Answer:
Step-by-step explanation:
Answer:
194.8 miles
Step-by-step explanation:
510 - 315.2 = 194.8
Hope this helps!
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:
First plane: 496x
<span>Second plane: 558( x - 1/2) </span>
<span>Equation: 496x = 558( x - 1/2) </span>
<span>Solving x = 9/2 , or x = 4.5 hours.
Hope this helps.</span>
Answer:
5x^2 + xy + 20
Step-by-step explanation:
Begin with 5x^2+3xy+12, Subtracting 2xy yields 5x^2 + xy + 12. Next, subtracting -8 yields 5x^2 + xy + 12 - (-8), or 5x^2 + xy + 20