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The marginal rate of substitution between perfect substitutes is likewise constant. An example of a utility function that is associated with indifference curves like these would be (,) = +. If two goods are perfect complements then the indifference curves will be L-shaped. Examples of perfect complements include left shoes compared to right ...
For example, if both the numerator and the denominator of the fraction are divisible by , then they can be written as =, =, and the fraction becomes cd / ce , which can be reduced by dividing both the numerator and denominator by c to give the reduced fraction d / e .
(For example, for fractions written in horizontal format, adding spaces to a fraction like 123456/127 would cause it to be misread as 123 456 / 127 or 1 23456 / 127 .) Markup: Templates {} or {} may be used to produce this formatting.
If the discriminant is zero the fraction converges to the single root of multiplicity two. If the discriminant is positive the equation has two real roots, and the continued fraction converges to the larger (in absolute value) of these. The rate of convergence depends on the absolute value of the ratio between the two roots: the farther that ...
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This is a common procedure in mathematics, used to reduce fractions or calculate a value for a given variable in a fraction. If we have an equation =, where x is a variable we are interested in solving for, we can use cross-multiplication to determine that =.
For example, the numerators of fractions with common denominators can simply be added, such that + = and that <, since each fraction has the common denominator 12. Without computing a common denominator, it is not obvious as to what 5 12 + 11 18 {\displaystyle {\frac {5}{12}}+{\frac {11}{18}}} equals, or whether 5 12 {\displaystyle {\frac {5 ...
For recipes that use eggs as a binder or for moisture, substitutes like applesauce or oil can do the trick. If the eggs act as a leavener, try a combination of vinegar and baking powder .
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