5/4+5/4=_ × 1/4 plz help me

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

If a swimming pool is being filled at a rate of 1 liter per second, how long will it take in minutes to fill a 6,000 liter pool?

Valentin [98]

Time taken
= 6000/1
= 6000s
= 100 min
= 1 hour 40 minutes

4 0

3 years ago

Does someone know how to solve this problem?

Naddika [18.5K]

Answer:

Acute scalene triangle.

Step-by-step explanation:

Acute scalene triangle.

Sides: a = 4 b = 7 c = 8

Area: T = 13.998

Perimeter: p = 19

Semiperimeter: s = 9.5

Angle ∠ A = α = 29.995° = 29°59'41″ = 0.524 rad

Angle ∠ B = β = 61.028° = 61°1'42″ = 1.065 rad

Angle ∠ C = γ = 88.977° = 88°58'37″ = 1.553 rad

Height: ha = 6.999

Height: hb = 3.999

Height: hc = 3.499

Median: ma = 7.246

Median: mb = 5.268

Median: mc = 4.062

Inradius: r = 1.473

Circumradius: R = 4.001

Vertex coordinates: A[8; 0] B[0; 0] C[1.938; 3.499]

Centroid: CG[3.313; 1.166]

Coordinates of the circumscribed circle: U[4; 0.071]

Coordinates of the inscribed circle: I[2.5; 1.473]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 150.005° = 150°19″ = 0.524 rad

∠ B' = β' = 118.972° = 118°58'18″ = 1.065 rad

∠ C' = γ' = 91.023° = 91°1'23″ = 1.553 rad

7 0

3 years ago

Which is bigger, 7/8" or 9/16"?

Iteru [2.4K]

7/8 and 9/16

7*2/8*2 = 14/16

14/16 and 9/16

Now since we have a common denominator, we can compare the numerators.

14/16 is greater, so 7/8 is greater than 9/16

Answer: 7/8 is bigger

5 0

3 years ago

Read 2 more answers

Find the value of x in 5rasised to power x=125

mestny [16]

5^3=125
Hope this helps

7 0

3 years ago

Read 2 more answers

5/4+5/4=_ × 1/4 plz help me​

5/4+5/4=_ × 1/4 plz help me