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Serhud [2]
3 years ago
13

Find the curl of ~V ~V = sin(x) cos(y) tan(z) i + x^2y^2z^2 j + x^4y^4z^4 k

Mathematics
1 answer:
ch4aika [34]3 years ago
7 0

Given

\vec v =  f(x,y,z)\,\vec\imath+g(x,y,z)\,\vec\jmath+h(x,y,z)\,\vec k \\\\ \vec v = \sin(x)\cos(y)\tan(z)\,\vec\imath + x^2y^2z^2\,\vec\jmath+x^4y^4z^4\,\vec k

the curl of \vec v is

\displaystyle \nabla\times\vec v = \left(\frac{\partial h}{\partial y}-\frac{\partial g}{\partial z}\right)\,\vec\imath - \left(\frac{\partial h}{\partial x}-\frac{\partial f}{\partial z}\right)\,\vec\jmath + \left(\frac{\partial g}{\partial x}-\frac{\partial f}{\partial y}\right)\,\vec k

\nabla\times\vec v = \left(4x^4y^3z^4-2x^2y^2z\right)\,\vec\imath \\\\ - \left(4x^3y^4z^4-\sin(x)\cos(y)\sec^2(z)\right)\,\vec\jmath \\\\ + \left(2xy^2z^2+\sin(x)\sin(y)\tan(z)\right)\,\vec k

\nabla\times\vec v = \left(4x^4y^3z^4-2x^2y^2z\right)\,\vec\imath \\\\ + \left(\sin(x)\cos(y)\sec^2(z)-4x^3y^4z^4\right)\,\vec\jmath \\\\ + \left(2xy^2z^2+\sin(x)\sin(y)\tan(z)\right)\,\vec k

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Someone please help​
dedylja [7]

Answer:

1. y = -2x + 5

2.  y = 3/5x + 5

3. y = -4/5x - 4

4. y = - 1

5. yes

6. yes

7. yes

8. no

Step-by-step explanation:

1.   (4,-3) parallel to y= -2x

     -3 = -2(4)+b

     b=5

2. (-5,2) parallel to y = 3/5x

    2= 3/5(-5)+b

     b=5

3. (-5,0) -4/5x

   0 = -4/5(-5)+b

    b = -4

4. (-4,-1)

    y= -1

5. yes

6. yes

7. yes

8. no

  • Same slope = parallel ex. y = -5x +7, y = -5x +12
  • opposite reciprocal  = perpendicular ex. y = -5x +7, y = 1/5x + 12
  • to find "b" with slope and point

          (x,y)  y = mx + b

          plug in the y value and x value in the eqaution and m=slope, solve for b

7 0
2 years ago
Can you help me please??
VLD [36.1K]
B.6 would be the right answer because thats the ratebin which it drops
6 0
3 years ago
Read 2 more answers
Which equation is it? plz help ​
zvonat [6]

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

8 0
3 years ago
Sierra is saving money to buy a bike the bike costs $245. she has $125 saved and each week she adds $15 to her savings. how many
beks73 [17]
You should start with an equation.
245 = 125 + 15x
The 'x' represents the week.

so now, we have to subtract 125 from the total amount which is 245.
245 - 125 = 120
now we have
120 = 15x
to find 'x', we must divide 15 on each side
\frac{120}{15}  =  \frac{15x}{15}
we are now left with
8 = x
that means Sierra will have 8 weeks until she has enough money to buy the bike
4 0
2 years ago
if you horizontally strech the quadratic parent function, f(x)=x^2, by a factor of 4, what is the equation of the new function?
max2010maxim [7]

Answer:

     g(x) = x^2/16

Step-by-step explanation:

To stretch a function horizontally by a factor of k, replace x with x/k.

You want a stretch factor of 4, so your function is ...

  g(x) = f(x/4) = (x/4)^2

  g(x) = x^2/16

__

The attached graph shows the horizontal stretch.

8 0
2 years ago
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