separate equation

简明释义

各个方程

英英释义

例句

1.When analyzing the data, it was necessary to create a separate equation 单独方程 for each dataset.

在分析数据时，有必要为每个数据集创建一个单独方程。

2.In order to solve the problem, we need to set up a separate equation 单独方程 for each variable involved.

为了求解这个问题，我们需要为每个相关变量建立一个单独方程。

3.The physicist derived a separate equation 单独方程 to explain the motion of the particles.

这位物理学家推导出了一个单独方程来解释粒子的运动。

4.To find the intersection points, we can use a separate equation 单独方程 for each line.

要找到交点，我们可以为每条线使用一个单独方程。

5.The engineer proposed a separate equation 单独方程 to model the stress on the bridge.

工程师提出了一个单独方程来模拟桥梁上的应力。

作文

In the world of mathematics, equations serve as fundamental building blocks that help us understand various phenomena. Among the different types of equations, one particular concept stands out: the separate equation. A separate equation refers to an equation that is considered independently from other equations in a system. This means that the solution to a separate equation can be found without needing to reference or solve other equations simultaneously. Understanding this concept is crucial for students and professionals alike, as it allows for a more straightforward approach to problem-solving.To illustrate the idea of a separate equation, let’s consider a simple example involving two variables, x and y. Suppose we have the following equations:1. 2x + 3y = 62. x - y = 2In this case, we can treat each equation as a separate equation. By isolating one variable in one of the equations, we can easily find the values of x and y without needing to solve both equations at the same time. For instance, from the second equation, we can express x in terms of y:x = y + 2Now, we can substitute this expression into the first equation to solve for y:2(y + 2) + 3y = 6This simplifies to:2y + 4 + 3y = 65y + 4 = 65y = 2y = 0.4Once we have the value of y, we can substitute it back into the equation for x:x = 0.4 + 2 = 2.4Thus, we have solved the system of equations by treating them as separate equations to simplify our calculations.The ability to identify and work with separate equations can significantly enhance one's efficiency in solving mathematical problems. It allows individuals to break down complex systems into manageable parts, making it easier to understand relationships between variables. Furthermore, this strategy is not limited to just algebraic equations; it can also apply to differential equations and other mathematical constructs where independent solutions are possible.In real-world applications, the concept of separate equations is vital in fields such as engineering, physics, and economics. For instance, in engineering, when analyzing structures, engineers often encounter multiple forces acting on a beam. Each force can be represented as a separate equation, allowing engineers to calculate the resulting stress and strain without needing to consider all forces simultaneously.Moreover, in physics, the laws of motion can be expressed through separate equations for different objects. By analyzing each object independently, physicists can derive conclusions about their behavior in a given scenario. Similarly, economists use separate equations to model supply and demand, enabling them to predict market trends based on individual factors.In conclusion, mastering the concept of separate equations is essential for anyone looking to excel in mathematics and its applications. Whether in academic settings or professional environments, the ability to isolate and solve separate equations can lead to clearer insights and more effective problem-solving strategies. As we continue to explore the vast world of mathematics, let us appreciate the power and utility of separate equations in simplifying our understanding of complex systems.

在数学世界中，方程是帮助我们理解各种现象的基本构件。在不同类型的方程中，有一个特定的概念脱颖而出：separate equation。separate equation指的是在一个系统中独立考虑的方程。这意味着，separate equation的解可以在不需要同时参考或解决其他方程的情况下找到。理解这一概念对学生和专业人士来说至关重要，因为它允许更简单的方法来解决问题。为了说明separate equation的概念，让我们考虑一个涉及两个变量x和y的简单例子。假设我们有以下方程：1. 2x + 3y = 62. x - y = 2在这种情况下，我们可以将每个方程视为separate equation。通过在其中一个方程中孤立一个变量，我们可以轻松找到x和y的值，而无需同时求解两个方程。例如，从第二个方程中，我们可以用y表示x：x = y + 2现在，我们可以将这个表达式代入第一个方程来求解y：2(y + 2) + 3y = 6这简化为：2y + 4 + 3y = 65y + 4 = 65y = 2y = 0.4一旦我们得到了y的值，就可以将其代入x的方程中：x = 0.4 + 2 = 2.4因此，我们通过将它们视为separate equations来简化计算，解决了方程组。识别和处理separate equations的能力可以显著提高解决数学问题的效率。它使个人能够将复杂的系统分解为可管理的部分，从而更容易理解变量之间的关系。此外，这种策略不仅限于代数方程；它也可以应用于微分方程和其他数学构造，在这些构造中，独立解是可能的。在实际应用中，separate equations的概念在工程、物理和经济等领域至关重要。例如，在工程中，当分析结构时，工程师常常遇到作用在梁上的多个力。每个力都可以表示为separate equation，允许工程师在不需要同时考虑所有力的情况下计算结果应力和应变。此外，在物理学中，运动定律可以通过不同物体的separate equations来表达。通过独立分析每个物体，物理学家可以得出关于它们在给定情境下行为的结论。类似地，经济学家使用separate equations来建模供需，使他们能够根据单独因素预测市场趋势。总之，掌握separate equations的概念对于任何希望在数学及其应用中出类拔萃的人来说都是必不可少的。无论是在学术环境还是专业环境中，孤立和解决separate equations的能力都能带来更清晰的见解和更有效的解决问题策略。随着我们继续探索广阔的数学世界，让我们欣赏separate equations在简化我们对复杂系统理解中的力量和实用性。