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Chapter 3: Problem 43

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

Short Answer

Expert verified
Combined variation is a combination of direct and inverse variation, where a quantity depends on more than one other quantity. An example is the time 't' to travel a distance varying directly with the weight 'w' of a vehicle and inversely with the speed 's' of the vehicle, represented as \( t = k \frac{w}{s} \).

Step by step solution

01

Understanding Combined Variation

Combined variation is the combination of direct variation and inverse variation. When 'y' varies directly as 'x' and inversely as 'z', it can be represented as \( y = k \frac{x}{z} \) , where 'k' is the constant of variation.
02

Providing an example

For example, suppose the time it takes to travel a certain distance depends on the speed of travel and the weight of the vehicle. Let 't' be the time, 's' be the speed and 'w' be the weight. If 't' varies directly with 'w' and inversely with 's', we can represent this as \( t = k \frac{w}{s} \)

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Most popular questions from this chapter

The number of houses that can be served by a water pipe varies directly as the square of the diameter of the pipe. A water pipe that has a 10 -centimeter diameter can supply 50 houses. a. How many houses can be served by a water pipe that has a 30 -centimeter diameter? b. What size water pipe is needed for a new subdivision of 1250 houses?

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies directly as \(x\) and inversely as the square of \(z . y=20\) when \(x=50\) and \(z=5 .\) Find \(y\) when \(x=3\) and \(z=6\).

Use the four-step procedure for solving variation problems given on page 424 to solve. The distance that a spring will stretch varies directly as the force applied to the spring. A force of 12 pounds is needed to stretch a spring 9 inches. What force is required to stretch the spring 15 inches?

Begin by deciding on a product that interests the group because you are now in charge of advertising this product. Members were told that the demand for the product varies directly as the amount spent on advertising and inversely as the price of the product. However, as more money is spent on advertising, the price of your product rises. Under what conditions would members recommend an increased expense in advertising? Once you've determined what your product is, write formulas for the given conditions and experiment with hypothetical numbers. What other factors might you take into consideration in terms of your recommendation? How do these factors affect the demand for your product?

The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage remains constant, what needs to be done to triple the amount of heat generated?
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