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Tomtit [17]
3 years ago
15

¿Cuál es la capital final de $3800 al 4% anual durante 14 años?

Mathematics
1 answer:
dedylja [7]3 years ago
3 0

La respuesta es:

2780.37

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B. 28.26

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Find a compact form for generating functions of the sequence 1, 8,27,... , k^3
pantera1 [17]

This sequence has generating function

F(x)=\displaystyle\sum_{k\ge0}k^3x^k

(if we include k=0 for a moment)

Recall that for |x|, we have

\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k

Take the derivative to get

\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k

\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k

Take the derivative again:

\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k

\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k

Take the derivative one more time:

\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k

\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k

so we have

\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}

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3 years ago
The Rodriguez family went to the movies on Friday night. At AMC, adult tickets are $13 and children tickets are $7. The family o
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Alonzo will participate in a charity walkathon.Her Mother will donate $10 for Alonzo participation plus and additional $2 for ea
umka2103 [35]

Answer:

Total donation by Alonzo's mother = $40.

Step-by-step explanation:

Complete Question.

Alonzo will participate in a charity walkathon.Her Mother will donate $10 for Alonzo participation plus and additional $2 for each mile that Alonzo walks.

If Alonzo walks 15 miles, What will be the amount of her mother’s donation?

Alonzo's mum donates $10 for participation and an additional $2 per mile.

Alonzo walks 15 miles, this translates to an additional donation of (15×$2) = $30

Total donation by Alonzo's mother = $10 + $30 = $40.

Hope this Helps!!!

5 0
3 years ago
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