Answer:
![H)39.6](https://tex.z-dn.net/?f=H%2939.6)
Step-by-step explanation:
To get the mean, you have to add all the numbers, then divide the sum by the amount of individual numbers there are.
In this problem, we see that there are 5 different numbers. If we add all those numbers together, they will equal 198.
÷ ![5 = 39.6](https://tex.z-dn.net/?f=5%20%3D%2039.6)
Answer:
do you have an attachment or anything?
Step-by-step explanation:
The length of the towel bar is 9.5 inches.
<em><u>Explanation</u></em>
Suppose, the length of the towel bar is
inches.
The distance from each end of the towel bar to the end of the door is 9 inches. So, <u>the total width of the door</u> will be: ![[x+(9*2)] = (x+18)inches](https://tex.z-dn.net/?f=%5Bx%2B%289%2A2%29%5D%20%3D%20%28x%2B18%29inches)
Given that, the <u>width of the door</u> is
inches or 27.5 inches. So, the equation will be........
![x+18=27.5\\ \\ x=27.5-18= 9.5](https://tex.z-dn.net/?f=x%2B18%3D27.5%5C%5C%20%5C%5C%20%20x%3D27.5-18%3D%209.5)
Thus, the length of the towel bar will be 9.5 inches.
Answer:
![A_1 = 12](https://tex.z-dn.net/?f=A_1%20%3D%2012)
![A_n = A_{n-1} + 3](https://tex.z-dn.net/?f=A_n%20%3D%20A_%7Bn-1%7D%20%2B%203)
Step-by-step explanation:
Given
![A_n =12+(n-1)3](https://tex.z-dn.net/?f=A_n%20%3D12%2B%28n-1%293)
Required
Write as recursive
We have:
![A_n =12+(n-1)3](https://tex.z-dn.net/?f=A_n%20%3D12%2B%28n-1%293)
Open bracket
![A_n =12+3n-3](https://tex.z-dn.net/?f=A_n%20%3D12%2B3n-3)
![A_n =12-3+3n](https://tex.z-dn.net/?f=A_n%20%3D12-3%2B3n)
![A_n =9+3n](https://tex.z-dn.net/?f=A_n%20%3D9%2B3n)
Calculate few terms
![A_1 =9+3*1 = 9 + 3 = 12](https://tex.z-dn.net/?f=A_1%20%3D9%2B3%2A1%20%3D%209%20%2B%203%20%3D%2012)
![A_2 =9+3*2 = 9 + 6 = 15](https://tex.z-dn.net/?f=A_2%20%3D9%2B3%2A2%20%3D%209%20%2B%206%20%3D%2015)
![A_3 =9+3*3 = 9 + 9 = 18](https://tex.z-dn.net/?f=A_3%20%3D9%2B3%2A3%20%3D%209%20%2B%209%20%3D%2018)
The above shows that the rule is to add 3.
So, we have:
![A_1 = 12](https://tex.z-dn.net/?f=A_1%20%3D%2012)
![A_n = A_{n-1} + 3](https://tex.z-dn.net/?f=A_n%20%3D%20A_%7Bn-1%7D%20%2B%203)
Answer:
A.![y(x) =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}](https://tex.z-dn.net/?f=y%28x%29%20%3D%5Csqrt%7B%202%28%5Cfrac%7Bx%5E5%7D%7B5%7D%20-%5Cfrac%7B6%5E5%7D%7B5%7D%29%7D)
B.Therefore the solution is defined on the interval:
6≤ x ≤ +∞
Step-by-step explanation:
Given differential equation is
![\frac{dy}{dx} = x^4y^{-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20x%5E4y%5E%7B-1%7D)
![\Rightarrow \frac{dy}{dx} =\frac{ x^4}{y}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cfrac%7B%20x%5E4%7D%7By%7D)
![\Rightarrow y dy = x^4dx](https://tex.z-dn.net/?f=%5CRightarrow%20y%20dy%20%3D%20x%5E4dx)
Integrating both sides:
![\Rightarrow\int y dy = \int x^4dx](https://tex.z-dn.net/?f=%5CRightarrow%5Cint%20y%20dy%20%3D%20%5Cint%20x%5E4dx)
........(1)
Given y(0)= 6
it means y=0 when x=6
Putting x=6 and y=0 in the equation (1)
![\therefore \frac{0^2}{2} =\frac{6^5}{5} +C](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cfrac%7B0%5E2%7D%7B2%7D%20%3D%5Cfrac%7B6%5E5%7D%7B5%7D%20%2BC)
![\Rightarrow C=-\frac{6^5}{5}](https://tex.z-dn.net/?f=%5CRightarrow%20C%3D-%5Cfrac%7B6%5E5%7D%7B5%7D)
Equation (1) become:
![\Rightarrow \frac{y^2}{2} =(\frac{x^5}{5} -\frac{6^5}{5})](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7By%5E2%7D%7B2%7D%20%3D%28%5Cfrac%7Bx%5E5%7D%7B5%7D%20-%5Cfrac%7B6%5E5%7D%7B5%7D%29)
![\Rightarrow y} =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}](https://tex.z-dn.net/?f=%5CRightarrow%20y%7D%20%3D%5Csqrt%7B%202%28%5Cfrac%7Bx%5E5%7D%7B5%7D%20-%5Cfrac%7B6%5E5%7D%7B5%7D%29%7D)
Therefore ![y(x) =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}](https://tex.z-dn.net/?f=y%28x%29%20%3D%5Csqrt%7B%202%28%5Cfrac%7Bx%5E5%7D%7B5%7D%20-%5Cfrac%7B6%5E5%7D%7B5%7D%29%7D)
(B)
The quantity under root must greater than or equal to zero.
Therefore,
![2(\frac{x^5}{5} -\frac{6^5}{5})} \geq0](https://tex.z-dn.net/?f=2%28%5Cfrac%7Bx%5E5%7D%7B5%7D%20-%5Cfrac%7B6%5E5%7D%7B5%7D%29%7D%20%5Cgeq0)
![\Rightarrow \frac{x^5}{5} -\frac{6^5}{5}} \geq0](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bx%5E5%7D%7B5%7D%20-%5Cfrac%7B6%5E5%7D%7B5%7D%7D%20%5Cgeq0)
![\Rightarrow \frac{x^5}{5} \geq\frac{6^5}{5}}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bx%5E5%7D%7B5%7D%20%5Cgeq%5Cfrac%7B6%5E5%7D%7B5%7D%7D)
![\Rightarrow x^5\geq {6^5](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E5%5Cgeq%20%7B6%5E5)
![\Rightarrow \sqrt[5]{x^5} \geq \sqrt[5]{6^5}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%5B5%5D%7Bx%5E5%7D%20%5Cgeq%20%5Csqrt%5B5%5D%7B6%5E5%7D)
![\Rightarrow x\geq {6](https://tex.z-dn.net/?f=%5CRightarrow%20x%5Cgeq%20%7B6)
When x≥0 then the value of
is real other wise the value of
is imaginary.
Therefore the solution is defined on the interval:
6≤ x ≤ +∞