Chain Rule
Table of Content:
Direct proportion
Direct proportion: Direct proportion refers to a mathematical relationship between two variables such that a change in one variable results in a corresponding change in the other variable, while their ratio remains constant.
In other words, if two variables x and y are directly proportional, we can write y = kx, where k is a constant of proportionality.
Example Direct proportion: speed and time
An example of direct proportion is the relationship between speed and time. If you are traveling at a constant speed, the distance you cover will be directly proportional to the time you spend traveling. If you double the time you spend traveling, you will cover double the distance, and if you halve the time you spend traveling, you will cover half the distance.
Example Direct proportion: workers and the amount of work done
Another example is the relationship between the number of workers and the amount of work done. If you have a certain number of workers working at a constant rate, the amount of work done will be directly proportional to the number of workers. If you double the number of workers, you will get the work done in half the time, and if you halve the number of workers, you will take twice the time to complete the work.
Indirect proportion
Indirect proportion: Indirect proportion refers to a mathematical relationship between two variables such that a change in one variable results in a corresponding change in the other variable, but their product remains constant.
In other words, if two variables x and y are inversely proportional, we can write xy = k, where k is a constant.
Example Indirect proportion: An example of indirect proportion is the relationship between speed and time taken to cover a certain distance. If you are traveling at a constant speed, the time you take to cover a certain distance will be inversely proportional to your speed. If you double your speed, you will cover the same distance in half the time, and if you halve your speed, you will take twice the time to cover the same distance.
Example Indirect proportion: Another example is the relationship between the number of workers and the time taken to complete a certain amount of work. If the workers are working at a constant rate, the time taken to complete a certain amount of work will be inversely proportional to the number of workers. If you double the number of workers, you will get the work done in half the time, and if you halve the number of workers, you will take twice the time to complete the same amount of work.