Given the differential equation and its initial conditions y" - 4y' + 5y = 4 e" with y(0) = 2 and y'(0) = 7 Use the Laplace Transform rules for derivatives to convert this function into F(s) and then solve for Y(s). L{y(1)) = Y(s) L{ y'(1)} = S Y(S) - y(0) L{ y"(1)} = s2 Y(s) - Sy(0) - y'(0)
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- Where does the s+4 come from on step 2 (line 6)Suppose that there are 4 deaths due to stomach can- cer among workers in a tire plant from 1/1/64 to 12/31/83, while 2.5 are expected based on U.S. mortality rates. Provide a 95% CI for the expected number of deaths from stomach cancer over 20 years among the tire workers. Is the number of cases of stomach cancer excessive?It took 65 million years from the time the dinosaurs were wiped out by an asteroid impact until humans arrived on the scene. Today, we have technology that could wipe out all humans if we do not use it wisely. Suppose we wipe ourselves out, and it then takes 65 million years for the next intelligent species to arise on Earth. Then suppose the same thing happens to them, with another intelligent species arising 65 million years later. If this process could continue until the Sun dies in about 5 billion years, how many more times could intelligent species arise on Earth at 65-million-year intervals?
- How can I get rid of the highlighted x in this u-substitution problem?An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns.(x, y)= What is the optimal profit?$An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns. What are the (x,y) values? What is the optimal profit?
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