Answer: Work done by the particle is 78 N.
Step-by-step explanation:
If C is the path the particle follows, then work done is
.
According to the question the force
and all four points are in the plane
.
therefore, if S is the at surface with boundary C, so that S is the portion of the plane
over the rectangle D=[0,2]\times [0,4].
Now,

By the Stoke's theorem:
![\int_{C}^{}F.dx=\iint_{s}^{}curlF.dS\\\\=\iint_{D}^{}[-8y(0)-2z\left ( \frac{1}{4} \right )+5y]dA\\\\=\iint_{D}^{}\left ( -\frac{1}{2}z+5y \right )dA](https://tex.z-dn.net/?f=%5Cint_%7BC%7D%5E%7B%7DF.dx%3D%5Ciint_%7Bs%7D%5E%7B%7DcurlF.dS%5C%5C%5C%5C%3D%5Ciint_%7BD%7D%5E%7B%7D%5B-8y%280%29-2z%5Cleft%20%28%20%5Cfrac%7B1%7D%7B4%7D%20%5Cright%20%29%2B5y%5DdA%5C%5C%5C%5C%3D%5Ciint_%7BD%7D%5E%7B%7D%5Cleft%20%28%20-%5Cfrac%7B1%7D%7B2%7Dz%2B5y%20%5Cright%20%29dA)

![\int_{0}^{2}\left [ \frac{39}{16}y^2 \right ]_{0}^{4}dx\\\\=\int_{0}^{2}39\, \, dx\\\\=39\times 2\\\\=78 \, N](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B2%7D%5Cleft%20%5B%20%5Cfrac%7B39%7D%7B16%7Dy%5E2%20%5Cright%20%5D_%7B0%7D%5E%7B4%7Ddx%5C%5C%5C%5C%3D%5Cint_%7B0%7D%5E%7B2%7D39%5C%2C%20%5C%2C%20%20dx%5C%5C%5C%5C%3D39%5Ctimes%202%5C%5C%5C%5C%3D78%20%5C%2C%20N)
Answer:
X =6
Step-by-step explanation:
Angles on a straight line add up to 180°
180-110=70
The 70° is the same on the angles above
70+8+17x=180
180-70=110
110-8=102
102/17=6
X=6
I think it’s 22.4
the total is 37 then divided by 5 for each person. after you divide you add the $3 coupon so for each person would be 3 by 5 to equal 15. so 37 divided by 5 is 7.4 and then add 15 to get 22.4. If this is wrong please correct me :)