Posted by alya on Saturday, October 15, 2011 at 5:28am.
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)

HELPPROBLEM SOLVING IN MATHEMATICS  drwls, Saturday, October 15, 2011 at 7:02am
How long is a "pai" ? I am not familiar with that unit of length

HELPPROBLEM SOLVING IN MATHEMATICS  alya, Saturday, October 15, 2011 at 7:59am
3.142

HELPPROBLEM SOLVING IN MATHEMATICS  Writeacher, Saturday, October 15, 2011 at 8:02am
I think you mean pi, right?
http://www.google.com/search?rlz=1C1GGGE_enUS379US379&gcx=c&sourceid=chrome&ie=UTF8&q=pi

HELPPROBLEM SOLVING IN MATHEMATICS  alya, Saturday, October 15, 2011 at 9:03am
yup.. pi.. so i want to know how to solve it

HELPPROBLEM SOLVING IN MATHEMATICS  drwls, Saturday, October 15, 2011 at 9:12am
pi is the number but what is the dimension? Is the original wire length 136 pi centimeters?

HELPPROBLEM SOLVING IN MATHEMATICS  Reiny, Saturday, October 15, 2011 at 9:26am
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 + .. (n1) ) = 190π
5+6+... + 5+n1 = 95
(n/2)(5 + 5+n1) = 95
n(9+n) = 190
n^2 + 9n  190 = 0
(n10)(n+19) = 0
n=10 or a negative
So he will be able to form 10 complete circles.
check:
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