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Chapter 3: Q 3.6-15E (page 131)
The solution to the initial value problemcrosses the x-axis at a point in the interval [0,14].By experimenting with the improved Euler’s method subroutine, determine this point to two decimal places.
The solution on the given conditions and on the interval cross x-axis at x = 1.27.
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Use the improved Euler’s method with tolerance to approximate the solution to , at x= 1. For a tolerance of , use a stopping procedure based on the absolute error.
On a mild Saturday morning while people are working inside, the furnace keeps the temperature inside the building at 21°C. At noon the furnace is turned off, and the people go home. The temperature outside is a constant 12°C for the rest of the afternoon. If the time constant for the building is 3 hr, when will the temperature inside the building reach 16°C? If some windows are left open and the time constant drops to 2 hr, when will the temperature inside reach 16°C?
In Problems 23–27, assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes for one-half of the substance to disintegrate. The only undiscovered isotopes of the two unknown elements hohum and inertium (symbols Hh and It) are radioactive. Hohum decays into inertium with a decay constant of 2/yr, and inertium decays into the nonradioactive isotope of bunkum (symbol Bu) with a decay constant of 1/yr. An initial mass of 1 kg of hohum is put into a non-radiaoctive container, with no other source of hohum, inertium, or bunkum. How much of each of the three elements is in the container after t yr? (The decay constant is the constant of proportionality in the statement that the rate of loss of mass of the element at any time is proportional to the mass of the element at that time.)
Transmission Lines.In the study of the electric field that is induced by two nearby transmission lines, an equation of the formarises. Letand. If z(0)=1, use the fourth-order Runge–Kutta algorithm to approximate z(1). For a tolerance of, use a stopping procedure based on the absolute error.
In Problem 13, if a larger tank with a heat capacity of per thousand Btu and a time constant of 72 hris use instead (with all other factors being the same), what will be the temperature in the tank after 12 hr?
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