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3 years ago

Find the size of angle of cuz give your answer to 1 decimal place 13cm and 4cm

Mathematics

1 answer:

liberstina [14]3 years ago

5 0

Step-by-step explanation:

<h2>2.1</h2><h2>that's the answer.</h2><h2>thank you.</h2>

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For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f

Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0$

We want to find $f$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)$

$\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C$

$\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)$

$\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)$

$\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C$

$\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0$

so $\vec F$ is not conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)$

$\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)$

$\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C$

$\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}$

so $\vec F$ is conservative.

4 0

3 years ago

longitud del radio de la circunferencia circunscrita a un heptágono regular si su diagonal de menor longitud mide 42 cm

oksano4ka [1.4K]

Answer:

The answer is easy.

Step-by-step explanation:

6 0

2 years ago

(1/2)+(1/2) lets see who can solve this problem the fastest

lys-0071 [83]

The answer would have to be 1.

8 0

2 years ago

Plz help :( im trying to understand this but Idk how it works?

djyliett [7]

Answer:

LEFT

k + 3 = 20,

k = 17

RIGHT

3x + 5 = 32,

k = 9

Step-by-step explanation:

For the left side, you have k + 3 on one side equaling 20, so the equation is

k + 3 = 20

To solve is as follows

k + 3 = 20

- 3 - 3

k = 17

For the right side,

You have 3 x's and 5 1's right? Adding them together will equal 32 (Other side

So your equation is 3x + 5 = 32

To solve is as follows

3x + 5 = 32

- 5 -5

3x = 27

Dividing both sides by 9 we get x = 9

Reasoning; you want to cancel out everything with x so that you got x alone on one side.

Hope this helps, if not comment on this telling me which step I did that you dont understand and I'll explain it.

4 0

2 years ago

What is the average rate of change for this function for the interval from x=2 to x=4

maria [59]

Answer:

6×=

Step-by-step explanation:

try it if not 6-×=

its one of those trust me lsggsgsgsoshhshshsbsbslshshsjjsjsllslslslslsdnndndnsnsnanjs

6 0

3 years ago

Read 2 more answers