In order for two triangles to be considered as similar, they must be
- equiangular (all angles equal)
- all sides equal (sss)
- if two pairs of two sides are in proportion or are matching, and one included angle is equal
Q4a) yes, because all the angles are equal (equiangular)
b) yes, because all sides are in matching ratio (so 10/5 is 2, 6/3 is 2 and 8/4 is 2; so they are in matching ratios)
c) yes, because if you plus 60 and 70, you get 130. Minus 180 and 130, you get 50. So, in both triangles the angles will be 60,70 and 50; so they're equiangular
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:
1. $60
2. 600 Calories were burned
3. D
Step-by-step explanation:
1. $75 x .20=$15
75-15=$60
2. What I started with is 200/40=5 calories burned per min
60 plus 60=120
5x120=600
3. It's the only option that has something decreasing. and there is a -5 which means it's getting subtracted or its decreasing.
Answer:
Step-by-step explanation:
oh boy
1) 9 < 16
2) -4 < 5
3) 18 > -19
4) -38 < -16
5) 6 > 4
6) -14 > -25
7) -45 > -55
8) -2 > -10
9) -4, -1, 1, 3, 6
10) -15, -13, -5, 8
11) -9, -6, -5, -1, 0
12) -4, -2, 1, 3
13) -10, -9, 7, 8, 11
14) -33, -25, -14, -4, 7
hope this helps <3
