2. A tank containing 100 gallons of water initially has 10lbs of salt dissolved in it. Asolution containing 0.55 lbs of salt per gallon is pumped into the tank at a rate of 2gallons per minute. The solution is then mixed thoroughly and is removed from thetank at the same rate of 2 gallons per minute.Set up a differential equation and solve for Q(t) the amount of salt indQamount out.dta.b.the tank at time t. Recall that = amount inWhat is lim Q (t)?t→∞

Before more salt is added to the tank at time t=0:The volume of brine V(0)=100 gal.The quantity of…

Answered: 2. A tank containing 100 gallons of…

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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Suppose 135 small business firms are threatened by bankruptcy. If y is the number bankrupt by time t, then 135 - y is the number not yet bankrupt by time t. The rate of change of y is proportional to the product of y and 135 - y. Let 2010 correspond to t= 0. Assume 20 firms are bankrupt at t= 0. Complete parts a. and b. below. a. Write a differential equation using the given information. Use 0.003 for the constant of proportionality. dy The differential equation is dt
The rate of change in the number of deer, D, within a town is inversely proportional to the number of people, p, living within the town. Write the differential equation to solve for D(t). Do not solve. dD dp dD dp dD dp dD dp D = pk = Dk k P =
1. Miles' neighbor, Andy says his maximum heart rate is 90 BPM at 50% intensity. Use your model to determine how old Andy is. Be prepared to explain HOW you got the answer. V=1.37⋅y+17.8V=1.37⋅y+17.8 V = value of CA wine market in billions y = years since 2000 Q. In what year should the CA wine market be worth $45 billion (assuming this equation applies at that time)?
The deceleration of a certain tugboat in the water is directly proportional to the cube of the speed of the tug at any time t. The velocity of the tug is initially 5 m/s? and reduces to 3 m/s? after 2s. Show that the equation of motion of the tug is 225 V² = by using differential equations. 8t+9
A 288 pound object is suspended from a spring. The spring stretches an extra 9 inches with the weight attached. The spring-and-mass system is then submerged in a viscous fluid that exerts 16 pounds of force when the mass has velocity 2 ft/sec. What is the differential equation for this spring-and-mass system? (Use u as the dependent variable.) This system is ? For what value of y would the system be critically damped? (if the given system is already critically damped, enter the given value for y.)
Please solve this Chemical Mixture Problem (Differential Equation) and provide a complete solution. A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 liters per minute. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes?
dw To determine how fast a change in weight will occur, the most plausible assumption is that is proportional to the net excess (or deficit) C - 19.25w in the number of calories per day. Answer parts a. through e. dt below. a. Assume C is constant and write a differential equation to express this relationship. Use k to represent the constant of proportionality. dw dt
Write a differential equation to model this physical situation. Snow is falling at a constant rate of 3/5 in per hour. It is being removed at a constant rate of 45% of the amount of snow on the ground per hour. If we use h(t) as the height of the snow at time t, and the removal of snow began at a height of 4 in --such that h(0)=4 --what would be the equation for the rate of change of the height as a function of time?

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