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
OAB
I have solved till - k = 3√x/12.
Now what will be the next?
Please advise..
Thanks
rectangular carton
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- MartyMurray
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Since the height is 2k, you just multiply your number by 2, and work your way to the correct answer.rsarashi wrote: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
OAB
I have solved till - k = 3√x/12.
Now what will be the next?
Please advise..
Thanks
I did it below, so if you want to do it own your own, don't look at what I did until you after you do it yourself.
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[spoiler]2 * ∛(x/12) = ∛(2³x/12) = ∛(2x/3)[/spoiler]
The correct answer is B.
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- DavidG@VeritasPrep
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You can also just pick easy numbers.rsarashi wrote: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.∛x
B.∛[(2x)/3]
C.∛[(3x)/2]
D.(2/3) ∛x
E.(3/2) ∛x
OAB
Thanks
Length: 3
Width: 2
Height: 2
x = 2 * 2 * 3 = 12
When x = 12, the height is 2. No just plug and chug with the answers, inserting 12 for x, until one of them spits out a height of 2.
A.∛x = ∛12 --> not 2
B.∛[(2x)/3] --> ∛(2*12/3) --> ∛8 = 2. And we're done. B is the answer.
- DavidG@VeritasPrep
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(And in the future, please be careful about formatting. I initially read ∛ as 3 * √, and I'd imagine I'm not the only one who misinterpreted this way. )