equation is satisfied

USAGE SUMMARY

The phrase "equation is satisfied" is correct and usable in written English.
It can be used in mathematical contexts to indicate that a particular equation holds true under certain conditions or values. Example: "When x equals 2, the equation is satisfied, resulting in a true statement."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

43 human-written examples

A slight variation of this problem occurs when there are points inside the disk at which heat is added (sources) or removed (sinks) as long as the temperature still remains constant at each point (stationary flow), in which case Poisson's equation is satisfied.

Encyclopedia Britannica

The continuity equation is satisfied using Eq. (2.10).

Boundary Value Problems

The second structure equation is satisfied as an equality.

The Journal of Mathematical Neuroscience

and therefore by (7.8) the differential equation is satisfied.

Boundary Value Problems

The complete convective-diffusion equation is satisfied when integrated across the concentrated particle layer.

Chemical Engineering Science

If the parity-check equation is satisfied, decoding is completed even before the maximum number of iteration is reached.

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

17 human-written examples

More precisely it depends on the following equation being satisfied: dim ( W u ( x i ) ∩ I c ( i ) ) + dim ( W s ( x i + 1 ) ∩ I c ( i ) ) ≥ dim ( I c ( i ) ) + 1 (8).

The Journal of Mathematical Neuroscience

Recall that if the following system of equations is satisfied (22) γ 1 + γ 2 + γ 3 = 1, (23) γ 1 p + 1 + γ 2 p + 1 + γ 3 p + 1 = 0, the composition results in a scheme of order at least p + 1.

Computers and Mathematics with Applications

According to this method, kinematic analysis is carried out in the sense that only constraint equations are satisfied exactly, while requirements are satisfied at best.

Mechanism and Machine Theory

For example, in the system both equations are satisfied by the solution x = 2, y = 3.

Encyclopedia Britannica

The coupled governing partial differential equations are satisfied in a weak-form on small fictitious subdomains.

International Journal of Solids and Structures

Expert writing Tips

Best practice

When using "equation is satisfied", ensure that the context clearly defines the conditions or values under which the equation holds true. This adds clarity and precision to your writing.

Common error

Avoid using "equation is satisfied" without specifying how or why the equation is satisfied. Provide the necessary information (e.g., specific values or conditions) for the reader to understand the equation's validity.

Linguistic Context

The phrase "equation is satisfied" functions as a declarative statement asserting that a mathematical equation holds true given specific conditions. Ludwig AI confirms that this phrase is grammatically sound and frequently used within technical domains.

Expression frequency: Common

Frequent in

Science

80%

Encyclopedias

10%

Formal & Business

5%

Less common in

News & Media

2%

Wiki

2%

Reference

1%

Ludwig's WRAP-UP

In summary, the phrase "equation is satisfied" is a grammatically correct and commonly used expression, particularly in scientific and mathematical contexts. Ludwig AI states the phrase is accurate and usable in written English. It serves to confirm the validity or truth of an equation when certain conditions are met. While it's most prevalent in formal and scientific writing, awareness of context and provision of specifics are crucial for effective communication. Alternatives like "equation holds true" or "equation is valid" can be used. This analysis offers insights into the phrase's usage, register, and semantic relationships, providing a comprehensive understanding for writers.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

equation holds true

Emphasizes the truthfulness or validity of the equation under specific conditions.

equation is valid

Focuses on the correctness and applicability of the equation.

equation is fulfilled

Highlights the accomplishment or completion of the equation's requirements.

equation is verified

Stresses the confirmation or validation of the equation through testing or proof.

equation is confirmed

Indicates that the equation has been substantiated or proven correct.

equation is met

Suggests that the conditions necessary for the equation to be true have been achieved.

equation is proven

Focuses on the fact that the equation has undergone a formal proof.

equation is true

States a basic fact about the equation's condition.

solution satisfies the equation

Shifts focus to the solution and its relation to the equation.

solution validates the equation

Like above but more formal expression.

FAQs

What does it mean when an "equation is satisfied"?

When an "equation is satisfied", it means that the values or conditions inputted into the equation result in a true statement or a balanced equality. In other words, the equation holds true for those specific inputs.

How can I verify that an "equation is satisfied"?

To verify that an "equation is satisfied", substitute the given values into the equation and perform the calculations. If the left-hand side of the equation equals the right-hand side, then the equation is satisfied.

What are some alternatives to saying "equation is satisfied"?

You can use alternatives like "equation holds true", "equation is valid", or "equation is fulfilled" to express the same idea.

In what contexts is the phrase "equation is satisfied" typically used?

The phrase "equation is satisfied" is commonly used in mathematical, scientific, and engineering contexts to describe the validity or correctness of an equation under specific conditions.