Problem 47 Explain what is meant by combine... [FREE SOLUTION]

Chapter 7: Problem 47

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

Short Answer

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Combined Variation is a direct and inverse variation relationship, expressed as \(y = k * \frac{a}{b}\), where a change in one variable directly influences the dependent variable and inversely impacts the other variable. An example is the time taken by a car to travel varies directly with the distance and inversely with the speed.

Step by step solution

- Define Combined Variation

Combined Variation is a combination of direct variation and inverse variation. In a direct variation, the value of one variable increases or decreases along with the increase or decrease of another variable. In an inverse variation, the value of one variable increases while the other decreases, and vice versa. In a combined variation, a variable varies directly with one variable while inversely with another.

- Explain relation

In mathematical terms, combined variation is usually expressed as \(y = k * \frac{a}{b}\) where \(y\) is the dependent variable, \(a\) and \(b\) are the independent variables, and \(k\) is the constant of variation. As \(a\) increases or decreases, \(y\) will also increase or decrease, respectively (direct variation). As \(b\) increases or decreases, \(y\) will decrease or increase, respectively (inverse variation). The constant of variation \(k\) remains unchanged in any circumstance.

- Provide an Example

For instance, consider the scenario of a car travelling at constant speed. The time taken (\(t\)) by the car to travel a certain distance (\(d\)) varies directly with the distance and inversely with the speed (\(s\)). Therefore, the relationship can be expressed as \(t = k * \frac{d}{s}\). Here, if the distance increases or decreases, the time taken will accordingly increase or decrease (direct variation), and if the speed increases or decreases, the time taken will decrease or increase, respectively (inverse variation). The constant of variation \(k\) will be the same regardless of changes in \(d\) and \(s\).

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91影视

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

Short Answer

Step by step solution

- Define Combined Variation

- Explain relation

- Provide an Example

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