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
Answer:
Step-by-step explanation:
㏒ 3+㏒(x+2)=1
㏒3(x+2)=1
3(x+2)=10^1
3x+6=10
3x=10-6=4
x=4/3
so A
3.
![log_{2}x+log_{2}(x+2)=3\\or~log_{2}[x(x+2)]=3\\x(x+2)=2^3\\x^2+2x-8=0\\x^2+4x-2x-8=0\\x(x+4)-2(x+4)=0\\(x+4)(x-2)=0\\x=2,-4\\x=-4 ~is~an~extraneous~solution.\\B](https://tex.z-dn.net/?f=log_%7B2%7Dx%2Blog_%7B2%7D%28x%2B2%29%3D3%5C%5Cor~log_%7B2%7D%5Bx%28x%2B2%29%5D%3D3%5C%5Cx%28x%2B2%29%3D2%5E3%5C%5Cx%5E2%2B2x-8%3D0%5C%5Cx%5E2%2B4x-2x-8%3D0%5C%5Cx%28x%2B4%29-2%28x%2B4%29%3D0%5C%5C%28x%2B4%29%28x-2%29%3D0%5C%5Cx%3D2%2C-4%5C%5Cx%3D-4%20~is~an~extraneous~solution.%5C%5CB)
Answer:
36°
Step-by-step explanation:
I used an online protractor to solve it
Answer:

Step-by-step explanation:
The general rule for vertical translation of a function ƒ(x) ⟶ ƒ(x) + k
.
A positive value of k means that the graph is shifted up by k units.
The graph of ƒ(x) was shifted from (0, 1) to (0, -6).

Answer:
D. x = 7 and x = 14
Step-by-step explanation:
this is a quadratic equation, so use the quadratic formula: (-b+-√b^2-4ac) / 2a for ax^2+bx+c=0