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This trigonometry math tutorial from NutshellMath offers homework help with working with different types of variation. Variations in algebra and trigonometry refer to how two variables are related to each other. A direct variation between two variables indicates that the relationship between the variables is generally proportional. A simple way of picturing the concept of direct variation is if the relationship were expressed as a proportion, with each variable on its own side, then both variables would be in the numerator at the same time, or in the denominator at the same time. Simple direct variation relationships are expressed algebraically as y=kx, where k is a constant. A variable can also vary directly with a power of the other variable, such as y=k(x^n), where n is a power.
Inverse variation between two variables is the second major type of variation. With inverse variation, one variable will vary directly with the reciprocal of the second variable. With the proportion example used before, with inverse variation, one variable would be in the numerator on one side of the proportion, and the other variable in the denominator on the other side. Often these inverse variations will be to a certain power of one of the variables, so the algebraic representation is y=k/(x^n), where k is a constant, and n is a power.
When solving word problems involving models with variation, the most important step is to determine which type of variation is being used. Typically, this information is in the wording of the problem. One variable will be said to “vary directly” or “vary indirectly” with the other. The next step is to set up the algebraic model of the variation, with the unknown constant represented by k. Known values that are given can be used to solve for the constant, and then the equation can be rewritten with a numeric value for k. This algebraic formula can then be used to solve for one variable when given a value for the other.
Other types of variation covered by this tutorial include combined variation and joint variation. Combined variation uses more than 2 variables, and will have one variable vary differently with respect to the two other variables. Joint variation also uses more than two variables, but instead, the first variable will vary in the same manner with respect to both of the other variables. Both of these more advanced types of variation can be treated as combinations of the simpler types of variation, and solved in nearly the same way.
This introduction to variation in algebra and trigonometry should be valuable in understanding how to set up algebraic models of real world situations. Modeling with variation can be used to solve word problems in homework, as well as to describe situations in physics and other sciences.
This trigonometry math tutorial from NutshellMath offers homework help with working with different types of variation. Variations in algebra and trigonometry refer to how two variables are related to each other. A direct variation between two variables indicates that the relationship between the variables is generally proportional. A simple way of picturing the concept of direct variation is if the relationship were expressed as a proportion, with each variable on its own side, then both variables would be in the numerator at the same time, or in the denominator at the same time. Simple direct variation relationships are expressed algebraically as y=kx, where k is a constant. A variable can also vary directly with a power of the other variable, such as y=k(x^n), where n is a power.
Inverse variation between two variables is the second major type of variation. With inverse variation, one variable will vary directly with the reciprocal of the second variable. With the proportion example used before, with inverse variation, one variable would be in the numerator on one side of the proportion, and the other variable in the denominator on the other side. Often these inverse variations will be to a certain power of one of the variables, so the algebraic representation is y=k/(x^n), where k is a constant, and n is a power.
When solving word problems involving models with variation, the most important step is to determine which type of variation is being used. Typically, this information is in the wording of the problem. One variable will be said to “vary directly” or “vary indirectly” with the other. The next step is to set up the algebraic model of the variation, with the unknown constant represented by k. Known values that are given can be used to solve for the constant, and then the equation can be rewritten with a numeric value for k. This algebraic formula can then be used to solve for one variable when given a value for the other.
Other types of variation covered by this tutorial include combined variation and joint variation. Combined variation uses more than 2 variables, and will have one variable vary differently with respect to the two other variables. Joint variation also uses more than two variables, but instead, the first variable will vary in the same manner with respect to both of the other variables. Both of these more advanced types of variation can be treated as combinations of the simpler types of variation, and solved in nearly the same way.
This introduction to variation in algebra and trigonometry should be valuable in understanding how to set up algebraic models of real world situations. Modeling with variation can be used to solve word problems in homework, as well as to describe situations in physics and other sciences.