Answer: 3
Step-by-step explanation:
The sine of an angle is equal to the cosine of its complement, so

<span>From the message you sent me:
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>
Answer: the first one is the answer I think
Step-by-step explanation:
Here I copy the steps and indicate where the error is.
Square root of negative 2x plus 1 − 3 = x=> <span>this is the starting equation
</span>
√[ - 2x + 1] - 3 = x
Square root of negative 2x plus 1 − 3 + 3 = x + 3 in this step she added 3 to each side, which is fine
<span> Square root
of negative 2x plus 1 = x + 3 <span>she made the addtions => fine</span></span>
Square root of negative 2x plus 1 − 1 = x + 3 – 1 due to <span>plus 1 in inside the square root, this step will not help</span>
<span> Square root
of negative 2 x = x + 2 <span>wrong! she cannot simplify - 1 that is out of the square root with +1 that is inside the square root
</span></span>
<span>Then, from here on all is wrong, but she made other additional mistakes.</span>
(Square root of negative 2 x)2 = (x − 4)2 −2x <span> the right side should be (x+2)^2 which is x^2 + 4x +4 not (x-4)^2 - 2x</span>
Later she made a mistake changing the sign of -8x to +8x
Those are the mistakes. Finally, the global error is that she should verify whether the found values satisfied the original equation.