For any integer x,x2-x will always produce an even value
1 answer:
Consider expression First, you can factor it:
Since x is integer number, then you can see that x-1 is previous integer number (x-1 is 1 unit smaller than x).
Therefore, x-1 and x are two consecutive integers. When you have two consecutive integers, one of them is always even and one is always odd. Multiplying even integer number by odd integer number you always get even integer number.
Thus, is always even.
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when you breathe normally, about 12 % of the air of your lungs is replaced with each breath. how much of the original 500 ml remains after 50 breaths
If you think of number of breaths that you take as a time measurement, you can model the amount of air from the first breath you take left in your lungs with the recursive function
Why does this work? Initially, you start with 500 mL of air that you breathe in, so
. After the second breath, you have 12% of the original air left in your lungs, or 
. After the third breath, you have 
, and so on.
You can find the amount of original air left in your lungs after
breaths by solving for 
explicitly. This isn't too hard:
and so on. The pattern is such that you arrive at
and so the amount of air remaining after
breaths is
which is a very small number close to zero.</span>
when you breathe normally, about 12 % of the air of your lungs is replaced with each breath. how much of the original 500 ml remains after 50 breaths
If you think of number of breaths that you take as a time measurement, you can model the amount of air from the first breath you take left in your lungs with the recursive function
Why does this work? Initially, you start with 500 mL of air that you breathe in, so
You can find the amount of original air left in your lungs after
and so on. The pattern is such that you arrive at
and so the amount of air remaining after
which is a very small number close to zero.</span>