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Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
The question is then posed—which of the two mixtures is purer? [1] The answer is that the mixtures will be of equal purity. The solution still applies no matter how many cups of any sizes and compositions are exchanged, or how little or much stirring at any point in time is done to any barrel, as long as at the end each barrel has the same ...
An ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. [ 1 ] [ 2 ] The enthalpy of mixing is zero [ 3 ] as is the volume change on mixing. [ 2 ]
In addition, a heterogeneous mixture may have a uniform (e.g. a colloid) or non-uniform (e.g. a pencil) composition. Several solid substances, such as salt and sugar, dissolve in water to form homogeneous mixtures or "solutions", in which there are both a solute (dissolved substance) and a solvent (dissolving medium) present.
An ideal mixture is any in which the arithmetic mean (with respect to mole fraction) of the two pure substances is the same as that of the final mixture. Among other important thermodynamic simplifications, this means that enthalpy of mixing is zero: Δ H m i x , i d e a l = 0 {\displaystyle \Delta H_{mix,ideal}=0} .
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. [1] In an ideal mixture, the microscopic interactions between each pair of chemical species are the same (or macroscopically equivalent, the enthalpy change of solution and volume variation in mixing is zero) and, as a result, properties of the mixtures ...
It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.