Five eighths times seven elevenths =
5/8 x 7/11 =
35/88
Answer:
108 meters with the formula lxhxw
Answer:
40 ft squared
Step-by-step explanation:
On the top right corner cut the shape and you will have a length of 4 ft and width of 2 ft. 4ft x 2ft = 8ft squared. Now your other shape at the bottom which would be a big rectangle has a width of 8ft and a length of 4ft. 8ft x 4ft = 32 ft squared. Now 8ft squared + 32 ft squared = 40 ft squared that would be its area.
Answer:
![\dfrac{d}{dx}f(x)=\dfrac{e^{2x}+e^{-2x}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cdfrac%7Be%5E%7B2x%7D%2Be%5E%7B-2x%7D%7D%7B2%7D)
Step-by-step explanation:
It is given that
![\sinh x=\dfrac{e^x-e^{-x}}{2}](https://tex.z-dn.net/?f=%5Csinh%20x%3D%5Cdfrac%7Be%5Ex-e%5E%7B-x%7D%7D%7B2%7D)
![\cosh x=\dfrac{e^x+e^{-x}}{2}](https://tex.z-dn.net/?f=%5Ccosh%20x%3D%5Cdfrac%7Be%5Ex%2Be%5E%7B-x%7D%7D%7B2%7D)
![f(x)=\sinh x\cosh x=](https://tex.z-dn.net/?f=f%28x%29%3D%5Csinh%20x%5Ccosh%20x%3D)
Using the given hyperbolic functions, we get
![f(x)=\dfrac{e^x-e^{-x}}{2}\times \dfrac{e^x+e^{-x}}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Be%5Ex-e%5E%7B-x%7D%7D%7B2%7D%5Ctimes%20%5Cdfrac%7Be%5Ex%2Be%5E%7B-x%7D%7D%7B2%7D)
![f(x)=\dfrac{(e^x)^2-(e^{-x})^2}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B%28e%5Ex%29%5E2-%28e%5E%7B-x%7D%29%5E2%7D%7B4%7D)
![f(x)=\dfrac{e^{2x}-e^{-2x}}{4}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Be%5E%7B2x%7D-e%5E%7B-2x%7D%7D%7B4%7D)
Differentiate both sides with respect to x.
![\dfrac{d}{dx}f(x)=\dfrac{d}{dx}\left(\dfrac{e^{2x}-e^{-2x}}{4}\right )](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cdfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cdfrac%7Be%5E%7B2x%7D-e%5E%7B-2x%7D%7D%7B4%7D%5Cright%20%29)
![\dfrac{d}{dx}f(x)=\left(\dfrac{2e^{2x}-(-2)e^{-2x}}{4}\right )](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cleft%28%5Cdfrac%7B2e%5E%7B2x%7D-%28-2%29e%5E%7B-2x%7D%7D%7B4%7D%5Cright%20%29)
![\dfrac{d}{dx}f(x)=\left(\dfrac{2(e^{2x}+e^{-2x})}{4}\right )](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cleft%28%5Cdfrac%7B2%28e%5E%7B2x%7D%2Be%5E%7B-2x%7D%29%7D%7B4%7D%5Cright%20%29)
![\dfrac{d}{dx}f(x)=\dfrac{e^{2x}+e^{-2x}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7Df%28x%29%3D%5Cdfrac%7Be%5E%7B2x%7D%2Be%5E%7B-2x%7D%7D%7B2%7D)
Hence,
.
A= 1/2(7 + 11)(5)
A = 1/2(18)(5)
A = 45 square units