It’s either b or c. One of those two is the answer for sure
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:
The volume of the cylinder is 2520.64ft³
Step-by-step explanation:
To calculate the volume of a cylinder we have to use the following formula:
v = volume
h = height = 19ft
π = 3.14
r = radius = 6.5ft
v = (π * r²) * h
we replace with the known values
v = (3.14 * (6.5ft
)²) * 19ft
v = (3.14 * 42.25ft²) * 19ft
v = 132.665ft² * 19ft
v = 2520.64ft³
The volume of the cylinder is 2520.64ft³
