What is the solution to the system of equations represented by these two lines?
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:
Answer:
a) The hot tub can hold 90 cubic feet when completely full.
b) the Hot tub ca hold 667.62 gallons.
c) It will cost approximately $3.34 to fill the hot tub with water.
Step-by-step explanation:
Given:
Length of the tub = 6 feet
Width of the tub = 5 feet
Height of the tub = 3 feet.
a) We need to find how many cubic feet can the hot tub hold if it is completely full.
Now we will find the volume of the tub;
Now Volume of the tub is given by length times width times height.
framing in equation form we get;
Volume of the tub =
Hence The hot tub can hold 90 cubic feet when completely full.
b) Now we need to find how many gallons can it hold.
Given:
1 cubic foot = 7.418 gallons
90 cubic foot = number of gallons hot tub can hold.
By using Unitary method we get;
number of gallons hot tub can hold =
Hence the Hot tub ca hold 667.62 gallons.
c) Now we need to find how much will it cost to fill the hot tub if water costs $5 per 1000 gallons.
Now Given:
1000 gallons = $5
667.62 gallons = Cost to fill the hot tub with water.
By Using Unitary method we get;
Cost to fill the hot tub with water =
Hence It will cost approximately $3.34 to fill the hot tub with water.