Answer:
t = 5.59x10⁴ y
Explanation:
To calculate the time for the ¹⁴C drops to 1.02 decays/h, we need to use the next equation:
(1)
<em>where 
: is the number of decays with time, A₀: is the initial activity, λ: is the decay constant and t: is the time.</em>
To find A₀ we can use the following equation:
(2)
<em>where N₀: is the initial number of particles of ¹⁴C in the 1.03g of the trees carbon </em>
From equation (2), the N₀ of the ¹⁴C in the trees carbon can be calculated as follows:
<em>where 
: is the tree's carbon mass, 
: is the Avogadro's number and 
: is the ¹²C mass. </em>
Similarly, from equation (2) λ is:
<em>where t 1/2: is the half-life of ¹⁴C= 5700 years </em>
So, the initial activity A₀ is:
Finally, we can calculate the time from equation (1):
I hope it helps you!
Answer:
The water level in the bath tub is rising at a rate of 0.0111 ft/s
Explanation:
Volume of the bath tub = (Area of base) × (height)
Area of base = 18 ft² (constant)
Height = h (variable)
V = 18h
(dV/dt) = 18 (dh/dt)
If (dV/dt) = 0.2 ft³/s
0.2 = 18 (dh/dt)
(dh/dt) = (0.2/18)
(dh/dt) = 0.0111 ft/s
Hope this Helps!!!
Answer:
Explanation:
Acceleration is defined as the change in velocity divided by the time it took to produce such change. The formula then reads:
Where Vf is the final velocity of the object, (in our case 80 m/s)
Vi is the initial velocity of the object (in our case 0 m/s because the object was at rest)
and t is the time it took to change from the Vi to the Vf (in our case 0.05 seconds.
Therefore we have:
Notice that the units of acceleration in the SI system are 
(meters divided square seconds)
Sound travels better in water
