Answer:
1. Product
2. Difference
3. Difference
Step-by-step explanation:
:)
Notice that the 2 expressions have 2 common terms.
(r-s) is just (s-r) times (-1)
similarly
(t-s) is just (s-t) times (-1)
this means that :
(r-s) (t-s) + (s-r) (s-t)=-(s-r)[-(s-t)]+(s-r) (s-t)
the 2 minuses in the first multiplication cancel each other so we have:
-(s-r)[-(s-t)]+(s-r) (s-t)=(s-r) (s-t)+(s-r) (s-t)=2(s-r) (s-t)
Answer:
d)<span>2(s-r) (t-s) </span>
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: