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.
Using the equation of the proportional relationship:
Average rate of speed = 60
Time taken to go 300 miles = 5 hrs
Distance travelled in 2.5 hrs = 150 miles
<h3>What is a Equation of a Proportional Relationship?</h3>
A equation of a proportional relationship models the relationship between two variables, x and y, that has a constant of k. It is expressed as y = kx.
Given the following:
Equation: d = 60t
d = distance in miles
t = time in hours
Average rate of speed for the bus = k = 60
Time (t) it would take to go 300 miles (d):
300 = 60(t)
300/60 = t
t = 5 hours
Distance (d) it would travel in 2.5 hours (t):
d = 60(2.5)
d = 150 miles
Learn more about the equation of a proportional relationship on:
brainly.com/question/6869319
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Answer:
Before this problem gets an answer, can you define "gotta." Does this work mean isosceles?
Step-by-step explanation:
The first step is to find the CHANGE. This is done by subtracting the two values and taking the absolute value. Next step is to find the ratio of the change to the original and multiplying by 100% to make it a percentage.
So;
a) change = Ι60 - 25Ι = 35.
ratio of change to original = 35:25,
multiplying by 100% will give 35/25 × 100% = 140%.
Hence it is a 140% INCREASE.
b) change = | 30 - 66 | = 36
the ratio is 36:66
multiplying by 100% = 36/66 × 100% = 0.545454... ×100% ≈ 54.5%
Hence it is a 54.5% DECREASE.
Helpful?
Answer:
138.80
Step-by-step explanation:
I took 149.99 times 15% then times that by the tax rate to get your final answer.
