arrive at the equation

USAGE SUMMARY

"arrive at the equation" is a correct and usable phrase in written English.
It is typically used in mathematics and science contexts when referring to discovering a particular equation. For example: After a thorough analysis of the data, we were able to arrive at the equation y = 2x + 10.

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

4 human-written examples

Thus, we arrive at the equation (1).

Advances in Difference Equations

By differentiating and making the proper substitutions we arrive at the equation u ″ ( t ) + ( a 2 − b 2 ) u ( t ) = 0, t ∈ R. (2.7).

Boundary Value Problems

At ξ → ∞, proceeding analogously to the solution of Equation 21, one should again arrive at the equation of Kummer (24) but with different parameter λ.

Nanoscale Research Letters

Substituting (18) into this relation, we arrive at the equation eta x, lambda) + frac{1}{2 pi i} int_{gamma} eta x, mu) tilde{r} x, lambda, mu),dmu= 0_{m},quad lambdain gamma, (25) with respect to (eta x, lambda) = ellvarphi x, lambda) - lambdavarphi x, lambda)).

Boundary Value Problems

Human-verified similar examples from authoritative sources

Similar Expressions

56 human-written examples

This can be expressed as a rate, k, by 8Using the Chapman Kolmogorov equation, eq 6, for pΔ t, we get 9After some manipulation of this expression, we arrive at the master equation for the transition probability densities 10If we want to obtain a master equation for the state probability density itself, we can multiply this equation by p x1, t) and integrate over x1.

Chemical Reviews

Combining this inequality with (3.2) and (3.3), we arrive at the desired equation (3.1).

Boundary Value Problems

From Eqs. (A.11), (A.17), and (A.18), we arrive at the following equation which gives the temperature of the disk surface: (A.19).

Earth, Planets and Space

We employ the equation of motion technique to calculate both the retarded and the lesser Green's functions by adopting the Hartree-Fock truncation approximation, and arrive at the Dayson equation form for the retarded one [28]: (5).

Nanoscale Research Letters

Substituting the trial solution into the partial differential equation (21) and considering only the terms with the highest asymptotic order (those containing the fourth-order derivative of the wavelet f), we arrive at the kinematic equation (17).

Journal of Petroleum Exploration and Production Technology

The solution to the system of first-order differential equations (18) may be obtained in the form (tilde {pi }(x) = e^{lambda x} phi ), ϕ∈R 1×M [28], such that after substituting it back into our system we arrive at the characteristic equation: phi left(lambda I - tilde{Q} tilde{R}^{-1} right) = 0, (22).

EURASIP Journal on Wireless Communications and Networking

Substituting Equations (2) and (3) to the above, we get: ε eff ∥ E ∥ = ρ ε m E ∥ + 1 − ρ ε d E ∥ (10 If we cancel out the common parallel electric field components, we arrive at the final equation: ε ∥ = ρ ε m + 1 − ρ ε d (11).

Nano Convergence

Expert writing Tips

Best practice

When using "arrive at the equation", ensure the context clearly indicates the steps or process that led to the equation's derivation. For instance, "After applying the principles of thermodynamics, we arrive at the equation governing energy transfer."

Common error

Avoid using "arrive at the equation" in non-mathematical or non-scientific contexts. It is specific to quantitative or logical derivations, and its use in other contexts can sound unnatural. Instead, use phrases like "reach a conclusion" or "come to an agreement".

Linguistic Context

The phrase "arrive at the equation" functions as a verbal phrase indicating the culmination of a process of deduction, calculation, or experimentation that results in a specific mathematical relationship. As Ludwig AI confirms, this phrase is common in mathematical and scientific contexts. The provided examples from Ludwig showcase its usage within research papers and academic writing.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, the phrase "arrive at the equation" is a grammatically correct phrase primarily used within formal and scientific writing, particularly in contexts involving mathematical derivations and experimental results. Ludwig AI also confirms its correct usage. While infrequent overall, its use is highly concentrated within the realm of science, as evidenced by the source analysis. When employing this phrase, ensure the surrounding context clearly illustrates the methodology or logical progression that leads to the equation's derivation. Alternative phrases such as "derive the equation" or "deduce the equation" may also be suitable, depending on the specific emphasis desired.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

reach the equation

Similar to the original phrase but uses a different verb.

derive the equation

Focuses on the mathematical steps taken to reach the equation.

deduce the equation

Emphasizes logical reasoning to obtain the equation.

determine the equation

Focuses on finding out or calculating the equation.

obtain the equation

A more general term indicating the equation was acquired.

find the equation

Emphasizes the discovery aspect of the equation.

formulate the equation

Highlights the act of creating or expressing the equation.

develop the equation

Highlights the process of building or refining the equation.

establish the equation

Suggests the equation has been proven or validated.

ascertain the equation

Emphasizes the effort to find something out for certain.

FAQs

What does it mean to "arrive at the equation" in a scientific context?

In a scientific context, to "arrive at the equation" means to deduce or derive a mathematical relationship through a series of logical steps, calculations, or experimental observations. It implies a process of discovery and validation.

Can I use "reach the equation" instead of "arrive at the equation"?

Yes, you can use "reach the equation" as a synonym for "arrive at the equation". Both phrases indicate that you have successfully obtained or derived the equation after a certain process.

What's the difference between "derive the equation" and "arrive at the equation"?

While both phrases are similar, "derive the equation" emphasizes the mathematical steps involved in obtaining the equation, whereas "arrive at the equation" focuses more on the final result of the process.

Is "arrive at the equation" suitable for informal writing?

The phrase "arrive at the equation" is generally more suited for formal and scientific writing. In informal contexts, it may sound overly technical. Simpler phrases like "find the answer" or "figure out the solution" may be more appropriate.