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2 years ago

The domain of the following relation has how many elements?

Mathematics

1 answer:

Ivahew [28]2 years ago

5 0

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1

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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

A circle in the xy plane has a center at (3/4, 1/2)

Leokris [45]

Answer:

(x - 3/4)^2 + (y - 1/2)^2 = r^2

<em>Brainliest, please!</em>

Step-by-step explanation:

Equation of a circle: (x - h)^2 + (y - k)^2 = r^2

(x - 3/4)^2 + (y - 1/2)^2 = r^2

We do not have enough information to find the radius. Were you given another point that lies on the circle?

3 0

2 years ago

Find the slope of the line

morpeh [17]

Slope is 2/5

Step by step you go up 2 and over 5 to reach the next point

4 0

2 years ago

Read 2 more answers

An unbiased coin is tossed 15 times. In how many ways can the coin land tails either exactly 8 times orexactly 5 times?

Kitty [74]

Answer:

Probability to get tails exactly 8 times or exactly 5 times is 0.29

Step-by-step explanation:

No of ways the coins lands tails exactly 8 times

P(8) = 15C8 × $0.5^{8}$ × $0.5^{15-8}$

No of ways the coin lands tails exactly 5 times

P(5) = 15C5 × $0.5^{5}$ × $0.5^{15-5}$

Probability to get tails exactly 8 times or 5 times

P(8)+P(5) = 15C8 × $0.5^{15}$ + 15C5 × $0.5^{15}$

P = $0.5^{15}$ ( 15C8 + 15C5 )

P = $0.5^{15}$ ( ( $\frac{15!}{8!(15-8)!}$ ) + ( $\frac{15!}{5!(15-5)!}$ ) )

P = $0.5^{15}$ ( 6435 + 3003 )

P = $0.5^{15}$ ( 9438)

P = $0.5^{14}$ ( 4719)

P = $\frac{4719}{16384}$

P = 0.29

8 0

2 years ago

4x - 2y = 5<br> y= 2x + 10

Helga [31]

Answer:

There is no solution

Step-by-step explanation:

4x - 2y = 5 --> 4x - 2(2x + 10) = 5

4x - 4x - 20 = 5

4x - 4x -25 = 0

Final answer is -25 = 0 and so therefor it is no solution

7 0

2 years ago