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Inga [223]
3 years ago
12

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

Mathematics
1 answer:
schepotkina [342]3 years ago
4 0
\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
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Fred solved the equation 8(3x – 7) = -6(x + 7) + 4 as shown.
OleMash [197]

Answer: He added 4 to a negative 42 and said it was 46 but its supposed to simplify to -38. X=3/5

3 0
2 years ago
If m∠4 = 35, find m∠2. Explain.
Bad White [126]

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

Triangle CAB is a right triangle.

Therefore, m∠1 = 90°

Similarly, m∠ACD = 90°

m∠ACD = m∠ACB + m∠BCD = 90°

             = m∠3 + m∠4 = 90°

Since m∠4 = 35°,

m∠3 + 35° = 90°

m∠3 = 90° - 35°

        = 55°

In the triangle ABC,

m∠ACB + m∠CBA + m∠BAC = 180° [Property of a triangle]

m∠3 + m∠2 + m∠1 = 180°

55° + m∠2 + 90° = 180°

m∠2 + 145° = 180°

m∠2 = 180° - 145°

        = 35°

Since, AB║CD and BC is a transverse,

Therefore, m∠2 = m∠4 = 35° [Alternate interior angles]

Option (1) is the correct option.

4 0
3 years ago
What is the slope-intercept form of the equation of the line that passes through (0, 5) and (2, 1)?
11Alexandr11 [23.1K]

Answer:

Y= -2x + 5

Step-by-step explanation:

6 0
3 years ago
Lucio quiere repartir su colección de estampillas entre la mayor cantidad de amigos pero de manera que todos reciban la misma ca
Daniel [21]

Answer:

Lucio podrá armar 5 grupos iguales de estampillas.

Step-by-step explanation:

El problema plantea un caso de distribución mediante la aplicación del divisor común mayor a todos los números involucrados. Para ello, primero debemos analizar los divisores de cada uno de estos números:

-30: divisible por 2, 3, 5, 6, 10, 15 y 30.

-75: divisible por 3, 5, 15, 25 y 75.

-160: divisible por 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 y 160.

Así, podemos ver que el divisor común mayor a los tres números es 5, ya que 30, 75 y 160 dan como resultado un número entero tras ser divididos por 5.

Entonces, para poder repartir equitativamente sus estampillas entre la mayor cantidad de amigos posibles, deberá repartir 6 estampillas de animales, 15 estampillas de flores y 32 estampillas de ciudades a 5 amigos. De esta manera, Lucio podrá armar 5 grupos iguales de estampillas.

4 0
3 years ago
I need help ASAP ! Nd plz help me how to show work
Kisachek [45]

Answer:

x = -3

Step-by-step explanation:

y = -x + 2

7x + 4y = -1

Subsitution method: (Substitute y)

7x + 4(-x+2) = -1

Expand.

7x + (-4x + 8) = -1

One plus and one minus make one minus. Two plus makes a plus.

7x -4x + 8 = -1

Simplify.

3x + 8 = -1

Isolate 3x.

3x = -1-8

    = -9

Find x.

x = -9 ÷ 3

  = -3

4 0
3 years ago
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