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nydimaria [60]
3 years ago
11

Winton wants to find the volume of a cube. He uses the formula for volume of a cube V = s to the power of 3 where s is the lengt

h of one side of the cube. if s = 0.5 centimeter, what is the volume of the cube?
Mathematics
1 answer:
VARVARA [1.3K]3 years ago
8 0

Answer:

Answer: 0.125 cm^3

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iogann1982 [59]

If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

then

y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

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We can solve the recurrence exactly by substitution:

a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0

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y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

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\boxed{y(x)=a_0e^{-2x}}

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Answer:

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