The performance level of someone learning askill P(t) is a function of the training time tdPdtand given by the differential equationk(M – P(t)), where k is a positive constant.Two new workers were hired for an assemblyline. Jim processed 26 units during the firsthour and 47 units during the second hour.Mark processed 33 units during the first hourand 49 units the second hour.Estimate the maximum number of units perhour that each worker is capable of processing.Assume that P(0) = 0.1. 131 for Jim and 62 for Mark2. 135 for Jim and 64 for Mark3. 133 for Jim and 58 for Mark4. 148 for Jim and 80 for Mark5. 144 for Jim and 60 for MarkC

Given differential equation is dPdt=kM-Pt. where Pt is the performance level at some time t and k…

Answered: The performance level of someone…

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 a person's utility function for items x and y is u = ln(x) + ln(y), and he currently has $200 in his pocket, and the price of x is $10 per item and the price of y is $20 per item, find the combination that maximises his utility.
A tank contains 350 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t. A(t) = 9
b The number of liters of blood pumped through the lungs in one minute is given by C = where b is quantity of oxygen used by the body in one minute, a is the quantity of oxygen per liter of a-v blood that has just gone through the lungs, and v is the quantity of oxygen per liter of blood that is about to enter the lungs. Suppose a = 160, b=205, and v= 125. Estimate the change in C if a becomes 150, b becomes 200, and v changes to 125. Find the equation for the total differential of C to estimate the change in C. dC=da+db + dv
Newton’s law of cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e., the temperature of its surroundings). We let (t) denote time, T(t) be the temperature of the object at time (t), (T0 = T(0)) (the object’s temperature at (t = 0)), and Tomg be the constant ambient temperature. Set u(t) = T(t) - Tomg and show from Newton’s law of cooling that (u) satisfies the initial value problem (*) u’(t) = ku(t), u(0) = T0 - Tomg for a constant (k). Solve the initial value problem (*), i.e., find u(t)) (expressed in terms of (k), T0, and Tomg . Find T(t).
A tank contains 210 liters of fluid in which 50 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t. Find the number A(t) of grams of salt in the tank at time t.
Newton's law of cooling relates the rate at which a body cools to the difference in temperature between the body and the environment into which it is introduced. The formula is F(t) = To + Cb¹, where F(t) is the temperature of the body at time t, To is the constant temperature of the environment into which the body is introduced, and C and b are constants. Use Newton's law of cooling to solve the problem below. A cup of coffee has cooled from 98° to 50° after 15 minutes in a room at 23°. How long will it take to cool to 30°? It will take approximately minutes. (Round to the nearest integer as needed.) (...)
On a monthly basis, when a factory employs L worker-hours of labor, they can produce Q(L) = 7L + 40L/6 scooters. An investment in labor of K dollars gives them an employment level of L(K)=0.055K – 12,500 K worker-hours. The factory currently invests 2,000 dollars in labor. At what rate is the number of scooters being produced changing with respect to the amount they invest in labor? Round your final answer to 2 decimal places and include units with your answer. а.
A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg

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