u varies inversly as n
To understand the inverse variation relationship between two variables, "u" and "n," let's break it down step by step:
1. Inverse Variation: Inverse variation, also known as inverse proportion, states that two quantities are inversely proportional if an increase in one variable leads to a decrease in the other variable, and vice versa.
2. Equation: When "u" varies inversely as "n," it can be expressed using the mathematical equation: u = k / n, where "k" is a constant of variation.
3. Interpreting the Equation: In the equation u = k / n, as "n" increases, "u" decreases. Similarly, if "n" decreases, "u" increases. The constant "k" remains the same in this scenario.
4. Finding the Constant: To determine the constant of variation, "k," you need specific values of "u" and "n." Once you have a pair of values for "u" and "n," substitute these values into the equation and solve for "k." For example, if "u" = 3 and "n" = 5, you can write the equation as follows: 3 = k / 5. You can then solve for "k" by multiplying both sides of the equation by 5, resulting in k = 15.
5. Predicting Values: Once you have found the constant of variation, you can use it to predict one variable's value when you know the other. For example, if "k" = 15, and you have "n" = 4, you can solve for "u" as follows: u = 15 / 4, which equals 3.75.
By understanding the concept of inverse variation and following these steps, you can work with the given equation and find values for "u" and "n" or make predictions based on known values.