Answer:
13) x = 30
14) x = 22.5
15) x = 36
Step-by-step explanation:
13) 4x+2x = 180
6x = 180
x = 30
14) 3x+5x = 180
8x = 180
x = 22.5
15) 2x+3x+2x+3x = 360
10x = 360
x = 36
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:
12 wins and 4 losses
Step-by-step explanation:
3 wins and 4 losses means they have played so far 7 games.
They play a total of 16 games in a season.
16 - 7 = 9
They still have to play 9 more games.
Add 9 wins to the 3 wins.
9 + 3 = 12
That means they'd finish the season with 12 wins and 4 losses.
Answer:
Step-by-step explanation:
the slope is the change in y over the change in x
From the points given, your y's are 10 and 1.
From the points given, your x's are 7 and 2. To find the changes subtract them.
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