Nuclear decay formula is N(t)=N₀*2^-(t/T), where N(t) is the amount of nuclear material in some moment t, N₀ is the original amount of nuclear material, t is time and T is the half life of the material, in this case carbon 14. In our case N(t)=12.5% of N₀ or N(t)=0.125*N₀, T=5730 years and we need to solve for t:
0.125*N₀=N₀*2^-(t/T), N₀ cancels out and we get:
0.125=2^-(t/T),
ln(0.125)=ln(2^-(t/T))
ln(0.125)=-(t/T)*ln(2), we divide by ln(2),
ln(0.125)/ln(2)=-t/T, multiply by T,
{ln(0.125)/ln(2)}*T=-t, divide by (-1) and plug in T=5730 years,
{ln(0.125)/[-ln(2)]}*5730=t
t=3*5730=17190 years.
The bone is t= 17190 years old.
The magnitude of the magnetic dipole moment of the bar magnet is 1.2 Am²
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Magnetic dipole moment of the bar magnet</h3>
The magnitude of the magnetic dipole moment of the bar magnet at distance from its axis is calculated as follows;

where;
- B is magnetic field
- m is dipole moment
- μ is permeability of free space
m = (4π x 0.1³ x 2.4 x 10⁻⁴)/(2 x 4π x 10⁻⁷)
m = 1.2 Am²
The complete question is below:
What is the magnitude of the magnetic dipole moment of the bar magnet from 0.1 m of its axis and magnetic field strength of 2.4 x 10⁻⁴ T.
Learn more about dipole moment here: brainly.com/question/27590192
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Answer:
when a magnet is hanged freely in air it turns in the direction of the north and south while the magnetic north pole faces the south pole of the earth and magnetic south pole faces the north pole if the earth
Answer:
f1 = 12.90 Hz
Explanation:
To calculate the first harmonic frequency you use the following formula for n = 1:

( 1 )
It is necessary that the unist are in meters, then you have:
L: length of the string = 60cm = 0.6m
M: mass of the string = 0.05kg
T: tension on the string = 20 N
you replace the values of L, M and T in the expression (1) for getting f1:

Hence, the first harmonic has a frequency of 12.90 Hz