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2 years ago

14

Is prime or composite?

2 answers:

kakasveta [241]2 years ago

8 0

Answer:

Is wut prime or composite

Step-by-step explanation:

jeyben [28]2 years ago

4 0

Answer:

What do you mean? Did you forget to add a picture or something? Please reply to my comment if so, and I'll tell you the answer.

Do you want to know what a prime or composite number is? If so, a prime number is a number that has no factors except for itself and 1. A factor is what you multiply by a number to get another number. A composite number has factors other than itself and 1.

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2 years ago

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3 years ago

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Evaluate the expression for x = 6 <br>3 x + 5 =

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23

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2 years ago

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The figure below has a perimeter of 20 cm. Jinaiya wants to scale this figure by a factor of 0.75

Dmitrij [34]

Answer:

15cm

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2 years ago

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

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

5 0

3 years ago