I see that 16 increases by 2 to get 18.
I see that 18 increases by 2 to get 20.
I see that 20 does the same to get 22.
SO - using inductive reasoning, I deduce that the number after 22 will be 24.
I deduce that the number after 24 will be 26.
Answer:
152
Step-by-step explanation:
So first I find the area of the big rectangle going down, which is 14x8=112
And then I do the flap thingies on the side: 5x4=20x2=40
112+40=152
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)
Answer:
5 trapezoid 6 polygon 7 Parrelogram 8squaare
1/3 = 4/12
(4/12 + 11/12) * 2/3
= 15/12 * 2/3
15/ 12 can also be written as 5/4
5/4 * 2/3 = 10/12
10/12 can be simplified into 5/6
Therefore, the answer is 5/6