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Unformatted text preview: DIFFERENTIAL EQUATIONS AND THEIR APPLICATION and tank 2 contains 250 gal of brine with 14 lb of salt. Brine containing 3 lb of salt per gallon enters tank 1 at the rate of 13 gal/s. Mixed 200 gal of brine (salt water) with 55 lb of salt, brine in tank 1 flows out into tank 2 at the rate tank 2 contains 500 gal of brine with 35 lb of of 7 gal /s. The mixture in tank 2 flows away at salt, and tank 3 is empty. Suppose the mixture the rate of 28 gal /s. How much salt is there in flows out of tank 1 into tank 2 at the rate of 8 each tank as a function of time? gal/ min and the mixture flows out tank 2 into tank 3 at the rate of 22 gal /min. How much 10. Consider two tanks. Initially, tank 1 contains salt is there in each tank as a function of time? 100 gal of brine (salt water) with 35 lb of salt, 13. Consider three tanks. Initially, tank 1 contains and tank 2 contains 400 gal of brine with 15 lb 100 gal of brine (salt water) with 17 lb of salt, of salt. Suppose the mixture flows out of tank 1 tank 2 contains 200 gal of brine with 19 lb of into tank 2 at the rate of 17 gal/ min and the salt, and tank 3 contains 300 gal of brine with mixture flows out of tank 2 into tank I at the 21 lb of salt. Brine containing 5 lb of salt per rate of 6 gal/ min. How much salt is there in gallon enters tank 1 at the rate of 11 gal/s. each tank as a function of time? Mixed brine in tank 1 flows out into tank 2 at 11. Consider two tanks. Initially, tank 1 contains the rate of 18 gal/s and the mixture also flows out of tank 2 into tank 3 at the rate of 18 230 gal of brine (salt water) with 28 lb of salt, gal/s. How much salt is there in each tank as a and tank 2 contains 275 gal of brine with 7 lb function of time? of salt. Brine containing 5 1b of salt per gallon enters tank 1 at the rate of 21 gal/s. Mixed 14. A large tank contains 7 gal of pure water. brine in tank 1 flows out at the rate of 18 Polluted water containing 7 g of bacteria per gal/s, half flowing into tank 2. The mixture in gallon enters at the rate of 14 gal/h. A well- tank 2 flows away at the rate of 4 gal/s. How mixed mixture is removed at the rate of 4 much salt is there in each tank as a function of gal/h. However, it is also known that the bac- teria multiply inside the tank at a growth rate time? of 2% per hour. Determine the amount of 12. Consider three tanks. Initially, tank 1 contains bacteria in the tank as a function of time. 1.10 Electronic Circuits One of the applications of differential equations that will frequently recur throughout this book is the theory of electronic circuits. There are several reasons for this, among them the importance of circuit theory and the pervasiveness of differential equations in circuit theory. (One of the authors received his first exposure to circuit theory from a highly mathematical electrical engineering professor by the name of Amar Bose. You would be correct if you recognized the significance of his last name.) Also, circuits are one example of what could be called network models. Network models are widely used, for example, in manufacturing and other economic systems. Circuits will be covered again in greater detail later. In this section we shall introduce the basic circuit concepts we shall use and give some simple examples of circuits that are described by first-order differential equations. We consider only lumped-parameter circuits. In circuit theory, the word circuit means that quantities such as current are determined solely by...
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  • Fall '10
  • capretta

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