Since the difference between the U. S. and International acre is only about a quarter of the size of an A4 sheet of paper ( 0. 016 square metres, 160 square centimetres or 24. 8 square inches ), it is usually not important which one is being discussed.

" Since the statement is a sūtra, it is necessarily compressed and what the ropes produce is not elaborated on, but the context clearly implies the square areas constructed on their lengths, and would have been explained so by the teacher to the student.

Since its establishment in Ann Arbor, the university has physically expanded to include more than 584 major buildings with a combined area of more than 31 million gross square feet ( 712 acres or 2. 38 km² ), and transformed its academic program from a strictly classical curriculum to one that includes science and research.

Since the efficiency of a rocket engine is related to the square root of the temperature of the working fluid, the solid core design needs to be constructed of materials that remain strong at as high a temperature as possible.

Since a laser can heat propellant to extremely high temperatures, this potentially greatly improves the efficiency of a rocket, as exhaust velocity is proportional to the square root of the temperature.

Since the Indic writing systems used for Sanskrit are syllabic, each syllable can be thought of as representing a square on a chess board.

Since the surface area of a sphere ( which is 4πr < sup > 2 </ sup > ) is proportional to the square of the radius, as the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source.

Since intensity is proportional to the square of pressure amplitude, this is just a variation on the inverse-square law.

Since power is proportional to the square of the voltage, return loss is given by,

Since the standard deviation of shot noise is equal to the square root of the average number of events N, the signal-to-noise ratio ( SNR ) is given by:

Since shot noise is a Poisson process due to the finite charge of an electron, one can compute the root mean square current fluctuations as being of a magnitude

Since the MRI signal drops off as the square of the magnetic field, a SQUID is used as the detector because of its extreme sensitivity.

Since the 1970s modern Western square dance has been promoted and standardized by Callerlab, the " International Association of Square Dance Callers ".

Since the 19th century, much of the square dance repertoire has been derived from jigs and reels from Scotland and Ireland, sometimes in relatively unaltered form, sometimes as played in the old time music tradition or as adapted by other cultures such as that of Quebec.

Since the tidal force is linear in Δd, the related potential is proportional to the square of the variable and for we have

Since the field of constructible points is closed under square roots, it contains all points that can be obtained by a finite sequence of quadratic extensions of the field of complex numbers with rational coefficients.

Since all of the newspapers have different styles, concentrating on one of them is likely to lead to proficiency in only one style of clue-writing ; moving to a different series, after perhaps years spent with just one, can leave the solver feeling as if they gone back to square one.

Since 2002, the HRS instrument on SPOT 5 has acquired over 100 million square kilometers of stereo pairs used to produce a DTED2 format DEM ( with a 30-meter posting ) DEM format DTED2 over 50 million km².

Since the intensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:

Since the power dissipation, P = I < sup > 2 </ sup > R, increases with the square of the current but only increases approximately linearly with the number of windings, the power lost in the windings can be minimized by reducing I and increasing the number of turns N proportionally.

Since 1993, the museum has doubled in size, from 2, 000 to 4, 000 square meters.

Since 1993, the museum has doubled in size, from 2, 000 to 4, 000 square meters.

Since medical literature began to describe homosexuality, it has often been approached from a view that sought to find an inherent psychopathology as the root cause, influenced by the theories of Sigmund Freud.

Since enthusiastic congregational singing was a part of the early Evangelical movement, Wesleyan theology took root and spread through this channel.

Since the root can always be changed from red to black, but not necessarily vice-versa, this rule has little effect on analysis.

Since it is nonnegative it has at most one real root in z, whence its discriminant is less than or equal to zero, that is,

Since Mac OS X v10. 2, windows have a root HIView.

Since soil salinity makes it more difficult for plants to absorb soil moisture, these salts must be leached out of the plant root zone by applying additional water.

Since many East European people accepted Christianity from the Greeks, many of these peoples have Makara in the root of some names: Makarios ( Greeks ).

Since an nth degree polynomial equation can only have n distinct roots, this implies that the powers of a primitive root z, z < sup > 2 </ sup >, ... z < sup > n − 1 </ sup >, z < sup > n </ sup >

Since the thematic vowel is between the stem ( root + suffix ) and ending, it may be analysed as belonging to one or the other, depending on the situation.

Since the radical of a European word is not only its root but also the portion bearing the core of its meaning, some have applied the term radical not to the original root of a character, such as the 采 in the above example, but to any portion bearing meaning.

Suppose that ζ is an lth root of unity for some odd regular prime l. Since l is regular, we can extend the symbol

Since 7 > 3, the black tree on the left ( with root node 7 ) is attached to the grey tree on the right ( with root node 3 ) as a subtree.

Since a frequency raised by one cent is simply multiplied by this constant cent value, and 1200 cents doubles a frequency, the ratio of frequencies one cent apart is precisely equal to 2 < sup > 1 / 1200 </ sup >, the 1200th root of 2, which is approximately 1. 0005777895.

Since Lie groups ( and some analogues such as algebraic groups ) and Lie algebras have become important in many parts of mathematics during the twentieth century, the apparently special nature of root systems belies the number of areas in which they are applied.

Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their common denominator, a quadratic irrational is an irrational root of some quadratic equation whose coefficients are integers.

Since b and 2a are both integers, asking when the above quantity is irrational is the same as asking when the square root of an integer is irrational.

Since uncolonized land may have thin, poor quality soils with few nutrients, pioneer species are often hardy plants with adaptations such as long roots, root nodes containing nitrogen-fixing bacteria, and leaves that employ transpiration.

Since October 2005, cacert offers class1 and class3 root certificates.

Since the polynomials with integer coefficients are countable, and since each such polynomial has a finite number of zeroes, the algebraic numbers must also be countable.

Since f is a polynomial, this definition is purely algebraic and makes no assumption about the nature of the field F, which in particular need not be the real or complex numbers.

Since algebraic extensions of fields of characteristic zero, and of finite fields, are separable, separability is not an obstacle in most applications of Galois theory.

Since, is a linear algebraic group.

In the case that V is a non-singular algebraic curve and i = 1, H < sup > 1 </ sup > is a free Z < sub > l </ sub >- module of rank 2g, dual to the Tate module of the Jacobian variety of V, where g is the genus of V. Since the first Betti number of a Riemann surface of genus g is 2g, this is isomorphic to the usual singular cohomology with Z < sub > ℓ </ sub > coefficients for complex algebraic curves.

Since the number of homology theories has become large ( see: Category: Homology theory ), the terms Betti homology and Betti cohomology are sometimes applied ( particularly by authors writing on algebraic geometry ) to the singular theory, as giving rise to the Betti numbers of the most familiar spaces such as simplicial complexes and closed manifolds.

Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.

Since any eigenvector is also a generalized eigenvector, the geometric multiplicity is less than or equal to the algebraic multiplicity.

Since it also includes the theory of the Jacobian variety of an algebraic curve, the study of this functor is a major issue in algebraic geometry.

Since the 1980s, algebraic K-theory has increasingly had applications to algebraic geometry.

Since his 1958 thesis on algebraic geometry he has worked in a number of fields.

Since the logical and netlist views are only useful for abstract ( algebraic ) simulation, and not device fabrication, the physical representation of the standard cell must be designed too.

Since − i is algebraic, but certainly not rational, e < sup > π </ sup > is transcendental.

Since a t-norm is a binary algebraic operation on the interval, infix algebraic notation is also common, with the t-norm usually denoted by.

Since a general algebraic space does not satisfy this requirement, it allows a single connected component of U to cover X with many " sheets ".