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Effectus [21]
3 years ago
15

Are the following statements true or false? 1. If F⃗ is a vector field in 3-dimensional space, and W is a solid region with boun

dary surface S, then ∬SF⃗ ⋅dS⃗ =∭Wdiv(F⃗ )dV. 2. If F⃗ and G⃗ are vector fields satisfying div(F⃗ )=div(G⃗ ), then F⃗ =G⃗ . 3. If ∬SF⃗ ⋅dS⃗ =12 and S is a flat disk of area 4π, then div(F⃗ )=3/π. 4. If F⃗ is a vector field in 3-dimensional space satisfying div(F⃗ )=1, and S is a closed surface oriented outward, then ∬SF⃗ ⋅dS⃗ is equal to the volume enclosed by S. 5. If F⃗ is a vector field in 3-dimensional space, then grad(div(F⃗ ))=0⃗ .
Mathematics
1 answer:
Masteriza [31]3 years ago
8 0

Answer:

Step-by-step explanation:

1) True. This is because the divergence of F is 1, thus, F is a linear function. Orientation is given outward to the surface. Linear function double integrated over a surface with outward orientation gives volume enclosed by the surface.

2) True. This is primarily what the Divergence theorem is.

3) False. If F was 3/pi instead of div(F), then the statement would have been true.

4) False. The gradient of divergence can be anything. The curl of divergence of a vector function is 0, not the gradient o divergence.

5) False. While finding Divergence, derivatives are taken for different variables. Since the derivatives of constants are 0, therefore, both the vector functions F and G can be different constant parts of there components even if their divergences are equal.

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Area triangles? it says show work so pls do
coldgirl [10]

\large{\underline{\underline{\pmb{\sf {\color {blue}{Solution:}}}}}}

Given,

Area = 225 yd²

Base = 30 yd

Height = [To be calculated]

To find:

The height of the given triangle.

We know that, area of a triangle is:

\frac{1}{2}  \times (b \times h) \\  \\  \leadsto \frac{1}{2} \times (30 \times h) \\  \\  \leadsto \frac{1}{2}   \times 30h \\  \\  \leadsto  \frac{1}{ \cancel{2}} \times  \cancel{30}h \\  \\  \leadsto1 \times 15h \\  \\  \leadsto \: h = 15 \: yd

Therefore, the require height is 15 yd.

\green\starProof:

\frac{1}{2}  \times (b \times h) \\  \\  \leadsto \frac{1}{2}  \times (30 \times 15) \\  \\  \leadsto \frac{1}{ \cancel{2}}   \times  \cancel{450} \\  \\  \leadsto1 \times 225  \\  \\  area = 225  {yd}^{2}

\boxed{ \frak \red{brainlysamurai}}

6 0
2 years ago
Solve √(3x+7)+2√(x-8)=0.
laiz [17]

Answer:

The solution to this question is 39

Step-by-step explanation:

Given that :

√(3x+7)+2√(x-8)=0.    

√(3x+7)=-2√(x-8)           (i)

square of the equation (i)

Then

(√(3x+7))^2=(-2√(x-8))^2

we know that √a*√a=(√a)^2=a So,

(3x+7)=4(x-8)      

3x+7=4x-32        //multiply by 4

32+7=4x-3x  exchange the value.

39=1x

x=39.

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The answer is 84 degrees you just subtract 180-90
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lutik1710 [3]
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Note that <width of wood>+<space between shelf and well> =width of closet
I challenge you to finish this on your own - good luck, and feel free to ask with any further questions! 

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Well there are 200 chickens and 16 goats 
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