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
Paul and Matt will take
![9.9 \: \: hours](https://tex.z-dn.net/?f=9.9%20%5C%3A%20%5C%3A%20hours)
to install the floor working together.
EXPLANATION
First, calculate Paul's rate, which is
![= \frac{1}{18}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B1%7D%7B18%7D%20)
Next, calculate Matt's rate, which is,
![= \frac{1}{22}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B1%7D%7B22%7D%20)
Let us assume that, Paul and Matt took
![x \: hours](https://tex.z-dn.net/?f=x%20%5C%3A%20hours)
to do the work together.
Then, the rate of working together is,
![= \frac{1}{x}](https://tex.z-dn.net/?f=%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20)
Now, add the individual rates and equate to the rate of working together to form an equation that will help us solve for x.
![\frac{1}{18} + \frac{1}{22} = \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B18%7D%20%2B%20%5Cfrac%7B1%7D%7B22%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20)
Simplify the left hand side
![\frac{11 + 9}{198} = \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B11%20%2B%209%7D%7B198%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20)
![\frac{20}{198} = \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B20%7D%7B198%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20)
We reciprocate both sides to get (You could have also done cross multiplication).
![\frac{198}{20} = \frac{x}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B198%7D%7B20%7D%20%3D%20%5Cfrac%7Bx%7D%7B1%7D%20)
Answer:
45
Step-by-step explanation:
the slope is 8/3 so you can use y = 8/3x
make the y-value equal to 120
120 = 8/3x
cross-multiply to get:
8x = 360
x = 45
Answer:
40 ÷
=
40 x 5 = 200 miles
Step-by-step explanation:
distance from Shawna's house to the mountains = distance from her house to the ocean ÷ 1/5
40 ÷ 1/5
40 x 5 = 200 miles
ANSWER
622.113821138 is the answer