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:
x=16
Step-by-step explanation:
You multiply 4 by 4 because when you multiply 3by 4 you get 12, when you multiply 5by 4 you get twenty and since they are similar triangles you have to multiply 4 by 4
Answer: y = -3
<u>Step-by-step explanation:</u>
-8x - 5y = -1
<u>+8x </u> <u>+8x </u>
-5y = 8x - 1
<u> ÷-5 </u> <u> ÷-5</u> <u>÷-5</u>
y = ![-\frac{8}{5}x + \frac{1}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B8%7D%7B5%7Dx%20%2B%20%5Cfrac%7B1%7D%7B5%7D)
y(2) = ![-\frac{8}{5}(2) + \frac{1}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B8%7D%7B5%7D%282%29%20%2B%20%5Cfrac%7B1%7D%7B5%7D)
= ![-\frac{16}{5} + \frac{1}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B16%7D%7B5%7D%20%2B%20%5Cfrac%7B1%7D%7B5%7D)
= ![-\frac{15}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B15%7D%7B5%7D)
= -3
Answer:
-14. Aunque podría estar equivocado. Espero poder ayudar
Step-by-step explanation: