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khurram
- Master | Next Rank: 500 Posts
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Q27.
The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?
A. 3√x
B. 3√[(2x)/3]
C. 3√[(3x)/2]
D. (2/3) 3√x
E. (3/2) 3√x
3a.2a.2a = x
a^3 = x/12 = 2x/3.1/8 (I was fine until right here)
a = 3√[(2x)/3]/2
2a = 3√[(2x)/3] (The Q asks for the height, which is 2a, not just a)
Per thankont:
a^3=x/12=2x/24 = 2x/(3*8)
They are doing this since cube root of 8 is 2.
yeah u're right TBAY it's better to leave it there and look at the answers(divide by 2 and raise to the third power and try to bring one of the answer choices to this form)
Thanks
khurram
I am thinking of picking a smart number like 12 and then match answer to each one but even that takes long.
The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?
A. 3√x
B. 3√[(2x)/3]
C. 3√[(3x)/2]
D. (2/3) 3√x
E. (3/2) 3√x
3a.2a.2a = x
a^3 = x/12 = 2x/3.1/8 (I was fine until right here)
a = 3√[(2x)/3]/2
2a = 3√[(2x)/3] (The Q asks for the height, which is 2a, not just a)
Per thankont:
a^3=x/12=2x/24 = 2x/(3*8)
They are doing this since cube root of 8 is 2.
yeah u're right TBAY it's better to leave it there and look at the answers(divide by 2 and raise to the third power and try to bring one of the answer choices to this form)
Thanks
khurram
I am thinking of picking a smart number like 12 and then match answer to each one but even that takes long.
