find the divergence and curl of the vector
F=(3x²y² +2z)i + (3x² + y +yz )j - (3x²z² +2yx + xyz)k

Answers

Answer 1

Divergence:

div(F) = ∂(3x²y² + 2z)/∂x + ∂(3x² + y + yz)/∂y - ∂(3x²z² + 2yx + xyz)/∂z

div(F) = 6xy² + 1 + z - 6x²z - xy

Curl:

curl(F) = [∂(3x² + y + yz)/∂z + ∂(3x²z² + 2yx + xyz)/∂y] i

… … … … … - [∂(3x²y² + 2z)/∂z + ∂(3x²z² + 2yx + xyz)/∂x] j

… … … … … + [∂(3x²y² + 2z)/∂y - ∂(3x² + y + yz)/∂x] k

curl(F) = (-xz - 2x - y) i + (6xz² + yz + 2y + 2) j + (6x - 6x²y) k


Related Questions

Francine recorded today's high
temperature as 78.6°F. Today's low
temperature was 4.7°F less than
that. How much cooler was today's
low temperature than yesterdays low
temperature, which was 77.4°F?

Answers

Answer:

3.5

Step-by-step explanation:

the problem says 4.7 less than which refers to subtraction so we can plug our numbers into a subtraction problem like so

78.6-4.7 which equals 73.9

the second part of the problem asks the difference between yesterday's low and today's.

we can take the two lows and subtraction them to find this answer.

77.4-73.9 which equals 3.5

so today's low was 3.5 degrees cooler than yesturdays

A rectangular plot,72 metre long and 20 metre wide on a school farm,is divided into 18 equal plots, what is the area of each plot?​

Answers

It is 80 meter square

Answer:

80 square metres

Step-by-step explanation:

A = L× w

= 72×20

= 1440

answer ÷ 18 = 80

In this triangle, cosA/cosB=

Answers

Answer:

1

Step-by-step explanation:

In sohcahtoa:

Cos (c) = adjacent (a) / hypotenuse (h)

cosA = adjacent / hypotenuse. The hypotenuse is 4.24 (the side opposite the right angle) and the side next to A is 3, so cosA = 3/4.24

cosB = adjacent/hypotenuse. The side next to B is 3, so cosB = 3/4.24 as well

Therefore, cosA = cosB

cosA/cosB = cosA/cosA = 1

Jaime is three years younger than his brother Keegan. In five years, the sum of their ages will be thirty-nine.
How old are they now?

Answers

Answer:

Keegan is 16 and Jamie is 13.

Step by Step Explanation:

So if we were to take the number 39 and divide it by 2, we would get 19.5. Since Jaime is 3 years younger, we would subtract 3 from one of the 19's. Then we would add 1.5 to both of the numbers since that 3 we subtracted has to go somewhere in that 39, and we come up with the numbers 21 and 18. Since it is asking how old they are NOW and not in the future, we subtract 5 from both numbers to account for the 5 years, and we end up with the years 16 and 13.

Math:

39÷2 = 19.5

19.5 19.5

-3

___________

16.5 19.5

+1.5 +1.5

___________

18 21

-5 -5

13 16

-) Which is a valid velocity reading for an object? O 45 m/s O 45 m/s north 23 O O m/s south O 0 m/s ok Save and Exit Next Mark this and return​

Answers

Answer:

Step-by-step explanation:

0 can't have a direction. It does not move. It has no speed component. Therefore 0 m/s south is not the answer.

45 m/s has no direction stated. It is just a speed, not a velocity.

45 m/s north is a velocity. It has both speed and direction.

HELP PLEASE
To divide the function f(x) by (x2-4x-12), we find that the quotient is Q(x) and the
remainder is (x+6). If f(-2)=a and f(6)=b, what is the value of b/a?

Answers

Answer:

b/a = 3

Step-by-step explanation:

f(x) / (x²-4x-12) = Q(x) + (x+6)/(x²-4x-12)

f(x) = Q(x)*(x²-4x-12) + (x+6)

x= - 2   ... when f(x) is f(-2)        x²-4x-12 = 4+8-12 = 0

a = f(-2) = Q(x)*0 + (-2 + 6) = 4

x= 6   ... when f(x) is f(6)        x²-4x-12 = 36-24-12 = 0

b = f(6) = Q(x)*0 + (6 + 6) = 12

b/a = 12/4 = 3

An arts academy requires there to be 5 teachers for every 90 students and 3 tutors for
every 36 students. How many students does the academy have per teacher? Per tutor? How many
tutors does the academy need if it has 108 students?


PLSS

Answers

Three tutors for 108 students, if the total number of teacher is 5 then the academy would have around 450 students srry if im wrong

2x2 is what its due in 1 minute

Answers

Answer: 4

Step-by-step explanation: You multiplied 2 and 2 which equals to 4

Answer:

9

Step-by-step explanation:

9 9 9 9 9 9 9 9 9  9 9 9 9 9  9 9 9 9 9 9  9 9 9 9 9  9 9 9 9 9 9 9  9 9 9 9 9

3+3=6! Easy for kids to learn!

Answers

Answer:

indeed

Step-by-step explanation:

3+3=6

CAN YOU PLS HELP MEEEE

Answers

Answer:

10x - 2y

Step-by-step explanation:

simplify the expression.

8x2y + x + x

combine numbers that have the same variables

8x + x + x

*those x have 1 coefficient each.

it will be 8x+1x+1x = 10x then 2y

10x2y.

Hope it helps :)

an object is dropped from a height of 25 meters at what velocity will it hot the ground​

Answers

Given data

height (h) = 25 m ,

velocity (v) = ?

we know that,

                    v²-u² = 2as

                     initial velocity (u) = 0,

                                               a = g = 9.8 m/s ,

                 Now the equation becomes,

                                    v² = 2 × g × h

                                        = 2 × 9.8 × 25

                                    v² = 490.5

                                    v = √490.5

                                   v = 22.1 m/s

Therefore answer is C , i.e., 22 m/s

Simplify the product.
(16+13)(12-2)

Answers

Answer:

290

Step-by-step explanation:

(16+13)(12-2)= 29 * 10 = 290

Answer:

290

Step-by-step explanation:

(16+13)(12-2)

29*10

290

which car can travel furthur on one gallon of gas/ green car 18.4 miles on 0.8 gallons or black car 17.4 miles on 0.75 gallons

Answers

Answer:

The black car

Step-by-step explanation:

First, we need to fin the mile to gallon ratio.

To get this we would divide the number of miles by the gallon for each car

Green Car:

18.4/0.8

23 miles per gallon

Black car:

17.4/0.75

23.2 miles per gallon

In conclusion, The black car would travel further on one gallon of gas than the green car would.

Hope this helps!!

Please tell me if I have messed up!!

I enjoy learning from my mistakes:)

In the multiplication sentence below, which number is the product?
9x 10 = 90
A. 9
B. 10
C. 90
SUBMIT

Answers

Answer:

  C.  90

Step-by-step explanation:

The numbers being multiplied are "factors." The result of multiplication is a "product." In this problem, the product is 90.

Sal bought x shares of a stock that sold for 31.50 per share. He paid a 1% commission on the sale. The total cost of his investment, including the broker fee, was $5,726.70. How many shares did he purchase.

Answers

Answer:

180

Step-by-step explanation:

add 1% to 31.50 to get 31.815

then take the total 5276.70 and divide by 31.815

Jake has two dogs, Euclid and Pythagoras. Euclid is a smaller dog and Pythagoras is larger. Jake found that
Pythagoras lost 13 pounds from January to June. If Pythagoras gains 1.2 times Euclid's weight, Pythagoras's
weight would still be á pound less than he did in January. What is Euclid's weight?
4
(a) Write an equation that represents the scenario. Begin by defining your variable.
(b) Solve the equation. Show your work.
(c) What is Euclid's weight?
(d) Jake adopts a third dog, Riemann. Riemann weighs exactly twice what Euclid weighs. The combined
weight of the three dogs is 603 pounds. What is Riemann's weight, and what is Pythagoras's
2
weight? Show your work.

Answers

We want to answer different things about the weight of the dogs, with simple algebra we will find that the answers are:

a) P - 13lb + 1.2*E = P - 1lbb) E =  10lbc) Euclid's weight is 10 pounds.d) Pythagora's weight is 33 pounds and Riemann's weight is 20 pounds.

We start by defining the two variables we will be using:

E = Euclid's weightP = Pythagoras's weight

First, Pythagoras loses 13 lb, then his new weight is:

P' = P - 13lb

We know that if he wins 1.2 Euclid's weight, he will still have a pound less than before.

A) using the above information we can rewrite:

P - 13lb + 1.2*E = P - 1lb

This is the equation we need to solve.

b) So we want to solve this for E, then we move all the other terms to the right side:

1.2E = P - 1lb - P + 13lb

1.2E = 12lb

E = (12lb)/1.2 = 10lb

c) The solution of the above equation tells us that the weight of the dog is 10lb.

d) Let's define R as the weight of the third dog.

We know that:

R = 2*E = 2*10lb = 20lb

We also know that the combined weight of the 3 dogs is 63 lb, then we have:

E + R + P = 63lb

10lb + 20lb + P = 63lb

P = 63lb - 10lb -20lb = 33lb

If you want to learn more about algebra, you can read:

https://brainly.com/question/20607627

10+8x > 2 Solve each inequality

Answers

Answer:

x>-1

Step-by-step explanation:

8x>2-10

8x>-8

x>-1

Answer:

x>-1

interval notation: (-1,infinty)

Help help help help math math math

Answers

Answer:

55º

Step-by-step explanation:

The 125º angle makes a straight angle (180º) with the one next to it. This makes the angle next to it (adjacent angle) 55º. According to the rules of a transversal, the adjacent angle said above and angle 2 are alternate interior angles, making them equal.

Select all the correct answers.
Which equations have a greater unit rate than the rate represented in the table.

Answers

We need slope/rate of the table

(3,2)(6,4)

[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{4-2}{6-3}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{2}{3}[/tex]

Slopes of all options

5/7=25/213/5=9/151/37/9 7/11=21/33

Option D is correct

Option

How do I figure this out

Answers

Answer:

D

Step-by-step explanation:

yeah-ya....................... right?

Answer:

D

Step-by-step explanation:

hope it help correct me if wrong

Please help me solve this problem, thank you.

Answers

Step-by-step explanation:

first you need to find the 17 and 8 triangles missing sides length so we do a squared plus b squared equals c square and since we have c which is 17 we subtract 8 squared or 64 from 17 square and we get 225. next the missing line from the next one is done the same way 225 minus 9 squared or 81 and we get 144 and the square root of that is 12 we do 12 squared 144 minus 6 squared because we already know that the side is six because it gives it to us and we get 10.392

HELP I'LL GIVE BRAINLY​

Answers

Answer:

code is 4163

Step-by-step explanation:

x-35=27;x=64

-96=-8x;x=12

6=x/4 +2;x=16

76-3x=-29; x=31

code is 4163

Answer:

at least 8

Step-by-step explanation:

im from k12

Expand and simplify

(7-3x) (6x + 1)

Answers

Answer:

-18x^2+39x+7

Step-by-step explanation:

7-3x + 6x + 1
7 + 1 + 3x
8 + 3x
Or 3x + 8
I hope this helps.

Use the distributive property to simplify this expression -2x(3x + x-5)

Answers

Answer:

− 8 x ^2  +  10 x

Step-by-step explanation:

-6x-2x+10x
8x+10x
18x.

Determine the y-intercept of the following equation.
(-2 - 1)(2+3) = y

Answers

Answer:

(0,-15)

Step-by-step explanation:

i think.. trust someone else!! I'm not 100% sure...

HELP PLEASE 20 POINTS

Answers

Answer:

a b and j?

Step-by-step explanation:

Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
9W + 1 = 19
9w =
Subtract 1 from both sides
W =
Divide both sides by 9

Answers

Answer:

see explanation

Step-by-step explanation:

9W + 1 = 19 ( subtract 1 from both sides )

9W = 18 ( divide both sides by 9 )

W = 2

A number x is no less than 18

Answers

Answer:

x>18

Step-by-step explanation:

That's the answer if x can't be 18.

Answer:

x ≥ 18

Step-by-step explanation:

I'm not really sure how to explain how it's correct but, the given statement can also be written as " a number, x,  can be equal or more than 18

How to find the area of a missing square

Answers

Check the picture below.

btw, when Pythagoras said the square of this equals that and so on, he really meant the square or square area.

Brainliest for right answer.

Answers

Answer:

441 millimeters of compound B

Step-by-step explanation:

4 + 7 = 11

693/11 = 63

7 · 63 = 441

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