Answer:
m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ
Half-Life = 46.21 years.
Step-by-step explanation:
Radioactive reactions always follow a first order reaction dynamic
Let the initial mass of radioactive substance be m₀ and the mass at any time be m
(dm/dt) = -Km (Minus sign because it's a rate of reduction)
The question provides K = 0.015 from the given differential equation
(dm/dt) = -0.015m
(dm/m) = -0.015dt
∫ (dm/m) = -0.015 ∫ dt
Solving the two sides as definite integrals by integrating the left hand side from m₀ to m and the Right hand side from 0 to t.
We obtain
In (m/m₀) = -0.015t
(m/m₀) = (e^(-0.015t))
m = m₀ e^(-0.015t)) = m₀ e⁻⁰•⁰¹⁵ᵗ
m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ
At half life, m(t) = (m₀/2), t = T(1/2)
(m₀/2) = = m₀ e⁻⁰•⁰¹⁵ᵗ
e⁻⁰•⁰¹⁵ᵗ = (1/2)
In e⁻⁰•⁰¹⁵ᵗ = In (1/2)
-0.015t = - In 2
t = (In 2)/0.015
t = (0.693/0.015)
t = 46.21 years
Half life = T(1/2) = t = 46.21 years.
Hope this Helps!!!
Hello !
If you mist find the area of the rhombus,you need to calculate the length of the diagonals.
We have the rhombus ABCD.The diagonals are are AC and BD .
<span>Here's a formula to find out the distance between two points in the Cartesian system : (let's take randomly 2 point and their coordinates)
</span>
<span>
M (m₁,m₂) ; N (n₁,n₂) ⇒ MN = \sqrt{ (m_{1} - n_{1})^{2} + (m_{2} - n_{2})^{2} } </span>
Now it's simple to calculate the diagonals :

The area is :
Answer: 60 u²
The representation is below.
Have a nice day :)
The answer I believe is 5 because 2 vases hold 10 red roses and 5 yellow roses. But since the person has 3 vases but it has to be the same amount as the first person. They would both have 30 flowers in their vases. But then each of the vases has 6 red roses so you just do 30 divided by 6 and you get 5.
Answer:
it will probably take the same amount of time since they are cooking the same amount and the food doesn't take any less to cook if there's more people but they could tidy and bring the food out faster but the time to cook the food will remain the same.
Answer:
3/4=3/4
Step-by-step explanation: