Proof with Step-by-step explanation:
Since it is given that f(x) is decreasing thus we infer that
![\frac{d}{dx}f(x)=f'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7Df%28x%29%3Df%27%28x%29%3C0)
Similarly it is given that g(x) is decreasing thus we infer that
![\frac{d}{dx}g(x)=g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7Dg%28x%29%3Dg%27%28x%29%3C0)
Now let ![y=fog=f[g(x)]\\\\](https://tex.z-dn.net/?f=y%3Dfog%3Df%5Bg%28x%29%5D%5C%5C%5C%5C)
Differentiating both sides with respect to 'x' and using chain rule of differentiation we get
![dy/dx=\frac{d}{dx}f[g(x)]\\\\y'=f'[g((x)]\times g'(x)\\\\\\](https://tex.z-dn.net/?f=dy%2Fdx%3D%5Cfrac%7Bd%7D%7Bdx%7Df%5Bg%28x%29%5D%5C%5C%5C%5Cy%27%3Df%27%5Bg%28%28x%29%5D%5Ctimes%20g%27%28x%29%5C%5C%5C%5C%5C%5C)
Now since both f'(x) and g'(x) are both negative(<0) we can infer that their product is always positive (>0)
![\therefore y'(x)>0](https://tex.z-dn.net/?f=%5Ctherefore%20y%27%28x%29%3E0)
Thus fog(x) is an increasing function.
Answer:
ty can buy 7 journals
Step-by-step explanation:
Answer:
![cm](https://tex.z-dn.net/?f=cm)
Step-by-step explanation:
![\pi \times 16 \times 50/360](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%2016%20%5Ctimes%2050%2F360)
![=6.981317](https://tex.z-dn.net/?f=%3D6.981317)
![\pi \times 7 \times 50/360](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%207%20%5Ctimes%2050%2F360)
![=3.054326](https://tex.z-dn.net/?f=%3D3.054326)
![4.5+4.5+6.981317+3.054326](https://tex.z-dn.net/?f=4.5%2B4.5%2B6.981317%2B3.054326)
![=19.035643](https://tex.z-dn.net/?f=%3D19.035643)
I believe the answer is x=4