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Step-by-step explanation:
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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:
I believe it’s pie times radius squared so 6ft = 3.14•3 squares and 8ft = 3.14•4 squares and then subtract
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Answer: x = 16</h3>
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Explanation:
On that diagram, the unmarked angle above the (6x-8) is equal to (5x+12). This is because the unmarked angle and the angle marked with (5x+12) are corresponding angles. Corresponding angles must be congruent if you want line m to be parallel to line n.
From here we add up (5x+12) and (6x-8) and set that sum equal to 180. Solve for x
We get the following:
(5x+12)+(6x-8) = 180
5x+12+6x-8 = 180
(5x+6x)+(12-8) = 180
11x+4 = 180
11x = 180-4
11x = 176
x = 176/11
x = 16