Write an equation that expresses the following relationship. P varies directly with the cube of D and inversely with U. In your equation, use K as the constant of proportionality.
To write an equation that expresses the relationship described, we need to understand the concept of direct and inverse variation.
Direct variation means that when one variable increases, the other also increases proportionally. Inverse variation means that when one variable increases, the other decreases proportionally.
In this case, we are told that P (the dependent variable) varies directly with the cube of D (the first independent variable) and inversely with U (the second independent variable). This can be expressed as:
P = K (D^3 / U)
In this equation:
- P represents the dependent variable (e.g., pressure)
- D represents the first independent variable (e.g., distance)
- U represents the second independent variable (e.g., velocity)
- K represents the constant of proportionality, which will be determined by the specific problem or experiment
Using this equation, you can calculate the value of P for different values of D and U, with K being determined by the specific context or problem you are working with.
The equation that expresses the given relationship can be written as:
P = K * (D^3/U)
Here:
- P represents the variable that varies directly with the cube of D and inversely with U.
- D represents the variable that is cubed and placed in the numerator of the equation.
- U represents the variable that is placed in the denominator of the equation.
- K represents the constant of proportionality, which ensures that the relationship is maintained.