According to the equation vs to the well know closed formula

The two phrases are not directly comparable as they serve different purposes. "According to the equation" is used to introduce a mathematical relationship or calculation, while "to the well-known closed formula" is used to refer to a specific formula that is commonly recognized. They are used in different contexts and cannot be interchanged.

Last updated: March 15, 2024

According to the equation

This phrase is correct and commonly used in mathematical contexts to introduce a mathematical relationship or calculation.

This phrase is used to indicate that a statement or result is based on a specific mathematical equation or formula.

Examples:

According to the equation x + y = 10, the value of x is 5.
According to the equation of motion, the velocity of the object is given by v = u + at.

Show examples from the web [+]

Mar 10, 2009 ... According to the equation (1.1.) -- where it's quite clear what "the equation" refers to because there are no other equations in the context, or it ...
SOLUTION: A particular compound decays according to the equation y =ae^- 0.0974t, where t is in days. Find the half-line of this compound.
SOLUTION: A particular compound decays according to the equation y=ae^(- 0.974t), where t is in days. Find the half-life of this compound.
A 0.5 kg mass vibrates according to the equation x=0.45cos(8.4t), where x is in meters and t is in seconds. Determine a) the amplitude b) the frequency.

to the well know closed formula

This phrase is incorrect. It should be "to the well-known closed formula". This phrase is used to refer to a specific formula that is commonly recognized.

This phrase is used to indicate that a calculation or result is based on a widely recognized and established formula.

Examples:

The solution can be found by applying the values to the well-known closed formula for quadratic equations.

Alternatives:

to the well-known closed formula
using the established formula
applying the recognized formula
based on the common formula
according to the widely accepted formula

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According to the equation vs to the well know closed formula