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In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
Using the usual notations for a triangle (see the figure at the upper right), where a, b, c are the lengths of the three sides, A, B, C are the vertices opposite those three respective sides, α, β, γ are the corresponding angles at those vertices, s is the semiperimeter, that is, s = a + b + c / 2 , and r is the radius of the inscribed circle, the law of cotangents states that
In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α , β , and γ are the angles opposite those three respective sides.
≡ 1 ft 3 /min = 4.719 474 432 × 10 −4 m 3 /s: cubic foot per second ft 3 /s ≡ 1 ft 3 /s = 0.028 316 846 592 m 3 /s: cubic inch per minute in 3 /min ≡ 1 in 3 /min = 2.731 177 3 × 10 −7 m 3 /s cubic inch per second in 3 /s ≡ 1 in 3 /s = 1.638 7064 × 10 −5 m 3 /s: cubic metre per second (SI unit) m 3 /s ≡ 1 m 3 /s = 1 m 3 /s ...
Composite Simpson's 3/8 rule is even less accurate. Integration by Simpson's 1/3 rule can be represented as a weighted average with 2/3 of the value coming from integration by the trapezoidal rule with step h and 1/3 of the value coming from integration by the rectangle rule with step 2h. The accuracy is governed by the second (2h step) term.
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
siemens (S = Ω −1) L −2 M −1 T 3 I 2: scalar Electrical conductivity: σ: Measure of a material's ability to conduct an electric current S/m L −3 M −1 T 3 I 2: scalar Electric potential: φ: Energy required to move a unit charge through an electric field from a reference point volt (V = J/C) L 2 M T −3 I −1: extensive, scalar ...
In this case the volume of the band is the volume of the whole sphere, which matches the formula given above. An early study of this problem was written by 17th-century Japanese mathematician Seki Kōwa. According to Smith & Mikami (1914), Seki called this solid an arc-ring, or in Japanese kokan or kokwan. [1]