Examples of using Mathrm in English and their translations into Indonesian
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Colloquial
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Ecclesiastic
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Ecclesiastic
Mathrm{erf}(x)$ is also everywhere negative and everywhere strictly monotonically increasing.
The classical electron radius isbuilt from m e{\displaystyle m_{\mathrm{e}}}, c{\displaystyle c} and e{\displaystyle e.
The second law of thermodynamics for a reversible process yields δQ T d S{\displaystyle\delta Q=T\,\mathrm{d} S.
The Compton wavelength isbuilt from m e{\displaystyle m_{\mathrm{e}}}, ℏ{\displaystyle\hbar} and the speed of light c{\displaystyle c.
The equilibrium constant expression is therefore usually written as K K c{\displaystyle K={\frac{\mathrm{}}{\mathrm{}}}=K_{\mathrm{c.
D S{\displaystyle\mathrm{d} \mathbf{S}\!\} is a differential vector area element of surface S, with infinitesimally small magnitude and direction normal to surface S.
The Bohr radius is built from theelectron mass m e{\displaystyle m_{\mathrm{e}}}, Planck's constant ℏ{\displaystyle\hbar} and the electron charge e{\displaystyle e.
It can be considered as multiple transmission line segments connected in series, with the characteristic impedance ofeach individual element to be Z 0, i{\displaystyle Z_{\mathrm{0,i}}}.
The Michaelis constant K M{\displaystyle K_{\mathrm{M}}} is the substrate concentration at which the reaction rate is half of V max{\displaystyle V_{\max.
The Bohr radius of the electron is one of a trio of related units of length, the other two being the Compton wavelengthof the electron λ e{\displaystyle\lambda_{\mathrm{e}}}.
For an electron with rest mass m0, the rest energy is equal to:E p m 0 c 2,{\displaystyle\textstyle E_{\mathrm{p}}= m_{ 0} c^{ 2},} where c is the speed of light in a vacuum.
The usable capacity of aRAID 10 array is(N/2)\cdot S_{\mathrm{min}}, where N is the total number of drives in the array and Smin is the capacity of the smallest drive in the array.
Simple examples are provided by potential energy functions of the form H p ot C q s,{\displaystyle H_{\mathrm{pot}}=Cq^{s},\,} where C and s are arbitrary real constants.
W∫ C F⋅ d s{\displaystyle W=\int_{C}\mathbf{F}\cdot\mathrm{d}\mathbf{s}} This says that the work( W{\displaystyle W}) is equal to the line integral of the force F along a path C; for details see the mechanical work article.
Assuming a constant density throughout the star, this integration yields the formula H g r a v-3 G M 2 5 R,{\displaystyle H_{\mathrm{grav}}=-{\frac{ 3GM^{ 2}}{ 5R}},} where M is the star's total mass.
An alternative formulation is d ln K d( T- 1)-Δ H m⊖ R{\displaystyle{\frac{d\ln K}{dT^{-1\frac{\Delta H_{\mathrm{m}}^{\ominus}}{R}}} At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of K with temperature.
More generally, a typical energy function of a one-dimensional system has a Taylor expansion in the extension q: H p o t∑ n 2∞C n q n{\displaystyle H_{\mathrm{pot}}=\sum_{n=2}^{\infty} C_{ n} q^{ n}} for non-negative integers n.
The effective nuclear charge(often symbolized asZ e f f{\displaystyle Z_{\mathrm{eff}}} or Z∗{\displaystyle Z^{\ast}}) is the net positive charge experienced by an electron in a polyelectronic atom.
The Bohr radius of the electron is one of a trio of related units of length, the other two being the Compton wavelength of the electron λ e{\displaystyle\lambda_{\mathrm{e}}} and the classical electron radius r e{\displaystyle r_{\mathrm{e.
The unit siemens for the conductance G is defined by S Ω- 1 A V{\displaystyle\mathrm{S}=\Omega^{-1}={\dfrac{\mathrm{A}}{\mathrm{V}}}} where Ω is the ohm, A is the ampere, and V is the volt.
The correct equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected/accreted mass; the result is F+ u d m d t m d v d t{\displaystyle\mathbf{F}+\mathbf{u}{\frac{\mathrm{d} m}{\mathrm{d} t}}=m{\mathrm{d}\mathbf{v}\over\mathrm{d} t}} where u is the velocity of the escaping or incoming mass relative to the body.
In SI units, the nuclear magneton is μ Ne ℏ 2 m p{\displaystyle\mu_{\mathrm{N}}={{e\hbar}\over{2m_{\mathrm{p}}}}} where e is the elementary charge and ħ is the reduced Planck constant.
From electrostatics theory, the potential energy of a sphere with radius r and charge e is given by: E p e 2 8π ε 0 r,{\displaystyle E_{\mathrm{p} }={\frac {e^{2}}{8\pi \varepsilon_{0}r}},} where ε0 is the vacuum permittivity.
The number of different binary trees on n{\displaystyle n}nodes is C n{\displaystyle\mathrm{C}_{n}}, the n{\displaystyle n} th Catalan number assuming we view trees with identical structure as identical.
Applying the general formula for an equilibrium constant to the specific case of a dilute solution of acetic acid in water one obtains CH3CO2H+ H2O⇌ CH3CO2-+ H3O+ K c{\displaystyle K_{\mathrm{c}}={\frac{\mathrm{}}{\mathrm{}}}} For all but very concentrated solutions, the water can be considered a"pure" liquid, and therefore it has an activity of one.
The kinetic energy which is also called the energy of motion: E m e c h a n i ca l U+ K{\displaystyle E_{\mathrm{mechanical}}=U+K\,} The potential energy, U, depends on the position of an object subjected to a conservative force.
The electric flux ΦE is defined as a surface integral of the electric field: Φ E{\displaystyle\Phi_{E}=} S{\displaystyle\scriptstyle_{S}}E⋅ d A{\displaystyle\mathbf{E}\cdot\mathrm{d}\mathbf{A}} where E is the electric field, dA is a vector representing an infinitesimal element of area of the surface, and· represents the dot product of two vectors.
The effect of changing temperature on an equilibrium constant is given by the van't Hoff equation d ln K d T Δ H m⊖R T 2{\displaystyle{\frac{d\ln K}{dT}}={\frac{\Delta H_{\mathrm{m}}^{\ominus}}{ RT^{ 2}}}} Thus, for exothermic reactions(ΔH is negative), K decreases with an increase in temperature, but, for endothermic reactions,(ΔH is positive) K increases with an increase temperature.
The molality(b), of a solution is defined as the amount of substance(in moles) of solute, nsolute, divided by the mass(in kg) of the solvent, msolvent: b n s o l u t e m s o l v e n t{\displaystyle b={\frac{n_{\mathrm{solute}}}{m_{\mathrm{solvent}}}}} In the cases of solutions with more than one solvent, molality can be defined for the mixed solvent considered as a pure pseudo-solvent.
A particular case is the self-ionization of water itself 2 H2O⇌ H3O++ OH- Because water is the solvent, and has an activity of one, the self-ionization constant of water is defined as K w{\displaystyle K_{\mathrm{w}}=\mathrm{}} It is perfectly legitimate to write for the hydronium ion concentration, since the state of solvation of the proton is constant(in dilute solutions) and so does not affect the equilibrium concentrations.