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"lengths at which" is correct and usable in written English.
You can use it to refer to a certain range of measurements or the level of detail or intensity of something. For example, "We discussed the lengths at which we should go in order to meet our goal."
Exact(13)
There are two characteristic lengths at which the strength and toughness are optimized respectively.
However, for some signal wavelengths, the erbium-doped fiber (EDF) lengths at which the gain is temperature independent are observed.
Peak forces developed by the uniarticular hip and knee extensors, as well as the normalized fiber lengths at which these muscles developed their peak forces, correlated more closely with changes in step length than step frequency.
Lastly, the interaction between added SO2 and intended cellaring length is statistically significant and positive in the regressions containing all non-AOC wines and only red AOC wines.8 The AOC and Non-AOC columns of Table 6 show the intended cellaring lengths at which the effect of added SO2 becomes positive.
The film reflects this urge to incorporate spontaneity and new experiences into our daily lives and the lengths at which we will go to do so.
In case of rbcL, 457 bp and 407 bp were the minimum average lengths at which maximum species recovery were obtained when trimmed off from 5' (Figure 4A) and 3' (Figure 4B) ends respectively.
Similar(47)
The exact length at which this passive force occurs depends on the particular muscle.
This maximum point is the length at which the heart normally functions.
Generally there is a length at which the force generated is maximal.
Whatever the length at which he writes, Mr. King leaves readers with a simple, one-word message: Gotcha!
Rich's essays tend to be very, very short — about 200 words, a length at which many humorists are only beginning to get their conceit across.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com