C
there can be more than one mode. 20 and 30 have the same amount and are most frequent
Answer:
The circulation of the field f(x) over curve C is Zero
Step-by-step explanation:
The function 
and curve C is ellipse of equation
Theory: Stokes Theorem is given by:
Where, Curl f(x) = ![\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7Bi%7D%26%5Chat%7Bj%7D%26%5Chat%7Bk%7D%5C%5C%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82x%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82y%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82z%7D%20%5C%5CF1%26F2%26F3%5Cend%7Barray%7D%5Cright%5D)
Also, f(x) = (F1,F2,F3)
Using Stokes Theorem,
Surface is given by g(x) = 
Therefore, tex]\hat{N} = grad(g(x))[/tex]
Now,
Curl f(x) =
Curl f(x) = ![\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\x^{2}&4x&z^{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7Bi%7D%26%5Chat%7Bj%7D%26%5Chat%7Bk%7D%5C%5C%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82x%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82y%7D%20%26%5Cfrac%7B%E2%88%82%7D%7B%E2%88%82z%7D%20%5C%5Cx%5E%7B2%7D%264x%26z%5E%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Curl f(x) = (0,0,4)
Putting all values in Stokes Theorem,
I=0
Thus, The circulation of the field f(x) over curve C is Zero
Answer:
1. To eliminate x-term, multiply the second by -2
2. To eliminate y-term, multiply the second by 3
Step-by-step explanation:
4x - 9y = 7 (1)
-2x + 3y = 4 (2)
1. To eliminate x-term, multiply the second by -2
-2x + 3y = 4 (2) × 2
-4x + 6y = 8 (3)
4x - 9y = 7 (1)
Add (3) and (1)
6y - 9y = 8 + 7
-3y = 15
y = 15/-3
y = -5
4x - 9y = 7 (1)
4x - 9(-5) = 7
4x + 45 = 7
4x = 7 - 45
4x = -38
x = -38/4
x = -9.5
4x - 9y = 7 (1)
-2x + 3y = 4 (2)
2. To eliminate y-term, multiply the second by 3
-2x + 3y = 4 (2) × 3
-6x + 9y = 12 (3)
4x - 9y = 7 (1)
-6x + 4x = 12 + 7
-2x = 19
x = 19/-2
x = -9.5
4x - 9y = 7 (1)
4(-9.5) - 9y = 7
-38 - 9y = 7
-38 - 7 = 9y
-45 = 9y
y = -45/9
y = -5
Answer:
The best answer would be C
Step-by-step explanation:
The square has two parallel lines and the rhombus has parallel lines as well. And when you turn the square, it looks like a rhombus. They are both parallelograms and quadrilaterals.
Hope this helps
Answer c I’m pretty sure
Step-by-step explanation:
