average gradient

简明释义

平均坡度

英英释义

例句

1.The trail's average gradient was steeper than expected, requiring more effort to hike.

小径的平均坡度比预期的陡峭，需要更多的努力才能徒步行走。

2.The average gradient of the hill made it a challenging climb for beginners.

这座山的平均坡度使得初学者攀爬起来很有挑战性。

3.The road has an average gradient of 5% over the first mile.

这条路在前一英里内的平均坡度为5%。

4.In engineering, understanding the average gradient is crucial for designing safe slopes.

在工程领域，理解平均坡度对于设计安全的坡道至关重要。

5.To calculate the average gradient, you need to find the change in height divided by the distance traveled.

要计算平均坡度，你需要找出高度变化与行驶距离的比值。

作文

In the study of mathematics and physics, the concept of average gradient plays a significant role in understanding changes in different contexts. The average gradient is defined as the ratio of the change in the value of a function to the change in the independent variable over a specific interval. This measurement is crucial in various applications, such as analyzing the steepness of a hill or the rate at which a car accelerates. To illustrate the importance of the average gradient, let us consider the example of a cyclist riding up a hill. The cyclist's performance can be evaluated by calculating the average gradient of the hill they are climbing. If the hill rises 100 meters over a distance of 500 meters, the average gradient can be calculated as follows: Average Gradient = (Change in height) / (Change in distance) = 100m / 500m = 0.2This result indicates that for every 5 meters the cyclist travels horizontally, they gain 1 meter in elevation. Understanding this average gradient helps the cyclist gauge the difficulty of the climb and manage their energy accordingly.Moreover, the average gradient is not limited to physical activities; it is also applicable in economics and finance. For instance, when analyzing the growth of a company’s revenue over several years, the average gradient can provide insights into the company's performance. If a company’s revenue increased from $1 million to $1.5 million over five years, the average gradient of revenue growth can be calculated similarly:Average Gradient = (Change in revenue) / (Change in time) = ($1.5M - $1M) / 5 years = $0.1M/yearThis calculation reveals that, on average, the company’s revenue grew by $100,000 each year during that period. Investors and analysts can use this information to predict future performance and make informed decisions.In the field of environmental science, the average gradient can also be applied to understand the impact of climate change on natural landscapes. For example, researchers may measure the average gradient of a riverbank eroding over time due to rising water levels. By determining how much the bank has receded over a given period and the corresponding distance, scientists can assess the severity of erosion and its potential effects on local ecosystems.In conclusion, the concept of average gradient serves as a powerful tool across various disciplines. Whether in sports, business, or environmental studies, understanding the average gradient allows individuals to analyze trends, make predictions, and enhance decision-making processes. As we continue to explore the complexities of our world, the average gradient will undoubtedly remain a vital concept in our analytical toolkit.

在数学和物理的研究中，平均梯度的概念在理解不同背景下的变化中扮演着重要角色。平均梯度定义为函数值的变化与自变量在特定区间内的变化之比。这一测量在各种应用中至关重要，例如分析山坡的陡峭程度或汽车加速的速度。为了说明平均梯度的重要性，让我们考虑一个骑自行车的人上坡的例子。通过计算他们所攀爬的山的平均梯度，可以评估骑自行车者的表现。如果山坡在500米的距离内上升了100米，则可以按如下方式计算平均梯度：平均梯度 = (高度变化) / (距离变化) = 100米 / 500米 = 0.2这个结果表明，骑自行车者每水平行驶5米，就会在高程上升1米。理解这个平均梯度有助于骑行者评估爬坡的难度，并相应地管理他们的能量。此外，平均梯度不仅限于体育活动；它还适用于经济学和金融。例如，在分析一家公司的收入在数年内的增长时，平均梯度可以提供对公司表现的洞察。如果一家公司的收入在五年内从100万美元增加到150万美元，则可以类似地计算收入增长的平均梯度：平均梯度 = (收入变化) / (时间变化) = ($1.5M - $1M) / 5年 = $0.1M/年这一计算表明，在此期间，该公司的收入平均每年增长10万美元。投资者和分析师可以利用这些信息来预测未来的表现并做出明智的决策。在环境科学领域，平均梯度也可以用于理解气候变化对自然景观的影响。例如，研究人员可能会测量由于水位上升而导致河岸侵蚀的平均梯度。通过确定在给定时期内河岸退缩的程度和相应的距离，科学家可以评估侵蚀的严重程度及其对当地生态系统的潜在影响。总之，平均梯度的概念在各个学科中都是一种强大的工具。无论是在体育、商业还是环境研究中，理解平均梯度使个人能够分析趋势、做出预测并增强决策过程。随着我们继续探索世界的复杂性，平均梯度无疑将继续作为我们分析工具箱中的一个重要概念。