chetan2u wrote:
sagnik242 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
Given: \(length:width:height=3k:2k:2k\), for some positive number \(k\). Also: \(volume=x=3k*2k*2k\) --> \(x=12k^3\) --> \(k=\sqrt[3]{\frac{x}{12}}\) --> \(height=2k=\sqrt[3]{\frac{2x}{3}}\).
Answer: B.
confused how you got from : \(k=\sqrt[3]{\frac{x}{12}}\) --> \(height=2k=\sqrt[3]{\frac{2x}{3}}\). can you break this down further please?[/quote]
Hi,
\(k=\sqrt[3]{\frac{x}{12}}\) ..
height is 2k as ratios are 3k:2k:2k
so \(2k=2\sqrt[3]{\frac{x}{12}}\)..
=> \(2k=\sqrt[3]{8}\sqrt[3]{\frac{x}{12}}\)..
\(2k=\sqrt[3]{\frac{8x}{12}}\)..
\(height=2k=\sqrt[3]{\frac{2x}{3}}\)..
hope this is what you were looking for[/quote]
How does 2k become: \(\sqrt[3]{8}\sqrt[3]{\frac{x}{12}}\)..
Where you get the 8 from?