Question

Can Someone Answer My Final Answers :) I’d appreciate it so much :)

Answer 1

Hello,
Please, see the attached files.
Thanks.

Answer 2

1. Remember that the perimeter is the sum of the lengths of the sides of a figure.To solve this, we are going to use the distance formula:
`d= \sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`
where

`(x_(1),y_(1))` are the coordinates of the first point

`(x_(2),y_(2))` are the coordinates of the second point
Length of WZ:
We know form our graph that the coordinates of our first point, W, are (1,0) and the coordinates of the second point, Z, are (4,2). Using the distance formula:

`d_(WZ)= √((4-1)^2+(2-0)^2)`

`d_(WZ)= √((3)^2+(2)^2)`

`d_(WZ)= √(9+4)`

`d_(WZ)= √(13)`

We know that all the sides of a rhombus have the same length, so

`d_(YZ)= √(13)`

`d_(XY)= √(13)`

`d_(XW)= √(13)`

Now, we just need to add the four sides to get the perimeter of our rhombus:

`perimeter= √(13) + √(13) + √(13) + √(13)`

`perimeter=4 √(13)`
We can conclude that the perimeter of our rhombus is
`4 √(13)` square units.

2. To solve this, we are going to use the arc length formula:
`s=r \alpha`
where

`s` is the length of the arc.

`r` is the radius of the circle.

`\alpha` is the central angle in radians

We know form our problem that the length of arc PQ is
`(8)/(3) \pi` inches, so
`s=(8)/(3) \pi`, and we can infer from our picture that
`r=15`. Lest replace the values in our formula to find the central angle POQ:

`s=r \alpha`

`(8)/(3) \pi=15 \alpha`

`\alpha = ((8)/(3) \pi)/(15)`

`\alpha = (8)/(45) \pi`

Since
`\alpha =POQ`, We can conclude that the measure of the central angle POQ is
`(8)/(45) \pi`

3. A cross section is the shape you get when you make a cut thought a 3 dimensional figure. A rectangular cross section is a cross section in the shape of a rectangle. To get a rectangular cross section of a particular 3 dimensional figure, you need to cut in an specific way. For example, a rectangular pyramid cut by a plane parallel to its base, will always give us a rectangular cross section.
We can conclude that the draw of our cross section is: