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Chapter 2: Problem 43

Explain what is meant by combined variation. Give an example with your explanation.

Short Answer

Expert verified
Combined Variation involves direct and inverse variations, expressed using the formula \(y = k \cdot \frac{x}{z}\). An example is a scenario where the time to construct a building varies directly with the number of workers and inversely with the number of days, expressed as \(T = k \cdot \frac{W}{D}\).

Step by step solution

01

Explanation of Combined Variation

Combined (or joint variation) involves both direct and inverse variation. When 'y' varies directly with 'x' and inversely with 'z', it is described as combined variation. This can be mathematically expressed as \(y = k \cdot \frac{x}{z}\), where 'k' is the constant of variation.
02

Illustrate with an Example

Consider a scenario where the time it takes to construct a building (T) varies directly with the number of workers (W) and inversely with the number of days (D). This is a combined variation and it can be expressed as \(T = k \cdot \frac{W}{D}\). For instance, if it takes 5 workers 10 days to construct a building, then the constant 'k' can be determined from these values by substituting them into the equation; hence, \(T = k\). With W=5 and D=10, it stands that \(k = T \cdot D / W = 2\).

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