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1. Study the stability of the limit cycle r=1 for the system given in polar coordinates by the equations r ? =(r^2 -1)(2x-1) , φ ? =1 . (where x=rcosφ ).
2. Solve the equation dy/dx =y+h N , where h N (x)=N for |x-1|<1/2N and 0 for |x-1|≥1/2N with initial condition y(0)=0 , and find the limit of the solution as N→∞ .
3. Prove that δ(αx)=δ(x)/|α| . ( In particular, if α=-1 , we can see δ(x) is an even "function".
Two ships leave port at the same time. Ship X is heading due north and Ship Y is heading due east. Seven hours later they are 350 miles apart. If the Ship X had traveled 280 miles from the port, how many miles had Ship Y traveled?
Write he expression as a single logarithm
During the last hour, a telemarketer dialed 20 numbers and reached 4 busy signals, 3 answering machines, and 13 people. Use this information to determine the empirical probability that the next call will be answered in person.
Karla Harby Communications, a small company of science writers, found that its rate of profit (in thousands of dollars) after t years of operation is given by the function.
Let m =17 and n=23. Evaluate the expression (m-n)2-2mn/m3-n2
Before noon he averaged 60 miles per hour, and after noon he averaged 50 miles per hour. At what time did he begin his trip and when did he end it?
the distanc3e between points A and B is 50 ft. Angle A measures 70 degrees, and angle B measures 65 degrees. A bridge will be built between points A and C.
In any group G, some of the elements of G commute with all of the other elements in G. The set of all such elements in G is called the centre of G, and is denoted by Z(G).
Computer analysis showed that the surface of a certain drumlin can be approximated by y= 10(1-0.0001x^2) revolved 180 about the x-axis from x= -100 to 100.
1. repeatedly 104 times simulate the standardised sum of independent and identically distributed variates x1 . . .
A moving body is opposed by a force per unit mass of value cx and resistance per unit mass value of bv^2 where x and v are the displacement and velocity of the particle at that instant. Determine the velocity of the particle in terms of x, if it s..
An office supply company sells x mechanical pencils per year at $p per pencil. The demand equation for these pencils is p=10-0.001x. The total annual cost of manufacturing x mechanical pencils is C(x)=5000+2x.
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