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2 years ago

Which expression is equivalent to (10 +7r−r2)+(−6r2−18+5r)

2 answers:

5 0

Answer: -7r^2+12r-8
Explanation;
1. Combine -r^2 and -6r^2 to get -7r^2
2. Subtract 18 from 10 to get -8
3. Combine 7r and 5r to get 12r

vichka [17]2 years ago

4 0

Answer: after adding them -7r^2+12r-8

Step-by-step explanation: add them

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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

2 years ago

Phillip's Soup Kitchen charges the same price, $8.95, for a bowl of any of their soups. The Rag-dale Family Reunion was being he

777dan777 [17]

P = 8.95R Hope this helps!!

8 0

3 years ago

A pretzel recipe calls for 3.325

Zepler [3.9K]

Answer: 0.35

Step-by-step explanation:

3.325 divided by 9.5 = 0.35

3 0

2 years ago

Find the solution and enter your answer as an ordered pair (x, y). Be sure to include parentheses and a comma.

ipn [44]

Answer:

Step-by-step explanation:

the first one is:

x= 3

y= 2

the second one is:

x= -2

y= 8

8 0

1 year ago

Line segment AB is the diameter of a circle. Find the center of the circle if:

katovenus [111]

Answer:

$midpoint = \frac{-1 + -5}{2} , \frac{7+ 2}{2}$

(-3, $\frac{9}{2\\}$ ) is the center of the circle

Step-by-step explanation:

You use the midpoint of the two point given to us.

Hope this helped

4 0

2 years ago

Read 2 more answers