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Please be very careful with writing down all calculations step by step and also explain all conclusions and results thoroughly in words using mathematical language:
1. All solutions to the differential equation y'-2y=0 should also be solutions to the differential equation y''-ay'+ay=0. Determine the constant a such that this is true.
2. Determine if the inverse applies for this value of a, that is, if all solutions to y''-ay'+ay=0 are solutions to y'-2y=0.
suppose a function f is conjugate to a function g by the homeomorphism h. show that g is conjugate to f by the homeomorphism h-inverse. Use the fact that h-inverse is a homeomorphism whenever h is.
A cup of coffee at 173 degrees is poured into a mug and left in a room at 65 degrees. After 4 minutes, the coffee is 142 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case) .
What exactly is an improper integral? Why is there a difference between improper and proper integrals?
The half-life of radioactive radium is 1620 years. Suppose that a sample of this substance has 300 mg. Determine the time T it will take for the sample to decay to a mass of 200 mg.
What is the median weight of the group?
Saunders Corp. has current liabilities of $440,000, a quick ratio of 0.81, inventory turnover of 5.7, and a current ratio of 1.8. What is the cost of goods sold for the company?
Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.
A total of 258 tickets were sold for a school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
Which of the following gives the general rule for simplifying the product of two powers with the same base?
Let X be uniform on the set {1/2,1/3,1/4}, and let the distribution of Y |X = x be geometric with parameter x; that is, P(Y = k|X = x) = (1 - x)kx, for k = 0,1,2,..
Find the probability of random co-incidence, if the probability to get a certain value in both studies was the same, I would expect to have (125/1389)*38=3.41973 data-points with a larger value than the largest value in my study
A rectangular package can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume. Assume cross section is square.
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