Via the half-life equation:

Where the time elapse is 11,460 year and the half-life is 5,730 years.

Therefore after 11,460 years the amount of carbon-14 is one fourth (1/4) of the original amount.
Answer:
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The volume of the object must be no larger than
.
Explanation:
In order for an object to be able to float in water, its density must be equal or smaller than the water density.
The density of water is:

This means that the density of the object must be no larger than this value.
We also know that the density of an object is given by

where
m is the mass of the object
V is its volume
For the object in this problem, the mass is

Therefore, we can re-arrange the equation to find its volume:

So, the volume of the object must be no larger than
.
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The feather's vertical position
is determined by

We take the feather's starting position to be the origin, and the downward direction to be positive. Then

so the answer is D.
Answer:
It is used in MRI because it does not damage cells
Radio waves are used for space research because they have very long wavelengths
Explanation:
Many parts of the electromagnetic spectrum are applied in clinical diagnosis and treatment of illnesses. However, these highly ionizing radiation damage cells and its dosage must be carefully managed to avoid creating radiation related health problems for the patients.
Radio waves can be used in MRI without issues because the energy of the radiation is not sufficient to cause damage to cells but is sufficient to provide images for the sake of medical diagnosis.
Secondly, radio waves have long wavelength. This property is suitable for long range
communication. Hence it can be used in space research