Answer:
160,000,000,000,000
Step-by-step explanation:
M= 200,000,000,000,000
P= $40,000,000,000,000
200,000,000,000,000 - 40,000,000,000,000=
160,000,000,000,000
All you have to do is do 10x10 14/13 times or cause it's 10 just add 14/13 zeros
Me don’t understand it i need more info
Answer:
please make the image less blurry
Step-by-step explanation:
Cos(x) is infinitely differentiable, can be expanded using Taylor's series.
The series about c can be expressed as
![f(x)=\sum_{n=0}^{\infty}\frac{f^{n}(c)}{n!}(x-c)^n](https://tex.z-dn.net/?f=f%28x%29%3D%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7Bf%5E%7Bn%7D%28c%29%7D%7Bn%21%7D%28x-c%29%5En)
Substituting cos(x), c= π /4,we have
![cos(x)=\sum_{n=0}^{\infty}\frac{f^{n}(\frac{\pi}{4})}{n!}(x-\frac{\pi}{4})^n](https://tex.z-dn.net/?f=cos%28x%29%3D%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%5Cfrac%7Bf%5E%7Bn%7D%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%7D%7Bn%21%7D%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5En)
and since
![f'(\frac{\pi}{4})=-sin(\frac{\pi}{4})=-\sqrt{2}/2](https://tex.z-dn.net/?f=f%27%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-sin%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-%5Csqrt%7B2%7D%2F2)
![f"(\frac{\pi}{4})=-cos(\frac{\pi}{4})=-\sqrt{2}/2](https://tex.z-dn.net/?f=f%22%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-cos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-%5Csqrt%7B2%7D%2F2)
![f^{(iii)}(\frac{\pi}{4})=sin(\frac{\pi}{4})=\sqrt{2}/2](https://tex.z-dn.net/?f=f%5E%7B%28iii%29%7D%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3Dsin%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D%5Csqrt%7B2%7D%2F2)
![f^{(iv)}(\frac{\pi}{4})=cos(\frac{\pi}{4})=\sqrt{2}/2](https://tex.z-dn.net/?f=f%5E%7B%28iv%29%7D%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3Dcos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D%5Csqrt%7B2%7D%2F2)
we can simplify the expansion to
![cos(x)=\frac{\sqrt{2}}{2}(1-(x-\frac{\pi}{4})/1!-(x-\frac{\pi}{4})^2/2!+(x-\frac{\pi}{4})^3/3!+(x-\frac{\pi}{4})^4/4!-(x-\frac{\pi}{4})^5/5!-...)](https://tex.z-dn.net/?f=cos%28x%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%281-%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%2F1%21-%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5E2%2F2%21%2B%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5E3%2F3%21%2B%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5E4%2F4%21-%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5E5%2F5%21-...%29)
Note that the sign pattern is - - + + - - + + - - ..... following the sign pattern of the derivatives of cos(x).