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First Order Linear Quiz#2
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Questions in this quiz (6)
1Find the general solution to dx/dt = 1 + t − x−xt.
(In each option, C is an arbitrary constant.)- Ax = Ce^−t
- Bx = 1 − Ce^(t + t^2/2)
- Cx = 1− Ce^(−t − t^2/2)
- Dx = (t + t^2/2 + C) e^(−t − t^2/2)
2Find the general solution to x^2y'(x) + 2xy=cos^2(x).
(In each option, C is an arbitrary constant.)- Ay = 1/2x + sin(2x)/4x^2 + C/x^2
- By = 1/2x + sin(2x)/4x^2 + C
- Cy = [sin^2(x) + C]/x^2
- Dy = x^2 + sin^2(x)/4 + C
3A cup of coffee has a temperature of 95∘C and is in a room where the temperature is 20∘C.
Let T= the temperature of the coffee after t minutes.
Assuming Newton’s Law of Cooling, which of the following options describes T ?- AdT/dt = k(T−20), k a positive constant.
- BdT/dt = −k(T−20), k a positive constant.
- CdT/dt = −k(T−95), k a positive constant.
- DdT/dt = k(T−95), k a positive constant.
4A learning curve is the graph of a function P(t), the performance of someone learning a skill as a function of the training time. Let M be the maximum level of performance of which the learner is capable. Suppose that the rate at which the performance improves is proportional to the difference between the maximum level and the current level. Write down the differential equation which models the learning.
- AdM/dt = k(M−P), k a positive constant.
- BdP/dt = kM−P, k a positive constant.
- CdP/dt = −k(M−P), k a positive constant.
- DdP/dt = k(M−P), k a positive constant.
5A tank holds 1000 litres of water, in which 15 kg of salt is dissolved. Pure water enters the tank at the rate of 10 litres per minute. The solution is kept thoroughly mixed and is drained from the tank at the same rate. If m is the mass of salt in the tank at time t, which of the following options describes the rate of change of the mass of salt in the tank?
- Adm/dt = 15 − m/100
- Bdm/dt = −m/100
- Cdm/dt = −15/100
- Ddm/dt = (15 − m)/1000
6A tank holds 1000 litres of pure water. Brine which contains 0.05 kg of salt per litre enters the tank at the rate of 5 litres per minute. The solution is kept thoroughly mixed and is drained from the tank at the rate of 5 litres per minute. If m is the mass of salt in the tank at time t, which of the following options describes the rate of change of the mass of salt in the tank?
- Adm/dt = −m/200
- Bdm/dt = 0.25
- Cdm/dt = 50 − m/200
- Ddm/dt = 0.05 − m/200
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- Quiz on First Order Linear Quiz#2, created by DSO_SCHOLARS on 07/03/2015.
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- DSO_SCHOLARS
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- English
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