Answer:
Not a function
Step-by-step explanation:
This is not a function because there are different outputs for the same input.
Answer:
look up answer key realy would help
Step-by-step explanation:
Calculate for the mean/ average of the given numbers:
μ = (1 + 2 + 3 + 4 + 5) / 5 = 3
Then, we calculate for the summation of the squares of differences of these numbers from the mean, S
S = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
S = 10
Divide this summation by the number of items and take the square root of the result to get the standard deviation.
SD = sqrt (10 / 5) = sqrt 2
SD = 1.41
Thus, the standard deviation of the given is equal to 1.41.
(yX3)+1 because product means multipy
Answer:
![v = \frac{32\pi}{3}](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B32%5Cpi%7D%7B3%7D)
or
![v=33.52](https://tex.z-dn.net/?f=v%3D33.52)
Step-by-step explanation:
Given
![f(x) = 4x - x^2](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%20-%20x%5E2)
![g(x) = x^2](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2)
![[a,b] = [0,2]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D%20%3D%20%5B0%2C2%5D)
Required
The volume of the solid formed
Rotating about the x-axis.
Using the washer method to calculate the volume, we have:
![\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx](https://tex.z-dn.net/?f=%5Cint%20dv%20%3D%20%5Cint%5Climit%5Eb_a%20%5Cpi%28f%28x%29%5E2%20-%20g%28x%29%5E2%29%20dx)
Integrate
![v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx](https://tex.z-dn.net/?f=v%20%3D%20%5Cint%5Climit%5Eb_a%20%5Cpi%28f%28x%29%5E2%20-%20g%28x%29%5E2%29%5C%20dx)
![v = \pi \int\limit^b_a (f(x)^2 - g(x)^2)\ dx](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5Cint%5Climit%5Eb_a%20%28f%28x%29%5E2%20-%20g%28x%29%5E2%29%5C%20dx)
Substitute values for a, b, f(x) and g(x)
![v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5Cint%5Climit%5E2_0%20%28%284x%20-%20x%5E2%29%5E2%20-%20%28x%5E2%29%5E2%29%5C%20dx)
Evaluate the exponents
![v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5Cint%5Climit%5E2_0%20%2816x%5E2%20-%204x%5E3%20-%204x%5E3%20%2B%20x%5E4%20-%20x%5E4%29%5C%20dx)
Simplify like terms
![v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5Cint%5Climit%5E2_0%20%2816x%5E2%20-%208x%5E3%20%29%5C%20dx)
Factor out 8
![v = 8\pi \int\limit^2_0 (2x^2 - x^3 )\ dx](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5Cint%5Climit%5E2_0%20%282x%5E2%20-%20x%5E3%20%29%5C%20dx)
Integrate
![v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2x%5E%7B2%2B1%7D%7D%7B2%2B1%7D%20-%20%5Cfrac%7Bx%5E%7B3%2B1%7D%7D%7B3%2B1%7D%20%5D%7C%5Climit%5E2_0)
![v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2x%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7Bx%5E%7B4%7D%7D%7B4%7D%20%5D%7C%5Climit%5E2_0)
Substitute 2 and 0 for x, respectively
![v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%28%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D%20-%20%5B%20%5Cfrac%7B2%2A0%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B0%5E%7B4%7D%7D%7B4%7D%20%5D%29)
![v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%28%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D%20-%20%5B%200%20-%200%5D%29)
![v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B2%2A2%5E%7B3%7D%7D%7B3%7D%20-%20%5Cfrac%7B2%5E%7B4%7D%7D%7B4%7D%20%5D)
![v = 8\pi [ \frac{16}{3} - \frac{16}{4} ]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B16%7D%7B3%7D%20-%20%5Cfrac%7B16%7D%7B4%7D%20%5D)
Take LCM
![v = 8\pi [ \frac{16*4- 16 * 3}{12}]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B16%2A4-%2016%20%2A%203%7D%7B12%7D%5D)
![v = 8\pi [ \frac{64- 48}{12}]](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%5B%20%5Cfrac%7B64-%2048%7D%7B12%7D%5D)
![v = 8\pi * \frac{16}{12}](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%2A%20%5Cfrac%7B16%7D%7B12%7D)
Simplify
![v = 8\pi * \frac{4}{3}](https://tex.z-dn.net/?f=v%20%3D%208%5Cpi%20%2A%20%5Cfrac%7B4%7D%7B3%7D)
![v = \frac{32\pi}{3}](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B32%5Cpi%7D%7B3%7D)
or
![v=\frac{32}{3} * \frac{22}{7}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B32%7D%7B3%7D%20%2A%20%5Cfrac%7B22%7D%7B7%7D)
![v=\frac{32*22}{3*7}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B32%2A22%7D%7B3%2A7%7D)
![v=\frac{704}{21}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B704%7D%7B21%7D)
![v=33.52](https://tex.z-dn.net/?f=v%3D33.52)