A tank holds 2000 liters of water in which 400 grams of salt have been dissolved. Saltwater with a concentration of 2 grams/liter is pumped in at 2 liters/minute and the well mixed saltwater solution ispumped out at the same rate. Write initial the value problem for:a) The mass (i.e number of grams) of salt in the tank at time t.dsdtS(0) = = 200The solution is: S(t)=b) The concentration, in grams/liter, of salt in the tank at time t (this should be very easy).dCdtC(0) =The solution is: C(t)=symbolic formatting help

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Answered: A tank holds 2000 liters of water in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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At what speed should a fish swim upstream so as to reach its destination with the least expenditure of energy? The energy depends on the friction of the fish through the water and on the duration of the trip. If the fish swims with velocity v, the energy has been found experimentally to be proportional to (for constant k > 2) times the duration of the trip. A distance of s miles against a current of speed c requires time -c (distance divided by speed). The energy required is then proportional to k = 3, minimizing energy is equivalent to minimizing |- v³ E(v) = = V C vk s v-c. For Find the speed v with which the fish should swim in order to minimize its expenditure E(v). (Your answer will depend on c, the speed of the current.)
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Set up an I.V.P. and solve using the following: Suppose a large mixing tank initially holds 500 liters of pure water. A brine solution is pumped into the tank at a rate of 3 L/min with a concentration of 0.2 kilograms of salt per liter. If the well-stirred solution is pumped out at the same rate, find the number of kilograms of salt in the tank at time t, A(t).
0.5 kg/L Pollutant Pure Water 15 L/min 5 L/min 1000 L 15 L/min 1000 L Pure Water with 5 kg pollutant Tank A Tank B 20 L/min For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are zero and 5kg, respectively. • It is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and yB(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. What is the final equation of yA(t)? What is the final equation of yB(t)?
Fast pls solve this question in 5 min pls I will give u like for sure . Soo
dC The rate of change in the concentration of a drug with respect to time in a user's blood is given by = - kC + D(t), where D(t) is dosage at time t and k is the rate that the drug leaves the bloodstream. Complete dt parts (a) and (b) below. t (a) Solve this linear equation to show that, if C(0) = 0, then C(t) = e -kt ,ky D(y)dy. dC dy Begin by writing the differential equation, = - kC + D(t), in the form dt + P(x)y = Q(x). dx dC + %3D dt
Water flows into a tank, and a certain part of it drains out through a valve. The volume v (in cubic feet) of water in the tank at time t satisfies the equation dv/dt = 5 − (v/3). If the process continues for a long time, how much water will be in the tank?a. 13 cubic feetb. 14 cubic feetc. 15 cubic feetd. 16 cubic feet

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