Let a, b, and c be positive real numbers. If ab = 48, bc = 96, and ac = 72, what is the value of abc?
2006-08-17 16:47:02 · 14 answers · asked by Jerry M 3 in Science & Mathematics ➔ Mathematics
If ab = 48, bc = 96, and ac = 72,
Multiply all the three we get
a^2b^2c^2 = (48)((96)(72)
= 331776
Taking square root we get
abc =576
2006-08-17 17:10:22 · answer #1 · answered by Amar Soni 7 · 0⤊ 0⤋
Funguy got the wrong answer, *AND* didn't show his work.
Grade = ZERO
Solution:
Given ab = 48, bc = 96, ac = 72
2ab = 96 = bc
divide by b 2a = c
substitute ac = 72 = a * 2a = 2a^2
divide by 2 a^2 = 36
Therefore a =6
b = 48/6 = 8
c = 2a = 12
Therefore abc = 6 * 8 * 12 = 48 x 12 = 48 * (10 + 2)
= 48 (10) + 48 (2) = 480 + 96 = 576
2006-08-18 00:03:27 · answer #2 · answered by dukefenton 7 · 0⤊ 0⤋
Given:
ab = 48, bc = 96, and ac = 72
Required to find: abc
ab = 48 so a = 48/b
bc = 96 so b = 96/c
ac = 72 so c = 96/a
abc = 48/b * 96/c * 72/c
abc = (331776)/ abc
(abc)² = 331776
abc = â(331776)
abc = ± 576
2006-08-18 06:59:30 · answer #3 · answered by Brenmore 5 · 0⤊ 0⤋
ab = 48
bc = 96
ac = 72
ab x bc x ac = 48 x 96 x 72
a^2 x b^2 x c^2 = 48 x 48 x 2 x 72 = 48 x 48 x 144= 48x48 x 12x12
a x b x c = 48 x 12 = 576
The value of abc is 576
2006-08-18 00:53:12 · answer #4 · answered by Julian 3 · 0⤊ 0⤋
ab=48 , so a=48/b
bc=96 , so c=96/b
ac=72 , so 48/b * 96/b = 72
48*96 = 72 b^2
64 = b^2
b = 8
So, a=48/8=6 and c=96/8=12.
The answer :
a=6
b=8
c=12
2006-08-18 00:10:32 · answer #5 · answered by ArcherOmega 4 · 0⤊ 0⤋
72
2006-08-17 23:59:50 · answer #6 · answered by fumeluv 2 · 0⤊ 0⤋
a=6;b=8;c=12
2006-08-18 03:59:15 · answer #7 · answered by prabu m 1 · 0⤊ 0⤋
tired and sullen
anyways:
ab = 48
bc = 96
(ab) / (bc) = 48/96
a/c = 1/2 ----> c = 2a
ac = 72 ------> a*(2a) = 72
a^2 = 36
a = +/- 6
b = +/- 8
c = +/- 12
abc = +/- 576
2006-08-18 23:38:00 · answer #8 · answered by Anonymous · 0⤊ 0⤋
120
2006-08-17 23:53:44 · answer #9 · answered by fun_guy_otown 6 · 0⤊ 0⤋
6(a) * 8(b) = 48
8(b) * 12(c) = 96
6(a) 8 12(c) = 72
a = 6
b = 8
c = 12
abc=576
2006-08-17 23:57:47 · answer #10 · answered by Archangel 4 · 0⤊ 0⤋