Answer:
x=0, y=1.
Step-by-step explanation:
-8x+12y= 12
-2x-12y= -12 Adding these 2 equations:
-10x = 0
x = 0.
Plug this into equation 1:
-8(0) + 12y = 12
12y = 12
y = 1.
The decimal equivalent to 5/8 is .625
Step-by-step explanation:
-5n-10=10
-5n=10+10
-5n=20
n=20/-5
n=-4
C
You need to solve for x or y in one equation and and substitute it into the other equation in place of the variable that corresponds to it.
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: