Answer:
x = 50*e∧ -t/100
Step-by-step explanation:
We assume:
1.-That the volume of mixing is always constant 300 gallons
2.-The mixing is instantaneous
Δ(x)t = Amount in - Amount out
Amount = rate * concentration*Δt
Amount in = 3 gallons/ min * 0 = 0
Amount out = 3 gallons/min * x/ 300*Δt
Then
Δ(x)t/Δt = - 3*x/300 Δt⇒0 lim Δ(x)t/Δt = dx/dt
dx/dt = - x/100
dx/ x = - dt/100
A linear first degree differential equation
∫ dx/x = ∫ - dt/100
Ln x = - t/100 + C
initial conditions to determine C
t= 0 x = 50 pounds
Ln (50) = 0/100 * C
C = ln (50)
Then final solution is:
Ln x = - t/100 + Ln(50) or
e∧ Lnx = e ∧ ( -t/100 + Ln(50))
x = e∧ ( -t/100) * e∧Ln(50)
x = e∧ ( -t/100) * 50
x = 50*e∧ -t/100
Answer:
A
Step-by-step explanation:
A
Answer:
im just going to copy and paste the correct ones and their answers:
<u>Problem: The sum of twice a number and −6 is 9 more than the opposite of the number. Find the number.</u>
<u>Equation: 2n − 6 = 9 − n</u>
<em>n = 5</em>
<u>Problem: Anna drove 450 km in 6 hours. Find her rate of travel.</u>
<u>Equation: 450r = 6</u>
<em>r = 75</em>
<u>Problem: Three times a number increased by 44 is the same as the opposite of the number. Find the number.</u>
<u>Equation: 3n + 44 = −n</u>
<em>n = -11</em>
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