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Assume a rod of material having a length L o at initial temperature T o . When the temperature changes by D T, the length changes by D L. Experiment shows that if D T is not too large (say, less than 100 o C or so), D L is directly proportional to D T. If two rods made of the same material have the..

When a rigid body such as a merry-go-round rotates around an axis, each particle in the body moves in its own circle around that axis. Since the body is rigid, all particles make one revolution in the same amount of time. i.e., they all have the same angular speed w . However, far a ..

Different forms of numbers Scientific notation, square roots, exponents, radicals, absolute value, factorial, logarithms Properties of numbers Estimation of solutions Sequences and series Proportionality/direct variation, exponential/fractional expressions Patterns, relations and ..

1) Both magnetic and electric field depend inversely on the distance between the source and the field point 2) Both are long-range forces 3) Principle of superposition applies to both fields as the fields are linearly related to the source..

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Theoretical/empirical probability Probability models Studying patterns and analyzing data Rates, linear functions, direct/inverse variation Problems related to personal income, credit, financial planning Transformations, symmetr..

Temperature Dependence of Resistivity - The resistivity of a metallic conductor nearly always increases with increasing temperature. As temperature increases, the ions of the conductor vibrate with greater amplitude, making it more likely that a moving electron will collide with an ion. This impede..

Proportional/non-proportional linear relationships Problems involving percents and other proportional relationships Various representations of a numerical relationship Terms in an arithmetic sequence Variables, expressions, equations, inequalities Single/multiple-step linear..

Rates of most chemical reactions increases with temperature because the rate constant 'k' increases with temperature. The temperature dependence of the rate constant is given by the Arrhenius equation, where..

Linear equations/inequalities Monomials and polynomials Factoring second and third degree polynomials Rational expressions/functions Quadratic equations Quadratic functions Exponents, factors, variation, exponential growth/decay Hypothesis, counterexamples Correlation for data ..