Which Of The Following Equations Is An Example Of Inverse Variation Between The Variables X And Y?

Most students in mathematics are familiar with the concept of direct variation between two variables, but fewer are familiar with inverse variation. Inverse variation occurs when one variable increases as the other decreases and vice versa. This type of relationship between two variables is found in many mathematical concepts, such as exponential growth and Newton’s law of cooling. In this blog post, we explore which of the following equations is an example of inverse variation between the variables x and y. We also discuss how to identify inverse variations in equations and practical applications for these equations.

Inverse Variation

The inverse variation between two variables is when one variable decreases as the other increases, or vice versa. In other words, their product is constant. For example, if y varies inversely as x and y = 12 when x = 3, then we can find that y = 6 when x = 2 since their product must always be 12. We can also write this relationship as yx = k or y = k/x. You can see how this would work in the graph below, where the line representing the inverse variation equation would have a negative slope since one variable is increasing while the other is decreasing.

What is an example of inverse variation?

When two variables are inversely proportional, their relationship is governed by an equation of the form y = k/x, where k is a constant. This means that as x increases, y decreases; and as x decreases, y increases. An example of this can be seen in the way that water flows through a pipe. The larger the diameter of the pipe, the greater the flow rate; but as the diameter decreases, so does the flow rate.

How to solve inverse variation equations

To solve inverse variation equations, you need to first identify the constant of proportionality. The constant of proportionality is represented by the letter k. Once you have identified the constant of proportionality, you can then solve for the value of x or y.

For example, let’s say we have the equation: k = xy

We can solve for the value of x by first multiplying both sides by y: ky = xy^2

Then we can divide both sides by y^2: k/y^2 = x

Therefore, the value of x is equal to k/y^2.

Applications of inverse variation

Inverse variation is a mathematical relationship between two variables in which one variable decreases as the other increases. In an inverse variation, the product of the two variables is constant.

There are many applications for inverse variation in the real world. For example, when two objects are connected by a string or rope, the tension in the string will be inversely proportional to the distance between the objects. This means that if one object is twice as far from the other object as it was before, the tension in the string will be half of what it was before.

Other examples of inverse variation include:

• The amount of time it takes to complete a task is inversely proportional to the number of people working on it.

• The brightness of a light bulb is inversely proportional to its distance from the light source.

• The intensity of sound waves is inversely proportional to their distance from the source.

Conclusion

In conclusion, we can see that inverse variation between two variables is a powerful mathematical concept that helps us understand how two related quantities depend on each other. By understanding the equations of inverse variation and being able to recognize them when they appear in our problem sets, we can use this knowledge to solve some complex problems with ease. We hope that this article has helped you better understand inverse variations and their applications in real-world scenarios.