X-0.075x=7400
Solve for x
0.925x=7400
x=7,400÷0.925
X=8,000
Answer:
Step-by-step explanation:
Volume of tank is 3000L.
Mass of salt is 15kg
Input rate of water is 30L/min
dV/dt=30L/min
Let y(t) be the amount of salt at any time
Then,
dy/dt = input rate - output rate.
The input rate is zero since only water is added and not salt solution
Now, output rate.
Concentrate on of the salt in the tank at any time (t) is given as
Since it holds initially holds 3000L of brine then the mass to volume rate is y(t)/3000
dy/dt= dV/dt × dM/dV
dy/dt=30×y/3000
dy/dt=y/100
Applying variable separation to solve the ODE
1/y dy=0.01dt
Integrate both side
∫ 1/y dy = ∫ 0.01dt
In(y)= 0.01t + A, .A is constant
Take exponential of both side
y=exp(0.01t+A)
y=exp(0.01t)exp(A)
exp(A) is another constant let say C
y(t)=Cexp(0.01t)
The initial condition given
At t=0 y=15kg
15=Cexp(0)
Therefore, C=15
Then, the solution becomes
y(t) = 15exp(0.01t)
At any time that is the mass.
Answer:
Step-by-step explanation:
C(x) = 15x + 25,500....cost function
R(x) = 32x .....revenue function
break even point (when they are equal)....so set them equal and solve for x
15x + 25,500 = 32x
25,500 = 32x - 15x
25,500 = 17x
25,500 / 17 = x
1500 = x.......so the break even point is when 1500 benches are sold
15x + 25,500 = 32x =
15(1500) + 25,500 32(1500) =
22,500 + 25,500 48,000
48,000
and after selling 1500 benches, they will both equal $48,000
Since drapes have to be covered all over the window and the beneath of the window, both lengths have to be added.
(2 2/3) + ( 2 3/4)
(8/3) + (11/4)
(32+33)/12
65/12
5 5/12
