Answer:
7
Step-by-step explanation:
Answer:
$0.59
Step-by-step explanation:
We first find the unit rate of the large water bottles after the promotion. To do this we divide 6.3 by 3 to get 2.1. Then we want to subtract 2.69 by 2.1 to get our final answer, $0.59.
Answer:
![(a)\ r = 8cm](https://tex.z-dn.net/?f=%28a%29%5C%20r%20%3D%208cm)
![(b\ Area = 200.96cm^2](https://tex.z-dn.net/?f=%28b%5C%20Area%20%3D%20200.96cm%5E2)
![(c)\ Volume = 2143.573cm^3](https://tex.z-dn.net/?f=%28c%29%5C%20Volume%20%3D%202143.573cm%5E3)
Step-by-step explanation:
The largest cross-section of a sphere is the center.
So, we have:
![A : C = 4 : 1](https://tex.z-dn.net/?f=A%20%3A%20C%20%3D%204%20%3A%201)
Where
![A = \pi r^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%20r%5E2)
![C =2\pi r](https://tex.z-dn.net/?f=C%20%3D2%5Cpi%20r)
Solving (a): The radius
implies that
![\pi r^2 : 2\pi r = 4 : 1](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%20%3A%202%5Cpi%20r%20%3D%204%20%3A%201)
Express as fraction
![\frac{\pi r^2 }{ 2\pi r} = \frac{4 }{ 1}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20r%5E2%20%7D%7B%202%5Cpi%20r%7D%20%3D%20%5Cfrac%7B4%20%7D%7B%201%7D)
![\frac{\pi r^2 }{ 2\pi r} = 4](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20r%5E2%20%7D%7B%202%5Cpi%20r%7D%20%3D%204)
Divide by ![\pi r](https://tex.z-dn.net/?f=%5Cpi%20r)
![\frac{r}{ 2} = 4](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7B%202%7D%20%3D%204)
Make r the subject
![r = 4 * 2](https://tex.z-dn.net/?f=r%20%3D%204%20%2A%202)
![r = 8cm](https://tex.z-dn.net/?f=r%20%3D%208cm)
Solving (b): Area of the largest cross-section.
![Area = \pi r^2](https://tex.z-dn.net/?f=Area%20%3D%20%5Cpi%20r%5E2)
![Area = 3.14 *8^2](https://tex.z-dn.net/?f=Area%20%3D%203.14%20%2A8%5E2)
![Area = 200.96cm^2](https://tex.z-dn.net/?f=Area%20%3D%20200.96cm%5E2)
Solving (b): Volume of the sphere
![Volume =\frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=Volume%20%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
![Volume =\frac{4}{3} * 3.14 * 8^3](https://tex.z-dn.net/?f=Volume%20%3D%5Cfrac%7B4%7D%7B3%7D%20%2A%203.14%20%2A%208%5E3)
![Volume = 2143.573cm^3](https://tex.z-dn.net/?f=Volume%20%3D%202143.573cm%5E3)
Answer:
See below
Step-by-step explanation:
Three lengths will be a triangle only if the sum of two sides is greater than the third side.
![19+11 > 17](https://tex.z-dn.net/?f=19%2B11%20%3E%2017)
This is a triangle.
![23+28> 52\\51>52\\51 \ngtr 52](https://tex.z-dn.net/?f=23%2B28%3E%2052%5C%5C51%3E52%5C%5C51%20%5Cngtr%2052)
This is not a triangle.
![9+25> 34\\34>34\\34\ngtr 34](https://tex.z-dn.net/?f=9%2B25%3E%2034%5C%5C34%3E34%5C%5C34%5Cngtr%2034)
This is not a triangle.
![13+14> 22\\27>22](https://tex.z-dn.net/?f=13%2B14%3E%2022%5C%5C27%3E22)
This is a triangle.