Answer:
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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:
Answer:
The difference is 4–3. If you want the difference between 3 and -4, then the difference is 7.
Step-by-step explanation:
Answer:
<u>x = 1.07</u>
Step-by-step explanation:
13 ( 6x - 9) = -33
78x - 117 = -33 ( opening brackets and multiplying )
78x = 84 ( - 117 taken to the other side makes it positive)
x = 84 / 78
x = <u>1.07</u>