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.
Each person gets 2 2/3 cups of ice-cream
Step-by-step explanation:
First, you convert 6 quarts to cups. For every quart, there are 4 cups so you do 6 times 4 and you get 24 then you divide 24 by 9 and you get 2 2/3
Answer:
first one is SAS
Step-by-step explanation:
Answer: Greater of equal sign
Step-by-step explanation:
5+10+x is greater than or equal to 30 ( use the greater of equal to sign)
Answer:
Option A earns higher interest($84115.58)
the difference in interest between the two option is $197.9
Step-by-step explanation:
In the problem we are going to apply both the simple interest formula and compound interest formula and compare which has the best/higher returns
Given data
Principal P= $43,000
Rate r= 6%= 0.06
time t= 3years
n= 4 (applicable for compound interest compounded quarterly)
solving for option A gives her 6% compounded quarterly
the compound interest formula is
Interest is 
=$8411.58
solving for option B which gives her 6% simple interest annually
the simple interest formula is
Interest is
= $8213.68
calculating the diference in interest between the two options we have
= $197.9
Option A earns higher interest
