Answer:
Number of teams remaining after n rounds of play, p(n) = 2⁶⁻ⁿ
Step-by-step explanation:
This is an example of geometric progression,
Let p(n) represents the number of participants remaining after n rounds of play.
First term = 64
![\texttt{Common ratio = }\frac{1}{2}](https://tex.z-dn.net/?f=%5Ctexttt%7BCommon%20ratio%20%3D%20%7D%5Cfrac%7B1%7D%7B2%7D)
We have
![p(n)=a\times r^{n}\\\\p(n)=64\times \left (\frac{1}{2} \right )^{n}=2^{6}\times \left (\frac{1}{2} \right )^{n}\\\\p(n)=2^{6-n}](https://tex.z-dn.net/?f=p%28n%29%3Da%5Ctimes%20r%5E%7Bn%7D%5C%5C%5C%5Cp%28n%29%3D64%5Ctimes%20%5Cleft%20%28%5Cfrac%7B1%7D%7B2%7D%20%5Cright%20%29%5E%7Bn%7D%3D2%5E%7B6%7D%5Ctimes%20%5Cleft%20%28%5Cfrac%7B1%7D%7B2%7D%20%5Cright%20%29%5E%7Bn%7D%5C%5C%5C%5Cp%28n%29%3D2%5E%7B6-n%7D)
Number of teams remaining after n rounds of play, p(n) = 2⁶⁻ⁿ
S1 = speed of boat 1
<span> t1 = time to do 1400 meters (boat 1) </span>
S1*t1 = 1400
<span><span>S2 </span>= speed of boat 2 </span>
1400 + S2*t1 = X
t2 = time to do X + 600 (boat 2)
S1*t2 = X + 600
S2*t2 = 2X - 600
S1 = 1400/t1
S2 = (X-1400)/t1
<span>T = t2/t1 </span>
1400*T = X + 600
X*T - 1400*T = 2X - 600
X = 3600 meters
<span> River is 3600 meters wide</span>
The following answer is 10
1: They look fluffy but they're really just water
2: They make rain
3: They make lots of natural disasters
4: They help all ecosystems and species
5: They shade us and keep us cool, too
6: They use evaporation from the sun and suck in the water and make rain (condensation)
Step-by-step explanation:
Translation: (x,y)↦( 9, -12)
Scale factor: 2