By V.V. Amelkin

ISBN-10: 5030005218

ISBN-13: 9785030005218

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Two liquid chemical substances A and B occupying a volume of 10 and 20 liters, respectively, form as a result of a chemical reaction a new liquid chemical substance C. Assuming that the temperature does not change in the process of the reaction and that every two volumes of substance A and one vol3* r 36 Differential Equations in Applications ume of substanceBform three volumes of substance C, {ind the amount of substance C at an arbitrary moment of time t if it takes 20 min to form 6 liters of C.

Thus, the equation 1 dx 2w··b shows that constant b measures the average effectiveness of each man on side y. The same interpretation can be given to the term ——cx (t). Of course, there is no simple way in which we can calculate the effectiveness coefficients b and c. One way is to write these coefficients in the form b == I',/py, C == Txpx, (48) 60 Differential Equations in Applications where ry and rx are the coefficients of firepower of sides y and x, respectively, and py and px are the probabilities that each shot fired by sides y and x, respectively, proves accurate.

The aforesaid implies that the destroyer must first go straight to point O until it finds itself at the same distance x from O as the submarine. Obviously, distance x can be found either from the equation 27 _ 3--:1: 72-- 2v or from the equation x _ 3-]-:: T `"` -5- ’ where v is the submarine’s speed a11d 20 the destr0yer’s speed. Solving these equations, we find that this distance is either one mile or three miles. Now, if the two still have not met, the destroyer must circle pole O (clockwise or counterclockwise) and head away from the pole at a speed equal to that of the submarine, v.

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