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A path that passes through a pasture rises 323 feet over a horizontal distance of 4600 feet. Find the slope of the path. Round your answer to two decimal places.
Suppose that f: C->C and that f is analytic at a point z0 element of C. Prove that there exists a real number r>0 such that, the nth derivative of z0=[n!/(2 pi r^n)]x[int(e^(-niy)f(z0+re^(iy)) from 0 to 2pi with respect to y for all n element of N..
Develop a joint probability table and show the marginal probabilities. What is the probability of a household whose income exceeds $40,000 and who rejects the offer?
Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).
Evaluate the constant of variation and write an equation of direct variation
The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per second, how far will the car travel in one minute?
The inflation rate for Britain is 6.8. Use the least squares line to estimate Britain's independence rating.
find the average distance to the x-axis for points in the region bounded by the x-axis and the graph of y = x - x^2.
No fencing is required along the river. (See the figure below.) What are the dimensions of the largest area that can be enclosed?
The circumference of a sphere was measured to be 79000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.
A motorboat travels 356 miles in 4 hours going upstream and 357 miles in 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
at full speed a motorboat can travel 64 miles upstream in 8 hours, but it can travel the same distance downstream in 4 hours. In miles per hour, what is the maximum speed of the motorboat in still water?
The dimensions of a rectangle are such that its length is 3 in. more than its width. If the length were doubled and if the width were decreased by 1 in., the area would be increased by 234 in.^2. What are the length and width of the rectangle?
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