Curl is defined as:
![\bigtriangledown \times F=\frac{ \int F.dr}{Area}](https://tex.z-dn.net/?f=%5Cbigtriangledown%20%5Ctimes%20F%3D%5Cfrac%7B%20%5Cint%20F.dr%7D%7BArea%7D)
Which can be rewritten as:
![\frac{ \int F.dr}{Area}=\frac{ \int_{C_1} Fdr}{Area}\widehat{k}+\frac{ \int_{C_2} Fdr}{Area}\widehat{i}+\frac{ \int_{C_3} Fdr}{Area}\widehat{j}](https://tex.z-dn.net/?f=%5Cfrac%7B%20%5Cint%20F.dr%7D%7BArea%7D%3D%5Cfrac%7B%20%5Cint_%7BC_1%7D%20Fdr%7D%7BArea%7D%5Cwidehat%7Bk%7D%2B%5Cfrac%7B%20%5Cint_%7BC_2%7D%20Fdr%7D%7BArea%7D%5Cwidehat%7Bi%7D%2B%5Cfrac%7B%20%5Cint_%7BC_3%7D%20Fdr%7D%7BArea%7D%5Cwidehat%7Bj%7D)
This is because C1 lies on the xy plane and thus it's unit vector will be
.
By similar arguments the rest will follow too.
Now, area of each circle will be: ![\pi \times (0.1)^2=0.01 \pi](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%20%280.1%29%5E2%3D0.01%20%5Cpi)
Therefore, Curl, as per our definition will be:
![\frac{\int F.dr}{Area}=\frac{0.01\pi}{0.01\pi}\widehat{k}+\frac{0.4\pi}{0.01\pi}\widehat{i}+\frac{5 \pi}{0.01\pi}\widehat{j}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cint%20F.dr%7D%7BArea%7D%3D%5Cfrac%7B0.01%5Cpi%7D%7B0.01%5Cpi%7D%5Cwidehat%7Bk%7D%2B%5Cfrac%7B0.4%5Cpi%7D%7B0.01%5Cpi%7D%5Cwidehat%7Bi%7D%2B%5Cfrac%7B5%20%5Cpi%7D%7B0.01%5Cpi%7D%5Cwidehat%7Bj%7D)
Thus, Curl=![40\pi \widehat{i}+500\pi \widehat{j} +\widehat{k}](https://tex.z-dn.net/?f=40%5Cpi%20%5Cwidehat%7Bi%7D%2B500%5Cpi%20%5Cwidehat%7Bj%7D%20%2B%5Cwidehat%7Bk%7D)
Which is the required answer.
Answer:
m= 3/7
Step-by-step explanation:
I'm assuming the question is solve for the variable, m.
First step is to isolate the variable
In other words, let's move everything (but m) from the left side to the right side
To move 7 to the right side, we can either divide both sides by 7 or multiply both sides by 1/7 (both equal the same thing)
7/3m × 1/7 = 1 × 1/7
1/3m = 1/7
Now we must move 1/3 from the left to the right side
We can use the reciprocal, 3/1, to do this
1/3m × 3/1 = 1/7 × 3/1
m = 3/7
Certtrcrhvy tvttbttbttyyvuvyccyyttv
B
Answer:
Part A: 24
Part b: 384
Part c: larger over the interval
Step-by-step explanation:
Answer:
Why you just copy and paste it