Answer:
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.
Step-by-step explanation:
The graph shows the relationship between gravitational potential energy and mass, for objects at a height of 10 meters. What conclusion is supported by the graph?
A) The height of an object does not affect the amount of gravitational potential energy the object has.
B) The mass of an object does not affect the amount of gravitational potential energy the object has. Eliminate
C) An object with greater mass will have less gravitational potential energy than an object with less mass, when the objects are at the same height.
D) An object with greater mass will have more gravitational potential energy than an object with less mass, when the objects are at the same height.
Answer:
d
Step-by-step explanation:
Gael has a car loan for $34,570. This loan has a simple interest rate of 3% per year. What is the amount of interest Gael will be charged on his car loan at the end of 5 years?
Answer:
5185.5
Step-by-step explanation:
I=PRT
I=$34570×0.03×5
=5185.5
HELP ME PLEASE! Solve for the value of a.
Answer:
The angle is 90 degrees since it is a right angle.
90-50=40 gives us how much the equation 6a-8 is worth
Set it so
6a-8=40
6a=48
a=8
Hope this helps and lmk if it
Answer:
[tex]a=8[/tex]
Step-by-step explanation:
The total angle is 90° and 90° - 50° is 40° so [tex]6a-8=40[/tex].
After you add 8 to both sides you get [tex]6a=48[/tex].
Divide both sides by 6 and you get [tex]a=8[/tex].
Write an inequality to represent each
situation:
A. A number, n, is greater than 22
B. The value, v, does not equal 2.5
C. Sally’s age, a, is at most 15
joey made an deposit into an account that earns 6% simple interest. after 3 years joey had earned 400$. how much was joey's initial deposit ?
I need help with all of It pls
Answer:
can you retake it
the ans is the 3 one
Step-by-step explanation:
Rita bakes cakes to earn money she spent $30 for supplies to make 15 cakes which inequality shows how much Rita has to change per cake to earn a profit of a least $150. show work ill mark brainliest
Which expressions represent exponential growth? Check all that apply.
0.2t
1.2t
2x2 – 17
300(1.2)2y
3000(0.12)y
4y + 3
1.12x + 67
Which expressions represent exponential growth? Check all that apply.
0.2t
1.2t
2x2 – 17
300(1.2)2y
3000(0.12)y
4y + 3
1.12x + 67
Answer: 17.300
Answer:
Which expressions represent exponential growth? Check all that apply.
A. 0.2t <<----CORRECT
B. 1.2t <<-------CORRECT
C. 2x2 – 17
D. 300(1.2)2y
E. 3000(0.12)y
F. 4y + 3
G. 1.12x + 67
Step-by-step explanation:
See picture below
Show the work please
10 Points And Brainliest IF Correct
Answer:
1. 12 x 6 = 72 area of parallelogram: B x H (BH)
2. 15 + 23 = 38 x 10 = 380 divided by 2 = 190 area of trapezoid: (B1 + B2) x Height x 1/2 (basically dividing by 2)
3. 8 - 2 = 6 (b1) for the trapezoid, 6 (b1) + 8 (b2) = 14 x 4 (height) = 56 divided by 2 (multiplying 1/2) = 28. (Area of the triangle in the figure) 4 x 4 = 16 divided by 2 = 8. 28 + 8 = 36
Using the formula of a triangle: BH x 1/2 (basically dividing by 2)
A recipe for maroon paint says, “Mix 5 ml of red paint with 3 ml of blue paint.” Use snap cubes to represent the amounts of red and blue paint in the recipe. Then, draw a sketch of your snap-cube representation of the maroon paint. Your teacher will provide directions on how to use the snap-cubes. What amount does each cube represent? How many milliliters of maroon paint will there be?
Answer:
8 ml
Step-by-step explanation:
Each cube equals 1ml add them up dude...
Brad paid for a book that cost $13.40 with a $20 bill. What is the least combination of coins and bills that can be used to make his change? What are two other different combinations of coins and bills that can be used to make the change?
Answer:
First combination: One $5 bill, one $1 bill, two quarters and one dime.
Second combination: One $5 bill, one $1 bill, two quarters and two nickles.
Step-by-step explanation:
I highly suggest reading it to make sure you understand it
Okay so for this one you're going to want to do 20.00-13.40. The answer to that is 6.60
So we have to work with $6.60
Now lets think of the obvious/easiest.
A $5 bill is going to be our best friend in this.
We have to do
6.60-5.00=x
(Don't freak out about x, it's just our place marker!!)
The reason we do 5.00 is because that's what $5 is.
So let's solve now.
6.60-5.00=1.60
So x=1.60
But you don't have to worry about x, I'm just explaining it from before.
So we have to keep in mind that we used one $5 bill. Now let's use one $1 dollar bill.
1.60-1.00=0.60
So now we only have to figure out how to get 60 cents from any of the coins.
A quarter is 25 cents so lets use two of those
25+25=50
60=50=10
Lets recap on everything we've used so far.
We've used one $5 bill, one $1 bill, and two quarters.
Now we're going to add a dime to the mix.
A dime is worth 10 cents.
So for the first combination we used: One $5 bill, one $1 bill, two quarters and one dime.
Now our second combination is going to be really easy.
We can use almost everything the exact same, we're only going to switch up the dime part.
1 dime = 2 nickles
Nickles are worth 5 cents
So we take out the dime and replace it with two nickles.
So for the second combination we use: One $5 bill, one $1 bill, two quarters and two nickles.
At a dinner, a meal costs $22 and a sales tax of $1.87 was added to the bill.
1. How much would the sales tax be on a $66 meal?
2. What is the sales tax rate in this city?
Answer:
$8.50, the rate is 9.65%
Step-by-step explanation:
Please help me with this-
Set one:
Mean: -6
Median: -6
Mode: -9, -3
Range: 6
Set two:
Mean: -6
Median: -6
Mode: -9, -6
Range: 8
Have a wonderful day/night! <3
What is the best way to display data if there is a wide range and we want to see individual data?
frequency table with intervals
stem-and-leaf plot
line plot
frequency table
How do you think workers rights are abused today?Explain.
PLZ HELP :( I DONT GET IYTTTT
Answer:
the last one
Step-by-step explanation:
7 plus 3.5 equals 10.5
Answer: It ish the last one uwu chu ish welcome
Step-by-step explanation:
hi pls help will give branliest to the first answer its a math question
Answer:
3x+6
Step-by-step explanation:
Okay so the reason behind this is the 3 x blocks then we have 6 one blocks which is how you would get answer.
Moira mailed two birthday presents in a box weighing 1/4 pound. One present weighed 1/5 pound. The other present weighed 1/2 pound. what was the total weight of the box and presents?
Answer:
19/20LBS
Step-by-step explanation:
Can u figure out the surface area and volume i will give brainlest
Answer:
Volume: 120
SA: 400
Step-by-step explanation:
Volume = Bh
Volume = (1/2 x b x h) h
Volume = (1/2 x 6 x 4) 10
Volume = 120
SA = 2B + Ph
SA = 2(1/2 x b x h) + (s + s + s)h
SA = 2(1/2 x 6 x 4) + (5 + 5 +6) 10
SA = (24 + 16) 10
SA = 40 x 10
SA = 400
Answer:
V:240
S: 400
im think that its right
Find the value of x, the problem is below.
what is 100 div 2 div 10
The answer you get is the number of points your getting
Answer:
5
because:
100 ÷ 2 = 50
then:
50 ÷ 10 = 5
Answer:
5
Step-by-step explanation:
How to find
Divide the one-column dividend by the divisor.
Multiply the divisor by the quotient in the right place column.
Subtract the product from the one's column.
Solve
100 ÷ 2 = 50
Then:
50 ÷ 10 = 5
HELP ME!!!!!!!!!!!!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
Multiply 120 by 5/8
please HELP ME omg istggg plsss im begging yalll
HELP ASAP I WILL GIVE BRAINLIEST
Which of the following can be measured?
radii
chords
circumference
diameters
you can choose more than one answers
Answer:
Diameters
Step-by-step explanation:
Answer:
Chords n circumference
Pls help with this. I am try to do it help 2 sentences!!!!!!!!!!!!!
Answer: see below
Step-by-step explanation:
1.
Facts:
Justin jogs 3 2/3 miles every morning
Jogs 4 6/10 miles every evening.
Miles jogged per day=?
To solve this question,add the 2 fractions.This makes sense because let's say you ran 3 miles in the morning and 2 miles in the evening, nothing more nothing less, and you wanted to find how much you ran in a day, you'd add these 2 nummbers.
3 2/3 + 4 6/10
Step 1: Add the whole numbers
3 2/3 + 4 6/10
3+4= 7
7 + 2/3 + 6/10
Step 2: Find a common denominator between 10 and 3
10x1= 10
10x2= 20
10x3= 30 (works for both 3 and 10)
7 + __ + __
30 30
Step 3: Change the neumerators
Now when adding fractions this way, you have to multiply and change the neumerator:
In the 1st fraction, the original denominator was 3. And 3x10= 30, right? So you must also multiply the neumerator by 10 so that they are equivalent to each other
2x10= 20
In fraction #2, the neumerator was 6. 6x3= 18
7 + 20 + 18
30 30
7+38/30= 7 38/30= 8 8/30 miles per day
QUSTIION 2
Facts:
Last year, the tree was 5 11/12 feet long.
This year, the tree is 7 2/3 feet long.
How many feet did it grow?
Convert to decimals and subtract:
7 2/3= 7.66667
5 11/12= 5.9166667
7.66667- 5.916667= about 1.75, which becomes 1 3/4
It grew 1 3/4 feet
7th grade math help!!
Dani experimented with a dollar bill and the copy machine a dollar bills length is 6.1 inches and width is 2.6 inches, she reduced the dollar bill so its length was 80% of its original size. Dani then reduced the copy of the dollar bill a second time by making at 15% smaller than the copy, what is the new length of the second copy? NO LINKS PLS
Answer:
4.148 inches
Step-by-step explanation:
Add all of the numbers, and use percentages to figure.
Hope this helped, and please mark as Brainliest :)
Answer:
4.148
Step-by-step explanation:
Just add everything up and you will get your answer! :)
Use the key features of the polynomial f(x) = 6x4 + 4x3 − 5x2 − 2x + 1 to describe its end behavior.
The left side continues up, and the right side continues up.
The left side continues down, and the right side continues down.
The left side continues up, and the right side continues down.
The left side continues down, and the right side continues up.
Answer:
Step-by-step explanation:
The highest power in this function is x^4, which is an even function. If we start at the y-axis and move left, the graph goes UP; similarly if we move right, the graph goes UP. The first possible answer is the correct one.
Answer:
The left side continues up, and the right side continues up
Step-by-step explanation:
I took the test:)
If the height of the box is 7 inches, what is the volume of the box?
Answer:
The volume of this shape is 41 inches sq. :)
Step-by-step explanation:
7 x 3 = 21
2 x 2 = 4/2 = 2
2 x 2 = 4/2 = 2
2 x 2 = 4/2 = 2
2 x 2 = 4/2 = 2
2 x 3 = 6
2 x 3 = 6
21 + 2 + 2 + 2 + 2 + 6 + 6 = 41
help, please
I really need help
Answer:
I agree because 2 4/5 of 2 1/2 is 2 and there still is a half left
Step-by-step explanation:
please mark this answer as brainlest
Answer:No i do not agree because 4/5 of 2 is 8/5 which is 1 3/5
Step-by-step explanation:
I had to multiply 2(the whole number)by the numerator which is 8 then i divide it by the denominator and you get 1 3/5