Answer:
Q(t) = Q_o*e^(-0.000120968*t)
Step-by-step explanation:
Given:
- The ODE of the life of Carbon-14:
Q' = -r*Q
- The initial conditions Q(0) = Q_o
- Carbon isotope reaches its half life in t = 5730 yrs
Find:
The expression for Q(t).
Solution:
- Assuming Q(t) satisfies:
Q' = -r*Q
- Separate variables:
dQ / Q = -r .dt
- Integrate both sides:
Ln(Q) = -r*t + C
- Make the relation for Q:
Q = C*e^(-r*t)
- Using initial conditions given:
Q(0) = Q_o
Q_o = C*e^(-r*0)
C = Q_o
- The relation is:
Q(t) = Q_o*e^(-r*t)
- We are also given that the half life of carbon is t = 5730 years:
Q_o / 2 = Q_o*e^(-5730*r)
-Ln(0.5) = 5730*r
r = -Ln(0.5)/5730
r = 0.000120968
- Hence, our expression for Q(t) would be:
Q(t) = Q_o*e^(-0.000120968*t)
Answer:
A.
Step-by-step explanation:
A. is the answer because they list all of the sandwiches, soups, and beverages with every possible combination.
Answer:
This was already asked
Step-by-step explanation:
Answer is 4 lb.,12 oz. As one pound has 16 ounces. When we convert the given 5 lb. into ounces we multiply it by 16. 5 lb = 5 x 16 oz 5 lb = 80 oz When we subtract 4 oz from 80 oz We get 80 - 4 = 76 oz Which is 64 oz + 12 oz (16 x 4) oz + 12 oz Which will be 4 lb. + 12 oz So the answer will be 4 lb., 12 oz.
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Should would have ran 8.6 KM
First, multiply the top equation by 2 and bottom by -3.
60x+60y=900
-60x-75y=-1035
————————
-15y=-135
—————-
-15=-15
y=9
So the answer should be 9.
