Answer:
144
Step-by-step explanation:
<u>To </u><u>Find</u><u> </u><u>:</u><u>-</u><u> </u>
- Least Common denominator .
<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>
We have ,
> 1/8 , 2/9 , 3/12 .
The denominator of the fractions are ,
> 8 , 9 , 12
The LCM of 8,9,12 will be ,
2 |<u> </u><u>8</u><u> </u><u>,</u><u> </u><u>9</u><u> </u><u>,</u><u> </u><u>1</u><u>2</u><u> </u>
2 <u>| 4 , 9 , 6</u>
2 |<u> </u><u>2</u><u> </u><u>,</u><u> </u><u>9</u><u> </u><u>,</u><u> </u><u>3 </u>
3 |<u> </u><u>2</u><u> </u><u>,</u><u> </u><u>3 </u><u>,</u><u> </u><u>1</u><u> </u>
Therefore , LCM will be ,
> 2⁴ × 3² = 16 × 9 = 144
the solid is made up of 2 regular octagons, 8 sides, joined up by 8 rectangles, one on each side towards the other octagonal face.
from the figure, we can see that the apothem is 5 for the octagons, and since each side is 3 cm long, the perimeter of one octagon is 3*8 = 24.
the standing up sides are simply rectangles of 8x3.
if we can just get the area of all those ten figures, and sum them up, that'd be the area of the solid.
![\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=5\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(5)(24)\implies \stackrel{\textit{just for one octagon}}{A=60} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{two octagon's area}}{2(60)}~~+~~\stackrel{\textit{eight rectangle's area}}{8(3\cdot 8)}\implies 120+192\implies 312](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dap~~%20%5Cbegin%7Bcases%7D%20a%3Dapothem%5C%5C%20p%3Dperimeter%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D5%5C%5C%20p%3D24%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%285%29%2824%29%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bjust%20for%20one%20octagon%7D%7D%7BA%3D60%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Btwo%20octagon%27s%20area%7D%7D%7B2%2860%29%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7Beight%20rectangle%27s%20area%7D%7D%7B8%283%5Ccdot%208%29%7D%5Cimplies%20120%2B192%5Cimplies%20312)
Answer:
Step-by-step explanation:
Assuming we are doing an arithmetic sequence
It depends on where you start
If the first term is a₁ and the term number is n
each subsequent term is
aₙ = a₁ + 4(n - 1)
a₁₀ = a₁ + 4(10 - 1) = a₁ + 36
a₅₃ = a₁ + 4(53 - 1) = a₁ + 208
a₂₀₀ = a₁ + 4(200 - 1) = a₁ + 796
How about water, its always changing and moving.
Answer:
c
Step-by-step explanation:
1 1/2 cups x 2 bread = 12
12 cups x 3 for 1/3 per recipe =36