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!!!
Answer:
The lines are parallel
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
Remember that
If two lines are parallel, then their slopes are the same
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
step 1
Find the slope JK
we have
substitute the values
step 2
Find the slope LM
we have
substitute the values
step 3
Compare the slopes
so
therefore
The lines are parallel
Answer:
Step-by-step explanation:
In math, a term is a combination of coefficients, constants and /or variables, each combination being separated by either a + sign or a - sign.
The "median" of a set is just the middle value for an odd number of ordered elements or the average of the middle two values for an even number of ordered elements. In this case you are four elements so it would be the average of the second and third terms...
median=(12.5+13.24)/2
median=12.87 (exactly, no rounding needed)
Answer:
I believe it's the 1st one.
HOPE IT HELPS! BE SAFE :3
