Coefficients Meaning: Definition, Examples, and Translations
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coefficients
[kษสษชหfษชสษnts ]
Definitions
mathematics
Coefficients are the numbers which multiply the variables in an algebraic expression. They are the numerical constants that are placed before the variables.
Synonyms
Which Synonym Should You Choose?
| Word | Description / Examples |
|---|---|
| coefficients |
Used frequently in mathematics and statistics to describe numbers or constants that multiply variables in equations and expressions. Commonly seen in algebra, calculus, and physics.
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| constant |
Describes a quantity that does not change. Used widely in mathematics, physics, and engineering to signify a fixed value.
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| factor |
Commonly used in mathematics to describe numbers that are multiplied together to get another number. Also used to describe elements contributing to a result in various fields like business, science, and everyday language.
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| multiplier |
Often used in mathematics and economics to describe a number by which another number is multiplied. In economics, it refers to the factor by which an increase in spending produces an increase in income and consumption greater than the initial amount spent.
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Examples of usage
- In the equation 3x + 4y = 10, 3 and 4 are the coefficients of x and y respectively.
- The coefficient of x^2 in the expression 2x^2 + 5x - 3 is 2.
chemistry
In chemistry, coefficients refer to the numbers placed before the chemical formula in a balanced chemical equation, indicating the relative amount of each substance involved in the reaction.
Synonyms
Which Synonym Should You Choose?
| Word | Description / Examples |
|---|---|
| coefficients |
Used in mathematics and science, particularly in equations where they represent constant values that multiply variables.
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Examples of usage
- In the reaction 2H2 + O2 -> 2H2O, the coefficients 2 and 1 indicate the balanced ratio of hydrogen and oxygen to form water.
Translations
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Interesting Facts
Mathematics
- In algebra, coefficients are the numbers in front of variables, like the '2' in '2x', which means you have two of 'x'.
- They are crucial in forming equations and help us understand the relationship between different quantities.
- The absence of a coefficient means thereโs an implicit '1', as in '1x' for just 'x'.
Physics
- In physics, coefficients quantify relationships in formulas, like the coefficient of friction, affecting how objects move.
- Scientific equations often use coefficients to express measurements that describe properties like speed or energy.
- Coefficients can also appear in statistical studies, indicating the strength or direction of relationships between variables.
Statistics
- In statistics, coefficients in regression models help us understand how changes in one variable impact another.
- A positive coefficient suggests a direct relationship, while a negative one indicates an inverse relationship.
- These numbers help scientists and researchers predict outcomes based on data analysis.
Engineering
- Engineers use coefficients to calculate load and stress in structures, ensuring safety and stability.
- In thermal engineering, coefficients can indicate heat transfer effectiveness, guiding design choices for cooling systems.
- Material coefficients help determine how substances will react under different conditions, vital for building and manufacturing.
Economics
- In economics, coefficients in models can predict how changes in supply affect demand, helping to shape policy decisions.
- Elasticity coefficients measure how responsive one economic variable is to changes in another, like price changes on quantity demanded.
- These numeric indicators are crucial for understanding market dynamics and making informed investment choices.
Origin of 'coefficients'
The word 'coefficients' has its origins in Latin, where 'co-' means 'together' and 'efficient' comes from 'efficere' meaning 'to accomplish'. The term was first used in mathematics to indicate the constants that accompany variables. Over time, the term was adopted in various fields, including chemistry, to represent the relative amounts of substances in a reaction.