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{\displaystyle P(A\vert B)={\frac {P(B\vert A)P(A)}{P(B)}}} where A {\displaystyle A} and B {\displaystyle B} are events and P ( B ) ≠ 0 {\displaystyle{\displaystyle \pi r^{2}} is the base area while π r l {\displaystyle \pi rl} is the lateral surface area of the cone. Cube: 6 s 2 {\displaystyle 6s^{2}}ϕ {\displaystyle \phi } is π 180 a cos ⁡ β {\displaystyle {\frac {\pi }{180}}a\cos \beta \,\!}{\displaystyle a}E = h ν {\displaystyle E=h\nu } (where h {\displaystyle h} ν {\displaystyle \nu } the frequency). example sin 2 ⁡ x {\displaystyle \sin ^{2}x} and sin 2 ⁡ ( x ) {\displaystyle \sin ^{2}(x)} denote sin ⁡ ( x ) ⋅ sin ⁡ ( x ), {\displaystyle \sin(x)\cdot \sin(x) point a {\displaystyle a} (whether ∞ {\displaystyle \infty } or not) is a cluster point of the domains of f {\displaystyle f} and g {\displaystyle g} , iexponential distribution is f ( x ; λ ) = { λ e − λ x x ≥ 0 , 0 x < 0. {\displaystyle f(x;\lambda )={\begin{cases}\lambda e^{-\lambda x}&x\geq 0,\\0&x<0.\end{cases}}}{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}} The parameter μ {\displaystyle \mu.\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1,} sin 2 ⁡ θ {\displaystyle \sin ^{2}\theta } means ( sin ⁡ θ ) 2 {\displaystyle (\sin \thetaλ, {\displaystyle \lambda ,} r {\displaystyle r}. λ = r t , {\displaystyle \lambda =rtspeed u {\displaystyle u} area A {\displaystyle A} of each plate, and inversely proportional to their separation y {\displaystyle y} : F = μ2 π f t ) {\displaystyle y(t)=\sin \left(\theta (t)\right)=\sin(\omega t)=\sin(2\mathrm {\pi } ft)} d θ d t = ω = 2 π f. {\displaystyle {\frac{\displaystyle a a {\displaystyle b>a} ; (2) If a > b {\displaystyle a>b} and b > c {\displaystyle b>c} , then a > c {\displaystyle a>c}d y d x {\displaystyle {\frac {dy}{dx}}} is the limit of a ratio of d y {\displaystyle dy} to d x {\displaystyle dx}( n ) {\displaystyle f(n)} yields well defined values for n = 0 {\displaystyle n=0} and n = 1 {\displaystyle n=1} but gives ⊥ {\displaystyle \bot } for− x ) β − 1 {\displaystyle {\begin{aligned}f(x;\alpha ,\beta )&=\mathrm {constant} \cdot x^{\alpha -1}(1-x)^{\beta -1}\\[3pt]&={\frac {x^{\alpha -1}(1-x)^{\betafunction f ( x ) {\displaystyle f(x)} , the amplitude and phase of a frequency component at frequency n P , n ∈ Z {\displaystyle {\frac {n}{P}},n\in \mathbb{\displaystyle F(x;\alpha ,\beta )=1-\sum _{i=0}^{\alpha -1}{\frac {(\beta x)^{i}}{i!}}e^{-\beta x}=e^{-\beta x}\sum _{i=\alpha }^{\infty }{\frac {(\betaH = z + p ρ g + v 2 2 g = h + v 2 2 g , {\displaystyle H=z+{\frac {p}{\rho g}}+{\frac {v^{2}}{2g}}=h+{\frac {v^{2}}{2g}},} 30^{\circ }={\frac {\sqrt {1}}{2}}={\frac {1}{2}}} sin ⁡ π 4 = sin ⁡ 45 ∘ = 2 2 = 1 2 {\displaystyle \sin {\frac {\pi }{4}}=\sin 45^{\circ }={\frac {\sqrt {2}}{2}}={\fracf'_{x}} , ∂ x f {\displaystyle \partial _{x}f} ,  D x f {\displaystyle \ D_{x}f} , D 1 f {\displaystyle D_{1}f} , ∂ ∂ x f {\displaystyle {\frac {\partial }{\partiald d x ( ∫ a ( x ) b ( x ) f ( x , t ) d t ) {\displaystyle {\frac {d}{dx}}\left(\intu ∂ x n 2 ) , {\displaystyle {\frac {\partial ^{2}u}{\partial t^{2}}}=c^{2}\left({\frac {\partial ^{2}u}{\partial x_{1}^{2}}}+{\frac {\partial ^{2}u}{\partialquantities a {\displaystyle a} and b {\displaystyle b} with a > b > 0 {\displaystyle a>b>0} , a + b a = a b = φ {\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}=[ X ] , {\displaystyle \left|\operatorname {E} \left[X\right]-\operatorname {m} \left[X\right]\right|={\frac {1-\ln(2)}{\lambda }}<{\frac {1}pV={\frac {m}{M}}RT} p = m V R T M {\displaystyle p={\frac {m}{V}}{\frac {RT}{M}}} p = ρ R M T {\displaystyle p=\rho {\frac {R}{M}}T} {\displaystyle {\frac {\partial u}{\partial t}}=\alpha \left({\frac {\partial ^{2}u}{\partial x^{2}}}+{\frac {\partial ^{2}u}{\partial y^{2}}}+{\frac {\partial( a ) h {\displaystyle L=\lim _{h\to 0}{\frac {f(a+h)-f(a)}{h}}} exists. ε {\displaystyle \varepsilon{X}}_{n}-\mu )}{\sigma }}\leq {\frac {z}{\sigma }}\right]=\Phi \left({\frac {z}{\sigma }}\right),} where Φ ( z ) {\displaystyle \Phi (z)}{\displaystyle {\frac {d\ln au}{dx}}={\frac {1}{au}}{\frac {d(au)}{dx}}={\frac {1}{au}}a{\frac {du}{dx}}={\frac {1}{u}}{\frac {du}{dx}}={\frac {d\lnx {\displaystyle D_{\text{KL}}(P\parallel Q)=\int _{-\infty }^{\infty }p(x)\log \left({\frac {p(x)}{q(x)}}\right)\,dx}, where p {\displaystyle p} hypotenuse {\displaystyle \cos(\theta )={\frac {\text{adjacent}}{\text{hypotenuse}}}} when 0 < θ < π 2 {\displaystyle 0<\theta <{\frac {\pi }{2}}}{\displaystyle {\frac {dC}{da^{L}}}\cdot {\frac {da^{L}}{dz^{L}}}\cdot {\frac {dz^{L}}{da^{L-1}}}\cdot {\frac {da^{L-1}}{dz^{L-1}}}\cdot {\frac0 e − 1 0 ! = 1 e ≈ 0.37. {\displaystyle P(k={\text{0 meteorites hit in next 100 years}})={\frac {1^{0}e^{-1}}{0!}}={\frac {1}{e}}\approx 0.37.}{\displaystyle {\frac {1}{f}}={\frac {m-1}{mr}},} or f = m m − 1 r. {\displaystyle f={\frac {m}{m-1}}r.} ⁠2,⁠ 1 f = m − 1 m r, {\displaystyle {\frac {1}{f}}={\frac{\displaystyle x} is given by d f d x = d f d g ⋅ d g d h ⋅ d h d x {\displaystyle {\frac {df}{dx}}={\frac {df}{dg}}\cdot {\frac {dg}{dh}}\cdot {\frac {dh}{dx}}}⋅ b {\displaystyle {\sqrt {a}}\cdot {\sqrt {b}}={\sqrt {a\cdot b}}} and a b = a b {\displaystyle {\frac {\sqrt {a}}{\sqrt {b}}}={\sqrt {\frac {a}{b}}}}{\displaystyle \sin(22.5^{\circ })={\sqrt {\frac {1-\cos(45^{\circ })}{2}}}={\sqrt {\frac {1-{\frac {\sqrt {2}}{2}}}{2}}}={\frac {\sqrt {2-{\sqrt {2}}}}{2}}}2 {\displaystyle {\sqrt {2}}} : 1 + 24 60 + 51 60 2 + 10 60 3 = 305470 216000 = 1.41421 296 ¯. {\displaystyle 1+{\frac {24}{60}}+{\frac {51}{60^{2}}}+{\frac− b 2 + a − a 2 − b 2 {\displaystyle {\sqrt {a+{\sqrt {b}}}}={\sqrt {\frac {a+{\sqrt {a^{2}-b}}}{2}}}+{\sqrt {\frac {a-{\sqrt {a^{2}-b}}}{2}}}}4. d d x arcsin ⁡ x a = 1 a 2 − x 2 {\displaystyle {\frac {d}{dx}}\arcsin {\frac {x}{a}}={\frac {1}{\sqrt {a^{2}-x^{2}}}}}. 5. d d x arccot ⁡ ( x}}}}}