Answer:
It is called this
Step-by-step explanation:
Since the three points are all on the same line, they are called collinear points.
#20)
18 cups together but ratio of purple to orange = 4:5
4 + 5 = 9
so 18/ 9 = 2
2 x 4(cups of purple) = 8
2 x 5(cups of orange) = 10
Answer:
10 cups of orange
Yes, because a negative number multiply by itself it is positive.
Answer:
![f_{avg}=\frac{1}{e-1}](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D)
Step-by-step explanation:
We are given that a function
![f(x)=2lnx](https://tex.z-dn.net/?f=f%28x%29%3D2lnx)
We have to find the average value of function on the given interval [1,e]
Average value of function on interval [a,b] is given by
![\frac{1}{b-a}\int_{a}^{b}f(x)dx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bb-a%7D%5Cint_%7Ba%7D%5E%7Bb%7Df%28x%29dx)
Using the formula
![f_{avg}=\frac{1}{e-1}\int_{1}^{e}lnx dx](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%5Cint_%7B1%7D%5E%7Be%7Dlnx%20dx)
By Parts integration formula
![\int(uv)dx=u\int vdx-\int(\frac{du}{dx}\int vdx)dx](https://tex.z-dn.net/?f=%5Cint%28uv%29dx%3Du%5Cint%20vdx-%5Cint%28%5Cfrac%7Bdu%7D%7Bdx%7D%5Cint%20vdx%29dx)
u=ln x and v=dx
Apply by parts integration
![f_{avg}=\frac{1}{e-1}([xlnx]^{e}_{1}-\int_{1}^{e}(\frac{1}{x}\times xdx))](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%28%5Bxlnx%5D%5E%7Be%7D_%7B1%7D-%5Cint_%7B1%7D%5E%7Be%7D%28%5Cfrac%7B1%7D%7Bx%7D%5Ctimes%20xdx%29%29)
![f_{avg}=\frac{1}{e-1}(elne-ln1-[x]^{e}_{1})](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%28elne-ln1-%5Bx%5D%5E%7Be%7D_%7B1%7D%29)
![f_{avg}=\frac{1}{e-1}(e-0-e+1)=\frac{1}{e-1}](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%28e-0-e%2B1%29%3D%5Cfrac%7B1%7D%7Be-1%7D)
By using property lne=1,ln 1=0
![f_{avg}=\frac{1}{e-1}](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D)
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