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Direct and inverse proprtions, with examples


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Directly and Inversely Proportional

A well known physical law describing the relationship between electrical current, voltage and resistance in a circuit is called Ohm's law, which can be paraphrased as follows: The current in a circuit is directly proportional to the voltage drop and inversely proportional to the resistance.

a) What does it mean for something to be proportional to something else? What does it mean to be inversely proportional?

b) Give an example (besides Ohm's Law) of things that are proportional to each other, and another example of two things that are inversely proportional.

c) List some other types of mathematical relationships between two variables.

Solution Preview

a) We say that one quantity, say, represented by a variable z, is directly proportional to another quantity, represented by a variable, say x if there's a constant, k, such that
z = k*x
In which case we observe the following situation: if k>0, then an increase in x results in an increase in z. A decrease in x will result in a decrease in z. The variables change "in the same way". For example, if gas costs $k per gallon, then the amount z of money you pay for x gallons of gas is z=k*x, and the more gas you buy, the more money you ...

Solution Summary

We explain the notions of the direct and the inverse proportions between variables and give examples of such and other relations in Mathematics.