Answer:
Step-by-step explanation:
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
Suppose,
x = distance of the man
<span>s = length of the shadow</span>
<span>Using the idea of similar triangles</span>
<span>6/s = 23/(x + s) </span>
<span>Simplifying:</span>
we get,
<span>6(x + s) = 23s </span>
<span>6x + 6s = 23s </span>
<span>6x = 17s </span>
<span>Differentiating with respect to time, </span>
<span>6(dx/dt) = 17(ds/dt) </span>
<span>Manipulating the above equation for ds/dt,</span>
<span>ds/dt = (17/6)(dx/dt) </span>
<span>ds/dt = (17/6)(6) </span>
<span>ds/dt = 17 ft/sec.</span>
Answer:
1) Who wear: 2:5
Whi don't wear: 3:5
2) 10 don't wear spectacles
3) 25
Hope it helps!!!
