Step-by-step explanation:
Given:
and ![f(0) = 0](https://tex.z-dn.net/?f=f%280%29%20%3D%200)
We can solve for f(x) by writing
![\displaystyle f(x) = \int f'(x)dx=\int x^2e^{2x^3}dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cint%20f%27%28x%29dx%3D%5Cint%20x%5E2e%5E%7B2x%5E3%7Ddx)
Let ![u = 2x^3](https://tex.z-dn.net/?f=u%20%3D%202x%5E3)
![\:\:\:\:du=6x^2dx](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3Adu%3D6x%5E2dx)
Then
![\displaystyle f(x) = \int x^2e^{2x^3}dx = \dfrac{1}{6}\int e^u du](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cint%20x%5E2e%5E%7B2x%5E3%7Ddx%20%3D%20%5Cdfrac%7B1%7D%7B6%7D%5Cint%20e%5Eu%20du)
![\displaystyle \:\:\:\:\:\:\:=\frac{1}{6}e^{2x^3} + k](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%5Cfrac%7B1%7D%7B6%7De%5E%7B2x%5E3%7D%20%2B%20k)
We know that f(0) = 0 so we can find the value for k:
![f(0) = \frac{1}{6}(1) + k \Rightarrow k = -\frac{1}{6}](https://tex.z-dn.net/?f=f%280%29%20%3D%20%5Cfrac%7B1%7D%7B6%7D%281%29%20%2B%20k%20%5CRightarrow%20k%20%3D%20-%5Cfrac%7B1%7D%7B6%7D)
Therefore,
![\displaystyle f(x) = \frac{1}{6} \left(e^{2x^3} - 1 \right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B6%7D%20%5Cleft%28e%5E%7B2x%5E3%7D%20-%201%20%5Cright%29)
Hey! :)
The total cost of the item is the second choice which is $14,372.08. I arrived to the answer by simply:
1) multiplying the sales tax to the negotiated price (15640*.072 = 1126.08)
2) adding the sales tax to the negotiated price and the registration as well (15640+1126.08+106= 16872.08)
3) subtracting the trade in allowance from the computed value (16872.08 - 2500 = 14372.08)
Hope this helps! :)
Answer: 22 people will be riding the lady trip on the ferry
1) Domain: x is greater than -2 and greater than or equal to 5
Range: y is greater than -1 and less than or equal to 3
2) No the function is not one to one because one to one functions can’t have multiple points on a function with the same y value.
Answer:
![x - 7.1 = 8.8](https://tex.z-dn.net/?f=x%20-%207.1%20%3D%208.8)
Step-by-step explanation:
where x represents his original number. to solve and find his original number, add 7.1 to both sides.