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The phrase "a correspondingly high" is correct and usable in written English.
It can be used to describe a level or degree that is proportionate or similar to something else that is also high.
Example: "The study found that participants with a higher level of education had a correspondingly high income."
Alternatives: "a similarly high" or "an equally high".
Exact(36)
Venus is the hottest planet in the solar system, so any endotherm originating from there would have a correspondingly high internal temperature, and may appreciate the cooling effects of yogurt.
The problem: Sony was selling a machine with lots of elaborate multimedia features and a correspondingly high price just as competitors were marketing cheaper machines that played games just as well.
The reason we're not always managing is because we've faced year upon year of cuts which have resulted in frozen or reduced wages, an increasing workload as we're asked to do more for less and a correspondingly high turnover of staff.
This sort of rich-world tax burden inevitably increases the pressure on the state to deliver public services of a correspondingly high quality and helps to explain public disgruntlement if they do not.If taking in more tax and spending it well are different things, so are raising tax and doing so equitably.
The supercapacitor, also called the electrical double layer capacitor, has a correspondingly high power density but low energy density.
Of the 11 LUC units that occurred in the study area, slope failures were densest (0.23 ha−1) for unit VIe11 (Table 2) with a correspondingly high sediment generation rate of ~100 t ha−1 (Additional file 4).
Similar(24)
In a reverse split, a company reduces the number of its outstanding shares, which results in a correspondingly higher price.
But Waleed Salman, the plant manager, said the high temperatures and pressures needed for operation with crude meant the turbines had to be serviced twice as often and parts had to be replaced at a correspondingly higher pace.
In contrast, the 4th/1st instar ratio for subplots with other water management regimes ranged between 0.27 and 0.68, suggesting a correspondingly higher survival than observed with intermittent irrigation.
Lower temperature and concentration are generally associated with a lower Li Cl coordination number and a correspondingly higher number of unpaired/unclustered ions in the system.
For Wundt, the distinguishing feature of the apperceptive focus is that it "always forms a unitary representation," so that a narrower focal point (or rather, the focal "field"[50]) results in a correspondingly higher intensity of attention (PP II: 269).
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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