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Week 2 Algebra Talk Variation is a great example of how mathematics is used to model and solve real-world problems. Many fields of study contain examples of the three different kinds of variation:Direct variation (for example, y = kx)Inverse variation (for example, y = k/x)Joint variation (for example, z = kxy)Definition of Joint VariationJoint variation is the same as direct variation with two or more quantities.That is:Joint variation is a variation where a quantity varies directly as the product of two or more other quantities.Let’s first understand direct variation.Direct variation occurs when two quantities change in the same manner.That is:Increase in one quantity causes an increase in the other quantity.Decrease in one quantity causes a decrease in the other quantity.For example:The cost of a pencil and the number of pencils you buy.Buy more pay more….Buy less pay less.Direct variation between variables x and y can be expressed as:y = kx, where ‘ k’ is the constant of variation and k ≠ 0.y = kxz represents joint variation. Here, y varies jointly as x and z.More Examples on Joint Variationy = 7xz, here y varies jointly as x and z.y = 7x2z3, here y varies jointly as x2 and z3.”Math DictionaryThe variable is in the bottom of a fraction or in the denominator. (The Opposite of Direct Variation) In an inverse variation, the values of the two variables change in an opposite manner – as one value increases, the other decreases. For example, a biker traveling at 8 mph can cover 8 miles in 1 hour. If the biker’s speed decreases to 4 mph, it will take the biker 2 hours (an increase of one hour), to cover the same distance. Please start by addressing one or more of the following topics to get the discussion going:How would you describe the difference between direct variation and joint variation in words? Use examples to help illustrate.Pick a field of study of interest to you and give an example of variation in that field. Some possible areas to consider are: Economics, Finance, Geometry and Physics. Example: If your hourly pay rate is $15/hour, then your weekly pay p is given by the formula p=15h where h is the number of hours worked in a week. So, your weekly pay varies directly as the number of hours worked in a week with the constant of variation = 15.Most formulas are actually examples of variation. Pick a well-known formula and describe the type of variation as well as the constant of variation, k. Example: The area A of a triangle with base b and height h is given by the formula A=½bh. So, the area of a triangle varies jointly as the base and height (both direct) with the constant of variation = ½.Give an example from real life where composite functions are utilized. For ideas, you may look it up on the internet or find examples in the book.
