Answer:
Step-by-step explanation:
Find the width as below
- l² + w² + h² = d², where l- length, w- width, h- height, d- the distance between top and bottom corners
Substitute the values and solve for w
- 4² + w² + 12² = 13²
- w² + 160 = 169
- w² = 9
- w = 3 feet
Now find the volume
- V = lwh
- V = 4*3*12 = 144 ft³
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
G(X)=6X-3
Y=6X-3
X=6Y-3
X+3=6Y
Y=(X+3)/6
G^-1(9)=(X+3)/6
G^-1(9)=(9+3)/6
G^-1(9)=2
circumference = pi*d
70cm*pi = 219.8cm
219.8cm × 240 rev = 52752 cm
52752cm/100 = 528m
It’s d, looks like you got it already! With ratios, just pay attention to not only the numbers but order of the words as well, so you can be sure the ratio follows the problem.