ANswer this question!!!!!

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

Jeff has $1.35 in nickles and dimes. He has a total of 15 coins. How many of each coin does he have?

dlinn [17]

For this case we propose a system of equations.

We know that a dime equals 10 cents and a nickel equals 5 cents.

So:

x: Let the variable that represents the number of dimes

y: Let the variable that represents the number of nickels

According to the statement we have:

$x + y = 15\\0.10x + 0.05y = 1.35$

We multiply the first equation by -0.10:

$-0.10x-0.10y = -1.5$

We have the following equivalent system:

$0.10x + 0.05y = 1.35\\-0.10x-0.10y = -1.5$

We add the equations:

$0.10x-0.10x + 0.05y-0.10y = 1.35-1.5\\-0.05y = -0.15\\y = \frac {-0.15} {- 0.05}\\y = 3$

So, Jeff has 3 nickels

$x + y = 15\\x + 3 = 15\\x = 15-3\\x = 12$

Jeff has 12 dimes.

Answer:

12 dimes and 3 nickels

4 0

3 years ago

Jada has a stand in the marketplace where she sells ground cumin. Her weekly expenses are $300, and she sells her cumin at a fix

Scrat [10]

P = R - E
600 = 120x - 300
The value of x from the equation is 7.5. The answer therefore for the first question is $7.5. Then, the number of kilogram of cumin she needs to sell to cover the expenses is $300/$7.5 and that is equal to 40.
I tried my best hope this helps

7 0

4 years ago

One line passes through the points \blueD{(-3,-1)}(−3,−1)start color #11accd, (, minus, 3, comma, minus, 1, ), end color #11accd

mart [117]

Answer:

The lines are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

Remember that

The formula to calculate the slope between two points is equal to