Answer:
A...
Step-by-step explanation:
Not completely sure. :<
For a function (fn) to be odd:
f(x) = - f(-x)
For a fn to be even:
f(x) = f(-x)
For a fn to be neither even nor odd
f(x) != f(-x) [No Relation]
(-x)^n = x^n for n -> even
(-x)^n = -x^n for n -> odd
In your example:
f(x) = -4x^3 + 4x
f(-x) = -4 (-x)^3 + 4 (-x)^1 ( 3 and 1 are odd powers )
f(-x) = 4x^3 - 4x (take -1 common to do the check)
f(-x) = -( -4x^3 + 4x ) = - f(x) [between the bracket was the original fn]
f(x) = - f(-x)
so the function is odd also called symmetric about the origin
Answer:
6.3
Step-by-step explanation:
First off, we need the distance formula, which is:
![\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D)
If we plug in the points, we get:
![\sqrt{(-4 - 2)^2 + (4 - 2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-4%20-%202%29%5E2%20%2B%20%284%20-%202%29%5E2%7D)
If we simplify everything under the square root, we get:
![\sqrt{(-6)^2 + (2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-6%29%5E2%20%2B%20%282%29%5E2%7D)
![\sqrt{36 + 4}](https://tex.z-dn.net/?f=%5Csqrt%7B36%20%2B%204%7D)
![\sqrt{40}](https://tex.z-dn.net/?f=%5Csqrt%7B40%7D)
In decimal, the answer is 6.3
Answer:
The volume of the tumor experimented a decrease of 54.34 percent.
Step-by-step explanation:
Let suppose that tumor has an spherical geometry, whose volume (
) is calculated by:
![V = \frac{4\pi}{3}\cdot R^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B3%7D%5Ccdot%20R%5E%7B3%7D)
Where
is the radius of the tumor.
The percentage decrease in the volume of the tumor (
) is expressed by:
![\%V = \frac{\Delta V}{V_{o}} \times 100\,\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%20%5Cfrac%7B%5CDelta%20V%7D%7BV_%7Bo%7D%7D%20%5Ctimes%20100%5C%2C%5C%25)
Where:
- Absolute decrease in the volume of the tumor.
- Initial volume of the tumor.
The absolute decrease in the volume of the tumor is:
![\Delta V = V_{o}-V_{f}](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%20V_%7Bo%7D-V_%7Bf%7D)
![\Delta V = \frac{4\pi}{3}\cdot (R_{f}^{3}-R_{o}^{3})](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B3%7D%5Ccdot%20%28R_%7Bf%7D%5E%7B3%7D-R_%7Bo%7D%5E%7B3%7D%29)
The percentage decrease is finally simplified:
![\%V = \left[1-\left(\frac{R_{f}}{R_{o}}\right)^{3} \right]\times 100\,\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%20%5Cleft%5B1-%5Cleft%28%5Cfrac%7BR_%7Bf%7D%7D%7BR_%7Bo%7D%7D%5Cright%29%5E%7B3%7D%20%5Cright%5D%5Ctimes%20100%5C%2C%5C%25)
Given that
and
, the percentage decrease in the volume of tumor is:
![\%V = \left[1-\left(\frac{0.77\cdot R}{R}\right)^{3} \right]\times 100\,\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%20%5Cleft%5B1-%5Cleft%28%5Cfrac%7B0.77%5Ccdot%20R%7D%7BR%7D%5Cright%29%5E%7B3%7D%20%5Cright%5D%5Ctimes%20100%5C%2C%5C%25)
![\%V = 54.34\,\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%2054.34%5C%2C%5C%25)
The volume of the tumor experimented a decrease of 54.34 percent.
Answer:
Yes it is a Function
Step-by-step explanation:
Because there are no same x-values with the same y-values