HELP-PROBLEM SOLVING IN MATHEMATICS

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a piece of wire of length 136(pai) is cut to form 8 circles. the radius of the circles differ from each other, in sequence, by 1 cm.
a) find the radius,r
b) find the number of complete circles that can be formed if the original length of the wire is 190(pai)

  • HELP-PROBLEM SOLVING IN MATHEMATICS -

    How long is a "pai" ? I am not familiar with that unit of length

  • HELP-PROBLEM SOLVING IN MATHEMATICS -

    3.142

  • HELP-PROBLEM SOLVING IN MATHEMATICS -

    I think you mean pi, right?

    http://www.google.com/search?rlz=1C1GGGE_enUS379US379&gcx=c&sourceid=chrome&ie=UTF-8&q=pi

  • HELP-PROBLEM SOLVING IN MATHEMATICS -

    yup.. pi.. so i want to know how to solve it

  • HELP-PROBLEM SOLVING IN MATHEMATICS -

    pi is the number but what is the dimension? Is the original wire length 136 pi centimeters?

  • HELP-PROBLEM SOLVING IN MATHEMATICS -

    I agree that you probably meant 136π for the length of the wire

    let the first circle have a radius of r
    then the others are
    r+1, r+2 ,.. , r+7
    so the circumferences would be
    r(2π) + (r+1)(2π) + ... + (r+7)(2π)
    = 2π[ r + r+1 + ... + r+7 ]
    = 2π[ 4(r + r+7) , using (n/2)(first + last) as the sum of n terms of an AS
    = 2π(8r + 28)
    = 136π

    2π(8r+28) = 136π
    8r + 28 = 68
    r = 5

    check:
    circumferences are
    2π(5+6+...+12)
    using (n/2)(first + last) as the sum of n terms of an AS
    = 2π(4)(5+12) = 136π
    length of wire = 136π , perfect!

    b)
    I assume your circles will start with a radius of 5 and increase by 1
    let the number of complete circles be n, where n will have to be a whole number

    2π(5 + 6 + .. (n-1) ) = 190π
    5+6+... + 5+n-1 = 95

    (n/2)(5 + 5+n-1) = 95
    n(9+n) = 190
    n^2 + 9n - 190 = 0
    (n-10)(n+19) = 0
    n=10 or a negative

    So he will be able to form 10 complete circles.

    check:

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