ANSWER
![S_5=91\frac{10}{81}](https://tex.z-dn.net/?f=S_5%3D91%5Cfrac%7B10%7D%7B81%7D)
EXPLANATION
The sum of the first
terms of a geometric sequence is given by;
![S_n=\frac{a_1(1-r^n)}{1-r} ,-1](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D%20%2C-1%3C%5C%3Ar%3C%5C%3A1)
Where
, is the number of terms and
is the first term.
When
, we have
, we get;
![S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B81%281-%28%5Cfrac%7B1%7D%7B9%7D%29%5E5%29%7D%7B1-%5Cfrac%7B1%7D%7B9%7D%7D)
![S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B81%281-%5Cfrac%7B1%7D%7B59049%7D%29%7D%7B1-%5Cfrac%7B1%7D%7B9%7D%7D)
![S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B81%28%5Cfrac%7B59048%7D%7B59049%7D%29%7D%7B%5Cfrac%7B8%7D%7B9%7D%7D)
![S_5=\frac{7381}{81}](https://tex.z-dn.net/?f=S_5%3D%5Cfrac%7B7381%7D%7B81%7D)
![S_5=91\frac{10}{81}](https://tex.z-dn.net/?f=S_5%3D91%5Cfrac%7B10%7D%7B81%7D)
Answer:
Step-by-step explanation:
![\frac{dy}{dx}=x^{2}(y-1)\\\frac{1}{y-1} \text{ } dy=x^{2} \text{ } dx\\\int \frac{1}{y-1} \text{ } dy=\int x^{2} \text{ } dx\\\ln|y-1|=\frac{x^{3}}{3}+C\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3Dx%5E%7B2%7D%28y-1%29%5C%5C%5Cfrac%7B1%7D%7By-1%7D%20%5Ctext%7B%20%7D%20dy%3Dx%5E%7B2%7D%20%5Ctext%7B%20%7D%20dx%5C%5C%5Cint%20%5Cfrac%7B1%7D%7By-1%7D%20%5Ctext%7B%20%7D%20dy%3D%5Cint%20x%5E%7B2%7D%20%5Ctext%7B%20%7D%20dx%5C%5C%5Cln%7Cy-1%7C%3D%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2BC%5C%5C)
From the initial condition,
![\ln|3-1|=\frac{0^{3}}{3}+C\\\ln 2=C](https://tex.z-dn.net/?f=%5Cln%7C3-1%7C%3D%5Cfrac%7B0%5E%7B3%7D%7D%7B3%7D%2BC%5C%5C%5Cln%202%3DC)
So we have that ![\ln |y-1|=\frac{x^{3}}{3}+\ln 2\\e^{\frac{x^{3}}{3}+\ln 2}=y-1\\2e^{\frac{x^{3}}{3}}=y-1\\y=2e^{\frac{x^{3}}{3}}+1](https://tex.z-dn.net/?f=%5Cln%20%7Cy-1%7C%3D%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B%5Cln%202%5C%5Ce%5E%7B%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B%5Cln%202%7D%3Dy-1%5C%5C2e%5E%7B%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%7D%3Dy-1%5C%5Cy%3D2e%5E%7B%5Cfrac%7Bx%5E%7B3%7D%7D%7B3%7D%7D%2B1)
I believe that the number of miles traveled would be 8. This is because you would subtract $5.00 from the $13.80 and then divided by $1.10.
Answer:How many fives are in 15? ... How many three-fourths are in 2? ... There are 6 half-sized pieces in 3 wholes. ... and we can see that there are 4 wholes with 6 sixths in each whole, so there are 4\times 6 = 24 sixths in 4. ... Each whole yields a two-thirds and one half of another two-thirds, therefore 3 sets of two-thirds can be ...
Step-by-step explanation: