Answer:
See below,please.
Step-by-step explanation:
Volume of water = meter reading (11) - meter reading (8)
=
![= 4598 - 4559 = 39 {m}^{3}](https://tex.z-dn.net/?f=%20%3D%204598%20-%204559%20%3D%2039%20%7Bm%7D%5E%7B3%7D%20)
Answer:
6x +3w
Step-by-step explanation:
3(2x + w)
Distribute
3*2x +3*w
6x +3w
I'm guessing the sum is supposed to be
![\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5E%5Cinfty%5Cfrac%7B10%7D%7B%285k-1%29%285k%2B4%29%7D)
Split the summand into partial fractions:
![\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%285k-1%29%285k%2B4%29%7D%3D%5Cdfrac%20a%7B5k-1%7D%2B%5Cdfrac%20b%7B5k%2B4%7D)
![1=a(5k+4)+b(5k-1)](https://tex.z-dn.net/?f=1%3Da%285k%2B4%29%2Bb%285k-1%29)
If
, then
![1=b(-4-1)\implies b=-\frac15](https://tex.z-dn.net/?f=1%3Db%28-4-1%29%5Cimplies%20b%3D-%5Cfrac15)
If
, then
![1=a(1+4)\implies a=\frac15](https://tex.z-dn.net/?f=1%3Da%281%2B4%29%5Cimplies%20a%3D%5Cfrac15)
This means
![\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}](https://tex.z-dn.net/?f=%5Cdfrac%7B10%7D%7B%285k-1%29%285k%2B4%29%7D%3D%5Cdfrac2%7B5k-1%7D-%5Cdfrac2%7B5k%2B4%7D)
Consider the
th partial sum of the series:
![S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)](https://tex.z-dn.net/?f=S_n%3D2%5Cleft%28%5Cdfrac14-%5Cdfrac19%5Cright%29%2B2%5Cleft%28%5Cdfrac19-%5Cdfrac1%7B14%7D%5Cright%29%2B2%5Cleft%28%5Cdfrac1%7B14%7D-%5Cdfrac1%7B19%7D%5Cright%29%2B%5Ccdots%2B2%5Cleft%28%5Cdfrac1%7B5n-1%7D-%5Cdfrac1%7B5n%2B4%7D%5Cright%29)
The sum telescopes so that
![S_n=\dfrac2{14}-\dfrac2{5n+4}](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac2%7B14%7D-%5Cdfrac2%7B5n%2B4%7D)
and as
, the second term vanishes and leaves us with
![\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5E%5Cinfty%5Cfrac%7B10%7D%7B%285k-1%29%285k%2B4%29%7D%3D%5Clim_%7Bn%5Cto%5Cinfty%7DS_n%3D%5Cfrac17)
The equation you had:
6x + 5y = 45
Solve for Y:
5y = (-6x) + 45 divide by 5
y = (-6/5)x + 9
y = -1 1/5x +9
First things first.. What type of triangle
If u are taking about a normal triangle here is some:
∠60+∠60+∠60
∠30+∠90+∠60
∠11+∠82+∠87