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)
Its not one so 52 would be right
Answer: The coordinates of the midpoint of CM with endpoints C(1, -6) and M(7,5) are 
.
Step-by-step explanation:
We know that the coordinates of the midpoint(x,y) of line joining A(a,b) and B(c,d) is given by :-
.....(i)
Given : The coordinates of endpoints of CM are C(1, -6) and M(7,5)
Then , by using (i) , the coordinates of the midpoint of CM would be :-
Hence, the coordinates of the midpoint of CM with endpoints C(1, -6) and M(7,5) are .
Answer:
75°
Step-by-step explanation:
firstly, use the pythagoras theorem
Square root(8²-2²) = 7.75
Then, use sine
sine A= 7.75/8
Sine A=0.9688
A= (sine power of -1) x (0.9688)
A=75.63
1. HI Because two parallel lines have to be on the same plane and never intersect.
2. Skew means the never intersect and they aren't on the same plane so it is GK and DH
3. Angle 3 corresponds because it is the bottom left and 7 is the bottom left.
4. 3 and 5 are same-side interior because they are both on the left side and both are inside.
Hope this helps!
