All categories

3 years ago

How old is a bone that has 12.5% of the original amount radioactive carbon 14 remaining?

1 answer:

4 0

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.

You might be interested in

A helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation. (a) Calculate the

Illusion [34]

angular vel to tangential vel

v=r omega

v = 56 x 100/60 x 2 pi

v = 56x5/3x6

v=560m/s as estimate

100 revs, 5.00m

5 0

2 years ago

Read 2 more answers

A man stands on his balcony, 130 feet above the ground. He looks at the ground, with his sight line forming an angle of 70° with

jenyasd209 [6]

Answer:

d = 380 feet

Explanation:

Height of man = perpendicular= 130 feet

Angle of depression = ∅ = 70 °

distance to bus stop from man = hypotenuse = d = 130 sec∅

As sec ∅ = 1 / cos∅

so d = 130 sec∅ or d = 130 / cos∅

d = 130 / cos(70°)

d = 380 feet

8 0

3 years ago

The water from a fire hose follows a path described by y equals 3.0 plus 0.8 x minus 0.40 x squared (units are in meters). If

ivanzaharov [21]

Explanation:

It is given that, the water from a fire hose follows a path described by equation :

$y=3+0.8x-0.4x^2$ ........(1)

The x component of constant velocity, $v_x=5\ m/s$

We need to find the resultant velocity at the point (2,3).

Let $\dfrac{dx}{dt}=v_x$ and $\dfrac{dy}{dt}=v_y$

Differentiating equation (1) wrt t as,

$\dfrac{dy}{dt}=0.8\times \dfrac{dx}{dt}-0.8x\times \dfrac{dx}{dt}$

$v_y=0.8\times v_x-0.8x\times v_x$

$v_y=0.8v_x(1-x)$

When x = 2 and $v_x=5\ m/s$

So,

$v_y=0.8\times 5\times (1-2)$

$v_y=-4\ m/s$

Resultant velocity, $v=\sqrt{v_x^2+v_y^2}$

$v=\sqrt{5^2+(-4)^2}$

v = 6.4 m/s

So, the resultant velocity at point (2,3) is 6.4 m/s. Hence, this is the required solution.

8 0

3 years ago

The state highway patrol radar guns use a frequency of 8.94 GHz. If you're approaching a speed trap driving 32.3 m/s, what frequ

DaniilM [7]

Answer:

962.5 Hz

Explanation:

given,

frequency = 8.94 GHz

speed of the trap = 32.3 m/s

frequency shift = ?

frequency of shift is calculated using formula

$\Delta f = \dfrac{u}{c}f_o$

c is the speed of light

f_o is the frequency of the radar gun

$\Delta f = \dfrac{32.3}{3\times 10^8}\times 8.94 \times 10^{9}$

$\Delta f = 962.5\ Hz$

the frequency of shift is equal to 962.5 Hz

7 0

3 years ago

Examine the diagram below, which shows stages in the water cycle.

Andru [333]

<span>The stages of the water cycle is caused when water absorbs heat energy from the sun is evaporation because the hint the question gives you is absorbs and absorb means take </span><span>in. Evaporation means is a type of vaporization of a liquid that occurs from the surface of a liquid into a gaseous phase that is not saturated with the evaporating substance.
</span>So i think that B is correct

6 0

3 years ago

Read 2 more answers