If R=[(30 raised to the power 65)-(29 raised to the power 65)]/[(30 raised to the power 64)+(29 raised to the power 64)],then R lies between 0 & 0.1 or
0.1 & 0.5 or
0.5 & 1 or
greaer than 1
2006-07-03 02:51:32 · 4 answers · asked by Rohit C 3 in Science & Mathematics ➔ Mathematics
Do you want us to do your homework? I hope you know the answer, cause I dont. Good luck
2006-07-03 02:56:43 · answer #1 · answered by Charlotte 2 · 0⤊ 0⤋
I'm going to use a^b to mean "a raised to the power b".
A useful formula is (a^n - b^n)/(a-b) =
a^(n-1) + b(a^(n-2)) + (b^2)(a^(n-3)) + ... + (b^(n-2))a + b^(n-1)
From this we see that (30^65 - 29^65) = (30^65 - 29^65)/(30 -29) =
30^64 + 29(30^63) + (29^2)(30^62) + ... + 29^64 > 30^64 + 29^64.
Since (30^65 - 29^65) > 30^64 - 29^64,
(30^65 - 29^65)/(29^64 + 30^64) > 1
2006-07-03 03:38:12 · answer #2 · answered by Anonymous · 0⤊ 0⤋
It should be greater than 1.
See 30^65 - 29^65 = (30 - 29) [30^64 + 30^63*29^1 + ... + 29^64]
= [30^64 + 30^63*29^1 + ... + 29^64]
> 30^64 + 29^64
So that means the numerator is larger than the denominator.
R would thereby be greater than 1.
2006-07-03 03:36:53 · answer #3 · answered by Chong Min 2 · 0⤊ 0⤋
Yes,it lies between 0 and 1.
2006-07-03 02:59:08 · answer #4 · answered by Anonymous · 0⤊ 0⤋