We can use the fact that, for 
,
Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)
By the ratio test, this series converges if
so the series has radius of convergence 
.
3.2128 is a rational number
Hello!
To solve, we want to isolate the x on one side of the equation. We can use inverse operations to put numbers on the other side to find x.
First we undistribute our parentheses.
12x-66+15=21
We subtract 15 from both sides (it cancels out the 15 on the left side, making it 0).
12x-66=6
Now we add 66 to both sides, as -66+66=0
12x=72
Finally, we divide both sides by 12.
x=6
I hope this helps!
Answer:
10.37
Step-by-step explanation:
find the area of the whole rectangle which is 30 then find the area of the circle which is 19.63 then subtract 30-19.63
Answer:
Step-by-step explanation:
Total outcomes
Favorable outcomes
Probability
- P( < 3) = favorable outcomes / total outcomes = 2/6 = 1/3
