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The number of rabbits in a forest varies with time. During the period of 1980 to 1990 the number is given approximately by the formula where t is the number of years after 1980. (a) Sketch on graph paper the population during 1980-1990
Explain the importance of Euclid's parallel postulate in the development of hyperbolic and spherical geometry.
Suppose that at a certain instant the volume is 590 cubic centimeters and the pressure is 97 kPa and is decreasing at a rate of 13 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?
Estimate the error in evaluating ln(3/2) by using only the first five nonzero terms of the series in part a). Justify your answer.
How much should he invest in each to maximize his return? Assume the investment returns are as expected.
The trough in the figure is to be made to the dimensions shown. Only the angle theta can be varied. What value of theta will maximize the trough's volume?
Suppose T is a Mobius transformation such that the image of the real axis under T is the real axis. Prove that T may be written in the form T(z) = (az+b)/(cz+d) with a, b, c, and d real.
Conduct the appropriate analysis of these data and determine whether there are any significant differences.
Solve the given triangle.
Let f:R->R be a function that satisfies f(x+y) = f(x)+f(y) for all x,y in R. Suppose that f is continuous on R and that f(1)=k. Prove that f(x)=kx for all x in R.
Mary works due north of home. her husband Juan works due east. They leave for work at the same time. By the time Mary is 3 miles from home, the distance between them is one mile more than Juan's distance from home. How far from home is Juan?
A city lot has the shape of a right triangle whose hypotenuse is 4 ft longer than one of the other sides. The perimeter of the lot is 360 ft. How long is each side of the lot?
You own a portfolio that is 38 percent invested in Stock X, 22 percent in Stock Y, and 40 percent in Stock Z. The expected returns on these three stocks are 10 percent, 15 percent, and 12 percent, respectively.
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