SOLUTION
The question simply means that we should find the sum to infinity of the geometric series.
The formula of sum to infinity of a geometric serie is given by
![S_{\infty}=\frac{a}{1-r}](https://tex.z-dn.net/?f=S_%7B%5Cinfty%7D%3D%5Cfrac%7Ba%7D%7B1-r%7D)
Where
![\begin{gathered} S_{\infty}\text{ is the sum to infinity} \\ \\ a\text{ is the first term = 1} \\ \\ r\text{ is the common ratio = }\frac{2}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20S_%7B%5Cinfty%7D%5Ctext%7B%20is%20the%20sum%20to%20infinity%7D%20%5C%5C%20%20%5C%5C%20a%5Ctext%7B%20is%20the%20first%20term%20%3D%201%7D%20%5C%5C%20%20%5C%5C%20r%5Ctext%7B%20is%20the%20common%20ratio%20%3D%20%7D%5Cfrac%7B2%7D%7B3%7D%20%5Cend%7Bgathered%7D)
So, this becomes
![\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ \\ S_{\infty}=\frac{1}{1-\frac{2}{3}} \\ \\ S_{\infty}=\frac{1}{\frac{3-2}{3}} \\ \\ S_{\infty}=\frac{1}{\frac{1}{3}} \\ \\ S_{\infty}=3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20S_%7B%5Cinfty%7D%3D%5Cfrac%7Ba%7D%7B1-r%7D%20%5C%5C%20%20%5C%5C%20S_%7B%5Cinfty%7D%3D%5Cfrac%7B1%7D%7B1-%5Cfrac%7B2%7D%7B3%7D%7D%20%5C%5C%20%20%5C%5C%20S_%7B%5Cinfty%7D%3D%5Cfrac%7B1%7D%7B%5Cfrac%7B3-2%7D%7B3%7D%7D%20%5C%5C%20%20%5C%5C%20S_%7B%5Cinfty%7D%3D%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%5C%5C%20%20%5C%5C%20S_%7B%5Cinfty%7D%3D3%20%5Cend%7Bgathered%7D)
Therefore, option b is the correct answer
Answer:
I think 30
Step-by-step explanation:
Answer:
<h2>C.</h2>
Step-by-step explanation:
The equationof a circle:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
<em>(h, k)</em><em> - center</em>
<em>r</em><em> - radius</em>
<em />
We have <em>center = (4, -1) → h = 4, k = -1</em>, and <em>r = 9</em>.
Substitute:
![(x-4)^2+(y-(-1))^2=9^2\\\\\huge\boxed{(x-4)^2+(y+1)^2=81}](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y-%28-1%29%29%5E2%3D9%5E2%5C%5C%5C%5C%5Chuge%5Cboxed%7B%28x-4%29%5E2%2B%28y%2B1%29%5E2%3D81%7D)
Answer:
$7.85
Step-by-step explanation:
2 pizzas at 11.99=23.98
4 soft drinks at 1.85=$7.40
23.98+7.40=31.38
31.38/4=7.845
Each friend pays $7.845, or $7.85 .........
Answer:
12 feets
Step-by-step explanation:
Let the area of the pool be Length×width
There will be 2lengths and 2widths as well so the perimeter of the pool will be the addition of all the sides of the pool i.e 2L + 2W = 96... (1)
And since the length of the pool is 3 times its width, we have
L = 3W... (2)
Substituting equation 2 into 1 to get the width 'W'
2(3W) + 2W = 96
6W + 2W = 96
8W = 96
W = 96/8
W = 12feets
The width of the pool is 12feets