📈college algebra review

key term - Z = kxy/w

Definition

The term 'z = kxy/w' represents a mathematical expression that describes a relationship between several variables. In the context of Modeling Using Variation, this expression is used to model and analyze how changes in one or more variables can affect the value of the dependent variable, 'z'.

5 Must Know Facts For Your Next Test

  1. The term 'z = kxy/w' represents a mathematical model that can be used to describe various real-world relationships and phenomena.
  2. The variable 'k' in the expression is a constant that represents the proportionality between the other variables.
  3. The variables 'x' and 'y' are independent variables, meaning their values can be changed independently, while 'z' is the dependent variable that changes in response to the changes in 'x' and 'y'.
  4. The variable 'w' is a third independent variable that can also affect the value of the dependent variable 'z'.
  5. The expression 'z = kxy/w' can be used to model various types of relationships, including direct variation, inverse variation, and combined variation.

Review Questions

  • Explain how the term 'z = kxy/w' can be used to model direct variation between the variables.
    • In the expression 'z = kxy/w', if the variable 'w' is held constant, then the relationship between 'z' and the product of 'x' and 'y' becomes one of direct variation. This means that as the values of 'x' and 'y' increase, the value of 'z' will also increase proportionally, and vice versa. The constant 'k' represents the proportionality factor between the variables.
  • Describe how the term 'z = kxy/w' can be used to model inverse variation between the variables.
    • When the expression 'z = kxy/w' is used to model inverse variation, the variable 'w' is the independent variable that is inversely proportional to the dependent variable 'z'. This means that as the value of 'w' increases, the value of 'z' will decrease, and vice versa. The constant 'k' represents the proportionality factor between the variables. In this case, the product of 'x' and 'y' would remain constant as 'w' changes to maintain the inverse relationship.
  • Analyze how the term 'z = kxy/w' can be used to model combined variation, where multiple variables affect the dependent variable 'z'.
    • The expression 'z = kxy/w' can be used to model combined variation, where the dependent variable 'z' is affected by changes in multiple independent variables ('x', 'y', and 'w'). In this case, the value of 'z' will depend on the combined effects of the changes in 'x', 'y', and 'w', as well as the proportionality constant 'k'. This allows for more complex and realistic modeling of real-world relationships, where multiple factors can influence the dependent variable simultaneously.

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