Determine the recursive formulas for the Taylor method of order 4 for the initial value problem .
Apply the chain rule.
So, the equation is
Apply the same procedure as step 1
The recursive formula is
Where starting points are .
Hence the solution is
An object of mass 5 kg is given an initial downward velocity of 50 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -10v, where v is the velocity of the object in m/sec. Determine the equation of motion of the object. If the object is initially 500 m above the ground, determine when the object will strike the ground.
Beginning at time t=0, fresh water is pumped at the rate of 3 gal/min into a 60-gal tank initially filled with brine. The resulting less-and-less salty mixture overflows at the same rate into a second 60-gal tank that initially contained only pure water, and from there it eventually spills onto the ground. Assuming perfect mixing in both tanks, when will the water in the second tank taste saltiest? And exactly how salty will it then be, compared with the original brine?
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.
To see how sensitive the technique of carbon dating of Problem 25 is
(a) Redo Problem 25 assuming the half-life of carbon-14 is 5550 yr.
(b) Redo Problem 25 assuming 3% of the original mass remains.
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