Give him a toy or a treat or just some one on one attention
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!!!
That means that, for example:
if your number is 49 the nearest whole number would be 50.
so by saying estimate the figure to the nearest whole number , they are basically saying find your nearest whole number.
Answer:
Step-by-step explanation:
p = power washer and g = generator
6p + 6g = 90 .....multiply by 4
4p + 8g = 100 ....multiply by -6
---------------------
24p + 24g = 360 (result of multiplying by 4)
-24p - 48g = -600 (result of multiplying by -6)
---------------------add
-24g = - 240
g = -240 / -24
g = 10 <=== the generator cost $ 10 per hr
6p + 6g = 90
6p + 6(10) = 90
6p + 60 = 90
6p = 90 - 60
6p = 30
p = 30/6
p = 5 <==== the power washer costs $ 5 per hr
check...
4p + 8g = 100
4(5) + 8(10) = 100
20 + 80 = 100
100 = 100 (correct)
Answer:
x = 20
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Using ΔAHC , then
∠ACH = 180 - (2x + 100) = 180 - 2x - 100 = 80 - 2x
∠ECD = ∠ACB ( vertical angles are congruent ), thus
∠ECD = ∠ACH + ∠HCB, that is
3x = 80 - 2x + x
3x = 80 - x ( add x to both sides )
4x = 80 ( divide both sides by 4 )
x = 20
