain one negative value and one positive value.

    5) Let x be the number of middle pieces.
    The probability to pick one is \displaystyle\frac{x}{500}.
    On the other hand, the same probability is 1-0.008-0.164.
    Equalize the two values and solve for x.
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  3. #3
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