Answer:
A(t) = 160 - 130 e^(-t/40)
Explanation:
At the start, the tank contains A(0) = 30 g of salt.
Salt flows in at a rate of
(1 g/L) * (4 L/min) = 5 g/min
and flows out at a rate of
(A(t)/160 g/L) * (4 L/min) = A(t)/40 g/min
so that the amount of salt in the tank at time t changes according to
A'(t) = 4 - A(t)/40
Solve the ODE for A(t):
A'(t) + A(t)/40 = 4
e^(t/40) A'(t) + e^(t/40)/40 A(t) = 4e^(t/40)
(e^(t/40) A(t))' = 4e^(t/40)
e^(t/40) A(t) = 160e^(t/40) + C
A(t) = 160 + Ce^(-t/40)
Given that A(0) = 30, we find
30 = 160 + C
C = -130
so that the amount of salt in the tank at time t is
A(t) = 160 - 130 e^(-t/40)
Answer:
Steel and wood
Explanation:
For a material to resist stress and vibration, it must have high ductility, which is the ability to undergo large deformations and tension. Modern buildings are often constructed with structural steel, a component that comes in a variety of shapes and allows buildings to bend without breaking.
Answer:
the percent increase in the velocity of air is 25.65%
Explanation:
Hello!
The first thing we must consider to solve this problem is the continuity equation that states that the amount of mass flow that enters a system is the same as what should come out.
m1=m2
Now remember that mass flow is given by the product of density, cross-sectional area and velocity
(α1)(V1)(A1)=(α2)(V2)(A2)
where
α=density
V=velocity
A=area
Now we can assume that the input and output areas are equal
(α1)(V1)=(α2)(V2)
Now we can use the equation that defines the percentage of increase, in this case for speed
Now we use the equation obtained in the previous step, and replace values
the percent increase in the velocity of air is 25.65%