Answer:
1. B
2. C
3. A
4. D
Step-by-step explanation:
The parametric equations of the circular cylinder are:
![x(u,v)=a\cos v\\y(u,v)=a\sin v\\z(u,v)=u](https://tex.z-dn.net/?f=x%28u%2Cv%29%3Da%5Ccos%20v%5C%5Cy%28u%2Cv%29%3Da%5Csin%20v%5C%5Cz%28u%2Cv%29%3Du)
If the orientation of the cylinder is changed to have the height
along the x-axis, the parametric equations of the cylinder match:
![3. \mathbf{r} \left( u, v \right) = u \mathbf{i} + \cos v \mathbf{j} + \sin v \mathbf{k}](https://tex.z-dn.net/?f=3.%20%5Cmathbf%7Br%7D%20%5Cleft%28%20u%2C%20v%20%5Cright%29%20%3D%20u%20%5Cmathbf%7Bi%7D%20%2B%20%5Ccos%20v%20%5Cmathbf%7Bj%7D%20%2B%20%5Csin%20v%20%5Cmathbf%7Bk%7D)
The parametric equations of the circular paraboloid are:
![x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2](https://tex.z-dn.net/?f=x%28u%2Cv%29%3Du%5Ccos%20v%5C%5Cy%28u%2Cv%29%3Du%5Csin%20v%5C%5Cz%28u%2Cv%29%3Du%5E2)
Using the units vectors the parametric equations match:
![1. \mathbf{r} \left( u, v \right) = u \cos v \mathbf{i} + u \sin v \mathbf{j} + u^{2} \mathbf{k}](https://tex.z-dn.net/?f=1.%20%5Cmathbf%7Br%7D%20%5Cleft%28%20u%2C%20v%20%5Cright%29%20%3D%20u%20%5Ccos%20v%20%5Cmathbf%7Bi%7D%20%2B%20u%20%5Csin%20v%20%5Cmathbf%7Bj%7D%20%2B%20u%5E%7B2%7D%20%5Cmathbf%7Bk%7D)
The parametric equations of the cone are:
![x(u,v)=au\cos v\\y(u,v)=au\sin v\\z(u,v)=u](https://tex.z-dn.net/?f=x%28u%2Cv%29%3Dau%5Ccos%20v%5C%5Cy%28u%2Cv%29%3Dau%5Csin%20v%5C%5Cz%28u%2Cv%29%3Du)
Using the units vectors and rotating the base of the cone from
to
the parametric equations match:
![2. \mathbf{r} \left( u, v \right) = u \mathbf{i} + u \cos v \mathbf{j} + u \sin v \mathbf{k}](https://tex.z-dn.net/?f=2.%20%5Cmathbf%7Br%7D%20%5Cleft%28%20u%2C%20v%20%5Cright%29%20%3D%20u%20%5Cmathbf%7Bi%7D%20%2B%20u%20%5Ccos%20v%20%5Cmathbf%7Bj%7D%20%2B%20u%20%5Csin%20v%20%5Cmathbf%7Bk%7D)
The equation left is the equation of a plane:
![4. \mathbf{r} \left( u, v \right) = u \mathbf{i} + v \mathbf{j} + \left( 2u - 3v \right) \mathbf{k}](https://tex.z-dn.net/?f=4.%20%5Cmathbf%7Br%7D%20%5Cleft%28%20u%2C%20v%20%5Cright%29%20%3D%20u%20%5Cmathbf%7Bi%7D%20%2B%20v%20%5Cmathbf%7Bj%7D%20%2B%20%5Cleft%28%202u%20-%203v%20%5Cright%29%20%5Cmathbf%7Bk%7D)
Answer:
C
Step-by-step explanation:
180-123=57
Answer:
a) 27. b) 8/3
This is your answer ☺️☺️☺️
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![\pmb{\qquad{\qquad{\qquad{\underline{\green{\underline{\sf{Filtration}}}}}}}}](https://tex.z-dn.net/?f=%5Cpmb%7B%5Cqquad%7B%5Cqquad%7B%5Cqquad%7B%5Cunderline%7B%5Cgreen%7B%5Cunderline%7B%5Csf%7BFiltration%7D%7D%7D%7D%7D%7D%7D%7D)
Filtration is a physical or chemical separation process that separates solid matter and flu.id from a mixture using a filter medium that has a complex structure through which only the flu.id can pa.ss.
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