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Joint variation
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Joint variation refers to a mathematical relationship between three variables, where the value of one variable is directly proportional to the other two variables. In other words, if one variable increases by a certain factor, the other two variables will also increase by the same factor, and if one variable decreases, the other two variables will also decrease by the same factor.
The general formula for joint variation is:
kxy = z
where k is a constant, x and y are the two variables that are directly proportional to z. The constant k represents the proportionality constant or the factor by which x and y are multiplied to produce z.
For example, if the cost of building a house is directly proportional to the number of workers and the time it takes to complete the job, we can write this as:
C = kWT
where C is the cost of building the house, W is the number of workers, T is the time taken to complete the job, and k is the proportionality constant. This means that if we double the number of workers and the time taken to complete the job, the cost of building the house will also double. Similarly, if the number of workers and the time taken to complete the job are halved, the cost of building the house will also be halved.
The general formula for joint variation is:
kxy = z
where k is a constant, x and y are the two variables that are directly proportional to z. The constant k represents the proportionality constant or the factor by which x and y are multiplied to produce z.
For example, if the cost of building a house is directly proportional to the number of workers and the time it takes to complete the job, we can write this as:
C = kWT
where C is the cost of building the house, W is the number of workers, T is the time taken to complete the job, and k is the proportionality constant. This means that if we double the number of workers and the time taken to complete the job, the cost of building the house will also double. Similarly, if the number of workers and the time taken to complete the job are halved, the cost of building the house will also be halved.