Math, asked by nalanicaban, 4 months ago

Solve 5 and 3/6 minus 2 and 1/3.
-Answers-
A: 2 and 3/18
B: 2 and 2/9
C: 3 and 2/9
D: 3 and 3/18

Answers

Answered by bryarbentley
0

Answer:

Asnwer below

Step-by-step explanation:

F=dA

dF=0

d⋆F=⋆J

where in fact the second equality is not needed because of the identity  d2=0 . In abstract tensor notation, these equations expand to

Fab=2∇[aAb]

∇[aFbc]=0

∇aFab=Jb

where in the above, additional compact notation has been used to simplify things: square brackets mean antisymmetrizing indices, and the covariant derivative  ∇a  is related to a flat derivative  ∂a  and a connection  Γbac . Now, performing a 3+1 decomposition (here in flat space-time) Maxwell's equations break down as

∇⋅B⃗ =0

∇⋅E⃗ =4πρ

∂B⃗ ∂t=−∇×B⃗  

∂E⃗ ∂t=+∇×B⃗ −4πJ⃗ .

In the above, there is yet more compactifying notation: the divergence is defined as

∇⋅v⃗ =∂vi∂xi

and the curl is defined as

(∇×v⃗ )i=ϵijk∂vk∂xj.

In the above, still more compactifying notation has been used, namely the Einstein summation convention. Written out in components, the divergence is

∇⋅v⃗ =∂vx∂x+∂vy∂y+∂vz∂z

and curl is defined as

(∇×v⃗ )z=∂vy∂x−∂vx∂y

and similarly for the other two components.

As you can see, the extremely compact and powerful notation

dF=0

d⋆F=⋆J

expands out to a large set of component equations—but they have the same content, so it's not very meaningful that the equations in components are much longer than in terms of differential forms.

As another example, Elson Liu answered with an exploded-out form of the Standard Model Lagrangian. However, it can be written much more compactly:

L=LYM+LHiggs+Llep.+Lqrk.+LYuk.

where

LYM=−14TrFabFab

LHiggs=−(Daϕ†)(Daϕ)+14λ(ϕ†ϕ−12v2)2

Llep.=iℓ†I/DℓI+ie¯†I/De¯I

Lqrk.=iq†I/DqI+iu¯†I/Du¯+id¯†I/Dd¯I

LYuk.=−yIJϕℓIe¯J−y′IJϕqId¯J

−y′′IJϕ†qIu¯J+h.c.

and specifying that F is the curvature on the gauge group  G≃SU(3)⊗SU(2)⊗U(1) ,  Da  is the gauge covariant derivative on G,  /D  is the gauge covariant Dirac operator on G, and specifying the representations of the fields: the scalar  ϕ  in the rep (1,2,-1/2), and the fermions  ℓ  in the rep (1,2,-1/2),  e¯  in (1,1,+1),  q  in (3,2,+1/6),  u¯  in  (3¯,1,−2/3) , and  d¯  in  (3¯,1,+1/3) ; where I is a generation index running over 1,2,3, and where everything else is a constant.

Answered by khashrul
1

Answer:

D is correct option.

Step-by-step explanation:

5\frac{3}{6}  - 2\frac{1}{3} = \frac{33}{6}  - \frac{7}{3} = \frac{33-14}{6} = \frac{19}{6} = 3\frac{1}{6}

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