Examples of associative in the following topics:
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- The associative property describes equations in which the grouping of the numbers involved does not affect the result.
- As with the commutative property, addition and multiplication are associative operations:
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- We will use the x-axis hyperbola to demonstrate how to determine the features of a hyperbola, so that $a$ is associated with x-coordinates and $b$ is associated with y-coordinates.
- For a y-axis hyperbola, the associations are reversed.
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- The eccentricity, denoted $e$, is a parameter associated with every conic section.
- Recall that hyperbolas and noncircular ellipses have two
foci and two associated directrices, while parabolas have one focus and one
directrix.
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- We will use the horizontal case to demonstrate how to determine the properties of an ellipse from its equation, so that $a$ is associated with x-coordinates, and $b$ with y-coordinates.
- For a vertical ellipse, the association is reversed.
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- Multiplying a polynomial by a monomial is a direct application of the distributive and associative properties.
- for all real numbers $a,b$ and $c.$ The associative property says that
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- Matrix addition is commutative and is also associative, so the following is true:
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- In other words, each number you put in is associated with each number you get out.
- In a function every input number is associated with exactly one output number In a relation an input number may be associated with multiple or no output numbers.
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- In linear algebra, the determinant is a value associated with a square matrix.
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- Recall that for any point on the circle, the $x$-value gives $\cos t$ for the associated angle $t$.
- Applying the $x$- and $y$-coordinates associated with angle $t$, we have
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- Thus, for example, complex number $-2+3i$ would be associated with the point $(-2,3)$ and would be plotted in the complex plane as shown below.