Answer:
8%
Step-by-step explanation:
let,
this year population of students (pt)= 195
last year population of students (p)= 210
time(t)= 1 year
Population Change( R)= ?
we have,
pt= p( 1 - R/100)^t
195 = 210 ( 1 - R/100)^1
0.92= 1 - R/100
0.92-1= R/100
- 0.08 = - R/100
R= 0.08×100
R= 8%
Answer:
The volume of the solid = π²
Step-by-step explanation:
As per the given data of the questions,
The diameter of each disk is
D = 2 sin(x) - 2 cos(x)
So its radius is
R = sin(x) - cos(x).
The area of each disk is
![= \pi \times [sin^{2}(x) - 2 sin(x) cos(x) + cos^{2}(x)]](https://tex.z-dn.net/?f=%3D%20%5Cpi%20%5Ctimes%20%5Bsin%5E%7B2%7D%28x%29%20-%202%20sin%28x%29%20cos%28x%29%20%2B%20cos%5E%7B2%7D%28x%29%5D)
![= \pi[1-2sin(x)cos(x)]](https://tex.z-dn.net/?f=%3D%20%5Cpi%5B1-2sin%28x%29cos%28x%29%5D)
![= \pi[1-sin(2x)]](https://tex.z-dn.net/?f=%3D%20%5Cpi%5B1-sin%282x%29%5D)
Now,
Integrate from 
, we get volume:
![V=\int_{\frac{\pi}{4}}^{\frac{5\pi}{4}} \pi[1-sin(2x)]dx](https://tex.z-dn.net/?f=V%3D%5Cint_%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%7D%5E%7B%5Cfrac%7B5%5Cpi%7D%7B4%7D%7D%20%5Cpi%5B1-sin%282x%29%5Ddx)
After integrate without limit we get
![V=\pi[x+\frac{cos2x}{2}]](https://tex.z-dn.net/?f=V%3D%5Cpi%5Bx%2B%5Cfrac%7Bcos2x%7D%7B2%7D%5D)
Now after putting the limit, we get
V = π²
Hence, the required volume of the solid = π²
<span><u>Answer
</u>
31.12 in
<u>Explanation
</u>
To get the length required, lets first find angle mF,
mF = 180 – (43 + 62) =75o
Now we can use the sin rule to find length DE.
a/sinA =b/sinB Where a and b are the length opposite to angle A and B respectively.
DE/sin75=22/sin43
DE=(22 sin75)/sin43
DE=31.12 in
</span>
Replace x in each equation and see which ones are true.
The answers are:
C. If 5x + 10 =20 then x =2
D. If 6x-12=48, then x=10
F. If 8x(x-4)=32, then x=8
