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A quantity varies inversely with the square of If when find when is 4.
Many situations are more complicated than a basic direct variation or inverse variation model. One variable often depends on multiple other variables. When a variable is dependent on the product or quotient of two or more variables, this is called joint variation . For example, the cost of busing students for each school trip varies with the number of students attending and the distance from the school. The variable cost, varies jointly with the number of students, and the distance,
Joint variation occurs when a variable varies directly or inversely with multiple variables.
For instance, if varies directly with both and we have If varies directly with and inversely with we have Notice that we only use one constant in a joint variation equation.
A quantity varies directly with the square of and inversely with the cube root of If when and find when and
Begin by writing an equation to show the relationship between the variables.
Substitute and to find the value of the constant
Now we can substitute the value of the constant into the equation for the relationship.
To find when and we will substitute values for and into our equation.
A quantity varies directly with the square of and inversely with If when and find when and
Access these online resources for additional instruction and practice with direct and inverse variation.
Visit this website for additional practice questions from Learningpod.
Direct variation | |
Inverse variation |
What is true of the appearance of graphs that reflect a direct variation between two variables?
The graph will have the appearance of a power function.
If two variables vary inversely, what will an equation representing their relationship look like?
Is there a limit to the number of variables that can vary jointly? Explain.
No. Multiple variables may jointly vary.
For the following exercises, write an equation describing the relationship of the given variables.
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