Answer:
870
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
x² - 3x - 54 = 0
x² - 9x + 6x - 54 = 0
x(x - 9) + 6(x - 9) = 0
(x - 9)(x + 6) = 0
x = -6,9
Answer:
y = 30x
Step-by-step explanation:
y is the amount of money
30 is the constant, the amount of money she gets per x, month
Write them out as a fraction then reduce them. If theyre the same then its proportional.
25/45 can be cancelled down to 5/9
15/27 can be cancelled down to 3/9
So no theyre not.
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: