If
and
are perpendicular, then their dot product is zero. This means

Solving for n is trivial; it follows that n = 3.
Answer:
Effective half-time of the tracer is 3.6 days
Explanation:
The formula for calculating the decay due to excretion for the first process is ;

here ;
= initial number of tracers
Then to the second process ; we have :

The total decay is as a result of the overall process occurring ; we have :
------ (1)
here ;

Putting the values in (1);we have :


As we also know that:
![\frac{1}{t_{1/2}} = \frac{[t_{1/2}]_{radiation}+[t_{1/2}]_{excretion}}{[t_{1/2}]_{radiation}*[t_{1/2}]_{excretion}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bt_%7B1%2F2%7D%7D%20%3D%20%5Cfrac%7B%5Bt_%7B1%2F2%7D%5D_%7Bradiation%7D%2B%5Bt_%7B1%2F2%7D%5D_%7Bexcretion%7D%7D%7B%5Bt_%7B1%2F2%7D%5D_%7Bradiation%7D%2A%5Bt_%7B1%2F2%7D%5D_%7Bexcretion%7D%7D)
![\frac{1}{t_{1/2}}_{effective}} = \frac{[t_{1/2}]_{radiation}+[t_{1/2}]_{excretion}}{[t_{1/2}]_{radiation}*[t_{1/2}]_{excretion}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bt_%7B1%2F2%7D%7D_%7Beffective%7D%7D%20%3D%20%5Cfrac%7B%5Bt_%7B1%2F2%7D%5D_%7Bradiation%7D%2B%5Bt_%7B1%2F2%7D%5D_%7Bexcretion%7D%7D%7B%5Bt_%7B1%2F2%7D%5D_%7Bradiation%7D%2A%5Bt_%7B1%2F2%7D%5D_%7Bexcretion%7D%7D)



= 3.6 days
Mountains, tops of buildings, and high-flying aircraft are all part of Earth's atmosphere, no matter how high they are. On the other hand, space doesn't belong to our atmosphere, it is outside of it. Having this in mind, the best location to place a telescope used to observe x-rays from stars is in space.
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