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2 years ago

Find the output, y, when the input, x, is 7. y=__

Mathematics

2 answers:

serg [7]2 years ago

5 0

Answer:

y=4

Step-by-step explanation:

Read off the graph. The corresponding y-coordinate when the x-coordinate is 7 is 4.

nata0808 [166]2 years ago

4 0

Answer:

Step-by-step explanation:

You look for the point on the teal line that has an x-coordinate of 7.

You could also go to the point (7,0), which is on the x-axis, and draw an imaginary vertical line and see which point hits it.

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Anastaziya [24]

Answer:

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Step-by-step explanation:

25% of 4 gallons is 1 gallons, which means that 75% of the hand sanitizer is not alcohol, and is 3 gallons. since that is the amount of not alcohol, and we want it to be 50% solution, it has to be 3 gallons of alcohol in total, and 3-1=2.

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dlinn [17]

Answer:

y=3x+2

Step-by-step explanation:

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2 years ago

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liubo4ka [24]

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2 years ago

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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

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

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3 years ago