Answer:
5+5 is 10 is simple question
Subtract the given score x from the mean µ and divide it by the standard deviation σ :
z = (x - µ) / σ = (302 - 300) / 20 = 0.1
Answer:
Required volume is
unit.
Step-by-step explanation:
Given equations of curves,
,
substitute second in first we will get,
![x^2=36-x^2\implies x^2=16\implies x=\pm 4](https://tex.z-dn.net/?f=x%5E2%3D36-x%5E2%5Cimplies%20x%5E2%3D16%5Cimplies%20x%3D%5Cpm%204)
When
and
. Thus both curves intersect at the points (4,16),(-4,16). And thus
.
Considering width of the representative rectangle as
which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,
![V_{Shell}=(\textit{Length of box})\times (\textit{Width of box})\times (\textit{Thikness of box})](https://tex.z-dn.net/?f=V_%7BShell%7D%3D%28%5Ctextit%7BLength%20of%20box%7D%29%5Ctimes%20%28%5Ctextit%7BWidth%20of%20box%7D%29%5Ctimes%20%28%5Ctextit%7BThikness%20of%20box%7D%29)
Now,
Length of generating box=Length of
from line x=4(axis of revolution)=circumference of the shell=(4-x)
Width of box=![(36-x^2)-x^2](https://tex.z-dn.net/?f=%2836-x%5E2%29-x%5E2)
Hence,
![V_{Shell}](https://tex.z-dn.net/?f=V_%7BShell%7D)
![=2\pi\int_{-4}^{4}(144-36x-8x^2+2x^3)dx](https://tex.z-dn.net/?f=%3D2%5Cpi%5Cint_%7B-4%7D%5E%7B4%7D%28144-36x-8x%5E2%2B2x%5E3%29dx)
![=2\pi\{144\big[x\big]_{-4}^{4}-18\big[x^2\big]_{-4}^{4}-\frac{8}{3}\big[x^3\big]_{-4}^{4}+\frac{1}{2}\big[x^4\big]_{-4}^{4}\}](https://tex.z-dn.net/?f=%3D2%5Cpi%5C%7B144%5Cbig%5Bx%5Cbig%5D_%7B-4%7D%5E%7B4%7D-18%5Cbig%5Bx%5E2%5Cbig%5D_%7B-4%7D%5E%7B4%7D-%5Cfrac%7B8%7D%7B3%7D%5Cbig%5Bx%5E3%5Cbig%5D_%7B-4%7D%5E%7B4%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cbig%5Bx%5E4%5Cbig%5D_%7B-4%7D%5E%7B4%7D%5C%7D)
![=\frac{4864\pi}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4864%5Cpi%7D%7B3%7D)
which is required volume of generating area.
Answer:
-3q² + 3qp + 2rp - 2rq + Sq - Sp
Step-by-step explanation:
first part
3q(p-q) = 3qp - 3q²
second part
2r(p-q) = 2rp - 2rq
third part
S(q-p) = Sq - Sp
then we put it all together
3qp - 3q² + 2rp - 2rq + Sq - Sp
in the right place possibly
-3q² + 3qp + 2rp - 2rq + Sq - Sp