Kayla has a piece of blue ribbon that is 18.35 inches long and a piece of

Match the parametric equations with the verbal descriptions of the surfaces by putting the letter of the verbal description to t

alukav5142 [94]

Answer:

1. B

2. C

3. A

4. D

Step-by-step explanation:

The parametric equations of the circular cylinder are:

$x(u,v)=a\cos v\\y(u,v)=a\sin v\\z(u,v)=u$

If the orientation of the cylinder is changed to have the height $u$ along the x-axis, the parametric equations of the cylinder match:

$3. \mathbf{r} \left( u, v \right) = u \mathbf{i} + \cos v \mathbf{j} + \sin v \mathbf{k}$

The parametric equations of the circular paraboloid are:

$x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2$

Using the units vectors the parametric equations match:

$1. \mathbf{r} \left( u, v \right) = u \cos v \mathbf{i} + u \sin v \mathbf{j} + u^{2} \mathbf{k}$

The parametric equations of the cone are:

$x(u,v)=au\cos v\\y(u,v)=au\sin v\\z(u,v)=u$

Using the units vectors and rotating the base of the cone from $z=0$ to $x=0$ the parametric equations match:

$2. \mathbf{r} \left( u, v \right) = u \mathbf{i} + u \cos v \mathbf{j} + u \sin v \mathbf{k}$

The equation left is the equation of a plane:

$4. \mathbf{r} \left( u, v \right) = u \mathbf{i} + v \mathbf{j} + \left( 2u - 3v \right) \mathbf{k}$

5 0

3 years ago

form a 6 digit number divisible by 1 first 2 divisible by 2, first 3 digits divisible by 3, first 4 digits divisible by 4, first

photoshop1234 [79]

Answer:

111111

Step-by-step explanation:

Digit 1: This can be any digit as all numbers are divisible by 1. I picked 1 because it was simplest.

Digit 2: The total needs to be divisible by 2, so I picked my total to be 2. I knew I already had 1 from the previous digit, so 2-1 =1 was my next digit.

Digit 3: The total must be divisible by 3, so I picked my total to be 3. I already had 2 from the two previous digits, so 3-1 = 1 was my next digit.

I hope you get the idea now, it follows the same pattern for the rest of the numbers.

Hopefully this helps, any questions let me know :)

7 0

2 years ago

Y=3/2(x-5) horizontal <br> Vertical

vampirchik [111]

Hello, the answer is vertical. It also shifts down 15/2 units.

3 0

2 years ago

THe question asked what is 0.35 written as a ratio?

Masja [62]

Step 1: 0.35 = 35⁄100
Step 2: Simplify 35⁄100 = 7⁄20
answer: 7/20

5 0

3 years ago

Mr. Akika has 30 24-cent and 33-cent stamps all told. The stamps are worth $8.91. How many of each kind of stamp does he have?

riadik2000 [5.3K]

Answer:

24-cent: 11
33-cent: 19

Step-by-step explanation:

I find it easiest to solve these using the variable to represent the number of the most-expensive item. Let x represent the number of 33-cent stamps. Then the total value (in cents) is ...

33x +24(30 -x) = 891

9x = 171 . . . . . . . . . . . . . subtract 24(30), collect terms

x = 19 . . . . . . . . . . . . divide by 9

30-x = 11 . . . . . . . find the number of 24-cent stamps

Mr. Akika had 11 24-cent stamps and 19 33-cent stamps.

_____

<em>Additional comment</em>

You seem to have several of these to solve. They all have a similar solution.

If we let x represent the number of higher-value items, N, the total number of items, V the total value, and v1 and v2 the individual values (v2 > v1), the equation is ...

v2(x) +v1(N -x) = V

x(v2 -v1) = V -v1·N

x = (V -v1·N)/(v2 -v1) . . . . generic solution

Using this formula in the problem here, we find ...

x = (891 -24(30))/(33 -24) = 171/9 = 19 . . . as above

7 0

2 years ago