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Actually, most elements occur in nature as uniform mixtures of two or more kinds of atoms that have slightly different masses, which we call isotopes. An iron nail, for example, is made up of a mixture of four iron isotopes, and the chlorine in salt is a mixture of two chlorine isotopes.
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In our description of the makeup of a compound, there is a subtle but significant point to be understood. For example, we say that the compound carbon dioxide, a substance formed in the combustion of many fuels, is composed of carbon and oxygen. However, in this compound these two elements are not present in the same form as we find them in their pure states. We can see this by comparing the properties of the compound with those of the elements from which it’s formed. Ordinarily, carbon is found as a black solid, as in coal and charcoal. But at room temperature, carbon dioxide isn’t a solid, it’s a colorless gas. Oxygen is also a gas, but it supports combustion, whereas carbon dioxide is used to extinguish fires. Thus, the properties of carbon dioxide are much different from those of both carbon and oxygen. When carbon and oxygen combine to form carbon dioxide, the properties of carbon and oxygen disappear and in their place we find the unique properties of the compound carbon dioxide.
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word problems
express the relationship:
input (x) rate = output
number of variables (x, y) represent number of rates (or concentrations, a kind of rate)
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In 1679, Leibnitz expressed the need for a ‘geometry of situation’ that would be independent of the geometry of magnitude.
P. N. Ruane on vector analysis
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Astronomers in ancient Greece had already invented trigonometry to predict the motions of the heavenly bodies.
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