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3 years ago

NEED HELP NOW!!

Mathematics

2 answers:

irinina [24]3 years ago

8 0

Answer:

i am not sure to my answer

my answer is letter D

Komok [63]3 years ago

8 0

Answer:

yes answer is d.. this is clear

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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

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

5 0

3 years ago

(X to the fourth power) squared equals

Viktor [21]

Answer:

$(x^4)^2=x^8$

Step-by-step explanation:

Because of the power of a power property, which states that $(x^n)^m=x^{n\times{m}}$ , where m and n are real numbers, the expression you mentioned can be simplified by applying this property like this: $(x^4)^2=x^{4\times2}=x^8$

4 0

2 years ago

Sin and cos <br>sin Y= ___ in fraction form if you can explain it that would be very helpful

Valentin [98]

Check the picture below.

6 0

3 years ago

4 times[9-6 divided by three

djyliett [7]

Answer:

Step-by-step explanation:

9-6/3=9-2=7

4*7=28

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3 years ago

What is slope of line f?

padilas [110]

<h3>Answer: The fraction 2/5</h3>

=========================================================

Explanation:

We have three points marked on this diagonal line. Each point has integer or whole number coordinates. I find it is easiest to start with the y intercept, which in this case, is the point (0,0). This is the origin.

From the origin, move 2 units up and 5 units to the right to arrive at the next neighboring point (5,2).

This shows that,

slope = rise/run = 2/5

The rise indicates how much we have gone up or down. The run is the amount you move to the right. If the rise is negative, then you have gone downhill. By "downhill", I mean when the graph is read from left to right.

-------

Optionally you can use the slope formula

m = (y2-y1)/(x2-x1)

with any two points you want from the graph.

4 0

2 years ago