Answer:
Power series representation of given f(x) is ![\sum^{\infty}_{n=0}(-1)^{n}(\frac{x^{6n+3}}{a^{6n+6}})](https://tex.z-dn.net/?f=%5Csum%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%28-1%29%5E%7Bn%7D%28%5Cfrac%7Bx%5E%7B6n%2B3%7D%7D%7Ba%5E%7B6n%2B6%7D%7D%29)
Step-by-step explanation:
Given that:
--- (1)
writing it in form
for which power series is:
---(2)
--- (3)
consider:
![u=\frac{x^{6}}{a^{6}}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7Bx%5E%7B6%7D%7D%7Ba%5E%7B6%7D%7D)
substituting above eq. in (3)
![f(x)=\frac{x^{3}}{a^{6}}\frac{1}{1-u}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx%5E%7B3%7D%7D%7Ba%5E%7B6%7D%7D%5Cfrac%7B1%7D%7B1-u%7D)
Expanding
using (2)
![=\frac{x^{3}}{a^{6}}\sum^{\infty}_{n=0}(-1)^{n}u^{n}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%5E%7B3%7D%7D%7Ba%5E%7B6%7D%7D%5Csum%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%28-1%29%5E%7Bn%7Du%5E%7Bn%7D)
Back-substituting value of u in above
![=\frac{x^{3}}{a^{6}}\sum^{\infty}_{n=0}(-1)^{n}(\frac{x^{6}}{a^{6}})^{n}\\=\sum^{\infty}_{n=0}(-1)^{n}(\frac{x^{6n+3}}{a^{6n+6}})](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%5E%7B3%7D%7D%7Ba%5E%7B6%7D%7D%5Csum%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%28-1%29%5E%7Bn%7D%28%5Cfrac%7Bx%5E%7B6%7D%7D%7Ba%5E%7B6%7D%7D%29%5E%7Bn%7D%5C%5C%3D%5Csum%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%28-1%29%5E%7Bn%7D%28%5Cfrac%7Bx%5E%7B6n%2B3%7D%7D%7Ba%5E%7B6n%2B6%7D%7D%29)
Answer:
Each bag has 5 coins.
Step-by-step explanation:
There are 20 total coins on the right side of the equation. if both sides are equal then you set up a two step equation.
3b + 5 = 20
-5. -5
3b = 15
divide both side by 3
b=5
It is a Rational Number because it eventually ends.
Answer:
108 inches = 9 feet
3 yards = 9 feet
274.32 centimeters = 9 feet
I hope this helps you!
-Mikayla
To obtain 58 percent of 18 multiply 18 by 0.58, because 58 percent is equal to 58/100. That said, your result rounded to two decimals is 10.44.
This answers what is 58% of 18. If you have a currency, such as in the case of 18 dollars, proceed as outlined in the example right below.