PLEASE HELP!! I will UPVOT

Verify that the divergence theorem is true for the vector field f on the region

schepotkina [342]

$\mathbf f(x,y,z)=5x\,\mathbf i+xy\,\mathbf j+2xz\,\mathbf k$

$\mathrm{div}(\mathbf f)=\dfrac{\partial(5x)}{\partial x}+\dfrac{\partial(xy)}{\partial y}+\dfrac{\partial(2xz)}{\partial z}=5+x+2x=5+3x$

By the divergence theorem, the flux of $\mathbf f$ across the boundary of $E$ is given by

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_E\mathrm{div}(\mathbf f)\,\mathrm dV$

$=\displaystyle\int_{z=0}^{z=2}\int_{y=0}^{y=2}\int_{x=0}^{x=2}(5+3x)\,\mathrm dx\,\mathrm dy\,\mathrm dz=64$

4 0

3 years ago

What are the equivalent ratios shown in the table? Complete the statement.

Radda [10]

I will !

This is five-fold proportion
The first ratio gives solution namely
We will write general proportion
a:b= c:d= e:f = g:h= i:j = k
According to this the first ratio gives coefficient k
When we divide 24/2 =12 our coefficient k=12

In the second ratio we will multiply 3 with 12 and get 36.
In the third ratio we will multiplu 5.5 with 12 and get 66.
In the fourth we will divide 108 with 12 and get 9.
In the fifth we will multiply 15 with 12 and get 180.

Finally the ratio is 24:2=36:3=66:5.5=108:9=180:15

Good luck!!!!

6 0

2 years ago

Read 2 more answers

HELP ME IF RIGHT MARK BRAINLY

aalyn [17]

Answer:

A. m+7n+14

Step-by-step explanation:

Add parenthesis to help simplify.

(5m-4m)+(22-8)+7n

Simplify the expression.

m+7n+14

7 0

2 years ago

3

zlopas [31]

The answer would be C. 5(5) + 2(2) = 29
(5) + 4(2) = 13

3 0

2 years ago

Bruno and Willie need a total of $50,000 to start an accounting business. Bruno has spent a lot of time getting the business set

Gnom [1K]

The amount contributed by Willie and Bruno is $31000 and $19,000 respectively.

Let amount contributed by Willie be x

Let amount contributed by Bruno be y

Since Willie agreed to contribute $12,000 more than Bruno;

Therefore;

x - y = 12000....…....... equation (1)

x + y = 50,000...…....... equation (2)

By solving the system of equations simultaneously;

2x = 62000

x = 31000

and y = 50,000 - 31000

y = 19,000

In essence; The amount contributed by Willie and Bruno is $31000 and $19,000 respectively.