This being a piecewise function, trying to solve f(2), we must find which two equations we can use.
We can use the function '3x + 1' because its domain is 'x is greater than or equal to 2
--> <u>f(2) = 3(2) + 1 = 7</u>
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Hope that helps!
Answer:
22.74 liters
Step-by-step explanation:
Answer:
![y(x) = \sqrt[5]{\frac{e^{2x}}{2} + \frac{2047}{2}}](https://tex.z-dn.net/?f=y%28x%29%20%3D%20%5Csqrt%5B5%5D%7B%5Cfrac%7Be%5E%7B2x%7D%7D%7B2%7D%20%2B%20%5Cfrac%7B2047%7D%7B2%7D%7D)
Step-by-step explanation:
![\displaystyle\frac{dy}{dx} = \displaystyle\frac{e^{2x}}{5y^4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7Be%5E%7B2x%7D%7D%7B5y%5E4%7D)
Cross multiplying, we have,
![5y^4 dy = e^{2x} dx](https://tex.z-dn.net/?f=5y%5E4%20dy%20%3D%20e%5E%7B2x%7D%20dx)
Integrating both sides,
![\int 5y^4 dy = \int e^{2x}dx](https://tex.z-dn.net/?f=%5Cint%205y%5E4%20dy%20%3D%20%5Cint%20e%5E%7B2x%7Ddx)
We obtain,
, where C is the constant of integration.
![y(x) = \sqrt[5]{\frac{e^{2x}}{2} + C }](https://tex.z-dn.net/?f=y%28x%29%20%3D%20%5Csqrt%5B5%5D%7B%5Cfrac%7Be%5E%7B2x%7D%7D%7B2%7D%20%2B%20C%20%7D)
We know that y(0) = 4
Putting these value in the above equation, we get C = ![\frac{2047}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2047%7D%7B2%7D)
Thus,
![y(x) = \sqrt[5]{\frac{e^{2x}}{2} + \frac{2047}{2}}](https://tex.z-dn.net/?f=y%28x%29%20%3D%20%5Csqrt%5B5%5D%7B%5Cfrac%7Be%5E%7B2x%7D%7D%7B2%7D%20%2B%20%5Cfrac%7B2047%7D%7B2%7D%7D)
The scarves should each be 3 1/4 feet long
hope it helps
I'm pretty sure 16.024 is greater.