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.
Look up the law of sines, I suggest Khan Academy. It is better if you know how to do it, it is very useful.
The coordinate of point S from the giving coordinate point is (-8,4)
<h3>Midpoint of coordinates</h3>
The formula for calculating the midpoint of coordinate point is expressed as:
M(x,y) = {(x₁+x₂)/2, (y₁+y₂)/2}
Determine the measure of the coordinate S
-2 = 4+x₂/2
2(-2) = 4+x₂
x₂ = -4-4
x₂ = -8
Similarly
0 = -4+y₂/2
0(2) = -4+y₂
y₂ = 4
Hence the coordinate of point S from the giving coordinate point is (-8,4)
Learn more on midpoint here: brainly.com/question/5566419
#SPJ1
So first you would divide the 9 on both sides then 6 divided by 9 would be .6 repeating so m=.6 repeating.
Take the root of both sides and solve.
