NEED HELP ASAP!!!!!!!

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Law Incorporation [45]

Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by $\nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}$

- (Gauss' theorem)Given a closed surface S, the following applies

$\int_{S} F\cdot \vec{n} dS = \int_{V} \nabla \cdot F dV$

where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

$\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8$

Hence, by the Gauss theorem we have that

$\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}$

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

$\sqrt[]{(1-1)^2+(1-1)^2+(1-(-1)^2} = \sqrt[]{4} = 2$ .

Hence, the volume of V is $2\cdot 2 \cdot 2 = 8$ . Then, the final answer is

$\int_{S} F\cdot \vec{n} dS =8\cdot 8 = 64$

5 0

3 years ago

Product is a 12 ounce bottle of generic mouthwash that sells $4.39 product B is a 24 ounce bottle of mouthwash that cost $2.79 w

Anna35 [415]

Hi there,
To compare we can look at the amount of (ounces)
A: 12 B:24
so as it appears B wins this part
Now price
A: $ 4.39 B:$2.79
A is relatively expensive than B
B is cheaper with more ounces
A is less ounces and relatively expensive
which one would you buy?

5 0

3 years ago

Baker made 5 pounds of icing. He used 4/9 of the icing to decorate. How much did he have left over?

Elena L [17]

If the baker made 5 pounds of icing and used 4/9 of the icing to make decorations, then he used:

5 * 4/9 =
= 20/9 =
= 2 2/9 [of icing]

To find out how much he has left over, we just need to substract 2 2/9 from 5:

5 - 2 2/9 =
= 3 - 2/9 =
= 2 7/9

Answer: The baker has <u>2 7/9</u> of the icing left.

6 0

3 years ago

Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.

Dmitry [639]

Answer:

Step-by-step explanation:

I'm sure you want your functions to appear as perfectly formed as possible so that others can help you. f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation: f(x) = 4(2)^x

f(b) - f(a)

The formula for "average rate of change" is a.r.c. = --------------

b - a

change in function value

This is equivalent to ---------------------------------------

change in x value

For Section A: x changes from 1 to 2 and the function changes from 4(2)^1 to 4(2)^2: 8 to 16. Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2. Thus, in this Section, the a.r.c. is:

8

------ = 8 units (Section A)

1

Section B: x changes from 3 to 4, a net change of 1 unit: f(x) changes from

4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units. Thus, the a.r.c. is

224 units

----------------- = 224 units (Section B)

1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").

7 0

3 years ago

Can someone help me solve for x in this equation?? 25+3.50x < 17+7.50x

Lelu [443]

So we want to solve like if it was just a basic equation. We start with 25+3.50x<17+7.50x and get rid of our smallest x. That means we get rid of the 3.50x by subtracting from both sides and our new equation is 25<17+4x. Let’s get our x by itself shall we, so let’s subtract 17 from both sides and we get 8<4x. Finally all we do is divide by 4 and just like that 2

4 0

3 years ago