notes 2-3

# notes 2-3 - in the tank at any time before the instant when...

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SECTION 2.3 MODELING We may be faced with a problem of designing a system to produce a certain output, or we may want to make predictions about the behavior of some physical system. Here’s what we might do. 1. Construct a mathematical model, that is, translate the physical situation into mathe- matics. You’ll need to choose variables, functions, units, etc., and decide what physical laws to use. For more details, see p. 7. 2. Do the mathematics. 3. Compare your results with observations/experiments. 4. Repeat as needed. EXAMPLE. A tank with capacity 500 gallons originally contains 200 gallons of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon runs in at 3 gal/min, and the mixture is allowed to ﬂow out of the tank at a rate of 2 gal/min. Find the amount of salt

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Unformatted text preview: in the tank at any time before the instant when the solution begins to overﬂow. Find the concentration of salt in the tank at this instant. How does it compare with the theoretical limiting concentration if the tank had inﬁnite capacity? HOMEWORK: SECTION 2.3 EXAMPLE (if time). Snow starts falling early in the morning at a constant rate. A snowplow that clears snow at a constant rate by volume (perhaps a constant number of cubic feet per hour) starts at 7 a.m. and by 8 a.m. has traveled two miles. The snowplow then takes two more hours to go an additional two miles. When did it start snowing?...
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notes 2-3 - in the tank at any time before the instant when...

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