(
(
4
/10
x)(6)
/4
x)(2)
/3
Product: 2
/5
x^2
Simplified: You can't simply that.
(I hope this is correct, correct me if I'm wrong.)
Answer:
Step-by-step explanation:
From the law of variation,
y <> 1/x, where <> is the constant of proportionality. Therefore
y = k/x where k is a constant
3 = k/5 and k = 15
To find x when y = 2.5(5/2)
Go back to the second equation
y = k/x
5/2 = 15/x
When you cross multiply
5x = 30.
Divide through by 5,
x = 6.
Answer:
Step-by-step explanation:
The rate of change of the situation is known as the slope:
Slope = Δy/Δx
Slope = y2-y1/x2-x1
From the graph, x2 = 10.5, x1 = 0. y2 = 32, y1 = 0
Slope = 32-0/10.5-0
Slope = 32/10.5
Slope = 3.047
Hence the rate of change is 3.047 ounces per minutes and the situation represents the slope of the graph.
Answer:
[/tex]
Step-by-step explanation:
The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence
![1,1,1,2,3,4,5,6,...](https://tex.z-dn.net/?f=1%2C1%2C1%2C2%2C3%2C4%2C5%2C6%2C...)
the generating function would be
![P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\](https://tex.z-dn.net/?f=P%28x%29%3D1%2Bx%2Bx%5E2%2B2x%5E3%2B3x%5E4%2B4x%5E5%2B5x%5E6%2B...%5C%5C)
we can multiply P(x) by x to get
Note that
![P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)](https://tex.z-dn.net/?f=P%28x%29-xP%28x%29%3D1%2B%282x%5E3-x%5E3%29%2B%283x%5E4-2x%5E4%29%2B%284x%5E5-3x%5E5%29%2B%285x%5E6-4x%5E6%29%2B...%5C%5C%20%20%20%5C%5C%3D1%2Bx%5E3%2Bx%5E4%2Bx%5E5%2Bx%5E6%2B...%3D1%2Bx%5E3%281%2Bx%2Bx%5E2%2Bx%5E3%2Bx%5E4%2B...%29)
which for
can be rewritten as
![(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}](https://tex.z-dn.net/?f=%281-x%29P%28x%29%3D1%2B%5Cdfrac%7Bx%5E3%7D%7B%281-x%29%7D%20%5Cquad%20%5CRightarrow%20%5C%5C%5C%5CP%28x%29%3D%5Cdfrac%7B1%7D%7B%281-x%29%7D%2B%5Cdfrac%7Bx%5E3%7D%7B%281-x%29%5E2%7D)
Answer:
81
Step-by-step explanation:
x² + 18x
x² + 2(x)(9) + 9²
x² + 2(x)(9) + 81
(x + 9)²