Answer:
Number 1 is 10 and number 2 is 7
14/2 = 7
7 + 3 = 10
No 5/8 is bigger because half of 8 is 4 and 5 is greater than 4
Answer:
0.2601
Step-by-step explanation:
There are 19C16 = 969 ways for Lester to choose 16 of the 19 objects.
There are 12C11 = 12 ways to choose 11 vases, and 7C5 = 21 ways to choose a non-vase, for a total of (12)(21) = 252 ways to choose exactly 11 vases in 16 objects.
So, the probability of interest is ...
252/969 ≈ 0.2601
_____
nCk = n!/(k!(n-k)!) ... the number of ways to choose k objects from n
Answer:
its 16
as we know the square root of 64 is 6 and when it is multiplied by 2 its answer is 16.
Step-by-step explanation:
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) = ![\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)
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