Answer:
Arithmetic sequence:
Geometric sequence:
Step-by-step explanation:
The arithmetic sequence: is the sequence whos terms increased or decreased by a constant amount.
Examples:
- 4, 7, 10, 13, 16, ........................ (increased by 3)
- 25, 20, 15, 10, ......................... (Decreased by 5)
The explicit formula for the nth term of the arithmetic sequence is:
is the first term
- d is the constant difference between each two consecutive terms
- n is the position of the number in the sequence
The geometric sequence: is the sequence whos consecutive terms have a constant ratio
Examples:
- 1, 2, 4, 8, 16, ........................ (Multiplying by 2)
- 625, 125, 25, 5, ......................... (Dividing by 5)
The explicit formula for the nth term of the geometric sequence is:
is the first term
- r is the constant ratio between each two consecutive terms
- n is the position of the number in the sequence
* Arithmetic sequence →→→→→→ Geometric sequence
Has a constant difference →→→→→→ Has a constant ratio
→→→→→→
→→→→→→ ![r=\frac{a_{n}}{a_{n-1} }](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7Bn%7D%7D%7Ba_%7Bn-1%7D%20%7D)
Answer:
A, D
Step-by-step explanation:
The graph of a proportional relation is a straight line that passes through the origin.
Answer: A, D
12 turns.
360 degrees is a full turn, so if you multiply 30 degreed by 12, you go around in a circle.
Given:
The equation of a circle is
![10y+x^2=-18+5x-y^2](https://tex.z-dn.net/?f=10y%2Bx%5E2%3D-18%2B5x-y%5E2)
To find:
The center and radius of the given equation by completing the square.
Solution:
The standard form of a circle is
...(i)
where, (h,k) is center and r is radius of the circle.
We have,
![10y+x^2=-18+5x-y^2](https://tex.z-dn.net/?f=10y%2Bx%5E2%3D-18%2B5x-y%5E2)
It can be written as
![(x^2-5x)+(y^2+10y)=-18](https://tex.z-dn.net/?f=%28x%5E2-5x%29%2B%28y%5E2%2B10y%29%3D-18)
![\left(x^2-5x+\left(\dfrac{5}{2}\right)^2\right)+\left(y^2+10y+\left(\dfrac{10}{2}\right)^2\right)=-18+\left(\dfrac{5}{2}\right)^2+\left(\dfrac{10}{2}\right)^2](https://tex.z-dn.net/?f=%5Cleft%28x%5E2-5x%2B%5Cleft%28%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%5Cright%29%2B%5Cleft%28y%5E2%2B10y%2B%5Cleft%28%5Cdfrac%7B10%7D%7B2%7D%5Cright%29%5E2%5Cright%29%3D-18%2B%5Cleft%28%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B10%7D%7B2%7D%5Cright%29%5E2)
![\left(x-\dfrac{5}{2}\right)^2+\left(y^2+10y+5^2\right)=-18+\dfrac{25}{4}+5^2](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28y%5E2%2B10y%2B5%5E2%5Cright%29%3D-18%2B%5Cdfrac%7B25%7D%7B4%7D%2B5%5E2)
![\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=-18+\dfrac{25}{4}+25](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%28y%2B5%29%5E2%3D-18%2B%5Cdfrac%7B25%7D%7B4%7D%2B25)
![\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{-72+25+100}{4}](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%28y%2B5%29%5E2%3D%5Cdfrac%7B-72%2B25%2B100%7D%7B4%7D)
![\left(x-\dfrac{5}{2}\right)^2+(y+5)^2=\dfrac{53}{4}](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cdfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%28y%2B5%29%5E2%3D%5Cdfrac%7B53%7D%7B4%7D)
...(ii)
On comparing (i) and (ii), we get
![h=\dfrac{5}{2},k=-5,r=\dfrac{\sqrt{53}}{2}](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B5%7D%7B2%7D%2Ck%3D-5%2Cr%3D%5Cdfrac%7B%5Csqrt%7B53%7D%7D%7B2%7D)
Therefore, the center is
and the radius is
units.
Answer:
0.0201
Step-by-step explanation:
2.01 / 100 = 0.0201