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kupik [55]
2 years ago
15

I DONT UNDERSTAND THIS I NEED HELP

Mathematics
1 answer:
musickatia [10]2 years ago
6 0

Answer:

It is -4 :)

Step-by-step explanation:

I just did this lol

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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.

1.

\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.

2.

\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.

3.

\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.

4.

\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
Can someone solve this?
romanna [79]

Answer:

u=4

v=2√3

Step-by-step explanation:

The 30-60-90 triangle theorem states that the shortest side of a triangle is half of the hypotenuse, so 2*2=4. So, the hypotenuse, <em>u</em>, is 4.

The longest leg is √3 times greater than the shortest leg, so 2*√3=2√3. So, the longest leg, <em>v</em>, is 2√3.

4 0
2 years ago
The magnitudes of the moon and sirius are -12.5 and -1.44, respectively. approximately how many times is the moon brighter than
Lelu [443]

Solution:

we are given that

The magnitudes of the moon and Sirius are -12.5 and -1.44 respectively.

we have been asked to find approximately how many times is the moon brighter than Sirius?

The word magnitude is used by the scientist to describe the brightness of moon/star/object etc.

So we can find the brightness by dividing the given values. so we get

\frac{-12.5}{-1.44} =8.6805

Hence we can say

The moon is 8.68 times brighter than Sirius.

3 0
3 years ago
Please help????????????? (ASAP)
Rina8888 [55]

Answer: 12

Step-by-step explanation:

\frac{b}{3}+16=20

Subtract 16

\frac{b}{3}=20-16

\frac{b}{3}=4

Multiply by 3

b=4*3

b=12

8 0
3 years ago
PLEASE HELP!!!!!!!!!!!
goblinko [34]
The correct answer is Choice A I hope it helps :)
5 0
3 years ago
Read 2 more answers
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