Answer:
x=24
y=21
Step-by-step explanation:
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Answer:
The right options are C and E.
Step-by-step explanation:
I got it right on Edge.
QUESTION:
When you factor a little perfect square trinomial, which pattern results?
ANSWER:
[2] The square of a binomial pattern.
EXPLANATION:
<u>Squaring a binomial creates a perfect square trinomial</u>:–
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)