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2 years ago

What is 3-7/12 in a mixed number

Mathematics

1 answer:

Sidana [21]2 years ago

5 0

Answer:

3 1/2

Step-by-step explanation:

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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

in order to be invited to tutoring or extension activities a student's performance must be at least 20 points higher or lower th

Ad libitum [116K]

Answer:

p ≤ 85 or p ≥ 125

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

4 cot theta = tan theta how do I I find the value of quadrant?

Ray Of Light [21]

Answer:

4cotα=tanα

4(1/tanα)=tanα

(4/tanα)=tanα

cross multiply

=> 4=tan²α

√4=√tan²α

±2=tanα

α=arc( tan) |2|

α=63.4° ( in first quadrant)

and

α=180+63.4=243.4 in the third quadrant

since we also found a negative answer( i.e –2) then α also lies in quadrants where it gives a negative value(i.e second and fourth quadrants)

α=180–63.4=116.6° in the second quadrant

α=360–63.4=296.6 in the fourth quadrant

therefore theta( in my case, alpha) lies in all four quadrants and is equal to:

α=63.4°,243.4°,116.6°and 296.6°

5 0

3 years ago

The paper feed on a copying machine has room for a stack of paper 4.0 cm high. If 10 sheets of paper are 0.08 cm thick, how many

Ierofanga [76]

I don't know but I know it is going to be a lot

7 0

2 years ago

(2x-1)^2= Some one plz help.....

Arlecino [84]

Answer: 4x^2−4x+1

Step-by-step explanation:

(2x-1)^2

Square of Difference: (a−b)^2=a^2−2ab+b^2.

(2x)^2−2*2x+1

Multiplication Distributive Property: (xy)^a= $x^{a} y^{a}$

2^2x^2−2*2x+1

4x^2−2*2x+1

4x^2−4x+1

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)

- Cutiepatutie ☺❀❤

3 0

2 years ago