10/12 plus 9/12 equals 19/12. this means that there are 7 left over...
6 7/12 is the answer
Answer:
45
Step-by-step explanation:
Answer:
sports Inc sold more helmets
![\mathcal L\{f(t)\}=\displaystyle\int_{t=0}^{t\to\infty}f(t)e^{-st}\,\mathrm dt](https://tex.z-dn.net/?f=%5Cmathcal%20L%5C%7Bf%28t%29%5C%7D%3D%5Cdisplaystyle%5Cint_%7Bt%3D0%7D%5E%7Bt%5Cto%5Cinfty%7Df%28t%29e%5E%7B-st%7D%5C%2C%5Cmathrm%20dt)
Given that
![f(t)=\begin{cases}\cos t&\text{for }0\le t](https://tex.z-dn.net/?f=f%28t%29%3D%5Cbegin%7Bcases%7D%5Ccos%20t%26%5Ctext%7Bfor%20%7D0%5Cle%20t%3C%5Cpi%5C%5C0%26%5Ctext%7Bfor%20%7Dt%5Cge%5Cpi%5Cend%7Bcases%7D)
the Laplace transform of
![f(t)](https://tex.z-dn.net/?f=f%28t%29)
is given by the definite integral
![\displaystyle\int_{t=0}^{t\to\infty}f(t)e^{-st}\,\mathrm dt=\int_{t=0}^{t=\pi}\cos t\,e^{-st}\,\mathrm dt+\int_{t=\pi}^{t\to\infty}0\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7Bt%3D0%7D%5E%7Bt%5Cto%5Cinfty%7Df%28t%29e%5E%7B-st%7D%5C%2C%5Cmathrm%20dt%3D%5Cint_%7Bt%3D0%7D%5E%7Bt%3D%5Cpi%7D%5Ccos%20t%5C%2Ce%5E%7B-st%7D%5C%2C%5Cmathrm%20dt%2B%5Cint_%7Bt%3D%5Cpi%7D%5E%7Bt%5Cto%5Cinfty%7D0%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^\pi\cos t\,e^{-st}\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E%5Cpi%5Ccos%20t%5C%2Ce%5E%7B-st%7D%5C%2C%5Cmathrm%20dt)
![=\dfrac{(1-e^{-\pi s})s}{s^2+1}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%281-e%5E%7B-%5Cpi%20s%7D%29s%7D%7Bs%5E2%2B1%7D)
(which you can find by integrating by parts twice)