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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:
Step-by-step explanation:
Distance upstream = (34-c)(39/60) miles
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Distance downstream = (34+c)(29/60) miles
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Equation:
distance = rate*time
distance up = distance down
(34-c)(39/60) = (34+c)(29/60)
Multiply both sides by 60 to get:
39(34-c) = 29(34+c)
39*34 - 39c = 29*34 + 29c
68c = 340
c = 5 mph speed of the current
Answer:
The method of separation is chromatography.
Step-by-step explanation:
It is given that a drawing of a circle made in the center of a piece of paper with a black marker gets wet, the marker bleeds, and as the water moves through the paper the ink separates into several colors. Here, the method of separation used is chromatography. It is a laboratory technique for the separation of a mixture. When water or dye passes through a medium and changes color, then that means chromatography is used there.
Answer:
The correct answer is the first set {(-1, 8), (0, 5), (2, -1), (3, -4)}
Step-by-step explanation:
In order to determine if the set works, input each ordered pair to see if the statement ends up true. The first two ordered pairs are done below.
(-1, 8)
f(x) = -3x + 5
8 = -3(-1) + 5
8 = 3 + 5
8 = 8 (TRUE)
(0, 5)
f(x) = -3x + 5
5 = -3(0) + 5
5 = 0 + 5
5 = 5 (TRUE)
