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:
Greater Than
Step-by-step explanation:
edge
A) P(t) = Po(1 - 0.06)^t
P(t) = Po(0.94)^t
where Po is the initial population of the fish and t is the time.
b.) Monthly rate of decrease = 6%/12 = 0.5%
Answer:
7.50 stuped
Step-by-step explanation:
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Answer:
1)v=-2/45 2)y=-6.31
Step-by-step explanation:
1) -9/4v+4/5=7/8
-9(10)v+4(8)=7(5)
-90v+32=35
-90v=4
v=-4/90
v=-2/45
2)7.3y-5.81=-51.9
7.3y=-51.9+5.81
7.3y=-46.09
y=-6.31