Using a geometric sequence, it is found that after 3 rounds, 8 teams are left.
In a geometric series, the quotient between consecutive terms is always the same, and it is called common ratio q.
The general equation of a geometric series is given by:
![a_n = a_1q^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1q%5E%7Bn-1%7D)
In which
is the first term.
In this problem:
- 64 teams were invited, thus
. - After each round, half the teams are eliminated, thus
.
The <u>number of teams after 3 rounds</u> is the 4th term of sequence, as the first is the initial number(0 rounds), thus:
![a_n = a_1q^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1q%5E%7Bn-1%7D)
![a_4 = 64\left(\frac{1}{2}\right)^{4-1}](https://tex.z-dn.net/?f=a_4%20%3D%2064%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B4-1%7D)
![a_4 = 8](https://tex.z-dn.net/?f=a_4%20%3D%208)
After 3 rounds, 8 teams are left.
A similar problem is given at brainly.com/question/25317689
Answer:
![(7,\frac{13}{3})](https://tex.z-dn.net/?f=%287%2C%5Cfrac%7B13%7D%7B3%7D%29)
Step-by-step explanation:
we have
<em>The equation of the first line</em>
------> equation A
<em>The equation of the second line</em>
------> equation B
Solve the system of equations by elimination
Multiply equation A by -4 both sides
--------> equation C
Adds equation B and equation C
![y=\frac{4}{3}x-5\\-4y=-\frac{4}{3}x-8\\--------\\y-4y=-5-8\\-3y=-13\\y=\frac{13}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B3%7Dx-5%5C%5C-4y%3D-%5Cfrac%7B4%7D%7B3%7Dx-8%5C%5C--------%5C%5Cy-4y%3D-5-8%5C%5C-3y%3D-13%5C%5Cy%3D%5Cfrac%7B13%7D%7B3%7D)
<em>Find the value of x</em>
substitute the value of y
![\frac{13}{3}=\frac{1}{3}x+2](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B3%7D%3D%5Cfrac%7B1%7D%7B3%7Dx%2B2)
![\frac{1}{3}x=\frac{13}{3}-2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%3D%5Cfrac%7B13%7D%7B3%7D-2)
Multiply by 3 both sides
![x=13-6](https://tex.z-dn.net/?f=x%3D13-6)
![x=7](https://tex.z-dn.net/?f=x%3D7)
therefore
The solution to the system of equations is the point ![(7,\frac{13}{3})](https://tex.z-dn.net/?f=%287%2C%5Cfrac%7B13%7D%7B3%7D%29)
Answer:
3550
Step-by-step explanation:
C.P=Rs 1250
S.P=8(12)(50)
Rs4800
P=S.P-C. P
=Rs4800-Rs1250
= Rs3550
Answer:
4
Step-by-step explanation:
First use... reflection , and then use.. rotation