Answer:
Step-by-step explanation:
Given that during the period from 1790 to 1930, the US population P(t) (t in years) grew from 3.9 million to 123.2 million. Throughout this period, P(t) remained close to the solution of the initial value problem.
a) 1930 population is the population at time t = 40 years taking base year as 40
We can solve the differential equation using separation of variables
Resolve into partial fractions
Integrate to get
ln P -0.00474/0.0001489 (ln (0.0001489P-0.03135) = t+C
ln P -31.833 (ln (0.0001489P-0.03135) =t+C
Limiting population would be infinity.
The equation which can be used to find the number of quarters and nickels is; n + q = 84, 0.05n + 0.25q = 17.80.
<h3>Quarters and nickels</h3>
- Total coins = 84
- Total value = $17.80
let
- Number of quarters = q
- Number of nickels = n
n + q = 84
0.05n + 0.25q = 17.80
From equation (1)
n = 84 - q
Substitute into (2)
0.05n + 0.25q = 17.80
0.05(84 - q) + 0.25q = 17.80
4.2 - 0.05q + 0.25q = 17.80
- 0.05q + 0.25q = 17.80 - 4.2
0.20q = 13.60
q = 13.60 / 0.20
q = 68
Substitute q = 68 into
n + q = 84
n + 68 = 84
n = 84 - 68
n = 16
Therefore, the number of quarters and nickels are 68 and 16 respectively.
Learn more about quarters and nickels:
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Answer:
13, 13√3, 26
Step-by-step explanation:
30 60 90 right triangle
Ratio of short leg : long leg : hypo = a : a√3 : 2a
Given short leg = 13, so long leg = 13√3 and hypo = 13 * 2 = 26
Answer:
13, 13√3, 26
Answer:
5/16
Step-by-step explanation:
In 5/2 the time, we expect that 5/2 × 1/8 = 5/16 of the test will be complete.
_____
5/2 × (2/5 h) = 1 h
15 + 0.75x = 57
-15 -15
0.75x = 42
0.75x/0.75 = 42/0.75
x = 56 people
The student interviewed 56 people on the day he earned $57
