equations

简明释义

英[ɪˈkweɪʒənz]美[ɪˈkweɪʒənz]

n. 方程式；等式；均等；均势（equation 的复数形式）

英英释义

单词用法

同义词

反义词

例句

1.So I want to understand the equations and solve them.

因此，我想要理解这些方程并解决他们。

2.What if these equations are slightly off?

如果这些方程稍微偏离一点会怎么样呢？

3.The equations have the same equation form.

方程式的形式相同。

4.It has all the key equations.

有所有关键的方程序。

5.The equations are basically the same.

等式也基本是相同的。

6.Some movements involving primarily vertical or horizontal motions of the body as a whole, in which rotations can be ignored, can be studied using simple equations of linear motion in three dimensions.

有些运动主要涉及整体的垂直或水平运动，其中转动可以忽略，可以用三维线性运动的简单方程来研究。

7.In October 1915, Einstein threw himself into a month-long frantic endeavor in which he returned to an earlier mathematical strategy and wrestled with equations, proofs, corrections and updates.

在1915年的10月，爱因斯坦投身于长达一个月的疯狂工作中。在此期间，他回顾了早先的一个数学策略，并且与方程式、证明法、修正法、数据更新等展开了一番搏斗。

8.In physics, we often solve complex equations to understand the behavior of particles.

在物理学中，我们经常解决复杂的方程以理解粒子的行为。

9.The engineer used several equations to design the new bridge safely.

工程师使用了几个方程来安全地设计新桥。

10.In mathematics, linear equations can be represented graphically as straight lines.

在数学中，线性方程可以用图形表示为直线。

11.The chemist balanced the equations to ensure the reaction would proceed correctly.

化学家平衡了方程以确保反应能够正确进行。

12.Calculating the trajectory of a rocket involves multiple equations of motion.

计算火箭的轨迹涉及多个运动方程。

作文

In the realm of mathematics, few concepts are as fundamental and powerful as equations. An equation is a statement that asserts the equality of two expressions, typically separated by an equal sign. This simple yet profound idea forms the backbone of algebra and serves as a gateway to understanding more complex mathematical principles. From basic arithmetic to advanced calculus, equations allow us to describe relationships between quantities, solve problems, and model real-world scenarios. One of the most appealing aspects of equations is their versatility. For instance, in physics, we often encounter equations that describe the laws of motion. Newton's second law, F = ma, is a prime example, where F represents force, m is mass, and a stands for acceleration. This equation not only provides a relationship between these three variables but also enables us to predict the behavior of objects under various forces. The ability to manipulate equations and derive meaningful conclusions is a skill that extends beyond mathematics and into the sciences, engineering, economics, and beyond. Moreover, equations can be classified into different types, each serving a unique purpose. Linear equations, for example, represent straight lines when graphed on a coordinate plane. They take the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear equations is essential for analyzing trends and making predictions based on data. On the other hand, quadratic equations, which take the form ax² + bx + c = 0, introduce a level of complexity due to their parabolic nature. Solving quadratic equations often involves using the quadratic formula, factoring, or completing the square, each method revealing different insights about the roots of the equation. The importance of equations extends into the field of technology and computer science as well. Algorithms, which are essentially step-by-step procedures for calculations, often rely on equations to process data and generate results. For instance, in machine learning, models are trained using equations that minimize error and optimize performance. The ability to formulate and solve equations is crucial for data scientists and engineers who strive to create innovative solutions to complex problems. In addition to their practical applications, equations also hold a philosophical significance. They challenge us to think critically and abstractly, encouraging a deeper understanding of the world around us. The process of deriving equations requires logical reasoning and creativity, skills that are invaluable in any field of study. Furthermore, equations serve as a universal language that transcends cultural and linguistic barriers, allowing people from different backgrounds to communicate complex ideas effectively. In conclusion, equations are much more than mere symbols on a page; they are powerful tools that help us navigate and understand the complexities of our world. Whether we are solving everyday problems or exploring the frontiers of science and technology, equations play a crucial role in shaping our understanding and driving innovation. By mastering the art of working with equations, we empower ourselves to tackle challenges and contribute meaningfully to society. As we continue to explore the vast landscape of mathematics, it is clear that equations will remain at the heart of our journey, guiding us toward new discoveries and insights.

在数学领域，少有概念如方程般基础而强大。方程是一个声明，断言两个表达式的相等性，通常用等号分隔。这一简单而深刻的思想构成了代数的骨干，并作为理解更复杂数学原理的门户。从基础算术到高级微积分，方程使我们能够描述数量之间的关系，解决问题，并建模现实世界的场景。 方程最吸引人的方面之一是它们的多功能性。例如，在物理学中，我们经常遇到描述运动定律的方程。牛顿第二定律F = ma就是一个典型例子，其中F代表力，m是质量，a代表加速度。这个方程不仅提供了这三个变量之间的关系，还使我们能够预测物体在各种力作用下的行为。操纵方程并推导出有意义的结论是一种技能，这种技能超越了数学，延伸到科学、工程、经济学等领域。 此外，方程可以分为不同类型，每种类型都有其独特的目的。例如，线性方程在坐标平面上表示直线。它们的形式为y = mx + b，其中m是斜率，b是y截距。理解线性方程对于分析趋势和基于数据进行预测至关重要。另一方面，二次方程，其形式为ax² + bx + c = 0，由于其抛物线性质，引入了一定的复杂性。解决二次方程通常涉及使用二次公式、因式分解或完全平方，每种方法都揭示了关于方程根的不同见解。 方程的重要性还延伸到技术和计算机科学领域。算法，基本上是用于计算的逐步程序，通常依赖于方程来处理数据并生成结果。例如，在机器学习中，模型是通过最小化误差和优化性能的方程进行训练的。制定和解决方程的能力对数据科学家和工程师来说至关重要，他们努力创造创新的解决方案来应对复杂问题。 除了实际应用外，方程也具有哲学意义。它们挑战我们进行批判性和抽象思维，鼓励我们对周围世界有更深刻的理解。推导方程的过程需要逻辑推理和创造力，这些技能在任何学科中都是无价的。此外，方程作为一种超越文化和语言障碍的通用语言，使来自不同背景的人能够有效地沟通复杂的思想。 总之，方程不仅仅是页面上的符号；它们是帮助我们导航和理解世界复杂性的强大工具。无论我们是在解决日常问题还是探索科学和技术的前沿，方程在塑造我们的理解和推动创新方面都发挥着至关重要的作用。通过掌握与方程打交道的艺术，我们赋予自己应对挑战并为社会做出有意义贡献的能力。当我们继续探索广阔的数学领域时，显然方程将始终处于我们旅程的核心，引导我们走向新的发现和见解。