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jolli1 [7]
3 years ago
14

34% of $1000? Please help.

Mathematics
2 answers:
katrin [286]3 years ago
7 0
The answer is $340 because the formula is ?/1000=34/100 solving for the ?
yKpoI14uk [10]3 years ago
6 0
The answer is 34% of (US$ 1000) = <span>340 US$ 
~hope this helps! :D</span>
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Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions
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I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take z=y', so that z'=y'' and we're left with the ODE linear in z:

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\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0

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We can solve explicitly for a_n quite easily:

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and so on. Continuing in this way we end up with

a_n=\dfrac{a_1}{n!}

so that the solution to the ODE is

y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x

We also require the solution to satisfy y(0)=a_0, which we can do easily by adding and subtracting a constant as needed:

y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}
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