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2 answers:
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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:
Hey!
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x – 3y = 3 is written in standard form. We can write in the slope-intercept form.
x - 3y = 3
x - 3y - x = 3 - x
3y = 3 - x
3y/3 = 3/3 - 3/x
y = 1 - 3/x
y = 1/3x - 1
Now, we know that the y-intercept is -1 and the slope is 1/3
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Hence, the answer is
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Hope This Helped! Good Luck!
