Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.
Step-by-step explanation:
Salt in the tank is modelled by the Principle of Mass Conservation, which states:
(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)
Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

By expanding the previous equation:

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

Since there is no accumulation within the tank, expression is simplified to this:

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:
, where
.

The solution of this equation is:

The salt concentration after 8 minutes is:

The instantaneous amount of salt in the tank is:
The absolute value of -81 has the same absolute value as that of 81 because they both have the same distance to 0.
I think you can multiply how many are defective in a sample by how much more stuff there is
9514 1404 393
Answer:
(x, y) = (2/5, 1)
Step-by-step explanation:
Substitute for y and solve for x.
1 = -5x +3
-2 = -5x . . . . . . subtract 3
2/5 = x . . . . . . divide by -5
The solution is (x, y) = (2/5, 1).