Answer:
3(3a+4)
Step-by-step explanation:
3(3a+4)
use distributive property
9a+12
Answer:
r = 6
Step-by-step explanation:
Hello!
-8 - 2(7r + 1) = -94
Add 8 to both sides
-2(7r + 1) = -86
Divide both sides by -2
7r + 1 = 43
Subtract 1 from both sides
7r = 42
Divide both sides by 7
r = 6
Hope this Helps
Looks like your function is
![f(x)=\dfrac x{6x^2+1}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%20x%7B6x%5E2%2B1%7D)
Rewrite it as
![f(x)=\dfrac x{1-(-6x^2)}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%20x%7B1-%28-6x%5E2%29%7D)
Recall that for
, we have
![\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n](https://tex.z-dn.net/?f=%5Cdfrac1%7B1-x%7D%3D%5Cdisplaystyle%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En)
If we replace
with
, we get
![f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%20x%5Csum_%7Bn%3D0%7D%5E%5Cinfty%5Cfrac%28-6x%5E2%29%5En%3D%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20%28-6%29%5En%20x%5E%7B2n%2B1%7D)
By the ratio test, the series converges if
![\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cleft%7C%5Cfrac%7B%28-6%29%5E%7Bn%2B1%7D%20x%5E%7B2%28n%2B1%29%2B1%7D%7D%7B%28-6%29%5En%20x%5E%7B2n%2B1%7D%7D%5Cright%7C%3D6%7Cx%5E2%7C%5Clim_%7Bn%5Cto%5Cinfty%7D1%3D6%7Cx%7C%5E2%3C1)
Solving for
gives the interval of convergence,
![|x|^2](https://tex.z-dn.net/?f=%7Cx%7C%5E2%3C%5Cdfrac16%5Cimplies%7Cx%7C%3C%5Cdfrac1%7B%5Csqrt6%7D%5Cimplies%20-%5Cdfrac1%7B%5Csqrt%206%7D%3Cx%3C%5Cdfrac1%7B%5Csqrt%206%7D)
We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.
Answer:
459
Step-by-step explanation:
First line:
clock showing 9 o'clock + clock showing 9 o'clock + clock showing 3 o'clock = 9 + 9 + 3 = 21
Second line:
The calculators look exactly the same.
3 * calculators = 30
1 calculator = 10
Third line:
1 bulb + 1 bulb - 1 bulb = 15
Since 1 bulb - 1 bulb = 0, we have 1 bulb + 0 = 15, or
1 bulb = 15
Last line:
Clock showing 9 o'clock = 9
Calculator = 10
3 bulbs = 3 * 15 = 45
Total = 9 + 10 * 45 = 9 + 450 = 459