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.
Answer:
Efficiency = 52%
Explanation:
Given:
First stage
heat absorbed, Q₁ at temperature T₁ = 500 K
Heat released, Q₂ at temperature T₂ = 430 K
and the work done is W₁
Second stage
Heat released, Q₂ at temperature T₂ = 430 K
Heat released, Q₃ at temperature T₃ = 240 K
and the work done is W₂
Total work done, W = W₁ + W₂
Now,
The efficiency is given as:

or
Work done = change in heat
thus,
W₁ = Q₁ - Q₂
W₂ = Q₂ - Q₃
Thus,

or

or

also,

or

thus,

thus,

or

or
Efficiency = 52%
Answer: Proxima Centauri is the closet star about 40,208,000,000,000 km away.
Explanation:
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The answer is:
The first option, the walker traveled 360m more than the actual distance between the start and the end points.
Why?
Since each block is 180 m long, we need to calculate the vertical and the horizontal distance, in order to calculate how farther did the travel walk between the start and the end points (displacement).
So, calculating we have:
Traveler:


Actual distance between the start and the end point (displacement):

Now, to calculate how much farter did the traveler walk, we need to use the following equation:

Therefore, we have that distance differnce between the distance covered by the walker and the actual distance is 360m.
Hence, we have that the walker traveled 360m more than the actual distance between the start point and the end point.
Have a nice day!
Answer:
Increasing the mass and decreasing the distance between the two objects.
Explanation:
An increase in mass will cause them to have a stronger pull or gravity. A decrease of distance will make it easier for the objects to fall into each other because they would be further into the other objects area of influence.