Answer:
Step-by-step explanation:
For this case the solution flows at a rate of 2L/min and leaves at 1L/min. So then we can conclude the volume is given by
Since the initial volume is 10 L and the volume increase at a rate of 1L/min.
For this case we can define A as the concentration for the salt in the container. And for this case we can set up the following differential equation:
Because at the begin we have a concentration of 8 gr/L and would be decreasing at a rate of
So then we can reorder the differential equation like this:
We find the solution using the integration factor:
And then the solution would be given by:
And if we simplify this we got:
And after do the integral we got:
And using the initial condition t=0 A= 20 we have this:
So then we have this function for the solution of A:
And now replacinf t= 40 we got:
The two numbers are 41 & 37.
The way to solve this is by setting up an equation. We know that 2 numbers are going to equal 78, so here would be the general equation (let x represent the number we don't know):
(x) + (x + 4) = 78
Now, we need to simplify it (combine like terms):
2x + 4 = 78
Then you can solve it like any other equation. Subtract 4 on both sides:
2x = 74
Divide by 2 on both sides:
x = 37.
So, now you know one number is equal to 37 and that the other is 37 + 4.
That's how you get 37 & 41.
The two consecutive integers would be 112 and 114