It’s B
Cause if 400+80 is 480+9=489+0.6=489.6+0.05 and the final results it’s 489.65
![\frac{1}{2} \times 5 \times 16 \\ 40 \\ ke = 40joules](https://tex.z-dn.net/?f=%20%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%205%20%5Ctimes%2016%20%5C%5C%2040%20%5C%5C%20ke%20%3D%2040joules)
if correct mark me as brainiest
Answer:
Greatest: 531
Least: 135
Step-by-step explanation:
In order to make the greatest number, you want the highest number to be in the highest digits place.
In this case, 5 is the largest number
This is because having a number that is 500 is greater than a number that is 300 or 100.
Then, the next biggest number will be used for the next digit, which is 3, so 3 will be in the 10s place
Then the left over 1 will be in the single digits place, so the greatest number is
531
This is the same process as before, just instead of big numbers, you want little numbers
For the least number, you want the lowest number to be in the 100s place, which is 1
Then 3 is the next lowest number
and the left over is 5
So the least number you can make is:
135
Answer:
im pretty sure its B
Step-by-step explanation:
Step (1)
We know that the sum of all the terms in an infinite geometric sequence finding from following equation whenever |q| < 1 .
q = magnitude
![s( \infty ) = \frac{t(1)}{1 - q} \\](https://tex.z-dn.net/?f=s%28%20%5Cinfty%20%29%20%3D%20%20%5Cfrac%7Bt%281%29%7D%7B1%20-%20q%7D%20%5C%5C%20%20)
So :
![s( \infty ) = \frac{t(1)}{1 - q} \\](https://tex.z-dn.net/?f=s%28%20%5Cinfty%20%29%20%3D%20%20%5Cfrac%7Bt%281%29%7D%7B1%20-%20q%7D%20%5C%5C%20%20)
![81 = \frac{t(1)}{1 - q} \\](https://tex.z-dn.net/?f=81%20%3D%20%20%5Cfrac%7Bt%281%29%7D%7B1%20-%20q%7D%20%20%5C%5C%20)
![81(1 - q) = t(1)](https://tex.z-dn.net/?f=81%281%20-%20q%29%20%3D%20t%281%29)
Remember it I'll use it again.
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Step (2)
We know that the sum of the n first terms of a geometric sequence finding from following equation.
![s(n) = \frac{t(1) \times (1 - {q})^{n} }{1 - q} \\](https://tex.z-dn.net/?f=s%28n%29%20%3D%20%20%5Cfrac%7Bt%281%29%20%5Ctimes%20%281%20-%20%20%7Bq%7D%29%5E%7Bn%7D%20%7D%7B1%20-%20q%7D%20%20%5C%5C%20)
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Sum of all terms starting from the third is 9.
So :
![s(2) + s(3 - \infty ) = 81](https://tex.z-dn.net/?f=s%282%29%20%2B%20s%283%20-%20%20%5Cinfty%20%29%20%3D%2081)
![s(2) + 9 = 81](https://tex.z-dn.net/?f=s%282%29%20%2B%209%20%3D%2081)
Sides minus 9
![s(2) = 81 - 9](https://tex.z-dn.net/?f=s%282%29%20%3D%2081%20-%209)
![s(2) = 72](https://tex.z-dn.net/?f=s%282%29%20%3D%2072)
So :
![t(1) + t(2) = 72](https://tex.z-dn.net/?f=t%281%29%20%20%2B%20t%282%29%20%3D%2072)
![t(1) + t(1) \times q = 72](https://tex.z-dn.net/?f=t%281%29%20%2B%20t%281%29%20%5Ctimes%20q%20%3D%2072)
Factoring t(1)
![t(1) \times (1 + q) = 72](https://tex.z-dn.net/?f=t%281%29%20%5Ctimes%20%281%20%2B%20q%29%20%3D%2072)
We have found t(1) = 81 ( 1 - q ) in step (1).
So :
![81(1 - q)(1 + q) = 72](https://tex.z-dn.net/?f=81%281%20-%20q%29%281%20%2B%20q%29%20%3D%2072)
Divided sides by 81
![(1 - q)(1 + q) = \frac{72}{81} \\](https://tex.z-dn.net/?f=%281%20-%20q%29%281%20%2B%20q%29%20%3D%20%20%5Cfrac%7B72%7D%7B81%7D%20%20%5C%5C%20)
![(1 - q)( 1 + q) = \frac{8}{9} \\](https://tex.z-dn.net/?f=%281%20-%20q%29%28%201%20%2B%20q%29%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20%5C%5C%20%20)
![1 - {q}^{2} = \frac{8}{9} \\](https://tex.z-dn.net/?f=1%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20%5C%5C%20%20%20)
Subtract sides minus -1
![- {q}^{2} = \frac{8}{9} - 1 \\](https://tex.z-dn.net/?f=%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20-%201%20%5C%5C%20%20%20)
![- {q}^{2} = \frac{8}{9} - \frac{9}{9} \\](https://tex.z-dn.net/?f=%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20-%20%20%5Cfrac%7B9%7D%7B9%7D%20%5C%5C%20%20%20%20)
![- {q}^{2} = - \frac{1}{9} \\](https://tex.z-dn.net/?f=%20-%20%20%7Bq%7D%5E%7B2%7D%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20%5C%5C%20%20%20)
Negatives simplifies
![{q}^{2} = \frac{1}{9} \\](https://tex.z-dn.net/?f=%20%7Bq%7D%5E%7B2%7D%20%3D%20%20%5Cfrac%7B1%7D%7B9%7D%20%5C%5C%20%20%20)
Radical sides
![q = + \frac{1}{3} \\ q = - \frac{1}{3}](https://tex.z-dn.net/?f=q%20%3D%20%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%20q%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20)
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Step (4)
If q = 1/3 :
![81(1 - q) = t(1)](https://tex.z-dn.net/?f=81%281%20-%20q%29%20%3D%20t%281%29)
![81(1 - \frac{1}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%281%20-%20%20%5Cfrac%7B1%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20%20)
![81( \frac{2}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%28%20%5Cfrac%7B2%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20%20)
![t(1) = 27 \times 2](https://tex.z-dn.net/?f=t%281%29%20%3D%2027%20%5Ctimes%202)
![t(1) = 54](https://tex.z-dn.net/?f=t%281%29%20%3D%2054)
So :
![t(2) = t(1) \times q](https://tex.z-dn.net/?f=t%282%29%20%3D%20t%281%29%20%5Ctimes%20q)
![t(2) = 54 \times \frac{1}{3} \\](https://tex.z-dn.net/?f=t%282%29%20%3D%2054%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%20%20)
![t(2) = 18](https://tex.z-dn.net/?f=t%282%29%20%3D%2018)
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
If q = - 1/3 :
![81(1 - q) = t(1)](https://tex.z-dn.net/?f=81%281%20-%20q%29%20%3D%20t%281%29)
![81(1 - ( - \frac{1}{3})) = t(1) \\](https://tex.z-dn.net/?f=81%281%20-%20%28%20-%20%20%5Cfrac%7B1%7D%7B3%7D%29%29%20%3D%20t%281%29%20%5C%5C%20%20)
![81(1 + \frac{1}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%281%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20)
![81( \frac{4}{3}) = t(1) \\](https://tex.z-dn.net/?f=81%28%20%5Cfrac%7B4%7D%7B3%7D%29%20%3D%20t%281%29%20%5C%5C%20%20)
![t(1) = 27 \times 4](https://tex.z-dn.net/?f=t%281%29%20%3D%2027%20%5Ctimes%204)
![t(1) = 108](https://tex.z-dn.net/?f=t%281%29%20%3D%20108)
So :
![t(2) = t(1) \times q](https://tex.z-dn.net/?f=t%282%29%20%3D%20t%281%29%20%5Ctimes%20q)
![t(2) = 108 \times - \frac{1}{3} \\](https://tex.z-dn.net/?f=t%282%29%20%3D%20108%20%5Ctimes%20%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%20%20)
![t(2) = - 36](https://tex.z-dn.net/?f=t%282%29%20%3D%20%20-%2036)
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And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️